On the miscibility gap of spinels MnxFe3−xO4+γ

J. Phys. Chrm. Solids. 1973. Vol. 34. pp. 387-395.

Pergamon Press.

ON THE MISCIBILITY

Printed inGreat

Britain

GAP OF SPINELS Mn,Fe,-xO,+,

P. HOLBA, M. A. KHILLA* and S. KBUPICKA Institute of Solid State Physics, Czechoslovak Academy of Science, Prague, Czechoslovakia (Received

22 May

1972)

Abstract-Annealing experiments at 940& S”C on Mn,Fe 3- r 0 4+y system were carried out in order to determine the equilibrium miscibility limits. The samples were annealed for 200 hr in sealed quartz tubes and quenched. Coexisting phases and relevant parameters were determined by X-ray diffraction. The immiscibility interval at the annealing temperature has been found by converting the c/a ratios to corresponding x-values to be x,,~ = 2.54 f 0.03, x,,.~= 2.73 -+0.03. The experiments concerning the possible influence of the oxygen content are also reported. A corrected version of the phase diagram based on the results obtained as well as on the critically selected data published previously by other authors had been suggested and discussed on the basis of a simple model. 1. INTRODUCTION

does not occur because of the insufficient diffusion rate. Instead of it a diffusionless transition of metastable cubic to metastable tetragonal phase appears [5,6] that is analogous to the transition between the stable phases observed e.g. for the pure hausmannite MqO, at 1172°C [7]. The origin of the macroscopical tetragonal distortion of the lattice for the manganese rich spinels is the cooperative Jahn-Teller effect of Mn3+ ions in octahedral positions [8,93. The tetragonality (expressed by the c/a ratio) of the frozen-in one-phase samples increases with the increasing manganese content X. The changes of this dependence due to different heat treatment were observed by Brabers[S]. This variability was found to be well pronounced particularly at lower manganese contents (- 1.9 < x < 2.5) and was ascribed to the combined effect of varying cation distribution among A and B position and of Mn3+ clustering. An important role may be also played by the oxygen nonstoichiometry as indicated in the present study. The first suggestion of the shape of miscibility gap (Fig. 1) was done by Mason[ll based on both analysis of natural vredenburgites and annealing experiments. A thorough investigation of the miscibility gap in the spine1 system Mn,Fes-,01 was performed by

minerals of system Fe,O,Mn304 of the general formula Mn,Fe,-,O, were classified by Mason [ I] into four groups: magnetite or manganomagnetite (0 S x s 0*5), jacobsite (0.5 s x s l-62), vredenburgite (l-62 G x s 2.73) and hausmannite (2.73 s x s 3-O). Magnetite and jacobsite are one-phase minerals of the same cubic spine1 structure, hausmannite is one-phase mineral with the structure of tetragonally distorted spinel. Vredenburgite contains two coexisting phases, cubic and tetragonal spinels. This indicates the existence of a miscibility gap in the given system of spine1 solid solutions as confirmed experimentally by several investigators. On the other hand, when materials having their compositions inside the existence region of natural vredenburgite are prepared by sintering at 1200°C or at even higher temperatures (or annealed at such temperatures) and then rapidly cooled only one-phase spine1 is obtained which is cubic for x up to = 2.0 and tetragonal for higher manganese contents [l-5]. The decomposition into two phases

THE

NATURAL

*On leave from Inorganic Chemistry Department, National Research Centre, Dokki-Cairo. E.A.R. 387

P. HOLBA,

388

Mn, Fe3+04

M. A. KHILLA

and S. KRUPldKA

expected. In order to find the reason of such a discrepancy simple annealing experiments were proposed. Their aim was to limit the immiscibility interval for a single temperature 940°C by approaching the phase boundaries from both inside and outside, i.e. (1) by decomposition at frozen-in one-phase spine1 samples (2) by reacting properly chosen mixtures of single phases with compositions laying outside of the expected miscibility gap. 2. EXPERIMENTAL

AND

RESULTS

Five basic materials x = 2.0, 2.32, 2.61. 2.74 and 3.0 were prepared from analytical grade MnCO, and Fe,O, by homogenization, calcination (800°C 24 hr in air), powdering, X Fig. 1. Survey of published miscibility boundaries and sintering (12OO”C, 25 hr in oxygen or in argon) diffisionless transition temperatures T, of spinels and quenching into liquid nitrogen. Besides Mn,Fe,-,O,. 0 -limits of natural vreddenburgites [ 11, these, manganese oxide MnO and manganese m-limits by Mason[l]. O-limits by Brabers[S]. V-difsesquioxide Mn,OS were prepared from MnO, fusionless transition by O’Bryan [6]. A-diffusionless (p.a.) by reduction in hydrogen at 600°C for transitions by Brabers [5]. 8 hr and by firing in air at 800°C for 24 hr, respectively. The oxygen content of the reMcMurdie et al. [ 141 using a high-temperature X-ray diffraction camera. They showed that sulting samples was determined by chemical an additional anneal of the frozen-in samples analysis using the cerimetric method in order at temperatures between 400 and 1200°C to start with chemically well-defined materials. leads to a decomposition into cubic and tetraThe following procedure was used at the gonal phases in the region also represented in annealing experiments. The initial samples Fig. 1. The previous results obtained by were powdered, mixed in required ratios, Mason at 750°C as well as the recent ones pressed into pellets (4 6 mm), covered by reported by Brabers[5] for the temperature platinum foil and placed into a quartz tube. 890°C match the miscibility gap found by The tube was then evacuated (at 150-2OO”C), McMurdie. On the other hand the lower part sealed, heated at 940 *5”C for 200 hr and of the McMurdie’s phase diagram does not quenched into liquid nitrogen. Powdered agree with the limits of natural vredenburgite. annealed samples were then investigated by (using Fe,, radiation) Later Hook and Keith [IO] tried to revise X-ray diffractometer to determine coexisting phases and the tetrathe previous data on the miscibility gap by gonalities of spine1 phases present. The experiments in which the mixture of MnO,, Mn, Fe (eventually FeZOR) were annealed and oxygen content was determined for most of ratio was reacted. They found substantially wider mis- the samples, iron-to-manganese cibility gap (Fig. l), the low temperature part checked at one mixture and found to equal the required one. of which was compatible with the existence region of natural vredenburgites. The results of the annealing experiments at The disagreement between Hook’s and 940°C are summarized in Table 1. The annealing of the original samples with x = 2.32. 2.74 McMurdie’s diagrams is surprising particularly at temperatures above 900°C where the gave single-phase X-ray diagram of tetragonal errors arising from equilibration are not to be spinels the c/a ratio of which exhibited a small zoo-

Total composition

Original components 2.32 2.54 2.57 2.53 2.54 2.52 (2.47) (2.36)

I .095 I.123 I.126 1.122 I.123 I.121 I.115 I.101

I.144 I.142 I.143 I.144 I.140 I.141 I.140

2.75 2.73 2.74 2.75 2.71 2.72 (2.71)

Resulting spine1 phases x* c/a x*

c/a

*For conversion of c/a data to the corresponding x-values see Fig. 2 (solid line).

x = 2.32 Mn2.:oFeo.6*O~.~,,,, x = 2,74 Mnz.i,Fel,.280iOl.~,,, x = 2.61

.r = 2.32 (c/a = 1.101) s = 2.74 (c/a = I. 145) x= 2.61 (c/a = 1.130) x=2.32+x= 2.74 i:G y5 Mnn.sIFe,,.,,,Or.,,,,,..,,,,, MnlFe0,+Mn,,0.,+(95%)x = 2.61 MIX E Mn,FeO., + Mn,OJ MIX R Mn2.,aFe,,.510J.lza Mn,FeO., + Mn:,O, + MnzO, MIX P MnZ.siFe,,.a:,On.H,s Mn,FeO, + Mn901+ MnO MIX F Mn2.~~sFe~l.r,50:I.X75 Fe,O, + Mn203 + MnO

Sample

Table 1. The results of annealing experiments at 940°C

Bixbyite (Mn, Fe)zOzl Manganosite MnO Manganosite MnO

Coexisting nonspinel phases

390

P. HOLBA,

M. A. KHILLA

and S. KRUPICKA

shift to smaller values with respect to that mixing Mn,FeO,, Mn,O, and 50 per cent of spine1 with x = 2.61. The aim of this experidetermined on the samples before annealing. This may be attributed to the effect of heat ment was to check the rate of equilibration at treatment as reported by Brabers [5]. The this temperature and to get some idea about diffraction diagram of the sample x = 2.61 the reliability of some data reported in the having an intermediate composition contained literature for the lower part of the phase reflections of two tetragonal spine1 phases. diagrams. After two week’s anneal the mixture Occurence of two phases was evident pre- still contained three spine1 phases, which may dominantly at the reflections of crystallobe considered as a consequence of an insufgraphic planes 004,105,321 and 400 (indexed ficient equilibration. according to the Dz 14/amd group). EquilibraFor the determination of the miscibility tion from outside composition points was limits at 940°C the dependence c/a vs x was studied on mixtures, the total composition of used indicated by the full line in Fig. 2. It which corresponded to the same formula Mn,!.G,Feo.,,04.000~o.oos. The starting phases were Mn,FeO, (x = 2.0) and Mn,O, (x = 3.0) I 16 t for MIX E, x = 2.32 and x = 2.74 for MIX M and Mn,FeO,, Mn304 and 95 per cent of x = 2.61 for MIX 95. All three mixtures contained after annealing and quenching two tetragonal spine1 phases with c/a ratios very close to those of phases prepared by de0 + composition of homogeneous (frozen-in) t 106 sample x = 2.61. / The effect of oxygen content on the imt n”i o I I miscibility interval at 940°C was tested on mixtures R and P having total metal-to-oxygen ratio different from 3 : 4. The starting components and compositions are given in the table. I ,.00-*-:-a Annealed mixtures contained three phases: 20 25 30 X two spine1 phases and manganosite (MnO) or bixbyite ((Mn, Fe),O,), respectively. The Fig. 2. Dependence of c/a ratio on manganese content for spine1 Mn,Fe3-,O+ A- Verwey 121, V - Montoro [3]. tetragonalities of spine1 phases corresponded q - Mason[ll. 0-McMurdie[4]; XBrabers, sintered to those determined on annealed materials at 11’7%14OO”C[5]. +-Brabers, annealed at 900, 600 of total composition x = 2.61, except a rather and 3OO”C[51, O’Bryan[6], 4 -this work, sintered at low c/a value of the iron-rich spine1 phase of 1200” and quenched, 0 -this work annealed at 940°C and quenched, v-this work, MIX F, A-this work, MIX P. An additional annealing experiment MIX P. at 940°C was accomplished with the mixture of the chemical formula Mnp.525Fe0.~r7503.875 corresponds to the Braber’s results on samples (MIX F) mixed from phases Fe203, MnO and annealed at 900, (3 hr), 600” (16 hr) and 300°C (3 hr) that show reasonable agreement with Mn,O,. After anneal this mixture contained one spine1 tetragonal phase and manganosite. our own data. The values of x obtained by The tetragonality of this spine1 is considerably converting of the found c/a ratios of spine1 low. phases according to this dependence are given Supplementary annealing at 710°C was in Table 1. carried out using the mixture with total chemThe lower tetragonality of the iron-rich ical composition Mn2.61Fe,,.3y04 prepared by phase of MIX P is to be ascribed to the de-

THE

MISCIBILITY

pendence of c/a on the oxygen content rather than to a direct effect of latter upon the position of the phase boundary in the (x, T) plane. This may be understood on the basis of Fig. 3, taking into account the results on the MIX F. This figure represents a part of isothermal cut of the phase diagram Mn-FeO*, in which the positions of all investigated total compositions are given. Because the maximum oxygen excess of manganosite should not exceed MnO,.M at = lOOO”C[13] any conode in the two phase region cubic spinel-manganowiistite that goes through the point of MIX F will cross the line of stoichiometric spinels (y L- 0) at x L 2.45. On the other hand if the experimental c/a ratio found for spine1 phase of MIX F is converted to xvalue using the same c/a vs x curve as in the case of other spine1 phases in the absence of manganowustite the value x = 2.36 is found. This means that c/a vs x dependence given by full line in Fig. 2 cannot be valid for oxygen deficient spinels coexisting with the manganowustite phase in equilibrium and a curve represented by the dotted line in the same figure is expected. From the above results and considerations the miscibility limits are determined as follows

GAP OF SPINELS

391

xc,,, = 2-54 AI O-03, X tetr = 2.73 k O-03 at 940 + 5°C. They may be considered as corresponding to the stable equilibrium and independent of oxygen content within the uncertainties indicated above. This result is in accord with limits observed by McMurdie ef al. for the high temperature range and corresponds to the decomposition of Mn2.67Fe0.3304 observed by Brabers at 890°C. The data of Van Hook and Keith are not confirmed by this work. Their misleading results may be probably due to an insufficient equilibration of their samples. The heating periods used by them were probably not long enough to achieve the equilibrium, taking into account that starting materials had chemical compositions lying very far from the equilibrium ones. As it was mentioned above, the diagram of McMurdie agrees roughly also with the results of Mason at 750°C. If the tetragonalities (c/a = 1.09 and l-132) of coexisting phases found by him are transformed to the x values according to c/a vs x dependence used in this work, however, better agreement to McMurdie is obtained. 3. PHASE DIAGRAM

The results reported in the previous part (narrow two-phase region) confirm the correctness of the phase boundaries essentially given by McMurdie et al., at least for higher temperatures. They are mutually consistent and show that at 940°C the same miscibility limits can be attained by convergency of starting compositions laying outside of these limits as in decomposition experiments. For temperatures below = 7OO”C, however, the very low reaction rate makes reaching equiFig. 3. The part of isothermal cut (940°C) of phase diagram of ternary Mn-Fe-O system. The points representing the libria under laboratory conditions difficult and total compositions of the investigated mixtures indicated thus the reliability of McMurdie’s data quesby x. tionable. So the only limits which can be taken as corresponding to equilibrium are *The chemical compositions for bixbyite and man- those deduced by Mason from natural vredenganowiistite phases coexisting with two spine1 phases are chosen according to the data of Muan and Somiya[l 11 burgites. In this part we wish to suggest a corrected version of equilibrium phase diagram and Tretyakov [ 121.

P. HOLBA,

392

M. A. KHILLA

fitting all these reliable data and to discuss its main features on the basis of a simple model. The corrected boundaries we suggest for the two-phase region in the Mn,Fes-,O,spine1 system are drawn in Fig. 4. At the first sight this diagram resembles a combination of McMurdie’s and Mason’s diagrams. It probably reflects some general features of analogous binary systems the extreme mem1500,

I

// I’

01to

/

\“\\ \. \:I

/p i t5

20

25

30

X

Fig. 4. The probable miscibility gap suggested on the basis of selected data (solid line, O-limits of vredenburgite[l], +-corrected limits of Mason[l], O-limits by Brabers[5]. O-limits by McMurdie[4], O-this work). The results of calculations based on the simple model are given by dot- and dashed line. The transition temperatures T, both experimental and calculated are represented by the dotted and dashed line respectively

bers of which are cubic and tetragonal distorted respectively (see e.g. the similarly shaped phased boundary in UO,-ZrO, system [ 141. The reason for such a behaviour may be sought in the combined effect of two factors, (1) the existence of tetragonal + cubic transition and, (2) the tendency to decomposition into phases. While the first is related to the entropy term in the free energy and hence prevails at higher temperatures, the second one is governed by the composition depen-

and S. KRUPICKA

dence of the inner energy of both cubic and tetragonal phases and comes into effect mainly at lower temperatures. One of the rather surprising feature of the diagram suggested by the full line in Fig. 4 is a well pronounced retrograde shape of the phase boundary on the manganese rich side. We will show now that such a behaviour in reality represents nothing strange and can be theoretically predicted on the basis of a very simple model. Let us try to derive the shape of miscibility gap under following simplifying assumptions: (1) The crystal structure is assumed to be normal spine1 (cubic or tetragonal) throughout the composition interval 1 s x s 3 and only MrP+ ions are in tetrahedral positions while both Fe”+ and Mn”+ are present in octahedral positions the fraction of the latter being of MB 3+] = (x- 1)/2 independently temperature. The system thus effectively becomes that of binary solid solutions of octahedral cations with the configurational entropy

s,..“r=R

[

(*-l)ln++(3-X)lnF]

(1) (2) The difference of the orientation entropy connected to the distorted Mn3+ octahedra between cubic and tetragonal hausmannite

(x = 3) equals the entropy

change determined at the corresponding transition temperature (AS = 3.45 cal/deg[7]) and is considered as temperature independent. For other compositions this difference is supposed proportional to [Mnf13+]. i.e. As orient= 3.45 (x- 1)/2 cal/deg

(2)

(3) Stabilization energy of tetragonally distorted spine1 is proportional to [Mnp3+]2 = (X - 1)‘/4 and for Mn,O, equals the enthalpy change at the

THE

MISCIBILITY

GAP

OF

SPINELS

cubic-tetragonal transition (AH = - 5.0 kcal[7] independently of temperature i.e.

AHstat,= -5*0(x-1)‘/4.

(3)

This assumption corresponds to the simplest form of the expression for the cooperative Jahn-Teller stabilization energy based on linear distorting effect and elastic coupling to the lattice[l5, 161: For T = 0 K it isgiven by Higher

E,,*r = -acu

+ Q31r’.

Here u denotes the distortion, c concentration of the distorting ions (MnJ+) and CY,p are constants characterising strengths of the Jahn-Teller effect and elastic coupling respectively. The assumption of the temperature independence of both ASoplenland AH,,, is evidently an oversimplification but the commited error need not be serious due to the small change of c/a ratio between 0 K and the tetragonal-cubic transition temperature [41.

Our task is now to compute the free energy as a function of compositional parameter x and temperature for both cubic and tetragonal phases. The relevant formulae are Acrib” = - T(umnr + uorient)

(3

AGmiX = H slab

(6)

te1r

-

T A

Scan,.

order

term

(4)

The miscibility limits at a given temperature are then determined by the common tangent of both free energy curves for cubic and tetragonal phases. The intersection of these curves may be interpreted as the transition point of the diffusionless tetragonai-cubic transition. The details of the procedure are illustrated in Fig. 5. The resulting model phase diagram is given by dot-dashed line in Fig. 4. It fits well the originally suggested diagram at elevated temperatures and exhibits at least qualitatively the retrograde character of the phase boundary at the manganese-rich side.

-600

20

30

X

Fig. 5. To the calculation of model phase diagram. (a) Construction for the determination of diffusionless transition point (T,) and miscibility limits M, (for T 1000°K) (b) Illustration of the influence of higher order JahnTeller energy terms and lattice anharmonicity on the concentration dependence of stabilization enthalpy.

The critical temperatures for the diffusionless metastable tetragonal to cubic transition deduced from our simple model are also plotted in Fig. 4. While the agreement with experiment may be considered as satisfactory for greater x the discrepancies at lower manganese contents may be attributed to the principial sensitivity of the transition temperature upon the actual state of the sample, (existence of clusters, degree of inversion, mechanical stress) and to the fact, that our simple model entirely disregards the local correlations connected to the short-range energy terms. In fact, the higher Tt values are hard to be exactly determined in the experiment and only a finite interval is used to be found [5, 181. This effect may be ascribed to the partial decomposition of the original tetragonal phase at temperatures near the expected transition point: The fluctuations both compositional

394

P. HOLBA,

M. A. KHILLA

and orientational increase considerably in the vicinity of this point which lower the stability of the tetragonal phase and initiate the seggregation process. We believe that some McMurdie’s manganese-rich boundary data lower temperatures may be influenced by this effect. There are several factors omitted in the above simple model that may account for the remaining discrepancies in the lower part of the phase-boundary. For the sake of convenience they can be classified into two groups according to their expected effect upon the width of the miscibility gap: (1) The gap should become broader by (a) taking into account the temperature dependence of both the stabilization energy UIstab and the orientational entropy uorient. (b) The effect of the short range interactions leading to formation of clusters [171.

(2) The gap should be narrower when (a) the higher terms are added to (4) corresponding to the higher order terms of the Jahn-Teller effect and to the lattice anharmonicity, respectively (concerns mainly lower temperatures and the right hand side of the phase boundary). The qualitative change in AHshb course is sketched in Fig. Sb. (b) The partially inverted structure including possible (minor) changes in the valency states of cations (effective mainly for the left hand side of the diagram). The comparison of the model phase diagram and the reliable experimental data shows that effect of the group (2) corrections should prevail over the influence of that of (1) at least at lower temperatures. On the other hand the real situation seems to be too complicated so that it would be of less importance to try to analyse the influence of the mentioned effects individually and more thoroughly. Nevertheless, it would be interesting to examine

and S. KRUPICKA

the phase diagram of some analogous system but not exhibiting difficulties connected to cation and valency distribution e.g. MnCr,O, - Mn,O,. 4. CONCLUSIONS

By annealing mixtures of different compositions, lying both outside and inside the miscibility gap of the spine1 system Mn,Fe,-,01 the immiscibility interval at 940°C was found t0 be x,-b = 2.54 5 0.03 and xteti = 2.73 2 0.03. This result is compatible with the high temperature data given by McMurdie er al. and Brabers, but differs from the phase diagram given by Hook and Keith. A corrected version of the diagram originally proposed by McMurdie has been suggested and its main features reproduced by the calculations based on a simplified model. authors wish to express their gratitude to Drs. Z. SimSa and P. Novak for stimulating discussions, to Ing L. Matejkova for the chemical analyses, to lng E. Pollert for the friendly assistance in X-ray analysis and to Mrs. M. Holeckova for numerical calculations. We are also indebted to Dr. Z&eta for his reading the manuscript and for helpful comments. Acknowledgemenr-‘lie

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B.,

Geol. FGreningens 65,97 ( 1943).

2. VERWEY

Fiirhandligar.

E. J. W. and BRUGGEN M. G., Z. 136 (1935). 3. MONTORO V., Gazz. chim. ital. 68,728 (1938). 4. McMURDlE H. F.. SULLIVAN B. M. and MAUER F. A.,J. Res. NBS45,35 (1950). 5. BRABERS V. A. M., Thesis, Eindhoven University of Technology (1970): BRABERS V. A. M., j. Phvs. Chem. So/ids 32.2 I8 I (I 97 I). 6. O’BRYAN H. M. and LEVINSTEIN H. J., J. Phys. Chem. Solids 30, I7 I9 ( 1969). 7. IRANI K. S., SINHA A. P. B. and BISWAS A. B., J. Phys. Chem. So/ids 23.7 I I (1962). 8. DUNITZ J. D. and ORGEL L. E.,J. Phys. Chem. Solids 3,20 (I 957). 9. WOJTOWICZ P. J., J. appl. Phys. 30, 308 (1959); WOJTOWICZ P. J., Phys. Rev. 116.32 (1959). 10. HOOK H. J. and KEITH M. L., Amer. Mineral. 43, 69(1958). I I. MUAN A. and SOMIYA S., Am. J. Sci. 260. 230 (1962). 12. TRETJAKOV Ju. D., Tirmodinamika ferritou, p. 129 Chimia, Moskva (I 967). Kristallogr.

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THE 13. HED A. Z. and TANNHAUSER them. Sot. 114.3 14 (1967). 14. COHEN I. and SCHAUER 9,18(1963). 15. SLONCZEWSKI J. C., Bull. 53 (1964).

MISCIBILITY

GAP

D. S., J. elecfroB. E.. J. nrccl. Sot.

Sri.

Mufer.

Bre/ugne

39,

OF

SPINELS

16. KANAMORIJ.,J.opp/.Phys.31, 14S(1960). 17. KRUPldKA S., SIMSA Z. and SMETANA Czech.J. Phys. 18B, 1016(1969). 18. SIMSA Z., HOLBA P.. Unpublished results DTA in argon.

395

Z., on