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ABSTRACT

THE EFFECT OF INCLUDED PHASES ON THE
. GROWTH OF PLAGIOCLASE PORPHYROBLASTS

by
Kim Kathleen Ryan

Burke (1968)* has developed a model for abnormal
(porphyroblastic) grain growth that can be tested on natural
metamorphic systems. His model states that when inclusion
coalescence or dissolution is controlling the rate of normal
grain growth, the grain size, D, is directly related to d/f
where d is the average inclusion diameter and f is the
inclusion volume fraction. .The presence of inclusions in
the matrix material during growth is critical in order to
establish the proper conditions for the occurrence of por-
phyroblasts.

This study tests this model using samples of a
metapelite containing plagioclase porphyroblasts. Correlation
coefficients between D and d/f of plagioclase matrix grains
are highly positive when these grains reach their optimum

size. However certain matrix grains show high negative

 

* . :

Burke, J.E. 1968: -Grain growth in Fulrath, R.M.
and Pask, J.A. (Editors) Ceramic Microstructures. John
Wiley 5 Sons, New York, pp. 681-700.

correlations and these are the precursor of porphyroblasts.
Thus, if the grain has reached a particular size and the
inclusions are no longer controlling the rate of growth,

porphyroblasts develop with inclusion free outer margins.

THE EFFECT OF INCLUDED PHASES ON THE
GROWTH OF PLAGIOCLASE PORPHYROBLASTS

BY

Kim Kathleen Ryan

A THESIS

Submitted to
Michigan State University.
in partial fulfillment of the requirements
for the degree of '

MASTER OF SCIENCE

College ofNatural Science
Department of Geology

1973

\? ACKNOWLEDGEMENTS

The author is deeply indebted to Dr. Thomas A.
Vogel who-served as my thesis advisor for his support and
friendship throughout the past two years.

Special thanks are extended to Dr. Samuel B.
Upchurch for his encouragement and help during the final
stages of this study.

Thanks are also expressed to John L. Mrakovich,
Michael P. Ryan, Barb Fishel, Dennis P. McDonald and all
my other friends in the Geology Department for their

support.

ii

TABLE OF CONTENTS

Page
LIST OF TABLES . . . . . . . . . . . . . . . . iv
LIST OF FIGURES . . . . . . .‘. . . . . . . . v
INTRODUCTION . . . . . . . . . . . . . . . . . 1
BURKE'S MODEL: GRAIN GROWTH AND
EFFECT OF IMPURITIES . . . . . . . . . . . . . 4
TEST OF BURKE'S MODEL: AREA SELECTED
AND METHOD OF STUDY . . . . . . . . . . . . . 12
CONCLUSIONS . . . . . . . . . . . . . . . . . 38
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . 39

iii

Table
1.

LIST OF TABLES

Page
Ranking and Grouping of Grains
according to Size Distribution . . . . . 19
Dm vs. d/f: Correlation Coefficients,
r, per Size Grouping . . . . . . . . . . 23

iv

LIST OF FIGURES

Figure Page

1. Plagioclase porphyroblast with
inclusions in center (about 50K)

crossed pOIEI‘S o o o o' o o o o o o o o o z
2. Plagioclase matrix grain with

inclusions in center (about lOOX)

Crossed polars . . . . . . . . . . . . . 2

3. Grain growth limits from Hillert
(1965) 0 O O O O O O 0 O O O O O O O O O 8

4. Stabilization of variance of inclusion
diameters. Selected examples demon-
strate variation of curves . . . . . . . 15

5. Size-frequency diagram of plagioclase
matrix grains . . . . . . . . . . . . . 17

6. Dm vs. d/f correlation diagram . . . . . 21

7a. Inclusion-filled plagioclase grain
with straingt boundaries (about 100K)
Plane light 0 O O O O O O O O O O O O 0 25

7b. Same grain as 7a. Shows distribution
of inclusions (about 100K)
Plane light . . . . . . . . . . . . . . 25

8a. Plagioclase matrix grain with
relatively inclusion-free areas
(about 200K)

Crossed 1301815 0 o 'o o o o o o '. o o o o 27

8b. Same grain as 8a (about ZOOX)
Plane light . . . . . . . . . . . . . . 27

9. Plagioclase matrix grain with
inclusions in center and clear rim.
Note curved boundaries (about 100K)
Crossed polars . . .‘. . . . . . . . . . 29

V

Figure Page

10. Plagioclase matrix grain. Note
coalesced quartz inclusions in
center (about 100K)
Crossed polars . . . . . . . . . . . . . 29

11a. Plagioclase porphyroblast with
well-developed plagioclase rim
(about 50X) ‘
Crossed pelars . . . . . . . . . . . . . 31

11b. Enlargement of right half of 11a
showing rim and cuspate boundaries
(about 50K)
Crossed polars-. . . . . . . . . . . . . 31

12. Compositional ranges of An content
between plagioclase matrix grains
and plagioclase porphyroblasts . . . . . 33

13a. Na-Ka X-ray microprobe image. Note
variable concentration of sodium.
Dark areas are quartz grains . . . . . . 35

13b. Ca-Ka X-ray microprobe. Same

area as 13a. Note calcium
deficiency in upper portion . . . . . . 35

vi

INTRODUCTION

The exaggerated or abnormal growth of certain
minerals has long been an enigma to metamorphic petrologists.
The purpose of this study is to test a model for abnormal
grain growth proposed by Burke (1968) in order to ascertain
why some minerals attain porphyroblastic size during growth
in polycrystalline aggregates whereas others of the same
species do not (Figure 1, 2). Porphyroblasts are grains in
la metamorphic rock that exhibit this abnormal growth and are
frequently five to ten times larger than the matrix grains
(Spry, 1969).

Plagioclase commonly assumes porphyroblastic habit
in metamorphic rocks (Crawford, 1966; Cooper, 1972). Various
theories (Turner, 1948; Ohta, 1972) have been formulated to
explain the development of plagioclase porphyroblasts, but
noneof them provide a satisfactory general model. Turner
(1948) proposes that metasomatic processes form albitic
porphyroblasts while Ohta (1972) formulates that they are
developed through the coalescence of a mosaic of plagioclase
matrix grains under high vapor pressure and temperature.
Metallurgists and ceramists have studied exaggerated grain
growth for many years. J. E. Burke (1968) proposed a general
,model for their development which was based to a large extent
on the earlier work of Kingery (1962).

1

Figure 1.--Plagioclase porphyroblast with inclusions in
center (about 50X). Crossed polars.

Figure 2.--Plagioc1ase matrix grain with inclusions in
center (about lOOX). Crossed polars.

 

 

 

 

 

 

 

I
I

BURKE'S MODEL: GRAIN GROWTH AND
THE EFFECT OF IMPURITIES

Burke's (1968) model for abnormal or porphyroblastic
grain growth is dependent upon the coalescence or dissolution
of included phases within a grain. The effect of the inclu-
sions is to alter the energy relationships so that an
imbalance is created and growth occurs.

During recrystallization in a polycrystalline solid
the grain size increases once a critical temperature is
reached. The grain boundaries migrate and the size distri-
bution and relative orientation of the grains within the
aggregate change. During growth, the neighboring grains are
consumed as others enlarge. Impurities in the material
radically alter the resulting texture.

Growth, impurity segregation at low temperatures or
grain boundary migration at higher temperatures, occurs in
order to minimize the energy of the system involved. The
rate of normal or continuous growth of a grain can be stated

as:

v = f(M,P)

where V is the velocity: M, the mobility: and P, the

driving force.

5

The driving force of grain growth, P, is due to
the difference in surface energies between two boundaries.
These boundary energies are predominantly caused by
lattice strain (Westbrook, 1967). Since boundaries are
thought to be an equilibrium state, grain boundaries migrate
towards their center of curvature (Harker and Parker, 1945).
Thus P is given by:
P ' 0(1/91 + 1/02) .
(Hillert, 1965)
where o is surface free energy and p1 and p2 are the two
principal radii of curvature.

Therefore the rate of growth can be represented by:
v - MOC1/pl + 1/p2).

The mobility of the boundary is dependent on tempera-
ture and the atomistic configuration of the boundary. Bound-
aries become mobile when an external energy source, usually
temperature, is raised to a level which exceeds the activation

threshold for the substance:

(Turnbull, 1951)

Qb is the activation energy; R, the universal gas constant;
T, temperature. Aust and Rutter (1962) have determined the

boundary mobility for a substance, Mo’ to be:

erb

Mo = ET—

6

e, the Naperian base; r, the atomic jump frequency; b, the
local distance of boundary movement per atomic jump; k,
Boltzmann's constant; and T, temperature.

This rate of continuous grain growth, V = f(M,P) is
profoundly changed by the presecence of included phases in the
growing substrate. The salient effect of inclusions is to
create a drag on the migrating boundary. This is caused by the
tendency of moving boundaries to cohere to stationary bound-
aries. ,

Zener (1949) quantified the amount of coherence of

drag as:
S = 0-2

where S is the amount of drag; 0, surface free energy; and

Z is related to the size and volume fraction of the dispersed
(included) phase. The drag per unit area of a migrating
boundary is inversely proportional to the particle radius for
a given volume fraction of a dispersed phase (Cahn, 1966).
The drag effect becomes critical during normal growth since
the driving force decreases as the grain approaches its
ultimate size.

Lficke and Detert (1957) proposed a theory which
stated that the rate of grain boundary migration is controlled
by the diffusion rate of the impurity atoms behind the bound-
ary. However if the driving force of the boundary is great
enough to overcome the impurity atmosphere, the boundary will

abruptly breakaway from the impurities. This breakaway is

7

dependent on the concentration of the impurities and temper-
ature. Lficke and Detert's theory was modified by Gordon and
Vandemeer (1962) and Cahn (1962) in order to better fit
experimental data (Aust and Rutter, 1959). One of the
principal modifications was that rather than an abrupt break
at a critical temperature a transition zone was defined
where abnormal growth may start.

The drag effect of inclusions can also be overcome
in two other ways either through dissolution or coalescence.
Turnbull (1951) states that the retardation of boundary
migration by inclusions is less effective at higher tempera-
tures due to coalescence. Beck g£_al. (1949) found that the
initial volume of the dispersed phase, the temperature
reached, and the resolution or coalescence of the dispersed
phase greatly effected the ultimate grain size.

For abnormal growth to occur the presence of impur-
ities in the matrix material is necessary during growth. As
the ultimate grain size is approached, the inhibiting effect
of the inclusions must decrease in order for further growth
to occur. Hillert (1965) defines two grain size limits, 1/22
above which no grain growth occurs and 1/3Z which is the limit
for normal grain growth, where Z is equal to 3f/4r and f is
the volume fraction of the inclusions and rris the average
radius of the inclusions. The grain sizes inbetween the two
limits are the critical ones for abnormal growth to begin

(Figure 3). Hillert further states that to initiate abnormal

Figure 3.--Grain growth limits from Hillert (1965).

 

 

Average Grain N0
Size Limit

A A

\

No Grain Growth

I...
l
r

/\

N
N

 

Abnormal Grain Growth -*~

Sir

Normal Grain Growth

 

\/\

 

 

10

growth the Z value must decrease either by increasing the
particle size (r) through coalescence or by decreasing the
volume fraction of the impurity (f) by dissolving the
included phase. Hillert's theory, which is to a large
extent a mathematical model, has been confirmed experi-
mentally by the earlier work of Beck gt_§1. (1949). In
addition, Beck §£_al, (1949) state that favorable sites for
growth (inclusion-free areas) must exist in some part of

the grain.
Burke (1968) emphasizes the importance of included

phases in order to establish the prOper conditions for
abnormal growth. Burke (1968) states that when inclusion
coalescence or dissolution is controlling the rate of
normal growth the grain size of the matrix material is

approximately:
D : 2d/3f = d/f

where D is the grain size; d, the inclusion diameter; and

f, the volume fraction of the inclusions. D1 is a critical

average grain size where the uniform dispersion of the

second phase prevents further growth:
D1 = (4/3)cr/£)

(Cahn, 1966;
Burke, 1968)
where r is the particle radius. As D approaches D1, the rate

of growth approaches zero. However as D approaches D1, a

11

highly curved boundary may have sufficient energy to con-
tinue migrating providing the concentration of the impur-
ities was not sufficient to prevent growth. As a conse-
quence of this condition local growth areas, free of
inclusions, would develop. If a series of local growth
events occurred around the periphery of the grain, the
grain would have a large enough number of sides for con-
tinuous growth assuming a sufficient material supply was
available (Von Neumann, 1952). Thus, abnormal growth would

occur.

TEST OF BURKE'S MODEL: AREA
SELECTED AND METHOD OF STUDY

Porphyroblastic and non-porphyroblastic rocks
were collected from a pelitic schist belt of the Grenville
Series located near Fernleigh in southeastern Ontario
(Hounslow and Moore, 1967) in order to test Burke's model
on the development of plagioclase porphyroblasts. The area
has been regionally_metamorphosed and the schist belt
exhibits a metamorphic gradient from chloritoid grade on the
southeast end to upper amphibolite on the northeast end.
In the Fernleigh area well developed porphyroblasts of
garnet, kyanite, staurolite, and plagioclase occur. Plar
gioclase was chosen for this study due to its known textural
responsiveness to changes in metamorphic gradient (Ehrlich
g£_al. 1972; Byerly and Vogel, 1973). The plagioclase
porphyroblasts increase in size up to approximately five
centimeters in diameter at Fernleigh as the metamorphic

gradient increases.
In order to ascertain if normal growth of the matrix

grains was being controlled by inclusion coalescence or
dissolution, the matrix grain size D was compared to d/f
by using standard petrographic techniques. Plagioclase
l-matrix grains were used exc1usively in this study because

12

13

these grains reflect normal growth conditions (i.e. less
than 1/32 or over 1/22 in size), and because the conditions
that lead to abnormal growth, due to included phases,
should be preserved in these grains. Porphyroblasts are
of little value for determining the initial cause of run-
away growth because they have exceeded the 1/32 limit and
did not stabilize. In order to reduce textural variation,
the plagioclase matrix grains studied were from rocks
collected only from the Fernleigh site.

USing a petrographic microscope a plagioclase matrix
grain was randomly Selected_on a thin section. The stage*
orientation and the traverse direction of the count were
randomized.

I For each of thirty-three plagioclase matrix grains,
the volume fraction of the inclusions, the diameters of the
inclusions, and the diameter of the matrix grain were measured.
The volume fraction of the inclusions, f, with in a plagio-
clase matrix grain was measuredby a point counting technique
described by Underwood (1970). A grid was inserted into one
ocular and superimposed on the grain at the appropriate power
so that unity during the count was not exceeded. The phases
counted were either plagioclase or inclusions, the inclusions
‘consist of quartz, magnetite, tourmaline, muscovite, and a
biotitic mica. To insure that a sufficient number of measure-
ments were taken with a ninety-five percent probability of

obtaining a significant result at the one percent level, a

14

total of 200 points were counted per matrix grain (Beyer, 1966).

The volume fraction was computed by the formula:
f = Pa /PT

where Pa is the total number of points falling on inclusions
and PT is the total number of points counted.

The longest diameters of the inclusions, d, which
fell beneath one of the random lines of the grid were
measured with a micrometer. The total variance of the
diameters was calculated after each ten measurements and
found to stabilize at fifty inclusion diameters (Figure 4).
After this only fifty diameters were measured and the mean
diameter for 50 measurements was used in further computations.

The maximum diameter of the entire matrix grain, Dm,
was measured optically using a micrometer.

As visual proof for the development of plagioclase
porphyroblasts from matrix grains, photographs were taken
to document the various stages of growth.

To detect compositional differences, preliminary micro-

probe analysis of a limited number of grains was performed.

Test of Model

 

In order to test the hypothesis that normal growth
\in plagioclase matrix grains was being controlled by inclu-
sion coalescence or dissolution (Dm = d/f), a size-frequency
diagram (Figure 5) (Table l) was constructed for the matrix

grains. Correlation coefficients, r, (Beyer, 1966) were

15

Figure 4.--Stabilization of variance of inclusion diameters.
Selected examples demonstrate variation of curves.

16

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17

Figure S.--Size-frequency diagram of plagioclase matrix
grains.

 

18

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19

TABLE l.--Ranking and Grouping of Grains according to
Size Distribution.

 

 

 

Grain Size(D ) d/f Groups Group
Number in mmm Numbers
4 .29585 .02161 1

20 .3298 .02725
3 .3492 .03420 2
17 .3492 .03815
8 .35405 .03194
29 .36375‘ .03320
14 - .3686 .03244
18 .3686 .04640 3
15 .38315 .03405
26 .38315 .01318
16 .38315 .04297
23 .3880 .04618
5 .40255 .02618
22 .40255 .04020
19 .4268 .02489 4
21 .4462 .03362 ‘
24 .4947 .00909
7 .4995 .01758
9 .5044 .00988
28 .5044 .01554 5
31 .5432 .03485
12 .5626 .01687
27 .5626 .01246 6
2 .56745 .02350
1 .5723 .04349
30 .5723 .03278
10 .5917 .01869
13 .6014 .03560
33 .6014 .03341 7
32 .6208 .04024
11 .6528 .01332
25 .7275 .01559 8

6 1.1058 .06925

 

20

calculated for each class interval to determine the degree
of covariance between Dm and d/f (Figure 6) (Table 2).

Correlation coefficients were also calculated for
the sample population (33 grains), for individual rock
samples and by thin section sample (5 grains), but no
significant differences in the magnitude of the coeffi-
cients were found.

As shown in Figure 6 and Table 2 moderately high
negative correlations were found for groups four and seven.
The grain sizes for these two groups fall into the upper
size classes of the bimodal distribution. These negative
correlations indicate that the grains which fall within
these c1asses.are no longer being controlled by inclusion
coalescence or dissolution or in other terms they are
potential grains for abnormal growth.

The high positive correlation for grain sizes which
lie in the size interval 5.01 to 5.50 millimeters demon-
strates that the growth of these grains is being controlled
by inclusion activity and possibly have almost reached their
most stable size under normal growth conditions.

Since the effect of inclusions does not become
critical until the ultimate grain size is closely approached,
the poor correlations for the other groups indicate that
during growth another inhibiting factor stopped the growth
of these grains. One cause is possibly that the initial
volume of the impurities within the grain was sufficient to

stop growth at a smaller size.

21

Figure 6.--Dm vs. d/f correlation diagram.

 

22

 

 

 

I
5.75

 

 

U
5.25

 

4.50

 

 

 

I
3.75

 

 

3.25

 

I
2.15

 

 

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o a. e.

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* MATRIX GRAIN SIZE (D...) in mmx 10'2

23

TABLE 2.--D vs. d/f: Correlation Coefficients, r,
pgr Size Grouping.

 

 

 

Group r
Number
1 ---
2 -0.05582
3 0.04789
4 -0.78266
5 0.97635
6 0.14108
7 -0.81357
3 ---

 

24

In Burke's model as the critical size (D1) is
approached growth will cease and the result should be
inclusion filled grains. Figures 7a, b shbws an inclusion
filled matrix grain with relatively straight boundaries.
However if the boundaries are sufficiently curved, the
driving force may be large enough to override the inclusion
drag effect and inclusion-free areas are produced and
Figures 8a, b display a matrix grain which has developed
this local inclusion-free growth areas. Figure 9 demonstrates
that through a series of local growth events a relatively
clear plagioclase rim has grown outwards from the inclusion
filled center of a matrix grain. Notice the curved boundaries.
Figure 10 shows coalescence of quartz within plagioclase
matrix grains. Figures lla, b are of a porphyroblast with a
well deve10ped plagioclase rim and with the majority of the
inclusions concentrated in the center. It is clear that in
many of the plagioclase porphyroblasts the grain boundary has
broken away from the inclusions. The driving force for this
breakaway may be highly curved, high-energy boundaries.

Preliminary microprobe analyses were run to detect
compositional differences between plagioclase matrix grains
and plagioclase porphyroblasts. The results are shown
graphically in Figure 12 and visually in Figures 13a, b.

The matrix grains are relatively homogeneous in composition
while the porphyroblasts show a wide range of anorthite con-

tent. This may suggest that part of the driving force for

 

25

Figure 7a.--Inclusion-filled plagioclase grain with
straight boundaries (about 100K). Plane
light.

Figure 7b.--Same grain as 7a. Shows distribution of
inclusions (about lOOX). Plane light.

26

 

 

 

 

 

27

Figure 8a.--P1agioc1ase matrix grain with relatively
inclusion-free areas (about ZOOX). Crossed
polars.

Figure 8b.--Same grain as 8a (about 200K). Plane light.

28

 

         

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.. .ge‘.t) b ,A‘.\

   

vlsv ‘4ch €50- a. . . . I .
a CNN.
0!“. .

2w 1.. ., .

 

 

 

 

 

 

 

 

 

 

I! I1.,l..iu|il .l‘ll... 2'

29

Figure 9.--Plagioclase matrix grain with inclusions in
center and clear rim. Note curved boundaries
(about lOOX). Crossed polars.

Figure 10.--Plagioclase matrix grain. Note coalesced
quartz inclusions in center (about lOOX).
Crossed polars. '

30

 

 

 

 

 

 

31

Figure lla.--Plagioc1ase porphyroblast with well-developed
plagioclase rim (about 50X). Crossed polars.

.Figure llb.--Enlargement of right half of 11a showing rim
and cuspate boundaries (about 50X). Crossed
polars.

‘

 

 

 

 

 

 

 

 

33

Figure 12.--Compositiona1 ranges of an content between
plagioclase matrix grains and plagioclase
porphyroblasts.

 

NUMBER

GRAIN

34

 

7:

H

31-

24

13.

12-

 

PORPHYROBLASTIC GRAINS

JL

1?
JL

MATRIX GRAINS

A

 

I I T W I
10 15 2. 25 3.

9a An Content

 

35

Figure 13a.--Na-Ka X-ray microprobe image. Note variable
concentration of sodium. Dark areas are
quartz grains.

Figure 13b.--Ca-Ka X-ray microprobe image. Same area as
13a. Note calcium deficiency in upper
portion.

36

 

 

 

 

 

 

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, .1”. III. ‘lfi

 

.41 I

37
the runaway growth of the porphyroblast is that the
plagioclase actually consists of two or more distinct

feldspars, one of which'is_a£ting as an included phase.

at,

CONCLUSIONS

The results of this study indicate that Burke's
model for abnormal growth is a viable one for the develop-
ment of plagioclase porphyroblasts and that the role of
included phases within a growing matrix grain is critical
during normal growth. This study has shown that grains in
which included phases are no longer controlling growth are
likely candidates for porphyroblastic development. Once
runaway growth is initiated, it is maintained either by
highly curved, energetic boundaries or by the development
of included phases of similar composition as the host.

The preliminary microprobe work has shed some
light on the included phases (i.e. two plagioclases) in
the porphyroblasts, but it is obvious that this work must
be expanded to encompass the effects of impurities which
will re-dissolve and diffuse through the grains at elevated
temperatures. The microprobe data showed that high concen-
trations bf anorthite and albite exist within the porphyro-
blasts (Figure 12a, b). Through dissolutidn these impurity
concentrations could greatly effect the extent of growth
and must be evaluated for our complete understanding of the

formation of plagioclase porphyroblasts.

38

B IBLIOGRAPHY

BIBLIOGRAPHY

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Westbrook, J. H. 1967. Impurity effects at grain boundaries
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