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111m

 

LIBRARY;LI

Michiga'ltt. l!
University :5

35:;

This is to certify that the

thesis entitled

THE THERMODYNAMICS OF CARBON IN NICKEL-BASED
MULTICOMPONENT SOLID SOLUTIONS

presented by

Daniel Joseph Bradley

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Chemistry

3644/34“

Major professor

 

 

 

[hue December 2, 1977

 

0-7639

 

 

THE THERMODYNAMICS OF CARBON IN NICKEL-BASED

MULTICOMPONENT SOLID SOLUTIONS

By

Daniel Joseph Bradley

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1978

ABSTRACT

THE THERMODYNAMICS OF CARBON IN NICKEL—BASED

MULTICOMPONENT SOLID SOLUTIONS

By

Daniel Joseph Bradley

The activity coefficient of carbon in nickel, nickel-
titanium, nickel-titanium-chromium, nickel-titanium—
molybdenum and nickel-titanium-molybdenum—chromium alloys
has been measured at 900, 1100 and 1215°C. The results
indicate that carbon obeys Henry's Law over the range
studied (0-2 at. %). The literature for the nickel-
carbon and iron-carbon systems are reviewed and corrected.
For the activity of carbon in iron as a function of
composition, a new relationship based on re—evaluation of
the thermodynamics of the 00/002 equilibrium is proposed.
Calculations using this relationship reproduce the data
to within 2.5%, but the accuracy of the calibrating
standards used by many investigators to analyze for
carbon is at best 5%. This explains the lack of agree-
ment between the many precise sets of data.

The values of the activity coefficient of carbon in

the various solid solutions are used to calculate a set

Daniel Joseph Bradley

of parameters for the Kohler-Kaufman equation. The cal-
culations indicate that binary interaction energies are
not sufficient to describe the thermodynamics of carbon
in some of the nickel-based solid solutions. The results
of previous workers for carbon in nickel-iron alloys are
completely described by inclusion of ternary terms in

the Kohler-Kaufman equation.

Most of the carbon in solid solution at high tem-
peratures in nickel and nickel-titanium alloys pre-
cipitates from solution on quenching in water. The
precipitate is composed of very small particles (>2.5
nm) of elemental carbon.

The results of some preliminary thermomigration
experiments are discussed and recommendations for further

work are presented.

To Kathleen and My Parents

11

ACKNOWLEDGMENTS

I wish to thank the Oak Ridge Associated Universities
and Michigan State University for their financial support
in the form of a Graduate Participantship and a teaching
assistantship, respectively. I would also like to thank
Oak Ridge National Laboratory for the use of its facilities
and for its financial support during the final term of this
work.

I am very appreciative of the help I received from the
staff of Oak Ridge National Laboratory. In particular, I
would like to thank: Mr. James Attril, Dr. James Bentley,
Mr. David Braski, Mrs. Sharon Buhl, Mr. O. B. Calvin, Mr.
Robert Crouse, Dr. J. C. Franklin, Mr. Greggory Gessel,
Dr. Gene Godwin, Dr. William Laing, Mr. John Houston, Dr.
Rodney McKee, Mr. Guy Peterson, Mr. Gregory Potter, Mr.
Jack Ogle, Mrs. Kay Russell, Dr. James Stiegler, Dr. Robin
Williams, Mr. Mark Williams, Mr. Clarence Zachery and Mrs.
Joanne Zody.

I am sincerely grateful to Dr. James Leitnaker for his
direction and encouragementthroughout my time at ORNL.

He gave willingly of his time to a sometimes less than
thankfulfpupil.

My genuine thanks to Dr. Frederick Horne for intro-
ducing me to the field of thermodynamics and for encourag—

ing my education. Without his counsel and help this work

111

would never have been started or finished.

I would also like to thank my fellow graduate students,
Dr. Robert Cochran and Mr. Richard Rice for their friend—
ship and the many favors they performed for me over the
last four years.

Finally I would like to thank my family and my wife
for their comfort and understanding throughout the long

course of formal education.

iv

TABLE OF CONTENTS

Chapter Page

.LIST OF TABLES . . . . . . . . . . . . . . . . . . .xvii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . ix

I. INTRODUCTION. . l

A. Purpose . . . . . . . . . 1

B. Experimental . . . 3

C. Results . . A

II. SOLUTION THERMODYNAMICS. . . . . . . . . . . . . 6
A. Chemical Potentials and Activity

Coefficients. . . . . . . . . . 6

B. Excess Functions. . . . . . . . . . . . . . . 9

C. Lattice Stabilities . . . . . . . . . . . . . 12

D. Models. . . . . . . . . . . . . . . . . . . . 13

III. CARBURIZATION THERMODYNAMICS. . . . . . . . . . 20

A. Choice of Carburizing Medium. . . . . . . . . 20

B. Analysis of the Thermodynamics of
the CO/CO2 Equilibrium. . . . . . . . . . . . 22

C. Analysis of the Literature Data on
the Iron-Carbon System. . . . . . . . . . . . 26

IV. ANALYSIS FOR CARBON. . . . . . . . . . . . . . . no
A. Introduction. . . . . . . . . . . . . . . . . no

B. Procedure for Total Carbon Determination
by the Combustion-Gas Chromatographic

MCthOd. o o o o o c o o o o o o o o o o o ’41
1. Summary . . . . .'. . . . . . . . . . . . Al

2. Equipment and Reagents. . . . . . . . . . Al

Chapter Page

3. Calibration . . . . . . . . . . . . . . . A2

A. Determination of Blank. . . . . a . . . . A2

5. Procedure . . . . . . . . . . . . . . . . A3

C. Precision of the Carbon Analyses. . . . . . . A3
D. Accuracy of the Carbon Analyses . . . . . . . M8
V. EXPERIMENTAL PROCEDURES . . . . . . . . . . . . . 52
A. Preparation of the Alloys . . . . . . . . . . 52
B. Carburization . . . . . . . . . . . . . . . . 59
l. Specimen Preparation. . . . . . . . . . . 59

2. Furnace and Auxiliary Equipment . . . . . 50

a. The Furnace . . . . . . . . . . . . . 60

b. Thermometry . . . . . . . . . . . . . 62
c. Gases . . . . . . . . . . . . . . . . 62

. d. Operating Procedure for the

Hydrogen Furnace. . . . . . . . . . . 63

C. Annealing . . . . . . . . . . . . . . . . . . 65
D. Electrolytic Extractions. . . v . . . . . . . 67
1. Description . . . . . . . . . . . . . . . 67

2. Discussion of Precision . . . . . . . . . "69

3. Procedure of Anodic Dissolution of
Nickel-Based Alloys for the Concen-
tration of Precipitated Carbide

Phases. . . . . . . . . . .'. . . . . . . 69
E. Electron Microprobe . . . . . . . . . . . . . 75
1. Introduction. . . . . . . . . . . . . . . 75

2.‘ Procedure for Analysis of Carbide
Precipitates. . . . . . . . . . . . . . . 77

vi

Chapter Page

3. Calibration Curves. . . . . . . . . . . . 78
F. X—ray Diffraction . . . . . . . . . . . . . .. 84
VI. THE NICKEL-CARBON SYSTEM . . . . . . . . . . . . 88

A. Results of the Carburization
Experiments . . . . . . . . . . . . . . . . . 88

B. Comparison with Previous Work . . . . . . . . 96

VII. CARBON PRECIPITATION IN NICKEL AND
NICKEL-TITANIUM ALLOYS. . . . . . . . . . . . . 110

A. Discovery of the Carbon Phase . . . . . . . . 110
B. Chemical Analysis of Additional

Residues. . . . . . . . . . . . . . . . . . . 112
C. Electron Microscope Results . . . . . . . . . 115
D. Discussion. . . . . . . . . . . . . . . . . . 120

l. Hydrolysis of Dissolved Carbon. . . . . . 120

2. Diffusion Mechanism for Precipitation

of Carbon . . . . . . . . . . . . . . . . 121
3. Previous Results. . . . . . . . . . . . . 126
E. Summary . . . . . . . . . . . . . . . . . . . 129

VIII. THE NICKEL-TITANIUM-CARBON SYSTEM. . . . . . . 131

A. Results of the Carburization
Experiments . . . . . . . . . . . . . . . . . 131

B. The Solution Thermodynamics of
Titanium in Nickel-Titanium Carbon
Solid Solutions . . . . . . . . . . . . . . . 1A2

IX. NICKEL-TITANIUM-MOLYBDENUM—CHROMIUM
CARBON SYSTEMS . . . . . . . . . . . . . . . . . 1M6

A. Results of the Carburization
Experiments . . ... . . . . . . . . . . . . . 1M6

vii

Chapter Page

B. Carbide Precipitates. . . . . . . . . . . . . 157
1. Carbide Composition . . . . . . . . . . . 157
2. Annealing Experiments . . . . . . . . . ._163
3. Carburization Experiments . . . . . . . . 168

C. An Unidentified Phase of High Carbon
Content . . . . . . . . . . . . . . . . . . . 177

)C. THE KOHLER—KAUFMAN EQUATION . . . . 182
A. Calculation of the Nickel-Carbon and
Iron Carbon Interaction Energies. . . . . . . 182

B. Analysis of the IroneNickel-Carbon
System. . . . . . . . . . . . . . . . . . . . 185

C. Calculation of Interaction Energies in

the Nickel-Titanium-Carbon-System . . . . . . 19“

D. Calculation of the Molybdenum—Carbon and
Chromium-Carbon Action Energies . . . . . . . 196
E. Prediction of Carbon Solubilities . . . . . . 203
)(I. THERMOMIGRATION... . . . . . . . . . . . . . . . 210
A. Introduction. . . . . . . . . . . . . . . . . 210
B. Experiments . . . . . . . . . . . . . . . . . 212
C. ReSults . . . . . . . . . . . . . . . . . . . 214
XII. SUGGESTIONS FOR FURTHER WORK. . . . . . . . . . 216
A. Analytical Chemistry. . . . . . . . . . . . . 216

B. Experiments . . . . . . . . . . . . . . . . . 217
APPENDIX.......................219
BIBLIOGRAPHY.....................2143

viii

Table

301

3.2

3.3

“.2
5.1

5.2

5-3

5.A

LIST OF TABLES

Thermochemical Data for the CO/CO2
System. . . . . . . . . . . . . . . . . .
The Solubility of Graphite in Gamma

Iron. . . . . . . . . . . . . . .

Date of R. P. Smith (19A6) for Activity
of Carbon in y-Iron in Equilibrium

with CO/CO2 Gas Mixtures. . .

Calibration Data for LECO Gas
Chromatograph Carbon Analyzer with
National Bureau of Standards Standard
Reference Material 121B

Analysis of NBS Standards . . . . . . .
Fabrication Schedule for Alloys

7261-7268 . . . . . . . . . . . . . .
Alloy Compositions as Determined by
Several Methods of Analysis, wt %
Composition of Alloys Used for
Calculations. . . . . . . . . . . . . . . .
Results of Multiple Extractions of

0.64 cm Rod Specimens of Ni + 2 wt %

Ti + 0.1 wt % C . . . . . . . . . . . .

ix

Page

27

29

32

A“
50

56

57

58

7O

Table

5.5

5.6

6.3

6.“

6.5

Analyses of Precipitates by a
Colorimetry or Atomic Absorption

Spectroscopy and by an Electron

Microprobe Energy Dispersive

x—ray Analysis .

Analysis of Precipitates by Pashen-
Runge Emission Spectroscopy and
Energy Dispersive x-ray Analysis.

Experimental Results for Carburiza-

tion of Nickel.

Carbon in Nickel.

Results of Wada 33 El-
Solubility of Carbon in Equilibrium
with Graphite (a0 = 1).
Results of Smith (1960) for the

Activity Coefficient of Carbon in

Nickel at lOOO°C.

Comparison of Activity Coefficients,

Excess Enthalpies, and Excess Entropies

of Carbon in Nickel

'The results of Wada 22 a1.

(1971 for the

(1971)
for the Activity Coefficient of

Page

79

81

89

101

102

106

108

Table Page

7.1 Results of the Extraction of Alloy

3 (Ni + 1.7 wt % Ti + 0.09 wt % c)

Annealed at Temperatures from 1260

to 760°C. . . . . . . . . . . . . . . . . . . 111
7.2 Results of Extraction of Ni—270 and

Ni-270 + T1 Alloys Carburized at

1215°C and Then Quenched. . . . . . . . . . . 113
8.1 Experimental Results of the Carburiza-

tion of Nickel-Titanium Solutions . . . . . . 132
8.2 Activity Coefficient of Carbon in

Nickel-Titanium—Carbon Solutions. . . . . . . 133
8.3 The Temperature Dependence of f0

and the Values of afig and ASE in

Nickel-Titanium-Carbon Solutions. . . . . . ..‘ 1A1
8.“ Activity Coefficient of Titanium in I

Nickel-Titanium Carbon Solid Solutions

in Equilibrium with Graphite and TiC. . . . . 14“
9.1 Activity Coefficient of Carbon as a

Function of Temperature and Composition

in Ni—Ti-Mo—Cr-C Solid Solutions. . . . . . . IA?
9.2 Comparison of Equilibrium Concentra—

tions of Carbon in Ni-Ti-Mo-Cr-C

Solutions . . . . . . . . . . . . . . . . . . 153

xi

Table

9.3

9.9
9.5

9.6

9.7

10.1

10.2

10.3

10.“

Page
The Results of the Analysis of the
Carbide Precipitates by the Electron
Microprobe and X-ray Diffraction. . . . . . . 158
Results of the Annealing Experiments. . . . . 16A
Solubility of CArbon in Several
Nickel-Based Alloys as Determined
from Carburization Experiments. . . . . . . . 169
X-ray Diffraction Data on the Un-
identified Phase Alloy 7266
A-7783-97 . . . . . . . . . . . . . . . . . . 178

X-ray Diffraction Data on the Un-

identified Phase in Alloy 7266-A-

7783-37 . . . . . . . . . . . . . . . . . . . 179
Calculated Values of Nickel-Carbon

and Iron-Carbon Interaction Energies,

wFCC
13 . . . . . . . . . . . . . . . .

Some Relative Lattice Stabilities for

183

Elements of Interest. . . . . . . . . . . . . 18A
The Reanalyzed Results of Smith (1960)

for the Activity Coefficient of Carbon

in Nickel-Iron-Carbon Alloys. . . . . . . . . 186
The Reanalyzed Results of Wada §t_31.

(1971) for the Activity Coefficient of

Carbon in Nickel-Iron-Carbon Alloys . . ... . 187

xii

Table

10.5

10.6

10.7

10.8

10.9

10.10

Interaction Energies Wigc for the

Kohler-Kaufman Formalism, wigc = AiJ
+ 313T + 01JT2 + D13T3. . . .
Incorrect Values for the Binary
Interaction Parameters, Wigc Calculated
with Only Binary Terms.
Interaction Energies in kJ-mol‘l
Calculated from the Kohler-Kaufman
Equation Including Ternary Terms.
Comparison of the Value of the
Activity Coefficient of Carbon
Calculated Using the Kohler-Kaufman
Equation and the Value Determined
Experimentally. . . . . . . . . .
Activities of the Alloying Elements
Calculated Using the Kohler-Kaufman
Equation,(Eq. 2.30)
Comparison of Calculated and Experi-
mental Value of the Carbon Activity
Where Precipitation of Titanium
Carbide Should Start. . . . . . .
Composition of Alloys Used for
Calculations. . . . . . . . . . .
Data From Carburization Experiment
A-7603-97 . . . . . . . . . . . .

' xiii

Page

198

200

202

20A

205

207

222

223

 
 

Table

A.”

A.5

A.6

A.7

A.8

A.9

Data from

Carburization

A-7603-105.

Data From Carburization

A-7603-106.

Data From

Carburization

A-7603-118.

Data From

Carburization

A-7603-121.

Data From

Carburization

A—7603-l23. . . . .

Data From
A-7783-A

Data From
A-7783-1N
Data From
A-7783-15
Data From
A-7783-16
Data From
A-7783-l7
Data From
A-7783-18
Data From

A-7783-19

Carburization
Carburization
Carburization

Carburization

Carburization
Carburization

Carburization

xiv

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment
Experiment

Experiment

Page

223

22A

225

226

227

227

228

228

229

229

230

230

A.17

A.18

A.l9

A.20

A.22

Data From
A-7783-20
Data From
A-7783-21
Data From
A-7783-32
Data From
A-7783-33
Data From
A-7783-35
Data From
A-7783-36
Data From
A-7783-37
Data From
A-7783-38
Data From
A-7783-NA
Data From
A-7783-“5
Data From
A-7783-“7
Data From

A-7783-98

Carburization
Carburization
Carburization
Carburization
Carburization

Carburization

Carburization
Carburization
Carburization
Carburization
Carburization

Carburization

Xv

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Page

231

231

232

232

233

233

23A

23A

235

235

236

236

Table

A.27

A.28

A.29

A.30

A.3l

A.32

A.33

Data From Carburization
A-7783-“9 .

Data From Carburization
A-7783-57 . . . . . .
Data From Carburization
A-7783-116.

Data From Carburization
A—7783-l20.

Data From Carburization
A-7783-l23.

Data From Carburization
A-7783-125. . . . .
Data From Carburization

A-7783-l36.

xvi

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Experiment

Page

.237

237

238

239

290

291

2A2

Figure

3.1

3.

3

LIST OF FIGURES

Page

The results of Herzberg and Rao (1999)

and Snow and Rideal (1929) displayed

as A2F"(J)-ABe(J+%) versus J, where

the terms have been defined in the

text. The relatively random appear-

ance of the Snow and Rideal results

indicates a lack of internal con-

sistency. 'The Herzberg and Rao results,

however, produce a smooth curve . . . . . . . 25
The results of Smith (1996) versus

Equation (3.6), tnyc vs y0 (y0 =

xC/(l-xc). The x's are experimental

points, the zeros, 0, are calculated

points and the equal signs, =, indi-

cates that the calculated and experi-

mental values differ by less than l.9%. . . . 3A
The results of Ban-Ya 33 a1. (1969, 1970)

versus Equation (3.6), in YC vs yC [y0 =
xC/(l-xC)]. The x's are experimental

points, the zero's, 0, are calculated

points and the equal signs, =, indi-

cate the calculated and experimental

values differ by less than 1.9% . . . . . . . 35

xvii

Figure

3.9

3.5

Page

The results of Scheil gt 31. (1961) versus
Equation (3.6). in YC vs. yC [yC =
xC/(l-xC)]. Scheil _t al. performed

sets of experiments at constant PgO/PCO2

rather at constant temperature. The

x's are experimental points, the zero's,

0, are calculated points and the equal

signs, =, indicate the calculated and

experimental values differ by less than

1.9%. (POO/P002 = r) . . . . . . . . . . . . 36
The results of Dunwald 32 a1, (1931) vs

Equation (3.6), in YC versus yc [yC =

xC(l-xC)]. The x's are experimental

points, the zero's, 0, are calculated

points and the equal signs, =, indicate

the calculated and experimental values

differ by less than 1.9%. . . . . . . . . . . 37
Calibration data for the LEGO carbon

analyzer. The data was taken on three

separate days . . . . . . . . . . . . . . . . 97
Optical photomicrographs illustrating

the "memory effect" in Ni-2.5 Ti-8

Mo-8 Cr-0.2 C (at. %) (a) as swaged

(b) after 1 hour at ll77°C, (c) after

xviii

Figure

5.2

5.3

5.9

Page

1 hour at 1177°C + 160 hours at

760°C . . . . . . . . . . . . . . . . . . . . 59
Electrolytic extraction equipment

constant voltage power supply, Pt

tipped forceps, Pt cathode and

magnetic stir plate . . . . . . . . . . . . . 73
The calibration curve for the

electron microprobe data. The

emission spectroscopy results

were not used for determining the

shape of the line . . . . . . . . . . . . . . 83
Calibration curve for the analysis

of M003 and Ti02 mixture for

Mo and Ti with the electron

microprobe. . . . . . . . . . . . . . . . . . 86
Activity coefficient of carbon in

nickel as a function of carbon

activity. Dashed lines are ex-

trapolations of solid (i.e., ex-

perimental) lines . . . . . . . . . . . . . . 92
in Y0 versus l/T for carbon in nickel.

The results of Smith (1960) and of

Wada, 32 11. (1971) are the corrected

results (see text). . . . . . . . . . . . . . 95

xix

Figure

6.3

6.9

6.5

7.1

The results of Smith (1960) and
Wada 23 .231. (1971) at 100000, as
reported, for the activity coefficient
of carbon YC in nickel 1s atom per-
cent carbon. Our results are
represented by the solid line

and the error bars.

Carbon activities in iron, at 1000°C
calculated from data of Smith (1960)
and of Banya £3 91. (1971) and Equa-
tion (3.6). The dashed line cor-
responds to Henry's Law. Note that
the departure from Henry's Law does
not occur until approximately 2 atom
percent carbon is in solution .

The recalculated results of Smith
(1960) and Wada ££.§l- (1971) for
the activity coefficient of carbon.
The results were calculated from
their raw data and Equation (3.6)
(a) Optical micrograph of nickel-
0.l39 wt % C Specimen quenched in
water after 38 hours at 1215°C

(b) Bright field electron micrograph

XX.

Page

98

100

109

 

Figure

7-3

Page

of nickel-0.139 wt % C specimen

quenched in water after 38 hours

at 1215°C . . . . . . . . . . . . . . . . . . 117
(a) Selected area diffraction

pattern of a Ni + 0.139 wt % C

specimen quenched in water after

38 hours at 1215°C.

(b) Dark field electron micro-

graph from the area marked by the

circle in (a). The average pre-

cipitate diameter is approximately

2.5 nm. . . . . . . . . . . . . . . . . . . . 119
Log10 96 (the time required to

achieve equilibrium) versus T/K

(6 is the time required for the

temperature to drop one degree, r

is the quench rate and (xc) has

sat
been defined by Equation (7.9). The
intersection of the horizontal lines
with the loglo (96) versus T curve

is the temperature below which, with
the quench rate indicated, equilibrium

cannot be maintained by diffusion, e.g.,

at r = 167 K-sec"1 diffusion can keep

xxi

Figure Page

the system at equilibrium down to
535°C and at r = 16.7 K-sec'l down
to 950°C. . . . . . . . . . . . . . . . . . . 129
8.1 Activity coefficient of carbon in
nickel—titanium alloys at 900°C.
N1 + 2.9 at. % Ti; ONi + 3.6 at.
% Ti; top line from Figure 6.1.
Note that experimental error is
exaggerated in that 9C, rather
than fin 9C, is plotted. . . . . . . . . . . . 135
8.2 Activity coefficient of carbon
in nickel titanium alloys at 1100°C.
N1 + 2.9 at. % Ti, ONi + 3.6 at.
% Ti, top line Figure 6.1. Note
that experimental is exaggerated
in that 90, rather than in 70 is
plotted . . . . . . . . . . . . . . . . . . . 137
8.3 Activity coefficient of carbon in
nickel titanium alloys at 1215°C.
Ni + 2.9 at. 1 Ti, Ni + 3.6 at. Z
Ti, top line Figure 6.1. Note that
experimental error is exaggerated
in that 70, rather than in 90, is
plotted . . . . . . . . . . . . . . . . . . . 139

xxii

Figure

9.1

9.3

9.9

Page

Activity coefficient of carbon in

nickel-titanium—molybdenum—chromium

»alloys at 1100°C. The lines repre-

sent average values. More data are

required, in light of the indications

in Chapters VI and VIII that Henry's

Law is obeyed in Ni-C and Ni-Ti-C alloys,

before a least squares fit is

Justifiable . . . . . . . . . . . . . . . . . 199
Activity coefficient of carbon in
nickel-titanium-molybdenum—chromium

alloys at 1215°C. The lines represent

average values. More data are required,

in light of the indications in Chapters

VI and VIII that Henry's Law is obeyed

in Ni-C and Ni-Ti-C alloys, before

a least squares fit is Justifiable. . . . . . 151
Lattice parameter of the carbide pre-

cipitate as a function of Mo/Ti in

the carbide. The line was determined

by a least squares fit of the data in

Table 9.3 . . . . . . . . . . . . . . . . . . 162
(a) The concentration of carbon in

alloy A (Ni + 2.6 at. % Ti + 8.9 at.

xxiii

Figure

9.5

Page

% Mo) in equilibrium with the cubic
carbide phase as a function of tempera-
ture o = 10% of the bulk carbon concen-
tration.

(b) The concentration of carbon in

alloy 999 (N1 + 2.0 at. % Ti + 8.3 at.

% Mo + 8.9 at. % Cr) in equilibrium
with the cubic carbide phase as a

function of temperature. 0 = 10% of

~the bulk carbon concentration . . . . . . . 166

Atom % carbon versus activity of carbon
in several nickel—based alloys at
1215°C. The intersection of the two
lines, with the same label, is the solu-
bility limit of carbon relative to the
carbide phase. The lower line represents
the solid solution where the slope is
100/90 (xC = Ac/?C). The dashed lines
are an extrapolation of the solid solu-
tion lines and represent the amount

of carbon in solution at any given
activity. The upper lines have been

fit by least squares to the data from

the two phase region, points that

xxiv

Figure

9.6

9.7

Page

diverged from the straight line behavior
exhibited near the intersection were
ignored . . . . . . . . . . . . . . . . . . . 171
Atom % carbon versus activity of carbon
in several nickel-based alloys at 1100°C.
The intersection of the two lines, with
the same label, is the solubility limit
of carbon relative to the carbide phase.
The lower line represents the solid
solution where the slope is 100/90

(xC = Ac/IC)’ The dashed lines are
extrapolations of the solid solution
lines and represent the amount of

carbon in solid solution at activities
exceeding the solubility limit. The
upper lines were fit by least squares

to the data from the two phase region . . . . 173
Atom % carbon versus activity of carbon
in several nickel-based alloys at 900°C.
The intersection of the two lines, with
the same label, is the solubility limit
of carbon relative to the carbide phase.
The lower line represents the solid
solution where the slope is 100/?C

(x0 = Ac/?c). The dashed lines are

XXV

Figure

9.8

10.1

Page

extrapolations of the solid solution
lines and represent the amount of carbon
in solid solution at activities exceed-

ing the solubility limit. The upper

‘ lines were fit by least squares to the

data from the two phase region. . . . . . . . 175
Specimen number 7266 A-7603-97 equilibrated

at 1215°C at AC = 0.268. Note the needle

like precipitates which are characteris-

tic of the unidentified phase. The other
precipitates are the MC phase . . . . . . . . 181
Comparison of calculated, 0, and experi-

mental, X, values of in 9: as a function

of XNi in the Ni-Fe-C system. The

experimental results are those of Smith

(1960) and Wada gt a1. (1971) (see

Tables 10.3 and 10.9).. (a) Calculated

points determined from Equation (10.9)

with the values wNiC and erC taken

from the binary results (Table 10.1).

(b) Calculated points determined as'a

"best fit" of Equation (10.9); the

experimental values were the independent

variable and wNiC and erC the dependent

xxvi

Figure

10.2

11.1

. Page

variables. wNiFe and erNi were taken
from Kaufman and Nesor (1975), Table
10.5. . . . . . . . . . . . . . . . . . . . . 190
Comparison of calculated, 0, and experi-
mental, X, values of 2n 7: as a function
of XNi in the Ni-Fe—C system. An

equal sign, =, indicates that the
experimental and calculated values
differ by less than 2%. The calcu-
lated values differ by less than 2%.

The calculated points were determined

as a best fit of Equation (10.5) to .
experimental results of Smith (1960)

and Wada 22.21- (1971) (see Tables

10.3 and 10.9). Values of‘ineNi and
wNiFe were taken from Kaufman and

Nesor (1975), Table 10.5. . . . . . . . . . . 193
Sample B-6-B at 25x annealed two hours
in the Gleeble. The right hand side of
photo is the hot end approximately
1300°C. Note decarburization in hot

zone. I O O O O O O O O O O O O O O O O O O. O 213

xxvii'

1R

CHAPTER I
INTRODUCTION

A. Purpose

Solid solutions are of great technological importance,
in particular in alloy metallurgy and semi-conductor manu-
facture. Solid solutions are also of considerable theo-
retical interest. According to Darken (1967), no general
theory for the solution thermodynamics of strongly inter—
acting components has been developed. The best theories
to date are the regular solution theory of Hildebrand
(1927) and the quasi-chemical theory of Herzfeld and Heit—
ler (1925) and Scatchard (1931). Regular solution theory
does not account for experimentally-observed negative heats
of mixing, and neither theory accounts for experimentally-
observed asymmetries in the relative exdess Gibbs free
energy.

A primary purpose of the work reported here was to
check the validity of extending to multicomponent solutions
the equation proposed by Kohler (1960) for the relative

excess Gibbs free energy of mixing for binary solutions

GE(re1) = x1x2(xlwl2 + 2.24.21) (1)

.u

a.

.-v

 

‘6‘:

.h-

where x1 is mole fraction and $13 is an interaction energy
dependent on temperature.

Sigworth and Elliott (1979,1976) and Chipman and
Brushy (l968)provide extensive lists of references on then—
modynamic investigations of multicomponent alloys. However,
no attempt has previously been made to use an analytical
expression for the integral relative excess Gibbs free
energy of the alloys.

The experiments reported here provide data that can
be used to determine whether interactions of elements in
metallic solutions can be described in terms of binary
interactions alone. The Kohler equation as modified by
Kaufman (1975) requires that the 013 depend only on com-
ponents i and 3: If this binary model can be verified,
then the number of experiments needed to describe most
systems can be reduced dramatically. There are 9.9 x 106-
possible elemental quaternary mixtures but only 5.2 x 103
binary mixtures.

A second purpose for the work reported here was to
obtain quantitative results for the thermodynamics of multi-
component solutions by a multi-pronged attack which includes
gas phase carburization coupled with electrolytic extrac—
tion and analysis of the carbide phases. Such results are
essential in attempting to understand the complicated pre-
cipitation processes that occur in multicomponent solid

solutions.

t §- In 4 I. s. ,.H V\ t... v.
a.‘ -.. x . q a. a . -\u .9 D n s . A.‘

'

‘t. .

i— v... a . v . .L . . L. t. . 2. n ..
.I- nu. us. In. .. ~,» .n a” u g a.‘ .l

 

 

 

B. Experimental Paths

Because diffusion in solids is both minuscule and slow,
experiments to,determine the thermodynamic properties of
solid solutions have been both difficult and time consum—
ing. In the study of interstitial elements such as carbon,
oxygen, and nitrogen in metal matrices, the problem of
slow diffusion rates is alleviated by performing experi-
ments at relatively high temperatures. All of the tech-
niques developed to take advantage of the relatively
large mobilities of the interstitial elements rely on
equilibrating the system of interest with a system of
known-prOperties.

The earliest investigations of the solution thermo-
dynamics of interstitial elements involved long term
annealing. A mixture of known composition is annealed
at a fixed temperature until equilibrium is achieved.

The sample is then quenched. The microstructure of the
quenched material is studied with an optical microscope
or other surface analytical techniques. This method is
still used in many phase diagram studies (Stover and

' Wulff, 1959). Although useful information is obtained
from this type of experiment, quantitative values for
thermodynamic functions are not available from it.

The method of welded samples employed by Darken (1999)

and Golovanenko, §t_§1, (1973) involves welding two

samples of different composition. The concentration de-
pendence of the activity for the element of interest is
known for one of the samples. After equilibrium is achiev—
ed, the composition of each half is determined. The
activity of the element of interest in the experimental
half is set equal to that in the reference half. The
method is limited due to the difficulty in obtaining good
bonding between dissimilar materials.

A third method, used here, involves annealing speci-
mens in an atmosphere in which the element of interest
has a constant activity (Dunn and McLellan, 1968; Ban-Ya,
gt a1., 1969 and 1970). The Specimens thus equilibrate
with a bathing medium. Knowledge of the thermodynamics
of the bath allows calculation of the equilibrium activity

of the element of interest.

C. Results

The relative partial molar excess Gibbs free energy
of carbon in nickel solid solutions have been determined
via a gas phase carburization technique, and quantitative
methods for the determination of carbon and metal element
concentrations in dilute solutions and in the carbide phase
have been developed. The data are used to test the ability
of the multi-component Kohler equation to describe the

solution thermodynamics of nickel alloys. We show that

the equation is adequate for our systems, but that a ternary
interaction term must be added to describe the Ni—Mo—C
and the Ni-CrbC systems. A ternary term is also necessary
to describe completely the Fe—Ni-C system. The application
of the parameters determined in nickel solid solutions to
other solVent systems are checked by comparing literature
values for iron-based systems with those determined here.
The results obtained for nickel solution are not always
applicable to iron solutions. Thermomigration of carbon in
nickel-based alloys is discussed in Chapter 11.

Appendix A includes all of the data obtained from the

carburization.experiments.

CHAPTER II
SOLUTION THERMODYNAMICS

A. Chemical Potentials and Activity Coefficients

For every component i in any mixture of n components,

the general formula for the chemical potential is

'= u: + RT in a

i’ i = l,...,n, (2.1)

11i
where pi is independent of composition and a1 is the activ-
ity. The values of a1 and u: depend upon each other through
the reference state and composition variable chosen.
For the pure component reference state and mole frac—

tion x1 as composition variable,

u: +~RT in X

“i 1 91, i = 1,...n, . (2.2)

O

I

where u: is the chemical potential of pure component i at
the temperature and pressure of interest and where the
activity coefficient 91 referred to the pure component has

the property

11m 91 = 1, i = l,...,n. (2.3)

Another useful reference state is the infinite dilution

state. For component 1 as solvent,

pi + RT Rn x

ui 1 i’ i = 2,...,n, (2.9)

with

“i = lim(u1 - RT 1n xi),

x + 1

1

lim *1 = 1, i = 2,...,n

x1 + l (2.5)
For the solvent itself,

A _ O = m
For the solutes, the chemical potential constants u: and

u: are related to each other by

- 0 Am
ui - 111 + RT in Y1,
u° = u” + RT 2n 7° (2 7)
i 1 ~ 1’ '
where
Aco_ A 0:
Y1 - lim Y1, 71 lim Y1. (2.8)
x

1 + 1 x1 + 1

Moreover, the two types of activity coefficients are

related to each other by

Yi

with

= ?1/?:, §i = Yi/Yi, (2'9)
y° ?” = l (2 10)
i i ' °

an ideal mixture would have

”i - “i + RT 2n x1, i=1,...,n, (2.11)
which is valid for all compositions if and only if u: =

u: for all components.

dilute solutions. The
00
U1=ui+

111

Thus,

Ideality is approached closely in

ideal dilute solution is defined by
RT in x1, i = 2,...,n,

= u; + RT 2n x1. (2.12)

71 = 1 for all the components in the ideal dilute

solute. In many cases of practical importance, including

most studies of interstitial elements in alloys, the concen-

trations of some solutes are so low that 71 = 1. Then the

first of Eqs. (2-12) holds for those solutes in the composi-
tion range studied. This does not imply, however, that Yi
would be unity over the entire composition range. In par-
ticular, effective ideality at high dilution does not imply

y: = 1. Thus, 9: f 1, and Eqs. (2.7) and (2.12) yield
pi = a? + RT in xi + RT in 9:. (2.13)

Thus, Ii is a constant(name1y, 9:), for compositions such
that Y1 = 1. Note that Eq. (2.13) is a form of Henry's

Law since all the composition dependence of ”i resides in
the in x1 term; stated otherwise, the activity of component
i is directly proportional to its mole fraction for highly
dilute solutions.

The formulas displayed so far in this section are valid
for any homogeneous phase. When two or more phases are in
equilibrium, or when two or more crystalline modifications
are stable, we designate the phase by a superscript. For
example, for a phase a, Eq. (2.2) becomes

a _ 00 a
“i - “i + RT 2n x1 + RT 2n 91. (2.19)

B. Excess Functions

 

For any intensive property y in a mixture, the excess

E

property y is defined (Scatchard, 1999; Haase, 1971) by

10
y E y - y . (2.15)

where y1d is the value of the same property in an ideal mix-
ture formed from the same pure components. Thus, by Eqs.

(2.2), (2.11) and (2.15)

E

pi = RT in 91, i = l,...,n. (2.16)

Any total molar property 3 is related to the partial

molar properties Z1 (32/3n1)T,P n by

9 J?1

IIMS

1x121. (2.17)

and the corresponding excess property is given by

n
zE = z — 219 = 2 x EB, (2.18)
_ i 1
1-1
with
-E g — -id

Equation (2.16) is an example of Eq. (2.19) for the Gibbs

free energy since G1 = ui.

s, = -(3ui/3T)p,n , H1 = u, + T Si’ (2.20)

11

we have

-E

.. A A —E _ 2 , A
Si - -R tn 71 - RT (Sin Yi/aT)p,nJ’ H1--RT (unfit/amp“!J
(2.21)
Moreover, for the total excess properties,
._E n A
S = -R 2 x1 [in Y1 + (Bin Yi/aznT)p,n J,
i-l J
E n .
H = -RT 2 x (Bin Y /3£nT) ,
i=1 i i p,nJ
_.E n
o = RT 121 x1 in yi. (2.22)

Note, for completeness, that

—-d —o —id
Hi = Hi, 81 = E0 (2.23)

p.
I
:13
20
:3
>4
p.

The reason for this rather thorough presentation of
well-known thermodynamic quantities is that although our
experiments are in the dilute solution range, where the
infinite dilution standard state and the 71 activity co-
efficients are useful, the mixture theories we wish to dis-
cuss are cast in terms of the excess functions Just listed.
For the excess functions the pure component reference

states are required by definition, and therefore so are

12

the 91 activity coefficients. Put another way, although
our solutions are dilute enough to be very nearly ideal,
the activity coefficients are 293 nearly unity because it
is the pure component—based activity coefficients, the 91,
that we calculate. Indeed, in most of our experiments the
Y1 are all unity and the Ii are all composition independent
constants, namely, 9:. The 9: do depend on temperature,
however, and we have,

Em

Hi

=-RT(3£n 7: /8£nT)p, 3'?” = -R[2n ‘7: + (Bin flown].

(2.29)

C. Lattice Stabilities

Suppose that at a given temperature and pressure, pure
component i can exist in two stable phases (crystalline
modifications) a and 8. Of course only one of these can
exist at equilibrium away from a transition point, but
instances of supersaturation, supercooling, etc., are

plentiful. The relative stability “:80 is defined by
pi : ui - ui . (2.25)

To see the importance of relative lattice stabilities,

consider an alloy which undergoes a phase transition from

13

the a modification to the B modification. Since the mole
fractions do not change, the change in Gibbs free energy

in the transition is

AGQIB = 68—5“

8 o
X xi“i ' Z xil‘i
= Z x ( B -u° ) = Z x [u80 - u°° + RT2n<?B/?“)J
= Z xiui + RT X x1£n(7E/7g)o (2.26)
1

Thus, AG is due both to changes in the chemical environment,
reflected in the activity coefficient terms, and to changes

in the structure, reflected in the lattice stability terms.

Kaufman (1959, 1967) and Kaufman and Nesor (1973, 1975)

have calculated lattice stability energies from phase

diagram data for a variety of systems.

D. Models

The Taylor series expansion of u? = RTRn?i in the mole

fractions x2...xn is
uE = RT£n§m + RT 1 E x + RT § § P x x + 0(x3)
i 3:2 13 J 3:2 k=2 iJk J k ’
(2.27)

where we use the Lupis and Elliot (1966) notation for the

 

 

‘9

1U

H'
Ill

‘1

".

‘..

19
partial derivative coefficients:

E1J s [(aznyi/axJ)T,P,*klxl=1

P (2.28)

_ 2 A
13k 3 [(3 lnyi/BXJOXk)T,P,x£]X =1

1
The coefficients are thus evaluated at infinite dilution.
The coefficients are called interaction coefficients by
Lupis and Elliott (1966). The expansion was suggested by
Wagner (1952) and has been used by Elliott and his students
(1966) extensively to describe interactions in liquid metals.
Chipman and Brushy'(l968)have tabulated the interaction co-
efficients for carbon in ternary iron alloys at 1000°C.
Chipman favors use of the lattice ratio, Zi = xi/(l-2xi),
as composition variable rather than mole fraction.

While the infinite Taylor series is mathematically
rigorous and can therefore be used in principle to describe
any system, the number of parameters becomes very large
for n13 even if the series is truncated at second-order
terms. In order to reduce the number of coefficients,
various simplifying models have been used, especially for
dilute solutions and for symmetric binary mixtures.

The regular solution model of Hildebrand is

E = m-B a-B 0.
G lel + x2G2 + xlx2 w

15

where w is an interaction parameter due principally to the
enthalpy of solution. This works well for many cases,
but asymmetric composition dependence of w is often ob-

served. Slight modification of Hildebrand's equation to

GE = xlal-B + X2Eg-B+xlx2(xlwi2 + x2¢gl)
permits first-order asymmetric composition dependence in
the excess free energy.

One type of desirable equation includes constant terms
which are independent of each other. An approach in this
direction is the model of Kohler (1960) modified by Kauf-
man and Nesor (1975) and generalized here for multi-

component systems,

n ._ _ n-l n x x
GE“: z xi G: 8+ xjrx [X1113 + ijgi] +
i=1 i=1 J=i+1 i J
n-2 n-1 n x x x we
1 J k 11k

 

a (2.29)
i=1 J=i+l k=i+2 (x1+x2+x3)
where we omit higher-order interaction terms. Note that in
the binary case if $13 = $51 and if wiJ is independent of
temperature, then Eq. (2.29) reduces to the regular solu-
tion model. Differentiation of Eq. (2.29) yields for the

partial molar excess Gibbs free energy of component n,

16

2
n-l x x x x
via a Ego =‘dfi’3 + 1 $23 [._a_i__§ + _£LJ_ (1-xn)]
J=l (Xn+xj) xn+x'j
n-l

+ Z wgn L———l——-<-—e1—-- xn )1

 

 

 

 

3:1 (X n+xJ) x r1+xJ
2
n—1 n-1 x x
' Z ng ( 1 )
i=1 J=1 +xJ
n-2 n-1
+ (x nxi‘J) 9:11
i=1 =1
J>i (xn+xi+xj)
nil nEZ x w“ [ xixJ _. 2xnxixj ‘- x nxixJ ]
J=:#:=1 J Jki xn+x1+xJ xn+x1+xJ (xn +x i+xj)2
n-1 n-2 n—1 2x x x
+ - 1 15“ (x1 113k) (2.30)
i=1 J=l k=1 (x1+xJ+xk)
J#i#k
k>J

To illustrate the physical implications of this model
on the chemical potential of a species in a multicomponent

system, consider a ternary solution:

17

2
ugasafiga: EWC31[_.:§__§__2+__3._L(1-3X)]
= (x3-I-xJ)2 x 3+xJ

 

 

2
2 x x x
+_z_w MGEJ(J -x3)1-w‘{2(21)

X3+XJ X3+XJ X1+X2

X2Xl

xl+x 2

- V21 (— —) + 7123 (1- -2x3)xlx2. (2.21)
The first two terms in Egg describe the binary interactions
of component 1 with the other components in the system.
They are due to the heats of solution in the binary mix-
tures. The next two terms appear to be independent of
component three and show that even if only binary interac-
tions are considered all binary interactions affect the
chemical potential of a species, not Just the terms involv-
ing it. The wg23 term involves ternary interactions, for
which there are few data. The wa3 term can be regarded
as the extra heat of solution in the ternary over that pre-
dicted from a linear combination of the binaries. A non-
symmetric function in x1 and x2 would be more appropriate in
the cases where the three—one and three-two interactions
are appreciably different.

In the limit as x3 + 0, Eq. (2.31) yields

lim
Ed 0 a a 2 a 2
x3 I 0 u3 1p13x1 + W23x2 ‘ *12x1x2 ‘ $21x2x1 (2°32)

18

If the $12 and 931 terms are small compared to the 933 and
713 terms, this equation is analogous to one suggested by

Wagner (1952).

In the limit of infinite dilution, with l = solvent,
Eq. (2.31) yields
lim Ea a Am
x1 + 0 u3 = $13 = RT in Y3,
lim a . a
x1 + 1 RT E33 = 2031 - 9w13,
lim a a
x1 + 1 RT P333 = 3¢31 - 5Wl3,
lim Ea
x1 + 1 p1 = 0. (2.33)

Thus, the Kohler equation reduces to Henry's Law for the
solute in the limit of a dilute solution and to Raoult's
Law for the solvent.

The experiments reported here provide a test of the

Kohler formalism and provide data on the solution thermo-

E
carbon

alone cannot lead to all the interaction energies. The

dynamics of nickel-based alloys. Measurements of u

other ones must be obtained from the literature. The solu—
tion thermodynamics of the transition metal binary systems
of interest have been determined more extensively and more
precisely than have the thermodynamics of these same

metals with interstitials such as carbon, oxygen, and

19

nitrogen, so the literature is rich in information on
binary metals.

If the model is correct, once precise values of wij
and wijk, for a system have been determined, then the chemi-
cal activity of all the species at all temperatures and
composition can be calculated. When the activity data
are coupled with thermodynamic data about precipitate
phases, the relative stabilities of the various phases

can be calculated as well as the phase diagram.

CHAPTER III
CARBURIZATION THERMODYNAMICS

A. The Choice of the Carburizing Medium

One of two gaseous equilibria is ordinarily used to

control the activity of carbon in solids; namely

 

P80
C02(g) + C(S.S.) : 2CO(g), Kl = —— (3.1)
P002%
_ PCH
+ 9
2H (g) + C(S.S.) 1 CH (g), K = . (3.2)
2 9 2 P2
A
H2 c

Samples are placed in a reaction chamber, at a tempera-
ture of interest, together with a gas mixture of known,
constant composition.) Knowledge of the value of the
equilibrium constant for the gas reaction allows the ac-
tivity of the carbon in the sample at equilibrium to be
calculated.

There are three difficulties with the C02-CO reaction:
(1) the amount of CO2 in the mixture becomes very small at
high temperatures, which complicates analysis of the gas
composition; (2) before it reaches the sample, carbon mon-
oxide gas tends to decompose in the furnace to carbon

dioxide and amorphous carbon, which causes uncertainty in

20

21

the carbon activity of the gas at the sample surface; and
(3) the presence of a small amount of oxygen in the carbon
monoxide-carbon dioxide mixture complicates the analysis

because of the reaction
2co2 z 200+02. (3.3)

The COB-CO reaction is thus unsuitable for use in studies
of materials containing stable oxide formers. Although
problems one and two have been avoided by most investi-
gatOrs, the problem of oxide formation cannot be overcome.
Reaction (3.3) controls the oxygen partial pressure, and
if an oxide is stable at that pressure it will form.

The methane-hydrogen reaction requires a cleaner system,
primarily because of the devasting effects small amounts of
water or oxygen can have on the gas compositions. Ellis 33 31
(1963) quantified this effect and found that even the addi-
tion of a phosphorous pentoxide trap does not eliminate
the problem. Bungardt 23 a1. (1969) have shown that
results comparable with those obtained from CO/CO2 studies
are possible if sufficient care is taken. The advantage
of the H2'CH9 reaction is that the oxygen potential can
in principle be kept as low as desired.

Since titanium and molybdenum are facile oxide formers,

the CHu-H2 reaction was used exclusively in this work.

22

Instead of direct analysis of the gas mixture, the carbon
content of a pure iron standard was used to determine the
carbon activity. The composition-activity relationship

for carbon in iron, determined by the CO/CO2 method, has
been studied extensively in the past 50 years. Dunwald and
Wagner (1931) performed the first quantitative experiments
on iron-carbon binaries, and the system has been studied

by many others including Smith (1996) and Ban-Ya 32 a1.
(1969) and (1970).

B. Analysis of the Thermodynamics of the CO/CO2 Equilibrium

“It appears superficially that literature data on the
iron-carbon system agrees to within 2%. Close examination,
however, shows that the apparent agreement is partially
a result of using different values for the equilibrium
constant for Reaction (3.1). Smith (1996) determined and
used a value 10% lower than that employed by Ban-Ya gt_91
(1970). A literature search undertaken to determine the
correct value of the equilibrium constant showed that the
disagreement results solely from the use of different
values of the absolute entropy, 8%, of carbon monoxide.
Ban-Ya 32 31. (1970) used values determined by Clayton and
Giauque (1932) from data taken by Snow and Rideal (1929).
Smith (1996), on the other hand, used a value determined

from his own experiments. The JANAF Thermochemical

23

Tables (1971) agree with Smith (1996), while the NBS
Series III Tables (1998) used values calculated by Clayton
and Giauque (1932). National Bureau of Standards Technical
Note TN 270-3 agrees with JANAF for 8298.15’ but no litera-
ture reference is given. JANAF uses the value for 8% of
carbon-monoxide determined by Belzer and Savedoff (1953)
from spectral data of Herzberg and Rao (1999).

In order to determine the correct value of 8%, we
checked the quality of the two sets of spectral data by
a graphical method due to Herzberg (1939). According to
Herzberg, a plot of {[A2 F"(J)]-[9 Be (J + %)1} versus J
highlights any systematic or random errors in the data
{[A2 F"(J)] equals [R(J-l)-P(J+1)], and Be is the equilib-
rium rotational constant for a rigid rotor. R and P refer

-1 bands of a vibration-rotation

to the J = +1 and J
band where J is the rotational quantum number.} Figure 3-1
compares the results of Herzberg and Rao (1999) to those
of Snow and Rideal (1929). One would expect a smooth curve
with a slightly decreasing slope at high J as the centri-

'b
fugal distortion constant, D becomes more important.

e’
Snow and Rideal (1929) quote a resolution of "at most"

0.1 cm-l, while Herzberg and Rao (1999) claim 0.01 cm'l.
Snow and Rideal (1929) do not state an absolute uncertainty,
while Herzberg and Rao (1999) claim an uncertainty of lees

than 0.03 cm'l. More recent data on carbon monoxide by

.o>g:o spooEm m oosposa .Lo>o3on .mpadmog 0mm cam mponnpom

one .mocopmfimsoo Hmcgopcfi mo xoma m wmpmofivzw mpadmop Hmopam pcm

30cm on» mo mocmgwoadm Eoocmb zao>fipmaoh one .pxmp on» CH owcfimmp
coon o>w£ mason on» when: .h mamuo> AM+hvomziflhvemm< mm oommadmfio

Ammmav Hmoofim Ucm 30cm ocm Annmav 0mm Ucm whonnpom mo mpadmmh one

.H.m crowns

25

 

 

n. o. n
o\
O
o\
\
\O
[I O O
.\
O O \
o o
\.\ o o
V.
\o o
“\O O O
\ o
o\0 . o
. o\ o No 7 23233911 024 262m o
\ 3»; Sea: oi... oz< 0535: o

 

 

 

anmTfib 030 In. zmo

OJ

0..

(alum'a t -(t‘),.-JZV

26

Rank gt a1. (1961) and Plyler §£_§1. (1955) do not differ

significantly from the results of Herzberg and Rao (1999).

The absolute entropy of Herzberg and Rao is the one to use.

C. Analysis of Literature Data on the Iron-Carbon System

The foregoing analysis dictates that the data of Smith
(1996) and Ban-Ya gt_a1. (1969, 1970), Scheil gt a1. (1961)
and Dunwald and Wagner (1931) be reanalyzed.

Table 3-1 contains the thermodynamic quantities used
to calculate the equilibrium constant for the CO/CO2 re-
action. The data for log K were fit by least squares,

with the result,

log10 x = A/T + B + C(T) (3.3)

:p
II

-9137 K, 0A = 9.9 K

(11
II

9.602, oB = 8.3 x 10’3

9 -1

, CC = 3.38 x 10'5x'1

‘ -2.272 x 10‘ K

C)
II

The carburization data were fit by a non-linear least
squares procedure to a model first suggested by Darken and

Smith (1996)

27

Table 3.1. Thermochemical Data for the CO/002 System.a

 

 

 

 

AG°/kJ-mol-1
f

Temp. b c d

(K) CO(g) C02(c) C(graphite) loglOK
1000 -200.29 -395.92 0.00 0.238
1100 -209.09 -396.05 0.00 1.096
1200 -2l7.77 ’396.15 0.00 1.715
1300 -226.96 -396.23 0.00 2.278
1900 -235.09 -396.29 0.00 2.757
1500 -293.68 -395.39 0.00 3.170

 

 

aJANAF Thermochemical Tables, 2nd Ed. (1971).

b -l -l -1
o o a 129 J-mol , 0 ° = 0.09 J-mol K .
AHf,298.15 8298.15
COAHO = 95 J-mol-l, 08° = 0.09 J-mol'1 K'l.
f,298.15 298.15

dC02(g) + C(gr) = 2CO(g). = 0.019 - calculated

a
loglOK

assuming 08° and OAH° are not functions of temperature.
f

28

2

P .
10le A0 = 108 E PEA/K] = 10s 70 + 108 ye. (3.9)

P
002

log 90 =1; yC + b + d/T.

yo = it; = atom ratio.
xFe

Darken (1996) derived this equation from a statistical
model for dilute interstitial alloys. In the model it is
assumed that the dissolved carbon is in one of two energy
states; namely, it has either no or one carbon atom in a
nearest neighbor interstitial position. Although very
simple, the model does an adequate Job of predicting the
behavior of carbon in binary metallic solutions.

The data from the four different investigations were
fit separately to Equation (3.9). Table 3.2 contains the
solubility of graphite in iron at various temperatures and
the standard deviation of the data for each investigation.
Also in Table 3.2 are the results of Gurry (1992) for the
solubility of graphite in iron at 957 and 1109°C and the
extrapolated value of Buckely and Hume-Rothery (1963) for
the solubility of graphite in iron at the iron graphite
eutectic (1153°C). Statistically, the data of Smith (1996)
and of Scheil g£_a1. (1961) fit the model best with the data
of Ban-Ya 33 31. (1969, 1970) being almost as good for

29

Table 3.2. The Solubility of Graphite in Gamma Iron.

 

 

Temperature (°C)

 

 

 

Std. Dev.
800 957 1000 1109 1153
Carbon Std. Dev.
Investigator at % (O) %a
Smithb 3.83 6.01 6.63 8.15 8.87 2.5
Ban-Ya gt g1,b’° 3.69 5.79 6.91 7.92 8.63 3.0
Scheil g§_g1P 3.78 5.78 6.37 7.77 8.91 2.7
Dunwald gt_§1P 3.62 5.99 6.68 8.90 9.22 5.9
Gurry 6.15 8.10
Buckley gt _1 8.98
a

o is the root mean square residual error.
bSolubility calculated using the investigators published
data and the model suggested by Darken (1996). .

cBan-Ya 33 31's 1300°c and 1900°c data were ignored.

3O

temperatures below 1300°C. If all of the data of Ban-Ya 22
a1. (1969, 1970) are used, the standard deviation Jumps
to 7%. Chipman (1972) observed that the 1300 and 1900°C
data of Ban-Ya gt_a1 (1970) are in error. Dunwald and
Wagner's (1931) data fit the model with a standard devia-
tion of 5%. When the values for the solubility of graphite
are calculated from each set of data it is obvious that
while each set is internally self-consistent, the results
do not agree with one another. A systematic error must be
present in at least three of the data sets and possibily
all four. Smith's (1996) results are the only ones that
agree with the graphite equilibration data within two
standard deviations over the temperature range 800 to
1153°C.

As a result of the systematic deviation among the data
sets, it was decided to use only one set of data rather
than an average of all the data. Smith's data were chosen

for the following reasons:

1. The fit to the model was very good._

2. He obtained the presently accepted value for the
CO/CO2 equilibrium constant using his equipment.

3. Care was used in checking the accuracy of the
National Bureau of Standards standard reference
material (NBS SRM) used in calibrating his carbon

analyzer.

 

31

9. His data agree closely with the graphite solu—
bility data of Gurry (1992) and Buckley and Hume-
Rothery (1963)-

The equation for the activity of carbon in iron derived

from Smith's data is:

logloAc = lOglchYc = (a/T)yC + b+d/T + logloyc (3.6)

CA = 2.5%

C

_ 3 2
a - 3.981 X 10 K, 0a = 1.09 x 10 K
b = -8 108 x 10"1 o = 1 33 x 10‘2

o , b o

d = 2.212 x 103 K, o = 1.69 x 101 K

Smith's (1996) published data are tabulated in Table
3.3. The precision of Smith's (1996) data is 2.5%. It
is heartening to note that the graphite and the most pre-
cise gas phase carburization data agree.

The results of Smith, Ban-Ya £E.§l-: Scheil gt a1,,
and Dunwald and Wagner are compared with Equation (3.6)
in Figures 3.2, 3.3, 3.9 and 3.5. The x's are experimental
points, the zeros, 0, are calculated from Equation (3.6)
and the equal signs, =, indicate that the calculated and

experimental points differ by less than 1.9%. Smith's

32

Table 3.3. Data of R. P. Smith (1996) for Activity of
Carbon in y—Iron in Equilibrium with CO/CO2
Gas Mixtures.

 

 

 

 

Carbon
T a 2

(°C) wt % at % yc PCO/Pco
800 0.393 1.58 0.0160 2.25
0.356 1.63 0.0166 2.96

0.377 1.73 0.0176 2.65

0.905 1.86 0.0189 2.85

0.993 2.03 0.0207 3.11

0.953 2.07 0.0212 3.12

0.522 2.38 0.0299 3.63

0.568 2.59 0.0266 9.21

0.608 2.77 0.0289 9.50

0.697 2.99 0.0303 9.87

0.661 3.00 0.0390 5.11

0.726 3.29 0.039 5.59

0.726 3.29 0.039 5.69

0.765 3.96 0.0358 6.07

0.815 3.68 0.0382 6.55

0.831 3.75 0.0390 6.75

0.838 3.78 0.0393 6.81

0.836 3.77 0.0392 6.89

0.875 3.99 0.0910 7.29

1000 0.0360 0.168 0.00168 1.98
0.0987 0.226 0.00227 2.99

0.0563 0.261 0.00262 3.12

0.0790 0.393 0.00399 9.21

 

33

 

 

 

 

Table 3.3. Continued.
Carbon
T a 2

(°C) wt % at % yc PCO/PCO

1000 0.133 0.615 0.00618 7.29
0.292 1.115 0.0113 13.8
0.955 2.081 0.0213 27.9
0.655 2.979 0.0307 93.9
0.810 3.658 0.0380 56.2
0.963 9.326 0.0952 70.8
1.081 9.836 0.0508 89.1
1.206 5.371- 0.0568 99.9
1.321 5.860 0.0622 113.3
1.962 6.953 0.0690 130.2
1.966 6.970 0.0692 131.7
1.971 6.991 0.0699 132.9

1200 0.0198 0.0688 0.000688 3.75
0.0191 0.0655 0.000655 3.80
0.0217 0.101 0.00101 5.83
0.0252 0.117 0.00117 7.19
0.0273 0.127 0.00127 7.23
0.0950 0.209 0.00209 12.96
0.109 0.505 0.00507 30.3
0.219 0.992 0.0100 61.9
0.916 1.905 0.0199 122.5
0.913 1.892 0.0193 123.1
0.738 3.391 0.0396 293.6
0.992 9.239 0.0992 352.2

 

 

a
yo = Xc/XFe

- atom ratio

of carbon to iron.

39

Ixo vcm UopmHSoHMo map pmsu mmeHccfi .u

ompMHSono.mpm .o fimopou mnp .mpsaoa Hmpcmefiamaxm mum m.x one

nomv 0% m> o>Ca “Am.mv soapmSUm mamhm> Aw3mav Sufism mo mpHSmmy one

.Rm.a can» mmoa an pommfic modaw> Housmefinma

\

.mcwfim fiasco mnu cum mosaoa

onuflv
. ox
.m.m mpswfim

 

 

3m.m OOH x cm mmmo.o
9 - II 1.1 c... mm .H
o -
. OOOONHHB n
K
K r C"
u o x x
. n
m
x u
. oooooaue m o
O n
I I
an or Ca
.8 o on
0 d On x x
. - K On I I v
D oowflB an n u x

35

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IHwo on» mmefiocfi .u .wcwfim Hmsoo on» cam mpcfioa UopmHSono who “0
.m.oaou map .mpcfioa Hmpcmefimoaxo mam m.x one .onxIHV\ox u omu om m>

0» Ca .Am.mv COHpmsum mammm> Aowma .mmmav am.mm wwucmm mo mpHSmon one
o

 

.m.m mhswfim

ooa x a-
o.oa wmm.o
no o
ooooiua on m. S H
x 000
o O 00
o O x X!
o x x
O O x “1
00 x x u
OOOOMHIE x x...“ 92.6;
x x 1. mo 0
XX X o x
x o
on
u xx
ooomfiaue m mm
o m 0 mu 0» Ca
0 x o x
0
mm .x x m x
o . m 1
O O X K n “0
OOOOOHNB x x
x m
o m
oooomae . m ..
mm.m

 

36

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can» wmma hp mommac modam> Hmpcoefipmaxm cam ompmHSOHmo map opMoHocfi .u
.mcwfim Hmsvo on» ocm mpcfioa ompmfizoamo mam .o .m.opou on» .mchoa Hmpcme
.mpSpmpoQEwp pampmcoo pm ponpmp moom\owm pampw

.mfioxnav\ox u emu om

Ifipoaxo ohm m.x one
Izoo pm mpcmefipoqu go mpom cosmommmm AM.MM Hfimnom

 

.m>.o> Cu .Am.mv coapmzum m5m9o> Aammflv_flm mm afionom mo mpHSmmp mnB .:.m madman
0»
m1; mim
- - 7 - - 1 - - - v.
. m 34
o x
o x
c
c x
O o K m x u
o o x c .
WomwfiuhO O x O O x x .M.
o o 7
x o x x o x N
x o x o x
.. SETH." . c x m
x
o
3.22” a. > 5
ex
3 m: r.
o x
on x . 4
K OCX h.
mm.:mu& 0 «xx 9 x
x
o
x
O
MOow .H o 02x
.1 .mx 2 Hma

 

37

.nm.H cos» mmoa an pmmmao mosam> Housmafinmaxm cum

oopmHSoHMo on» opmofiocfi .u .mcwfim fiasco on» new mpCHoa ompmasoamo who

.0 .w.opmu on» .mpcfioa Hmpcmefipmaxm mam m.x one .mfioxuavox u ozu om
m3m9m> 0» nu .Am.mv cofipmsum .m> AHmmHV AM.MM camzzso mo muHSmmp one .m.m maswfim

 

o.
OOH x >
mmw: . mmmo.
- . n . ,. . x a ,9“ mm.a
o x
OOONOHHB m
00 000
o .3. o
o > Cu
x x xx x
oooooane x
a on mo
0 O
X
0 I!
x x x
oooamue u
D
.x m>.m

 

38

results scatter uniformly about the calculated points and
seem to fit the model in both terms of temperature and
composition dependence. The results of Ban-Ya g£_al. for
in Y: versus yc, in Figure 3.3 are high compared to Equa-
tion (3.6) except at 1150°C, where the results are in better
agreement. The residuals at 1150°C, however, are biased

as a function of carbon concentration. The results of Ban-
Ya g§_§1. at 1150°C were obtained at a different time than
those at the other temperatures and this could explain the
difference. Figure 3.3 clearly shows that their 1300°C

and 1900°C results are not consistent with the model
having an intercept which is proportional to 1/T or l/T
plus a constant. This affirms Chipman's (1972) assertion
that the high temperature data of Ban-Ya gt a1. is in
error.

The resultscfi‘Scheil gt a; (Figure 3.9), like those of
Ban—Ya gt al., are high compared to Equation (3.6). When
fit directly to the model, Equation (3.6),Scheil's results
do not seem to fit. The residuals indicate that the inter-
cept would have to be a complicated function of tempera-
ture to fit all the results. Dunwald and Wagner's results
are also high compared to Equation (3.6). This is especial-
ly true at low carbon concentration where their data indi-
cate a zero slope for in Y:‘ Given the precision of the

other investigators' results, it is likely that Dunwald

39

and Wagner's results are incorrect at low carbon concentra-
tions.

Mainly, the results of the other investigators beside
Smith were systematically higher for 2n Y: than those of
Smith. The most probable reason for this is the gas com-
position or the carbon analyses, either of which could
conceal a systematic error that would effectively increase
the value of the activity coefficient of carbon. Figures
3.2-3.5 all tend to confirm our decision to use only one
set of data, that of Smith, in our experiments.

If greater accuracy is desired for the iron-carbon
system, the areas where improvement of technique would be
most valuable are: (1) carbon analyses; (2) analyses of
the gas mixtures, and (3) experiments at more, different
temperatures to obtain a better fit for the temperature

dependence of the activity coefficient.

CHAPTER IV

ANALYSIS FOR CARBON

A. Introduction

 

Analysis for carbon is critical to the results of
this work. Considerable effort was expended on develop-
ing the combustion method for analysis of carbon and in
demonstrating its precision and accuracy. The procedure
described here is the culmination of a many step process.
The attainable precision of the method is shown to be ap-
proximately 1% in Section B; not all analyses were of
this precision, however. Section C addresses the question
of the accuracy of the analyses. Since the analysis method
relies on National Bureau of Standards Standard Reference
Materials (NBS SRM), the accuracy of the results depends
on the accuracy of the certified analysis of the NBS
SRM. Analysis of several NBS SRM's Shows that they
scatter approximately 15% relative to their certified
concentrations. The scatter in the standards limits the
accuracy of the carbon analyses reported here to approxi—

mately 15%.

9O

91

B. Procedure for Total Carbon Determination by_the Com-

bustion—Gas Chromatographic Method

1. Summary

 

The carbon in the material is converted to carbon di—
oxide by combustion in an oxygen stream. The carbon dioxide
is then trapped on a zeolite column. After the combustion
is completed, the trap is heated, and the carbon dioxide
is released into a stream of helium and thence to a
chromatographic column. The amount of carbon dioxide is
measured in'a thermistor type conductivity cell. The
signal is automatically integrated and displayed on a
digital panel. The instrument must be calibrated with

material of known carbon concentration.

2. Equipment and Reagents

Reaction crucibles: fired at 1000°C for eight hours
and then stored in a desiccator until used.

Acetone: electronic grade, less than 0.0005 percent
residue.

Tin metal accelerator: washed in water and acetone
to remove organic impurities and then dried at 70 to 100°C.

Cupric oxide: fired at 1000°C for two to three hours

in air.

92

Helium, high purity: passed through a purification
train of ascarite, glass wool and Dri-rite.
Oxygen, ultrahigh purity: passed through a purifica-

tion train of ascarite, glass wool, and Dri-rite.

,3. Calibration

NBS Standard Reference Material 121B was used as the
calibration standard. Aliquots of less than 20 mg were
not used. Homogeneity for aliquots of 20 mg has been
demonstrated for National Bureau of Standards Standard

Reference Materials (ASTM, E350).

9. Determination of Blank

Before actually determining the blank, the instrument
is cycled several times with the standard until a constant
response is obtained.

To determine the blank, one scoop (apprbximately 0.75
gram) of tin granules and then two scoops of cupric oxide
are placed in a crucible. The crucible is then placed in
the combustion chamber and allowed to sit in the oxygen
stream for one to two minutes before cycling the instru-
ment. The blank determination is repeated several times
until a reading of :1 us is achieved for three consecu-

tive determinations. A blank greater than 15 ug indicates

93

that there is probably a leak in the system which must

be corrected.

5. Procedure

With the instrument stabilized and the average blank
determined, the analyses are undertaken according to the
following procedure: Each unknown determination is
preceded and followed by an aliquot of a SRM. The ali-
quots of 121B are measured to contain approximately the
same numbers of micrograms of carbon as the samples
(1100 pg). Aliquots of standard and sample of less than

100 pg or greater than 1000 pg are avoided. The factor

( ug carbon
number of counts

 

) used for calculating the concentration
of carbon in the unknown is obtained by averaging the
value obtained for the SRM. .If the instrument is not run
for an hour, or if different batches of gas, tin, copper
oxide or crucibles are used, the procedure for determining
stability and the blank is repeated before proceeding to

new samples.

C. Precision of the Carbon Analyses

Table 9.1 and Figure 9.1 contain data on National
Bureau of Standards Standard Reference Material 121B

collected in three sets over a period of three weeks. As

99

Table 9.1. Calibration Data for LECO Gas Chromatograph
Carbon Analyzer with National Bureau of Stan-
dards Standard Reference Material 121B.a

 

 

 

NBS SRM Instrument
121B Reading
Date (gms) (counts)
2/18/77 0.2213 307.1
0.3029 925.3
0.9395 609.9
0.5209 790.2
0.6091 898.3
0.9157 581.3
0.5192 725.9
0.9080 576.8
0.5182 . 721.6
0.9189 578.5
0.6939 899.0
0.9908 615.0
0.5139 721.7
0.9106 579.3
0.9110 592.0
0.9923 621.1
0.5208 739.1
0.9553 691.9
0.9030 566.2
3/3/77 0.9150 579.7
0.2318 319.9
0.9998 627.0
0.9299 592.8
0.6269 875.0

 

95

 

 

 

Table 9.1. Continued.
NBS SRM Instrument
121B Reading
Date (gms) (Counts

3/3/77 0.9550 639.1
0.2219 305.9
0.5113 729.0
0.5965 768.0
0.5089 718.0
0.9296 588.0

3/11/77 0.2927 338.7
0.5513 799.7
0.9302 598.8
0.2116 292.3
0.6199 858.0
0.3369 977.1
0.9158 589.0
0.9273 596.7
0.9159 592.2
0.9520 691.8
0.9199 597.1
0.9358 617.3
0.9085 577.0
0.9322 613.6
0.2277 329.2

 

 

aNBS SRM 1213 is stated to

contain 0.0720 wt%

carbon.

96

coxmp mmz mpmc one

.mmmo mumpmamm oops» so

.pwnmamcm conme coma map pom wumo coapmspfifiwo

.H.: opswam

97

3.208 hzutamhmz.
000 00k 000 00f. 00¢ 00m

_ 1 _ _ _

0

 

\Nd v.0

.3
I. 0 \1 n.0 Nd v.0

v.0 n.0 «.0

[K

0.0 0.0 n.0

T

0.0 n6 v.0

  
    

n no: I. I ah

72:3...v10; «0.54.70: ad a 2:29 . .
2.23 o I so no no

 

n 10:26 a ab 3.58. u '10. u 3‘. +70. x 06 I 2.. 2o
ks. \ n \n d
nno... to Ian .2568 :79... 9.6.5103. QT I 2.33

hhxgxm 0
I1 0.0 5.0 0.0

 

 

_ _ _ _ _ _

030.05h 030 In. 23.0

 

(“9015) 952} MS SON

98

shown in the figure the standard deviation in the weight

of 121B varied from 3.1 to 9.1 mg. To obtain one percent
precision one must use aliquots of 121B with a mass of
approximately 0.9 grams or larger. Since 1218 has a nominal
carbon concentration of 0.0720 weight percent, aliquots of
greater than 300 ug of carbon should be used to ensure

one percent precision. In practice it is not desirable to
exceed 1000 counts on the instruments. Above 1000 counts
the amplifiers begin to saturate and become non-linear in
their response. If aliquots of greater than 500 micro-
grams of carbon were desirable for some situation a lower
amplifier setting can be used, so that the number of counts

per microgram of carbon is decreased.

D. Accuracy of the Carbon Analyses

NBS Standard Reference Materials are used almost uni—
versally to standardize instruments for material analysis.
These materials undergo a rigorous testing for homogeneity
and composition at the Bureau of Standards Laboratory and
in private and industrial research laboratories. However,
the accuracies of the analyses are not stated or implied
by the National Bureau of Standards. The certificate of
analysis accompanying the standards shows that in many
cases the scatter in the certificate value as reported by

the various laboratories is :5 percent for carbon.

99

As part of this research effort several NBS Standard
Reference materials with certified carbon contents were
examined. Some of the results are tabulated in Table 9.2.
The instrument used for these analyses is a LECO carbon
analyzer with a gas Chromatograph-thermal conductivity
detector. The following procedure was used to measure the
carbon concentrations in the NBS materials. The instru-
ment was cycled several times until the response stabilized
and a constant blank was obtained. A NBS SRM was used to
calibrate the instrument. An aliquot of the standard
reference material preceded and followed each aliquot of
sample. The number of micrograms of carbon was approxi-
mately the same in both the calibrating standard and the
standard being checked.

Table 3.1 shows that the scatter in the data for each
standard is less than or equal to 11 percent of the value.
The discrepancy with the certified value is as much as :7
percent. The relative lack of accuracy in the certified

analysis leads to the following problems:

NBS SRM's

1. If one standard is used consistently the precision
of results can be greater than 1 percent. The calculated
data, however, will contain a systematic error due to the
accuracy of the certified analysis.

2. If many different standards are used to calibrate

50

.zonme w .pz omno.o .m Hma 2mm mmz op m>aawfioh mum mCOHumppcmocoo conpmo onem

 

 

 

 

s.o mmao.o mmao.o mmHo.o ozao.o ozao.o maoa
m.m- om:o.o mm:o.o mmzo.o emzo.o mzo.o momfi
H.mn mmmo.o :mmo.o :mmo.o mmmo.o o:mo.o maoa
o.m+ moa.o moa.o moa.o moa.o ooa.o QmH
~.m+ :om.o mom.o zom.o nomqo uma.o mma
m.=+ mam.o mmm.o mmm.o mmm.o owm.o mom

czam> mmz mwwnm>¢ m m H Apcoosma pnwfiozv monasz
Eoph conpmo , 2mm

cowpmfi>oa u pmnadz mammamc< mfimzamc¢
mmmno>¢ Am .pzv maoonmu mmeHMprmo

 

 

.mesmeeMpm mmz co mfimsflmc<

.m.: mfinme

51

an instrument, the precision of the measurement will be
limited by the scatter in the values of the certified
analyses relative to one another.

3. Comparison of data from various investigators is
difficult since different groups use different calibrating
standards. If different standards are used, discrepancies
as high as 10 percent could occur. These problems can be
mitigated to some extent if the calibrating standard is
cited in the literature. To eradicate the problems, in-
accuracies in the standards must be removed. Problems
related to inaccuracy have been caused by abuse of the
standards rather than by a failure on the part of the NBS.
The fact that a scatter of 5 percent is reported on the
certification should be sufficient to keep users from
claiming accuracies of :1 or 2 percent.

Initially, NBS SRM 19E was used to calibrate the
instrument and, hence, as a basis for analysis of a num-
ber of samples. When SRM 19E was exhausted, SRM 121B was
used. All the SRM 1213 data were converted to the SRM
19E after analysis. The correction is shown in Table 9.2.
Thus, the data in Appendix A based on SRM 121B were con-
verted to the SRM 19E base for all subsequent calculations

unless otherwise stated.

CHAPTER V

EXPERIMENTAL PROCEDURES

A. Preparation of the Alloys

In working with carbon in alloys containing strong
carbide forming elements, special care has to be taken
during fabrication. Precipitation of carbides during
processing can result in inhomogeneous alloys (Braski
and Leitnaker, 1977). The problems of inhomogeneity are
not restricted, unfortunately, to the as-fabricated
material. It has been found that the carbides cannot be
easily removed once formed. The slow diffusion rate of
carbide forming metals results in the enrichment of ti-
tanium and molybdenum in the former carbide areas even
after long anneals. This is demonstrated by the fact that
the carbides precipitate in "stringer" like patterns upon
aging at temperatures below the solubility limit. Figure
5.1 is an optical photomicrograph showing this so-called
"memory effect" in a nickel based alloy similar to those
used here.

Braski and Leitnaker (1977) concluded that a way to
achieve a homogeneous microstructure was to hot work the
material at temperatures in the solid solution regime and

that any intermediate recovery anneals after cold working

52

53

Figure 5.1. Optical photomicrographs illustrating the "memory
effect" in Ni-2.5 Ti-8 Mo—8 Cr-0.2 C (at. Z)
(a) as swaged (b) after 1 hour at ll77°C, (c)
after 1 hour at 1177°C + 160 hours at 760°C.

59

     

20 4o soiacnows l0 .0
WI5WX+4F1fl4

NCHES OMS

55

should be in the solid solution regime. As a result of
their work the eight primary alloys used in this study
were prepared using a slightly modified version of the
fabrication schedule suggested by Braski and Leitnaker.
Table 5.1 lists the procedure followed.

Table 5.2 gives the composition of the melts, as weigh—
ed prior to melting, and the composition of the analyzed
3 mm diameter rods. An extra 0.5 weight percent of
chromium was added to all of the alloys containing chromium
to correct for expected losses through evaporation. The
carbon concentration was lowered to one third of its initial
value, primarily due to losses during the final deoxidizing
anneal. 'As Table 5.2 shows, the molybdenum and the chrom-
ium contents of the alloys were analyzed in several dif-
ferent ways. Quantitative analysis for transition metal
elements in the concentration regimes in which this work
was performed is a difficult task due to the high concen-
tration of the different elements. The Paschen results for
the chromium and molybdenum and the atomic absorption
results for molybdenum appear to be unreliable because of
the non-reproducibility of these techniques for the elements
in question. Table 5.3 gives the values for the composi-
tion of the alloys that were Judged to be the best.

These values are used in all subsequent calculations.

 

56

.ummnop some nouns cococoso Loam: who: coEHomam

n

.AwanV nostpHoH cam memum up omaoHo>oo opsoooopmw

 

1‘

 

 

 

 

QOOOHH es s: m new mm ea assess wsfiueeexesa ma
H.mm m.m “chapmpmanp Eoopv owmzm oHoo NH
oasuHH um :HEan Hmmccm mumHnmEnoch HH
a.mm H.= Amszummoasmu Eoopv mwmsm oHoo 0H
mossHH um CHEImH Hmmccm opwHooEpoch m
m.om H.m msspmpoQEmu Eoopv mwmzm cHoo m
oossHH pm :HslmH Hmmccm mumHomEpoucH s
m.:: :.w Assaumsanmp Eoopv mwmsm uHoo o
oonnHH um sHEImH Hmmccm ouchoEpoch m
m.~m w.w Aosspmmean Eoosv owmzm oHoo :
coOOMH pm as H Hmmccm MCHuHcoonom m

~.mm m.oH 0 when

H.wH =.mH m nmmm

m.mm s.MH a sham

m.zm m.oH m.mmmm

0.5m m.mH m mmmm

mommmo comsuon pmmcms CHEumH m.:m H.mm H mmmm
oopsaH es swash uom m
=.mmAmmEHu w pHmEmnv ammo nopclpHoE op< H
uncoEpmmpe boom ARV AEEV mmmoopm COHumoHsnmm .oz
. mchmzm poumEmHo amum

wcHhsa com
mop< CH
coHposomm

.mmmhnHmms mmOHH< pom moHsomnom :oHpmoHsnmm .H.m mHan

57

.om u a: «.0 vocHaucoo onHa aOHHa anaz
.umu oH coHuaH>oo chaocmuo och .moo o» coauusnsoo pooaav on: can: conuozw
.ho um.o mhpxm 0:» onzHOCH nost> .COHUNuHHHuuHO> ho 0» OHQQpSDHLuuc aw

wchmwo co anH ucwHoz HHm was» on oHsoz cOHumEonuaaa coow < .uosvoua Hchu 0:» :H oopHnoo ucsosa on»
on cocoa no: no um.o .pHoE on» :H mucoEoHo bongo on» o» o>HuaHop .po «0 opsmnopn uona> st: on» on 0:00

.owsau :oHpmhucoocoo anu :H :OHpacHEnouov no you venues
chansons unoe on» couooHucoo nH uH .ous> on» no “He no huckupoocs so no: no sou anmana oHuuoesHo>o

.mo>p:o :oHuaunHHao any onanopa op can: no: mHOH.HdHhouaE oocououou opaccmuo mmz

.mqumou oHuuosHpoHOo on» o» o>HumHon osHm> ann on» you unencuoa mHnwnopn can mwms hoHHa you moon was
ano>00ou oann EscoonzHo: .90 new o: 2909 you nonHa> on» 00 am no mucHapnooc: cm was :oHunpouna oHaou<o
.osHm> on» no um“ u a: m.» 00 uHsnop a o>am no sou anmHocu oHuuoEHnoHooo

.ncfiooso so a e: H.o«m.o sooH space m om» «can

.AesmHv Ha uo howauHoH own ohsooooua Hao

nHumHmcw ho COHuoHaomoc a pom .0: you osHm> season on» go we can .no you osHa> coumpm on» «o uo.m one .HB
900 msHm> powwow on» go u .m zHomeonpaam nHmsco came on» nose acoHuwH>oo Upwccwum my Ho>oH mococHhcoo
umo one .woanwcw omozu sou own: no: mpHHHomu mHn» <Qmm on» an ngmswouaooan owczmncononwm an Hm ones

 

 

 

 

 

mmo.o o.ma o.HH m.HH om.» om.» =m.a oo.~ can:
moH.o om.s o=.e sm.H oo.~ o
omo.o am.H me.H m
soo.o e.Mfi . m.m~ em.H oo.~ a
owm.o a.m~ w.sfl H.4H . ss.m oo.m woos
mmH.o om.w wo.m aa.m cm.m duos
awo.o sH.m so.m woos
mHo.o mo.o ow.o ow.~ m.w ms.» mm.» as.» mm.e No.~ oo.~ some
wHo.o em.ms mo.ma mm.NH N.NH no.3 as.m so.s mo.m om.H mm.H hemp
Hmo.o mo.ma oe.mfl mm.ma A.NH mm.» we.» mm.» Ho.» em.H Hm.H some
oao.o o~.= mo.= so.m oo.~ moms
mHo.o me.o mw.w ms.o wm.o oe.m mm.H some
sHo.o mm.a we.» mo.m No.~ omens
sfio.o om.mH ~m.mfi ae.ma o.mH mm.a mm.H News
mHo.o oo.m oo.m some
one: eo sofloo o<< eoaewfiem use: so oossfio> sodomfism o<< . use: no soaonaem .oz

conunsusoo afico «cocommm uano acocomwm nQEoo acononmm ”Ho:
uooLHa aoHH<
wconhwo

Encovanoz EsHeouno Echpra

 

 

.u a: .uHmsz:< ho muocuoz Hmpo>om an cocHEnouoa um ucoHananoo >OHH< .m.m oHan

58

Table 5.3. Compositiona of Alloys Used for Calculations.

 

 

 

 

Alloy Element/wt %

Melt

No. Ti Cr Mo C N1
7068 2.97 0.087 96.99
7261 2.00 0.015 98.0
7262 1.95 . 12.81 0.019 85.3
7263 2.02 7.78 0.019 90.2
7269 1.95 6.68 0.015 91.9
7265 2.06 9.09 0.016 93.8
7266 1.91 7.08 12.76 0.021 78.2
7267 1.95 3.77 12.93 0.016 81.9
7268 2.00 7.33 6.66 0.015 89.0
7071 2.80 8.08 0.135 89.0
7095 3.06 13.9 0.380 82.7
A 2.00 13.0 0.099 89.9
B 1.73 0.086 98.2
C 2.00 7.90 0.109 90.5
999 1.99 7.36 11.9 0.035 79.0

 

 

aThese values were picked from those in Table 5.1.

59
B. Carburization

l. Specimen Preparation

For the carburization experiments the 3 mm nickel alloy
rods were cut into sections 9 cm long. Each specimen was
marked with a vibrator tool with the last two digits of
its respective melt number prior to cutting from the parent
rod. The specimens were then chemically cleaned in a solu-
tion of hydrochloric and nitric acid. 'The acid cleaning
was followed by washings in methanol and, finally, acetone.
After they were cleaned and dried, the specimens were weigh-
ed on a Mettler semi-micro balance to 0.002 mg.

The samples were next spot welded at each end to loops
of nickel wire. It was found that the wire could be re-
moved cleanly from the specimens if the welding was done
with the proper energy-input (25 watt-sec for 3 mm rod
and 0.5 mm wire worked well). If, however, too large an
energy—input was used during the welding or if the sample
surface became oxidized, then the wire could not be
easily removed after carburization. As many as ten samples
were welded to the loops in this fashion. The connected
set of samples was lowered into the hot zone of the furnace
on a nickel tether attached to an iron slug controlled by

magnets, as described in Section 2.

2.

a.

60

Furnace and Auxiliarnyquipment

The Furnace - The carburizing and annealing fur-

nace was one of the central pieces of equipment used in

this study.. In order to accommodate the wide range of uses

required of it, the furnace was designed according to the

following criteria:

(1)

(2)

(3)

(‘9)

(5)

(6)

(7)

It must be capable of being operated safely in
an atmosphere of H2 or Ar.

It must have incorporated in it a vacuum pump
to facilitate changes in sample atmosphere and
to check the system for leak tightness.

It must allow for cooling rates which vary from
a brine quench to a furnace cool. The cooling
must be done in an inert atmosphere.

It must be inert relative to the gases, e.g.
CH“ or H2. Specifically, it must not act as a
sink for carbon or a source for any other ele-
ments.

It must have a constant temperature zone of 9-6
inches.

It must allow for reproducible mixing of dif-
ferent gases.

It must have unobstructed flow of gas around

the samples while they are in the hot zone.

61

(8) It must have the capability to purify and monitor

the purity of the gas stream.

The furnace itself is a platinum resistance heated furnace
with a 55 mm bore. The temperature controller used through-
out most of the experiments was a Speed-Max G duration ad-
Justing (DAT) controller. The controller maintained a
constant temperature to 12°C. Toward the end of the in-
vestigation an Electromax III current adjusting type con-
troller (CAT) was substituted for the DAT. Temperature
control of better than 21°C is possible with the CAT
controller. '

To insure the inertness of the system the furnace
liner is made of DeGussitt-19 recrystallized high-purity
alumina. Smith (1996) noted that above 1000°C with a
mullite liner the reduction of 8102 becomes a major problem.
In this work we found that iron can also be transferred
from a mullite liner to samples in a reducing atmosphere.
Alumina reduction by hydrogen at the temperatures dealt
with here (900-1215°C) is not a problem.

The liner is sealed to a copper collar at both ends
with a viton O-ring. The water cooled copper collar
serves as inlet and exit for gas, as the connection to
the vacuum system, and for the removal and introduction
of samples. The lower collar contains the vacuum port

and connects to the quenching tank through an air—activated

62

gate valve.

The upper collar contains the vacuum gage and is fitted
with an O-ring groove which allows a pyrex extension tube
to be sealed to the collar. The pyrex extension functions
as the cold zone of the furnace. A magnet is used to
lower the samples into the hot zone. If a quench is de-
sired the magnet can be removed and the sample dropped
through the gate valve and into the quench tank. The gas
system is so arranged that the samples are in a controlled
atmosphere until they hit the quenching medium. If slower
cooling is desired, the samples can be raised with the

magnet into the extension tube.

b. Thermometry — The temperature in the furnace was
measured with a calibrated platinum-10% rhOdium (Type S)
thermocouple. A similar thermocouple was used to control
the furnace temperature. Before each set of runs, to
insure that the furnace was at the proper temperature, a
profile of the furnace temperature was taken. After ini—
tially adjusting the resistance across 6 taps the furnace
temperature was found to be constant within 2°C over the
100 mm center section of the muffle. No discernible drift

in the peak occurred with time.

c. Gases - The piping system to the furnace is de-

signed to allow three different gas cylinders to be used

63

together or separately. Each of the three lines feeds

gas through a Fisher—Porter Tri-flat variable area flow-
meter and intozicentral mixing chamber. The flowmeters,
with flow rates of 0-300 cc/min, can be used to mix gases
to ratios as low as 1:20 with little difficulty. After
passing through the mixing chamber the gas stream either
enters directly into the furnace or goes through a puri-
fication train and then into the furnace. The purification
train consists of a palladium catalyst followed by a column
filled with Linde 3A molecular sieve. The palladium con-
verted any free oxygen in the gas into H20(g) and then the
molecular sieve removed the water. The gas stream was
analyzed for water on the exit side of the furnace with a
Panametrics Model 1000 hygrometer. Water concentrations

of less than 0.5 ppm by volume were obtained with this

purification technique.

d. Operating Procedure for Safe Use of the Hydrogen
Furnace
1. Starting 0p
a. Close bottom gate valve and unplug electrical
Asocket.
b. Set all regulators at MS lbs and close all flow
meter valves.

c. Make sure vent valves are closed.

J.

69

Evacuate furnace system with fore pump. (If
the fore pump is not used to evacuate the
furnace system, a minimum of 0.5 cubic feet
of argon must flow through the furnace and more
than 1.5 cubic feet is not necessary since
the furnace volume is only m.15 cubic feet.
Back fill with argon.

Repeat d and e for 3 cycles.

Open exit valve to exhaust system. The pres-
sure in the furnace should be atmospheric or
very slightly above.

Light pilot light and open exhaust hood.
Begin flowing hydrogen with argon still flow—
ing.

Shut off argon.

Shutting Down

Start flowing argon.

Turn off hydrogen.

Flush the furnace with at least 0.5 cubic feet
of argon, not more than 1.5 cubic feet is need-
ed. (At the end of this time a platinum wire
near the pilot light should not be glowing.)
Open furnace to remove or insert samples.

Leave argon flowing while furnace is open and

reclose the furnace as soon as possible.

65

e. Shut off pilot light.
f. Shut off argon.

g. Close exhaust hood.

3. Use of Quench Tank

a. Secure quenching tank to the base of furnace
with C-clamps or bolts.

b. Flush quench tank with a minimum of 0.7 cubic
feet of argon or not more than 2.0 cubic feet.

c. Turn off argon first up stream from quenching
tank and then down stream Just prior to quench-
ing samples. (It is important not to build-
up pressure in the tank which may blow the
quenching media up into the furnace chamber
when the gate valve is opened.

d. Plug in gate valve.

e. Open gate valve - drop samples into quench

tank - close gate valve - unplug gate valve.

C. Annealing

 

,In order to obtain information on the solubility of
carbon in the carbide-forming alloys at relatively low
temperatures (BOO-1000°C), a procedure other than car-
burization was employed. The low solubility of carbon,
.<0.05 atom percent, and the slow kinetics of the carburiza-

tion reaction make carburization experiments extremely

66

difficult at these temperatures. (See Chapter IX for a
discussion of the results of the carburization experiments
at 900°C in the carbide forming alloys.) To circumvent
the problems of carburization, alloys with a fixed con-
centration of carbon were arc melted and cast. Three

(3) millimeter rod sections of these alloys were then
annealed at various temperatures.

For annealing, two platinum wound resistance fur-
naces with Inconel 600 furnace tubes were used. The sam-
ples were first cleaned as described in Section II B and
then wrapped tightly in a sheet of tantalum. The furnaces
were designed to allow a continuous flow of argon through
the hot zone. The tantalum foil acted as a getter for
Ithe impurities in the gas. When samples were being placed
in the furnaces the‘flow of argon was increased and was
kept high for approximately five minutes after closing
the furnace. At the end of an experiment the argon flow
was again increased, and the samples were quickly pulled
from the hot zone of the furnace and plunged into a 10%
sodium-chloride brine. A translucent oxide was visible
on alloys containing chromium and molybdenum after quench-
ing. Oxidation apparently occurred during the quench
rather than during the anneal.

The calibrated platinum-10% rhodium thermocouple used

in the carburization experiments was used to measure the

67

temperature in the annealing furnaces. The current adjust-
ing type of proportional temperature controller was used
throughout this series of experiments. The temperature

in the region of the furnaces containing the samples was

held constant to within 12°C.

D. Electrolytic Extractions

1. Description - In order to obtain precise information

 

about precipitated phases in metallic matrices, it is
necessary to isolate the precipitate. The precipitate
phases in the materials of concern have varied from 0.05

wt z to 5 wt %. Since quantitative determination of weight
fractions was desired, a highly specific isolation tech-
nique was required such that none of the precipitate phases
dissolves but all the matrix dissolves. The literature
[Donachie (1972) and Andrews (1966)] indicates that anodic
dissolution has been shown to be a highly selective tech-
nique. Donachie (1972) lists 9 different precipitate
phases that have been successfully isolated by the elec-
trolytic technique. Specifically, since MC type phases

can be quantitatively recovered and since MC was the phase
of primary import in this investigation, it was decided to
use anodic dissolution for the concentration of precipi-
tates.

Anodic dissolution involves using the sample material

68

as the anode and some inert material, such as platinum,

as the cathode in an electrolytic cell. The electrolyte
most often used, and that used for all this work, is a
solution of 10% by volume of concentrated HCl in methanol.
Donachie (1972) indicates that in alloys containing tung-y
sten, tantalum or niobium a complexing agent such as tar-
taric acid must be added to control oxidation since con-
siderable amounts of oxides of these elements can form
and precipitate.

In this connection it was discovered during this
investigation that nickel oxide forms in small quantities
during electrolytic polishing of surfaces. Oxide formation
can be a particularly severe problem in sample preparation
for the electron microscope or small angle x-ray scatter—
ing. The nickel oxide has only been detected by x—ray
diffraction in extracted residue which contained very
little MC phase. Since the N10 and MC phases have similar
structure and lattice parameters 0.920 nm and 0.931 nm,
respectively, the carbide phase, if present, would ob-
scure the nickel oxide. That the amount of oxide formed
is small is verified by analysis of the extracted material.
Nickel varied from a few parts per million to 1000 parts
per million but never higher.

Another problem cited in the literature [Andrews
(1966) Leitnaker (1977)] is the precipitation of silicon

in the form of a gelatinous silica during extraction.

69

Leitnaker determined that silica was not precipitating in
his high alloy steels with silicon concentration of 1 wt

1. Since the alloys in question here contained only traces
of silicon it is certain that, even if it occurred, it

would not pose a problem.

2. Precision - In order to insure that the best
precision available from the technique was obtained a
strict procedure was developed and followed closely in
all extractions. (The procedure is outlined at the end
of this section.) As a test of the procedure, two samples
that had been thoroughly homogenized by long term aging
were extracted several times. Table 5.9 contains the
results of these extractions. The standard deviation of
the procedure is 0.013 wt Z. If 1 gram of material is
dissolved, 0.013 wt % corresponds to 0.13 mg. Since each
extraction involves the weighing of a centrifuge tube
twice with a standard deviation of approximately 0.05 mg,
the precision obtained with the following technique is the
best that can be expected until a more precise balance and

better recovery technique become available.

3. Procedure for Anodic Dissolution of Nickel-Based
Alloys for the Concentration of Precipitated Carbide

 

Phases -
Equipment and Reagents

Semi-microgram balance

70

Table 5.9. Results of Multiple Extractions of 0.69 cm
Rod Specimensa of Ni + 2 wt % Ti + 0.1 wt % C.

 

 

 

 

Heat Treatment Quench Precipitate

Extracted
Temp. Time wt %

(°C) (hrs)
1100 16 02° 0.122
0.129
0.103
Avg=0.ll8, o°=0.013

1260 9 Oz 0.128
0.115
0.098
0.108

Avg=0.112, o°=0.013

 

 

aThe extraction solution wale% (volume) HCl in methanol.
The voltage was held constant 1.5 V for the duration of
the experiment «6 hours.

bCZ-cold zone cooled.

co is the root mean square residual.

71

Constant voltage power supply (0-9 V)
Platinum tipped forceps

Platinum sheet to serve as a cathode
50 x 70 mm pyrex dish

15 ml centrifuge tube
Multi-position centrifuge

Ultrasonic cleaner

Eye dropper

Magnetic stir bar

Plastic wrap

Methanol-analytical reagent grade

Hydrochloric acid-analytical reagent grade

Procedure

1. A solution of 10% hydrochloric acid, by volume,
in methanol solution is prepared.

2. Any surface oxide is removed from the sample with
sand paper.

3. The sample is cleaned by anodically dissolving it
for 1 hour. The specimen is held in the platinum
tipped forceps which are connected to the positive
terminal of the power supply. A piece of platinum
sheet functions as the cathode. It is molded to
fit the inside of the 50 x 70 mm dish (see Figure
5.2). The dish is filled with the acid solution

so that the sample is well covered. Finally, a

72

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79

piece of plastic wrap is placed over the dish and
around the forceps to help control evaporation of
the solution. The dissolution is carried out at 1.5
V. The mixture is stirred with a magnetic stir bar.
After it is clean, the sample is washed in methanol
in the ultrasonic cleaner, dried, and weighed to
0.05 mg.
After it is weighed, the sample is placed in a
clean dish with fresh solution and dissolved for
6-8 hours as in (3). Care is taken not to get
the sample too close to the cathode because the
high current that results causes plating on the
cathode.
A 15 ml centrifuge tube is cleaned with soap,
rinsed several times with methanol, and placed in
a vacuum dessicator. After 1 hour it is removed
and allowed to equilibrate with the air for 1 hour
before weighing to the nearest 0.02 mg. Since
the precision of the results depends strongly of
the precise weighing of the centrifuge tubes in
steps 5 and 9, the tube is weighed twice, and 8
the zero is checked both before and after the
weighing.
The remaining sample is placed in the preweighed

centrifuge tube partially filled with methanol,

10.

75

and the tube is then placed in an ultrasonic
cleaner to remove any precipitate adhering to the
rod. The sample is then removed from the tube,
dried, and reweighed.

The extraction solution in the dish is transferred
to the centrifuge tube with an eye dropper and

is spun at high speed for at least 2 min. The
supernate is decanted.

The precipitate in the tube is washed with methanol
and centrifuged again. This procedure is repeated
until the supernate is clear.

The tube containing the clear precipitate is
placed in a vacuum dessicator to remove the
methanol. After several hours of dessicating,

the tube is allowed to equilibrate with the air
for at least 1 hour and is then weighed as in

Step 5. If any discoloration or film is visible

in the tube, Steps 9 and 10 are repeated.

E. Electron Microprobe

1.

Introduction

The electron microprobe was used to analyze the car-

bide precipitates extracted from the nickel matrix. The

microprobe offers several advantages over conventional

techniques such as atomic absorption spectroscopy or

gravimetric analysis. The more conventional techniques

76

usually require large samples, are destructive, and re-
quire equipment that was not readily available for this
work. Besides requiring only small samples and being non-
destructive, the microprobe permits a rapid analysis

which is important when substantial numbers of samples
need to be analyzed. A method requiring only a small
amount of sample was important in this work because often
only 1 mg of material was available and several different
types of analysis were desired.

Abdel-Gawad (1966) and E. W. White 33 31. (1966) have
shown that the electron microprobe can be used to analyze
quantitatively micro—crystalline powders. The procedure
used in this study is essentially that described in their
papers. The assumption is that the intensity ratios for
elements in the powders are constants for any given com-
position. A series of powders was analyzed by conven-
tional techniques and then by the microprobe. A calibra-
tion chart was then constructed comparing intensity ratios
of elements of interest to weight percent ratios. The
use of intensity ratios and calibration curves severely
restricts the applicability of this technique. Light
elements are not detected by the instrument. The calibra-
tion curves are complicated with only three elements if
a wide range of concentrations are considered. Fortu-
nately, the system of interest here is essentially a two

component mixture of titanium and molybdenum. Chromium

77

and nickel are also present, but amount to only 1.0 and
0.05 wt %, respectively, and were not considered in the
calibration curve. Practically, one is limited to the
analysis of, at most, three elements of mass greater
than sodium.

The instrument used in this investigation was a
Materials Analysis Corporation electron microprobe coupled
with a Si(Li) energy dispersive x-ray detector and a

multichannel analyzer.

2. Procedure for Analysis of Carbide Precipitates

To obtain quantitative results from the microprobe
a substrate of atomic number less than 11 is necessary.
Elements above sodium emit x-rays that are detectable with
the energy dispersive x-ray detector, and there is also
a greater chance of absorption and fluorescence inter-
actions between the substrate and the sample at high
atomic number. Beryllium appears to be the best material
for our purposes. It has a low atomic number (four) and
is available in a sheet form that can be mounted in epoxy
and polished to a high sheen. Another requirement of the
substrate is that it be an electronic conductor because
the surface charge that could otherwise result would lead
to erroneous results.

The precipitates were dispersed in methanol and then

transferred onto the beryllium chip with a Pasteur

78

pipette. The crystallites adhered to the surface of the
polished beryllium after the methanol evaporated. It
was not necessary to further bind them to the surface with
glue or graphite.

A constant accelerating voltage of 25 keV was used
for the electrons. The beam was caused to raster over
an area of approximately 10,000 02. A window of 0.3 eV
was ordinarily used for each elemental peak. The peaks
normally used corresponded to the Ka of titanium and the
La of molybdenum. In a typical analysis the specimen was
counted for 20 seconds (N10,000 counts) in ten different
locations on the substrate.. The resultant intensity
ratios were then averaged. It was also part of the pro-
cedure to check for inhomogeneity in the sample by analyz-

ing very small areas but no gross inhomogeneity was dis-

covered.
3. Calibration Curve

Several different carbide precipitates were analyzed
by atomic absorption spectroscopy and with the microprobe.
The calibration curve was based on materials of very similar
composition and crystal structure to the precipitates.
Tables 5.5 and 5.6 and Figure 5.3 are the result of this

effort. The data were fit by least squares to

Intensity M0 (L0)

.. ls .M_o2
Tntensity Ti_(KE) - 0.006+0.980 (wt % T1)-0.016 (wt % Ti

 

79

Table 5.5. Analyses of Precipitates by a Colorimetry
or Atomic Absorption Spectroscopy and by an
Electron MicroprObe Energy Dispersive X-ray
Analysis.

 

 

 

d

Microprobea Titaniumb Molybdenumc %%—%4%%
IMO/IT1 (wt 7) (wt %)

7263e 37.65

A-7783-17

+ 8 Cr

7269f 0.91 92.99 91.37 0.97

A-7783-l7

+ 9 Mo

7262e 1.27 38.80 98.55 1.25

A-7783-l9

+ 8 Mo

7266e 1.98 36.06 52.91 1.97

A-7783-19

+ 8 Mo + 8 Cr

7267e 1.33 37.17 99.96 1.39

A-7783-l9

+ 8 Mo + 9 Cr

72689:f 0.85 99.35 37.60 0.85

A-7783-19

+ 9 Mo + 8 Cr

7266e 3.19 63.1 17.9 3.62

A-7783-37

+ 8 Mo + 8 Cr

 

 

aThe intensity ratio is the average of approximately ten
measurements. The root mean square residual is m¢2%.

The precipitates were dispersed on a Be wafer to facilitate
the analysis.
bThese analyses were performed by a colorimetric method.
The uncertainty is %5% of the value.

80

Table 5.5. Continued.

0These analyses were performed by atomic absorption spec-
troscopy. The uncertainty is m:5%. The weight percent
ratio is based on atomic absorption results.

th % Mo= 7%
wt 5 Ti °

8The base composition is Ni + 2.5 at. % T1. The additions
of the Mo and Cr are in atomic percent of the uncarburized
alloy.

dBy error analysis

fThe chemical analysis of this precipitate was performed

at a later date than the others in this table.

81

Table 5.6. Analysis of Precipitates by Pashen-Runge Emis—
sion Spectroscopy and Energy Dispersive X-ray
Analysis.

 

 

Microprobea Titaniumb Molybdenumb wt % Moc

 

IMO/1T1 (wt %) (wt %) Wt % Ti
7262
A-7603-97 1.50 30 50 1.66
+ 8 Mo
7266
A-7603-97 2.88 72 25 3.00
+ 8 Mo + 8 Cr
7095

A-7603-106 1.79 32 ' 67 2.09
+ 1.2 Ti + 8 Mo .

 

aThe intensity ratio is the average of approximately ten
measurements. The root mean square residual is approxi-
mately 2%. The precipitates were dispersed on a Be wafer
to facilitate the analysis.

bThe root mean square residual is approximately 10%.

0
wt % Mo _ 19%.

CBy error analysis _WE_%_T1 -

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The root mean square residual is 2%.

Initially it was hoped that a calibration curve could
be prepared by intimately mixing pure materials such as
titanium and molybdenum powders or titanium and molybdenum
oxides. Figure 5.9 shows the result of mixing molybdenum
oxide (M003) and titanium oxide (T102). A straight line
relationship was obtained between intensity ratio (I(Mo)/
I(Ti)) and weight percent ratio (wt T Mo/wt % Ti) however
when this result was applied to carbides of a known composi-
tion the calibration curve disagreed with the atomic ab-

sorption results by a factor of two.

F. X-ray Diffraction

 

Precipitates were examined by x-ray diffraction as
follows: The precipitates were first dispersed in methanol.
The suspension was then dropped onto a glass slide and the
methanol allowed to evaporate. The dried precipitate was
scrapped off the slide and placed on a silicon single,
crystal wafer. The wafer acts as a substrate in the dif-
fractometer and is oriented so that silicon diffraction
peaks were not detected. A small amount of TaC powder,
a0 = 0.995587 1 0.000020 nm, was then sprinkled on the
wafer as an internal standard. Finally, a drop of poly-

vinyl alcohol was used as a binder. A diffracted beam

graphite monochromator rejected all wavelengths except

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those corresponding to the copper Kc lines. The scan
speed was usually 0.25°/min. A typical experiment ran

from 20 to 80° 20.

CHAPTER VI
THE NICKEL-CARBON SYSTEM

A. Results of the Carburization Experiments

Appendix A contains a precis of all carburization ex-
periments. Table 6.1 contains a summary of the results
of these experiments for the nickel-carbon system. In
each experiment several specimens were carburized along
with an iron standard. Carbon activities relative to
graphite, were calculated from Eq. (3.6). The data set
numbers in Appendix A and in Table 6.1 refer to the Oak
Ridge National Laboratory notebook page numbers where
the experiments were recorded.

The activity coefficients in Table 6.1 were obtained
by dividing the activities by the respective atom frac—
tions. As Figure 6.1 shows, the activity coefficients
scatter uniformly about a constant value at each of the
three experimental temperatures. Calculated slopes were
of the same magnitude or smaller than the uncertainties.
Thus, the activity is proportional to the atom fraction
for these experiments - Henry's Law is obeyed. Solute-
solute interactions are therefore negligible or of the same
magnitude as solvent-solute interactions for the concentra-

tions studied.

88

89

 

 

 

Table 6.1. Experimental Results for Carburization of
Nickel.
(a) Temp. Carbon A
Date Set Ac (°C) (at. %) Y
A-7603-106 0.291 1215 0.729 39.9
A-7603-106b 0.291 1215 0.719 90.8
A-7783-37 0.295 1215 0.739 39.9
A-7783-38 0.198 1215 0.938 95.2
A-7783—116 0.138 1215 0.332 91.6
9—7783-120 0.288 1215 0.676 92.6
9-7783—123b 0.270 1215 0.618 93.7
A—7783-9 0.113 1100 0.177 63.8
A-7783-l9 0 129 1100 0.186 69.9
A-7783—15 0.295 1100 0.998 65.0
A-7783-17 0.709 1100 1.05 67.5
9-7783-18 0.596 1100 0.869 62.8
9-7783-19 0.212 1100 0.359 59.8
9—7783-35 0.922 1100 0.661 63.8
A-7783-32L 0.520 1100 0.816 63.7
A-7783-32Hb 0.520 1100 0.816 63.7
A-7783-33 0.967 1100 0.739 63.2
9.7783-125b 0.197 1100 0.303 65.0
A-7783-99 0.601 900 0.999 139
A—7783-95 0.356 900 0.257 139
A-7783-95b 0.356 900 0.259 190
A-7783-97 0.278 900 0.201 138
A-7783-98 0.256 900 0.200 128
A-7783-99 0.110 900 0.0782 191
A-7783-57 0.187 900 0.191 133
A-7783-136b 0.291 900 0.211 138

 

 

90

Table 6.1. Continued

aActivity of carbon relative to graphite, calculated from
Eq. (3.6). The concentration of carbon in iron for each
data set is given in Appendix A. NBS SRM 19E is the
analytical basis for the above data.

quuilibrium reached by decarburization.

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By Equation (2.19), the constant activity coefficient

7c is the reciprocal of the solubility (X the atom

c)sat’
fraction of carbon in a saturated solution in equilibrium
with graphite. The linear least-squares fit of loglo

70 as a function of reciprocal absolute temperature T

thus also yields an equation for the solubility as a func-
tion of T-l, gig. .

-log10 70 = log(Xc)Sat = a + bT‘l.

a = 0.260, 0

a 0.087, b = -2816 x, ob = 170 K (6.1)
This equation reproduces our log10 90 results with a root-
mean-square residual of o = 0.0081.

Thermodynamic excess functions can also be determined

from the activity coefficients since

E
c

E

E .—
TASc

AG = RT 2n Yc = AHC — (6.2)
Figure 6.2 is a plot of 2n9c versus l/T for our results

as well as for the results of other investigators. From
Eq. (6.1), the least squares line through our data, one
can calculate with the aid of Equation (6.2)

E

ARC = 59 kJmol-l, OH = 3.3 kJmol“1

l

ASE = 5.0 Jmol-1 K as 2.9 Jmol- K (6.3)

99

Figure 6.2. in 90 versus l/T for carbon in nickel. The
results of Smith (1960) and of Wada, pp a1.
(1971) are the corrected results (see text).

In 7c [N Ni

95

ORNL-DWG Tr4u46
TEMPERATURE (°C)

 

 

 

 

i215 1100 900
5.5
T l T A
5.0 -- —
0
I
A
4.5 -— 04 ——
I
A
O
4.0 — . —
A 0 THIS WORK
’4 0 SMITH
A WADA er al.
A DUNN
I SCHENCK
3.5 — ‘
3.0 I I l I
5 6 7 8 9

96

B. Comparison with Previous Work

Figure 6.3 shows the activity coefficient results re-
ported by Smith (1960) and by Wada gp_§1. (1971) and the

value of 9 calculated from Eq. (6.1) for 1000°C. It would

c
appear from their results that Henry's Law is not obeyed
for Ni - C system, contrary to our results. The results
of Schenck gp’al. (1965) agree with ours, namely: that the
activity coefficient of carbon is independent of composi-
tion. ioreover, Henry's Law is valid for dilute solutions
of carbon in iron, as shown in Figure 6.9, and one might
expect similar behavior in nickel.

Some of the reported results of both Smith (1960)
and of Wada, g; 31. (1971) were incorrectly calculated
by the authors. The latter authors used an equation of
Ban-Ya _p _1. (1970) which included the incorrect equi-
librium constant discussed in Chapter III. Their results
for carburization in the presence of an iron standard
are shown in Table 6.2 along with results corrected by
use of Equation (3.6). Table 6.3 lists the results of
Wada pt 31. (1971) for carburization in the presence of
graphite itself. The corrected results are displayed

in Figure 6.5. The least squares line for the corrected

results of Wada gp‘al. (1971) at 1000°C is

Y0 = 78.6 + 1270 XC (6.9)

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Figure 6.9.

99

Carbon activities in iron, at 1000°C, cal-
culated from data of Smith (1960) and of
Banya 23 a1. (1971) and Equation (3.6).
The dashed line corresponds to Henry's
Law. Note that the departure from Henry's
Law does not occur until approximately 2
atom percent carbon is in solution.

ACTIVITY OF CARBON

ac

0.75

0.50

0.2 5

100

ORNL-DWG 7 7—1114 5

 

 

 

 

I I I T—UA I
1000°C, K=135.9
BAN-YA er a/. (1970)
SMITH (1946) O
A
o
A
/
/
o /
A
/
/
A /
/
/
A /
/
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/
o
I 1 I J
2 4 6 8

at. 7° CARBON

101

Table 6.2. The results of Wada 33 a1. (1971) for the
Activity Coefficient of Carbon in Nickel.

 

 

 

Uncorrected Correcteda
Temp. At % C, At % C, A A
°C in Fe in Ni AC Yc Ac Yc
800 3.96 0.963 1.03 222 1,092 225
2.60b 0.259 0.583 230 0.596 235
1000 5.93 0.777 0.693 89.2 0.733 99.3
3.09 0.919 0.307 79.2 0.333 80.9
3.09 0.929 0.307 72.9 0.333 78.5
2.91 0.919 0.291 70.3 0.315 76.1
2.01b 0.210 0.185 88.1 0.201 95.7
1.93 0.178 0.129 69.7 0.136 76.9
1200 5.99 0.97 0.999 95.8 0.960 97.9
3.57 0.608 0.215 35.9 0.223 37.6
1.11 0.122 0.0592 99.9 0.0589 98.3

 

 

aActivities recalculated using Equation 3.6 which corrects
for the CO/CO2 equilibrium constant.

quuilibrated starting from higher carbon content.

102

Table 6.3. Results of Wada gp.a1. (1971) for the Solubility
of Carbon in Equilibrium with Graphite (ac=l).

_l

 

Temp. At. 7 C

 

<°c) in/Ni, c
850 0.589b 171
1000a 1.07C 93.5

1.09° 91.7
1.02b 98.0'
1.02b 98.0
1.11b 90.1
1.11b 90.1
1.11b 90.1
1.07b 93.5
1197 1.87C 53.3
l.83° 59.6

 

 

aMeasured at 997°C and corrected to 1000°C.

bSpecimens were packed with graphite powder in an alumina
boat.

cCarburized by a controlled CHu-H2 mixture with a graphite
boat.

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The uncertainty in the slope (1270) is 0 = 670, and the
root-mean-square residual in Io calculated from Equation
(6.9) is = 6.2. For atom fractions greater than 0.001,
activity coefficients calculated from Equation (6.9) are
the same as the one calculated from Equation (6.1) within
the mutual experimental uncertainties.

Table 6.9 contains the results of Smith (1960) and the
values of the activity of carbon calculated using Equation
(3.6). Some of the values for the activity of carbon
listed in Table l of Smith (1960) cannot be calculated
from his Equation 1, even after Equation 1 is corrected
for the obvious typographical error. Equation 1 of Smith
(1960) should read, with N1 2 xi,

log Y2= 10g [(a2)(N1/N2)] = 3.37 (Nz/Nl), (6.5)

where the activity coefficient of carbon is relative to
the infinite dilution state of carbon in iron. The ac-
tivity coefficient 9c relative to graphite is calculated
from [see Equation (2.10)] ?c = Y/Ysat.5 likewise, the
corresponding activity Ac is calculated from Ac 2 a2/
a2,sat.‘

The "uncorrected" entries in Table 6.9 are calculated
from Smith's Table I, which itself contains two incorrect

entries: (1) for 6.61 carbon atomic percent in Fe, Smith

106

Table 6.9. Results of Smith (1960) for the Activity Co-
efficient of Carbon in Nickel at 1000°C.

 

 

 

 

Uncorrected Correcteda
At. % C At. % C, A A
in Fe in N1 Ac Yc Ac Yc
1.29 0.192 0.0979 68.9 0.116 81.7
2.75 0.331 0.250 75.5 0.293 88.5
9.99 0.632 0.979 75.8 0.557 88.1
6.19 0.970 0.816 89.1 0.897 92.5

 

aActivity calculated using Equations (3.6) and the raw
data of Smith (1960).

107

reports 0.191 for a2 whereas Equation (6.5) gives a2 =

0.123; (2) for 6.19 carbon atomic percent in Fe, Smith

reports 0.115 for a2 whereas Equation (6.5) gives a2
0.110.
The recalculated, corrected results of Smith (1960)

were fit by least squares to
Yc = 82.0 + 1100 Xc‘

The standard deviation of the slope 1100 is 210.. The
root mean square residual of Ic is o = 1.9. All of Smith's
recalculated results, except one point, lie within 10
of our interpolated results as shown in Figure 6.5.
Schenck, gt al., (1965) did not report their raw
data, and, although precise recalculatiOn of their results
was therefore impossible, they reported Henry's Law be-
havior up to the saturation limit of carbon. It is clear
from Table 6.5, however, that their results differ from
those reported here by about 15%.
After analysis of all available nickel-carbon data,
we conclude that Henry's Law is obeyed within the pre-
cision of the data. The present results and the report
of Schenck 33 a1, (1965) indicate the validity of Henry's
Law. IThe corrected results of Smith (1960) and Wada, pp
a1. (1971) show a slight dependence of activity coef-

‘ficient for any particular composition agrees within

108

Table 6.5. Comparison of Activity Coefficients,a Excess
Enthalpies, and Excess Entropies of Carbon

 

 

 

in Nickel.
Investigator

Temperature/°C Sgth?g e8u21.b e8a81.d Bradleye Smithf
7c, 900 119 102 138 136
9C, 1000 76.1 70.5 88.3 89.6 87.7
9c, 1100 53.9 51.9 65.0 69.3
90, 1215 38.3 37.7 96.3 92.0
AHE/kJomol-l 50.2 96 50.3 59
ASE/J-mol'l-K’l 3.9 0.97 1.9 5.0

 

 

aCalculated using iron standards and Equation (3.6).

bNo estimate of the error was stated by the author. The

graphite and the CH9/H2 carburization techniques were
used.

1 -1

C0Y=9.5%, 0H=l.0 kJ-mol'l, os=o.08 J-mol‘ °K The
graphite carburization technique was used.

0Y=9.2%, oH=3.5 kJ'mol'l, os=2.7 J°mol-1K'l. The graphite

and the CHu/H2 carburization techniques were used.

d

eoy=l.9, oH=3.3 kJ-mol’l, os=2.9 J mol'lx‘l, the CHu/HZ
carburization technique was used.

on=2.2%, the CO/002 carburization technique was used.

109

experimental error with the corrected results of Smith
(1960) and of Wada, et a1. (1971).

Table 6.5 is a comparison of the average value of Yo
obtained by five investigators. To obtain the value of

Y0 at non-experimental temperatures the average values of

70 were fit by least squares to Equation (6.1). Table 6.5

E

c and ASE calculated from

also contains the values of AH
these fits to the data.
Dunn and McLellan (1968) have the largest set of data

E and ASE

from which AHc c

have been calculated, and it is
apparent from the small size of the uncertainty in their
values for the excess functions that their data are
internally consistent. However, their activity results
are quite different from ours and from those of Wada,

g; a;. (1971) and Smith (1960). The differences are out-
side the experimental uncertainties of the various sets

of data. It appears likely, then, that Dunn and McLellan

(1968) have a systematic error in their data.

CHAPTER VII

CARBON PRECIPITATION IN NICKEL AND
NICKEL-TITANIUM ALLOYS

A. Discovery of the Carbon Phase

In the course of some of the aging experiments describ-
ed in Chapter V, electrolytic extraction of specimens of
alloy B(Ni + 1.7 wt % Ti + 0.09 wt % C) yielded a black
residue which we attributed initially to the presence of
titanium carbide in the specimens. This inference was
contrary to the Stover and Wulff (1959) nickel-titanium-
carbon phase diagram, which showed that the specimens
could contain neither titanium carbide nor graphite.

Thorough examination of the residue revealed: (1)

The residue had a lower density than that of titanium
carbide; (2) the residue lacked the characteristic metallic
appearance of titanium carbide; (3) x-ray experiments on
the residue gave diffraction patterns of much lower in-
tensity than patterns from similar quantities of titanium
carbide, and the lines were shifted to higher 28 values.
(9) Table 7.1 shows that the concentration of the residue
is not a function of temperature, whereas the solubility

of most carbides in metals increases rapidly as a function

of temperature. Clearly, the residue was not titanium

110

111

Table 7.1. Results of the Extraction of Alloy B (Ni+l.7
wt % Ti + 0.09 wt % C) Annealed at Tempera-
tures from 1260 to 760°C.

 

 

 

Bulka '
Sample Annealing Carbon Precipitate
Alloy Number Temp./°C Time/hrs. (wt %) (wt %)
B B-15 1260 16 0.08 0.19
B—15A 760 168 0.08 0.16
B A-7609 1100 16 0.09 0.12
A-7609 1260 9 0.09 0.11

 

 

8Specimens were analyzed after aging.

112

carbide.

Some remaining possibilities for the residue are:
(a) It is not present in the alloy specimen but is instead
a product of the extraction process; (b) it is free carbon
that has precipitated from solution during quenching; (c)
it is an amorphous phase produced by precipitation of alloy

impurities such as oxides and sulphides.

B. Chemical Analysis of Additional Residues

New alloys containing only small concentrations of
carbon were prepared. The carbon content was adjusted
to any desired level by annealing the specimens in CHu/H2
mixtures. The low carbon concentrations provided an easy
check of possibility (c) above and also provided homo-
geneous materials which could be examined by electron
microscopy.

The results of the electrolytic extraction of the gas-
carburized alloys are presented in Table 7.2 along with
the analyses of the extracted residue for carbon. Some
observations on and inferences from the table are: (1)

No measurable residue is collected from uncarburized nickel.
That is, no carbon means no residue, and possibility num-
ber (c) above is eliminated. (2) The residue is approxi-
‘mately 96 to 75 wt. % carbon. (3) Most of the carbon,
both in the nickel and in the nickel—titanium alloys, is

211.3

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wouooHHoo EH coEHoouw
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btoHuowpuxm coHpeNHssnsmo
HH 0H m m h w m a m N H

 

 

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COHuocLuxm 80 m uHfimmm

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119

recovered in the residue. The amount of carbon not ob-
tained as a residue from the electrolytic extraction of
the quenched alloys is 0.01710.019 wt % and there is no
statistically significant difference in the specimens with
and without titanium. (9) From column 11, the concentra-
tion of carbon remaining in solution after the quench is
slightly higher in the water quenched specimens. However,'
the difference is probably not significant because of ex-
perimental uncertainty and the small number of experi-
ments. (5) Chlorine analysis and metal analysis on both
of the A-7603-97 alloys gave a metal to chlorine atom
ratio of 3 to 5. The chlorine contamination is a result
of the extraction procedure. The precipitates were dif-
ficult to separate from the supernates due to their low
densities. There is little doubt that the chlorine is
present in the form of nickel and titanium chlorides, and
that if the chlorides were absent only carbon would re-
main. The non-reproducibility of chlorine is related to
the scatter in column 9. (6) X-ray experiments on the
residue yielded extremely weak, unidentified diffraction
patterns in the case of the residues from the nickel—
titanium alloys and no diffraction at all in the residue

extracted from samples of carburized nickel.

115

C. Electron Microscgpe Results

Examination of the quenched specimens in the electron
microscope did not clarify the nature of the residue. In
bright field the matrix of the specimens appeared to be
one phase (Figure 7.1). Selected area diffraction revealed
the presence of a second phase in both alloys (Figure 7.2).
However, the phase indexed as face centered cubic with a
lattice parameter aO N 0.92 nm, the same as nickel oxide.
Coatings of oxide have been recognized in other nickel-
based alloys (Kenik and Carpenter, 1977).' Stereoscopic
examination of the micrographs did not place the precipi-
tates conclusively. While it seemed clear that many were
on the surface, some particles appeared to one of the
three observers to be within the foil. Attempts
to adjust the sample preparation technique to avoid oxide
formation proved fruitless. The electron microscope work
indicates only that if a precipitate phase is responsible
for the residue, then the precipitates are smaller than
the 2.5 nm diameter particles shown in Figure 7.2.

Small angle x-ray scattering experiments undertaken
to determine whether precipitates exist in the alloy
matrix also failed to yield conclusive results, for the
same reason yi§., scattering of the nickel oxide layer on

the surface of the specimens.

116

Figure 7.1 (a) Optical micrograph of nickel-0.139 wt %
C specimen quenched in water after 38

hours at 1215°C.

(b) Bright field electron micrograph of
nickel-0.139 wt % C specimen quenched
in water after 38 hours at 1215°C.

117

 

20 40 60 MICRONS I O 140
500x
0.001 INCHES 0.005

 

Figure 7.2

(a)

(b)

118

Selected area diffraction pattern of a
Ni + 0.139 wt % C specimen quenched in
water after 38 hours at 1215%.

Dark field electron micrograph from the
area marked by the circle in (a). The
average precipitate diameter is approxi-
mately 2.5 nm.

119

 

120

D. Discussion

We have shown that a carbon residue is electrolytically
extracted from quenched specimens of nickel and nickel-
titanium initially at 900 to 1200°C. The cooling rates
used have no measurable effect on the amount of carbon
precipitated, and all but 0.017 wt % is in the residue.
There remain two possible explanations for the behavior
(1) the isolated carbon atoms in the matrix form the resi-
due during the electrolytic extraction process, or (2) the
carbon is precipitating from solution during the quench.
Hydrolysis experiments, discussed in the next paragraph,
show that the extracted residue is carbon that precipitates

during the quench.

l. Hydrolysis of Dissolved Carbon

Hydrolysis experiments on heavy metal carbides (not
alloys) by Bradley, Pattengill and Ferris (1965) and
Ferris and Bradley (1965) have shown that carbides hy-
drolyze to form methane and other alkanes in basic and
neutral aqueous solutions and to form carbon dioxide and
organic acids in acidic solutions. The authors state
that they have no experimental evidence to suggest that
graphite forms, during the hydrolysis, and moreover think
graphite formation unlikely because radicals such as HCO,

:CO and CH2 form instead of graphite.

121

The nickel-carbon solid solutions studied here are
essentially substoichiometric carbides with even less
carbon-carbon bonding than in the carbides discussed by
Ferris and Bradley (1965). If the carbon in our samples
were in solid solution, the hydrolysis experiments indicate
'that the individual carbon atoms would be oxidized to carbon
dioxide. On the other hand, if the carbon is present in
the alloy specimens as an elemental phase, then the extrac-
tion process would not affect it. Since the extraction
_ experiments resulted in the isolation of a carbon residue,
the carbon must not have been in solid solution; i.e., the

carbon precipitated during the quench.

2. Diffusion Mechanism for Precipitation of Carbon

In this section we show that the diffusion rate of
carbon is fast enough to account for the observed agglom-
eration during the time of cooling.8 Diffusion is a strong
function of temperature. Smith (1966) reported that the
diffusivity, D, of carbon in nickel varies with absolute
temperature, T, according to

D = 0.366 e-17’900/T cm2 sec-1 (7.1)

During diffusion carbon atoms migrate from solution at

t/0

a rate proportional to e- (deGroot, 1951), where the

122

relaxation time, 0, is given by
e = d2/n20, ' (7.2)

with d the distance over which diffusion occurs. Dif-
fusion is 99% complete when t Z 90.

In the precipitation experiments under discussion here,
the specimens were cooled at a rate of approximately 170
K sec"l (Beck and Bigot, 1965). The specimen temperature
thus decreases by one degree in about 6 milliseconds. When
90 is smaller than 6 msec, the diffusion process is fast
enough to be completed during the time interval required
for a one degree temperature decrease. When 90 is larger
than 6 msec, the diffusion process is too slow to be com-
pleted during the time interval, and precipitation begins
to cease. When the temperature falls low enough that 90
is very large compared to 6 msec, carbon atoms diffuso
so slowly that no further precipitation is observable.

Figure 7.3 is a plot of 90 versus absolute tempera-
ture on the assumption that the diffusion path length is
10 nm. This estimate is based on Figure 7.2 where any
carbon particle cannot be larger than the 2.5 nm par-
ticles observed. Assuming, then, that the precipitates
are 2.5 nm in diameter with a graphite crystal structure,
we may estimate the diffusion path length for the carbon

as follows: Graphite has a density of approximately

Figure 7.3.

123

Log 10 90 (the time required to achieve equilib-
rium) versus T/K (6 is the time required for
the temperature to drOp one degree, r is the
quench rate and (xc)Sat has been defined by
Equation (7.9). The intersection of the hori-
zontal lines with the log10 (90) versus T curve
is the temperature below which, with the quench
rate indicated, equilibrium cannot be maintain-
ed by diffusion, e.g., at r 167 K'sec'l dif-
fusion can keep the system at equilibrium down
to 535°C and at r = 16.7 K-sec'l down to 950°C.

129

ORNL DWG 77-18725

 

 

 

 

 

 

 

‘5
8=006msec /(X6)Sot'0.0053
(r-16.7OOK sec" )
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3: o 6 m sec (mm-0.0026
(781670 K sec")
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8860 m sec (r-16.7 Ksec") lIXCISat- 000062
-1 -
(XCISat -
B-GOOmsedr-IST Ksec") [0.00025
' I l \

 

 

800 600 - 400
TEMPERATURE/°C

125

2 ug/cm"3 or an atom density of 100 atoms nm'3. Nickel

has a density of 90 atoms nm’3. A 2.5 nm diameter sphere
has a volume of 8 nm3 and contains 800 atoms of carbon.
If the carbon concentration is 0.0073 atom fraction
(0.15 wt %), a volume containing 800 carbon atoms would
contain 1.1 x 105 nickel atoms. A sphere containing
1.1 x 105 nickel atoms has a radius of 6.6 nm. The
precipitates are taken to be at the center of spheres
20 nm in diameter. The diffusion path length is then 10
nm.

The horizontal lines in Figure 7.3 are the time inter-
vals required for the temperature to fall by one degree
at various cooling rates. If for some temperature he < 6
(6 is the time required for the temperature to drop one
degree), equilibrium is maintained and carbon precipitates
to the extent dictated by its solubility in nickel at
that temperature. When Me > 6, solubility equilibrium
cannot be attained by diffusion. Carbon continues to
precipitate, but slower and slower since the temperature
continues its rapid decline.

An independent estimate of the temperature below which
precipitation ceases is obtained from the experimental
result that the atom fraction of carbon remaining in solu-

-h

tion is 8.3 x 10 (0.017 wt %). The solubility of graphite

is given by Equation (6.1),

126

log10 (xc)sat = 0.260 - 2816/T - (7.3)

According to Spear and Leitnaker (1969), graphitic carbon
which forms at temperatures below about 2000 K has a Gibbs
free energy approximately 2.1 kJ mol'1 greater than true
graphite. To account for this fact we add 2lOO/R J-k'1

to the enthalpy in term in the solubility equation. Equa-
tion (7.3) thus modified reads:

loglo (x0)sat = 0.260 - 2563/T (7.u)

u

The temperature corresponding to x0 = 8.3 x 10- is 756 K.

At this temperature, he is 20 nsec and is rising rapidly.

1, would be re-

A slow quench rate, less than 50 deg sec-
quired for equilibrium to be maintained at this temperature.
Until the time when He exceeds 6, (i;e;, at temperatures
above about 800 K), diffusion is sufficiently rapid that

equilibrium is maintained.

3. Previous Results

 

Previously, Shriver and Wuttig (1972), Ulitchny and
Gibala (1973), and Stover and Wulff (1959) have used
optical metallography to infer that no precipitation
has occurred in their quenched specimens. Our results

indicate, however, that neither optical metallography at

127

1000x nor bright field TEM at 175,000x provides positive
evidence that precipitation has not taken place; neither
technique is always adequate.

Shriver and Wuttig (1972) have measured the magnetic
disaccommodation amplitude (the difference between the
magnetic permeability preceding and immediately following
demagnetization) of a Ni-0.3 wt % C Alloy. The magnetic
disaccommodation amplitude is, according to Shriver and
Wuttig (1972), proportional to the square of the amount
of carbon in solid solution. This implies that the ampli-
tude should continue to increase until all of the carbon
is in solution. Their Figure 2 shows no change after 550°C;
this indicates that the amount of carbon in solution was
not changed by anneals at temperatures above 550°C. Equa-
tion 6.1 indicates that 0.3 wt 1 carbon is not completely
soluble until approximately 1070°C. After annealing at
temperatures exceeding 550°C, the carbon in specimens of
Shriver and Wuttig (1972) must have precipitated on cool-
ing to approximately the equilibrium level at 550°C.
Although Wuttig (1977) admits that precipitation occurred
in his samples prior to the magnetic measurements he
assumes it occurred at the annealing temperature. Since
nickel carbide is not stable at the annealing temperature
(Hansen and Anderko, 1958) and since carbon has been showntx>
obey Henry's Law to the solubility limit in nickel, the

possibility of the formation of a precipitate which would

128

lower the solubility of carbon to that at 550°C seems
remote. If carbon were precipitating at the annealing
temperature, the alloys would not reach equilibrium with
graphite until all of the metal for the hypothetical
carbide had been used up or all of the graphite had been
transformed to the precipitate phase with the lower carbon
activity.

Ulitchny and Gibala (1973) measured the internal
friction of several iron-nickel-carbon austenitic alloys.
Internal friction peaks in austenitic alloys "have their
origin in the stress induced reorientation of inter-
stitial solutes which are paired (or clustered in larger
numbers) with other point defects", (Ultichny and Gibala,
1973). Large changes are observed in internal friction
peak heights as a function of quenching temperature and
quenching rate. If the carbon clusters responsible for
the peaks were the same as the residue we extract from
nickel alloys, quenching temperature and rate would not
affect the peak heights. Ultichny and Gibalas (1973)
specimens contained 2 atom percent carbon. From Smith's
results (1960) the solubility of carbon in iron-36 at %
nickel alloys at 1000°C is 1.75 at z and by extrapolation
is 1.15 at % at 900°C. Thus, all of the carbon was not
in solution at two out of three of Ulitchny and Gibala's
experimental temperatures. When the correction for the

amount of carbon in solution before the quench is made,

129

the peak height per atom percent carbon in solution be-
comes approximately independent of temperature, in agree-
ment with our results.

According to Ulitchny and Gibala the peak height is
decreased by a factor of approximately 5 on slowing the

1 to 0.017 K sec-1. Now, the

quench rate from 170 K sec-
peak height is proportional to the number of carbon clusters
and not to the number of carbon atoms in solution. By
optical microscopy Ultichny and Gibala observed graphite
precipitates in the slowly quenched specimens. Since the
size of the precipitates increases during the slow quench,
the number of precipitates decreases and the lower peak
height results. The results of Ulitchny and Gibala (1973)

are thus consistent with our both in terms of temperature

dependence and quench rate dependence.

E. Summary

The fact that a carbon residue can be electrolytically
extracted from nickel and nickel-titanium alloys contain-
ing carbon has been established. The most likely explana-
tion for the residue is that the carbon is precipitating
during the quench in a first step in the dissolution of
the super-saturated solution. This interpretation is
consistent with the results of Shriver and Wuttig (1972)

and of Ulitchny and Gibala (1973). The carbon "clusters"

130

that these sets of investigators discuss are very likely
the residue that we have extracted.

One consequence of the precipitation of free carbon
is that analysis of electrolytically extracted carbides
for carbon is considerably more difficult since carbon

is present in two different phases.

CHAPTER VIII
THE NICKEL-TITANIUM-CARBON SYSTEM

A. Results of the Carburization Experiments

The results of the carburization of two nickel-titanium
solid solutions are summarized in Tables 8.1 and 8.2 and
displayed in Figures 8.1, 8.2, and 8.3. The addition of
titanium to nickel increased the concentration of carbon,
relative to that in pure nickel, at all temperatures
studied (Table 8.1). At 1215°C, 2." atom percent titanium
increases the equilibrium carbon concentration by 3.0%,
at 1100°C by 9.0%, and at 900°C by 7.9%. Increasing the
titanium concentration by 50%, to 3.6 atom percent, ap-
proximately doubles the increase in the carbon concentra-
tion.

These results agree in magnitude and sign with the
only literature values, those of Golovanenko 93 al., (1973).
They reported the percent change in the concentration of
carbon relative to pure nickel at 800, 1000 and 1200°C
in an alloy containing 3.4 atom percent titanium and found,
according to a plot in their paper, that the carbon con-
centration was increased 18% at 1200 and 800°C and by 10%
at 1000°C. They did only one experiment at each tempera-

ture and used only one composition, so that uncertainty

131

1.322

Table 8.1 Experimental Results of the Carburization of Nickel-Titanium Solutions.

 

 

 

 

 

Composition
N1 N1 + 2.u at 1 T1 N1 + 3.6 at 1 Ti
Data Percent Percent
Set Temp./°C C, at 18 C, at ’a Increase C, at $3 Increase

A-7783-nu 900 0.uu9 0.u68 u.2 0.098 10.9
A-7783-u5 0.256 0.285 11.1 0.292 10.0
A-7783-h7 0.201 0.215 7.0 0.238 18.3
A-7783-136b 0.211 0.230 9.1

Avg-7.9(l.5)c Avg-lh.u(2.1)c
A-7783-u 1100 0.177 0.198 11.9
A-7783-17 1.05 1.10 8.6
A-7783-18 0.869 0.9111 8.3 1.03 18.5
A-7783-19 0.35“ 0.u08 15.2
A-7783-20 0.108 0.123 13.9
A-7783-35 0.661 0.825 2L.8
A-7783—32 0.816 0.909 16.3
A-7783—125b 0.303 0.32u 7.0 0.3u8 1u.8

Avg-9.0(1.0)c Avg-17.3(1.5)c
A—7603—97 1215 0.637 0.653 2.6
A-7603—118 0.161 0.16u 1.8 0.172 6.8
A-7603-12l 0.211 0.215 1.9 0.215 1.9
A-7603-123 0.178 1.85 1.0 2.07 16.2°
A-7783-ll6 0.332 0.350 5.u 0.366 10.3
A-7783-120 0.676 0.687 1.6 0.710 5.0
A-7783-123° 0.618 0.639 3.u 0.666 7.8.

Avg-3.0(O.S)° Avg-6.u(1.h)°

 

 

aConcentrations are relative to NBS SRM 195.

b

d

calculation of the average.

Equilibrium achieved by decarburization.
cParenthesized uncertainties are apI-Ia/lfi where a

I is the root mean square residual.

Precipitation of Tic may have oCcurred in this specimen. The result was not used in the

133

Table 8.2. Activity Coefficient3 of Carbon in Nickel—
Titanium-Carbon Solutions.

 

 

 

900°C 1100°C 1215°C
Composition
0 b c «a b xa c
(at %) Yo n CY Yc n oY Yc nb CY
N1 136 8 1.” 6U.3 11 0.8 “2.0 7 0.8
7261 128 u 1.5 61.0 5 1.5 M1.1 7 0.1
N1+2.u Ti
7068 120 3 1.5 5u.0 6 0.9 39.3 6 0.7
Ni+3.6 Ti

 

 

aActivity Coefficient calculated from carburization data
and Equation (3.6).

b
Number of measurements.

C0Y = 523 where c is the root mean square residual.
/n

Figure 8.1.

13“

Activity coefficient of carbon in nickel—
titanium alloys at 900°C.. Ni + 2.11 at. 7

Ti; ONi + 3.6 at. % Ti; top line from Figure

6.1. Note that experimental error is exaggerated
in that ye rather than 2n 7c, is plotted.

A
7c, CARBON ACTIVITY COEFFICIENT

135

ORNL-DWG 77-9401R

 

 

 

 

 

 

 

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I45 I_ 4 ._1
900°C
I35 Ni _
.
. Ni '7' 2.4 '70 TI
125 F- _.1
.
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n _ _ _ 1133713—
"5 -— O —
I L . L I
0 0.25 0.50 0.75 1.00

ac, CARBON ACTIVITY

136

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137

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138

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on

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11130133300 All/\llov NOSUVO‘

1M0

and composition dependence are unknown.

Figures 8.1, 8.2, and 8.3 show the scatter, approxi-
mately 3% at 900, 5% at 1100°C and 3% at 1215°C, and they
show further that the carbon activity coefficient can be
taken as independent of the carbon concentration over
the ranges investigated.

The decrease in the carbon activity coefficient (Table
8.2) upon the addition of titanium to nickel results in

an increased solubility of graphite in the solid solution

A-l

sat = Yc ). Above a certain level of titan-

(because (xc)
ium, precipitation of titanium carbide occurs in nickel-
titanium-carbon systems (Stover and Wulff, 1959). When
the activity of titanium is large enough, titanium carbide
can exist in equilibrium with both the nickel solution and
graphite. Addition of more titanium to the system at
this tricritical point at the same time decreases the value
of the carbon activity coefficient and decreases the
solubility of carbon in the solution.

Table 8.3 contains the values of ARE, ASE and the
parameters describing the temperature dependence of in ?c
in the nickel-titanium-carbon solutions studied. From the

results in Table 8.3 the composition dependence of in ?c

could be fit with an equation of the type

-<>
II

in in YC(N1) yc(Ti)

2n Yc(Ni) + 1n yc(Ti)

lhl

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where

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However, the composition range studied so far is too small

to warrant such a fit.

B. The Solution Thermodynamics of Titanium in Nickel-

Titanium—Carbon Solid Solutions

 

Stover and Wulff (1959) made a careful phase diagram
of the nickel-rich corner of the nickel-titanium-carbon
system. When their data are combined with titanium carbide
data from the JANAF Thermochemical Tables (1971) the ac-
tivity coefficient of titanium at the graphite, titanium
carbide, nickel solid solution tricritical point can be
calculated, as follows:

The equilibrium constant Kf for the formation reaction
Ti(s) + C (graphite) = TiC(s) is the same as the equilibrium

constant for

Ti(in N1) + C(graphite) = TiC(s).

Thus, for the three phase equilibrium here,

1H3
since
A (graphite) = 1 = ATiC'

(An additional point noted by Stover and Wulff (1959) and
confirmed in this study (see Chapter IX) is the minus-
cule solubility of nickel in titanium carbide. The low
solubility of nickel in the carbide Justifies the assump-
tion that the activity of titanium carbide can-be set to
unity.)

Table 8.“ contains the resulting activity coefficient
values. One notes immediately that the partial molar
excess free energy of titanium is large and negative.

To calculate the partial molar excess entropyaand enthalpy
a temperature dependent regular solution model is assumed.
The values of the regular solution parameter, A, in Table

8.3 allow the excess functions at XTi = 0 to be calculated.

1

2n 7T1 = -20.6 T- -2.5, = 0.001

0
£nyTi

E 1 K‘l, as = 0.8 J-mol‘

1 -1
Ti K

As = -21 J-mo1‘

E 1

T1

AH = -171 kJ'mol-l, 0H = 1.3 kJ-mol’

The assumptions in these calculations are that (l) nickel

and titanium behave like a regular solution over the range

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of 0-3.h atom percent titanium, that (2) the contribution
of carbon to the activity coefficient of titanium is
negligible and that (3) Afigi and A§gi are independent of
temperature. The fit of the equation appears to be very
good. The large negative A§gi would usually be taken to
indicate that a large amount of order exists in the system.
This is consistent with the fact that several ordered
phases (Ni3Ti, NiTi2 and NiTi2) exist in the nickel-
titanium binary system. The values of the titanium par-

tial molar excess Gibbs free energy are used in Chapter X

to obtain the value for the Kohler-Kaufman interaction

energy wNiTi'

CHAPTER IX

NICKEL—TITANIUM-MOLYBDENUM-CHROMIUM-

CARBON SYSTEMS

A. Results of the Carburization Experiments

Table 9.1 and Figures 9.1 and 9.2 contain the activity
coefficients of carbon calculated from experiments on
solid solutions containing nickel, titanium, molybdenum,
chromium, and carbon. Within experimental error, the
activity coefficient of carbon is independent of the carbon
concentration in all of the alloys. Thus, Henry's Law
is obeyed, as it is for the nickel-carbon and nickel-
titanium-carbon systems. Taken at face value some of the
data in Figures 9.1 and 9.2 could be fit with a line of
finite slope. However, in light of the indications in
Chapters 6 and 8 that Henry's Law is obeyed in Ni-C and
Ni-Ti-C alloys, more data are required before a linear
least-squares fit is Justifiable. As indicated in Table
9.1 too few successful carburization experiments were
performed in the solid solution region on these alloys at
900°C to warrant a plot.

The solid solution range in nickel-titanium—molybdenum—
carbon alloys is limited because of the ability of molyb-

denum carbide to form a solid solution with titanium carbide.

1&6

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152

The narrowness of the solid solution region increases the
difficulty of the carburization experiments. In particu-
lar, alloy 7266, which contains the largest concentra-
tions of both molybdenum and chromium has a single phase
region so narrow that quantitative data on the solution
phase were not obtained from carburization experiments.
Instead, annealing experiments discussed in Section 8.2
were performed in order to obtain data on this limited
region. Although alloys 7267, 7268 and 7262 also have
small carbon solubilities, it was possible to obtain quan-
titative carburization data on all three solutions at 1100
and 1215°C.

To determine effects of alloying additions on the
activity coefficient of carbon two procedures can be
followed: (1) compare the activity coefficients of carbon
as determined with the iron standard equation (3.6); or
(2) compare directly the difference in carbon concentration
of two alloys in equilibrium with the same gas composition.
The second method is necessary for some of this work be-
cause not all of the alloys were present in every run and
therefore the effect of the iron standard does not cancel
out. Such comparisons are shown in Table 9.2.

Compared to nickel + 2.H titanium, molybdenum decreases
the equilibrium concentration of carbon from 12% to 19%
at the H atom percent level and from 15% to 25% at the 8

atom percent level (Table 9.2). Percentage increases

153

 

 

 

 

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155

are larger at lower temperatures. No literature exists
on the effect of molybdenum on the equilibrium carbon
concentration in nickel solutions. The value for the
Kohler-Kaufman parameter (wMoC) estimated by Kaufman and
Nesor (1975) indicates that molybdenum should decrease the
equilibrium concentration of carbon in nickel solutions,
as found here. Wada £2.2l- (1972) indicate that molyb-
denum increases the equilibrium concentration of carbon
in iron solutions, opposite to the effect on nickel solu-
tions.

Compared to alloy 7261, chromium increases the
equilibrium concentration of carbon in nickel at 1100
and 1215°C but has no effect at 900°C (Table 9.2). The
decrease is from 3% to 6% at the u.6 % level and from 14%
to 15% at the 8.0 % level. Golovenenko gt a1. (1973)
measured the equilibrium concentration of carbon, relative
to nickel, in a solution containing “.0 at % chromium at
800, 1000 and 1200°C. They found that chromium decreased
the equilibrium concentration of carbon by 15% at 800°C,
6% at 1000°C and 3% at 1200°C. Neither the temperature
dependence nor the sign of the effect of chromium on the
equilibrium concentration agrees with our results.
Golovenenko gt a1. (1973) did not estimate the size of
their errors. Chipman and Brushy (1968) reviewed the data
on the effect of chromium in iron and indicate that 8 atom

percent chromium increases the equilibrium concentration

156

of carbon in nickel by about 7%. The reason for this
large difference is discussed in Chapter X.

In the more complex solutions containing both chromium
and molybdenum, the effect of additions on the equilibrium
concentration of carbon is more complicated. The addition
of 8 at.% chromium to a solution containing u at.% molyb-
denum (726M + 8 at.% Cr + 7268) increases the equilibrium
carbon concentration by as much as ”5% (Table 9.2). From
the previous discussion one would expect the carbon concen—
tration to be increased by W15%. Similarly the addition of
8 at.% molybdenum to a solution containing u atom percent
chromium (7265 + 8 at.% Mo + 7267) has little effect at
1100°C and increases the equilibrium concentration of carbon
by 6.8% at 1215°C. The results for the addition of 8 at.

% molybdenum to alloy 7261 suggest that the equilibrium
concentration should be decreased by from 15% to 20% upon
the addition of 8 at.% molybdenum. The relative change in
the equilibrium concentration of carbon depends on the
amount of both molybdenum and chromium added (Table 9.2).
In the case of chromium a much bigger relative change’
takes place upon the addition of 8 at. z than “.6 at. %.
The addition of u at. % molybdenum on the other hand has

larger relative effect than the addition of 8 at. %.

157

B. Carbide Precipitates

The solubility of carbon in equilibrium with the metal
carbide that forms in these alloys was determined in two
different ways. In one set of experiments alloys of
fixed composition were annealed at the desired temperature
and then quenched. The amount of carbon in solution was
determined from knowledge of the bulk carbon concentration,
the weight percent of precipitate in the alloy and the
concentration of carbon in the precipitated phase. This
method is particularly suited to alloys with low carbon
solubility. In the second method, the solubility of car-
bon was determined from the break in the concentration
versus activity curve obtained from gas phase carburiza-
tion experiments. The concentration above which the atom
percent carbon in the alloy is no longer directly propor-
tional to the activity of the carbon is the solubility
limit. This method is better suited for alloys of high

carbon solubility.

l. Carbide Composition

The precipitates extracted from the carburized alloys
were analyzed with an electron microprobe, by the method
described in Chapter V. Table 9.3 contains the results

of these analyses together with the lattice parameter

158

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159

of the precipitate phase as determined by powder x-ray
diffraction. The weight percent carbon in the precipitate
phase was calculated through a knowledge of the bulk
carbon concentrations, the weight percent precipitate,
the activity of carbon in the specimens and the activity
coefficient of carbon in the alloys. In this way the con-
centration of carbon in solution is calculated directly
and the concentration of carbon in the precipitate by
difference. The method for calculating the molybdenum
and titanium concentration is contained in Chapter V.
From Table 9.3 it appears that the Mo/Ti ratio in the
precipitate depends on the amount of molybdenum in the
matrix. It also appears that the ratio increases as the
weight percent precipitate in the alloys increases.

The Mo/Ti atom ratio in the cubic precipitates formed
in the allomscontaining u atom percent molybdenum (726“,
7268) is 0.H2 i 0.003. The value of 0.62 obtained for
alloy 726“ A7603-l23 (Table 9.3) is inexplicably high.
The lattice parameter of the 726“ A-7603-123 precipitate
is not different from those of the other two 726R specimens,
both of which have lower molybdenum concentrations.- Doubl-
ing the molybdenum concentration in the matrix, to 8 at.
z, increases the Mo/Ti atom ratio in the cubic precipitate
phase by almost 100% to 0.79i0.0l.

Nickel and chromium are minor elements in the

160

precipitate phase. Chromium is more soluble in the carbide
than nickel, but it is likewise depleted in the precip-
itate phase relative to the matrix.

Figure 9.3 shows the effect of changing the molyb—
denum concentration in the carbide on its lattice param-
eter. Over the range explored (Mo/Ti atom ratio 0.“ to
1.0), the lattice parameter is a linear function of the
MozTi ratio in the precipitate. The addition of molyb—
denum decreases the lattice parameter of the carbide.

Alloys 7268 and 7267 differ from alloys 7268 and 7262,
respectively, only in that they contain 8 at. % more chrom—
ium in the matrix. The addition of the 8 at. % chromium
to the matrix lowers the precipitate lattice parameter
by approximately 0.0005 nm. The effect of chromium on a
per atom percent basis is larger than that of molybdenum,
presumably because of chromium's smaller atomic radius
(Slater, 196“).

As shown in Table 9.3 the carbon-to-metal atom ratio
in the precipitate was almost always less than 1. The
average value is 0.85, o=0.ll, and o//fi=0.03. The Ti-Mo
carbide might be viewed as a solid solution between nearly
stoichiometric TiC and Mo3C2. Molybdenum increases the
lattice parameter of nickel at a faster rate than does
titanium, yet molybdenum is observed to decrease the

lattice parameter of TiC. Since the lattice parameter

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of Mo is 0.U28 nm and that of TiC is 0.N33 nm, a ready

302
explanation is provided by a TiC-M02C3 solid solution for
both the lowering of the carbon lattice parameter by

molybdenum and the substoichiometry.

2. Annealing Experiments

Table 9.“ and Figure 9.h contain the results of the
annealing experiments. Since the weight percent precipi-
tate extracted from alloy B (Ni + 2.1 at. % Ti) did not
change as a function of temperature, we infer, with the
help of the evidence of Chapter VII, that the extracted
material precipitated on cooling. This means that at
least 0.08 wt % carbon is soluble, in alloy B, at all the
temperatures investigated.

Alloy C (N1 + 2.” at. % Ti + 8.2 at. % Cr + 0.5 at.

% C) behaves like alloy B at high temperatures. The

weight percent precipitate extracted from alloy C annealed
at 1100°C is equal to that from specimens annealed at
1260°C. At 760°C, however, the weight percent precipi-

tate increases by a factor of two. The solubility of carbon
in alloy C at 760°C was calculated on the assumption that
the precipitate was stoichiometric TiC and that 0.07 wt

% of the precipitate formed during cooling (see Chapter
VII). The value of 0.0fl5 wt. 1 for the carbon solubility

at 760°C should be considered a minimum estimate since

1614

 

 

 

 

 

.lifv ¢.-. Fesults .f the Annetlinr Fxrerirents.
' wt. Sc
wt. 5‘ wt. Sb Carbon
Carbon in Precipitate in Solid
421‘“ Ste‘ireu Annealing Annealed in Annealed Solution
3‘. ' hunter Ristcrv Tcmp./°C Time/hr specimen specimen Solubility
a
x1+2.‘ *1
BIS As received 1260 16 0.08 0.1111d 0.08
815A 1: hr 3' :fr1 760 168 0.08 0.157d 0.08
N1+2.n Ti C-6 As recuizvd 1200 16 0.103 0.119d 0.1
+8.: Cr c-7 As 00:01:»1 1200 16 0.098 0.117d 0.1
C-6-A :6 hr a' 1210 760 168 0.108 0.359 o.ou5°
A 321 As received 1260 . a 0.083 0.037 0.078!
Ni+2.6 Ti A-B As received 1260 16 0.102 0.093 0.090
+8.“ Ho A-lO As received 1260 16 0.092 0.037 0.087
BAIH As received 1200 1 0.102 0.10“ 0.088
BAZH As received 1200 2 0.102 0.095 0.090
A-7783-1u7 u hrs at 116C 1100 18 0.083 0.328 o.ouo
A-7753-5 ' As received 1000 72 0.078 0.h21 0.023
A-7783-5 As received 900 118 0.083 0.533 0.013
A—7783-5 As received 800 500 0.08h 0.626 0.002
A-B-A 16 hr at 1‘60 760 100 0.096 0.732 -----
“99 1177 2 0.035 0.050 0.028
N1+2.5 71 A-7783-1u7 “ hrs at 11(0 1100 18 0.0265 0.070 0.017
07.2 no A-7783-5 ‘8 received 1000 72 0.0275 0.126 0.011
+ 8.8 Cr A-7783—5 A: rcceived 900 111 0.0303 0.223 0.001
A-7783-5 As received 800 500 0.0306 0.233 -----
760 100 0.035 ‘ 0.28 -----
a

a - 3! where a is the root mean square residual.

be - 0.015 wt. S where o is the root mean square residual.

cThe solubility of carbon in alloys hi9 and A was calculated on the assumption that the weitht percent carbon
in the precipitate was 131. This was based on the assurption that all of the carbon in the stnctrurs 35x98}-
ed at 760 had precipitated. Solubility - bulk carton concentratirn - (wt. 7 prt) x 0.11. The rvsul's frr
the weight percent carbon in the precipitate found in Table 9.? indicate a value of «10' fer o.

6This precipitate was free carbon as described in Charter VII.

eThe solubility of carbon in alloy C was calculated on the assumption that the precipitate wn: 3‘0
0

ichismetric
TiC and that 0.0? wt. % precipitate resulted from the precipitation of free carbon (see Chapter .II).

1.The solubility for this specimen antears low. It may be that the precipitate was free carbcn.

165

Figure 9.“. (a) The concentration of carbon in alloy A
(Ni + 2.6 at. % Ti + 8.“ at. % M0) in equi-
librium with the cubic carbide phase as a
function of temperature 0 = 10% of the bulk
carbon concentration.

(b) The concentration of carbon in alloy

““9 (Ni + 2.0 at. % Ti + 8.3 at. % Mo + 8.“ at.
% Cr) in equilibrium with the cubic carbide
phase as a function of temperature. a = 10%
of the bulk carbon concentration.

I00 [C '13-]

166

TPC)

out-0's 774m

 

INF-1'9]

Ml
“(caucus-#9

 

 

 

 

 

 

 

 

 

-u ._ _
JL
1 l
7 I .0
WT!!!
cam-owe 77-13518
rm
4 0 8200 9000 300
' l T I
-2.0 — .—
-3.0 —- —
ALLOY 449
he peuq- 4.32 - 1:99
l J I I
-Q.0 7 8 9

90.00%“)

10

167

TiC is often substoichiometric in carbon.

Alloy A (N1 + 2.6 at. % Ti + 8.“ at. % Mo + 0.5 at. %
C) has considerably smaller carbon solubility than either
B or C. Figure 9.“a is a plot of the logarithm of the
carbon solubility versus the reciprocal of absolute tem-
perature. The solubility was determined on the assump—
tion that the solubility of carbon at 760°C is zero and
that the weight percent carbon in the precipitate is not
a function of temperature. The addition of molybdenum
lowers the solubility of carbon from something over 0.08
weight percent at 760°C in alloy B to something less than
0.001 weight percent in alloy A. Molybdenum lowers the
carbon solubility relative to the carbide by three dif-
ferent processes: (1) molybdenum dilutes the nickel-
titanium solution and thus increases the titanium activity;
(2) molybdenum forms a solid solution with TiC (see IX
B.l) and the activity of the carbide is thus lowered; (3)
the molybdenum-carbon interaction is weak relative to
the nickel-carbon and titanium-carbon interactions, and
the addition of molybdenum to the solution increases the
carbon activity coefficient. All three of these effects

tend to displace the reaction
Ti(Ni) + C(Ni) 2 TiC(solid)

to the right.

168

Alloy ““9 (Ni + 2.0 at. % Ti + 8.3 at. % Mo + 8.“ at. %
Cr + 0.18 at. % C) results from the replacement of 8.“
at. % nickel with 8.“ at. % chromium in alloy A. Alloy
““9 and 7266 are essentially the same. Table 9.“ and
Figure 9.“b show that the addition of the 8.“ at. % chrom-
ium lowers the solubility of carbon relative to that in
alloy A by a factor of approximately 3 at 1215°C. The
decreased solubility of carbon in alloy ““9 is due pri-
marily to diluting the nickel-titanium interaction which
results in a higher titanium activity. That is, the Gibbs
free energy of mixing for titanium and chromium is much
less negative than for titanium and nickel. The chromium
does not form an appreciable solid solution with the car-
bide phase, and therefore the addition of chromium does

not alter the activity of the carbides.

3. Carburization Experiments

Table 9.5 and Figures 9.5, 9.6 and 9.7 contain the
result of the gas carburization experiments undertaken to
determine the solubility of carbon in various nickel alloys.
Since it has been shown in Chapters VI, VII and IX that the
carbon in solid solution in these alloys obeys Henry's Law,
any negative deviation from Henry's Law can be considered
evidence that carbide precipitation has taken place. The

solubility limit is the concentration at which the

169

 

 

 

 

 

Table 9.5. Solubility of Carbon in Several Nickel-Based
Alloys as Determined from Carburization Ex-
periments.

Temp. 900 1100 1215

(°c)

Alloy

gngi A:(sat) C(sat) A:(sat) C(sat) A:(sat) C(sat)

wt.% wt.% wt.%
7262 0.17 0.019 0.18 0.0“6 0.18 0.073
726“ 0.36 0.0“5 0.38 0.10 0.32 0.1“
7266b 0.0“6 0.016 0.067 0.037
7267 0.10 0.032 0.095 0.050
7268 0.11 0.0“3 0.13 0.079

7262 Ni + 2.5 Ti + 8.2 M0

726“ N1 + 2.“ Ti + “.2 Mo

7266 Ni + 2.“ Ti + 8.1 Mo + 8.3 Cr

7267 Ni + 2.5 Ti + 8.2 Mo i.“-" Cr

7268 Ni + 2.5 Ti 1 0.1 Mo + 8.“ Cr

aThe solubility was determined from the following eguation
= A . Activit coefficient 0 car on was
AC(sat) Ye xC(sat) Y

obtained from Tables 8.2 and 9.1.

bThe activity coefficient of carbon in alloy 7266 was not

experimentally determined therefore an approximate value
had to be used. The activity coefficient of carbon in
alloy 7266 was taken to be the average of those for alloys
7267 and 7268. This seems to be appropriate since alloy

7267 and “ at. % more Mo than 7268 and Mo and Cr have
opposite effects.

Figure 9.5.

170

Atom Z carbon versus activity of carbon in
several nickel-based alloys at 1215°C. The
intersection of the two lines, with the same
label, is the solubility limit of carbon
relative to the carbide phase. The lower
line represents the solid solution where

the slope is 100/9c (xC = AC/90). The dashed
lines are an extrapolation of the solid solu-
tion lines and represent the amount of carbon
in solution at any given activity. The

upper lines have been fit by least squares

to the data from the two phase region,

points that diverged from the straight

line behavior exhibited near the inter-
section were ignored.

ATOM PERCENT CARBON

171

ORNL-DWG 77-9398

 

 

 

l | l l l l

A

o 1215°C ,

7262 Ni-2.S Ti-8.2 Me (at. I)
726'! 111-2.0 71-0.2 lo (It. 5)
7266 Ni-2.“ Ti-8.1 Ho-8.3 Cr (at. S)
7267 211-25 T1-0.2 140-0.“ Cr (at. S)

C) 7268 Ni—2.5 Ti-“.1 Ho-G.“ Cr (at. I)
7267
7266 e 7268
7264 .

 

l l l

0.2 0.4 0.6 0.8
ac, ACTIVITY OF CARBON

Figure 9.6.

172

Atom % carbon versus activity of carbon in.
several nickel-based alloys at 1100°C. The
intersection of the two lines, with the same
label, is the solubility limit of carbon rela-
tive to the carbide phase. The lower line
represents the solid solution where the slope
is 100%?C (xC = Ac/yc). The dashed lines are
extrapolations of the solid solution lines and
represent the amount of carbon in solid solu-
tion at activities exceeding the solubility
limit. The upper lines were fit by least
squares to the data from the two phase

region.

ATOM PERCENT CARBON
u

N

173

ORNL-DWG 77-9396

l I l l I r T

 

7266
7267

7262

 

 

 

 

— —(
F 1100°C “
7262-Ni-2.5Ti-8.2M0
7267 - Ni - 2.5Ti - 4.4Cr - 8.2 M0
7268 - Ni - 2.5Ti - 6.4Cr -4.4 M0
7266-Ni-2.4Ti- 8.3Cr-8JMO
_l
/ 7268
/7257
’ 7262
I
I
O 0.4 0.6

ac, ACTIVITY OF CARBON

Figure 9.7.

1?“

Atom % carbon versus activity of carbon in
several nickel-based alloys at 900°C. The
intersection of the two lines, with the same
label, is the solubility limit of carbon rela—
tive to the carbide phase. The lower line
represents the solid solution where the slope
is 100/?c (xc = Ac/90). The dashed lines are
extrapolations of the solid solution lines and
represent the amount of carbon in solid solu-
tion at activities exceeding the solubility
limit. The upper lines were fit by least
squares to the data from the two phase

region.

ATOM PERCENT CARBON

4.25

0.75

0.50

0.25

175

ORNL-OWG 77-9397

 

. I l l l

 

 

7267 7264

7268

7262

 

Ali-270

I, 7264
/
/ I, 7262
A / / /
/’ / —
I/ / o
’ 900 C

7262-Ni- 2.5Ti-8.2 M0
7264- Ni- 2.4Ti- 4.2Mo
7268- Ni- 2.5Ti-8.4 Cr - 4.1Mo
7267-Ni- 2.5Ti- 4.4Cr - 8.2 MO

I I l |

0.4 0.6
ac, ACTIVITY OF CARBON

 

176

concentration versus activity line for carbon in the
alloy has a change in slope. In Figures 9.5, 9.6 and 9.7
the solubility limit has been determined by fitting the
solid solution carburization data and the carburization
data from the two phase region with least squares lines
and calculating their intersection.

The solubility of carbon in molybdenum-free alloys
was not determined by this technique because either the
carbide phase does not exist in the alloys at the tempera-
tures and activities investigated or only one data point
in the two phase region existed. The solubility limit
of carbon in alloys 7266, 7267 and 7268 was not determined
at 900°C because a diffusion barrier, possibly a layer of
chromium oxide, slowed the rate of carburization so much
that carburization experiments were impractical.

As Table 9.5 indicates, doubling the molybdenum con-
centration reduces the carbon solubility by a factor of 2.
The result of adding chromium to the carbide forming alloys
has a similar effect. Both the decrease in solubility of
carbon upon addition of chromium and the values of the
solubilities agree with results obtained for similar alloys
in the annealing experiments discussed in the previous
subsection.

The effects of additions of chromium and molybdenum

on the solubility of carbon relative to the carbide phase

177

in the alloys already forming a carbide phase thus follow
a regular pattern: doubling the molybdenum or chromium
concentration decreases the carbon solubility by a factor

of about two.

0. An Unidentified Phase of High Carbon Content

In alloys 7266 and 7267 some specimens contained an
unidentified carbide phase (see Table 9.3). The Mo/Ti
atom ratio is approximately 1.6 and the carbon to metal
ratio in the two phase precipitate is approximately 0.8.
Microprobe examination of precipitates, in the matrix (see
Figure 9.8) revealed that the precipitates with the needle
like morphology had the same Composition as the more
rounded precipitates. The new phase does not correspond
to any of the low carbon carbide such as M2C, M6C or M12C.

Attempts to index the x-ray diffraction characteristic
of the phase have failed as have attempts to identify it
with the ASTM x-ray card file. Tables 9.6 and 9.7 contain
the 26 values and relative intensities of the diffraction
peaks in the spectrums for 7266 specimens A-7603-97 and
A-7783-37. Figure 9.8 is an optical micrograph of the
precipitates in alloy specimen 7266 A—7603-97: the needle-

like morphology is not characteristic of TiC precipitates.

Table 9.6.

178

X-ray Diffraction Data on the Unidentified
Phase Alloy 7266 A-7783-973.

 

 

 

26 I
27.29 11
36.70 1100
“1.“8 85
““.30 25
“6.35 20
51.11 130
5“.82 80
58.95 30
61.37 30
63.17 “8
67.67 15
72.“3 5“
78.07 100

 

 

aCopper K0 radiation was used.

speed was 1/“° 26 per min.

The spectrometer travel

179.

Table 9.7. X-ray Diffraction Data on the Unidentified
Phase in Alloy 7266-A-7783-37.a

 

 

 

20 I 20 I
27.30 7 63.28 18
33.02 2 67.7“ “
35.56 7 72.“5 22
36.70 870 72.65 1“
37.0“ 73.73 6
39.00 “ 76.8“ “
“1.53 21 77.10 3
““.“l 6 78.11 100
“6.37 9 78.33
51.12 2 88.20 2
51.29 1 88.35 2
59.00 9 88.“3 1
61.“5 6 90.38 2

 

 

aCopper K radiation was used. The spectrometer travel
speed 1/fi° 26 per min.

t

 

180

Figure 9.8. Specimen number 7266 A-7603-97 equilibrated
at 1215°C at A0 = 0.268. Note the needle
like precipitates which are characteristic
of the unidentified phase. The other pre—
cipitates are the MC phase.

If

20

0.001

40
I

181

60 MICRONS
4— 500 ——lr
INCHES

 

120I HO
0.005

CHAPTER X
THE KOHLER-KAUFMAN EQUATION

A. Calculation of the Nickel-Carbon and the Iron-Carbon

Interaction Energies

Table 10.1 contains the values of the “ interaction
energies that describe the nickel-carbon and the iron-car-
bon systems. The relative lattice stabilities are listed
in Table 10.2. The equations used to calculate the inter-

action are from Equation (2.30). For each temperature

CE _ _—FCC- -gr+

2
xN1(1'2xc) wNiC

2xCx Ni wCNi

GE _'—FCC- -gr

2

2
2xCxFe wCFe' (10.1)

To obtain wNiC and erC’ Equations (10.1) are solved at

xC = 0, where

A°° *FCC-
RT 2n YC(N1) - G gr

“N10

—FCC-gr

182

183

Table 10.1. Calculated Values of Nickel-Carbon and Iron-

 

 

 

 

 

Carbon Interaction Energies, wigc.a
-l -1 -l -l -2, -3
A13 kJmol Bid/Jmol K Cij/Jmol K 10 (113

b
wNiC -135.52 87.31 -29.29

b
WCNi ‘163o7 l“.0 C

d
erC - 96.15 -0.88 0.0

d
wCFe -156.1 0.0 0.0
aw = A + B T + C T2.

13 id 13 1J

b 1

°“=O'3 kJmol' , calculated assuming a 3% error in ?C(Ni).

CAssumed zero.

d 1

°“=O'2 kJmol' , calculated assuming a 2.5% error in ?C(Fe).

18“

Table 10.2. Some Relative Lattice Stabilitiesa for Elements
of Interest.

 

 

c 0
Element Transformationb 'H'E-a/kJ-molul 'E'Iji-a/J-molDJ'K-1

 

C Graphitic FCC 138 15
T1 BCC FCC -l.0 3.8
Cr BCC FCC 10.5 0.63
Fe FCC FCC 0 0
Ni FCC FCC 0 0
Mo BCC FCC 10.5 0.63

 

 

aFrom Kaufman and Nesor (1973, 1975), Uncertainties not
stated.

bFCC=Face Centered Cubic, BCC=Body Centered Cubic.

c—b-a _ b —a b-a _ —b —a ' —b-a _ -b-a —b-a
Hi - (21 - Hi), 6: - (s1 - Si) and G1 - Hi - Tsi .

185

To solve for wCNi and wCFe’ Equations (10.1) are
evaluated at other values of xC. In the case of the nickel-
carbon system, 7C is a constant to the saturation limit,
and to insure that the interaction energies reflects this
we evaluate wCNi at (xc)sat'

For the iron-carbon system the results of Smith (19“6)
in the form of Eq. (3.6) were used to determine the values
of wCFe and erC from Eqs. (10.1) and (10.2).

Experimental values for 7C and (x0) from Chapter VI

were used together with EEOC-gr

sat
estimates of Kaufman and

Nesor (1975) to obtain wNiC and wCNi at 900°C, 1100°C,
and 1215°C. Data for nickel were fit with an equation

of the type

T2 (10.3)

= A1d + B1JT + C1;]

“’11

B. Analysis of the Nickel-Iron-Carbon System

Smith (1960) and Wada 33 a1. (1971) studied the nickel-

iron-carbon system from xFe = 0 to 1.00. Tables 10.3

and 10.“ contain the results of these two investigations.

The appropriate Kohler-Kaufman equation for 6% at xC = 0

is

E —FCC-gr

Gc = RT in YC ‘ G0 + xNiniC + xFeerC (10°“)

2 2
‘ xNixFewNiFe ' xFele‘VFeNl

186

Table 10.3. The Reanalyzed Results of Smith (1960) for
the Activity Coefficient of Carbona in Nickel-
Iron-Carbon Alloys.

 

 

 

Mole Fraction Activity Coefficient rms'

Nickel of Carbon Residual
xN1 Yc O

0.0 8.“5 0.2
0.0379 10.5 1
0.0775 13.2 1
0.1“8 17.3 1
0.258 29 3
0.395 5“ 6
0.599 119 9
0.787 1“8 7
0.99“ 87.6 “.5

 

 

aTable contains values of 9: calculated for xC < 0.02.
When xC<O.02 1C = 7: = a constant. (See Figure 6.“).
Equation (3.6) was used to recalculate the activity of
carbon in iron, which was used as a secondary standard
in all runs.

187

Table 10.“. The Reanalyzed Results of Wada 22.11- (1971)
for the Activity Coefficient of Carbona in
Nickel-Iron-Carbon Alloys.

 

 

 

Mole Fraction Activity Coefficient rms

Nickel of Carbon Residual
le Yc °

0.207 23 2
0.“01 - 57 6
0.506 85 9
0.598 130 18
0.655 139 23
0.792 .159 16
0.892 115 13

 

 

aThis table contains values of 1C calculated for xC<0.02.
When xC<0.02 90 = 1C = a constant (see Figure 6.“).
Equation (3.6) was used to recalculate the activity of
carbon in iron, which was used as a secondary standard
in all runs.

188

To use Equation (10.“) values of wNiFe and erNi were
taken from Kaufman and Nesor (1975) Table (10.1)). Figure
10.1a compares the values of 1n72 calculated using Equa-
tion (10.“) and the values of the interaction energies
listed in Tables 10.1 and Table 10.5 with the experimen-
tal results of Smith (1960) and Wada gt a1. (1971). In
Figure 10.12 the x's are experimental points and the zeros,
0, are points calculated from Equation (10.“) with only
the nickel-carbon and the iron-carbon binary interaction
energies of Table 10.1. The difference between calculated
and experimental points is very large, and at the nickel-
rich end the binary Kohler-Kaufman equation predicts that
the activity coefficient of carbon will decrease upon the
addition of iron. Experimentally, however, the activity
coefficient increases until xFe N 0.25 and then decreases
as more iron is added. Obviously the Kohler-Kaufman equa-'
tion with only binary interaction energies is unable to
predict the form of in 73 in the ternary mixture.

Figure 10.1b is an attempt to fit all of the ternary
data in Tables 10.3 and 10.“ with Equation (10.“). Again
only binary terms are considered. The difference between
Figures 10.1a and 10.1b is that the values of erC and
wNiC were determined as a best fit to all of the ternary
data. The fit is very poor. The calculated values are
high for the iron rich alloys and low for the nickel rich

alloys.

Figure 10.1.

189

Comparison of calculated, 0, and experimental,
X, values of in 9: as a function of XNi in the
Ni-Fe-C system. The experimental results are
those of Smith (1960) and Wada EE.E1- (1971)
(see Tables 10.3 and 10.“). (6) Calculated
points determined from Equation (10.“) with
the values wNiC and erC taken from the binary
results (Table 10.1). (b) Calculated points
determined as a "best fit" of Equation (10.“);
the experimental values were the independent
variable and wNiC and erC the dependent
variables. wNiFe and erNi were taken from

Kaufman and Nesor (1975), Table 10.5.

190

E
J

 

- - -c‘----‘o---S---_§--—

5.07

‘N

in93

.ID all!!!" i Ill‘ul'lslllps. . I
g .

a.

 

1.00

xN1

.---q----g----S-u‘-SO—-oS-‘p--fi----5----‘----S----s----s----§---cS-nc-s----'§----S----s----‘----s--;-§

V

5.07

.0 ' ' 'l—W'lll’i'ésll' vl' .<.ll' .‘VIKv 0108109-5 ll. .78 fl

 

30

‘X 0

IX 0

Am
inyc

fl

 

2.13

1.00

xN1

191

The values of wNiFe and erNi were taken from Kaufman
and Nesor (1975), (Table 10.5). The experimental results
for 9; in the nickel-iron-carbon system can be fit with
only binary terms if wNiFe and erNi are allowed to increase
by a factor of five. The resulting parameters, however,
would not correctly describe the thermodynamics of the
binary iron-nickel system. Kubaschewski g£_al (1977)
have reviewed the iron-nickel system and their results
agree with those of Kaufman and Nesor (1975). In no case
then were the values of wNiFe and erNi allowed to vary.

Figure 10.2 is the result of fitting the data of Smith
(1960) and Wada gt a1 (1971) to the Kohler-Kaufman equa-

tion where ternary terms have been added to Eq. (10.“).

+ lelec + xFe‘pFec

2 2

- 2
NixFewNiFe ' xFexNineNi

x W 2
Ni Fe NiFeC

' X PexNineNiC’

+X +X

(10.5)

The equal signs in this figure indicated that the experi-
mental and calculated points agree within 2%. The root
mean square residual of the fit to the Kohler-Kaufman equa-
tion was 5.6%. The values of the ternary parameters are

= 61.9 kJ mol‘l, 0 = 1.8 kJ mol"1 = 20.7

wNiFeC and erNiC

 

Figure 10.2.

192

Comparison of calculated, 0, and experimental,
X, values of in 9: as a function of xN1 in the
Ni—Fe-C system. An equal sign, 3, indicates
that the experimental and calculated values
differ by less than 2%. The calculated points
were determined as a best fit of Equation
(10.5) to experimental results of Smith

(1960) and Wada §£_al (1971) (see Tables

'10.3 and 10.“). Values of erNi and wNiFe

were taken from Kaufman and Nesor (1975), Table

10.5.

193

I
I
D
D
D
D
D
b
I

 

 

5 5
I .

.-

u

to s
o

o

o

s 2..
0 uh .

o

..

K. 5
o

o

n

5 h.
wa. o
9‘ c

o

u

.3 5
o

o

"

._- 5
a

o

n

K. O s
u

o

c

0

:- x- s
c

o

u

x. s
o

"

ox .

K. ‘-
c

c

g

c

l. s
u

o

”

5 OX! 5
o

o

c

c

5 5
o

o

o

.. ....
u .
c

. p
. I o
.5 5
. o
c o
a c
- I o
5 5
. .
. p
o u
. o
5 I 5
o o
g c
. .
. .
.5 s
o c
. x 0 .
o c
a o
5 5
. In .
u o
o u
o I —
llac"$.’lll.ha"'ll.llllll '8' 0‘-' . v I n .., . 8' I - 1|
0 A V: l
O O
5 2

m

1.00

xN1

19“

1 l

kJ mol' , 0 = 5.3 kJ mol' . The dramatic improvement in
the fit of the data to the equation clearly indicates

that ternary coefficients must be included.

C. Calculation of Interaction Energies in the Nickel-

Titanium—Carbon System

 

As mentioned in the Introduction, one of the goals of
this research was to test the validity of using only binary
parameters to describe the thermodynamics of multicomponent
solutions. Therefore, in this section and the next ter-
nary terms in the Kohler-Kaufman equation are initially

ignored.

The equations for Egi and 0% in the ternary alloy

are obtained from Equation (2.30). For figi

2
xTixNi lele

+
(l-x )]
(xT1+xN1)2 (XT1+XN1) T1

—E __—FCC-BCC
GT1"GT1 + wTiNiE

 

X x X x
T1 c + Ti C (1’XT1)3
(xTi+xC)

+

 

l"T10 [
(x +x )2
T1 0
2
X X
wNiTi E N1 < ”1 - xT1)]
(1T1+XN1) (XT1+XN1)

2
7m [—3— (4‘2— - in):
(x +x x +x
C Ti C Ti
2 2
x0le ( lexC
"“"° ' 7N10 ““"‘>

XC+XN1 XC+XN1

- “0N1 ( , (10.6)

195

where ternary interaction energies are excluded. At x0 =

0, Equation (2.30) yields for 0%,

E -FCC-gr

G0 = ET in Y0 ‘ G0 + xN1¢N1C + xT1‘pT10 I
- x2 x w - x2 x w (10 7)
Ni Ti N1T1 T1 N1 TiNi’ '

where ternary interaction energies are excluded.

Following Kaufman and Nesor (1975) we assume wTiC =
wCTi and wNiTi = wTiNi‘ In both cases this is Justified
because of narrow range of experimental data. These as-
sumptions result in a symmetric excess Gibbs free energy
as a function of composition in the binaries. While Eqs.
(10.6) and (10.7) could in principle be solved simultan-
eously they are easily solved by iteration. The estimate
of wTiC (= wCTi) proposed by Kaufman and Nesor (1975)
was used in Eq. (10.“) to solve for wTiNi (= wNiTi)'

Then a value for wTiC was calculated from the results in
Chapter 8 and Eq. (10.7). This value for wTiC was then
used to recalculate by Eq. (10.6) the value of wNiTi'
Kaufman and Nesorls (1975) estimate was close to our
calculated value and only one iteration was necessary.

The use of the value of wTiC obtained Eq. (10.7) to re-
calculate wNiTi changed the value of wNiTi by approximately
0.“ KJ-mol'l. Recalculation of wTiC produced no significant

change. The values for wNiTi at several temperatures were

196

fit by least squares to Eq. (10.3) wTiC was found to be
constant within experimental error and no ternary term

is needed.

D. Calculation of the Molybdenum-Carbon and Chromium-Carbon

Interaction Energies

 

The values of wMoC and wCrC were calculated at x0 = 0
from the results in Table 9.1 for alloys 7262 and 726“,
7263 and 7265, and the following equations which are de-
rived from Eq. (2.30).

E -FCC-gr

6 = G

C C + xN1“’N1C +

+ x

XT1"’T10 MowMoC

2 _ 2 2 2
’ xNixTiniTi ‘ leleleNl ‘ xNixMowNiMo ‘ xMoxNinoNi

2 2
' xTixMowTiMo ' XMoxTiwmoTi, (10.8)

—E _ —FCC-gr
, GC ‘ G0 + XN1“’N10 + xTiniC + xCerrC

2 2 2 2
’ xNixTiniTi ' xTixNiniNi ' xNixCrwNiCr ' xCrle‘chm

2 2 .
' xTixCeriCr ’ xCrxTiwCrTi’ (10'9)

where ternary interaction energies are excluded. The

previously calculated 013 were employed and the values of

leCr’ wCrNi’ wNiMo’ I"Mom, wCrTi’ wTiCr’ wMoTi’wTiMo and

197

EEOC-gr were taken from Kaufman and Nesor (1973, 1975)
(see Tables 10.2 and 10.5).

The values of the interaction energies calculated
assuming only binary terms were important are listed in
Table 10.6. It is clear from the results in Tably 10.6
that in the cases of wMoC and wCrC that the calculated
values are all composition dependent. Further, all of the
binary interaction energies become more negative as the
mole fraction of the total solute is increased. This means
that the activity coefficient is smaller in the more
concentrated solutions than would be expected from ex-
trapolation of the dilute results. The trend is to lower
than expected activity coefficients continued to an even
larger extent in alloys 7267 and 7268 as discussed in
Chapter IX. It thus appears that, as in the Fe-Ni-C
system, the binary interaction energies are not sufficient
to describe the systems in question.

At xC = 0 the appropriate ternary terms from Eq. (2.30)

are

6% (ternary) = Z 2 v
i=1 J=1

n-1 n-2 n-1 2x x x
+2 2 2-
i=1 J=l k=1 (x1+xJ+xk
k#1#J
J<k

 

) “13k (10.10)

Table 10.5.

Interaction Energies 013

198

FCC for the Kohler-

a FCC

Kaufman Formalism, $13 = A13 + BiJT +
+ D T3.

 

 

 

iJ
J/i Ti Cr Fe Ni Mo
A /kJ-mol-1
13
Ti -—-- 52.0 -33.5 -100 15.“
Cr 39.“ ---- 7.“1 -25.1 21.3
Fe -lo.5 7.“1 ---- -3“.8 25.3
N1 -100 -8.37 2.1 ------ 13.6
Mo 15.“ 3“.3 2u.8 -l3.6 --—-
» Bis/J’molulK-1
Ti ---- 0 0 -95.8 0
Cr 0 ---- -6 3 0 -5 9
Fe 0 -6.3 ----- 0 0
Ni -95.8 0 0 ---- 13.8
Mo 0 -ll.3 -8.“ 13.8 ----
Ci‘j/10"3J°mol-1K-l
T1 —-—- 0 0 “7.2 0
cr 0 ---- 0 9.“7 0
Fe 0 0 ---- 2“.“ 0
Ni “7.2 “.69 -3.83 —--- 0
M0. 0 0 0 0 0

 

199

Table 10.5. Continued.

 

 

 

J/i Ti Cr Fe Ni Mo
-6 -l -3
Did/10 J-mol K
Ti ---— 0 0 0 0
Cr 0 ---- 0 -2.61 0
Fe 0 0 ---- -10.“ 0
Ni 0 -7.85 1.63 ---- 0
Mo 0 0 0 0 ----

 

 

aAll values are from

wNiTi = wTiNi "hiCh
Chapter VIII.

Kaufman and Nesor (1973, 1975) except
were calculated from the results of

200

 

 

 

 

 

 

 

Table 10.6. Incorrect Values for the Binary Interaction
Parameters, ngc Calculated with Only Binary
Terms.
WFCC/kJ-mol-
1 Temperature (°C)
(Element) 900 1100 1215
N1a 473.“1 -70.86 -70.“6
T1 b
7261, xTi = 0.02““ -25“.8 -23“.7 -238.9
7068, xTi = 0.0361 -258.2 -263.6b -2“3.5
Cr
7265, xCr = 0.0“57 -76.8 -78.2 -75.9
7263, xCr = 0.0801 -81.6 -95.1 -90.7
M0
726“, xMO = 0.0“17 -10.9 -5.7 -6.5
7262, xMO = 0.0820 -29.9 --27.9 -27.3
a

b

wNiC was fit to a quadratic equation in temperature.

The 1100°C results appear to be in error.

The 7261

result being too large and the 7068 result being too
small. If the concentrations of carbon in 7261 and 7068
at 1100°C are compared directly to the nickel carbon con-

centrations the values of w
kJ-mol'l, respectively.

T10 become -250.3 and -258.9

201

From the array of alloys that have been studied here
we cannot discriminate between the possible ternary terms
in Eq. 10.10. It seems logical, however, to fit the results
with those terms having the largest concentration factors.
The terms with largest factors are wNiCrC’ wNiMoC and
u’N1T1C'

The difference in wTiC for alloys 7261 and 7068 is
not large enough (%3%) to Justify calculating a nickel-
titanium—carbon interaction. However, values for
wNiCrC and wNiMoC have been calculated from the results
because of the higher concentrations of Mo and Cr.

A ternary term, wNiMC (xfiixM), where M is either
molybdenum or chromium, was added to Equation (10.6) and
(10.7). Results for alloy pair 7262 and 726“ and pair
7263 and 7265 were used to solve for wMC and wNiMC simul-
taneously. The resulting values can be found in Table 10.7.
The fact that binary and ternary terms are approximately
the same magnitude agrees with the results of Section 10B

1

where it was calculated that wNiC = -71.8 kJ mol- and

1

= 61.9 kJ mol' at 1000°C. The absolute uncertainty

wNiFeC
in 0M0 and wNiMC is difficult to ascertain. The uncer-
tainty in the sum of wMC and wNiMC however is approximately
2 kJ. The precision in the values of the binary and ter-
nary interaction energies can be improved if more ternary

alloys, such as Ni-Cr-C and Ni-Mo-C, are investigated.

The larger the addition of the metal used the more precise

202

Table 10.7. Interaction Energies in kJ°mol-1 Calculated
from the Kohler-Kaufman Equationa Including
Ternary Terms.

 

 

 

Interaction Energy kJ mol"1
9583 -2“8.5
wflgg -2“7.5
wggg -2968
wgigoC 268'0
wgigrc 2“1.3

 

 

aEquat1ons (10.6), (10.7), (10.8), (10.9) and (10.10) or
(2.30).

203

the values of the interaction energies will be.

Table 10.8 contains the values of the activity 00-
efficient of carbon calculated using previously presented
interaction energies including both binary and ternary
terms from Tables 10.1, 10.“ and 10.6. Note that the
experimental values for alloys 7267 and 7268 agree within
10% with the calculated values. When the ternary terms
are not included the calculated results for 7267 and 7268
differ from the experimental by 20 to 30%. Furthermore,
the binary equations predict that the addition of molyb-
denum always result in an increase in the activity 00-

efficient of carbon, which is not observed.

E. Prediction of Carbon Solubilities

Another of the goals of this work was the prediction
of carbon solubility in multicomponent solutions. The
data of Kaufman and Nesor (1975, 1973) and Stover and
Wulff (1959) (see Section 8B) have been used to calculate
the activity of all the metallic solutes except carbon in
the various alloys studied in this work. Table 10.9
contains the values of the activity of the solutes at
900, 1100 and 1215°C. The activities were calculated using
a pure component reference state and a body centered cubic
crystal structure, the normal structure for these solutes

at the temperatures investigated. The activities in Table

20“

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206

10.9 have been used to calculate the solubility limit of
carbon in the various alloys in equilibrium with pure titan-

ium carbide according to

_ -1
Ac ’ (ATin,TiC)
where Kf TiC is the equilibrium constant for T1 (solv) +
, i

C (soln) = TiC (solid). Values of K are listed in

f,TiC
Table 8.“.

TableilO.10comtains values of the activity of carbon at
the titanium carbide solubility limit obtained from the
results presented in Chapters VIII and IX and the values
calculated with the Kohler-Kaufman equation. In this work
the highest carbon activities investigated were 0.76 at
1215°C, 0.72 at 1100°C, and 0.59 at 900°C. Titanium carbide
did not form, at any activity, in alloys 7261, 7265, and
7068. The lack of a two phase region, in these alloys, at
the experimental activities is in agreement with the cal-
culated solubility limit, in Table 10.10. In alloy 7263,
which contains no molybdenum, the precipitate can be assum-
ed to have an activity of one, based on arguments presented
in Chapter VII. Experimentally, it is found that precipi-
tation of titanium carbide does not commence, in alloy 7263,
until an activity 50% higher at 900 and 25% at 1100 and
1215°C than the calculated value. This discrepancy could

be due to experimental error. The data obtained from

2C)?

Table 10.10. Comparison of Calculateda and Experimental Value of the Carbon Activity
Where Precipitation of Titanium Carbide Should Start.

 

 

 

 

 

Temperature/°C
900 1100 1215
AC Ac AC AC AC AC

Alloy (Calc) (Exp) (Calc) (Exp) (Cale) (Exp)
7261 N1 + 2.“ T1 1.3 1.7 1.7
7262 N1 + 2.h Ti 0.33 0.17 0.56 0.18 0.63 0.18
+8.2 Mo
7263 N1 + 2.0 Tib 0.25 0.50 0.u3 0.50 0.u8 0.63
+ 8.0 Cr ‘
726” N1 + 2.“ Ti 0.66 0.36 0.99 0.38 1.0“ 0.32
+ “.2 Mo
7265 N1 + 2.5 T1 O.L8 0.75 0.81
+ u.6 Cr
7266 N1 + 2.“ Ti 0.06“ 0.1“ 0.0“6 0.19 0.067
+ 8.3 Cr + 8.1 No
7267 N1 + 2.5 Ti 0.1a 0.27 0.19 0.32 0.095
+ u.u Cr + 8.2 No
7268 N1 + 2.5 Ti 0.11 0.23 0.11 0.28 0.13
+ 8.“ Cr + “.1 Mo
7068 N1 + 3.6 T1 0.61 0.36 0.91

 

 

aActivities calculated using results in Table 10.9

bExperimental values are approximate. They were obtained by interpolating between
the solid solution data and one point in the two phase region.

208

Stover and Wulff (1959), although the best available, could
be in error by 25% in the solubility product for titanium
carbide. They relied on Curie point measurements, whose
precision was not stated, to determine the phase boundary.
Another possibility is that the model was not adequate.

The assumption that titanium and nickel form a_temperature
dependent regular solution in the nickel—rich corner of the
phase diagram may be incorrect. Unfortunately, the true
nature of Egi as a function of xT1 in nickel will have to
await further data. Stover and Wulff's (1959) data do not
cover a broad enough range of composition to yield more than
one point on the dfii curve.

TiC formed at all three temperatures in alloys 7262,
726“, 7266, 7267 and 7268. The solubility in these alloys
determined experimentally is 1/3 to 1/2 the calculated solu-
bility (Table 10.10). If the arguments in the preceding
paragraph are correct the agreement between predicted and
experimental solubilities are even worse. If one assumes
that the molybdenum carbide forms an ideal solid solution
with titanium carbide, the activity of the titanium, based
on the compositions discussed in Chapter IX, would be 0.7
in alloy 7264 and 7268 and 0.58 in alloys 7262, 7266 and 7267.
While lowering the activity of the carbide is a move in the
right direction, the change is not sufficient to bring the
calculated and observed values together. The most plaus-

ible explanation for the remaining discrepancy is that,

209

rather than forming an ideal solution, the carbides mix with
a negative heat of mixing. If a value of approximately

-6.7 i 2 kJ°mol-1 is assumed for the heat of mixing and if
the entropy of mixing is assumed to be ideal, the calculated
and experimental values of the solubility agree to :15 per-
cent. A slightly more negative value for the heats of mixing
is needed if the calculated values of AC are shown to be

too low. Clearly, more precise thermodynamic data are
required for the nickel-titanium system in order to resolve

the discrepancies.

CHAPTER XI

THERMOMIGRATION

A. Introduction

 

Until recently, thermomigration, the mass flux induced
by a temperature gradient, was studied exclusively in liquids
and gases. Experimental difficulties associated with
establishing and maintaining a large, well-defined tempera-
ture gradient in a solid dissuaded researchers from investi-
gating thermomigration in solids. Modern work in the field
started with Shewmon (1958) and Darken and Oriani (195“)
who investigated several metal-metal and metal-metalloid
systems. Oriani (1969) reviewed the 1960's experiments on
metal-metalloid binary systems, which yielded little quan-
titative data. Poor temperature control and poor chemical
analyses plagued most investigators.

Thermomigration in solids is an important phenomenon
in, for example, nuclear reactors and in welding. In nuclear
reactors, large temperature gradients are the norm rather
than the exception. Thermomigration of hydrogen in the
Zircalloy fuel cladding and in the oxide fuel are of great
technical importance. In welding the tremendous tempera-
ture gradients at the liquid-solid interface cause a mass

flux which may be responsible for cracks that form in many

210

211

welds after cooling.

Thermomigration experiments have as their immediate
goal the measurement of the "thermal diffusion factor",
01. For a binary system with a linear temperature gradient

in the Z direction, 01 can be determined from [Horne and

Anderson (1970)]

WI = alw1w2[l + H—-exp(— —t/0)]sin(T n) (11.1)
wl = weight fraction of component i
w; = initial weight fraction of component i
Z = coordinate in the direction of the temperature
gradient. At the center of the specimen Z = 0.
t = time

d = the diffusion pathlength
e = d2/n2D relaxation time

D = binary diffusion coefficient

Equation (11.1) indicates that the composition of the
specimen as a function of position will continue to change
until t 3 us, after which time a steady state will persist
as long as the temperature gradient is maintained. Measure-
ments made after t = H0 will not provide any information on
D but do provide data for calculation of 01. To date the
few thermomigration experiments in solids have all been

done at the steady state (t 5 he). In this work the

212

measurements were to be time dependent so that al and D

could be determined in the same experiment.

B. Experiments

 

Specimens were annealed in a temperature gradient of ap-
proximately 1000°C/cmixia.Gleeble. A Gleeble is an instru-
ment designed to simulate the large temperature fluctuations
produced in metal alloys during welding. A cylindrical
sample is clamped at both ends in water cooled copper
Jaws, and a large alternating current is then passed
through the sample. The sample is brought from 20 to 1300°
C in less than 10 sec. The temperature of the sample is
controlled via a feedback loop containing a thermocouple
attached to the center of the sample. Solution of the
heat conduction equation for this experimental arrangement
as well as actual experimental measurements show that the
temperature distribution in the sample is parabolic with
a maximum in the center. For sample B—6-B the temperature

was found to obey
T: = .2371d2 + 82.06d + 1350.

with the root mean square residual c = 10°C. The tempera-
ture of the sample was measured at three sites on the

specimen with platinumeplatinum 10% rhodium thermocouples

213

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21“

and recorded as voltage on a three pen pentiometric strip-
chart recorder. The end temperatures were also known.

The atmosphere around the samples was supposed to be con-

trolled by flowing pure argon at approximately 100 liters

per hour through a pyrex cover box surrounding the sample.

C. Results

Several specimens were annealed in the Gleeble for times
varying from five minutes to two hours. The results were
of two kinds: either a gradient of carbon concentration
was not observed or the sample was partially decarburized.
Figure]J:J.shows half of a sample annealed two hours in
the Gleeble and then annealed 100 hours at 760°C to pre-
cipitate the carbon from solution. The carbon distribution
in the sample approaches the shape of an hour glass. This
distribution would be expected in a sample with a sink at
the surface and a maximum in temperature at the center.
From these results it is apparent that better control over
the atmosphere surrounding the sample is necessary if
quantitative results are to be obtained. Cost, time con-
sideration, and the requirements of other users mitigated
against modification of the Gleeble for further study of
thermomigration. .

There is still a need for thermomigration experiments

in interstitial metal alloys, and a suitably modified

215

Gleeble would offer many advantages, such as rapid heat-up
and cool-down. The modification most needed is a high
quality vacuum system in order to control the chemical

environment surrounding the specimen.

CHAPTER XII

SUGGESTIONS FOR FURTHER WORK

A. Analytical Chemistry

 

While a great deal of effort has been expended in im-
proving techniques for analysis, further improvements are
still desirable. The carbon analyses are in need of ac-
curate standards; as discussed in Chapter III, the standards
currently available have an accuracy of about 15%. The
carbon analyses could also be improved if a more selective
detector were used. Our apparatus used a conductometric
detector. Newer instruments use infra-red detectors, which
are not as sensitive to impurities such as SO2 and do not
require CO2 traps and chromatographic columns.

In the area of metal analysis more study is needed on
"matrix" effects in the acidic solutions. These effects
require the use of standards of similar composition to the
samples. In some cases this is not convenient or possible.
For analysis of small quantities of solid material the de-
velopment of x-ray fluorescence capability would be desir-
able. The electron microprobe technique, while useful,
is limited in that only relative concentrations are readily

obtainable.

216

217

B. Experiments

Six different series of alloys need to be studied in
order to understand better the ternary interactions that
this research has revealed. The six systems are Ni—Mo—C,
Fe-Mo-C, Ni-Cr-C, Ni-Mo-Cr-C and Fe-Mo-Cr-C. Experiments
should be carried out with as high a concentration of Mo
and/or Cr as possible without leaving the faceacentered
cubic solid solution phase field. The goal of these experi-
ments would be to determine quantitatively the values of
the ternary interaction energies. The question of whether
there is any solvent dependence in the binary interaction
energy could also be reSolved by these experiments. If
the binary interaction energies determined in nickel and
iron solutionsckanot agree once ternary terms are taken
into account, still higher order terms will have to be
introduced into Kohler-Kaufman formalism.

In solutions with low carbon solubility the car-'
burization technique needs to be refined to facilitate
experiments at carbon activities of less than 0.05. This
would involve using gas mixtures of lower CHu/Hg ratios
and possibly lowering P02 in the furnace. The result
would be a better understanding of the titanium-molybdenum-
carbon precipitation process and the molybdenum-chromium-
carbon solid solution interaction.

More controlled experiments are necessary on the

218

precipitation of carbon upon quenching. Resistance heating
and a helium quench offer the most convenient methods of
controlling the quench rate. Annealing samples at tempera-
tures of around 500°C for short periods of times and observ-
ing changes in the weight percent of the precipitate and

in the x-ray diffraction patterns would provide insight

into the precipitation process. It is also hoped that short
anneals at low temperatures would allow the precipitates

to grow large enough to be viewed in the electron micro-

scope.

APPENDIX A

APPENDIX A

The compositionscfi‘the uncarburized alloys are given in
Table A-1. Tables A-2 through A-33 contain all of the gas
phase carburization data generated in this investigation.
The data in each table constitute one data set. That is,
all of the specimens in the set were carburized at the same
time in the same furnace run. Thus, the temperature and
the equilibrating gas are identical for all the specimens
described in a given table. For these two reasons all are
listed together.

Unfortunately, the analytical standards used for carbon
analysis of the specimens, even in a specific table, are
not all the same. This arose because the supply of National
Bureau of Standards Standard Reference Material (NBS SRM)
19E was exhausted. Thus, when rechecking specimens in some
tables, a different NBS SRM was used. (In some tables, of
course, only one NBS SRM was used.) As discussed in Chapter
III, it is important when using the carbon data to relate
all of the concentrations to the same NBS SRM. In all of the
calculations in this work the carbon concentrations are rela-
tive to NBS SRM 19E. Extensive comparison of SRM 19E and
121B (the only other standard used in the carbon analyses)
showed that a concentration relative to 121B must be multi-
plied by 0.966 to obtain the concentration relative to 19E.

Analytical carbon data were rechecked frequently, as is

219

220

partially apparent from examination of the variation of NBS
SRM's in the tables. Shortly after the gas phase carburiza-
tion studies began it was apparent that problems existed in
our ability to analyze for carbon. Comparison of weight
change and the carbon analysis did not always agree. In-
consistencies between data sets and the size of the aliquot
used in the analysis affected the results. Once it was
realized that analytical difficulties existed, the stringent
controls on the combustion procedure detailed in Chapter IV
were developed. Unfortunately, before all of the analytical
problems were solved, the supplies of four sets of specimens,
A—7603-118, A-7603-l2l, A—7783-20, and A-7783-21, had been
exhausted. When these specimens were analyzed the instru-
ment was giving consistently low values for the carbon
concentration when small aliquots were used. In the four
sets of specimens mentioned above all of the one phase
specimens, except the iron standards, contained less than
0.05 wt. % carbon. Analysis of data from these specimens
showed that they had uniformly low activity coefficients
relative to samples analyzed after the instrument problems
had been corrected. In the final analysis of the data,
therefore, the activity coefficient of the nickel alloys

in the aforementioned data sets was obtained from the ac—
tivity coefficient of carbon in nickel determined in the
data sets listed in Table 5.1. The carbon analyses of

specimens Ni-A7783—16 and 7068-A7603-106 were disregarded

221

in the analysis of the results. In both specimens the cal-
culated activity coefficients were more than 3 standard
deviations from the mean value and were not consistent with
the other data sets with respect to equilibrium concentra-
tions of carbon. That is, in data set A-7783—l6 the nickel
specimen analyzed to be lower in carbon than N1 + A at. %
Mo (726A) and in A-7603-106 alloy 7068 analyzed to be lower
in carbon than nickel. These are contrary to the results
of all the other data sets. Data set A-7783-36 has not
been considered in the analysis of the data. Repeated
analyses of the specimen from this set gave non-repro-
ducible results even when the carbon analyzer appeared

to be functioning properly.

The abbreviation T.P. in the tables indicates that the
specimen was assumed to be two phase, although the material
was not extracted. The specimens were Judged two phase
on the basis of their activity coefficients. A decrease
in the carbon activity coefficient at high carbon activity

indicates that precipitation has occurred.

222

a

Table A.l. Composition of Alloys Used for Calculations.

 

 

 

 

Alloy Element/wt %

MElt 2

Nb. T1 Cr Mb C N1
7261 2.0 0.015 98.0
7262 1.95 12.81 0.01“ 85.3
7263 2.02 7.78 0.01“' 90.2
726“ 1.95 6.68 0.015 91.4
7265 2.06 “.09 0.016 93.8
7266 1.91 7.08 12.76 0.021 78.2
7267 1.95 3.77 12.93 0.016 81.“
7268 2.00 7.33 6.66 0.015 8U.0
7071 2.8 8.08 0.135 89.0
7095 3.06 13.9 0.380 82.7
A 2.0 13.0 0.09“ 8U.9
B 1.73 0.086 98.2
C 2.0 7.UO 0.109 90.5
14149 1.95 7.36 11.14 0.035 79.0

 

 

8These values were picked from those in Table 5.1.

223

 

 

 

Table A.2. Data From Carburization Experiment A-7603-97.
Date: 4/28/76; Temperature: 1215°C; Duration: 40 hours
H20(g) Concentration: 1.5 ppm; Quench: Water.
Final Microprobe
[C] Cal. Intensity
Weight (wt %) Std. Ratio Lattice
Change by For Precip . (Mo ) Parameter
Alloy ( %) Analysis Carbon (wt . % ) IT aO/nm
7261 0.124 0.135 19E 0.24
7262 0.325 0.321 121B 1.57 1.50:0.03 0.43158
7263 0.132 0.160 1213 0.25
7266 0.832 0.852 19E 6.05 3.00 0.08
Ni 0.128 0.131 19E 0.22

 

 

aoa =0.0001 nm.

0

Table A.3.

Date:

1215°C; Duration:

Data From Carburization Experiment A27603-105
5/ 4/ 76 3 Temperature :

36 hours;

H20(g) Concentration: 1 ppm; Quench: Cold Zone.

 

 

 

Final Microprobe
[C] Cal. Intensity
weight (wt %) Std. Ratio Lattice
Change by For Precip. (Mb) Parameter
Alloy (% ) Analysis Carbon (wt . %) TI ao/nm
7264 0.125 0.138 19E 0.147
7265 0.147 0.162 19E
7267 0.687 0.708 1213 TP
7268' 0.487 0.523 121B TP
Ni-270 0.146 0.150 121B

 

 

22“

Table A.4. Data From Carburization Experiment A27603-106.

Date: 5/6/76; Temperature: 1215°C; Duration: 36 hours;
H20(g) Concentration: 1 ppm; Quench: Cold Zone.

 

 

 

Final ‘Microprobe
[C] Cal. Intensity
Weight (wt Z) Std. Ratio Lattice
Change by For Precip . (1&1) Parameter
Alloy (1) Analysis Carbon (wt. %) Ti aO/hm
7068 0.0663 0.140 19E
7071 0.0802 0.217 19E
7095 0.477 0.870 19E 6.19 1.75i0.02
'Ni-270 0.140 0.150 19E 0.24
Ni-270 0.110 0.147 19E

Fe'E' 0.941 0.981 19E

 

 

225

Table A.5. Data From Carburization Experiment A-7603-118.

Date: 5/17/76; Temperature: 1215°C; Duration: 22 hours;
H20(g) Concentration: 1 ppm: Quench: Cold Zone.

 

 

 

Final Nficroprobe
[0] Cal. Intensity
Weight (wt %) Std. Ratio Lattice
Change by For Precip . (Mg) Parameter
Alloy (%) Analysis Carbon (wt. %) Ti ao/nm
7261 0.020 0.0337 19E
7262 0.053 0.0274 19E
7263 0.038 0.0410 19E
7264 0.086 0.0285 19E
7265 0.040 0.0359 19E
7266 0.059 0.0557 19E TP
7267 0.047 0.0358 19E
7268 0.103 0.0414 19E
7068 0.188 0.0355 19E
Ni-270 0.023 0.0330 19E
Fe'E'a 0.261 121B
‘ 0.256 19E

 

 

ainitial wt not recorded.

226

Table A.6. Data From Carburization Experiment A-7603-121.

Date: 5/18/76; Temperature: 1215°C: Duration: 46 hours;
H20(g) Concentration: 1 ppm; Quench: Cold Zone.

 

 

 

 

 

Final Nflcroprobe
[0] Cal. Intensity

Weight (wt %) Std. Ratio Lattice

Change by For* Precip. (M60 Parameter
Alloy (%) Analysis Carbon (wt. %) Ti ao/nm
7261 0.035 0.0442 19E
7262 0.020 0.0337 19E
7263 0.019 0.0482 19E
7264 0.013 0.0364 19E
7265 0.018 0.0447 19E
-7266 0.124 0.142 19E 0.639 0.43113
7267 0.044 0.0461 19E
7268 0.019 0.0535 19E
7068 -0.044 0.0444 19E
7095 -0.301 0.0795 19E
7071 -0.067 0.0568 19E
Ni-270 0.041 0.0433 19E
Fe'E' 0.291 0.325 19E

0.330 1218

ac =0.0001 nm.

Table A.7.
Date:

227

Data From Carburization Experiment A27603-123.
5/20/76; Temperature:

215°C; Duration: 64 hours;

H20(g) Concentration: 1 ppm; Quench: Cold Zone

 

 

 

 

 

 

 

 

Final Microprobe
[C] Cal. Intensity
Weight (wt z) Std. Ratio Lattice
Change by For Precip. (M90 Parameter
Alloy (%) Analysis Carbon (wt. %) Ti aO/nm
7261 0.367 0.398 1218
7263 1.91 0.535 121B 0.963
7264 0.683 0.675 121B 2.55 1.15:0.03 .4326a
7265 0.441 0.447 121B
7268 1.058 1.085 19E TP
7068 0.377 0.449 121B
7071 0.657 0.832 121B
Ni-270 0.355 0.37 19E
a
Ca =0.0001 nm.
0
Table A.8. Data From Carburization Experiment A-7783-4.
Date: 6/16/76; Temperature: 1100°C; Duration: 48 hours;
H20(g) Concentration: 1 ppm; Quench: Gold Zone.
Final Nflcroprobe
[C] Cal. Intensity
Weight (wt %) Std. Ratio Lattice
Change by For Precip. (E20 Parameter
Alloy (%) Analysis Carbon (wt %) Ti aO/nm
7261 0.024 0.0407 19E
7262 0.027 0.0323 121B
7263 0.043 0.0450 121B
7266 0.185 0.190 1213 1.36 1.2410.02 .4311a
Ni-270 0.029 0.0376 1213
F'E' 0.324 0.355 121B

 

 

aoa =0.0001 nm.
0

Table A.9.

228

Data From Carburization Experiment A-7783-14

Date: 7/1/76; Temperature: 1100°C: Duration: 48 hours;
H20(g) Concentration: 2.5 ppm; Quench: Cold Zone.

 

 

 

 

 

 

 

 

Final Microprobe
[C] Cal. Intensity
Weight (wt 7:) Std. Ratio Lattice
Change For Precip. (M90 Parameter
Alloy (%) Analysis Carbon (wt. %) Ti aO/nm
7264 0.017 0.0363 19E
7265 0.019 0.0452 19E
7267 0.071 0.0852 19E 0.385 1.171001
7268 0.048 0.0577 1218 TP
Ni-270 0.032 0.0381 19E
Fe'E' 0.350 0.401 1218
Table A.10. Data From Carburization Experiment A-7783-l5.
Date: 7/3/76; Temperature: 1100°C; Duration: 72 hours;
H20(g) Concentration: 1 ppm; Quench: Cold Zone.
Final Nficroprobe
[C] Cal. Intensity
Weight (wt %) Std. Ratio Lattice
Change by For Precip. (M20 Parameter
Alloy (%) Analysis Carbon (wt. %) Ti ao/nm
7262 0.330 0.346 1218 2.14 1.29:0.02
7266 0.758 0.835 121B 6.53 2.44:0.06
.7267 0.561 0.610 1218 3.99 1.44:0.01
7268 0.424 0.467 1218 2.39 0.82:0.02
Ni-270 0.090 0.0951 121B
Fe'E' 0.733 0.796 1218

 

 

Table A.11.

Date:

Data From Carburization Experiment A-7783-l6
7/6/76; Temperature:

1100°C; Duration: 48 hours;

H20(g) Concentration: 1 ppm; Quench: Cold Zone.

 

 

 

 

 

 

 

 

Final ' Microprobe
[0] Cal. Intensity -
Weight (wt %) Std. Ratio Lattice
Change by For Precip. (M20 Parameter
Alloy (%) Analysis Carbon (wt. %) Ti ao/nm
7261 0.081 0.0959 1218
7263 0.118 0.116 1218
7264 0.065 0.082 1218 TP
7265 0.090 0.106 1218
Ni-270 0.077 0.0793 1218
Fe'E 0.784 0.811 1218
Table A.12. Date From Carburization Experiment A-7783-17
Date: 7/8/76; Temperature: 1100°C; Duration: 46 hours;
H20(g) Concentration: 1 ppm; Quench: Cold Zone.
Final 'Microprobe
[C] Cal. Intensity
Weight (wt 3) Std. Ratio Lattice
Change by For Precip. (M29 Parameter
Alloy' (%) Analysis Carbon (wt. %) Ti ao/nm
7261 0.210 0.244 1218
7263 0.345 0.383 1213 0.99 0.43248
7264 0.456 0.506 121B 2.14 0.91:0.03 0.43218
7265 0.228 0.252 1218
Ni -270 O. 208 0.225 1218
Fe'E' 1.424 1.49 19E

 

 

BO’a =0.0001 nm.

0

Table A.

13 0
Date :

1100°C; Duration:

Data From Carburization Emeriment A-7783-l8.
7/10/76; Temperature:

48 hours;

H20(g) Concentration: 1 ppm; Quench: Cold Zone.

 

 

 

 

 

 

 

 

 

 

Final Microprobe
[0] Cal. Intensity
Weight (wt %) Std. Ratio Lattice
by For Prec ip . (119) Parameter
Alloy (%) Analysis Carbon (wt. %) Ti aO/nm
7261 0 . 1614 0 . 202 1218
7263 0 . 227 O . 235 19E
72614 0 . 1814 0 . 325 19E TP
7265 0 . 314 0 . 196 19E
7068 0.1147 0.222 1218
Ni-270 0 . 161 0 . 179 198
Fe"E' 1.20 1.28 1213
Table A.1Ll. Data from Carburization Experiment A-7783-19.
Date: 7/13/76; Temperature: 1100°C; Duration: 48 hours;
H20(g) Concentration: 2 ppm; Quench: Cold Zone.
Final Microprobe
[C] Cal. Intensity
weight (wt %) Std. Ratio Lattice
Change by For Precip . (gig) Parameter
Alloy (%) Analysis Carbon (wt. Z) Ti ao/nm
7262 0.160 0.174 1213 0.945 1.27:0.02 0.4318a
7266 0.556 0.6214 121B 3.84 1.48:0.04
7267 0.431 0.460 193 2.95 1.33:0.02 0.43148
7268 0.283 0.310 1213 1.52 0.85:0.03 0.43198
7068 0.00 0.0873 1218
Ni-270 0 . 067 0 . 0726 19E
Fe'E' 0.577 0.616 1218
a

0

Ga =0.0001 nm.

231

Table A.15. Data From Carburization Experiment A27783-20.

Date: 7/16/76; Temperature: 1100°C; Duration: 60 hours;
H20(g) Concentration: 2 ppm; Quench: Cold Zone.

 

 

 

Final Microprobe
[C] Cal. Intensity
Weight (wt 5) Std. Ratio Lattice
Change by For Precip. (Mb) Parameter
Alloy (Z) Analysis Carbon (wt. %) TI' aO/nm
7262 0.014 0.0182 1218
7266 0.064 0.0633 19E
7267 0.033 0.0228 19E
7268 0.033 0.0285 19E
7068 -0.063 0.0253 19E
Ni-270 0.0128 0.0222 19E
Fe'E' 0.179 0.

205 1218

 

 

Table A.16. Data From Carburization Experiment A-7783-21

Date: 7/16/76; Temperature: 1100°C; Duration: 60 hours;
H20(g) Concentration: 2.5 ppm; Quench: Cold Zone.

 

 

 

Final Microprobe
[C] Cal. Intensity
Weight (wt %) Std. Ratio Lattice
Change by For Precip . ( Mg) Parameter
Alloy (%) Analysis Carbon (wt. 1) Ti ao/nm
7262 0.00 0.0106 198
7266 0.02 0.0192 19E
7267 0.01 0.0133 198
7268 0.00 0.0164 19E
Ni-270 0.00 0.0140 19E ,

Fe'E' 0.084 0.111 19E

 

 

232

Table A.17. Data From Carburization Experiment A-7783-32.

Date: 7/22/76; Temperature: 1100°C; Duration: 85 hours
H20( g) Concentration: 1 ppm QUench: Cold Zone.

 

r

 

 

Final Microprobe
[C] Cal . Intensity
Weight (wt 1) Std. Ratio Lattice
Change by For Precip. (Mo ) Parameter
Alloy (%) Analysis Carbon (wt . 1) TI ao/nm
Ni-270 ‘3 -0.177 0.169 19E
Ni-270 0 . 154 0 . 174 1218
Fe'E'a -0.271 1.206 19E
Fe'E l. 157 1. 191 19E
7068 0 . 116 0 . 204 1218

 

 

aEquilibrium approached by decarburization.

Table A.18. Data from Carburization Experiment A-7783-33.

Date: 7/24/76; Temperature: 1100°C; Duration: 60 hours;
H20( g) Concentration: 1 ppm; Quench: Gold Zone.

 

 

 

Final Mi croprobe
[C] Cal . Intensity
Weight (wt 1 ) Std. Ratio Lattice
Change by For Precip . (Mo ) Parameter
Alloy (%) Analysis Carbon (wt. 1) “TI ao/nm
Fe'E' 1.076 1.114 19E

 

 

Table A.19.

233

Data From Carburization Experiment A27783-35.

Date: 7/29/76; Temperature: 1100°C; Duration: 90 hours;
H20(g) Concentration: 1 ppm; Quench: Gold Zone.

 

 

 

 

 

 

 

 

Final Microprobe
[C] Cal. Intensity
Weight (wt 7) Std. Ratio Lattice
Change by For Precip. (Mb) Parameter
Alloy (1) Analysis Carbon (wt. 1) TT' aofimm
7068 0.102 0.174 1218
7264 0.170 0.177 19E 0.475 0.84:0.04 0.4324a
Ni-270 0.125 0.136 19E
Fe'E' 1.008 1.032 19E
8 _.
Ga -0.0001 nm.
0
Table A.20. Data From Carburization Experiment A-7783-36.
Date: 8/2/76; Temperature: 1215°C; Duration: 96 hours;
H20(g) Concentration: 1 ppm; QUench: Gold Zone.
Final Microprobe
[0] Cal. Intensity
Weight (wt 7) Std. Ratio Lattice
' Change by For Precip. (Mo) Parameter
Alloy ,(3) Analysis Carbon (wt. 1) TI' aO/nm
7261 0.152 0.183 1218
7263 0.191 0.250 1218
7264 0.146 0.181 1218 TP
7265 0.172 0.212 1218
7068 0.116 0.217 121B
Ni-270 0.150 0.174 1218
Fe'E' 1.01 1.18 1218

 

 

234

Table A.21. Data From Carburization Experiment A—7783-37.

Date: 9/8/76; Temperature: 1215°C; Duration: 108 hours;
H20(g) Concentration: 1 ppm; Quench: Cold Zone.

 

 

 

 

 

 

 

 

Final Microprobe
[C] Cal . Intensity

Weight (wt 1) Std. Ratio Lattice

Change by For Precip . (Mo ) Parameter
Alloy (%) Analysis Carbon (wt . 1) TI ao/nm
7262 0.415 0.462 1213 2.17 1.55:0.04 0.43133
7266 0.865 0.985 1213 7.20 3.19:0.04 0.42998
7267 0.670 0.677 19E 4.42 1.90:0.05 0.43038
7268 0.448 0.512 1213 2.11 0.92:0.03 0.4316a
Ni-270 0. 107 0 . 157 1218
Fe'E' 0.961 1.03 1218
a

da =0.0001 nm.
0

Table A. 22 . Data From Carburization Experiment A-778 3— 38 .

Date: 9/14/76; Temperature: 1215°C; Duration: 60 hours;

H20( g) Concentration: 1 ppm; Quench: Cold Zone .

Final Microprobe
[C1 Cal . Intensity

Weight (wt 1) Std. Ratio lattice

Change by For Precip . (Mo ) Parameter
Alloy ( % ) Analysis Carbon (wt . 1 ) TT ao/nm
7262 0 . 088 0. 0971 1218 TP
7266 0.526 0.626 1213 3.62 1.91:0.06 0.43008
7267 0.323 0.384 1213 1.85 1.50:0.02 0.43108
7268 0.146 0.202 1213 0.394 0.75:0.02 0.431b
Nil-270 0. 084 0. 0932 1218
Fe 'E' 0. 624 0.750 1218

 

 

aoa =0.0003 mn-
o

boa =0.0001 nm.

0

235

Table A.23. Data From Carburization Experiment A-7783-44.

Date: 10/9/76; Temperature: 900°C; Duration: 108 hours;
H20( g) Concentration: 1 ppm; Quench: Cold Zone.

 

 

 

 

 

Final. Microprobe
[C] Cal. Intensity
Weight (wt 1) Std. Ratio Lattice
Change by For Precip. (1142 Parameter
Alloy (Z ) Analysis Carbon (wt . X ) Ti ao/nm
7261 0. 075 0 . 100 1218
7263 0.195 0.218 1213 0.885 0.43208
7264 0.206 0.235 1218 1.342 0.90 0.02 0.43268‘
7265 0. 086 0 . 0987 1218
7068 0 . 031 0 . 107 1218
Ni-270 0.074 0.0953 121B
Fe'E' 0.781 0.832 1218
'87
0a =0 . 0001 nm.

0

Table A.24. Data From Carburization Experiment A-7783-45

Date: 10/16/76; Temperature: 900°C; Duration: 132 hours;
H20(g) Concentration: 0.5 ppm; Quench: Cold Zone

 

 

Final Microprobe
[C] Cal . Intensity
weight (wt 7) Std. Ratio Lattice
Change by For Precip . (Mo ) Parameter

Alloy (% ) Analysis Carbon (wt . Z ) TI ao/nm

 

7261 0.035 0.0603 1213
7263 0.038 0.0634 1213
7264 0.011 0.0580 1213
7265 0.037 0.0624 1213
7068a -0.031 0.0620 1213
Ni-270 0.049 0.0544 1213
Ni-27(? -0.058 0. 0538 1213
Fe'E' 0.501 0.544 1213

 

 

 

aEquilibrium approached by decarburization.

236

Table A.25. Data From Carburization Experiment A-7783-47.

Date: 10/23/76; Temperature: 900°C; Duration: 120 hours;
H20( g) Concentration: 0.5 ppm; Quench: Gold Zone.

 

 

Final Microprobe
[C] Cal . Intensity
Weight (wt 1) Std. Ratio Lattice
Change by For Precip . (Mo ) Parameter
Alloy ( Z ) Analysis Carbon (wt . Z) TI ao/nm

 

7261 0.024 0.0457 1218
7263 0.032 0.0445 1218
7264 0.026 0.0360 1218
7265 0.019 0.0436 1218
7068 -0.036 0.0505 1218
Ni-270 0.033 0.0425 1218
Fe'E' 0.407 0.444 1218

 

 

Table A.26. Data From Carburization hperiment A-7783-48.

Date: 10/28/76; Temperature: 900°C; Duration: 120 hours;
H20( g) Concentration: 0.5 ppm; Quench: Cold Zone.

 

 

 

Final Microprobe
[C] Cal . Intensity
Weight (wt 1) Std. Ratio Lattice
Change by For Precip. (Mo ) Parameter
Alloy ( Z) Analysis Carbon (wt . Z) T1 ao/nm
7262 0 . 083 0 . 10 2 1213
7266 0.083 0.081 1213 1.22 1.64:0.02
7267 0.202 0.243 1213 0.582 1.2510.02 0.43183
7268 0.176 0.191 1213 1.56 0.94:0.02 0.4320a
31-270 0.027 0.0423 1213
Fe'E' 0.380 0.411 1213

 

 

aoa =0.0001 nm.
0

Table A.27.

237

Data From Carburization Experiment A-7783-49.

 

 

 

 

 

 

 

 

Date: 11/3/76; Temperature: 900°C; Duration: 120 hours;
H20( g) Concentration: 0.5 ppm; Quench: Cold Zone.
Final Microprobe
[0] Cal . Intensity
Weight (wt Z) Std. Ratio Lattice
Change by For Precip. (Mg) Parameter
Alloy (Z) Analysis Carbon (wt. Z) Ti ao/nm
7262 0 . 007 0 . 0125 1218
72 66 0 . 007 0 . 0218 1218
7267 0.040 0.0458 1213 0.411 1.21:0.003 0.43138
7268 0 . 021 0 . 0349 1218 0. 042
Ni-270 0.0141 0.0166 1218
Fe'E' 0.168 0.191 1218
a ..
0a -000ml nm.
0
Table A.28. Data From Carburization Experiment A-7783-57.
Date: 11/9/76; Temperature: 900°C; Duration: 144 hours;
H20( g) Concentration: 0.5 ppm; Quench: Gold Zone.
Final Microprobe
[C] Cal . Intensity
Weight (wt 1) Std. Ratio Lattice
Change by For Precip . (Mo ) Parameter
Alloy (Z) Analysis Carbon (wt. Z) Ti- ao/nm
7262 0 . 0226 0 . 0326 1218
7266 0 . 0186 0 . 0362 1218
7267 0 . 0598 0 . 0465 1218
7268 0 . 0973 0 . 112 1218
Ni-270 0.0189 0.0299 1218
Fe'E' 0.287 0.312 1218

 

 

 

238

Table A.29. Data From.Carburization Experiment A27783-116.

Date: 1/22/77; Temperature: 1215°C; Duration: 48 hours;
H20(g) Concentration: 0.5 ppm; Quench: Cold Zone

 

 

 

Final Microprdbe
[0] Cal. Intensity
Weight (wt 1) Std. Ratio Lattice
Change by For Precip. (Q) Parameter
Alloy ( Z) Analysis Carbon (wt . Z ) Ti aO/nm
7261 0.064 0.0747 121B
7262 0.079 0.0628 1213
7263 0.065 0.0862 1213
7264 0.062 0.0640 1218
7265 0.057 0.0810 121B
7266 0.413 0.475 121B
7267 0.198 0.221 1218 T?
7268 0.072 0.109 1218 TP
7068 0.002 0.0783 121B
Ni-270 0.068 0.0704 1218
Fe‘E' 0.489 0.554 1218

 

 

Table A.30.

239

Data From Carburization Experiment A-7783-120.

 

 

 

Date: 1/25/77; Temperature: 1215°C; Duration: 60 hours;
H20( g) Concentration; Quench: Cold Zone.
I Final Microprobe .
[C] Cal . Intensity
Weight (wt 1) Std. Ratio Lattice
Change by For Precip. (Mo ) Parameter
Alloy (Z) Analysis Carbon (wt. Z) TI ao/nm
7261 0.132 0.147 1218
7262 0.352 0.361 1218 TP
7263 0.142 0.173 1218
7264 0.127 0.124 1218
7265 0.146 0.153 1218
7266 0.781 0.867 1218
7267 0.598 0.652 1218 TP
7268 0 . 423 0. 4 51 1218 T?
7068 0 . 084 0 . 1 52 1218
Ni-270 0 . 150 0 . 144 1218
Fe'E' 0.911 1.01 1218

 

 

 

240

Table A.31. Data From Carburization Experiment A.--7783-123a

Date: 2/8/77; Temperature: 1215°C; Duration: 72 hours;
H20(g) Concentration: 0.5 ppm; Quench: Cold Zone.

 

 

 

Final
[C] Cal.
Weight Initial (wt 1) Std. .
Change [C] by For Precip.
Alloy (Z) (wt Z) Analysis Carbon (wt. Z)
7261 +0.020 0.147 0.137 1218
7262 +0.001 0.361 0.346 1218 TP
7263 -0.027 0.173 0.163 1218
7264 +0.003 0.124 0.125 1218
7265 -0.085 0.153 0.143 1218
7266 -0.034 0.867 0.859 1218 TP
7267 -0.017 0.652_ '0.634 1213 TP
7268 -0.055 0.451 0.423 1218 -TP
7068 -0.005 0.152 0.143 1218
Ni-270 +0.008 0.144 0.131 1218
Fe'E' -0.106 1.01 0.959 1218

 

 

aEquilibrium approached by decarburization.

Table A.32.
Date:

Data From Carburization Experiment A.-7783-125.a

2/11/77 ; Temperature:
H20(g) Concentration: 0.5 ppm; Quench: Gold Zone.

241

1100°C; Duration: 96 hours;

 

 

 

Final
[C] Cal.
Weight Initial (wt Z) Std.
Change [C] by For Precip.
Alloy (Z) (wt. 5:) Analysis Carbon (wt. 1)
7261 -0.071 0.147 0.0691 1213
7262 -0.126 0.361 0.218 1213 TP
7263 -0.074 0.173 0.0745 1213
7264 -0.069 0.124 0.0570 1213
7265 -0.058 0.153 0.0714 1213
7266 -0.096 0.867 0.763 1213 TP
7267 —0.110 0.652' 0.515 1213 TR
7268 -0.135 0.451 0.316 1213 TR
Ni-270 -0.076 0.144 0.0643 1213
Fe'E' -0.352 1.01 0.565 1213

 

 

aEquilibriumapproached by decarburization.

242

Table A.33. Data From Carburization Experiment A.-7783-136.a

Date: 2/17/77; Temperature: 990°C; Duration: 192 hours;
H20(g) Concentration: 0.5 ppm; Quench: Gold Zone.

 

 

 

Final
[C] Cal.
Weight Initial (wt 1) Std.
Change [C] by For Precip.
Alloy (Z) (wt. Z) Analysis Carbon (wt. Z)
7261 -0.016 0.075 0.049 1213
7262b -0.002 0.218
7263 -0.006 0.087 0.0847 1213
7264 -0.011 0.064 0.0537 1213
7265 -0.030 0.081 0.0472 1213
7266b +0.004 0.763
7267b - +0.009 0.515
7268b +0.003 0.316
7068b -0.015 0.078 0.0578 1213
Ni-270 -0.030 0.070 0.0447 1213
Fe'E' -0.113 0.553 0.462 1213

 

 

aEquilibrium approached by decarburization.
quuilibrium.was not achieved in these alloys.

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I'. ll il."«.

I 111‘! 31’- .Ill.l J1