J.C.S. Faraday I, 1980,76,2448-2456Distribution of Cobalt Ions among Octahedral and TetrahedralSites in C0Ga,Al2-~0~ Spinel Solid SolutionsBY PIERO PORTA* AND ANNA ANICHINICentro di Studio su Struttura ed Attivita Catalitica di Sistemi di Ossidi del C.N.R.,Istituto di Chimica Generale ed Inorganica, Universiti di Roma, Roma, ItalyReceived 6th August, 1979The cation distribution in several CoGgA1,_,O4 solid solutions with x ranging from 0.00 to 2.00has been studied by magnetic susceptibility, reflectance spectroscopy, lattice parameter variation andanalysis of some reflections whose intensities are particularly sensitive to variation in the cationpositions.The results show that there is a small but definite change towards a random cation distributionwhen the preparation temperature is increased from 873 to 1473 K.The X-ray and magnetic results show, moreover, that the fraction of Co2+ ions in octahedralsites varies with gallium and aluminium contents for the whole temperature series ; this variation is,however, not linear.For samples quenched from 873 K, CoA1,04 is 16 % inverse ; with increasingx , cobalt octahedral occupation first decreases up to x w 0.25 and then continuously increasesreaching an inversion of 78 % for the pure CoGa204 spinel.The influence of x on cation distribution is explained in terms of anion polarization and/orcrystal field stabilization energy effects.A large number of compounds having the general formula XY,04 are known tocrystallise in the spinel structure which may simultaneously accommodate metal ions,X and Y, among the octahedral, Oh, and tetrahedral, Td, sites available in the close-packed oxygen framework.Studies of cation distribution in spinels are of considerable interest in solid statechemistry because they may allow investigation of the relative stabilities of metal ionsin Oh and Td coordination and better understanding of the correlations betweenstructure and properties such as colour, diffusivity, magnetic behaviour, conductivity,catalytic activity, etc., which are well known to be quite dependent on the relative Ohand Td occupancy by transition metal ions.This paper is one of a series which describes an investigation of the relation betweenstructure and variables such as temperature and composition of spinel solidsolutions.1-4 In this work the cation distribution in CoGaxA12-x04 solid solutionshas been studied by magnetic susceptibility, reflectance spectroscopy, lattice parametervariation and, mainly, by analysis of some X-ray reflections whose intensities areparticularly sensitive to variation in cation positions. The present system is ofinterest because the end members of the solid solution series, CoAl,04 and CoGa,O,,have previously been reported close to " normal " and " inverse " spinels, respec-tively ;5-6 by varying x one might thus expect, other than variation of cation distribu-tion with the temperature of preparation, gradual and substantial changes in thestructure and in the magnetic properties. We describe the combined use of the fourtechniques to evaluate the cobalt ion distribution and its dependence on temperatureand composition.244P .PORTA A N D A . ANICHINI 2449EXPERIMENTALPREPARATIONPure CoA1204, pure CoGa204 and 7 C O G ~ , A ~ ~ - ~ O ~ solid solutions with x = 0.25,0.50, 0.75, 1.00, 2.25, 1.50 and 1.75 were prepared by soaking A1203 and Ga203 with cobaltnitrate in stoichionietric quantities ; the soaked mass for each composition was dried at393 K and ground, heated in air at 873 K for 2 h in order to decompose the nitrates, carefullyre-ground and pressed into pellets (at a pressure of w 8000 kg cm-2). The compoundswere sintered in air at 1473 K for 100 h ; then for each composition one batch of pellets wasquenched in water from 1473 K, a second batch was cooled to 1073 K and equilibrated atthis temperature for 50 h before quenching in water and a third batch was cooled to 873 Kfor 50 h and then quenched in water. This procedure enabled the preparation of specimensof each of the 9 compositions at three different temperatures.The colour of the samplesranged from intense blue to deep green with increasing gallium content.X-RAY INVESTIGATIONS AND CALCULATION OF INTENSITIESIron-filtered Co Kg radiation was used to investigate all the compounds, both for thelattice parameters and for the intensity measurements. For all specimens X-ray diffractionpatterns showed no lines other than those belonging to the cubic spinel structure. For allsamples the reflections were very sharp.The details of the experimental methods used for precise determination of lattice para-meter and careful analysis of some X-ray reflections whose intensities are particularly sensitiveto variation in cation positions are reported el~ewhere.~ The method used for the calcula-tion of the intensities has already been described in previous papers 39 and is an extensionto solid solutions of the method applied by Bertaut to pure spinels.'.By considering that the cation distribution in the present CoGaXAl2-,O4 solid solutionsis characterized by the formula :where a, 18 and y are the parameters describing the fraction of Co2+, Ga3+ and A13+ ions onTd sites, respectively, the intensities of the 220,400 and 422 reflections were computed in 0.1intervals of both p and y, with the following data also taken into consideration : (i) the xmolar composition of the spinel ; (ii) the value of u, the oxygen parameter, which was takenas 0.387 for all solid solutions ; 5 7 (iii) the scattering factors for Co2+, Ga3+, A13+ and 02-,the real part of anomalous dispersion for cobalt and the Lorentz-polarization correction(International Crystallographic Tables).The 400/220 and 400/422 calculated reflection intensity ratios were displayed for eachsolid solution by constructing a family of curves of intensity ratio against fi with y alsovarying ; the experimental intensity ratios were then compared with the calculated valuesand the cation distribution for each spinel was determined.Co,GaaxAl,(2-x)[Co(l-a)Ga(l -p)xAl<~-y) (2-x)104 (1)MAGNETIC SUSCEPTIBILITYThe Gouy method over the temperature range 100-295 K was used.Correction wasmade for the diamagnetism of the sample. A check was made that the susceptibilities wereindependent of magnetic field strength. The values of the Curie constant C and hence ofthe magnetic moment ,u were taken for all specimens from the slopes of 1 /xat against T plots ;the values of the Weiss constant 8 were taken from the intercepts of the l/xat lines on theT-axi s .RELECTANCE SPECTRAReflectance spectra in the range 350-2500 nm (28 500-4000 cm-') were recorded on aBeckmann DK-1 spectrophotometer with a standard reflectance attachment, using MgO asreference.1-72450 Co" I N CoGa,Al,-,O, SPINEL SOLID SOLUTIONSRESULTSLATTICE PARAMETERSThe results for the lattice parameter Q of the cubic cell, reported in table 1 andin fig.1, show that : (i) there is an increase in lattice parameter with increasinggallium content; (ii) the variation of a with gallium content is not linear and anegative deviation from both Vegard's law and Zen's relationship is observed ; (iii) thevalues of a for specimens with the same x vary slightly with firing temperature and itis noted that for small gallium contents a decreases with increasing firing temperaturewhereas for high gallium concentrations the lattice parameter increases with quenchingtemperature.TABLE 1 .-CoGa,Al,~,O, SPECIMENS WITH GALLIUM CONTENTS x, LATTICE PARAMETERS a,WEISS CONSTANTS 8, CURIE CONSTANTS c AND MAGNETIC MOMENTS p873 K 1073 K~~ ~1473 KX - 0 C p1B.M.- 0 C p1B.M. - e c p / ~ . ~ .0.000.250.500.751 .oo1.251.501.752.008.10508.12698.14478.17748.19818.22978.25758.29928.3250105105908060605060702.71 4.662.67 4.622.76 4.702.83 4.762.88 4.802.97 4.883.08 4.973.08 4.973.10 4.988.10588.12648.14448.17648.19858.23278.25838.30098.3243110 2.83 4.7685 2.69 4.6480 2.75 4.6980 2.86 4.7880 2.96 4.8770 3.01 4.9160 3.08 4.9760 3.08 4.9770 3.08 4.978.10518.12618.14368.17588.20148.23858.26018.30088.3268110 2.75 4.69100 2.71 4.6680 2.74 4.6880 2.88 4.8070 2.96 4.8765 3.01 4.9165 3.01 4.9170 3.04 4.9370 3.06 4.95X-RAY DIFFRACTION INTENSITIESFrom the comparison of the experimental 400/220 and 400/422 intensity ratiosand those calculated for various cation distribution, the best values of /? and y wereobtained for each specimen.where [Px+y(2-x)] = 21 is the total amount of both Ga3+ and A13+ ions in Tdsites, the values of a, the fraction of Co2+ ions on T,, were also derived.Table 2reports the mean values of Co2+, Ga3+ and A13+ octahedral occupations. The valuesof the fraction of Co2+ ions in Oh sites are also shown in fig. 2.The main conclusions which can be drawn are as follows : (i) for a given con-centration in the solid solution, the octahedral cobalt increases with increasing firingtemperature from x = 0.00 to x M 1.25, whereas the inverse trend occurs betweenx M 1.25 and x = 2.00; (ii) for a given temperature the Co2+ cation distributionvaries with x ; the octahedral cobalt firstly decreases with increasing x (up tox M 0.25) and then there is a continuous increase of Co2+ octahedral occupation.These results imply that there is a minimum Oh cobalt occupation at x x 0.25.Since the following relation is valid :a = 1-21 = l-[Px+y(2-x)] (2)MAGNETIC SUSCEPTIBILITYMagnetic measurements can also be used to distinguish between Oh and T dcobalt(11).9, O For high-spin octahedral CO" the ground level (4T1,) is orbitallydegenerate and there is an appreciable orbital contribution to the magnetic moment ;observed p are, for Co2+ in Oh coordination, in the range 4.7-5.3 B.M., but most oP . PORTA AND A . ANICHINI 245 18.107 I I I I0 0.5 1.0 1.5 2.0XFIG.1 .-Lattice parameters a/A plotted against gallium content x in CoGa,A12-,04 solid solutions :(A) 873, (0) 1073 and (0) 1473 K ; (- - -) line corresponding to Vegard’s law.TABLE 2.-cATION DISTRIBUTION IN CoGaxA12-x04 SOLID SOLUTIONS WITH GALLIUM CONTENTx AND VALUES OF Co2+, Ga3+ AND A13+ OCTAHEDRAL OCCUPATION0.00 0.16 - 1.84 0.18 - 1.82 0.23 - 1.770.25 0.14 0.24 1.62 0.15 0.20 1.65 0.20 0.18 1.620.50 0.23 0.28 1.49 0.22 0.31 1.47 0.26 0.28 1.460.75 0.34 0.41 1.25 0.36 0.41 1.23 0.38 0.41 1.211.00 0.46 0.54 1.00 0.49 0.53 0.98 0.50 0.54 0.961.25 0.56 0.72 0.72 0.59 0.68 0.73 0.61 0.68 0.711.50 0.70 0.85 0.45 0.67 0.85 0.48 0.65 0.90 0.451.75 0.77 1.01 0.22 0.72 1.05 0.23 0.70 1.07 0.232.00 0.78 1.22 - 0.74 1.26 - 0.72 1.28 2452 col* IN CoGa,Al,-,O, SPINEL SOLID SOLUTIONSthem are % 5.1 B.M.ll For Td cobalt(I1) the ground term is , A 2 ; spin-orbitcoupling thus causes some mixing-in of the ,TI and ,T2 terms to the ground term 4A2and an effective magnetic moment peff.= pss0. (1 -4L/lODq), where il is the spin-orbit coupling constant, Dq is the crystal field strength and p-ls.o. is the spin-only valueof the magnetic moment (for Co" in both 0, and Td coordination pse0. = 3.9 B.M.).12Observed moments for Co" in tetrahedral configuration are in the range 4.2-4.7 B.M.I10 0.5 1.0 1.5 2.0XFXG. 2.---Fraction of Co2+ in octahedral sites plotted against gallium content x in CoGa,A1,-,04solid solutions : (A) 873, (0) 1073 and (0) 1473 K ; (- - .) and (- - -) lines passing through thepoints 873 and 1473 K, respectively.The results of the magnetic measurements are presented in table 1 ; the values ofthe magnetic moments p are also shown in fig.3. The complete set of results showsthat the magnetic moments are all in the anticipated range for a cobalt distributionintermediate between Oh and Td sites. A slight decrease in the magnetic moment forsmall additions of Ga3+ ions to cobalt aluminate and then a continuous increase inp, up to the value of = 5.0 B.M., are observed for each series at constant quenchingtemperature. Small differences in p for specimens at equal x but treated at differenttemperatures are also observed.From the intercepts with the T-axis of the linear plots of 1 /xat against T, the Weissconstants 0, of the Curie-Weiss law xat = C/(T+8), were derived and found to be inthe range - 110 to - 50°C, as reported in table 1 .Therc is a continuous decrease in8 up to x =5: 1.50 and then an increase from x = 1.50 to pure cobalt gallateP . PORTA AND A . ANICHINI4.52453l$(Co)tet ------- -I I -p (CO) oc t 5.1 ,-.--.-.-.-.-.-.-.-.-.-..- I-XFIG. 3.-Magnetic moments p/B.M. plotted against gallium content x in CoGa,A1,_,O4 solidsolutions : (A) 873, (0) 1073 and (n) 1473 K ; (- - -) and (- - - .) lines passing through the points873 and 1473 K, respectively ; the expected values of p for CoII in octahedral and tetrahedral co-ordination are also shown.REFLECTANCE SPECTRAReflectance spectra are another tool for detecting octahedrally and tetrahedrallycoordinated cobalt ions in solids, although when both coordinations are present, asin our case, the strongest intensities of Td bands with respect to those of Oh bandsdo not help much on the quantitative determination of the concentration of bothspecies.Only an indication of the presence of these species may be drawn from thereflectance spectra in the present case.The Td bands dominate the spectra of all our samples. We observed the occur-rence of the following bands: (i) a broad band centred around 4200-4650cm-l,(ii) a group of 3 bands at 6000-7400 cm-l, (iii) a shoulder at x 9200 cm-l, (iv) 3bands at 15 3000-18 000 cm-I and (v) a group of 3 bands in the region 20 300-24 400 cm-l.Our spectra accord very closely with those reported in the 1iterat~re.l~. l4 Band(i) is an envelope of the unresolved bands corresponding to the Td4A2(F) -+ 4T2(F)transition ; bands of group (ii) are associated with the Td4A,(F) -+ "T,(F)transition ;bands (iv) are the Td4A2(F) -+ 4T1(P) transitions and the group (v) correspond to theTd spin-forbidden 4A2(F) -+ 2T(G) transitions. The shoulder at 9200 cm-' can beattributed to the octahedral 4T1,(F) -+ 4T2,(F) transition.All bands moved to lower energies with increasing gallium content.Inspectionof the relative intensities of T d bands with respect to the Oh one (shoulder at 9200 cm-l)revealed that the shoulder becomes more and more pronounced with increasinggallium content.No significant variation of the relative intensities of Td and O h bands has beenobserved for samples at equal x prepared at different temperatures2454 CO" IN CoGa,Al,-,O, SPINEL SOLID SOLUTIONSDISCUSSIONIn the spinel structure the close-packed array of negative ions can accommodatecations either in Td or in O h interstices. The cation distribution in spinels is deter-mined by various energy terms, such as the Madelung energy, the Born repulsiveenergy, the electrostatic ordering energy, anion polarization and the individualcrystal field stabilization energy (c.f.s.e.).For spinels containing divalent and tri-valent cations, in the absence of site-preference energy, the " normal " distribution,i.e., that structure in which all trivalent cations are in the Oh sites and all divalentcations in the Td interstices, is favoured by the Madelung energy and anion polar-ization ; when the octahedral-c.f.s.e.of divalent cations makes a significant con-tribution to the total lattice energy or when trivalent cations exhibit a strong preferencefor Td coordination, the " inverse " distribution is favoured. C.f.s.e., when high,has thus been used to predict the cation distribution in binary spinels and the observeddistributions of metal cations between Oh and T d sites in spinels have so far beenregarded as signifying the influence of this energy l6 It has, however, beenargued that any given structure cannot be predicted by the c.f.s.e. alone, even whenits value is non-zero, and that a quantitative calculation of the change in lattice energyon inversion, mainly in the Madelung term, must be made as the most important testto verify the occurrence of any observed structure.17In the present CoGa,Al,-,O, system the CoAI,O, and CoGa,O, end membershave been observed close to normal and inverse spinels, respectively ; 5 9 the occur-rence of normality in CoAl,O, is easily understood since all the energy terms tend tofavour this structure and no pronounced difference in site-preference energy ispresent between Co2+ and A13+ ions.On the other hand, since Ga3+ and Co2+ ionsshow Td and Oh site-preference energies, respectively, it may easily be realized whyCoGa20, has experimentally been found a nearly inverse spinel. CoGa,Al,-,O,is therefore a very useful system for investigating the variation, if any, of the cationdistribution with thermal treatment as well as with composition.A definite trend towards more random cobalt distribution with increasingquenching temperature has firstly been evidenced from our investigation. Consider-ing that the " random " cation distribution in a 2-3 spinel corresponds to two-thirdsof divalent cations in Oh sites, i.e., [Co],, = 0.67, analysis of the X-ray intensitymethod (table 2 and fig.2) gives an explanation of most of the observed results. Infact, from x = 0.00 up to x = 1.25 all spinels have been found more normal thaninverse, [Co],, < 0.67, whereas above x = 1.25 the spinels are more inverse,[Co],, > 0.67 ; the increase of quenching temperature then favours, as expected,the randomization process.The same effect is observed from magnetic measure-ments, as shown in table 1 and in fig. 3. Reflectance spectra and lattice parametersdo not reveal any detectable variation of cation distribution with thermal treatment,probably due to the smallness of the effect.Let us now consider the relation between cation distribution and x . Thereflectance spectra show a shift of all the observed bands towards lower energies withincreasing gallium content, in agreement with the expansion of the unit cell volume,i.e., with increasing anion-cation distances ; moreover, the shoulder observed at9200 cm-l, attributable to the octahedral Co" ,TIg(F) 3 ,T2JF) transition, becomesmore and more pronounced (with respect to the relative intensities of T d bands)with increasing gallium content, thus indicating an increase of octahedral cobaltoccupation.The expansion of the lattice on going from CoA1204 to CoGa204 (table 1 andfig.1) is explained in terms of substitution of smaller A13+ ions (Goldschmidt ioniP. PORTA AND A . ANICHINI 2455radius = 0.57A) with larger Ga3+ ions (Goldschmidt ionic radius = 0.62A). Ithas already been said that the lattice parameter is also affected by the cation distribu-tion (inversion is well-known to decrease its value)12 and we think that the non-linearity in the increase of a with x is an indication of the dependence of cationdistribution on composition.The influence of composition on cobalt distribution may be derived from themagnetic and X-ray intensity results which both show, for all series of compounds, afirst slight decrease in cobalt octahedral occupation and then a continuous increaseof [CO]~,, by progressive addition of gallium.We suggest that the presence of sucha minimum in [CO]O, at a given value of x (= 0.25) is brought about in this case bypolarization effects. The trend may be explained as follows : on going from pureCoA1204 to gallium spinels, the Ga3+ ions, due to their preference for Td coordination,tend to substitute A13+ ions in the Td sites. A lower positive charge density thusresults in the Td sites, since the ionic radii of tetrahedral Ga3+ and A13+ ions are0.47 and 0.39 A, respectively.' As a consequence, oxygens are more polarisedtowards the octahedral sites favouring a major tendency for trivalent ions (namelyA13+) to occupy the Oh sites and for divalent ions (Co2+) to occupy the T d sites.Thisoccurs for relatively small gallium content. With increasing gallium content, nomore A13+ ions are available to change their coordination from tetrahedral to octa-hedral (see table 2) and the Ga3+ ions are forced to occupy the Td sites with the spinelsbecoming more and more inverse.A variation of cation distribution with composition has also been observed forother spinel solid solutions studied by us, such as Ni,Mgl-,A1204,1 CU,M~,-,A~,O,,~COG~,R~,-,O,,~ CoxMgl-,A1204 and Ni,Znl-,A1204.4It should also be pointed out that an effect similar to that observed by us, i.e., adiscontinuous dependence of cation distribution on composition, has indeed beenfound by Delorme in the CuA1,Fe2-,04 system l 9 and by Bracconi et al.in theCo2+Cr: +Coi ZxO4 spinel solid solutions.20 We believe that the results found bythese authors are covered by our explanation.Finally, the negative values of the Weiss constant 8 (table 1) obtained from theplots of 1 /xat against T confirm the predominance of antiferromagnetic interactionsfor all the samples. A decrease in 0 is observed up to z 67 % of [ C O ] ~ , , with asubsequent increase of 8. The variation in 6 values with [Co],, has also beenevidenced in a more detailed magnetic investigation (in the range 4.2-300 K) per-formed by other authors 21 on the CoGaxA12-,04 series prepared by us at 1073 Kand it has been suggested that the variation is indicative of the presence of anti-ferromagnetic and/or ferromagnetic interactions.We think that spin-orbit coupling,which modifies the values of p and also contributes to 8, should also be considered,especially when varying amounts of Co2+ ions in Td coordination are present in thesolid solutions.We thank Mr. G. Minelli for technical assistance and Mr. M. Inversi for thedrawings.P. Porta, F. S. Stone and R. G. Turner, J. Solid State Chem., 1974, 11, 135.F. Pepe, P. Porta and M. Schiavello, Proc. 8th Znt. Symp. Reactivity of SoZids (Gothenburg,Sweden, June 1976), 1P27.C. Angeletti, F. Pepe and P. Porta, J.C.S. Faraday I, 1977, 73, 1972.P. Porta, A. Anichini and U. Bucciarelli, J.C.S. Furaday I, 1979, 75, 1876.H. Furuhashi, M. Inagaki and S. Naka, J. Inorg. Nuclear Chem., 1973,35, 3009.M. Lensen and A. Michel, Compt. rend., 1958,246, 1977. ' E. F. Bertaut, Compt. rend., 1950, 230, 2132456 Col* I N CoGa,Al,-,O, SPINEL SOLID SOLUTIONSL. Weil, E. F. Bertaut and L. Bochirol, J. Phys. Radium, 1950, 11, 208.C. J. Ballhausen, Introduction to Ligand Field Theory (McGraw Hill, New York, 1962).lo B. N. Figgis, Introduction to Ligand Field (J. Wiley, New York, 1966).l 2 E. J. W. Verwey and E. L. Heilmann, J. Chem. Phys., 1947, 15,174.I3 M. Drifford and P. Rigny, Compt. rend., 1966,263, 180.l4 0. Schmitz DuMont, H. Brokopf and K. Burhardt, 2. anorg. Chem., 1958,295, 7.D. S. McClure, J. Phys. and Chem. Solids, 1957, 3, 311.l6 J. D. Dunitz and L. E. Orgel, J . Phys. and Chem. Solids, 1957, 3, 318.C. Glidewell, Inorg. Chim. Acta, 1976, 19, 445.R. D. Shannon and C . T. Prewitt, Acta Cryst., 1969, B25, 926.' M. M. Schieber, Experimental Magnetochemistry (North Holland, Amsterdam, 1967).l9 C . Delorme, Bull. SOC. Franc. Miner. Crist., 1958, 81, 79.2o P. Bracconi, L. Berthod and L. C . Dufour, Proc. 8th Int. Symp. Reactivity of Solids (Gothen-'' D. Fiorani and S . Viticoli, J. Solid State Chem., 1978, 26, 107.burg, Sweden, 1976), 2Mll.(PAPER 9/1240