$52. HHHIHH NIH; THS PREFERENTIAL TONIC SUBSTITUTLON IN THE CRYSTAL LATTICE OF THE CHROMITE SPiNEL SERIES Thesis for ihe Degree cf M. S. ‘MICHLGAN STATE UMKE’ERSITY Davie! W'aii'er Chipman 1.96:6 ABSTRACT PREFERENTIAL‘IONIC SUBSTITUTION IN THE CRYSTAL LATTICE OF THE CHROMITE SPINEL SERIES By David Walter Chipman The present study was carried out in an attempt to determine the factors which influence ionic substitution in crystals in which the bonding is neither predominantly ionic nor predominantly covalent. The chromite spinel series was chosen as the subject of this investigation because it offers the advantage of allowing a wide range of substitution of ions in a particular lattice site. Several of the end members of the chromite series were synthesized by heating mixtures of the proper oxides at 875° C. to 10000 C. for 12 hours. Binary samples were also prepared and heated in a similar manner. Analysis of the products of these syntheses by means of X-ray diffraction allowed the compositions of the chromites formed from the binary samples to be determined. The order of preference of ions for the tetrahedral site in the chromite lattice was found to be Zn>Mg>Cd>Mn>Ni. It is concluded that the factor which controls this substitution is the electron configuration of the compet- ing ions. This is explained on the basis of crystal-field stabilization theory, which states that nickel and possibly manganese ions would prefer the octahedral David Walter Chipman coordination of their respective monoxides to the tetrahedral sites of the chromite lattice. PREFERENTIAL IONIC SUBSTITUTION IN THE CRYSTAL LATTICE OF THE CHROMFTE SPINEL SERIES By David Walter Chipman A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1966 A CKNO’JILEDG MET-3T S I would like to thank Dr. James Trow for the aid and advice which he gave during the course of the research and the writing of this thesis. I would also like to express appreciation to Dr. Justin Zinn and Dr. Robert Ehrlich for reading the manuscript and offering many pertinent criticisms. Thanks are also due to the Department of Metallurgy, Mechanics and Materials Science, and especially to Dr. D. E. Scherpereel, for the use of their X-ray diffractometer. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . iv LIST or FIGURES . .3 . . . . . . . . vi INTRODUCTION . . . . . _. . . . .‘ .y l Spinels . . . . . . . . . . . l Isomorphism . . . . . . . . .1 . 5 EXPERIMENTAL PROCEDURE . . . . . . . . 10 Synthesis . . . . . . . . . .‘11 Analysis . . . . . . . . . . . l2 DATA . . . _. . . . . . . . . . 15 Introduction . . . '. . . . .. . . 15 , Control Samples . . . . . . . . . 15 Binary Samples . . . . . . . . . 2O ' Discussion of Data . . . A . . . . . 31 CONCLUSIONS . . . . . . . . . . . 33 RECOMMENDATIONS FOR FUTURE WORK . . . . . . 35 BIBLIOGRAPHY . . . . . . .. . . . . 36 iii Table 10 LIST OF TABLES Page Theoretical and experimental cation distribu- tion in spinels, based on crystal-field stabilization theory. N a normal, I : inverse, 0: no prediction. (From McClure, 1957) . . 6 Properties of the ions which were used in the .present study. Ionic radii are from Evans 1964). Electronegativities and percent cova- lency of the bond with oxygen are from Pauling (1960). Number of d-electrons and octahedral site preference energy are from McClure (1957). . . . . . . . . 7 Sizes of crystal lattices and compositions of binary chromites which contain magnesium. . . 21 X-ray data from samples which contain magnesium, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. . . . . . . . 22 Sizes of crystal lattices and compositions of binary chromites which contain manganese. . . 23 Sizes of crystal lattices and compositions of binary chromites which contain cobalt.. . . 23 X-ray data from samples which contain manganese, giving intensity of peak and size of d—spacing for each identified crystallographic plane of the spinel structure. . . . . . . . 2A X-ray data from samples which contain cobalt, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. . . . . . . . 25 Sizes of crystal lattices and compositions of binary chromites which contain nicke1.. . . 26 X—ray data from samples which contain nickel, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. . . . . . . . 27 iv Table Page 11 Sizes of crystal lattices and compositions of binary chromites which contain zinc. . . . 28 12 Sizes of crystal lattices and compositions of binary chromites which contain cadmium. . . 28 3—: U) X-ray data from samples which contain zinc, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. . . . . . . . 29 14 X-ray data from samples which contain cadmium, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. . . . . . . . 3O LIST OF FIGURES Figure Page 1 Plan of the unit cell of the normal spinel structure of chromite, projected on a plane perpendicular to one of the a—axes. (a) is the lower half. Heights of the ions are indicated in units of 1/8 of the axial length. (After Evans, 1964) . . . . . . . 3 vi INTRODUCTION The factors influencing the acceptance of ions of various elements into the crystal lattice of a specific mineral are of great importance to the fields of mineral- ogy, geochemistry and petrology. These factors can be most easily examined and their relative importance deter- mined if an investigation is confined to a mineral series which is isostructural. This study is an investigation of preferential acceptance of certain transition metals into the lattice of the double oxides of the chromite series. Spinels The chromite series is a group of minerals and artificial chemical compounds which have the general formula A"Cr204 and which crystallize in the spinel structure. The A" in the general formula may be any of a large number of divalent metallic ions. The spinel structure is basically a cubic close packed array of oxygen ions with metal ions in some of the interstices. In the cubic close packed array there are two types of interstitial sites-- those with four oxygen neighbors (tetrahedral sites) and those which are surrounded by six oxygen ions (octahedral sites). In a normal spinel structure all of the trivalent ions occupy octahedral sites and all of the divalent ions are found in the 1 2 tetrahedral sites. (See figure I.) There is also a second type of spinel structure, known as the inverse spinel, in which the divalent ions and half of the tri- valent ions are located in the octahedral sites, while the remainder of the trivalent ions occupy the tetra- hedral sites. A study of the structure type, normal or inverse, taken by the various spinels leads to some interesting results. Magnetite, Fe304, is an inverse spinel while 'hausmannite, Mn304, has the normal spinel structure. This difference in structure can not be predicted on the basis of ionic bonding alone, for there are then two conflicting factors involved. It would be expected, from a consideration of ionic radius ratios alone, that the smaller triValent ion should be tetrahedrally coordinated, and that the larger divalent ion should be in the octahedral sites. On the other hand, it can be argued with equal validity that the lattice will be ' more stable when the ion of higher charge has the greatest number of neighbors, and thus that the trivalent ion should be favored in the octahedral site. There is no way by which it can be determined which of these contradictory factors will be the more important in a -specific case, and therefore no predictions can be made. It is possible to explain the difference in the structures shown by magnetite and hausmannite on the Asmma .mcm>m ampuav .cumsma Hafixm mg» mo m\H no means 2H empMOAUQH.msm mcoa on» mo mpnwfimm .mamn smzoa on» ma Adv .mmxmum 0:» mo mco Op smHSOcheQmom ocean s so ompoenoma .mufisopco mo weapospum Hmsfiam Haemos oSu mo HHoo pass esp mo swam H.mnswfim so“ cmmzxo sowmn QOH cmmmxo ebonm . Goa , mcfiha QOH ssfisomno msfiha GOA Edasomco oaaadpes pcmflm>flm soa.sew>xo O O E. 11. basis of covalent bonding. This should be as valid as the ionic model, fOr the metal to oxygen bond is approximately 50 percent ionic and 50 percent covalent. Orgel (1960) points out that Fe (II) and Mn (III) are stabilized by a crystal-field and will thus seek the site which provides the maximum amount of stabilization. As tetrahedral sites provide only about 4/9 as much stabilization energy as do octahedral sites, the divalent iron and trivalent manganese will tend to be octahedrally coordinated. The other ions, Fe (III) and Mn (II), are not stabilized by weak crystal-fields and will therefore have no preference between the tetrahedral and octahedral sites and will occupy whatever sites remain. For this reason the Fe (II) of magnetite is located in the octahedral site, and the mineral is an inverse spinel, while the Mn (III) of hausmannite is also octahedrally coordinated and this mineral is a normal spinel. McClure (1957) was able to carry this line of reasoning even further. From spectroscopic data he was able to determine quantitatively the amount of crystal-field stabilization energy for various ions in octahedral and tetrahedral sites. The difference between the energies of the two sites is the site preference energy for a particular ion. As mentioned above, any stabilization energy will be greater for ions in octahedral coordination than for those in tetrahedral 5 sites. Whenever two of these metals are paired in a spinel structure the one with the greater site preference energy should be found in the octahedral site of the crystal lattice. The experimentally determined distri- bution of cations in spinels agrees well with the predictions of this theory. (See tablej_.) The trivalent chromium ion has a site preference energy which is greater than that of any of the divalent ions which are known to combine with it in spinel structures. (See table22.) For this reason all of the members of the chromite series are normal spinels. Isomorphism The terms isomorphism and solid solution are often used synonymously in the sense of the substitution of one ion for another in a crystal lattice. There have been a number of theories or rules proposed to explain the degree to which one ion can substitute for another and the tendency for one ion to be preferred over another in a particular site in a crystal lattice.v The rules of V. M. Goldschmidt (1937) were among the first proposed, and have long been accepted as generally valid. These rules state that: 1. For two ions to be able to substitute for each other, they must not differ by more than 15 percent in size. 2. If two ions have the same charge, the smaller of the two will be preferred over the larger. _| - n Inll 6 2 H z z 2 H How” H H st z 2 H H z st z z 2 H H 2 EH 2 z z 2 H H z z z z z z o H z z z z z o z z z z z z z z o z z z z z z z o H :hH.QsH .ge :ss. ;:..asH he .aé, .gm.asH a Hammad Hlmj and 3 .COHHOHUmHQ ocuuo qempm>CH "H .HmEHo: .mHmcHom CH mcoHHSQHpumHU COHpmo HmpsmeHHedxm was HmOHummomse co Ummmn 1 II. t. .. 15351! i H “Hm H H H o o z o z o H .ee .axm 3 OOOI—II—II—II—I O Hmw. ZZZZZ wa. .ze .Qsm NMHHV Ha AHHV so AHHV Hz AHHV oo AHHV mm AHHV c2 HHHV so AHHV cw AHHV m2 AsmmH .mszHoo: copay "HA .mmoenp COHpmNHHHQmpm @HmHm Hmpmzpo .H mHQmB 5.0: m H: ©.H m.mH m Hm o.m 0 0H m: S.H 0 OH H: ©.H m.mm w m: m.H H.m s as . w.H m.m m m: m.H AeHmHH smeav o m em m.H o o A . Hm m.H Nefios\afimoxv msoppoeHeuv cmmhxo suHs econ HpH>Hpmmmc .mpmcm mocepemeoo mo Hmoesz mo Hocmfim>oo &. nogpomHm mpHm Hmsemsmpoo mm.o mm.o Hm.o :m.o mm.o mw.o ow.o om.o mw.o A.00 pgmopmd new moHpH>HHMbmcoppoeHm OHCOH . ommHv wsHHsmm song mpm cemmxo :pHs econ .Azmmfiv mcm>m 509m mam HHUmp .hGSHm pcmmeQ map CH Umms ohms SOHQB mcoH ecu mo mmeHerpm .m manna 8 3. If two ions are of differing charges and similar sizes, the ion with the higher charge will be preferred. I w. s. Fyfe (1951 and 1964) pointed out that Gold- schmidt's rules were founded on the assumption that bonding in crystals is essentially ionic, whereas actually bonding may vary from nearly ionic to completely covalent. He demonstrated that the directional properties of covalent bonds may determine the structure of a mineral, and will thus influence ionic substitution. ' & He also stated that in cases in which the bonding is in the range of 25 percent to 75 percent covalent, predic- tions using either the ionic or the covalent model will not necessarily hold. A Ringwood (1955) offered the hypothesis that cations of lower electronegativity will be preferred over those which are of similar size and which have a higher electronegativity. His explanation of this effect is that the bonding involving a cation of lower electro- negativity will be more nearly ionic in nature and therefore Stronger. On the basis of a study of the preferential acceptance of ions into the ferrite spinel lattice, A. V. Shaw (1965) suggested that the electron configura- tion of the competing ions can be an important factor in controlling the substitution. However, inasmuch as 9 the ferrite series has members with both normal and inverse structures, it was decided to test Shaw's hypothesis by investigating members of the chromite series, each of which orrurs only as a normal structure. By this procedure ionic competition for the same site would be unambiguous. EXPERIMENTAL PROCEDURE It is desired to study the preferential acceptance of various ions into a particular site of the crystal lattice of a mineral. The chromite series was selected because it is strictly isostructural and shows nearly complete solid solution among the various end members. Each of the end members of the chromite series (magnesium chromite, MgCr204; manganese chromite, MnCr204; cobalt chromite, CoCrEOu; nickel chromite, NiCreou; zinc chromite, ZnCrEOu; and cadmium chromite, CdCrQOM) was synthesized by heating mixtures of the single oxides. Binary samples were also prepared which contained the oxides of two divalent metals plus enough chromic oxide to combine with either one or the other of these oxides, but not with both. Eabh of the oxides was paired with each of the other oxides in this manner to form a complete set of binary samples. Each of the binary and control samples was then analyzed by means of X-ray 'diffraction, and the length of the edge of the cubic unit cell was calculated. The composition of each of the binary chromites was then computed by a comparison of the size of the binary chromite with that of each of the end members which were combined in that binary pair. The divalent ion of the end member which constituted more than 50 percent of the binary chromite was 10 l_r"¥ -..- 11 considered to be preferred over that of the other end member. In this manner, an order of preference of all of the ions was determined. Synthesis The chromites produced in this study were synthesized by a solid-state reaction between the metallic oxide or oxides and chromic oxide. All of the starting materials were of C. P. or Reagent Grade. A The samples containing magnesium, nickel, zinc, cadmium or copper were prepared from 1:1 molar ratio mixtures of Cr203 and MgO,‘NiO, ZnO, CdO or CuO respec- tively. Those samples which contain manganese were prepared from mixtures of Cr2O and MnCO The carbonate 3 3' decomposes to MnO and 002 at temperatures between 3000 and LIOOO C. and any reaction above these temperatures is between the oxides alone. Those samples containing iron or cobalt were synthesized from mixtures of Cr203 and the respective hydroxide-4 Fe(OH)2 or Co(OH)2. These hydroxides were precipitated from solutions of the. chlorides of the metals by reaction with NaOH. The hydroxides decompose at fairly low temperatures to give the monoxides of the metals and H O. In these 2 cases also the reaction at the temperature at which the experiment was run was between the oxides only. All of the reactants were weighed on a Chain—o-matic balance and were then thoroughly mixed in a Spex sample l2 mixer. The samples were placed in platinum crucibles and were heated for a period of 12 hours in an electric furnace. The temperature at which the samples were run was 10000 C., with the exception of samples which contain either cadmium or copper. The oxides of these metals undergo unfavorable reactions in the temperature range of 9000 to 10000 C. and therefore were kept Just under f 9000 C. In the case of cupric oxide, the reaction is a reduction to the cuprous form at 9000 C. 'Cadmium oxide, on the other hand, decomposes completely between 900° and 10000 c. The heating of all of the samples E was done at one atmosphere pressure and with free access to air. At the end of the 12 hour heating period the furnace was allowed to cool to 8000 C. and the samples 'were removed and cooled in air to room temperature. The samples, which at this point had the form of slightly hardened cakes, were crushed to fine powders With a porcelain mortar and pestle. Analysis . The powdered samples were analyzed by means of, X—ray diffraction, using a Norelco diffractometer which was equipped with a copper target X—ray tube and a Geiger-type detector. Iron radiation was found to cause considerable fluorescence by the chromium atoms and therefore was not used in the analysis. The inten- sity of radiation was measured at a sweep rate of 10 13 of 2 6 per minute and was recorded continuously on a strip chart. Those peaks on the records which represent spinel structures were identified and from them the d-spacings between the various crystallographic planes were calculated, using the Bragg equation A-2 d sin 6. From these d-spacings the size of the unit cell of each spinel was calculated. The compositions of the binary chromites were then computed through comparison of the size of the binary with that of the end members which were involved in the solid solution. w For the interpretation of the X-ray data, the d-spacing of the (440) crystallographic planes of each chromite lattice was taken as a measure of the size of the unit cell. A single plane was chosen, rather than the average of several planes, because the peaks for differ-' ent directions were found to give slightly different values for the length of the unit cell edge. This variation was in a constant direction, with larger values of 2 O consiStently giving larger values of unit cell size. It is probable that this was caused by a slight lag in the recorder of the diffractometer, which caused all of the peaks to be recorded with a slight but constant positive error in the angle 2 6. This would cause all of the calculated d-spacings to be too , small. The error would be greatest at the lowest angles and would decrease regularly as the angle was 1A increased. The (440) peak was the one with the largest angle 2 6 which was measured for all of the samples and thus should give the most accurate measure of unit cell size. The use of the same crystallographic plane in each sample should allow for a high degree of precision, if not absolute accuracy, in the measurement of the lattice dimensions. rm... DATA Introduction The X-ray data from all of the samples are given in tables A, 7, 8, 10, 13 and 1A. The interpretation of these data is given in the following two sections and in tables 3, 5, 6, 11, and 12. The final section F1 of this chapter includes a discussion of these data. y Control Samples Magnesium-- The control sample of pure MgCr2Ou was H synthesized by heating a 1:1 molar ratio mixture of MgO and Cr203 at 10000 C. for 12 hours. X-ray analysis of the products of this reaction revealed that a chromite was formed which has a unit cell edge of 8.327 A. This value compares favorably with that of 8.333 A. given by Berry and Thompson (1962) for pure synthetic material. Manganese-- The manganese chromite was synthesized from a mixture of MnCO3 and Cr2O3 which was heated at 10000 C. for 12 hours. The analyzed material contained a chromite which had a unit ce11 edge of 8.429 A. This size also compares very well with the theoretical value of 8.u36 A. which was reported by Wyckoff (1965). The material did not show the tetragonal distortion which would be expected if hausmannite (Mn304) were present. Iron-- An attempt to synthesize the iron chromite l5 16 failed to produce any material with a spinel structure. The reactants, Fe(OH)2 and Cr203, were held at 10000 C. for 12 hours. The product of this reaction had the structure of hematite, but the size of the crystal . lattice was between that of hematite and eskolaite (Berry and Thompson, 1962), a mineral which is essen- tially hematite with variable amounts of Cr (III) and v (III) substituting for part of the Fe (III). It is thus believed that the material which was produced has a composition intermediate between Fe203 and Cr2O3. This would be very likely, for ferrous iron is easily oxidized to the ferric state. Cobalt-- A cobalt chromite control sample was synthesized by heating a mixture of Co(OH)2 and Cr2O3 at 10000 C. for 12 hours. X-ray analysis of the products indicated that the chromite formed had a unit cell edge length of 8.304 A. This is somewhat smaller than the theoretical value of 8.32 E. (Smith, 1960) and possibly indicates that some of the cobalt was oxidized to Co (III), which then substituted for some of the Cr (III) in the chromite lattice. Since pure Co 04 has 3 a unit cell edge of 8.084 A., the size discrepancy found could be accounted for by the substitution of as little as 7 percent Co (III) for Cr (III). Nickel-- The pure nickel chromite control sample was prepared by heating a mixture of N10 and Cr2O3 for l7 12 hours at 10000 C. The analyzed material was found to be tetragonal, with axial lengths of a 8.192 A. and c 8.392 A. The ratio c/a of 1.0244 is in excellent agreement with the value of 1.025 given by Dunitz and Orsel (1957). None of the binary samples containing nickel dis- played the tetragonal distortion which is shown by the pure nickel chromite, and thus it was necessary to determine the length of the edge of the unit cell of . the undistorted cubic form. Fortunately, the temperature at which the tetragonal form inverts to the cubic form is only 350 C. The sample was analyzed under a heat lamp, and was found to have inverted to the cubic form, which had a unit cell edge of 8.282 A. The exact temperature at which the sample was analyzed could not be determined, but was estimated to be in the range of 400 to 600 c. The thermal coefficient of expansion of nickel chromite is not known, but is unlikely to exceed 2 x 10'5-per degree 0. This would cause the measured value at 450 C. to be approximately 0.003 A. larger than at 250 C. A variation of this size should not seriously affect the results of the experiment, and therefore has been ignored. Zinc—- The zinc chromite control sample was synthe- sized by heating a mixture of ZnO and Cr203 at 10000 C. for 12 hours. The resulting chromite was found to have ,3 J. 1&2; . 18 a size of 8.304 A. This is in fair agreement with the published value of 8.32 A. (Smith, 1960). Cadmium—- The control sample of cadmium chromite was prepared from a mixture of cadmium monoxide and chromic oxide. This mixture Tas heated for 12 hours at a temperature of 8750 to 9000 C. The lower temperature used for this synthesis was necessitated by decomposition of the CdO at higher temperatures. The chromite formed has a unit cell edge of 8.560 A., as compared with the theoretical size of 8.596 A. (Wyckoff, 1965). The comparison of results of syntheses which were carried out at different temperatures requires some justification. It is anticipated that, barring any phase changes, a change in temperature will not cause a change in the direction of preference of one ion over another, but merely in the intensity of the preference. The effect of temperature on preference which is controlled primarily by size of competing ions may be used for illustration of this point. It is well known that solid solution between albite and orthoclase is quite limited at low temperatures and that it increases with increasing temperatures until it finally becomes complete. Similarly, the fractionation of isotopes, which is dependent upon the preference of a crystal site for the heavier of two isotopes, is greatest at low temperatures and decreases towards zero as the temperature is raised. This ll 19 increased tolerance at higher temperatures is caused by the expansion of the crystal lattice and the weak- ening of the bonds which reflects the increased vibration of the atoms. It is to be expected that a crystal lattice will tend to become more telerant of variations in other properties as well as in ionic radius and mass as the temperature is increased, and therefore that preferences will tend to decrease. As the results from the syntheses which were run at 9000 C. were found to be compatible with those which were run at 10000 C., it is believed that comparison of the two sets of data is valid. Copper—- An attempt was made to synthesize the cupric chromite (CuCr20y). A mixture of CuO and Cr203 was heated for 12 hours at 8750 to 9000 C. The lower temperature was used to prevent the reduction of CuO to Cu20, which occurs at 9000 C. The material produced did not have a cubic spinel structure but rather appeared to be tetragonal. The peaks could not be identified with any certainty, and therefore it was not possible to determine either of the axial lengths. Cupric chromite is reported to be tetragonally distorted with a c/a ratio of 0.91 (Dunitz and Orgel, 195T). It appears that this 9 percent distortion is sufficient ' to cause the peaks of the record to become confused. It was not found possible to determine the length of 20 the edge of the unit cell of the undistorted copper chromite, and thus the compositions of the binary samples containing copper could not be determined. Binarquamplcs The compositions of the binary chromites were calculated through a comparison of the size of the lattice of the binary with that of each of the pure end members. It would be natural to expect that these calculations would be most accurate in the cases in which there is a large difference in the sizes of the end members and less accurate when there is less difference. Indeed, no calculation of the composition of the chromite which combines zinc and cobalt could be made, for the end members were found to have lattices of the same size. The zinc and the cobalt chromites are also close in size to the pure nickel and magnesium chromites. For this reason it would be logical to (expect the binary samples which contain either cadmium or manganese to be the most accurate, and to consider the preferences shown by the samples containing two of the other four ions only when the preference is large.‘ This line of reasoning has been followed in the discussion of the binary sample data which follows. 21 Magnesium Table 3. Sizes of crystal lattices and compositions of binary chromites which contain magnesium. Cation of Size of Other End Size of Other End Size of Composition of- Member MgCrOOQ Member Binary Binary Chromite Mn 8.327 A. 8.429 A. 8.361 A. 67 % Mg, 33 % Mn Co . " 8.304 8.293 ----- . Ni " 8.282 8.304 50 % Mg, 50 % Ni -? Zn " 8.304 8.298 approx. 100 % Zn Cd " 8.560 8.350 90 % Mg, 10 % Cd It can be seen from the above table that zinc is J preferred over magnesium, which is itself preferred over cadmium and manganese. There appears to be no preference between magnesium and nickel. ”The binary sample contain- ing cobalt and magnesium is smaller in size than either of the end members involved. It appears very likely that this discrepancy in size was caused by the oxidation of some of the 00 (II) to Co (III) and the subsequent substitution of this trivalent ion for some of the Cr (III) in the chromite lattice. 22 Table 4. X-ray data from samples which contain magne- sium, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. Control Manganese Cobalt D161 9.. T I ax .d. .141 I ax 9. .41 11a}. 220 2.930 A. 20 2.942 A. 20 ' 2.911 A. 30 311 2.505 100 2.510 100 2.489 100 400 2.082 60 2.086 40 2.066 40 g%% 1.605 70 1.608 40 1.595 40 440 1.472 90 1.478 50 1.466 40 Nickel Zinc Cadmium g- ax '0‘ 0‘41]: I max d {—411 max 220 2.919 A. 20 2.918 A. 50 2.933 A. 30 311 2.493 100 2.493_ 100 2.509 100 400 2.070 60 2.069 30 2.079 30 33% 1.597 40 1.597 40 1.607 30 440 1.468 50 1.467 60 1.476 35 Table 5. Siris of crystal lattices and compositions of binary chromites which contain manganese. Cation of Size of ther End Size of Other End Size of Composition of Member MnCrOOu, Member Binary Binary Chromite Mg 8.429 A. 8.327 A. 8.361 A. 33 % Mn, 67 % Ma 00 ” 8.304 8.350 36 % Mn, 64 % Co Ni . " 8.282 8.361 54 % Mn, 46 % Ni Zn " 8.304 8.344 32 % Mn, 68 % Zn Cd " 8.560 8.525 26 % Mn, 74 % Cd There are no apparent discrepancies in the sizes of any of the binary samples which contain manganese. _Magnesium, cobalt, zinc and cadmium are all preferred over manganese, while nickel alone is less favored than manganese. Cobalt Table 6. Sizes of crystal lattices and compositions of binary chromites which contain cobalt. Cation of ' Size of Other End Size of Other End Size of Composition of Member CoerO,L Member Binary Binary Chromite Ms 8.304 A. 8.327 A.. 8.293 A. ----- Mn " 8.429 8.350 64 % Co, 36 % Mn Ni ” 8.282 8.293 50 % Co, 50 % Ni Zn " 8.304 8.270 ..... Cd ” 8.560 8.361 78 5 Co, 22 s Cd 24 Table 7. X-ray data from samples which contain manga- nese, giving intensity of peak and size of d—spacing for each identified crystallographic plane of the spinel structure. Control Magnesium Cobalt hkl d. IéI.ax 'd Iii ax .g IgI ax 0 2.942 A. 20 2.930 A. 40 311 2.536 100 2.510 100 2.507 100 400 2.116 30 2.086 40 2.079 30. §§ 1.622 55 1.608 40 1.605 30 440 1.490 55 1.478 50 1.476 50 Nickel Zine - Cadmium 9- . max £1- , .E-[Ajimax 9-“?- I ax 220 2.938 A. 40 2.928 A. 50 2.994 A. 70 311 2.509 100 2.504. 100 2.560 100 400 2.084 30 2.081 20 ----- -- §§ 1.607 40 1.603 40 1.638 30 440 1.478 50 1.475 50 1.507 30 25 Table 8. X-ray data from samples which contain cobalt, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. Control Magnesium Manganese hkl .g 1 Imax g. Iéiiax g_ IKIJax 220 2.916 A. 40 2.911 A. 30 2.930 A. 40 311 2.490 100 2.489 100 2.507 100 400 2.068 20 2.086 40 2.079 30 811 1.597 30 1.595 40 1.605 30 J33 440 1.468 50 1.466 ’40 1.476 50 Nickel Zinc Cadmium eg- I .IQX g- I TICLX g— 'L Imax O 220 2.912 A. 40 2.907 A. 50 2.937 A. 60 311 2.489 100 2.482 100 2.509 100 400 2.067 35 2.060 20 2.086 15 §§§ 1.594 40 1.590 40 1.607 40 440 1.466 50 1.462 50 1.478 50 4.x.) From the table it can be seen that cobalt is preferred over manganese and cadmium and that there is no preference shown when it is paired with nickel. The binary sample which contains cobalt and zinc is smaller than either of the pure end members. The reason for this difference in size is undoubtedly the same as that in the case of the cobalt—magnesium sample—- the substitution of some 00 (III) for Cr (III) in the structure. .Size of Composition of Binary Chromite 9‘5 (7 ,0 (a '/J of ['0 0’ Ni, Ni, Ni, Ni, 50 54 % {/75 ‘63 Nickel Table 9. Sizes of crystal lattices and compositions of binary chromites which contain nickel. Cation of Size of Other End Size of Other E.d Member NiCrQOg Iember Binary o O 0 Mg 8.282 A. 8.327 A. 8.304 A. 50 Ni .” 8.429 8.361 46 Co ” 8.304 8.293 50 Zn ” 8.304 8.293 50 Cd . " ‘8.560 8.536 8 The binary samples containing nickel suggest that there is no preference of this metal over magnesium, cobalt or Zinc. Both manganese and cadmium are~ preferred over nickel. /0 Ni, ’b‘l Mn 00 Zn Cd f‘ 47 Table 10. X-ray data from samples which contain nickel, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. Control ' Magnesium Manganese 1 W...- .‘_ ‘ '1 hxl E. i Imax 2. I inax §_ llimax 220 2.913 A. 40 2.919 A. 20 2.938 A. 40 311 2.487 100 2 493 100 2.509 100 400 2.062 30 2.070 60 2.08 30 §§§ 1.593 35 1.597 40 1.607 40 440 1.464 40 1.468 50 1.478 50 Cadmium S. IZImax 2.990 A. 70 ifi‘ 311 2.489 100 2.489 100 2.558 100 4OO 2.068 35 2.079 40 ----- ~- §§§ 1.594 40 1.595 40 1.641 40 440 1.466 50 1.466 45 1.509 40 r-v Zinc Tablequ Sizes of crystal lattices and compositions of binary chromites which contain zinc. Cation 0: Size of Other End Size of ther End Size of Composition of Member Zn3r20g Member Binary Binary Chromite O 0 Mg 8.304 A. 8.327 A. 8.298 A. approx. 100 % Zn Mn " 8.429 8.334 68 % Zn, 32 % Mn 00 ” _8.304 8.270 ' ..... Ni " 8.282 8.293 50 % Zn, 50 % Ni Cd " 8.560 8.304 100 % Zn All of the binary samples which involve zinc, with the exception of the zinc-cadmium sample, have been dis- cussed above. The zinc—cadmium pair indicates that zinc is preferred over cadmium. Cadmium (Table lit Sizes of crystal lattices and compositions of binary chromites which contain cadmium. Cation of ther End Member Size of CQCrQON Mg Mn Co ' Ni Zn 8.560 A. Size of ther End Size of Composition of 'Member Binary Binary Chromite 8.327 A. 8.350 A. 10 % Cd, 90 3 Me 8.42 8.525 74 % Cd, 26 % in 8.304 8.361 22 % Cd, 78 % Co 8.282 8.536' 92 5 Cd, 8 % Ni 8.304 8.304 100 % Zn ‘7! 05‘. ‘-/ Table 13. X-ray data from samples which contain zinc, giving intensity of peak and size of d—spacing for each identified crystallographic plane of the spinel structure. Control Magresium Manganese hkl 9_ I Imax Q I I ax Q, lllmax 220 2.930 A. 3 2.918 A. 50 2.928 A. 50 311 2.495 100 2.493 100 2.504 100 400 2.073 25 2.069 30 2.081 20 §§§ 1.598 65 1.597 40 1.603 40 440 1.468 80 1.467 _60 1.475 50' Cobalt Nickel Cadmium 51—“: Imax Qwfimax d—fi I ax 220 2.907 A. 50 2.916 A. 50 2.918 A. 50 311 2.482 100 2.489 100 2.494 100 400 2.060 20 2.079 40 2.070 15 g%% 1.590 40 1.595 40 1.593 30 30 Table 11% X—ray data from samples which contain cadmium, giving intensity of peak and size of d-spacing for each identified crystallographic plane of the spinel structure. Control Magnesium. Manganese BE}. 9. is;max '.9 illmax ' E. illmax 220 2.995 A. 70 2.933 A. 30 2.994 A. 70 311 2.567 100 2.509 100 2.560 100 400 ----- -- 2.079 30 ----- ~- §%% 1.644 40 1.607 30 1.638 30 440 1.513 . 40 1.476 35 1.507 30 Cobalt Nickel ' A Zinc 9""?- I».... swam... i Elanax ' 220 2.937 A. 60 2.990 A. 70 2.918 A. 50 311 2.509 100 2.558 100 2.494 100 400 2.086 15 ----- ' -- 2.070 15 §§§ 1.607 40 1.641 40 1.598 30 440 1.478 50 1.509 40 1.468 ' 4O 31 All of the binary samples which contain cadmium have been discussed in the sections which deal with the other end members. Discussion of Data Examination of all of the binary pairs allows the following six partial orders of preference to be derived: Zn > Mg > Cd, Mn (Table 3.) Mg, Co, Zn, Cd>Mn >Ni (Table 5.) Co>I-”m, Cd (Table 6.) Cd, Mn>Ni (Table 9 ) Zn >Mg, Mn, Cd (Table11) Mg, Co, Zn >Cd >Mn, Ni (Table12) These relationships are consistent and can be compiled into a single order of preference, which is Zn>ng>0d >Ni) >111. The position of cobalt alone is not uniquely defined. The fact that trivalent cobalt was apparently produced in at least two of the samples is sufficient reason to doubt the validity of all of the samples which contain this metal. It is interesting to note that the final order of preference, which was determined on the basis of the direction of preference shown by each of the binary pairs is the same as the order which would result from a comparison of the degree of preference shown by ions when paired with cadmium (Table 12.) or manganese q 3 , I (Table 5. ). The fact that cadmium was preferred over manganese to a greater degree than were magnesium or zinc can be explained by the lower temperature used -. with the cadmium-manganese o'nary pair. As was men- tioned earlier, preference should increase as temperature is decreased. ‘ "in“. l s _ I; CONCLUSIONS The order of preference of ions for the tetrahedral site in the chromite lattice was found to be Zn >.Mg > Cd > Mn) Ni. This order is in good agreement with the order determined by Shaw (1965) in his work on the ferrites. The order emu. of preference which he found was A Zn > Mg > Ni > Cu > Mn. The only difference between these two orders is the "L... position of nickel relative to that of manganese. The preference of cadmium over manganese and nickel is not the result which would be expected on the basis of size, for the ionic radius of Cd (II) is larger than that of either of the other divalent ions. In addition, the position in the order of cadmium relative to manganese would appear to refute the hypothesis of Ringwood (1955), for both the electronegaoiVIty and the size of cadmium are greater than these of manganese. The position of cadmium in the order of preference is that which was predicted by Shaw, and thus appears to bear out his hypothesis that the electron configuration of the compet- ing ions is the major factor in controlling their accept- ance into the crystal lattice. This may be explained on the basis of crystal-field stabilization energy. McClure (1957) showed that ions which have 0, 5 or 10 electrons 33 34 in their outermost d-orbitals will not be stabilized by a weak crystal field, while ions with other numbers of d—electrons will be stabilized to varying degrees. .In addition, it is known that octahedral coordination provides more stabilization energy than does tetrahedral coordination. For these reasons, the divalent nickel ion, which has 8 d-electrons, will tend to occupy octahedral Sites in preference to tetrahedral ones. The octahedral sites of the chromite lattice are occupied by trivalent chromium ions, which have a higher crystal-field stabilization energy than those of Ni (11). The nickel could be stabilized by taking the tetrahedral sites in the chromite lattice, but it can receive even more stabilizatiOn in the octahedrally I coordinated sites in the NiO lattice. This will leave ' the tetrahedral sites in the chromite lattice available for whatever other ion is available. It thus appears that the preferences found in this experiment are not caused by a preference for tetrahedral coordination shown by the divalent zinc, magnesium, cadmium and manganese ions so much as by a tendency towards. octahedral coordination on the part of the divalent nickel ion. RECOMMENDATIONS FOR FUTURE WORK The results of this study make it clear that any .work which deals with the preference of ions for a particular site in a crystal lattice must consider all of the alternative sites which are available for these ions. For this reason, synthesis of minerals through crystallization from a melt or solution should yield less ambiguous results. The use of a flux, such as sodium carbonate, borax or lead oxide, is suggested in syntheses which involve the oxides of metals. In order to test the hypothesis that was suggested by this study, that the electron configurations of the competing ions and their octahedral site preference energies determine whether they will enter into the chromite or remain as the single oxide, it would be use- ful to determine the position of iron and cobalt in the order of preference. It would be necessary to perform these syntheses in a'non-oxidizing atmosphere in order to prevent the oxidation of the divalent ions to the trivalent state. BIBLICGRAPR Berry, L. G. and Thompson, R. M., 1962, X-ray powder data for ore minerals: The Peacock Atlas: Geological Society of America, Memoir 85. Dunitz, J. D. and Orgel, L. E., 1957a, Electronic proper- ties of transition—metal oxides--Part 1: Journal of Physics and Chemistry of Solids, v. 3, pp. 20-29. 'l957b, Electronic properties of transition-metal oxides-~Part II: Journal of Physics and Chemistry of SOlidS, V. 3: pp. 318’3230 Evans, R. C., 1964, An introduction to crystal chemistry, 2nd ed., Cambridge, Cambridge University Press. Fyfe, W. 3., 1941, Isomorphism and bond type: American Mineralogist, v. 30, pp. 530—542. 1964, Geochemistry of solids: New York, McGraw Hill, Inc. Goldschmidt, V. M., 1937, The principles of distribution of chemical elements in minerals and rocks: Journal of the Chemical Society, London, pp. 655—673. McClure, D. S., 1957, The distribution of transition metal cations in spinels: Journal of Physics and Chemistry of Solids, v. 3, pp. 311-317. Orgel, L. E., 1960, An introduction to transition-metal chemistry: ligand-field theory: London, Methuen & Co., Ltd. Pauling, L., 1960, The nature of the chemical bond: Ithaca, New York, Cornell University Press. Ringwood, A. E., 1955, The principles governing trace element distribution during magmatic crystallization -—Part I: The influence of electronegativity: Geochimica et Cosmochimica Acta, v. 7, pp. 189-202. Shaw, A. V., 1965, The preferential acceptance of certain ions into the ferrite spinel lattice: unpublished Master's thesis, Michigan State University. Smith, J. v. (ed.), 1960, x—ray powder data file: American Society for Testing Materials, Special Technical Publication 48-J. L0 0\ 37 Wyckoff, R. w. C., 1965, Crystal structures, 2nd ed.: New York, Interscience Publishers. unimm‘gngfli1;"ngngm