ESQ-905511024“. SUBSTSTUTION EN
CRYSTALUNE SUBSTANCES

Thesis for £116 Dogma 6% Ph. Ba
MICHEGAN STATE SNEVERSETY
Roy Meficeim Miiler
1960

 

'5

£1.13“:

This is to certify that the

thesis entitled

\

ISO- POSITIONAL SUBSTITUTION
IN
CRYSTALLINE SUBSTANCES

presented by

ROY MALCOLM MILLER

has been accepted towards fulfillment
of the requirements for

effiwzam

Major professor

Date May 19, 1960

 

0-169

   
     

  

LIBRARY

Michigan State
University

 

ISO-POSITIONAL SUBSTITUTION IN

CRY STALLIN E SUBSTANCE S

By

Roy Malcolm Miller

AN ABSTRACT

Submitted to the School for Advanced Graduate Studies
of Michigan State University in partial
fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Geology

1960

Approved ll 3 . 5&W

ABSTRACT

The iso-positional substitution of ions in crystalline sub-
stances is not clearly understood. V. M. Goldschmidt’s concept of
ionic size, valency, and temperature as factors controlling substitu-
tion in ionic crystals is subject to investigation. AnhydrOus alumi-
num phosphate was selected as a crystalline substance for experi-
mental purposes due to its exceptionally close structural similarity
to cx-quartz. Crystalline aluminum phosphate was produced from
aqueous solution under pressure at 163°C. Minor quantities of tri-
valent gallium, iron, chromium, cobalt, and vanadium were allowed to
enter the crystalline framework in turn. The percentage of impurity
substituted was determined by spectroscopic analysis while X-ray
diffraction patterns indicated the corresponding changes in cell di-
mensions. Gallium substitution caused an 3 axis contraction with
increasing impurity. Iron and chromium entered the structure in
amounts less than 1.0 percent, expanding the 3 axis and contracting
the 3 axis. Less than 0.05 percent cobalt and vanadium were ac-
cepted by the crystal. Neither the ionic radius, electronegativity,

or ionization potential of the cations used in this investigation

ii

appear to be the controlling factors in their success in substituting
iso-positionally for aluminum. The electron configuration of the
trace ion attempting to proxy for the aluminum in the framework

appears to be the prime factor in its occupying a given structural

site.

iii

ISO-POSITIONAL SUBSTITUTION IN

CRY STALLINE SUB STANCE S

By

ROY MALCOLM MILLER

A THESIS

Submitted to the School for Advanced Graduate Studies
of Michigan State University in partial
fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Geology

1960

C3 20 865
5/24/55.

ACKNOWLEDGMENT S

The author expresses deep appreciation to Dr. H. B. Stone-
house for the inspiration and direction given during the course of
this investigation. The cooperation of the Department of Geology
and guidance of the committee members are gratefully acknowledged.

Many thanks are due the Department of Soil Science, Michi-
gan State University, and the Department of Mineralogy, University
of Michigan, for the use of laboratory facilities. The advice and
encouragement of Professors Ralph Erickson and L. S. Ramsdell
of the respective departments are accepted with gratitude.

Dr. J. D. Hill and Dr. J. Zinn very kindly contributed to the
progress of this investigation. The author thanks Mr. Gene Mondro
for assistance with photography.

The help and stimulus provided by fellow staff members of the
Henry Ford Community College as the project grew are highly appre-
ciated.

The study was supported by a grant from the Petroleum Re-

search Fund administered by the American Chemical Society.

iv

TABLE OF CONTENTS

Page

ABSTRACT .................................. 11
ACKNOWLEDGMENTS ........................... 1v
LIST OF TABLES ............................. vi
LIST OF FIGURES ............................. ix
INTRODUCTION ............................... 1
CRYSTAL CHEMISTRY .......................... 8
Crystal Theory ........................... 9
Crystal Growth ........................... 21
EXPERIMENTAL PROCEDURE ..................... 32
Addition of Trace Ions ..................... 33
Analytic Procedure ........................ 41
Treatment of Data ......................... 46
RESULTS ................................... 55
DISCUSSION OF RESULTS AND CONCLUSIONS ........ 76
Acceptance of Impurities .................... 77
Variation of a and g with Impurities ............ 78
Reasons for Acceptance of Impurities ........... 84
Conclusions ............................. 98
SUGGESTIONS FOR FURTHER WORK ............... 99
BIBLIOGRAPHY ............................... 101

TABLE

LIST OF TABLES

A Comparison of Closely Measured Physical
Pr0perties of oc-Quartz and Aluminum

Phosphate ...........................

A Comparison of Less Well Defined Physical

Properties of SiSiO4 and AlPO4 ...........

A Comparison of Physical Constants of Silicon

and Phosphorus .......................

Physical Data Concerning Crystalline Ortho-
phosphate Compounds Displaying Structures

Similar to Silica ......................

A Comparison of X-Ray Diffraction Data for
Commercially Prepared Aluminum Phosphate
with the Standard d- Spacings for Aluminum

Phosphate Hydrate .....................

A Tabulation of the Impurity Content of Ortho-
phosphoric Acid as Supplied by the Manu-

facturer ............................

A Comparison of X-Ray Diffraction Data for
the AlPO4 Crystals with Standard Data

from the ASTM Index ..................

Ionic Radii Values Assigned the Cations Linking
the P04 Tetrahedra in the Crystal Structure

of AlPO4 ............................

A List of Substances Supplying Cation Impuri-

ties for Substitution in AlPO4 .............

vi

Page

11

13

16

23

24

29

34

36

TABLE

10.

11.

12.

13.

14.

15.

16.

17-A.

17-B.

17-C.

17-D.

1'7-E.

18-A.

A List of Proposed Mol Ratios between
Impurity Cations and AlPO4 ...............

A Table of Weights of Selected Impurities
Added to the Crystallizing AlPO4 Solution

The Most Effective Instrumental Settings for
the X-Ray Diffractometer ................

A Comparison of 20 Values for Selected Dif-
fraction Peaks with Those Determined by
Huttenlocher (1935) .....................

A Table of Weighting Coefficients Assigned to
Values of a and g .....................

Inherent Contamination of AlPO4 Crystals Due
to Trace Elements Present in the Reacting
Materials ............................

The Results of Spectrosc0pic Analysis of AlPO4
Crystals in Which Specific Impurities Were
Incorporated .........................

Experimental 26 Values for Crystals of AlPO4
Containing Gallium as an Impurity ..........

Experimental 26 Values for Crystals of AlPO4
Containing Iron as an Impurity .............

Experimental 20 Values for Crystals of AlPO4
Containing Chromium as an Impurity .........

Experimental 29 Values for Crystals of AlPO4
Containing Cobalt as an Impurity ...........

Experimental 26 Values for Crystals of AlPO4
Containing Vanadium as an Impurity .........

Unweighted a and 2/ 2 Values (in A) for Crystals
of AlPO4 Containing Gallium ..............

vii

Page

37

38

45

47

54

56

57

63

64

65

66

67

68

TABLE Page

18-B. Unweighted a and _c_/ 2 Values (in A) for Crystals
of A1P04 Containing Iron ................ 69

18-C. Unweighted _a_ and 2/2 Values (in A) for Crystals
of AlPO4 Containing Chromium ............. 71

18-D. Unweighted a and 3/ 2 Values (in A) for Crystals
of A1P04 Containing Cobalt ............... 72

18-E. Unweighted a and 9/ 2 Values (in A) for Crystals
of A1P04 Containing Vanadium ............. 73

19. The Best Experimental 3 and 9/2 Values for
AlPO4 Crystals Containing Gallium, Iron,
Chromium, Cobalt, and Vanadium ........... 74

20. Electronegativity Values Assigned the Cations
Linking the P04 Tetrahedra in the Crystal
Structure of A1P04 .................... 37

21. Ionization Potentials Assigned the Cations Linking
the P04 Tetrahedra in the Crystal Structure
of A1P04 ............................ 90

22. Electron Configurations Assigned the Cations

Linking the P04 Tetrahedra in the Crystal
Structure of A1P04 .................... 91

viii

Figure
1.

10.

LIST OF FIGURES

Schematic free-energy vs. temperature plot
showing stable and metastable equilibria

between phases in the system AlPO4 ........

A diagram of the orthophosphate ion without

regard for the electron pairs involved .......

The orthophosphate ion depicted as a resonance

hybrid ..............................

An idealized diagram of the structural arrange-

ment of the ions in crystalline A1P04 ........

An exploded drawing of the stainless steel
pressure vessel used in growing crystalline

AlPO4 ..............................

An enlarged photograph of assorted crystals

of AlPO4 ............................

An enlarged photograph of a representative

single crystal of A1P04 .................

A comparison of the internal structures of

aluminum phosphate and 0<~quartz ...........

A graphic solution of the quadratic formula as
applied to two lattice planes of a hexagonal

crystal and solved simultaneously for a and g . . .

A diagram of the weighting factors versus vari-
ation in axial lengths for different combina-
tions of the quadratic formula representing

lattice planes .........................

ix

Page

12

14

15

18

25

27

28

31

48

52

Figure
11.

12.

13.

14.

15.

16-A.

16-B.

16-C.

16-D.

16-E.

comparison of selected diffraction peaks of
crystalline A1P04 containing gallium with

those of uncontaminated AlPO4 .............

comparison of selected diffraction peaks of
crystalline AlPO4 containing iron with those

of uncontaminated A1P04 .................

comparison of selected diffraction peaks of
crystalline AlPO4 containing chromium with

those of uncontaminated A1P04 .............

comparison of selected diffraction peaks of
crystalline A1P04 containing cobalt with

those of uncontaminated A1P04 .............

comparison of selected diffraction peaks of
crystalline A1P04 containing vanadium with

those of uncontaminated A1P04 .............

diagram of axial length versus percent
impurity for A1P04 crystals containing

gallium .............................

diagram of axial length versus percent
impurity for A1P04 crystals containing

iron ...............................

diagram of axial length versus percent
impurity for AlPO4 crystals containing

chromium ............................

diagram 'of axial length versus percent
impurity for AlP04 crystals containing

cobalt ..............................

diagram of axial length versus percent
impurity for AlPO4 crystals containing

vanadium ............................

Page

58

59

60

61

62

79

80

81

82

83

INTRODUCTION

INTRODUCTION

Fractional crystallization from the melt and substitution of
one element for another appear to be the primary chemical mechan-
isms creating the crust of the earth. Bowen (1922) is credited with
establishing the general pattern followed in fractional crystallization,
while Clarke and Washington (1922, 1924) provided quantitative evi-
dence that eight elements (0, Si, Al, Fe, Ca, Na, K, and Mg) con-
stitute the bulk of the earth’s crust. All other elements are called
as a group, accessory, minor, or trace elements (Rankama and
Sahama, 1950, p. 34).

The classical investigation of the structure and properties of
crystals by V. M. Goldschmidt (1926) directed attention to the prin-
ciples governing distribution of trace elements among the magmatic
minerals. Substances of analogous chemical formula which show
similar crystal structure were described as isomorphous, a term
which Goldschmidt (1931) credits to Mitcherlich. According to Gold-
schmidt, isomorphism appears when the relative size of the crystal
unit and the relative strength of polarization (within limits) are equal
for the two substances in question. Considerable interest was de-
veloped in the phenomenon in which atoms or ions of particular

2

elements occupy the structural positions of atoms or ions of other
elements in a mineral. Strunz (1937) used the term “diadochic” in
discussing this structural relationship and attributes the word to
Professor Niggli.

Making the assumption that ionic bonding prevails and the ion
making the larger contribution to the energy of the crystal structure
is preferred, Goldschmidt (1937) proposed a set of rules governing
diadochic substitution of ions in magmatic minerals:

a. For two ions to substitute diadochically one for another in

a crystal structure, the ionic radii must not differ by more
than 15 percent.

b. When two ions possessing the same charge, but different
radii, compete for a position in the crystal structure, the
ion with the smaller radius is preferred.

c. Ions having similar radii but different charges (of the same
sign) may substitute diadochically in a crystal; in which
case the ion having the larger charge has preference over
the ion with the smaller charge.

The discovery that ionic size of trace elements govern their
substitutional behavior to a greater extent than their position in the
periodic table was accepted as a fundamental relationship. However,
in recent years workers in the field have expressed the need for
revision of the rules governing trace element distribution among

common rocks and minerals. Fyfe (1951) and Ramberg (1952) called

attention to necessary modifications. Shaw (1953) questioned the

validity of the rules and listed exceptions to them. Ahrens (1952)
points to chemical bonding as the answer to much of the questionable
geochemical phenomena, with ionization potential as the clue to be
investigated. Ringwood (1955) proposes to modify the Goldschmidt
rules dealing with replacement of trace elements in magmatic miner-
als to allow for differing electronegativities of elements which dis-
play diadochy. The recent work of Kaiser and Bond (1959) on dia-
mond structure is illustrative of the current interest displayed by
investigators in the fields of solid state physics, crystallography,
ceramics, and geochemistry, concerning the relationship between
very minor amounts of impurity in crystals and the corresponding
alteration in crystalline physical properties.

The occurrence of silicon in the upper lithosphere makes
diadochic substitution in silicates of extreme importance to mineralo-
gists and geochemists. W. L. Bragg (1930) outlined the general na-
ture of many crystalline silicates by means of X-ray diffraction
studies. Subsequent effort has been made to extend this knowledge
and to establish relationships between known silicate structures and
the elements occupying specific positions in the frameworks. One
recent investigation (Goldsmith, 1950) is that of iso-positional re-
placement of Ga (III) and Ge (IV) for Al (III) and Si (IV) in sodium

and potassium feldspars.

The production of silica tetrahedral structures requires
pressures and temperatures not ordinarily available in mineralogy
laboratories. In one of the early studies concerning the crystallog-
raphy and stereochemistry of the inorganic compounds Goldschmidt
(1932) points to the possibility of YPO4, YAsO4, and CaCrO4 form-
ing isomorphous structures with quartz. Research organizations en-
gaged in silicate studies have continued to investigate the silicate
structures evidenced. by phosphates, arsenates, and vanadates as in-
dicated by the recent publications of Mooney (1956); Perloff (1956);
Shafer, Shafer, and Roy (1956); and others. In the search for a
substitute for crystalline quartz, in short supply during World War
II, Gruner (1946) reported a ' Signal Corps investigation of synthetic
aluminum phosphate.

Aluminum phosphate as a mineral was first described by
Blomstrand in 1868 and named berlinite (Palache, Berman, Frondel,
1951). Strunz (1941) proved the relatively rare berlinite to be es-
sentially aluminum phosphate. A similarity in crystalline structure
between aluminum phosphate and o<-quartz was reported by Brill and
deBretteville (1948) as part of a Signal Corps project. Stanley
(1954) developed a method for growing aluminum phosphate crystals
from aqueous solution at near ordinary temperature and pressure.

However, the piezoelectric properties of the synthetic crystal were

not within the tolerance required and the Signal Corps investigation
was abandoned.

Interest in the similarity of aluminum phosphate and d-quartz
was maintained by geochemists, and Manly (1950) emphasized the
close duplication of the physical and chemical properties of the sub-
stances. On the basis of this similarity it would seem logical that
in an investigation of Goldschmidt’s rules for diadochic replacement
of ions, synthetic aluminum phosphate might conveniently be used to
provide a replica of the silicon tetrahedral structure so common in
the upper lithosphere and trace element substitution made for the
aluminum cation. To limit the number of variables the ions selected
for substitution need to be trivalent and within the limitation of 15
percent of the size of aluminum.

By standardizing the crystallization process, the manner in
which the replacement ions enter the structure may be dependent
upon their radii, ionization potential, electronegativity, electron
configuration, or a combination of these. The number of impurity
ions replacing the aluminum cations can be determined by spectro—
graphic analysis. The effect of iso-positional substitution of foreign
ions on the lattice parameters of the aluminum phosphate crystal
may be followed by X-ray diffraction techniques. Measurement of

these two variables, when correlated with data pertaining to the

particular ion being substituted, bears directly on the Goldschmidt

rules and the revisions being proposed by current investigators.

CRYSTAL CHEMISTRY

CRYSTAL CHEMISTRY

Crystal theory

 

Textbooks of geochemistry (e.g., Goldschmidt, 1954) usually
list several phosphate minerals as being isotypic1 with silicate min-
erals. Among these is the pair aluminum phosphate (AlPO4) and
Ot-quartz (SiSiO4
gated this relationship over twenty years ago, and their publications

). Strada (1934) and Huttenlocher (1935) investi-

are of considerable interest (see Table l).

The quantities measured by X-ray, optical, and analytical
balance methods are exact physical properties and show the isotypic
qualities of the minerals. Table 2 indicates that the less well-defined
characteristics of the two minerals appear even more similar. A
compound with such~ extensive similarities to <X-quartz as aluminum
phosphate is likely to display several polymorphic forms and the data
of E. C. Shafer and Roy (1957) support the validity of this assump-

tion (see Figure 1).

 

1Having analogous composition and closely similar crystal
structure, but not capable of intercrystallizing to form solid solu-
tion.

10

TABLE 1

A COMPARISON OF CLOSELY MEASURED PHYSICAL PROPER-
TIES OF CX-QUARTZ AND ALUMINUM PHOSPHATE

 

 

Item SiSiO4 ' A1P04

a 4.90 A 4.93 it

c 5.39 A 2 x 5.47 A
c/a 1.10 2 x 1.11
sp.g. 2.65 2.56

ne 1.553 1.524

nW 1.544 1.524
bi-ref. 0.009 0.006

 

aHuttenlocher (1935).

11

TABLE 2

A COMPARISON OF LESS WELL DEFINED PHYSICAL
PROPERTIES OF SiSiO AND AlPO a

 

 

4 4

Item fiSiSiO4 fAlPO4
Lattice hex-R hex-R
Crystal class 32 32
Cleavage not distinct none
Fracture conchoidal conchoidal
Hardness 7 6-1/2
Transmitted colorless transparent to

light translucent
Optic sign plus plus
Modifications alpha and beta alpha and beta
Temp. of inv. 573°C 585°C

 

aFord (1954).

12

 

 

 

-—-> Temperature (°C)
Figure 1. Schematic free-energy vs. temperature plot showing

stable and metastable equilibria between phases in the
system AlP04 (E. C. Shafer and Roy, 1957).

A comparison of the physical constants in Table 3 supports
the hypothesis that phosphate minerals should exist as isotypic with
silica minerals (Hendricks, 1944).

Van Wazer (1953) describes the orthophosphates as examples
of a simple tetrahedrally bonded phosphorus molecule-ion, with four
oxygen atoms arranged tetrahedrally about the phosphorous. Such
P0 tetrahedrons may produce chains, rings, or branched polymers

4
by sharing oxygen atoms between tetrahedra. The electronic

TAB LE 3

13

A COMPARISON OF PHYSICAL CON STANTS
OF SILICON AND PHOSPHORUS

 

 

Item Silicon PhOSphorus
Atomic number ............ 14 15
Atomic weight ............. 28.09 30.98 (phy. units)
Common isotopes ........... 27.98577 30.975
28.98566
29.98325
Common valence ........... 4 5
Ionic radius .............. 0.39 A 0.3—0.4 A
Electronegativity ........... 1.8 (ev) 2.1 (ev)
Ionization potential ......... 11.21 10.22 (ev/unit charge)

 

14

configuration of phosphorus (152, 232, 2p6, 3s2, 3p3, 3d0) appears to
account for its bonding properties. Quantum mechanical treatment
indicates the hybrid bond orbitals using _s and p electrons are such
that the bonds make tetrahedral angles of 109° (Van Wazer, 1953).
The five valence electrons of the atom are in the M or third quantum
shell. This shell can accommodate electron pairs in _s, p, and _d_
orbitals; the _s orbitals holding one electron pair, the p orbitals
three pairs, and the _d orbitals five pairs. In its normal state
phosphorus has two of its valence electrons in the s orbitals with
the three remaining electrons in the p orbitals. Thus three more
electrons can be acquired by sharing or taking those of other atoms
to fill the p orbitals. In representing the orthophosphate ion, Paul-
ing (1940, p. 242) used the notation shown in Figure 2 without re-

gard to the electron pairs involved.

 

. o .___
I
o—P=o
I
i. .0 .

 

Figure 2. A diagram of the orthophosphate ion without regard for
the electron pairs involved.

A more conventional configuration of the ion as a resonance hybrid

is shown in Figure 3.

15

 

 

 

 

F o '-3 ' o “-3 F o “-3 " o -3
I II | l
O=P-O O-P-O O-P=O 0—P-0
I I I u
_ O _ _ 0 _J - O a L O ..

 

 

 

 

Figure 3. The orthophosphate ion depicted as a resonance hybrid.

Interpretation of X-ray measurements (Van Wazer, 1953) shows
that in the orthophosphates all four P—O bonds average near 1.56 A;
whereas, Wells (1950, p. 569) lists the 81—0 bond lengths for 0(-
quartz as 1.61 A. The ionic radii of Si (IV) is 0.39 A (Table 3)
and Al (III) is 0.57 A (Table 8). The ability of aluminum to proxy
for silicon in the silicates is well known. It can be assumed that
the tightly bound PO4 tetrahedral unit of structure provides the alu-
minum phosphate crystal with quartz-like properties.

Aluminum phosphate is not unique as the only mineral re-
sembling O(-quartz. Caglioti (1935) and Braspeur (1936) investigated
ferric phosphate and noted its close resemblance to quartz while
among the recent investigators Dachille and Glasser (1959) report
BPO4 as a quartz analogue. However, Westbrook (1958) contributed
the interesting fact that aluminum phosphate is the only known com-

Pound exhibiting all the isomorphs of silica (see Table 4).

16

TABLE 4

PHYSICAL DATA CONCERNING CRYSTALLINE ORTHO-
PHOSPHATE COMPOUNDS DISPLAYING STRUC-
TURES SIMILAR TO SILICA

 

 

Phosphate a (A) _c_ (A) 111““:ng ' Sp. Gr.
AIPO4 4.93 5.47 x 2 585 :t 5 2.56
GaPO4 4.92 5.50 x 2 933 :i: 4 3.54
FePO4 5.04 5.62 707 :t 5 3.02
CrPO4 unknowna
CoPO4 unknownb
vpo4 unknownc
MnPO4 4.94 5.48 813 :t 5 3.20
BPO4 4.47 9.926 —— 2.22

 

aSee M. w. Shafer and Roy (1956).
bSee Rankama and Sahama (1950, p. 683).

cSee Rankama and Sahama (1950, p. 595).

17

The original study of aluminum phosphate is credited to the
German chemist, H. F. Huttenlocher (1935), and it is his work that
is cited in reference (Table 1). Huttenlocher was of the opinion
that aluminum phosphate existed as an ionic crystal containing Al
(III) and P (V) cations in combination with 0 (II) anions. The
crystal was indexed on a hexagonal lattice and the 3 axis length
reported to be double that of quartz. Renewed interest in aluminum
phosphate, created by the Signal Corps synthetic quartz investiga-
tion, caused its crystallography to be re-examined (Brill and
deBretteville, 1955). The essential conclusions of the recent in-
vestigation support Huttenlocher’s contention that Al (III) and P (V)
are the cations present. The structure is described as consisting
of an alternating sequence of planes which are occupied by aluminum
and phosphorus ions, respectively. The planes are perpendicular to
the _9 axis and the unit cell contains 3 molecules. Brill and de-
Bretteville assume the distance between 0 and Al differs from that
between 0 and P, and agree with the concept of ionic bonding.

The cell constants are reported by these authors as 4.97 A for a
and 10.84 A for 9.

The idealized aluminum phosphate crystalline framework

shown in Figure 4 is patterned after fl-quartz (Bragg, 1937, p. 84)

18

 

AlPOh projected on 001

o 'o o
Dunc;

5 O

o O)

O 30 O
o lo 0
AlPOh projected on hkO

Figure h. .An idealized diagram of’the structural
arrangement of the ions in crystalline AlPOh.

19

and represents the combined crystallographic data of Huttenlocher
and Brill and deBretteville. The ionic radii of oxygen (1.40 A),
aluminum (0.57 A) and phosphorus (0.35 A) are scaled to their re-
spective values but the framework is much expanded for illustrative
purposes. The tetrahedral groups lie on three layers at different
heights and probably the groups spiral as in quartz. The aluminum
phosphate crystal class is reported as 32 and very likely the bond-
ing shifts the cations from the idealized positions of the diagram to
those of less symmetry although no links between tetrahedral groups
need be broken and the spiral structure may be retained.

The question of the type bonding to be assigned AlPO4 is a
difficult one in the absolute sense. The coordinate structure of the
analogous silicate tetrahedron is established in the literature. This
tetrahedron is explained as due to the dimensions of the Si (IV) and
0 (II) ions. .

In an early paper on the structure of complex ionic crystals
Pauling (1929) wrote:

The crystals considered are to contain only small cations, with
relatively large electric charges, i.e., usually trivalent and
tetravalent cations, with crystal radii not over 0.8 A. All
anions are large (over 1.35 A) and univalent or divalent. The
most important anions satisfying this restriction are oxygen and
fluorine. Throughout our discussion the crystals will be re-

ferred to as composed of ions. This does not signify that the
chemical bonds in the crystal are necessarily ionic in the

20
quantum mechanical sense; they should not, however, be of the
extreme non-polar or shared electron pair type.

The difference in electronegativity is generally accepted as an indi-
cation of the amount of ionic bonding between atoms. Wells (1950,
p. 554) estimated the character of the Si—O bond as 37 percent ionic.
A recent inorganic chemistry reference (Moeller, 1957, p. 723) care-
fully points out there are no discrete Si (IV) and 0 (11) ions present
in the silica tetrahedron but each Si—O linkage is predominantly ionic
in character.

Considering the nature of the Al—O and P—O bonds existing
in aluminum phosphate, their ionic character may be estimated as
high as 50 percent for the former and near 35 percent for the latter.
It has been postulated in this discussion that the tetrahedral bonds of
the P04 unit are sp3 hybrid bond orbitals and obey the directional
characteristics of covalent bonding. Finding the argument on the
horns of a dilemma, the author prefers to follow the more recent
literature trusting future progress in bond theory will resolve the
problem. Investigation of the bonding of AlPO4 by Brill and de-
Bretteville (1955) produced evidence offered in support of its ionic

nature. By refined X-ray techniques the investigators captured 001

reflections and concluded the reflections from the aluminum and

21

phosphorus layers were cancelled by their ionic nature and the
faint line was due to the oxygen layers.

On this basis, aluminum phosphate meets the Goldschmidt re-
quirement that ionic bonding prevail in minerals to which the rules
of diadochic replacement apply and provides a crystalline structure
similar to that of o(-quartz. There remain the problems of producing
pure aluminum phosphate crystals and introducing impurities under

conditions normally found in a chemical laboratory.

Crystal growth

 

The following method for producing crystalline aluminum phos-
phate by a reaction between sodium aluminate and concentrated ortho-

phosphoric acid is described by Huttenlocher (1935).

NaAlO2 + 2H3PO4 ——> AlPO4 + NaH2P04 + 2H20

The product was formed by heating the reactants in a closed pipe
for several hours at 250°C. In attempting to produce AlPO4 by this
method, problems of contamination from the container surfaces, main-
tenance of the pressure seal at high temperature and the formation

of hydroxides were met with. Other methods were investigated

(Hummel, 1949) and the technique used by Stanley (1954) has been

22

selected as most advantageous for this particular study. In his re-
port, Stanley states:
Good quality aluminum phosphate crystals were produced from
a solution of 1.45 moles aluminum phosphate per liter of 6.5 M
phosphoric acid when held in a glass lined stainless steel auto-
clave for 48 hours at 167°C.
A commercial oven controlled by a thermo-regulator to 42°C was
available. BIOS Laboratories, 17 West 60th Street, New York 23,
New York, supplied precipitated aluminum phosphate. An X—ray
powder analysis of this aluminum phosphate was made using a 57.3
mm Buerger camera, Cu target and Ni filter. The film was meas-
ured to the nearest 0.1 mm and no attempt made to correct for
shrinkage. A comparison (Table 5) with the ASTM card file indi-
cated the sample to be AlPO4-2H20.

Upon establishing the true molecular nature of the specimen
as an aluminum phosphate hydrate (AlPO4-2H20), the decision was
made to delay determination of its purity until after the anhydrous
form was crystallized. Orthophosphoric acid (H3PO4) meeting
American Chemical Society specifications was obtained from J. T.
Baker Chemical Company, Phillipsburg, New Jersey. The acid
analysis supplied by the manufacturer appears in Table 6.

A stainless steel pressure vessel was constructed by the uni-

versity machine shop (Figure 5) to contain a platinum crucible of

23

TABLE 5

A COMPARISON OF X-RAY DIFFRACTION DATA FOR
COMNIERCIALLY PREPARED ALUMINUM PHOS-
PHATE WITH THE STANDARD d-SPACINGS
FOR ALUMINUM PHOSPHATE HYDRATE

 

 

Intensities 51385:???) AligfaIC-lgdisate
(1) 2.72 A 2.71 A
(2) 1.96 1 -95
(3) 2.22 2.21

 

approximately 20 ml capacity. 'The pressure vessel lid, secured by
6 machine screws to a flange, was sealed by a lead gasket. The
crucible was covered with a platinum lid and no attempt made to
confine the reactants inside the crucible.

The phosphoric acid (6.5 M) was mixed in 100 ml volumes
(73.2 g. of 877° H3PO4 per 100 ml soln) as needed. A 1.5 moi/liter
concentration of aluminum phosphate in the acid was desired and to
produce this concentration 23.6 grams of AlPO ~2H 0 were mixed

4 2
with each 100 ml of 6.5 M phosphoric acid. Aluminum phosphate

24

TABLE 6

A TABULATION OF THE IMPURITY CONTENT OF
ORTHOPHOSPHORIC ACID AS SUPPLIED
BY THE MANUFACTURER

 

 

Lot Number 90782 Percent
Assay (H3PO4) ............................. 87.0
Chloride (C1) .............................. 0.0002
Nitrate (N03) .............................. 0.0005
Sulfate (s04) .............................. 0.002
Volatile acids (as HC2H302) ................... 0.001
Alkali and other phosphates .................... 0.05
Arsenic (As) .............................. 0.00003
Heavy metals (as Pb) ........................ 0.0005

Iron (Fe) ................................. 0.003

L

 

 

 

 

 

 

 

 

 

 

  

DART? LIST
NC. DART NAME SIZE RES} 1"
_ ' "37555 H:
‘ :45331 'mewmx§” 6
LID
STA/NLESS' STEEL
f3 052/55
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SPACED

 

 

 

 

Figure 5. An exploded drawing of the stainless 3555:- «'6 i’ES‘F‘E.’
steel pressure vessel used in growing D“ “A av R ~ 575 PM k
l_/ _(A I ~ ~ A E 3'."

crystalline AlPOh .

26

hydrate is not immediately soluble in the acid and considerable heat
is evolved in mixing. If allowed to stand undisturbed for 6 or 8 days the
mixture will reach equilibrium, and with the exception of a small amount
of unidentified brown precipitate appears similar to pure orthophosphoric
acid. The precipitate was avoided in this experiment by drawing off su—
pernatant liquid by means of a pipette. Samples of the reactants (15—20
ml) were placed in the platinum crucible, sealed in the pressure vessel,
and raised to 163°C. After standing 24 to 48 hours at this temperature,
the pressure vessel was rapidly cooled by plunging into cold water
and then unsealed. The walls and bottom of the platinum crucible
supported the yield of crystalline aluminum phosphate.

When separated from the mother liquor, washed, and dried,
the crystals appear as in Figures 6 and 7. They are uniformly
small, clear, well-formed, and up to 1 mm in length. The scaleno-
hedron form is noticed and fully developed rhombohedral faces are
the rule. Despite the similarities of aluminum phosphate to cot-quartz,
the crystal habits do not bear a close resemblance. A sample of the
crystalline material (powdered in an agate mortar) was mounted in a
114.6 mm Buerger camera, placed in an X-ray beam (1.5418 A) and
exposed for 6 hours to capture the lines in the back reflection re-
gion. The measurements were corrected for film shrinkage and the

d-spacings compared (Table 7) with those listed in the ASTM index

for crystalline AlPO4.

 

 

Figure 6. Km enlarged photograph of assorted crystals of «‘l .a.

28

   

0.25 mm

Fizure T. An enlarged photograph of a representative sinrle crystal of 51“

29

TABLE 7

A COMPARISON OF X-RAY DIFFRACTION DATA FOR THE
A1P04 CRYSTALS WITH STANDARD DATA
FROM THE ASTM INDEX

 

 

Intensity ASTM Experimental
(100) 3.32 A 3.363 A
(100) 1.38 1.387

(80) 4.27 4.275

 

For the 29 values less than 90° listed in the ASTM index,
the film was overexposed and the discrepancy invalues is due to
inability to locate the centers of the diffraction lines. Comparison
of the weaker lines in the back reflection region with those of the
original work (Huttenlocher, 1935) confirm the crystals as A1P04.

In order to compare the internal crystal structure of alumi-
num phosphate with cat-quartz, samples of each were powdered and
subjected to X-ray analysis. The machine used was an X-ray

spectrometer (to be described) and a strip-recorder charted the

reflections between 29 angles of 20° and 60°. The close

30

resemblance of the internal structures (Figure 8) confirms the work
of earlier investigators reporting similarities in physical properties

of the two substances.

31

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2.: 5.. .« mm o. «055 mien
O C O
bm .3 .5 .3 .o N .o n .«n .3 .3 .o n .0: .9. .cv .3 .9 .0... . 3 .3 .w... .8 .3
. . . . _ . . . . . . . . . . . . . _ . .
‘ g5:§§23§§3::§§. ass. Snsggassxssssssassass xx
0. o. E a
1. my on c...
. to .m.w
C... 03
CV 01

 

 

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O
L"

EXPERIMENTAL PROCEDURE

32

EXPERIMENTAL PROCEDURE

Addition of trace ions

The ions selected to substitute diadochically for aluminum in
the structure of AlPO4 were gallium, iron, chromium, cobalt, and
vanadium. In making an arbitrary choice of experimental conditions
to satisfy Goldschmidt’s rule, the first consideration was that of
retaining the ionic radii within the 15 percent Size limitation and
second was that of selecting relatively stable trivalent ions. Values
for the ionic radii of the trivalent ions chosen are given in Table 8.

It is apparent that the value cited for the Fe (III) cation is
near the 15 percent tolerance set as an upper limit by Goldschmidt’s
rule. The ions listed in Table 8 are considered to have a coordi-
nation number of 6, with 4 as an alternative (Welcher and Hahn,
1957, p. 162). These elements are readily available as highly puri-
fied metals and they are also commonly found as salts and oxides.

A desirable procedure was to combine the Fe (III) and Cr (III)
ions with the crystallizing solution by adding hydrated phosphate com-
pounds obtained as fine chemicals from BIOS Laboratories. Cobaltic
oxide (Baker, CP) and powdered cobalt metal were in laboratory
stock. Gallium and vanadium were purchased in metallic form from

33

34

TAB LE 8

IONIC RADII VALUES ASSIGNED THE CATIONS LINKING
THE P04 TETRAHEDRA IN THE CRYSTAL
STRUCTURE OF A1P04a

 

Trivalent

 

Ion Value
Al (III) 0.57 A
Ga (III) 0.62
Fe (III) 0.67
Cr (III) 0.64
C0 (III) 0.65
v (III) 0.65

 

aEvans (1952, p. 171).

35

E. H. Sargent and Company, 4647 West Foster Avenue, Chicago 30,
Illinois.

It is assumed that iso-positional substitution of sufficient
numbers Of a given impurity ion will alter the a and c axial lengths
of the aluminum phosphate structure. One of the purposes of this
investigation is to explore the range of impurity necessary to change
the lattice parameters. Addition of impurity elements to the reactants
in amounts of 2.5, 5, 7.5, 10, 15, 20, and 25 percent, by mol weight,
seemed a practical first approximation toward determining the quan-
tity of impurity needed to produce a detectable structural change.
The chemicals listed in Table 9 were those selected to supply ions
for diadochic substitution in the crystalline framework.

The mol ratios, listed in Table 10, between trace element

compounds and AIPO provide the range of impurity desired. The

4
20 m1 volume limit of the platinum crucible (4.73 g. AlP04-2H20)
dictated the weights of impurity compounds as indicated in Table 11.
A high degree of accuracy in weighing was unnecessary to
present the crystal with relatively increased numbers of trace ions.
For any individual crystalline sample, the temperature was raised
without fluctuation from that of the room to the constant temperature
held by the oven. The regulation of the laboratory oven would not

permit constant temperature to be maintained above 163°C. In all

36

TABLE 9

A LIST OF SUBSTANCES SUPPLYING CATION
IMPURITIES FOR SUBSTITUTION
IN AIPO

 

 

4
Substance Q‘Ilglplttiirtftyd
Ga (metal) 69.72 g/mol
FeP04-2H20 186.86
CrPO4-3H20 201.03
C0203 165.88
Co (metal) 58.94

V (metal) 50.95

 

TABLE 10

A LIST OF PROPOSED MOL RATIOS BETWEEN
IMPURITY CATIONS AND AlPO

 

 

4
Percent M01 Ratio
2.5 .039/1.5

5 .079/1.5
7.5 .112/1.5

10 .150/1.5
15 .265/1.5
20 .390/1.5

25 .500/1.5

 

38

TABLE 1 1

A TABLE OF WEIGHTS OF SELECTED IMPURITIES ADDED
TO THE CRYSTALLIZING AlPO SOLUTION

 

 

4
Pet.
€512?“ (griaIInS) F333 035:3 CO203 V
limit)
2.5 0.054 0.0832 0.151 0.129 0.0298
5 0.080 0.205 0.318 0.262 0.083
7.5 0.128 0.305 0.450 0.372 0.114
10 0.210 0.416 0.603 0.498 0.155
15 0.259 0.694 1.065 0.880 0.210
20 0.464 0.916 1.568 —— 0.314
25 —— 1.194 2.010 0.460a _—
30 —— 1.388 —— _— _...

 

aPowdered metal.

39

trials the crystals formed on the sides of the crucible below the sur-
face of the liquid. The bottom of the crucible was covered in each
case with deposited crystalline material and in trials using more

than 5 percent impurities the bottom crystalline mass was contami-
nated by a residue of undissolved impurity.

Gallium as an impurity proved quite active when added to the
aluminum phosphate solution. The reaction was immediate, gaseous,
and the most pronounced of any observed, although the solution re-
mained clear and colorless. The crystals were the smallest pro-
duced and did not Show the characteristic well-formed faces found
in other series. They were opaque, white in color, and in good
yield. The mother-liquor remained clear.

The ferric phosphate hydrate was pale yellow-brown in color
and when mixed with AlPO4-H3PO4 solution the Slurry took on a
yellow-brown, milky appearance. The crystals produced were opaque,
grading from white to a shade of brownish-yellow with increasing
concentration of FePO4-2H20. The solution remaining at the end of
the crystallization process was clear and colorless. The blue-green
chromic phosphate hydrate mixed with the reactants in the same
manner as ferric phosphate hydrate. The crystals coming from a

clear solution at the end of the process were a pale shade of green

and the color intensified with increasing chromium content. No

40

marked chemical reaction was noticed while mixing either of these

phosphates with the crystallizing reactants. The crystals obtained
in these instances displayed the typical habit of aluminum phosphate
and were of relative uniform size.

The C0203 appeared to remain inert and settled to the bot-
tom of the crucible when added to the AlPO4-H3PO4 reactants. Af-
ter being subjected to the crystallization process, the undissolved
cobaltic oxide remained mixed with the crystalline material in the
bottom of the crucible. In this series the solution took on a slight
blue coloration and the crystals growing on the sides of the crucible
appeared to be tinted blue. For the last trial of the cobalt series,
powdered cobalt metal was used in an attempt to introduce a higher
concentration of cobaltic ions. There was an immediate reaction in
which the solution turned a cloudy pink and considerable gas evolved.
The crystalline product was removed from a pink solution and was
not appreciably colored. Specks of cobaltic oxide and cobalt metal
were observed incorporated in the crystals of this series.

Small fragments of vanadium metal added to the AlP04-H3PO4
reactants produced a number of gas bubbles, but the solution did not
color and the gas remained attached to the metal. Upon completion

Of the crystallization process, the color of the solution was a clear,

brilliant green. Large crystals displaying well-formed faces were

41

grown in this series. A unique feature was the pinkish coloration
of the crystals contrasted to the bright, green mother-liquor.

The same technique was used to collect samples in each
trial. The prime concern was avoiding mixed crystals and other
debris on the bottom of the crucible. The material selected for
analysis was washed thoroughly and rinsed in alcohol. After dry-
ing at 163°C, the crystals were placed on a watch glass and in-
spected under a low-power microscope for inclusions and foreign
material. The platinum crucible and lid were scoured with fine sand
after each trial, washed, and rinsed with alcohol. The interior Of
the stainless steel pressure vessel was also scoured with steel wool
and washed between trials. It is assumed a minimum of impurity
worked into the crystallizing solution from the pressure vessel
walls. Pressure vessel deterioration occurred on each trial run,
and the interior of the vessel was well pitted and corroded as a

result of the crystal-growing process.

Analytic procedure

 

The analysis of crystalline A1P04 consisted of an X-ray dif-

fraction examination of the structure and a spectrOSCOpical determi-

nation Of the impurity content. The amount of sample was small, and

42

the material was X-rayed before being subjected to spectroscopic
analysis.

The X-ray diffractometer was a standard Norelco recording
model (Parrish, Hamacher, and Lowitzch, 1954) made available by
the Department of Soil Science. This particular diffractometer is
normally used for analysis of silica-bearing minerals in the spec-
tral region 0°<<29<<90°. The general procedure followed that of
Klug and Alexander (1954). The finely powdered sample was packed
into a planchet which was inserted in a flat spinner designed to ro-
tate the powdered surface in the beam of X rays (Parrish, 1956).
The diffracted X rays were captured by a geiger tube for recording
purposes.

The back reflection region (90°<<29<<180°) is known to be
advantageous for accuracy and resolution (Azaroff and Buerger, 1958),
and in order to detect changes in lattice parameters caused by less
than 1.0 percent impurity as much precision as possible is desired.
The recording goniometer head traversed a 29 angle of 0° to 150°.
In this research the goniometer was manually set for the maximum
angle of 150° and in each trial run allowed to sweep back across the
29 region being examined. High resolution requires slow goniometer
scanning speeds with the ultimate limit of scanning each peak man-

ually. However, in this investigation the minimum machine scanning

43

speed of 1/ 4° per minute was preferred to manual scanning. The
count-accumulation-versus—time-lag problem (Norelco Reporter, 1953)
was considered negligible for the seaming speed and time element
used. The X-ray diffraction peaks over the 29 range under obser-
vation appeared symmetrical and the alignment and angular calibration
of the goniometer correct. According to the literature (Parrish,
1956), peak shifts for this type of diffractometer are less than 0.01°
of 29 and peak position corrections are unnecessary. A sample of
quartz produced a pattern similar to that of Klug and Alexander
(1954, p. 258), and the measured quartz d-spacings closely approached
the values given by the National Bureau of Standards (Swanson and
Fuyat, 1954). An examination of the pattern traced by the diffrac-
tometer near its maximum 29} angle indicated satisfactory resolution
of the copper K-O( reflections into K-Or1 and K-sz components, and
corresponding to theoretical requirements, the K-Ot1 peaks are ap-
proximately twice the intensity of the K-oz2 peaks.

Two unexpected experimental problems arose in the form of
insufficient sample material and unstable sample mounting. The
amount of sample used for each analysis was limited by the condi-

g tions of crystal growth and several samples were in short supply.
In trying to overcome this deficiency, (I) a small amount of powdered

sample, mixed with an ether-collodion solution, may be poured into

44

the planchet, or (2) the bottom of the planchet might be built up us-
ing inert material with powdered sample packed on top. The second
alternative proved the better technique. Considerable care was taken
in packing the powdered sample into the planchet for an inclination
of 150° since a 29 angle of 180° places the spinning sample upside
down. Despite precautions taken, one sample was lost and the prob-
lem of retaining the powdered sample through large inclination angles
remains. Toward the end of the experimental run, the strip-recorder
appeared to lose sensitivity; otherwise the diffractometer operated in
a consistent manner throughout the sequence of measurements. Ex-
perimentation proved the instrumental settings listed in Table 12 to
be most effective.

Emission spectroscopy provides information as to percent
metal impurity in a sample of the order of 0.01 percent and requires
only a minute quantity of sample for an analysis. Such character-
istics are highly desirable for this particular experimental situation.
Due to the lack of spectroscopic facilities, the analysis was performed
by the Chicago Spectro Service Laboratory, 2454 West 38th Street,
Chicago 32, Illinois. Spectral analyses were made of a sample of

uncontaminated AlPO and on five series of mixed crystals, each of

4
which contained a specific impurity ion. Sample crystals from the

series containing chromium were also examined for change in

TABLE 12

45

THE MOST EFFECTIVE INSTRUMENTAL SETTINGS
FOR THE X-RAY DIFFRACTOMETER

 

Item

Setting

 

X-ray tube voltage

X-ray tube current

Take-off angle . . .

Scatter slit width .

Receiving slit width

Horizontal divergence ................

Filter .........

Chart speed .......................

Time constant . . . .

Scanning speed (29)

35kv

20ma

30

10

0.006 inch

10

nickel foil

1/8 inch per minute

4 sec.

1/4" per minute

 

46

refractive index with added impurity (Zinn, 1959). The results of

these analyses appear in the following sections.

Treatment of data

 

In 1935, Huttenlocher listed ten X-ray diffraction lines of
AlPO4 of appreciable intensity between the 29 angles of 130° and
150°. In the present study, a diffractometer survey of the same re-
gion produced six prominent, well-defined peaks on the strip-recorder
chart. These data and the Huttenlocher powder-camera data are
compared in Table 13.

An application of the quadratic formula for hexagonal crystals
to each of the above-mentioned peaks will provide an equation in two

unknown lattice parameters _a_ and _c_.
(Eq. 1) 1/d2 = 4/3a2(h2 + hk + k2) + 12/c2

By solving these equations in combination, the best values for _a_ and
_c_ may be determined (fifteen possible combinations). To check the
assumption that all planes are of equal value in such an operation,
Hill (1959) suggested a graphic examination of the situation (see
Figure 9). Such an examination requires the quadratic equation to

be changed to the linear form

TABLE 13

47

A COMPARISON OF 20 VALUES FOR SELECTED DIFFRACTION

PEAKS WITH THOSE DETERMINED BY

HUTTENLOCHER (1935)

 

Observed

 

29 Huttenécgcher’s hkl
133.14° 133.6° 404
135.65 136.2 413
140.89 140.8 225
144.28 144.3 331
146.17 145.6 420
149.64 149.8 421

 

(a)

 

 

    

 

48

 

C
x
0‘1
x
cot d1 (b)-—enlargement of (a)
zMGH = 0Q
--..-..- 3------“ +11- 4NHL = on
; GH = x cot o<2
: HL = A C
A : .LM = A A
----------------- MN = x
l
I
l
l
‘ I
‘ :
i i 0(1‘ of:
C

Figure 9. A graphic solution of the quadratic formula as applied to
two lattice planes of a hexagonal crystal and solved si-

multaneously for a and g.

49

(Eq. 2) 4/3(h2 + hk + k2)A + 12C - D = 0

where A = 1/a2, C = l/cz, and D = 1/d2.

Rearrangement of the linear equation provides the slope form, y =

mx+b.
2' 2 2 2
(Eq. 3) A=-3/4(h +hk+k)C+3/4(h +hk+k)D

It is evident from Equation 3 that the Miller indices control
the slope while any experimental error in d-Spacing affects the
intercept. Thus, each equation may be represented by a line broad-
ened to a zone by the experimental error (Figure 9-a). The inter-
section of two such zones provides an area in which solutions for
a and _c_ exist. It is apparent that a set of two equations with simi-
lar slopes (planes 421—331) produces a zone of intersection entirely
different from a set with dissimilar slopes (planes 225—331). Lines
running parallel have no common intersection (indeterminate Solution)
while the lines meeting at right angles have the most clearly defined
intersection.

The angle at which lines meet (Figure 9-b) determines the
area and shape of the parallelogram of intersection containing a and
_0. Since this angle changes with the slopes, the variation created

in a and _c_ follows some trigonometric relationship. Consequently

50

every pair of quadratic equations containing measured 29 values need
not be of equal importance when solving for _a and g. The ability of
the diffractometer to record to the nearest 0.01° and of the experi-
menter to interpret the strip-record with comparable accuracy con-
trols the variation in the intercept on A (Figure 9-a). In each in-
stance the Miller indices assigned to the lattice plane determines
the angle oc at which the line representing the plane meets the C
axis.

In order to determine the significance factor to be assigned
to each such pair, the range of the resulting Slope and intercept
variation is derived for the general case. The possible values for
A and C exist within the parallelogram of intersection and the
ranges are denoted by AA and AC. In Figure 9-b the slope of
line 1 is represented by the tangent of 0(1 and this angle also oc-
curs in triangle NHL as angle NHL. From the definition of tangent

function:

NM+ ML __
———————-—HL -tanO(1

by substitution,

AA+x_
T—tanoq

51

In triangle MGL the angle MGL is equal to 0(2. By definition:

by substitution,

AA _
AC + x cotC>(2 - tanO<2

 

In order to solve for AA and AC the expressions for 0(1 and «2

are combined to produce:

x tan 0(2 (cot O(1 + cot 0(2) -x (tan 0C2 coto<2 + 1)

AA = 1 - tano<2 cotc>(z ’ AC = tanOC2 - tan<>(1

 

 

Since 0(1 and «2 are controlled by hkl values and x is as-
sumed to be a constant, AA and AC may be evaluated for any spe-
cific set of lines. Each lattice plane represented by a line is as-
signed (Eq. 3) a value for 0(1. Holding OS and x fixed, AA and AC
are determined by using any other line producing an angle 0(2 with
the axis and intersecting this reference line. Repeating the pro-
cedure, in turn, for each of the Six reflection peaks provides data
used in preparing the graphs required to weight the relative impor-

tance of each intersection (Figure 10).

52

413-331, 413—421

   
 
    
  

x 4 13—404

3! 404—331, 404—421

AA or AC x 10-4

25—413, 225—404

225-421

413-331, 413—421—
14 404-331, 404-421/
225—331, 225-421/

 

 

i 3 4 5 6 7 8 ‘9
Weighting Factor

5.1-1

Figure 10. A diagram of the weighting factors versus variation in
axial lengths for different combinations of the quadratic
formula representing lattice planes in crystalline AlPO4.

53

The 420 plane fails to fit the graphic scheme for testing the
solutions and is omitted from further consideration. The intersec-
tion of lines representing 421—331 planes is considered indeterminate
and this pair is rejected. Each of the remaining intersections is
significant and a coefficient assigned to the importance of its solu-
tion. Note that an intersection of two given lines need not provide
solutions of equal Significance for both a and g. The magnitudes of
the weighting coefficients are listed in Table 14.

The X-ray measurements were reproducible and any variation
in results appears experimental in nature and primarily due to in-
strumental and propagation errors. The diffraction angles (29) are
presumed to be correct to 40.01°. The hkl planes, 413—225, were
selected to provide numbers tending to create a maximum propaga-
tion error when used with the quadratic formula. A value 0.01°
above, or below, the true 29 value causes 1/d2 to vary 40.0001 A
(NBS Applied Math Series 10, 1950). Solving the quadratic formula
(Eq. 1) for 3 produces an error of 40.0004 A for the hkl combina-
tion chosen. However, when solved for c this same hkl combination
provides the limiting error of 40.0024 A. In the weighting process
the final values of _a_ and 3 obtained are considered the best possible

and the attached error a maximum.

54

TABLE 14

A TABLE OF WEIGHTING COEFFICIENTS ASSIGNED
TO VALUES OF _a_ AND 9

 

 

Intersecting “’23::ng wg‘ifltggg

hkl Planes (3) (53)
225—404 x 1 x 2.8
413—404 x 1.7 x 15
413—225 x 2.5 x 2.8
413-331 x 3.6 x 1
413—421 x 3.6 x 1
404—331 x 3.8 x 2.4
404—421 x 3.8 x 2.4

225-331 x 4.2 x 4.1

225-421 x 4.2 x 4.1

 

RE SULT S

55

56

TABLE 15

INHERENT CONTAMINATION OF AlPO4 CRYSTALS
DUE TO TRACE ELEMENTS PRESENT IN
THE REACTING MATERIALS

 

Trace ppm as

Element Metals
Gallium 35
Iron 125
Chromium 6
Cobalt < 10

Vanadium < 10

 

TABLE 16

57

THE RESULTS OF SPECTROSCOPIC ANALYSIS OF AlPO4

CRYSTALS IN WHICH SPECIFIC IMPURITIES
WERE INCORPORATED

 

 

Sample Percent Percent Percent Percent Percent
Ga Fe Cr Co V
A 2.0 0.16 0.10 0.01 0.01
B 3.0 0.15 -— 0.03 ——
C 4.0 0.25 0.13 0.02 0.03
D 5.6 0.23 0.11 0.04 0.035
E 10.6 0.32 0.17 0.05 0.04
F 18.4 0.60 0.18 0.33"‘ 0.05
G —— 0.57 0.19 —— __
H ——- 0.61 -- __ ._

aConsidered in error due to metallic cobalt mixed with

sample.

 

M ALPO4 ' I8.4v.6a

. 106% Ga

     
 

ALP04 r 5.S7. Ga

ALP04 * 43% Ga

‘ I

ALPO“ + 2.07. Ga

W‘MW ["W I W

«37 I38 I39 I40 MI 142 I43 I44
ALP04

29

133 I34

|45 146 I47 I48 I45

r A‘k‘“Y—‘

SCALE FACTOR 8 1/4- PER MIN

Figure 11. A comparison of“ selected diffraction peaks of crystalline AlPO4 containing gallium with those of uncontaminated AlPO4.

 

 

 

WW WWW
W WWWM

     
  
  

NAWWWMWMW

 

ALPqu

WFWW WWMW

CCCCCCCCCCC

    

AAAAAAA

4* M
WWWMWWWW/M .

'I

 

 

 

 

   
 

WWW WWW W
W MIWMICS‘
C WWWWWWMWWWM M/ “
V WMWWwawW WY”

J
W WNW mm

 

 
 

(1:;-

w
{I

WWW»? l MMWMWW
WMWM WWO W WWW WWW

AAAAA

Figure 15 A comparison of selected diffraction peaks of crystalline AlPO4 containing chromium with those 0 cont inate A P0 .

 

 

 

I33 I34

Figure 149

IILPO4 0 03374:.
ALP!)4 v 0.057. Cum
ALPO4 9 0.04% Co
ALI'C4 + 0.03% Cu

' ALPS4 + 0.013;“

ALPO“ + «3.on co

    

A comparison of selected diffra

61

I39 MD MI I42 I43 1"

2 9 SCALE FACTOR 8

ction peaks of crystaIline AIPO4 containing cobalt

+ W

I45 I46 |47 MB “9
”4' PER MIN

with those of uncontaminated AlPO4.

 

I

N

   

 

I. l ADI .IY[..

. .. I
f .h‘...’ I J

 

MINI '
MI...

MW

ALPO4‘ 4' 0.035% V

.
<

ill-Pep 0.037. v

ALPOq 9 (3.le V

WI

I33

MO

‘3‘ I33

Figure 15. A comparison of selected diffraction peaks of crystal

 

 

' 1
1 I
L .
WWW‘WW W \
I42 I43 «44 I45 I46 I47 I49 I49
SCALE FACTOR 3 IM- PER MIN

line AlPO4 containing vanadium with thoce of uncontaminated AlPO4.

 

 

 

TAB LE 17 -A

63

EXPERIMENTAL 28 VALUES FOR CRYSTALS OF AlPO4
CONTAINING GALLIUM AS AN IMPURITY

 

 

 

Percent Ga
hkl L L
2 3 4 5.6 10.6 18.4

421 149.75° 149.79° 149.75" 149.72° 149.84° 149.82°
420 146.24 146.29 146.19 146.29 146.23 146.24
331 144.39 144.37 144.37 144.42 144.46 144.51
225 140.95 141.03 140.96 141.01 141.06 141.03
413 135.72 135.75 135.76 135.77 135.75 135.80
404 133.15 133.18 133.20 133.15 133.12 133.12

 

TABLE 17-B

EXPERIMENTAL 28 VALUES FOR CRYSTALS OF AlPO4

CONTAINING IRON AS AN IMPURITY

64

 

 

 

 

 

 

Percent Fe
hkl
0.15 0.16 0.23 0.25
421 149.67° 149.65° 149.69° 149.63°
420 146.23 146.22 146.22 146.20
331 144.31 -— 144.30 144.30
225 140.94 140.85 140.85 140.90
413 135.68 135.64 135.67 135.64
404 133.15 133.11 133.13 133.15
Percent Fe
hkl
0.32 0.57 0.60 0.61
421 149.69" 149.64° 149.60” 149.56”
420 146.19 146.21 146.12 146.15
331 -— 144.25 144.26 144.18
225 140.99 140.87 140.85 140.81
413 135.67 135.65 135.60 135.55
404 133.18 133.10 133.10 133.05

 

TABLE 17-C

EXPERIMENTAL 26 VALUES FOR CRYSTALS OF AlPO4

CONTAINING CHROMIUM AS AN IMPURITY

65

 

 

 

Percent Cr
hkl
0.10 0.11 0.13 0.17 0.18 0.19

421 149.66° 149.63" 149.64° 149.63° 149.64° 149.59°
420 146.16 146.14 -— 146.14 146.13 146.18
331 144.33 144.26 144.27 144.26 144.26 144.31
225 140.88 140.87 140.83 140.87 140.91 140.80
413 135.62 135.68 135.67 135.68 135.67 135.67
404 133.11 133.11 133.13 133.11 133.11 133.09

 

TABLE 17-D

66

EXPERIMENTAL 28 VALUES FOR CRYSTALS OF AlPO4
CONTAINING COBALT AS AN IMPURITY

 

Percent Co

 

 

hkl
0.01 0.02 0.03 0.04 0.05 0.33
421 149.73° 149.65° 149.65° 149.67° 149.62° 149.68°
420 144.26 146.13 146.18 146.20 146.17 146.17
331 144.37 144.23 144.30 144.37 144.34 144.32
225 140.39 140.90 140.33 140.39 140.90 140.91
413 135.73 135.67 135.63 135.63 135.63 135.67
404 133.19 133.17 133.10 133.14 133.11 133.17

 

TABLE 17-E

EXPERIMENTAL 28 VALUES FOR CRYSTALS OF AlPO4

CONTAINING VANADIUM AS AN IMPURITY

67

 

 

 

Percent V
hkl
0.01 0.03 0.035 0.04 0.05

421 149.67° 149.71° 149.69° 149.720 1 49.67"
420 146.21 146.31 146.28 146.21 146.16
331 144.28 144.38 144.34 144.34 144.40
225 140.92 140.98 140.90 140.98 140.92
413 135.64 135.68 135.70 135.72 135.67
404 133.13 133.17 133.17 133.20 133.14

 

TABLE 18-A

68

UNWEIGHTED _a_ AND 9/2 VALUES (IN A) FOR CRYSTALS
OF AlPO4 CONTAINING GALLIUM

 

 

 

Percent Ga
hkl’s
2 3 4 5.6 10.6 18.4
421—225 4.9280 4.9278 4.9280 4.9286 4.9271 4.9275
5.4608 5.4584 5.4605 5.4583 5.4583 5.4586
331—225 4.9426 4.9415 4.9414 4.9407 4.9401 4.9394
5.4481 5.4466 5.4489 5.4479 5.4470 5.4483
413—225 4.9516 4.9515 4.9505 4.9508 4.9517 4.9502
5.4400 5.4385 5.4417 5.4393 5.4369 5.4385
404—225 4.9045 4.9072 4.9033 4.9082 4.9111 4.9104
5.4813 5.4763 5.4821 5.4761 5.4722 5.4735
421-404 4.9285 4.9282 4.9285 4.9290 4.9275 4.9278
5.4393 5.4393 5.4393 5.4312 5.4312 5.4393
404-331 4.9094 4.9083 4.9083 4.9073 4.9068 4.9061
5.4723 5.4744 5.4728 5.4776 5.4801 5.4814
404—413 4.9702 4.9691 4.9693 4.9677 4.9678 4.9659
5.3653 5 .3671 5.3654 5.3709 5.3722 5.3754
331—413 4.9062 4.9050 4.9050 4.9042 4.9036 4.9031
5.6407 5.6433 5.6424 5.6451 5.6505 5.6470
421—413 4.9264 4.9260 4.9264 4.9270 4.9255 4.9258
5.5479 5.5470 5.5445 5.5410 5.5496 5.5427

 

TABLE 18-B

UNWEIGHTED a AND _c_/2 VALUES (IN A) FOR CRYSTALS

OF AlPO4 CONTAINING IRON

 

 

 

Percent Fe
hkl’S

0.015 0.016 0.23 0.25
421—225 4.9293 4.9292 4.9294 4.9287
5.4626 5.4600 5.4670 5.4631
331—225 -— 4.9422 4.9424 4.9423
-—— 5.4489 5.4558 5.4514
413—225 4.9529 4.9526 4.9535 4.9521
5.4417 5.4401 5.4393 5.4425
404—225 4.9051 4.9057 4.9047 4.9041
5.4838 5.4806 5.4825 5.4847
421—404 4.9298 4.9296 4.9300 4.9293
5.4312 5.4393 5.4312 5.4393
404—331 -——~ 4.9091 4.9093 4.9092
-— 5.4744 5.4739 5.4753
404-413 4.9718 4.9711 4.9726 4.9711
5.3659 5.3652 5.3627 5.3662
331-413 -—- 4.9058 4.9058 4.9060
—— 5.4489 5.6505 5.4514
421—413 4.9276 4.9276 4.9278 4.9272
5.5504 5.5470 5.5496 5.5496

 

TABLE 18-B (Continued)

7O

 

Percent Fe

 

 

hkl’s
0.32 0.57 0.60 0.61

421-225 4.9289 4.9299 4.9294 4.9303
5.4587 5.4621 5.4618 5.4630

331-225 -— 4.9428 4.9430 4.9440
— 5.4509 5.4501 5.4511

413—225 4.9532 4.9542 4.9527 4.9549
5.4385 5.4417 5.4417 5.4417

404—225 4.9058 4.9056 4.9063 4.9074
5.4789 5.4834 5.4821 5.4831

421-404 4.9293 4.9305 4.9300 4.9308
5.4312 5.4312 5.4312 5.4393

404—331 — 4.9097 4.9099 4.9108
— 5.4759 5.4755 5.4769

404-413 4.9721 4.9735 4.9712 4.9737
5.3621 5.3636 5.3674 5.3661

331-413 — 4.9064 4.9066 4.9077
—— 5.6532 5.6451 5.6505

421—413 4.9272 4.9281 4.9278 4.9287
5.5496 5.5530 5.5487 5.5538

 

TABLE 18-C

71

UNWEIGHTED E AND 3/2 VALUES (IN A) FOR CRYSTALS
OF AlPO4 CONTAINING CHRONIIUM

 

 

 

Percent Cr
hkl’s
0.10 0.11 0.13 0.17 0.18 0.19
421—225 4.9292 4.9294 4.9295 4.9294 4.9301 4.9300
5.4611 5.4619 5.4631 5.4606 5.4609 5.4636
331—225 4.9419 4.9428 4.9427 4.9429 4.9429 4.9422
5.4508 5.4502 5.4516 5.4489 5.4499 5.4531
413—225 4.9536 4.9519 4.9518 4.9526 4.9544 4.9515
5.4409 5.4425 5.4441 5.4409 5.4409 5.4457
404—225 4.9061 4.9057 4.9034 4.9071 4.9056 4.9045
5.4820 5.4828 5.4861 5.4801 5.4823 5.4860
421—404 4.9296 4.9300 4.9300 4.9300 4.9306 4.9306
5.4393 5.4312 5.4312 5.4312 5.4312 5.4312
404-331 4.9087 4.9097 4.9096 4.9097 4.9097 4.9091
5.4771 5.4753 5.4742 5.4753 5.4748 5.4775
404—413 4.9725 4.9703 4.9711 4.9706 4.9739 4.9702
5.3647 5.3684 5.3662 5.3679 5.3619 5.3696
331—413 4.9052 4.9066 4.9064 4.9066 4.9064 4.9058
5.6550 5.6424 5.6450 5.6433 5.6532 5.6478
421—413 4.9274 4.9279 4.9279 4.9279 4.9283 4.9285
5.5530 5.5453 5.5462 5.5462 5.5521 5.5436

TABLE 18-D

72

U'NWEIGHTED a AND c/2 VALUES (IN A) FOR CRYSTALS

OF AIPOZ CONTAINING COBALT

 

 

 

Percent Co
hkl’s
0.01 0.02 0.03 0.04 0.05 0.33
225-421 4.9283 4.9293 4.9293 4.9292 4.9296 4.9290
5.4621 5.4613 5.4616 5.4614 5.4610 5.4609
225-331 4.9414 4.9428 4.9424 4.9414 4.9417 4.9420
5.4509 5.4496 - 5.4503 5.4509 5.4506 5.4497
225-413 4.9288 4.9298 4.9298 4.9296 4.9301 4.9295
5.4425 5.4417 5.4409 5.4400 5.4400 5 .4409
404-225 4.9083 4.9096 4.9092 4.9083 4.9086 4.9090
5.4850 5.4842 5.4815 5.4828 5.4813 5.4830
404-421 4.9288 4.9298 4.9298 4.9296 4.9301 4.9295
5.4393 5.4312 5.4312 5.4393 5.4393 5.4312
404-331 4.9083 4.9096 4.9092 4.9083 4.9086 4.9090
5.4738 5.4724 5.4769 5.4763 5.4773 5.4736
404—413 4.9701 4.9719 4.9719 4.9728 4.9722 4.9719
5.3649 5.3628 5.3663 5.3627 5.3653 5.3628
331—413 4.9050 4.9064 4.9058 4.9048 4.9052 5.9056
5.6451 5.6451 5.6515 5.6560 5.6541 5.5487
421-413 4.9268 4.9278 4.9276 4.9274 4.9279 4.9274
5.5453 5.5470 5.5513 5.5521 5.5496 5.5487

 

TABLE 18-E

73

UNWEIGHTED 3 AND 9/2 VALUES (IN A) FOR CRYSTALS
OF AlPO4 CONTAINING VANADIUM

 

 

 

Percent V
hkl’s
0.01 0.03 0.035 0.04 0.05
225-421 4.9291 4.9287 4.9288 4.9285 4.9291
5.4608 5.4592 5.4618 5.4593 5.4608
225431 4.9427 4.9412 4.9417 4.9418 4.9409
5.4490 5.4484 5.4506 5.4479 5.4507
225—413 4.9535 4.9529 4.9515 4.9518 4.9526
5.4393 5.4385 5.4425 5.4393 5.4409
404—225 4.9061 4.9059 4.9033 4.9039 4.9055
5.4810 5.4792 5.4842 5.4810 5.4815
404—421 4.9296 4.9291 4.9293 4.9290 4.9296
5.4393 5.4393 5.4393 5.4312 5.4393
404—331 4.9096 4.9081 4.9086 4.9087 4.9078
5.4745 5.4753 5.4743 5.4721 5.4774
404-413 4.9722 4.9715 4.9708 4.9709 4.9713
5 .3643 5 .3636 5 .3647 5 .3627 5 .3654
331—413 4.9062 4.9048 4.9052 4.9054 4.9044
5.6487 5.6515 5.6470 5.6442 5.6541
421—413 4.9274 4.9270 4.9272 4.9270 4.9276
5.5513 5.5496 5.5462 5.5453 5.5479

 

.....

TABLE 19

THE BEST EXPERIMENTAL E AND 3/2 VALUES FOR AlPO4
CRYSTALS CONTAINING GALLIUM, IRON, CHROMIUM,
COBALT, AND VANADIUMa

 

 

{55532; _a_ (A) 3/2 (A)
Gallium
0.0 4.9292 5.4633
2.0 4.9285 5.4629
3.0 4.9282 5.4615
4.0 4.9278 5.4633
5.6 4.9278 5.4615
10.6 4.9271 5.4615
18.4 4.9268 5.4629
11313
0.0 4.9292 5.4633
0.15 4.9354 5.4536
0.16 4.9289 5.4543
0.23 4.9292 5.4652
0.25 4.9289 5.4566
0.32 4.9352 5.4505
0.57 4.9299 5.4642
0.60 4.9296 5.4638
0.61 4.9306 5.4651

aError considered maximum for each value in column 2 is
10.0004; error considered maximum for each value in column 3 is
3:0.0024.

TABLE 19 (Continued)

 

 

 

 

Percent
Impurity _a_ (A) _C_/ 2 (A)
Chromium
0.0 4.9292 5.4633
0.10 4.9289 5.4651
0.11 4.9292 5.4624
0.13 4.9292 5.4647
0.17 4.9296 5.4624
0.18 4.9299 5.4633
0.19 4.9292 5.4661
Cobalt
0.0 4.9292 5.4633
0.01 4.9278 5.4647
0.02 4.9292 5.4629
0.03 4.9292 5.4638
0.04 4.9289 5.4647
0.05 4.9292 5.4647
0.33 4.9289 5.4629
Vanadium
0.0 4.9292 5.4633
0.01 4.9292 5.4638
0.03 4.9257 5.4629
0.035 4.9285 5.4647
0.04 4.9285 5.4615

0.05

4.9285

5.4647

 

_v--——L

DISCUSSION OF RESULTS AND CONCLUSIONS

76

DISCUSSION OF RESULTS AND CONCLUSIONS

Accgptance of impurities

 

The spectroscopic data (Table 16) indicate gallium entered
the crystalline structure of aluminum phosphate in amounts near
those predicted by stoichiometric calculation, whereas iron, chro-
mium, cobalt, and vanadium were not accepted as anticipated. The
iron and chromium ions entered the structure sufficiently to alter
the color but the inclusion of less than 1.0 percent places them in
a category different from gallium. The induced coloration is weak
and Zinn (1959) reported no significant change in refractive index
with addition of chromium. Cobalt and vanadium ions were the least
acceptable with a range of substitution from 0.0 to 0.05 percent. It
is possible that the cobalt and vanadium impurities were not incor-
porated in the crystal structure but were absorbed on the surface
or carried along as contamination.

The iron and chromium ions were incorporated in the crys-
tallizing structure in amounts ranging approximately 0.1 percent for
chromium and 0.5 percent for iron, 3 factor of ten more than cobalt
and vanadium. The number of foreign ions taken up increased with
the amount of impurity added to the crystallizing solution and the

77

78

crystal appearance altered to opaque or colored. Spectroscopic
analysis of the pure crystalline aluminum phosphate (Table 15) indi-
cates the inherent trace element concentrations are 100-fold less
than the amount Of added impurity and may be considered negligible.
The ease with which the gallium ion entered the structure
leads to the question whether it prefers to substitute diadochically
for aluminum or to form mixed crystals. There is no indication that
the upper limit of gallium substitution reached in this experiment
could not be exceeded by increasing the gallium content of the crys-

tallizing solution.

Variation of a and c with impurities

 

The replacement of aluminum ions in the crystalline structure
by ions Of different, but similar, physical properties altered the
lattice dimensions as anticipated. Both the amount and kind of im-
purity substituted affects the _a_ and _g axial lengths (Figures 16 A—E).
Gallium ions decreased the a dimension in a regular way correspond-
ing to increased gallium substitution. Change in the g dimension ac-
companying the decrease in a is either masked by the magnitude of
the propagated error or does not exist.

The substitution of iron for aluminum created the greatest

structural distortion. Both _a_ and _c are Observed to vary in a

79

 

 

 

 

 

 

 

 

L ...........
4.9295 - It
I. error :1: 0.0004 A
4.9285 «-
€
57
“I
4.9275 .
4.9265 1 ‘ . I
5 10 15 20
Percent Ga
5.4655 fun-”"n-“nn'ql
5.4645 -
62‘
7; 5'4635 ‘ e 0 0024 A
, a: x rror :i: .
A \,.
gl 5.4625 .-
5.4615 -‘ u ‘4 1k
..................... Y
5.4605 1 ' ‘ ‘
5 10 15 20
Percent Ga

Figure 16-A. A diagram of axial length versus percent impurity
for AlPO4 crystals containing gallium.

80

4.9340 «

4.9320 -

a axis (A)

4.9300 ..

I ------ -- ”\I

x/\x ierror 4 0.0004 A

 

 

 

4. 9280

.10 .20 .30 .40 .50 .60 .70
Percent Fe

5.4675 I

.---- ----------------

5'46“: error 4 0.0024 A ”‘5

A)

 
 

5.4605 -" """“““ " ""

c/2 axis (

5.4570 ~

5.4535 - \
5.4500 . , “ .
.20 30 40

 

.15 .5'0 .6'0 .70

Percent Fe

Figure 16-B. A diagram Of axial length versus percent impurity
for AlPO4 crystals containing iron.

(3)

4.92977

4.9293-

 

81

error :1: 0.0004 A

 

 

 

g 1 \ /x 3‘ x
(8| \

4.9239. L x

4.9285 , , . , L1

.04 .08 .12 .16 .20
Percent Cr
5.4660- "
”"1

5.4650. "
A X
‘5,
§ 5.4640.
:3 H/ error :I: 0.0024 A x
BI 5.4630- /

X

5.4620-

 

5.4610

X

 

 

U V

.04 .03 .1'2 .16 .20
Percent Cr

Figure 16-C. A diagram of axial length versus percent impurity for

AlPO4 crystals containing chromium.

82

 

‘61..“ ‘m—u gusto \ In.) an...._-‘1
I .

 

 

 

 

4.9299.
0:5 error 4: 0.004 A
V 4.92913 \ "
3 ,/
N
“I
4.9233-
4.9275 , , , , '
.01 .02 .03 .04 .05
Percent Co
5.4660I
--------------7I~
5.46504
X X X
a /
":1; 5.4640- ..
N 5 4630:. ,/
EI ' 3 error 4. 0.0024 A
5.4620“
5.4610 V

 

 

.0'1 .0'2 .63 .04 .05
Percent CO

Figure 16-D. A diagram of axial length versus percent im—
purity for AlPO4 crystals containing cobalt.

 

83

 

 

 

 

4.9305.
4. 9295 f“""““’“
I.——.. error :I: 0.0004 A
°$ 4.9235. """" --- ,.__.,.____,.
5‘3
“" 4.9273
4.9265«
4.9255 . ' f U '
.01 .02 .03 .04 .05
Percent V
5.4681.
“‘1: 5.4657~ ........... 7
m I
E .
N
bl /‘\
5.4633 I
'I \x
error :i: 0.002
5.4609 , Y , , ,
.01 .02 .(73 .04 .05
Percent V
Figure 16-E. A diagram of axial length versus percent im-

purity for AlPO4 crystals containing vanadium.

a: s9 '. mm nun-rat
I

fl s-_" ‘71: - _‘6 A ‘3dfl‘£-‘ .
. A

84

relative, but opposite, manner. The changes in axial length do not
appear to follow directly the increase in impurity content of the
crystal. It may be significant that the crystalline structure accom-
modated the iron impurity at certain concentrations with comparatively
large fluctuations of axial lengths while remaining relatively un-
changed for intermediate concentrations.

The chromium ion substituting in amounts Of the Same order as
iron increases the 3 axis length sufficiently to exceed the limiting
error (Figure 16-C). The pattern follows the one produced by iron
although in this case the c axis variation is not sufficient to escape
the error attached to the measurement.

The cobalt and vanadium series present a significant varia-
tion in the 3 axis length with added impurity (Figures 16 D—E). Both
ions cause a decrease in a for impurity amounts of the order of
0.01 percent. In the vanadium series the alteration is more pro-
nounced and the a axial length remains contracted. Lack of data
outside the limits Of experimental error prevent 2 axis measurements

from contributing to the Observations.

Reasons for acceptance of impurities

 

It is generally held that simple cations enter a crystalline

structure from a melt as a result Of changes in temperature, valence,

 

 

 

 

85

and ionic size. In this investigation the temperature and valence
were selected as experimental constants and the ionic radii allowed
to vary. The original Goldschmidt (1926) postulation of crystals
being built up by the packing Of spheres with the arrangement of
ions in the crystal determined by the radius ratio (cation radius/
anion radius) has proved suitable for many simple inorganic com-
pounds, however, there is a lack Of agreement on the Sizes of ions.
The large amount of data on crystals yields internuclear distances
and the problem of how to divide this distance into cationic and
anionic components in any given crystal is inescapable when at-
tempting tO determine ionic radii values. The earliest acceptable
system of ionic radii was developed by Wasastjerna (1923), who
based his data on 1.32 A for 0= radii and 1.33 A for F- radii.
Goldschmidt’s modification of these early figures was founded on
1.40 A for O: and 1.36 A for F- and based upon extensive labora-
tory data (Goldschmidt, 1929). Pauling (1927) developed a different
set of values for ionic radii by a wave mechanical treatment of the
factors involved which has proved extremely valuable. A late paper
by Stern and Amis (1959) discusses the attempts of various investi-
gators to establish more exactly the values of atomic and ionic
radii. At the present time the difficulties of the problem provide

a variation of 20—30 percent and have prevented these authors from

86

selecting any particular values as standard. The Goldschmidt radii
are as acceptable to most workers as those of Pauling, Zachariasen
(1931), Ahrens (1952), and others. Table 8 lists the empirical Gold-
schmidt radii values for aluminum and the other trivalent cations
used.

On the basis of similar ionic radii, gallium should be most
successful in substituting for aluminum in the crystal framework, as
is the case. Iron has the largest ionic radius of any of the cations
presented for substitution and Should be least successful in substi-
tuting for aluminum. This is not true as iron ranks second to gal-
lium in the ability to substitute for aluminum and creates the great-
est structural alteration Of any Of the five trace ions.

Electronegativity is an ionic property considered to be a
principle factor (Fyfe, 1951) in determining the structure of crystals.
Electronegativity is a combination of ionization potential and electron
affinity and extensive calculations were performed by Pauling and
Haissinsky (Fyfe, 1951) to provide the coefficients listed in Table .20.

As with ionic radii, recent work casts doubt on the accuracy
of these calculations. Fineman and Daignault (1959) question Paul-
ing’s relationships for bonds with a great deal of ionic character
and present coefficients 0.6 to 0.7 higher than those Of Pauling and

Haissinsky. Ringwood (1955) attributed a major significance to the

87

TABLE 20

ELECTRONEGATIVITY VALUES ASSIGNED THE CATIONS
LINKING THE P04 TETRAHEDRA IN THE
CRYSTAL STRUCTURE OF AlPO4

 

 

Element 115 £33261
Aluminum 1 .5
Gallium 1 . 6
Iron 1 .8
Chromium 1 . 6
Cobalt 1 .7
Vanadium 1 .35

 

Li‘s, .- “mute-v.1- ..

I“

88

role played by electronegativity in elements which display diadochy.
He is of the opinion an element displaying higher electronegativity
than the host forms a weaker bond and will not be accepted readily
while an element of lower electronegativity than the host will be
preferentially incorporated. Such a relationship is reported to ap-
ply when the electronegativity difference between the host and the
trace element is greater than 0.1 (approximately).

Using this criteria, vanadium should be accepted by the crys-
talline aluminum phosphate in the largest concentration, and in turn
provide the greatest change in lattice parameters while iron will be
least acceptable and provide the smallest alteration in the crystal
structure. Experimental evidence indicates this is not true.

Ionization potential in its own right may be considered to
play a fundamental part in the ability of an ion to substitute in a
structure. Ionization potential is a measure Of the energy required
to move a single electron from a free atom or ion to infinity, or
conversely, as a measure of the energy lost by a recombination of
the resulting ion and the electron. Ahrens and Morris (1956) em-
ployed the ionization potential of the cation as an approximate com-
parative measure of its power of attraction for the most loosely

bound electrons of the neighboring anions when considering the

89

formation of crystals from different cations of the same charge and
ionic radii with a given anionic constituent. According to their ar-
gument, the greater the ionization potential of the cation, the greater
the deviation from ionic bond character, the weaker the bond, and the
less desirable the cation to the structure. Recent values for ioniza-
tion potentials assembled by Basolo, Pearson, and others (1958) are
listed in Table 21.

Following the ideas presented by Ahrens and Morris, vanadium
Should be preferred by the crystalline structure over the gallium due
to the vanadium’s lower ionization potential. This is not found ex-
perimentally to be true.

The chemical nature of the trace ions entering a crystalline
structure affects the bonding and is necessarily a prime factor in
establishing any substitutional pattern. The electron configurations
of the metallic elements involved in this study are listed in Table 22
(Rankama and Sahama, 1950, p. 796). It is evident that the 8-electron
outer shell Of trivalent aluminum has reached a degree Of stability.
The 18-electron cation of gallium also contains the maximum number
of electrons in its M shell. This similarity plus the physical prop-
erties previously listed permit gallium to proxy for aluminum in a
predictable manner. X-ray evidence shows a reduction in the _a_ axis.

length with addition Of gallium (Figure 16-A), and, as the amount of

90

TABLE 21

IONIzATION POTENTIALS ASSIGNED THE CATIONS
LINKING THE P04 TETRAHEDRA IN THE
CRYSTAL STRUCTURE OF AlPO4

 

Total Ionization

 

Element Potential
(at 0°K)

Al (III) 1228 kcal

Ga (111) 1310

Fe (III) 1261

Cr (III) 1259

CO (III) 1365

V (III) 1094

 

TABLE 22

91

ELECTRON CONFIGURATIONS ASSIGNED THE CATIONS
LINKING THE P04 TETRAHEDRA IN THE
CRYSTAL STRUCTURE OF AlPO4

 

 

 

 

 

 

Ele- K L M N

ment (1s) (2s) (2p) (as) (33) (3d) (4s) (4p) (4d) (40
Al 2 2 6 2 1

Ga 2 2 6 2 6 10 2 1

Fe 2 2 6 2 6 6 2

Cr 2 2 6 2 6 5 1

Co 2 2 6 2 6 7 2

V 2 2 6 2 6 3 2

92

substituted gallium increases, the axial contraction is more pro-
nounced. Pauling (1929) noticed this type Of deformation and wrote:
Deforming action of an eighteen-shell ion is much greater than
the deforming action of an eight-shell ion of the same size and
valence. This is due to larger effective nuclear charge.
Iron, chromium, cobalt, and vanadium are transition metals and exist
with their M Shells containing less than a stable 18-electron con-
figuration. AS these atoms oxidize to the trivalent state it is as-
sumed the N shell loses its electrons first and then the 5 d-Orbitals
of the M shell may alter. The exact manner Of alteration and any
simple prediction for the relative stability Of a resulting ion is a
matter Of conjecture (Gould, 1955, p. 21).

The iron and chromium originally were put in the crystalliz-
ing solution as hydrated ferric and chromic phosphate. Spectro-
scopic evidence indicates only a few tenths of a percent Of either
the Fe (III) or the Cr (III) ions succeeded in proxying for aluminum.
Keeping in mind the specific crystallizing temperature, pressure, and
concentration, this failure to substitute may be due to either the in-
ability to become free, mobile ions or to the energy demands of the
lattice Sites. The latter possibility appears the more feasible.

The insolubility of the cobaltic oxide in addition to its elec-

tronic configuration may be a prime factor for its lack of success

in substitution. From the appearance of the reaction, the cobalt

93

metal added to enhance the cation concentration formed the cobaltous

ion and was not suited (smaller charge, larger size) to the diadochic

process. The vanadium metal was soluble and the presence Of large

numbers Of V (111) ions was indicated by the intensely green crystal-

lizing solution. However, to the same degree as cobalt these cations
appeared unable to occupy the structural aluminum sites, and spectro-
scopic analysis showed less than 0.05 percent concentration of either
ion under conditions which allowed gallium to substitute up to 18 per-
cent.

The presence Of transition metals in any compound character-
istically produces a strong coloration, and Pitzer and Hildebrand
(1941) point out that if the color of a compound differs from that of
its constituent ions in solution it may be an index of deviation from
pure ionic character. The AlPO4 crystals containing cobalt and va-
nadium Show only faint shades of color——blue, in the case of cobalt,
and, surprisingly, a tinge of lavender for the vandadium impurity.

The hydrated Co (11) ion is known to be pink, and the anhydrous

form is blue. The V (IV) ion is known to be blue, while the highly
unstable V (II) ion is violet. It is probably the V (II) ion entering
the structure instead of the common V (111) ion which existed in the

green mother-liquor. The trivalent vanadium ion is recognized to be

a comparatively strong reducing agent (Rankama and Sahama, 1950,

94

p. 596). However, this unexpected substitution of V (II) is postulated
on the evidence of a faint tinge of color, and until more concrete
data are Obtained it remains a highly conjectural phenomenon.

Inability to establish ionic bonds could be a reason for iron,
chromium, cobalt, and vanadium affecting the crystalline structure
differently from gallium. Such a possibility leads again to the prob-
lems of assessing the amount of ionic character Of a particular bond,
defining the meaning of bonds intermediate between ionic and coval-
ent, and justifying the concept Of orbital hybridization. It serves
little purpose to attempt to answer a question as to the scheme of
iso-positional substitution in aluminum phosphate by posing new prob-
lems based on conflicting theories although the ultimate answer may
lie contained therein.

As previously stated, iron was the most successful of the
transition metals in proxying for aluminum and provided a unique
change in the structural pattern of the crystal. Whereas the gal-
lium impurity contracted the _a_ axis by 0.003 A at the maximum sub-
stitution of 18 percent, iron expanded the 3 axis by 0.006 A with the
minimum substitution of 0.15 percent. This same percentage Of iron
decreased the 9 axis a measurable amount. It is significant that
(1) iron altered the axis in a manner Opposite from gallium, (2)

caused a relatively large axial change with trace substitution,

95

(3) shifted the axial lengths for discrete percentages of impurity,
and (4) allowed the lattice to remain relatively unchanged for inter-
mediate values.

One explanation for this may be a combination of electron
configuration and ionic size. The 18-electron gallium ion when
proxying for the 8-electron aluminum exerts a stronger Coulomb
force on its nearest neighbor oxygens. The net result is a partial
collapse of the structure as evidenced by a shrinkage of the 2 axis.
The similarity in ionic size of gallium to aluminum permits fourfold
coordination and fails to create a space demand. An iron cation in
the place of the aluminum in the structure will exert a different at-
traction on the surrounding oxygens. The electron structure of this
transition metal may react to the electrostatic field by altering the
valence configuration. If an electron should be shifted it would
polarize in a way to minimize the Coulomb energy of the local sys-
tem. An electron more strongly concentrated around one of the
Fe-O bonds not only would satisfy the minimum energy requirement
but might be responsible for a dimensional change in the structure.
The iron ion is assigned an ionic radius near 15 percent larger
than aluminum, which suggests sixfold coordination and enhances the
space demands in the structure. Rankama and Sahama (1950, p. 659)

discuss the diadochy of Fe (III) and Al (III) and observe that

96

considerable substitution comes about when the aluminum occurs as
a cation outside the silicon-aluminum network in the aluminum sili-
cates. This replacement does not occur when the aluminum replaces
silicon within the oxygen tetrahedra of the aluminosilicates.
Chromic compounds resemble ferric substances, although the
Cr (III) ion is known to be less strongly oxidizing than the Fe (111)
ion (Moeller, 1957, p. 880). In this study the chromium entered the
framework of AlPO4 and altered the lattice parameters in a weak
but similar manner to that of iron. The electron configurations of
these ions and their abilities to establish crystalline bonds appear
to be the major factors in their success in proxying for Al (III) in

the crystal.

The failure of cobalt and vanadium to substitute for aluminum
is postulated as due to their chemical nature. Trivalent vanadium
has been described as an unstable ion in need of additional electrons.
Trivalent cobalt is reported always to have a coordination number of
6 (Rankama and Sahama, 1950, p. 683), and Moeller (1957, p. 203) of-
fers it as an example of an ion having six bonds directed toward the
corners of a regular octahedron. The present investigation indicates
these two ions fail to enter the crystalline framework in more than

trace amounts. Again it seems the “size” of the ion is a function

97

of its environment and the chemical nature of the ion is the funda-
mental factor in establishing a substitutional pattern.

Welcher and Hahn (1958, p. 25) point out the relative stability
of the ionic state is often best correlated with nuclear charge and
size of the atom, but the electronic structure determines primarily
what oxidation state a given element will exhibit. In keeping with
the question of bonding between ions, Corwin (1958), in studying
reactions under controlled conditions between salts of alkaline earth
metals and silica, found that the rate of reaction and the formation
of crystalline structure are correlated with the initial pH of the
solution and the relative dimensions of the ions involved.

Since the X-ray diffraction peaks studied in this investigation
retain their identity with added impurity, it is assumed that the for-
eign ions are substituting for aluminum and no new crystal structure
is being formed. Concentrations of gallium approaching 18 percent
in the aluminum phosphate crystal tend to split the diffraction peaks
and create the impression that a super lattice of gallium phosphate
may be forming. The crystals bearing iron near the maximum of
0.60 percent evidence some broadening of the diffraction peaks, but

the data are considered insufficient to support any contention of an

ordered substitutional pattern.

98

In summary, it does not yet appear possible to distinguish
clearly between the space occupied by an atom within a crystalline
structure and the influence that it exerts. Until the present uncer-
tainty concerning atomic and molecular constants, accepted as known
a decade ago, is reduced, a concise explanation of structural alter-
ation in crystalline substance caused by iso-positional substitution

of foreign ions is impossible.

Conclusions

 

1. The tetrahedral structures A104 and P04 are replicas of

the SiO4

(Si 8104), may be produced under ordinary laboratory conditions.

tetrahedral unit, and crystalline AlPO , similar to 8102

2. Impurities of Ga, Fe, Cr, Co, and V may be introduced
into crystallizing AlPO4 without destroying its gross morphology or
lattice structure. With the exception of gallium, less than 1.0 per-
cent impurity enters the crystal.

3. The principal influence on the ability of an impurity to
substitute iso-positionally in a given structure (temperature and
charge constant) is not the similarity of ionic radii.

4. The electron configuration of an ion attempting to proxy
for another in a given structure is the prime factor in its occupying

a given structural site.

SUGGESTIONS FOR FURTHER WORK

99

SUGGESTIONS FOR FURTHER WORK

1. Continue increased substitution of gallium into the struc—

ture with the purpose of obtaining data concerning the binary system

AlPO4 -GaPO4.

2. Retrace the substitutional pattern of the iron impurity

with emphasis on concentrations above 0.61 percent.

3. Maintaining temperature, concentration, and radii constant,
investigate the substitutional behavior of ions with different charge,

e.g., Cr (III) radius 0.64 A and Ti (IV) radius 0.64 A.

4. Holding the experimental conditions constant, add equal
numbers of two or more foreign ions to the crystallizing solution
and determine the correlation of ionic radii, ionic potential, electron
configuration, and other parameters of the ions with their success

in competing for structural sites.

5. Determine variation in physical properties of the alumi-
num phosphate crystal (e.g., directional hardness) with the kind and.

amount of foreign ions substituted.

6. Investigate the effect of the pH of the reacting solution
on the crystalline product.
100

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101

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