70- 14,038

HOEKSTRA, Karl Egmond, 19 35- CRYSTAL CHEMICAL CONSIDERATIONS OF THE SPINEL STRUCTURAL GROUP.

'’’h e Ohio State University, Ph.D., 1969 Chemistry, inorganic

University Microfilms, Inc., Ann Arbor, Michigan

THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED CRYSTAL CHEMICAL CONSIDERATIONS OP THE SPINEL STRUCTURAL GROUP

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By Karl Egmond Hoekstra, B.A., M.S.

******

The Ohio State University 1969

Approved by

V Adviser Department of Mineralogy ACKNOWLEDGMENTS

The author wishes to express his appreciation to

Dr. Henry E. Wenden, under whose advisorship this work was done, for his helpful suggestions and criticism during the course of the study. The writer also wishes to thank Drs. Rodney T. Tettenhorst and Dan McLachlan, Jr. for advice and careful reading of the manuscript. Thanks are also due Dr. Wilfred R. Foster, Chairman of the Department of Mineralogy, Mr. George D. Brush of Harrop Ceramic Service Co. and Dr. Robert A. Schoenlaub, formerly of Harrop, for their assistance, encouragement and understanding while pursuing this degree.

ii VITA

October 9, 1935 Born - Battle Creek, Michigan 1958 ...... B.A. in Geology, Miami University, Oxford, Ohio

1958-1963 . . . Research Engineer, Ferro Corporation, Cleveland, Ohio

1965 ...... M.S. in Mineralogy, Miami University, Oxford, Ohio

1964-1967 . . . Manager, Materials Testing Laboratory, Harrop Precision Furnace Company, Columbus, Ohio

1967-Present Director, Harrop Laboratories, Columbus, Ohio

PUBLICATIONS With R. A. Schoenlaub and W. E. Troyer, "Burnout Rates on a Shale Body," Ceramic Bulletin, 45> No. 3, pp. 257-59, 1966.

"Horizontal Tube, Vertical Tube and Rod Dilatometers,11 Proceedings of the 1968 Symposium on Thermal Expansion of Solids, to be published

FIELDS OF STUDY

Major Field: Mineralogy Studies in X-ray Crystallography. Drs. H. E. Wenden and D. McLachlan, Jr. Studies in Crystallochemical Mineralogy. Drs. H. E. Wenden and R. T. Tettenhorst Studies in Phase Equilibria and Crystal Growth. Drs. W. R. Foster, D. McLachlan and E. Ehlers

iii TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS...... ii VITA ...... ill LIST OF T A B L E S ...... v LIST OF F I G U R E S ...... iv

INTRODUCTION ...... 1 HISTORY ...... 4

CRYSTAL CHEMISTRY OF SPINELS ...... 8 Chemistry of Spinels Structure of Spinels Distribution of Cations over Tetrahedral and Octahedral Sites Departures from Cubic Symmetry STATEMENT OF THE PROBLEM...... 40 SEMANTICS PROBLEMS ...... 41 STOICHIOMETRY-ELECTRONEUTRALITY ...... 46 RESIDUAL CHARGE PRINCIPLE ...... 59

CONCLUSIONS...... 78 BIBLIOGRAPHY ...... 80

iv LIST OF TABLES

Table Page 1. Cations Occurring in Spinels ...... 8

2. Common Spinel Types ...... 9 3. u Parameters for Various S p i n e l s ...... 18 4. Octahedral Crystal-Field Stabilization Energies for Ions with One to Five d-Electrons...... 27

5. Stabilization Energies Expected in Octahedral and Tetrahedral Environments for the First Series of the Transition Elements ...... 29 6. Octahedral Site Preference Energy for Various Cations ...... 31 7’. Comparison of "Normal and "Inverse" with "Homologic" and "Heterologic" Distribution . . 44 8. Mixed-Cation, Common-Anion Spinel Valence T y p e s ...... 51 9. Common-Cation, Mixed-Anion Spinel Valence T y p e s ...... 52 10. Lacunary Spinel Valency Types ...... 53 11. Residual Charges for Various Mixed-Cation, Common-Anion Valence Types ...... 65 12. Residual Charges for Various Common-Cation, Mixed-Anion Valence Types ...... 67

13. Cation Distribution in Existing Spinels ...... 69

v LIST OF FIGURES

Figure Page 1. Projection and Packing Drawing of the Spinel Structure ...... 13 2. Two Octants of the Spinel Structure...... 14

3. Basic Spinel Building Block ...... 16 4. Exploded View of Basic Spinel Building Block . . 17

5. Graphic Representation of the Five d-Electron O r b i t a l s ...... 25 6. Energy Splitting in an Octahedral Field ...... 26 7. Energy Splitting in a Tetrahedral Field ...... 28 8. X-Ray Peak Splitting in Cubic and Tetragonal Modifications in CuFe20]1 ...... 35 9. Polyhedral Structure Drawings of a Portion of the Spinel Structure— Showing Tetragonal Modifications ...... 36

10. Tetragonal Modifications (Elongation) in a Tetrahedral Field ...... 38 11. Tetragonal Modifications (Shortening) in a Tetrahedral Field ...... 38

vi INTRODUCTION

The structure of the mineral spinel was first des­ cribed independently by Bragg and Nishikawa in the same year,

1915. Since that time a score or more minerals and over one hundred synthetic compounds have been found to crystallize with the same structure. Thus, the term "spinel" has come to mean the entire group of compounds possessing this structure as well as the mineral spinel itself. The group has great chemical variety. It includes compounds of many anions, such as oxides, sulfides, fluorides, selenides, tellurides, nitrides and cyanides and at least thirty cations of valencies one through six are found as components of spinels. The spinels have received a great deal of attention from mineralogists, geologists, geophysicists, gemmologists, academicians and a host of industrially oriented scientists and engineers. Magnetite is second among ores of iron in economic importance and chromite is the chief source of chromium. Spinel group minerals are widely distributed throughout the earth’s crust as accessory minerals in igneous rocks, as constituents of metamorphic rocks, and in placers. A polymorph of magnesium silicate having the spinel structure may be the major constituent of the mantle of the earth. Colored spinels have long been known as gem- stones, and red spinels were not distinguished from rubies until 1783. Among the Crown Jewels of England, the "Black Prince's Ruby" is a spinel. Synthetic spinels are of in­ dustrial importance as semiprecious gemstones, pigments, refractories, catalysts and ferromagnets. The spinels have also undergone a great deal of ex­ posure in the literature. This is due, not only to the large number and ubiquity of the spinels, but also because the spinels have been used as a testing ground for many crystal chemical theories. This group presents a structure r well suited for this application since it allows great variations in composition, valence and even structure. The crystal chemistry of the entire spinel group is, however, still not well understood. The great amount of literature on the spinels, along with their great variety, has apparently discouraged attempts at a comprehensive treatment of spinels. The treatment of spinels by the standard crystal chemistry texts is very elementary and does not discuss adequately the many chemical, valence and structural variations and their crystal chemical causes.

Some technical papers have given good but not comprehensive treatments because they have placed emphasis on one peculiarity or physical property of particular relevance to their area of interest. The primary purpose of this dissertation is to organize existing crystal chemical information about the spinels and to clear the way for the understanding of spinels as a diverse but coherent struc­ tural group. A comprehensive treatment of the state of the art of spinel crystal chemistry follows after a brief historical orientation. HISTORY

The origin of the name spinel is unknown. The word spinella was used by Roman authors, perhaps as a diminutive of the Latin spina, a thorn, but probably not with refer­ ence to the mineral called spinel today. The form splnellus was used in the 16^7 edition of Boetius De Boodt's Lapidum Gemmarum Et Lapidum Historia, but spinel was not distinguished from ruby corundum. The distinction between red spinel and red gem corundum was first made by Rome'De L'Isle in 1783 on the basis of the difference in crystal habit.

The first chemical analysis of spinel was made in 1789 by Klaproth, who, on this occasion, found no magnesia. Dis­ satisfied with his first analysis, Klaproth repeated it in 1797 and this time found 8.25# MgO, 74.5# A1203 and 15-5# S102 . Vauquelin, who analyzed spinel in 1800, found no silica, but still reported only 8.5# MgO, as he was unable to make a clean separation of MgO from A^O^. The correct composition was finally established by Abich (Dissert.

Chem. de Spinello, Berol., 1831) as 28# MgO, 72# A1203. Wallerius had noted in 1772, that red spinel, when fused with borax, yielded an emerald-green glass. Vauquelin, in 1800, also detected the chromium present in ruby spinel. Thus, chemical variation and the effect of vicarious constituents was observed very early. In addition ferroan spinel was described as a new species ceylonite by Dela-

metherie in 1793. Gahnite, ZnAl2Oj^, was first recognized and described by Ekeberg in 1806. The mineral franklinite, ZnFe20jj was first found in 1819 at Franklin Furnace, New Jersey by Berthier. Magnetite, FeFe20/j, was known in very ancient times,

but its true analysis was not reported until Berzelius showed in 1813 that it consisted of 68.97? Fe2C>3 and 31.03?

FeO. Von Kobell recognized in 1831 that magnetite could contain a variable excess of Fe^^, and could be oxidized

completely to Fe203 to form martite with retention of the external octahedral habit.

Chromite, FeCr20^, was first analyzed about 1800, but its relationship to the spinels was not shown until 1831, when Abich studied well crystallized material from Balti­ more, Maryland. The concept of the minerals spinel, gahnite, franklinite, magnetite and chromite as a mineral group

seems to have arisen relatively early. Abich, in 1831, recognized the chemical relations and morphological similar­ ities in not only the aluminum but also in the iron and chromium series. Description of additional spinel varie­ ties, namely, hercynite, jacobsite, magnesioferrite and

magnesiochromite, in the middle l800’s lent additional sup­ port to the group concept. Hunt, Rivot, Landerer, Stan and Garrett, and Bechi, among others, analyzed many spinel varieties between 1850-

1853 and provided abundant evidence of the exchange of C'r2°3» A1203 and Fe203 as well as MgO and PeO and other metallic oxides in chromite. In 1851 Ebellman synthesized not only the naturally occurring species of spinel but several others as well. These syntheses were performed by crystallization from a fluxed melt. During the last of the 1800’s and the very early

1900’s, there occurred no contribution of much direct historical significance to the advancement of knowledge about the spinels. In 1915, however, one year after the first X-ray structural determinations were made, Bragg and Nishikawa, as a result of independent studies, described the structure of spinel. This event added the parameter of structure to the spinel classification where previously only morphology and chemical composition had been used. Struc­ ture soon became the prime criterion for the identification of the spinels. Had it not been so, the defect spinel maghemite, yPe203, which was described by Wagner in 1927 and ulvospinel, Fe2TiOjj, described in 19^3 by Mogensen would per­ haps not have been included in the spinel mineral group because of their chemistry.

In the 1930’s, crystal chemistry had its beginnings and this new discipline found a waiting testing ground in the spinels. Knowledge of the complexity and variability of the spinels has increased steadily along with the advance­ ment of this discipline. Indeed, some, if not most, crystal chemical theories were tested on the spinels to determine their validity. In the following sections the state of the art of the crystal chemistry of the spinels is discussed. CRYSTAL CHEMISTRY OP SPINELS

Chemistry of spinels The general formula for spinels is given by Many A-B-X combinations of many different valences have been described in the literature as possessing the spinel structure. Cations which have been reported are given In Table 1. The anions which have been reported are oxygen, sulfur, fluorine, selenium, tellurium, nitrogen and cyanide.

TABLE 1 CATIONS OCCURRING IN SPINELS

Mono- Di­ Trl- Tetra- Penta- Ilexa- Valent valent Valent Valent Valent Valent Na Mg A1 Ti Sb Mo

K Ca Cr Sn Nb W

Ag Sr Fe Ge Ta Te Cu Zn Sb Si Li Cd In V

Hg Ga Mn Mn V Pe Co Co Rh • Ni Cu Pb 8 It is customary to designate spinels by the use of a conven­

tional symbol of the type (2-3) which alludes to the val­ encies of the two cations in the order of increasing charge. The (2-3) type, then, describes the most common

spinel type in which A and B are divalent and trivalent cations, respectively. Examples of this type are MgA^Ojp ZnFe20i|, FeCr204 and CoA1202j. Several other spinel types have been reported and commonly accepted examples of each are given in Table 2. Of particular note is the (1-2) type which may be thought of as a "half charge model” of the (2-4) type and the (0-3) which is a defect spinel.

TABLE 2

COMMON SPINEL TYPES

Anion Valence 1 2 M1 Valence1I 1 0 1 2 2 Li2BeF4(l-2)

3 yFe203(0-3) LiAl50g(l-3) ZnAl20ij(2-3) ■°o § * L i ^ O ^ M Zn2Ti40(2_4) 0) H c d 0 ZnySb20^2(2—5) > Ag2MoOi4(l-6) % 6 a 1 M-1- Designates the metal ion of lower valence. Designates the metal ion of higher valence. It is not readily apparent how the various spinel types given in Table 2 may be made to conform with the ABgXjj formula where typically A is divalent and B is tri- valent. Examples of how this may be accomplished follow: Example (1) Lif+ Ti4+ 0 * ^ « V 3 ^ Regrouping to obtain a 1:2 ratio of A to B as

well as an average valence of 2+ for A and 6+ for two B ’s yields

A B Xjj

(Li2/3 Til/3^ ^Li2/3 Tll

charge on each cation by its proportion in A and B --

For the average charge on A

2/3 x (1+) + 1/3 x (4+) » 2+ For the average charge on two B ’s

2/3 x (1+) +4/3 x (4+) = 6+

Example (2) Zn2+Sb5+0,„ 7 2 12 + 3 Zn7/3Sb2/30|} Regrouping to obtain a 1:2 ratio of A to B as well as an average valence of 2+ for A and 6+ for two B ’s yields' A B Xjj 11

( Zn )

This arrangement may be shown to satisfy the

average requirements by multiplying the charge on each cation by its proportion in A and B — For the average charge on A 1 x (2+) = 2+ for the average charge on two B ’s

V 3 x (2+) +2/3 x (5+) = 6+

Example (3)

x3 Pe8/3°H With an anion basis of four there should exist a total of three cations but there are only 8/3

cations present to divide between A and B. This

means that there is 1/3 cation vacancy per formula unit. The arrangement whereby the 1/3

cation vacancy is considered to contribute to the A average charge is satisfactory. A B X

(D 1/3 ^®2/3^ ^ F©2 ^ This arrangement may be shown to satisfy the aver­ age requirements by multiplying the charge on each

cation by its proportion in A and B — For the average charge on A

1/3x0+ 2/3 x (3+) » 2+ For the average charge on two B ’s 2 x (3+) = 6+ 12 In Table 2 and in all subsequent discussions of the chemical composition of spinels, chemical formulas will be presented with cations arranged in increasing order of cation valence rather than attempting to conform to the order suggested by the general formula, AB2Xjj, e.g., Zn^TiOjj and AgjjMoOjj rather than TiZn20jj and MoAg20ij. In addition, whole number subscripts will be used, e.g., ZnySb20^2 rather than Zn(ZnQ ^g^Sb0 ^^3)2 °4 * The ability of the spinel structure to accept various combinations of cations with different charges led Evans (1964) to suggest that the most significant factor influenc­ ing the formation of the spinel structure is that the total cation charge yield a neutral structure.

Structure of spinel

The unit cell of the spinel structure consists of 32 oxygen ions approximating a cubic closest packed configura­ tion. Such an arrangement results in the formation of 64 tetrahedral and 32 octahedral voids of which 7 of the tetrahedral and 16 of the octahedral sites are occupied. The occupation of the available sites is such that the re­ sulting structure is cubic. A projection and a packing drawing of the spinel structure is given in Figure 1. One representation of the spinel structure which lends itself easily to visualJ zation has been given by Smit and Wijn (1959). The cubic unit cell is subdivided into eight cubic octants each with an edge of 1/2 the unit cell 13

O

B O o

' i D B u Ju

Figure 1. Projection (Top) and Packing Drawing (Bottom) of the Spinel Structure, 14 edge, i.e., l/2a. See Figure 2. Each octant contains four

anions which are arranged at the corners of a tetrahedron. All octants contain similarly positioned anions but differ

in the distribution of the cations so that, excluding cations on the corners of the octants, an octant contains either one tetrahedrally coordinated or four octahedrally

coordinated cations. There are four octants of each type per unit cell, with similar types sharing edges and dis­

similar types sharing faces.

u*a

a

Figure 2. Two Octants of the Spinel Structure. The Large Spheres Represent the Anion. The Small Black and White Spheres Represent the Metal Ions on Tetrahedral and Octahedral Sites, Respectively. (After Smit and Wijn, 1959) 15 7 The space group of the spinel structure is 0^-Fd3m and the atomic positions given by: 8 Tetrahedral Cations (8a): 000, + F.C.C.

16 Octahedral Cations (l6d): 5/8 5/8 5/8 5/8 7/8 7/8 V8 5/8 7/8 /8 7/8 5/8 + F.C.C. 1 32 Anions (32e) uuu; 7-u -u, ]j-u; i uuu; 4"U +u. y*-u; _ _ 1 uuu; -+u -u, |+u; uuu; —+u, —-u + F.C.C. 4+u

The value u (measurement shown in Figure 2) will be discussed in following paragraphs. Some of the complications and irregularities of the spinel structure may best be described by the use of a basic building block of one anion surrounded by one tetra- IV hedrally coordinated cation (M ) and three octahedrally coordinated cations (M^*) as shown in Figure 3. The posi­ tions of the cations may be described as occupying the apices of a somewhat distorted tetrahedrom, the angle IV VI VI VI between M and M being greater than between M and M 16

r I V

rVI

t V I ,VI

Figure 3. Basic spinel building block of anion surrounded by three octahedrally coordinated cations and one tetrahedrally coordinated cation.

Cations of varying size, charge and afinity for the anion can occupy these four sites. The effects of these variables is to shift the elements of the basic building block shown in Figure 3* The shift may be viewed as an increase or decrease in the distance between the anion and the MIV cation. This shift along the anion -M1^ axis is measured by the u parameter in the list of atom positions. The u parameter, however, is not measured along this axis but rather between the anion and the unit cell "face” or some quartered unit dimension as shown in Figure 2. An 17 exploded view of the basic building block showing the direc­ tion of shifting is given in Figure 4.

/✓

V/

Figure 4. Exploded view of basic spinel building block. (After Smit and Wijn, 1959)

The oxygens in the spinel structure are cubic clos­ est packed only to a first approximation. It is the shift mentioned above which in the majority of spinels causes the departure from the ideal closest packed configuration. The u parameter for ideally closest packed oxygens is 0.375. Some u values for actual spinels are less than the ideal value but the majority are greater as may be seen by the examples given in Table 3. Regardless of the value of u, IV the spinel structure is still cubic since the anion -M axis lies in the (111) direction and over the whole structure the basic building block occurs oriented with the 18 TABLE 3 u PARAMETERS FOR VARIOUS SPINELS

Spinel u Spinel u

CoAl2Oj| 0.390 Fe2TiOjj 0.390 FeAl2Ojj 0.390 Zn2T10ty 0.380 MnAl2Oij 0.390 Mg2Ti02, 0.390 NiAlgOjj 0.390 Zn2SnOi| 0.380 ZnA^Oij 0.390 Mg2SnOij 0.390 CdCr2Oi| 0.385 Co2SnOij 0.375 MgCr2Oij 0.385 Zn7Sb20^2 0.390

NiCr2Oi| 0.385 Co7Sb20^2 0.380 ZnCr2Ojj 0.375 Na^rfOj, 0.375 CuFe2Oij 0.380 Ag2MoOi| 0.364 MgFe20i| 0.382 Na2MoOi| 0.375 MnFe20ij 0.385 CdCr2Sj| 0.375 NiFe20ij 0.381 CinCr2S[| 0.381 ZnFe2Oj| 0.389 HgCr2Si} 0.392 FeFe2Oij 0.379 Nil^Sjj 0.384 MgGa2Oij 0.392 CdCr2Sei| 0.383 NiGa2Oij 0.387 CuCr2Seij 0.380 Cdln204 0.385 ZnC^Sei} 0.378 Mgln20ij 0.372 CuCr2Teij 0.379 CuMn20ij 0.390 K2Cd(CN)i, 0.370 NiMn204 0.384 K2Hg(CN)i| 0.370 MnV20|j 0.388 K2Zn(CH)i| 0.370

Source: Wyckoff (1948). 19 anion-MIV axis parallel to each of the four principal (111) symmetry directions.

The reasons that the u parameters for most existing spinel species are larger than 0.375 may be explained by considering the cation size. The tetrahedral voids present in the cubic closest packed anion structure are usually too small to accept those cations which prefer to enter them. This results in anions being forced away from the tetra­ hedral site in the (111) direction, thus making that site larger but at the same time making the octahedral sites smaller. This relationship is given by Smit and Wijn (1959) for small displacements of the radii of spheres in both types of interstitial sites as follows:

RIV = (u--J-)a VT-R o RVI = (5/8 -u)a -Ro where Ro is the radius of the oxygen ion and R*V and R ^ are the radii of the tetrahedral and octahedral voids, respectively. It is apparent, then, that two or more cations are in competition for space.

Distribution of cations over tetra­ hedral and octahedral sites

When Bragg (1915) and Nishikawa (1915) first des­ cribed the spinel structure, they assigned divalent mag­ nesium to the tetrahedral sites and trlvalent aluminum to the octahedral sites, an understandable choice from the standpoint of charge distribution. This arrangement was thus assumed for all (2-3) spinels until Barth and Posnjak (1932) described an alternate arrangement for sev­ eral spinels. This arrangement placed half the trivalent cations in the tetrahedral sites and the divalent cations along with the other half of the trivalent cations in t^e octahedral sites. With this discovery came the need for a term to distinguish between the two modes of distribution.

Barth and Posnjak termed the alternate to the Bragg and Nishikawa arrangement the "variate atom equipoint" distri­ bution. At a later time the Bragg and Nishikawa distribu­ tion became known as the "normal," and the Barth and Posnjak as the "inverse" arrangement. These terms have been universally adopted. Both normal and inverse spinels are extreme cases and are seldom actually obtained. Most spinels possess some intermediate arrangement with greater or lesser amounts of both cations in both sites. One special case exists with a statistically random distribu­ tion of cations over the tetrahedral and octahedral sites. This distribution is termed "random" and, it too, seldom strictly applies to any specific spinel; although, the possibility of obtaining this type is much greater than for either of the other two since it does not represent a dis­ tribution extreme as do the normal and inverse arrangements. Although distributions are seldom purely normal, ran­ dom or inverse, terms to describe the general cation arrangement are valuable for those spinels in which the ratio of the two cation species is the same as ratio of the 21 two sites in the structure, namely, 2:1. Spinels which possess this ratio are the (2-3), (2-4) and (1-6) types.

The following discussion considers the mere impor­ tant factors thought to influence cation environment pref­ erence in inorganic compounds and their application to the distribution of cations over the tetrahedral and octahedral positions in spinel.

(1) Radius Ratio

Pauling (i960) and several others have approached cation arrangement in ionic structures by considering the ions as rigid spheres. Packing of the larger anion spheres results in voids which are filled by the smaller cation spheres. The size of the cation which may be accommodated in a given void is determined by the cation to anion radius ratio Rm/Ro. The radius ratios which are of interest here are: Rm/Ro Site Preference 0.225 - 0.414 Tetrahedral 0.414 - 0.732 Octahedral If the radius ratio rule were strictly adhered to, very few of the cations listed in Table 1 could occupy tetrahedral sites in oxide spinels. Since it is known that a great many of these cations do occupy tetrahedral sites in oxide spinels, it is apparent that the radius ratio rule is not an important restriction upon the distribution of cations

in these spinels. Indeed, there often seems to be no relation between cation size and site occupancy in spinels 22 in general. In the mineral spinel, which is normal, the 0 L ® larger Mg (0.65 A) is in the tetrahedral sites and the o+ 0 smaller A1 (0.50 A) is in the octahedral sites. The reason that this rule is, in general, inapplica­ ble for spinels is believed due to the shift of the oxygens away from the tetrahedral sites. This phenomenon expressed by the parameter u has already been described. It suffices to say here that the enlargement of the tetrahedral site is made at the expense of the octahedral site size. It may easily be seen, therefore, that the size of the cations in tetrahedral sites may be larger and those in octahedral sites smaller than expectable on the basis of radius ratio rule. Nevertheless, size and distribution of cations do have an effect on unit cell dimension as has been-reported by Mikheev (1957) and Vermaas and Schmidt (1959). These cation distribution-unit cell relationships have been empirically developed. Unit cell dimension has been used to determine cation distribution where cations present are known but the method is considered inferior to X-ray inten­ sity measurements. A completely theoretical treatment on the relation­ ship of cation size and u parameter to unit cell dimension has been given by Saksonov and Somenkov (1964) but experi­ mental verification was not given. 23 (2) Simple Electrostatic Theory

Verwey and Heilman (19^7) explained cation distribu­ tion in spinels by electrostatic energy theory. Their lattic energy calculations, involving a three dimensional charge summation over eight unit cells, were found to be no more favorably correlative with experimental evidence than the simple observation that the cation with the smaller charge occupies the tetrahedral positions and the cation with the larger charge occupies the octahedral positions. Verwey and Heilman considered only (2-3) and (2—^4) spinels and with the examples they presented, there is good agree­ ment between theory and experiment with a few notable excep- "3 + 3J. tions. FeJ , InJ , and Ga show a decided preference for tetrahedral interstices and thus many, but not all, spinels containing these cations are inverse.

(3) Valence Bond Theory The strong affinity of certain cations for a given site may sometimes be explained on the basis of the valence bond or hybridization theory of Pauling (i960) as covalent contributions to the bond. 2+ The tetrahedral site preference of Zn , for instance, may be explained by assuming that three p-electrons are hybridized with one s-electron from the slightly lower 3 energy s-band to form a spJ hybrid with four bonds in the 2+ tetrahedral directions. The hydridized Zn ion in the tetrahedral site of the spinel structure thus has four 24 available bonding orbitals pointing directly towards the anions, allowing strong bonds to be formed. Other examples, however, do not agree with observa- tions on existing spinels. For instance, Co 2+ and Fe 2+ , 2 2 which should form d sp hybrids and enter octahedral sites are found in tetrahedral sites in CoA^O^ and FeA^O^. Thus valence bond theories have not been entirely success­ ful for the determination of cation distribution in spinels.

(4) Crystal-Field Theory One of the more successful theories to explain the distribution of transition metal ions in spinels has been the crystal-field theory. Orgel (1959) has given a compre­ hensive treatment of crystal-field theory. For the pur­ poses of this dissertation, however, a brief but lucid summary by Curtis (1964) will suffice and follows verbatim.

The wave-mechanical single electron wave functions for atoms can be written as the product of a radial function and a function dependent only upon the angular co-ordinates of the elec­ tron. In the case of a complete electron shell, the summation over all the electrons in that shell shows no net angular component. Thus the total wave function has only radial components, being spherically symmetrical. This is the theoretical basis for the concept of a spherical ion. In the case of the transition elements, however, the ions may not be symmetrical within a given field. Here the electronic structure of each ion must be considered further. The d-electron shell contains five electron orbitals, each of which can contain two electrons. The "density" or distribution pattern of an elec­ tron within an orbital is proportional to the square of the wave function, and hence the geom­ etry of the actual electron orbitals may be deduced from the relevant wave functions. They may be graphically represented as shown in Fig. 5.

xy xz yz

T t.

z

X

d r.2

T e

Figure 5. Graphic representation of the five d-electron orbitals (After Curtis, 1964). In Fig. 5, the intercept (intersection) of the axes (x,y,z) represents the location of the atomic nucleus, and the orbitals represents that portion of space within which each electron or electron pair is localized. It Is a property of atomic d-orbitals In an octahedral field, that their degeneracy Is removed and we can distinguish two sets. Such is the case when an Ion Is placed in an octahedral site within a crystal lattice. The e-orbitals ( d p p and d 0) will be the less stable x —y z group since electrons in these orbitals, and the negatively charged ions in the crystal, will be in closer proximity.

d„2 dx2-y2J,} S

>-i o K W 23 W } '2g

Figure 6. Energy splitting in an octahedral field. a=free ion b=ion in field (After Curtis, 196^)

The above concepts may be summarized by stating that when an ion is transferred from space into a field, the five normally degenerate d-orbitals split up into sub-groups of differing energies. This may be conveniently diagrammatically represented as In Fig. 6. A Is an arbitrary energy value attributed to this splitting, and is the difference in ener­ gies existing between the two orbital sub-groups. If the structure of ions containing more than one d-electron is now considered from the Aufbau approach, the electrons must be fed Into the or­ bitals according to Hund’s rules for determining the ground state of polyelectronic atoms. The Ions fill TABLE 4

OCTAHEDRAL CRYSTAL-FIELD STABILIZATION ENERGIES FOR IONS WITH ONE TO FIVE d-ELECTRONS

Number of Stabilization Total d-electrons Orbitals A stabilization

i < v + ! + l A

2 ^Xy)(dxz) +1+1- + r A 5 5 5

3 (dxy>(dxz>(dyZ) + ! + ! + ! + | A

4 (dxy)(dxZ)

5 (dXy)( dx z ^ dy z ^ dx2-y2) (dz2) Zero

Source: Curtis (1964). up with "maximum spin multiplicity," that is they will go into each of the five orbitals separately before any pairing of electrons will occur within a single orbital. The stabilities demonstrated in Figure 6 will then sum as shown in Table (4). The absolute energy of the free ion orbitals in space is arbitrarily fixed since we are only interested in relative ionic stabilities.

xy xz yz o 2/5 « w S3W 3/5

Fig. 7. Energy splitting in a tetrahedral field. a=free ion c=ion in field (After Curtis. 1964).

Note. If A is very large, Hund's'rules may be dis­ obeyed, and pairing will occur. In the case of the first transition series, this situation does not arise for oxide complexes, and thus will not be considered further. In a tetrahedral field, where an ion is sur­ rounded by four negatively charged immediate neigh­ bours, the situation with respect to orbital sub­ group stability is reversed. The e-sub-group of orbitals are now stabilized relative to the t2 group. The splitting is shown in Fig. 7, and is assigned the symbol A*. Calculations based on elec­ trostatic models give the theoretical relationship A 1 = 4/9 A. Table 5 is a summary of the stabilization ener­ gies expected in octahedral and tetrahedral environ­ ments for the first series of the transition elements. 29 TABLE 5

STABILIZATION ENERGIES EXPECTED IN OCTAHEDRAL AND TETRAHEDRAL ENVIRONMENTS FOR THE FIRST SERIES OF THE TRANSITION ELEMENTS

Stabilization Stabilization Number of in oxtahedral in tetrahedral Ion d-electrons field (A/10) field (A’/10)

Sc3+ 0 0 0

Ti3+ 1 4 6 V3+ 2 8 12

Cr3+ 3 12 8 Mn3+ 4 6 4

Fe3+ 5 0 0 Fe2+ 6 4 6

Co2+ 7 8 12 Ni2+ 8 12 8

Cu2+ 9 6 4 Zn2+ 10 0 0

Source: Curtis (1964). 30 Table 5 of the Curtis work is the key to site pref­ erence of a given cation, the greater the difference in the stabilization energies between octahedral and tetrahedral sites, the greater the preference. Thus, Cr^+ and Ni2+ would exhibit strong preference for octahedral sites, Cu2+ a strong tatrahedral preference. Notice that Zn 2+ and 3+ Fe , which both have a strong tetrahedral site preference as determined experimentally, exhibit no crystal-field effects.

McClure (1957) and Dunitz and Orgel (1957) applied crystal-field theory specifically to the problem of cation distribution in spinels. They found good agreement between theory and experiment for transition metal cations. Miller (1959) extended the concept of site preference energies to include, along with crystal-field stabilization energy and lattice energy, the short range energy. On the basis of his calculations, a set of site preference ener­ gies were formulated, which may be used to predict the ionic distribution of spinels involving the non-transition metals as well as the transition metal cations. In Table 6, the octahedral site preference energies are listed in increas- ing order of preference for the octahedral site with CrJ3+ showing the strongest preference of all those listed. The two or more cations present are in competition for the two available sites; therefore, the one with the greater octrahedral site preference will occupy that site while the TABLE 6

OCTAHEDRAL SITE PREFERENCE ENERGY FOR VARIOUS CATIONS Octahedral Site Preference Energy Cation K. Cal/Mole In3 + ...... -40.2 Zn2+ ...... -31.6

Ca2 + ...... -30.7 Cd2 + ...... -29.1

Ti3 + ...... -21.9 Ag1 + ...... -19.6

Ga3 + ...... -15.4 Mn2 + ...... -14.7 Fe3 + ...... -13.3 V3 + ...... -11.6

Co2 + ...... -10.5 Fe2 + ...... - 9.9 Cu1 + ...... - 8.6

Mg2 + ...... - 5.0 Li1 + ...... - 3.6

Al3 + ...... -2.5 Cu2 + ...... -0.1

Mn3 + ...... 3.1 Ni2 + ...... 9.0 Cr3 + ...... 16.6

Source: Miller (1959). 32 other(s) occupy the tetrahedral sites. Miller states that should two competing cations possess octahedral site pref­ erence energies within 3 K. Cal./Mole of one another, the resulting distribution is uncertain.

Miller (1959) and Hoekstra (1965) have found good agreement between these data and experimental observations.

The cation distribution has been shown to be dependent upon the thermal history of the spinel. Several reports on the temperature dependence of cation distribution in spinels have appeared in the literature. Greenwald et al. (195*0, Callen et al (1956), Schmalzried (I960), Datta and

Roy (1961), Datta (1962) and Hoekstra (1965) all report changes in cation distribution of various spinels as a func­ tion of temperature of formation. Experimental work is presently underv/ay to investi­ gate the variability of distribution as a function of pres­ sure. Results on NiAlgO^, thus far, have indicated changing distribution with changing pressure of formation (personal communication, Trent, 1969). Thus far, no consideration has been given to the man­ ner in which the cations are distributed over a given sub­ lattice, that is, over the specific sites within the unit cell. Barth and Posnjak (1932) assumed no ordering on the sites. It has since been learned, however, that whenever two or more cations occupy the same position there is a tendency towards long range ordering. Gorter (195*0 has described three types of long range order in sublattices of 33 the tetrahedral and octahedral positions in spinels: 1:1 order on the tetrahedral position; 1:1 order on the octa­ hedral position and; 3:1 order on the octahedral position. The last two types of ordering result in superlattices and a

reduction of space group to tetragonal or orthorhombic symmetry.

A type of disorder can also be imagined in spinels. In spinels, only 1/2 of the octahedral and l/8th of the tetrahedral interstices are filled. There is a certain probability, considering the flexibility of the spinel structure, that a fraction of the cations occupy these other

interstices, but disorder of this type has not been des­ cribed in the literature so far as the writer could deter­ mine .

Departures from cubic symmetry

Thus far, only cubic spinels have been considered; however, tetragonal and orthorhombic modifications of the

spinel structure have often been described. These have been referred to as "distorted" spinel structures. Li (1932) described Fe^O^ as being orthorhombic below 119°K but cubic above this temperature. Prince (1956) described a tetragonal CuFe20^ below 76o°C although quenching from above this temperature allowed the cubic structure to exist mctastably at room temperature. Cullity (1956) has treated

the subject of changes from cubic to tetragonal or orthor­ hombic symmetry with regard to splitting of X-ray peaks. 34 An example of this X-ray peak splitting in tetragonal CuFe20jj

synthesized by the writer is given in Figure 8. This figure shows the splitting of the (440) peak in the cubic phase to the (440) and (404) peaks in the tetragonal phase. Tetragonal modifications of the spinel structure may be shortened or lengthened along the c axis. Figure 9 shows polyhedral drawings of a portion of the spinel struc­ ture indicating tetragonal modifications of this type.

Theories which best explain tetragonal modifications of the cubic spinel structure are based on crystal-field effects. Certain cations with unfilled d-electron shells are not stabilized by the octahedral or tetrahedral field but are destabilized. The most common cation which under- goes this destabilization is Cu ? + (d^) Q in an octahedral field.

Curtis (1964) has explained the tetragonal modifica- P + tion by cations such as Cu in octahedral sites in the

following manner. The d-electron configuration of Cu?+ } (d^) is (tg ) (eg) • In an octahedral field a doubly de­ generate ground state is possible, i.e., (dz2)^ (dx2_y2) and (dz2) (dx2_y2)1 . In the latter case there are two electrons concentrated along the z-axis, and one In the xy axial plane. Hence the electrons in the xy plane screen the nuclear posi­ tive charge from the negatively charged (02-) ions less effectively than those centered on the z-axis. The ions in the xy plane (02-) will then be attracted by a larger apparent nuclear charge than those along the z-axis. Consequently the system would be expected to re-arrange to an equilibrium position, the re-arrangement involving the shortening of inter-ionic separation in the xy plane, and increasing the separation along the z-axis. 35

62°20

Cubic CuPe_0^ Tetragonal CuFe20a Quenched from 900°C Quenched from 500®C

Figure 8. X-ray peak splitting in cubic and tetra­ gonal modification of CuFe20||. 36

Shortening along z axis Normal

Elongation along z axis

Figure 9. Polyhedral structure drawings of a portion of the spinel structure— showing tetragonal modifications (After Hoekstra, 1965).

Orgel (I960) discussed the distortion in tetra­ hedral sites as follows:

. . . the unstable t2 orbitals in tetrahedral complexes interact more strongly than the e 'orbitals with the ligands. Thus large dis­ tortions are expected only when we have 1, 2, 4, or 5 electrons in the t2 orbitals, i.e., for the . . . d3, d^, d°, and d9 complexes. 37 First, let us suppose that there is just one’ (or four) electrons in the t2 orbital. Then if we take the tetragonal axis as the z axis it is clear that the d-electron must be present in the dxy orbital. It then follows that the tetrahedron must be elongate . . . for the dx2_y2 electron repels the ligands. This case would apply to Cr^+(d^) and Ni2+(d®) and would cause a distortion as shown in Figure 10. Orgel continued, If we have two (or five) electrons in the tg orbitals the situation is rather different. If the tetragonal symmetry is to be maintained we must put the two electrons in the dxz and dyZ orbitals and then the repulsion between electrons and ligands leads to a flattening of the tetra­ hedron towards a plane. This is most clearly seen by remembering that two electrons in the dXz or dyz orbital are equivalent to a positive hole in the dxy orbital, since three electrons would just half fill the t2 orbitals. Such a positive hole must atti’act the ligands. . . as shown in Figure 11. This case applies to Cu^+ (d9).

Goodenough and Loeb (1955) and V/ojtowitz (1959) re­ ported the cause for tetragonal modification in spinels to be the alignment of the d-orbitals which exhibit disorder by random alignment in the three crystallographic direc­ tions at higher temperatures. Hoekstra (1965) and Obryan et_al.(1966) have since related distortion, at least in CuFe20ij and CuCr2Oi}, to the distribution ratio of Cu2+ ions in octahedral and tetrahedral sites, respectively. It is quite possible that tetragonal modifications are due to either or both of the above effects. No one has yet des­ cribed the effect of temperature on crystal-field stabil­ ization energies. 38

Figure 10. Tetragonal modifications (elongation) in a tetrahedral field (After Orgel, i960).

Figure 11. Tetragonal modification (shortening) in a tetraedral field (After Orgel, i960). 39 Goodenough and Loeb attribute orthorhombic modifica­ tions to cation ordering on octahedral sites and the strength of covalent bonds on tetrahedral sites. No explanation of orthorhombic modifications on the basis of crystal field effects was located in the literature. This type of transformation, through distortion, of one spinel-like structure to another is a phase transition and the phases are polymorphs. No discussion of poly­ morphism in spinels would be complete without mention of the olivine-spinel transitionvhich is the basis of one theory on the constitution of the mantle. Although no one has successfully caused this transition by the application of pressure to MggSiO^, forsterite, there is little doubt that such a transition does occur. Many analogous transitions from the olivine structure to that of spinel have been re­ ported. Ringwood (1962) has produced these transitions in Fe2SiOij (fayalite), Co2SiOij, Mg2(Ge,Si)0ij and (Ni,Mg)2 (Ge, Si) 0 . Albers and Rooymans (1965) reported a high pressure transformation of FeCr2Sjj to a structure related to the common hexagonal NIAs type. Bouchard (1967) described a transformation of FeCr2S]j and CoCr2S/j to the monoclinic ordered defect NiAs type. This type of transformation might also have significance in theories involving the constitution of the mantle. STATEMENT OF THE PROBLEM

A comprehensive treatment of the crystal chemistry of the spinels has been given. This alone, should provide considerable understanding of the spinels as a structural group. There exist, however, two factors limiting under­ standing of the group as a whole.

First, certain terms and modes of notation which are conventionally used to describe spinels and their peculiarities are not consistent with present knowledge of the group as a whole. Continued use of terms which do not describe existing conditions for the entire group tends to restrict general understanding of the group. New terms and improved notation will be proposed.

Second, there exists no classification scheme into which the various spinel types may be placed; no common denominator to relate every spinel to every other spinel.

This too constitutes a restriction to understanding as well as to investigations into the synthesis of new spinel types. A classification scheme and a method to aid in the prediction of possible new spinels will be given.

40 SEMANTICS PROBLEMS

At the time that Barth and Posnjak (1932) first recognized that several modes of cation distribution could exist in spinels, the only spinel types known were the (2-3) and (2-4) types. Use of the terms "normal" and "inverse" wore adequate to describe distribution in these types since the two kinds of cations are present in the same ratio as the two kinds of structure sites, the octahedral and tetrahedral. The (2-3) and (2-4) types each have formulas of the form AB2X/j with twice as many of one cation as the other. At the same time the structure has twice as many octahedral as tetrahedral sites occupied.

"Normal" filling of the sites places all A cations in tetrahedral sites and all B cations in octahedral sites. The "inverse" distribution has half of the B cations in the tetrahedral sites and the other half of the B and the A cations on octahedral sites.

Only four of the spinel types listed in Table 2 have the proper ratios of the two types of cations to allow normal or inverse filling of the sites. These are the

(1-2), (2-3), (2-4) and (1-6) types. All other types do not contain the proper ratios of cations. For example, in the

(1-3) type, m 1+m 3+X?“, a distribution could not exist in 5 * 41 42 which one site was filled only with M*+ and the other site was filled only with m 3+ . The two possible extreme distri­ butions are (M1+M3+)IV (m 3+)vi Xg“and (M^+)IV(M1+M3+)VI Xj^" and neither of these may be called "normal" in the original sense of the term. On the other hand, both distributions

contain more than one cation species at either the tetra­ hedral or octahedral sites. Both distributions could

therefore be termed "inverse." This situation exists for the (0-3), (1-4) and (2-5) types as well.

It is the writer's contention that continued use of these terms perpetuates a barrier to understanding of the great diversity of the spinels as a structural group. Not only are the terms inapplicable for the description of cation distribution in the spinel group as a whole but they are also confusing because they cannot be used to describe cation distribution in all spinels. Lack of usage of com­ prehensive cation distribution terms tends to imply that distribution is not an important factor. This implication is not true. It will be shown later that in certain spinel

formula types a certain cation distribution exists but that another distribution does not. It is true that there are more (2-3) and (2-4)

spinels than all others combined; nevertheless, terms as definitive as the distribution terms should encompass the whole, not just a portion of the group. In the following paragraphs, terms are proposed which alleviate this problem. The basis for the "normal" and "inverse" distribution classification system is one of positive or negative cor­ respondence between the number of cations and number of sites. The basis for the proposed system is also one of correspondence but one between cation valence and coordi­ nation on the sites. In one distribution the lower charged cations occupy the sites with the lower or tetrahedral coordination and the higher charged cations occupy the sites with the higher, octahedral, coordination, as nearly as possible. This distribution is termed "homologic"

(from the Greek homo, same + logos, relation) alluding to the low to low, high to high correspondence. The alternate distribution has the higher charged cations occupying the lower coordinated tetrahedral sites and the lower charged cations occupying the octahedral sites, as nearly as pos­ sible. This distribution is termed "heterologic" (from the Greek hetero, different + logos, relation), alluding to low to high, high to low relation. "As nearly as possible" in these definitions simply means that if there are too few cations of one kind to fill all of one site, the shortage is made up by the other cation. These homologic or hetero­ logic distributions describe cation distribution in any spinel with no confusion of terms. Comparison of the "normal" and "inverse" distributions and the homologic and heterologic distributions for those spinel types given in Table 2 are given in Table 7. All the distributions given do not necessarily exist. 44

TABLE 7

COMPARISON OP "NORMAL" AND "INVERSE" WITH "HOMOLOGIC" AND "HETEROLOGIC" DISTRIBUTIONS

Proposed Old Spinel Distribution Distribution Distribution Type Formula Tetr. Oct. Designation Designation

(1-2) m 1+m 2+x 1- M1+ m 1+m 2+ Homologic Inverse

M2+ m !+ Heterologic Normal

(0-3) y m ^+x |” m 3+ m |+ Homologic - 2 m 3+ m |+ Heterologic - MH+xii 3 5 (1-3) M1+M3+X2- M1+M3+ Homologic - 5 5 M3+ m H-m 3+ Heterologic - 2 Mi+M4+ (1-4) Mj+M^+X2- m J+ Homologic - 3 5 m 4+ Heterologic - 3 4 2 (1-6) M1+M6+xf" M1+ jjl+Hj6+ Homologic Inverse 2 4 m 6+ m *+ Heterologic Normal

m 2+m |+x 2- m 2+ Homologic Normal (2-3) M2+ m 3+ m 2+m 3+ Heterologic Inverse m m (2-4) m2+m 4+x2- m 2+ 2+ 4+ Homologic Inverse 2 4 M^+ m 2+ Heterologic Normal

(2-5) m2+m5+x2- M§+ m ^+m 5+ Homologic - 7 2 12 M2+M5+ Heterologic - 2 m 6+ Note in Table 7 that the homologic distribution cor­ responds to the normal distribution in the (2-3) spinel type but nowhere else. The two sets of terms are not inter­ changeable, then, even for that portion of the group in which the normal and inverse terms were previously applied. The terms homologic and heterologic have been chosen carefully so as not to imply stability or preference of one distribution over another. This was also a drawback of the other system. At first glance the homologic distribution may appear to be more stable than the heterologic distribu­ tion because of maximum charge neutralization brought about by a cation’s coordination but it will be shown later that this is not necessarily the case.

This solves the greatest semantics problem to the understanding of the variety and extent of the spinel structural group. Other problems will be encountered in following sections and will be discussed at that time. These problems are minor and are primarily problems with notation. In all of the preceding discussion no mention was made of the term "random." This term, which was previously used, is completely compatible with the proposed system and correctly describes that distribution in which the cations occupy both sites in the same ratio in which they occur in the formula for that particular spinel type. STOICHIOMETRY-ELECTRONEUTRALITY

In the previous section on the chemistry of spinels, the various commonly recognized spinel types were des­ cribed, i.e., (1-3), (1-4), (1-6), (0-3),(2-3), (2-4) and (2-5). Hoekstra (1965) recognized that the (1-5) and (2-6) types were absent from this grouping even though they con­ tained no cation valences which did not occur in some existing spinel. It was proposed that these two types be added to the grouping even though neither type was repre­ sented at that time by an existing compound and neither type had been synthesized after several attempts. The value of considering these as spinel types lies in the fact that they might be considered as existing in solid solution if not by themselves. The compound Li^Zn^Sb^+Ojj described by Blasse (1963) could be represented by a 1:2 combination of the (1-5) and (2-5) types as follows:

7Li20 • 5 Sb205

2(7ZnO • Sb205)

adding and collecting terms Li-LijZni4Sbl4®56

-r 14 LiZnSbOjj

46 Bayer (1967) justified the proposal of the (2-6) type with the synthesis of Zn^+ Co^+Te^+0g. In this com- s pound, Zn occupies the tetrahedral sites and the octahedral sites are occupied by cobalt and tellurium. The series of possible combinations of divalent anions with cations one through six was thus completed. Many of the papers describing the synthesis of new spinel species begin, "in the course of an investigation

. . . ." or, "subsolidus equibrium studies in the system ______revealed," suggesting that the species described therein were discovered by accident, not by design. If spinel types representing possible combinations of anions and cations were to be used as building blocks, the number of theoretically possible combinations is very large. Systematic exploration of the possibilities sug­ gested by these numerous combinations would possess the value associated with designed Investigations. Many com­ binations have already been described as will be shown below, but many others undoubtedly remain to be discovered. Datta (1962) described a solid solution series be­ tween (1-3) and (2-3) types, namely, Li Al^ Og - Mg AlgO^. Durif and Jaubert (1962) and Jaubert and Durif (1964) described compounds formed from the (1-4) and (2-4) types

Li2(Zn, Co) Geg Og and LI2 Zn (Mn, Ti)^ Og. Perotta and McCallum (1963) reported the synthesis of a spinel, Lil+ Zn^+Fe^+ Ge!}+ 00/- which can be shown to break down into 5 8 5 9 36 48 the spinel types (1-3), (1-4) and (2-4) in the following manner: Li20 • 5Fe203 2(2Li20 • 5Ge02) 8(2ZnO * Ge02) adding terms ‘ and collecting LijL0Znl6Fe10Gel8°72

* 2 Li5Zn8Fe5Geg036

Dulac (1962) synthesized the spinel compound Li(Cr,Rh)GeO^ which is a combination of the (1-3) and (1-4) types. The writer's personal experience has shown solid solutions between certain (2-4) and (2-5) types. Study of the various spinel types in Table 2 and those complex compounds mentioned above leads to an ampli­ fication of Evan's statement that the total cation charge is the most significant factor influencing the spinel structure. This amplification is simply that for every four anions there are three cations which electrically balance the charge of the anions. The one notable exception to this rule, which the writer has chosen to term the Stoichiometry-Electroneutrality Rule, is that of the yFe2C>3 type but this exception will be discussed later.

Assuming, for a moment, the complete validity of this Stoichometry-Electroneutrality Rule, what would be the theoretically possible valence types? This question was answered by calculating all possible and reasonable 49- combinations which satisfied the rule. Valence limits were set at seven for cations and four for anions, each valence limit being one unit of charge greater than that of any cation or anion reportedly existing in any spinel. A formula was needed which could accommodate highly variable valences and numbers of cations. In order to eliminate the problem of balancing charges, constituent com­ pound formulas, similar to conventional oxide formulas, such as, M2+X2“ • M3+X2“(Zn0-Al20o) and M^+X2- • 5M^+X^“ ^ J J ^ 2 3 (Li20•5AI2O3), were used. The formula used to determine the proper combining ratio of the two constituent compounds to yield a cation to anion ratio of 3:4 follows: n(No. of M 1s in compound 1) + No. of M*s in compound 2 _ _ n(No. of X-'s in compound 1) + No.'of X’s in compound 2 ~

Examples demonstrating the manner in which n is used are:

(1) Given: M2+X+M^+S3

What is the mixing factor n to yield a M: X of 3:4?

P. +-?. = 3/4 n + 3 3/ n = 1, or the ratio of compound 1 to compound 2 is 1:1 .*. 1M2+X * 1m|+X3 (lZnO • 1A1203 = ZnAl204)

(2) Given: M ^ X + M ^ What is the mixing factor to yield a M:X of 3:4?

2n + 2 _ 3/4 n + 3 3/ n = 1/5, or the ratio of the first compound to the second is 1:5 .*. M*+X * 5m|+X3 (Li20 •5A1203 = LiAl50g) In this way Tables 8, 9 and 10 were formulated. Before discussing these tables several subjects should be covered.

To this point the various formulas which express the vari­ ous cation valence combinations that can exist in spinels have simply been called spinel types. Use of the term "type" alone is rather non-definitive and could mean differ­ ent things to different people. For this reason the writer proposes the term "valence type" to describe these formulas. The notation which designates the valence types is also in need of some revision. The present system of notation such as (1-3) takes no cognizance of the valence of the anion. Therefore, it is proposed that a superscript designating the valence of the anion be added— (1-3)^, (1-3)2, (2-3)2, (3-5)^, etc. This is particularly valuable since one grouping of valence types has common cation and mixed anion valences. This grouping of valence types uses a notation such as, (2)1-2, (3)2-^, etc. The valence type formulas given in Tables 8, 9 and 10 have been expressed in constituent compound formulas. No attempt to place these

formulas on the basis of either four or thirty-two anions was made because doing so would frequently require using other than whole number subscripts. Table 8 lists the theoretical spinel valence types 2+ 2- 3+ 2- with mixed cations and a common anion, such as M X and M ^ X ^ - * 5M2+X^~. This table contains the great majority of all existing spinels, namely, (l-2)\ (1-3)2, (l-1*)2, (1-6)2, (2-3)2, (2-iJ)2, (2-5)2 and the (2-6)2 recently Anion Valence cti > i 5 2 4 3 1 —I 3 2 1 1 2 0 c o o 2 M - L + X - * - V K 2+x j j j * Cationlower with valence. Cation withhighervalence. m M2+X275M3+X2' MIXED-CATION, COMMON-ANIONSPINEL VALEN 5 m 2+ 1 x +x 27 1 m tm |+ 3 x x- m+^t^x- UMI+X^t SmI+x^-tm^+xJ-+x^- §" 2M2+ X^ .5M2M^X 1 + x 2 2 5 4 TABLE8 m t - MhValenceb 1*+ x B“ 2 -

51 3M3+X3T 3M2+ 3 .M; X 7M 7M2+X m 2 1+ + x x |76 2 2 3 T51 t ' - m 9I i :

51

TABLE 8

D-CATION, COMMON-ANION SPINEL VALENCE TYPES

Mh Valence13

3 4 5 6 7 x !t m 3+X^- Sm I+x I-t m ^+x J- 11M1+x 1tM5+x 1“ 14m 1+X17M6+x J- 17m 1+x 1t m 7+x'i-

1+ 2- 4+ 2- 275M3+X2“ 2M^ X .5M Xj 7M2+X2 75M^+X^" 5M2+X275M6+X2_ 13m1+X275m£+X2-

27M3+X§" 2M2+X27M^+X§" 7M2+X27m^+X2“ 5M2+X27M6+X§- 13M2+X2t m 7+x 2_

1+ 3- 6+ 3- 3Ml+Xr379M^+X^- 2M3 X -9M Xj 9M^+X37 9M^+X3-

3M2+X376M^+x|” 2M2+X37 6M^+x2~ 9M2+X376M^+X3“

3M3+X37m|+ x|" 2M3+X37M6+X3“ 9M3+X37M^+X3”

Mj+X4713M^+X^" SMjtx^lSM^X^

M^X^TSMl+xjj” 5M2+X^7 5M^+Xy“

M 3+X377M2+X3~ 5M3+X377M^+X^”

M 1<+X1,7m|+X 3" 5M4+X^7m7+x;J- 5+ 4- 7+ 4- 5MjJ X5 .M^ X? m 4^+ x J- 5 m d^+ x 35_ ter valence.

;her valence. 52

TABLE 9 COMMON-CATION, MIXED-ANION SPINEL VALENCE TYPES

0) o c a) Anion (X) with Higher Valence rH c o cd 2+ 1- 2+ 3- 2+ 1- 2+ 4 > M2+X^"*2M2+X2“ 3M XY"1 M3 Xy2 5M Xj *2M X u 0) 7M3+X^"*5M3+X3 s 3 M3+X^“ ‘5M3+X3' o 4 M I,+X1" * 8M1,+Xl,“ A 4 ■p M5+x£“ -llMjj+x5“ •H 5 4 5

3 M3+X2-.M3+X3- 7M3+X2-.M3+X ^ 2 3 4 3 o 2 4 m 4+x 2-.2m 4+x 4- •H C 5 m 5+x 2-.7m §+X^-

M^+X^T3M§+X+v4- 5 53 TABLE 10

LACUNARY SPINEL VALENCE TYPES

Anion (X) Valence

1 2 3 4

1 a • 3M1+x 5 a • 3m J+X2~ 9a ♦ 3M*+X3- 13a • Sm J+X4'

2 2 □ * i}M2+X2~ a • 3M2+x 2- 6a •3M2+x |- 5a • 3m |+x 4- o G 3 5 □ ‘4M3+xi“ □ . 4M3+X2- a •3m 3+x 3- 7a • 3Mij+X^

a - Anion Vacancy. □ - Cation Vacancy. described by Bayer. Table 9 lists the theoretical spinel valence types with common cations and mixed anions, i.e., with the con­ stituent compounds having different anions, such as, m|+X3“ * M^+X^“ or (3)^"*^ which is represented by the exist­ ing species A-*-2®3 ’ a]lN as rePorted by Yamaguchi and Yanagida (1959)* No other existing spinels of this valence types are known to the writer. Table 10 lists the theoretical lacunary spinel valence types, i.e., with cation or anion vacancies viewed as cations or anions as far as the formula is concerned. For example:

3+ (1) □ + H Oj □= Cation Vacancy What is the mixing factor n to yield a M:X of 3:4?

P- f - o/lj 0 + 3 n = 1/4, or the ratio of compound 1 to compound 2 is 1:4

□ + 4m |+03 ( □ *4Fe203~ □ Fe8°12 or YFe203)

(2) Q + M^+N S = Anion Vacancy What is the mixing factor n to yield a M:X of 3:4?

0_t_l = 3/4 n + 1 n = 1/3, or the ratio (f compound 1 to compound 2 is 1:3 3 • 3M^+N (No reported examples) 55 Considering the vacancies as cations in the species yFegO^ eliminates the one commonly recognized exception to the

Stoichiometry-Electroneutrality Rule. Lacunary spinels which may be expressed as the com­ bination of two of the valence types given in the tables have been described by Joubert and Durif (1963 and 1964). These investigators have reported the synthesis of 2 □ZnjpTi^Og which is a 2:1 ratio of valence types (2-4) and

(0-4)2 and of DCo^V^g from a 3:1 ratio of (2-5)2 and

(0—5)2 valence types. Tables 8, 9 and 10 do not cover those cases in which both the cations and anions are mixed, e.g., M 4+ 1- and which, by use of the formula for combining ratio, is shown to be a 5M**+xJ~ • 8M2+X2~ complex valence type. That

this is actually a combination of the 8M-*-+X^” ' MI,+xJ" and 2M2+X2- ' 5M,,+X2- valence types may be demonstrated as

follows: By inspection the solid solution formula covering the case of the combination of the two valence types mentioned above is

M*!;+ M ^ x 1" X^ ~ (Basis 12 anions) 8-y y+l i2-3y 3y

where y-=0 represents 8M^+X^- *M1<+xJ"" or

M^+ M^+X^“ and y = 4 represents

2M*+X2- • 5M1,+X2~ or Mj+M^+X2- 56

The • 8m^+X2" or Mi6M5+X2oX8~

complex valence type which has a basis of 28

anions may be placed on the basis of 12 anions by dividing by 7/3 Y-^" y 2“ U8/7 15/7 60/7 24/7 clearing fractions yields M1+ M1,+ X1- X^. 6.857 2.143 8.571 3*^29 which satisfies the conditions of y=l.l43 of the solid solution formula given above for the 1 2 combination of the (1-4) and (1-4) valence types.

At least one existing spinel species has been reported with mixed cations and anions. Yanagida et al. (1966) described a LiF'A^O^ spinel which may be shown to be a mixture of the (1-3)^* which is apparently still another valence type which exists in solid solution but not by itself, and

(1-3)^ as follows: The valence types written as given in the tables are

5M1+X1- ' M3V “ and M ^ X 2- ' 5M^+X^-

These may be written

m J+M3+X^~ and M1+M3+X2“ 5 8 2 10 16 or in order to obtain an anion basis of 8 the 57 latter may be divided by 2 to give

M1+m3+x2- 5 o

By inspection the solid solution formula covering the case of the combination of these two valence types is

M3* x1“ X2“ 5-y y+l 8~2y 2y when y=o this formula yields M^+M3+Xq-

when y=4 this formula yields M^+m|+Xq”

if y=3 this formula yields Mj+Mjj+X^"X§” or M1+m3+X1"X2“ or

M1+X1_ *M^+X^“ — LiF*Al203

One theoretical spinel valence type which does not right­ fully belong in any of the tables is the (4)3 valence type which satisfies the Stoichiometry-Electroneutrality Rule with only one kind of cation and one kind of anion. It is important to remember that the valence types in these tables do not necessarily exist as actual spinels. The stoichiomctry-electroneutrality basis for the calcula­ tions assumes ionic bonding, a condition which could not possibly exist in certain of the valence types tabulated. The combination of a cation with a charge of seven and an anion with a charge of four is not likely to yield an ionic bond. Evans (1964) states that nitrides and carbides of the transition elements form a series of structures called interstitial structures which possess many of the properties of metals and act more like alloy systems than stoichiomet­ ric compounds. Some of the lacunary valence types show numerous cation or anion vacancies. A condition of many vacancies cannot be imagined in ionic structures. If ionic bonding character is important to spinel formation, as it appears to be, then the existence of these valence types seem unlikely. If ionic bonding character is not important to spinel formation some of these valence types may well be found to be represented by existing species. Nevertheless, these tables of theoretical spinel valence types should encompass every known or possible spinel, except for (4)3, and could greatly aid in the dis­ covery of new spinel species as well as forming a basis for classification of the existing members of the spinel struc­ tural group. RESIDUAL CHARGE PRINCIPLE

A large number of valence types has resulted from the stoichiometry-electroneutrality calculations, yet only a few of these are represented by existing species. It is of interest to speculate whether or not any of the many remain­ ing valence types might also be represented by valid spinel species which have not yet been synthesized. A method to designate which of these valence types are possible spinel formers would provide an extremely valuable aid in future experimental investigations into the synthesis of new spinel species. A discussion of such a method follows. The fact that the valence type tabulations, based on stoichiometry and electroneutrality principles, include every known existing species indicates that the spinel structure is basically ionic. This evidence justifies an electrostatic approach to determination of factors limiting spinel formation. Pauling's electrostatic valency princi­ ple, which states that the total strength of the valency bonds which reach an anion from all neighboring cations is equal to the charge of the anion, does not hold for many existing spinels. The heterologic (2-3) spinel is of this kind. In this spinel there are equal numbers of divalent and trivalent cations to fill the three octahedral sites

59 surrounding each anion. This means that the cation valence bonds are not balanced at neighboring anion sites but that

there must be two distinct kinds of anions, each with an equal residual charge of opposite polarity. In these cases

cationic charges are not neutralized directly by the coordi­ nated anion but through that anion to its surrounding anion neighbors. An attempt to define the extent of cation

valence combinations allowable in the spinels from the viewpoint of the partition of anion charge will now be undertaken. Consideration of the partition of an anion's charge among its cation neighbors in the various spinel valence types reveals that residually charged anions are the rule rather than the exception. This consequence leads to

speculation that the magnitude of the residual charge is a significant factor limiting spinel formation. That the

residual anion charges in ionic compounds should be low is a logical extension of the Electrostatic Valency Principle.

It is proposed as a general principle that, in those cases in which there must exist anions of varying residual charge, the most stable arrangement of cations is such that the

residual charges on the anions are held at a minimum. The writer has chosen to call this the Residual Charge Princi­ ple. To test this principle on the stability of spinels, calculations of residual anion charges were made. The

residual charge on the anions was calculated for each of the two distribution types, i.e., homologic and hetrologic for 61 each reasonable valence type. In doing this, the assump­ tion is made that the number of distinct anion types is limited to two, in accordance with Pauling's fifth rule that the number of essentially different kinds of constituents tends to be small. The determination of minimum residual charge on the two kinds of anions was determined by trial and error. The results of the calculations is given in

Tables 11 and 12. The residual charge calculations were made as fol­ lows: 1) the charge contributed to each anion by each cation in the different sites was determined by dividing the cation charge by the coordination number; 2) the relative number of cations per anion was determined; 3) the charges were then combined in such a way to give one type of anion with no charge or two types of anions with ‘the lowest possJble charge. Examples are shown on the following pages. Example (1) Valence Type (2-3)^ M^+ M3+ X^“

Homologic Heterologic

Tetrahedral Octahedral Tetrahedral Octahedral

1. Cation M2+ M3+ m3+ m2+ m3+ 2 2. Cation charge/ Coordination number 2/4 3/6 3/4 2/6 3/6

3. Na. of Cations/Anion 1 3 1 3/2 3/2 4. Clearing Fractions where required 1 3 2 3 3

5. Combination of Charges +2/4 +3/6 +3/6=24/12 +3/4 +3/6 +3/6 + 2/6=25/12 +3/4 +3/6 +2/6 + 2/6=23/12

6. Residual Charges 0 + 1/12 - 1/12 Example (2) Valence Type (2-6)2 m 2+ M^+ X2” 5 8

Homologic Heterologic Tetrahedral Octahedral Tetrahedral Octahedral 2+ 1. Cation M M2+ M6+ M2+ M6+ M2+

2. Cation Charge/ Coordination number 2/4 2/6 6/6 2/4 6/4 2/6

3. No. of Cations/Anion 1 9/4 3/4 1/2 1/2 3 4. Clearing Fractions where required

5. Combination of Charges 3(+2/4 +2/6 +2/6 +6/6) = 26/12 +6/4 +2/6 +2/6 +2/6 - 30/12 +2.4 +2/6 +2/6 +2/6 = 18/12 +2/5 +2/6 +2/6 +2/6 = 18/12

6. Residual Charges 3C+2/12) - 6/12 +6/12 - 6/12

NOTE: 3(+2/12) means that there are three anions with a residual charge of +2/12 to neutralize one anion with a -6/12 residual charge.

o^ OJ Example (3) Valence Type (3)^”^ M^+ ^3” x^~

M2- Anion M3- Anion

TetrahedralOctahedralTetrahedralOctahedral

1. Cation M3+ m 3+ m 3+ M3+ 2 2 2. Cation Charge/ Coordination number 3/4 3/6 3/4 3/6 3. No. of Cations/Anion 1 3 1 3 4. Combination of Charges 3(+3/4 +3/6 +3/6 +3/6 = 27/12 +3/4 +3/6 +3/6 +3/6 = 27/12 5. Residual Charges 3C+3/12) -9/12

NOTE: In common-cation, mixed-anion valence types there can be no anions without residual charges. At the same time homologic and heterologic have no real meaning here because all sites are occupied by the same cation. TABLE 11

RESIDUAL CHARGES FOR VARIOUS MIXED-CATION, COMMON-ANIONS VALENCE TYPES

Homologic Heterologic

Type Residual Average Residual Average Charge Charge Charge Charge

(1-2 1 +1/12 * -1/12 1/12 0 * 0 0 (1-3 l 3(+l/12) -3/12 1/8 + 3/12 -3/12 1/4 (I-1* 1 + 3/12 -3/12 1/4 +6/12 2(.-3/12) 1/3 (1-5 1 3(+5/12) 5(-3/12) 5/16 +9/12 3(-3/12) 3/8 (1-6 1 3(+7/12) 7(-3/12) 7/20 +12/12 4(-3/12) 5/12

(1-3 2 +3/12 * -3/12 1/4 +3/12 * 3(-l/12) 1/8 (1-4 2 +3/12 * -3/12 1/4 0 * 0 0 (1-5 2 7(+1/12) -7/12 7/48 3(+5/12) 5(-3/12) 5/16 (1-6 2 +5/12 -5/12 5/12 0 * 0 0 (1-7 2 +9/12 3(-3/12) 3/8 5(+3/12) -15/12 5/12 (2-3 2 0 * 0 0 +1/12 * -1/12 1/12 (2-4 2 +2/12 * -2/12 1/6 0 * 0 0 (2-5 2 0 * 0 0 2(+3/12) -6/12 1/3 (2-6 2 3(+2/12)* -6/12 1/4 +6/12 -6/12 1/2 2 (2-7 3(+4/12) 2(-6/12) 2/5 2(+9/12) 3(-6/12) 3/5 (1-5 3 +9/12 3(-3/12) 3/8 7(+1/12) -7/12 1/6 (1-6 3 7(+3/12) 3(-7/12) 7/20 2(+8/12) 8(-2/12) 4/5 (1-7 3 +9/12 3(-3/12) 3/8 3(+2/12) -9/12 3/8 TABLE 11 (Contd.)

Homologic Heterologic Valence Type Residual Average Residual Average Charge Charge Charge Charge (2-5)3 0 0 0 +3/12 -3/12 1/4 (2-6)3 +6/12 3(-2/12) 1/4 3(+2/12) -6/12 1/4 (2-7)3 I 4(+2/12) -8/12 V15 3(+7/12) 7(-3/12) 7/20 (3-5)3 + 3/12 3(-l/12) 1/8 3(+l/12) -3/12 1/8 (3-6)3 +3/12 -3/12 1/4 0 0 (3-7)3 +7/12 7(-l/12) 7/48 3(+3/12) -9/12 3/8 (0-2)1 0 0 +2/12 -2/12 1/6 (0-3)| 2C+3/12) -6/12 1/3 +3/12 * -3/12 1/4 (0-H)| 0 0 + 4/12 -4/12 1/3 (0-5) 2(+6/12) 3(-Vl2) 2/5 9(+l/12) -9/12 3/20 u> O

VJ1 0 0 0 +9/12 9(-l/12) 3/20

Indicates homologic and heterologic valence types which are represented by existing species. 67 TABLE 12 RESIDUAL CHARGE FOR VARIOUS COMMON-CATION, MIXED ANION VALENCE TYPES

Residual Charge Residual Charge on Anion with on Anion with Average Lower Valence Higher Valence Charge

U ) 1-2 +6/12 -6/12 1/2

(2)!-3 3(+6/12) -18/12 3/4

(3)1'3 3C+15/12) 5(-9/12) 15/16

<3)2-3* 3C+3/12) -9/12 3/8

* Indicates valence types which are represented by existing species. 68 The presence of large numbers of stoichiometrically required defects and the known character of four-valent anions (carbides and silicides) indicates that these classes of compounds are not likely to be ionic in character and, although some may crystallize with the spinel arrangement, they are omitted from this tabulation. Common-cation, mixed- anion valence types must of necessity have a residual charge, most very large. Many of these valence types, whose residual charges are intuitively apparent and are large, are also omitted from the tabulation. Note, in Tables 11 and 12, the correlation between low residual charge and existing spinel species (marked with an asterisk). Referenced examples of these existing species in light of their cation distribution are given in Table 13. The species in this table represent the empirical test for the calculations. Not every type with low residual charge is represented by an existing spinel but in that mixed-cation, common-anion series which includes the oxides, all homologic and heterologic valence types with an average residual charge of 0, 1/12, 1/6 or l / l\ are represented by at least one existing species. This is the one area that has been extensively studied and all stable compounds should already have been found or prepared. That the residual charge for the heterologic distri­ bution is lov; does not necessarily indicate that it is also low for the homologic distribution, or vice versa. The 69 TABLE 13 CATION DISTRIBUTION IN EXISTING SPINELS

Valence Type Homologic Heterologic (1-2)1 Li2Ni F^— Blasse (1964) Li2Be F4— Evans (1964*) Lej us & Lenglet & (1-3)2 LiAl^Og— Collongues (1962) LiFe^Os— Lensen (1964) Lenglet & (1--4)2 Li^KnijO-j^— Blasse (1963) LijjTiijO-L2— Lensen (1961) Donahue & (1—6)2 — Ag2MoOjj— Shand (1947)

(2-3)2 ZnCr20jj NiAl2On (2-4)2 Co2Ti Ojj— Romeijn (1953) Co2Ge 0i|— Romeijn (1953) Dulac & (2—5)2 ZnySb2012— Durif (I960) — Bayer (2—6)2 (Znt6N i ^ ) 5Te08— (1967) — Sinha & Sinha (0—3)2 — y Fo 2o 3— (1957) Yamaguchi & (3)2"3 A1203*A1N Yanagida (1959)

1 *. Evans does not give cation distribution but it is difficult to imagine Be2+ in any other than tetrahedral coordination in ionic structures under standard conditions. 70 2 (1-6) spinel, for Instance, Is represented only by the heterologic distribution in species such as Ag2MoOij which have no residual anion charge. The homologic distribution for the (1-6) valence type has an average residual anion charge of 5/12. There is no known existing spinel of this type.

On the other hand, if the residual charges are low for both distributions, both are represented. The common p (2-3) spinels have average residual charges of 0 and 1/12 for homologic and heterologic distributions, respectively.

Both distributions of the (1-3) valence type have some­ what higher residual charges than the (2-3)^ spinels but both are represented by existing spinels. The homologic (1-3) spinel has residual charges of +3/12 whereas the heterologic has residual charges of +3/12 and 3(-l/12) for an average of 1/8. The latter distribution would seem to be favored by having the lower average residual charge.

Perhaps this is reflected by the fact that the homologic (1-3)2 spinel, LiAl^Og, exists only at temperatures above

1290°C (Lejus and Collongues, 1962). This might, however, be a peculiarity of this species. The role of cation preference for either tetrahedral or octahedral coordination environments is also probably important in deciding whether or not a given cation assem­ blage will or will not form a spinel. In the case of the (2-5) valence type only the homologic distribution is 71 known to exist. This distribution results in no residual charge whereas the heterologic distribution results in residual charges of 2(+3/12) and -6/12 for an average charge of 1/3. Bayer (1961) described the synthesis of

ZnySbgO^ and ^°7^b2^12 and ^ imP°rtan^ to recognize that both Zn and Co have a strong preference for tetrahedral coordination. Attempts at synthesis of Ni^Sb20^2 were unsuccessful because nickel has a strong octahedral site preference and would require the heterologic distribution which is apparently prohibited on the basis of the high residual charge on the anion.

The one exception to the rule of low residual charge 2—? for existing spinels exists in the case of the (3) valence type which is represented by AI3O3N. This valence type has residual charges on the anion, not because of vari­ able cation surroundings, but because the anions have different charges. The residual charges are 3(+3/12) and -9/12 for an average charge of 3/8. Why this spinel should exist with a residual charge so much larger than any other encountered in existing spinels is not understood. It is a rather unusual species and not of a type familiar enough to allow unquestioned use of the standard rules for ionic structures. It is possible that Evan's statement about the metallic character of nitrides is in effect to some extent here even though only one nitrogen is present for every three oxygens. Throughout the foregoing discussion of residual

charge on the anion, one factor has been neglected; the

normal charge on the anion. Does the valence of the anion affect the size of residual charge which can be accommo­ dated by the anion matrix? For example, the (1-2)^ spinel p is a half charged model of the (2-4) valence type. In the homologic distribution of these valence types, the (1-2)^ p has an average residual charge of 1/12 and the (2-4)^ has an average charge of 2/12. Are these equivalent residual charges since the former valence type has a monovalent

anion and the latter a divalent anion? Can the monovalent anion matrix accommodate residual charges as large as 1/4

as can the divalent anion matrix, or would its charge limit be 1/8? At present not enough information exists to

answer these questions. Much experimental work will need to be done on possible spinels with monovalent or trivalent anions before they can be answered. Nevertheless, it seems

reasonable to suspect that the residual anion charge that may be tolerated by a given anion matrix depends on the

valence of that anion. Another observation can be made from Tables 11 and 12 about the residual anions in existing spinels. The two kinds of residually charged anions are always present in

ratios of either 1:1 or 3:1. It may be recalled that long

range order in spinels may be of three types, namely, 1:1 order on the tetrahedral position, 1:1 order on the octa­ hedral position and 3:1 order on the octahedral position. This correspondence is not coincidental. There are three examples of the 3:1 ratio of residually charged anions. Two of these valence types are represented by species for which a 3:1 order on octahedral sites have been described. Braun (1952) has described this form of order for the heterologic (1-3) valence type, LiFe^Og. Bayer (1967) has also described it for the homologic (2-6)2 valence type, Zn2CogTe0g. The third example of a 3:1 ratio of residually charged anions exists in the (3) 2 —*3 valence type. Any order here would need to be on the anion sites and this type of order was not noted by Yamaguchi and Yanagida (1959) who described the one known example of this type. In the lit­ erature, unfortunately, most descriptions of order in spinel are restricted to solid solution phases or complex com­ pounds. Nevertheless, the correspondence that is seen further confirms the contention that the number of kinds of residually charged anion be limited to two.

It has thus been established with reasonable certainty that spinel formation is dependent upon low residual charge on the anion and either 1:1 or 3:1 ratio of the two kinds of anions in those cases in which there is a residual charge. This premise should be quite helpful in indicating other homologic or heterologic valence types which might be synthesized. Coupling this indication with information about various cations' site preference should allow the would-be investigator much more chance of synthesizing a new spinel type. Valence types which show some promise for new spinel formation are given below.

The homologic (1-3)^ valence type has an average residual charge of 1/8 and would appear likely to form a spinel. It would be a half charge model of the existing (2—6)2 spinel. The heterologic (1-3)^ and the homologic (1-4)^ valence types each have an average residual charge of 1/4 which may or may not be too great a charge for a monovalent anion matrix. Both distributions of the (2-5) , (2-6)3, (3-5)3 and (3-6)3 valence types might be possible candidates although non-ionic behavior of compounds con­ taining trivalent anions could cause negative results. The defect valence types show some promise, specifically, both distributions of (0-2)and the homologic distributions of the (0-4) and (0-5)3 types. Other defect spinels do not appear likely because of numerous required vacancies. It is not possible to evaluate which of the common-cation, mixed-anion valence types might form spinels because the one existing species from that group does not offer much insight into possible limiting factors. It is of some interest to consider whether or not the restrictions placed on the various valence types hold true for solid solution phases and complex compounds which may be viewed as being made up of various mixtures. There is no reason to suspect that they should not hold true. A solid solution between two valence types may be viewed as a mixture of the various kinds of residually charged anions in those two valence types. If both end-members possess residually charged anions, four kinds of anions would coexist in the solid solution phase. If, however, one of the end-members had no residually charged anions, then only two charged anions and one uncharged anion would co­ exist. This type of arrangement is apparently also satis­ factory. Datta (1961) described the solid solution system LiAl^Og - MgA^O^ in which the former type has no average residual charge of 1/4 and the latter has no residual charge. He also describes the solid solution system

Co2GeO]j - ZnAl20jj in which neither end member has residual charges. The writer has worked on the system Zn2SnOjj - p 7ZnO’Sb20^. The former is a homologic (2-4) type with a residual charge of 1/6 and the latter is a homologic 2 (2-5) valence type with no residual charges. Considering the complex spinel compound, Li^+Zn^+Sb^+0i| (Blasse, 1963) which may be viewed as a mix- 2 2 ture of (1-5) and (2-5) valence types, it may be seen from Table 11 that neither distribution of the (1-5)^ satisfies the anion ratio requirements, and that the dis­ tributions yield the unusual residual charges of 7/^8 and

5/16. According to the concept of the residual charge principle adopted in this work, spinels of valence type

(1-5)^ are not possible. According to the arrangement described by Blasse, zinc occupies tetrahedral sites and 76 lithium along with antimony occupy octahedral sites. This arrangement yields anions with residual charges of +1/3 ancL -1/3. These charges are slightly larger than those o b s e r v e d in existing spinels for which values have been calculated, yet, according to Blasse, the compound is stable. These contradictions seem to indicate that the anion species proper to those valence types which are considered to make up a complex spinel compound such as this do not necessariBLy exist in the compound. Evidently, if the constituent

valence types are present in the proper proportions the cations will pack in such a way to give the lowest p o s s i b l e

residual charge on the anion. This may be seen easily wifclT. this example but not in all other complex compounds des­ cribed in the literature. Some examples would undoubtedly be best attacked with the aid of a computer to determine b l r i G proper combination of cations to yield the lowest residual

charges on the anions. There would also need to be exten­ sive experimental work in this area to obtain a satisfactoar*y number of tests from which to draw conclusions. Thus it appears that the residual charge principle ivhich holds so well for the individual valence types does,

in general, apply to solid solution phases and complex spinel compounds as well. While some changes are required,

in the various restrictions made for other spinels, the

tendency toward low residual anion charges is still

apparent. The correspondence between the preceding electro­ static tabulations and existing spinels is surprisingly

good, certainly good enough to verify the Residual Charge Principle in regards to spinels. While spinels might not be considered as typical ionic compounds, it has been well established that the exceptions to standard ionic rules do not indicate non-ionic behavior. Thus it might well be expected that other ionic compounds in which residual anion charges occur will be governed by this principle as well. CONCLUSIONS

A review of the history and the extensive literature concerning the crystal chemistry of the spinels has been undertaken. This review has provided some order to exist­ ing knowledge of this diverse yet coherent structural group. Certain semantic barriers to the understanding of the spinels have been removed. The conventional terms "normal" and "inverse" which are not capable of describing cation distribution for all spinels have been discarded. The basis for the proposed cation distribution classifica­ tion scheme is the correspondence between cation valence and coordination on the cation sites. The term "homologic" is proposed to describe distribution in which the lower charged cations occupy the sites with the lower, tetrahedral, coordination and the higher charged cations occupy the sites with the higher, octahedral, coordination. The term "heterologic" describes distribution in which the higher charged cations occupy the tetrahedral sites and the lower charged cations occupy the octahedral sites. A classification network of "valence types" based on electroneutrality and a stoichiometric ratio of three cations for every four anions has been proposed. This net­ work includes all existing spinels and should include any 78 79 new spinel species discovered in the future. The classifi­ cation scheme is comprised of three main categories, namely, lacunary, mixed-cation, common-anion and common- cation, mixed-anion valence types. A method has been devised to determine which of the many valence types might be expected to be represented by a valid spinel species. This method is based primarily upon a proposed residual charge principle which is a semi- quantitative measure of the stability of various cation arrangements within the structure. The residual charge principle states that in those cases for which the cation arrangement in the structure necessitates two kinds of anions, each with a residual charge, the most stable arrangement of cations is such that the residual charge on the anions tends to be low. Good correspondence exists between low residual charge and existing spinel species. It is a distinct possibility that the residual charge principle is applicable to ionic compounds in general. This possibility should be investigated by close examination of other ionic compound systems. REFERENCES

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