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Thermodynamics of Formation of Some Compgunds with The A merican M ineralogist, Volume60, pages249-256, 1975 Thermodynamicsof Formationof SomeCompgunds with the Pseudobrookite-Structureand of the FeTirOu-TisOrSolid SolutionSeries AtexnNone Nnvnorsrv Departmentof Chemistry,Arizona State Uniuersity, Tempe,Arizona 8528i, Abstract The enthalpyof formationof pseudobrookite,FezTiO,, from FezOaand TiO, is found by oxidemelt solutioncalorimetry to be *1.99 * 0.15kcal mol-r (*8.33 + 0.63KJ mol-'). Thermochemicaldata for other compoundswith the pseudobrookitestructure are summarized.Pseudobrookites are "entropy- stabilized"high temperaturephases with partiallydisordered cation distributions. Their decompositionat low temperaturesto assemblagesofbinary oxides(for,{rg+Ba+Ou pseudobrookites) or to assemblagesof phasesofilmenite and rutile structure(for A'+ Bzn+Oopseudobrookites) reflects the balancebetween en- dothermicenthalpies of formationfrom theseassemblages and the substantialpositive entropies of for- mation arisingfrom the substitutionaldisorder. A simplecation distribution model is appliedto the dis- tribution of iron between4c (A) and8/(A) sitesin the FeTizOu-TisO'system, from which high Ti'Oo is predictedto havethe cation distribution(Ti'+0 o6Tie+0 go)A(Ti'+o.e6Ti3+' o.)eOu. Interchange enthalpies (or freeenergies) for the reactions:Mg'+r * Tin+e= Mg'*g + Tio+A,Fe'+A + Til+B = Fe2+s* Tia+r,and Tis+A+ Ti'+a : Tio+B+ Ti'*a are +8.6, + 13,and * l0 kcalmol-r respectively(36.0, 54, and 42 KJ mol-', respectively).MgTtOc exhibitssomewhat disordered pseudobrookite structures derived from a "normal" structurestable at low temperature,while TirOoand probablyalso FezTiOu, AlrTios, and GazTiOuhave somewhatdisordered structures derived from an "inversestructure stable at low temperature.Thus Ti'+ appearsto havea strongpreference for the 8/(A) sitesin all thesecompounds ofpseudobrookite struc- ture. Introduction with 4 A82o' formula units in the unit cell, all the cationsare in octahedralcoordination. There are two Studyof lunar basaltshas resulted in considerable kinds of octahedralsites, with fourfold (4c or,4 sites) interestin mineralswith the pseudobrookitestruc- and eightfold (8/ or B sites)multiplicity. Three oc- ture. These include FezTiOs (pseudobrookite), tahedra share edgesto form units which are then FeTLOu(ferropseudobrookite), MgTirOu (karrooite), linkedtogether into doublechains as building blocks (Mg,Fe)TirOu(armalcolite), and solid solutionsin the for the structure. In monoclinic pseudobrookites FerTiOu-TirOuseries. The purposeof this paper,is such as TirOuand the titanium-richmembers of the threefold:(a) to presentnew high temperaturesolu- TirOu-FeTizOusolid solutionseries (Grey and Ward tion calorimetricdata for the enthalpyof formation (1973),the 8/ (B) site is further split into two non- of FezTiOs,(b) to reviewthe existingthermochemical equivalentsites. For armalcolite,Lind and Housley data for ternary oxides with the pseudobrookite (1972)give the following metal oxygendistances for structure, and (c) to correlatethe thermodynamic the 4c and 8/ octahedra-8f, 2.061, 1.845,l'993, and structural data and to apply a simple thermo- 2.172,1.938, and 1.938A;4c, 1.960,2.191,l'960, dynamic model to the cation distributions in 2.191.2.030.and 2.030A. Thus,both octahedraare MgTirOo, FeTizOu,and the FeTizOu-TirOusolid distorted.The averagebond lengthin 8/is 1.992+ solution series. 0.1l4(s.d.) A; thatin 4c is 2.072t 0'096A' Thusthe The PseudobrookiteStructure ,4 site is somewhatlarger and slightly lessdistorted Early structure determinationswere by Pauling than the B site. For the presentpaper' the most im- (1930) and Hamelin (1958). Recently,Lind and portant feature of the pseudobrookitestructure is Housley(1972) have performed structure refinements that the two sitesare sufficiently similar to allow con- on syntheticsingle crystalsof karrooite, MgTirOu, siderablesubstitutional disorder of the cationsoc- and armalcolite,Mgo.uFeo.6Ti2ou. In the orthorhom- cupyingthem. As in the spinels,we canrecognize two bic pseudobrookitestructure, spacegroup Bbmm, limiting distributions,the normal,(A)4"(B)BtOo and 249 250 ALEXANDRA NAVROTSKY TnsI-e l. Enthalpy of Solution of Pseudobrookite in of FezTiOu,although its molar enthalpy of solution 3NarO.4MoO, at 692"C was fortuitously very close to zero, so that the heat effects actually measured were always less than 0. 1 FerTiO, callobs I H"oa(kcal mol-}) calorie in magnitude.The resultsof five solution ex- (in mg) periments(Table 1)give a meanof -0.10 t 0.10kcal mol-1. One may then calculate,for 46.07 -0. 050 -o.26 the reaction: 86.06 -0. 020 -0. 06 FerO, (hematite)+ TiO" (rutile) : Fe"TiOs LL4.46 !0. 000 r0. 00 (pseudobrookite) (l) 43.60 -0. 015 -0. 08 49,25 -0. 0r9 -0. 09 AHo"uu= +1.99+ 0.15kcal mol-' Discussionof the Stability of FerTiOu AV = -0.10!0.10 and other Compoundswith the PseudobrookiteStructure the inverse,(B)k(AB)ErOu, and we cananticipate that, Fe"TiOu especially at high temperature,intermediate dis- tributions will be the rule rather than the exception. The calorimetric data show the enthalpy of forma- pseudobrookite CalorimetricDetermination of the tion of from hematite plus rutile to positiue. Enthalpy of Formation of be This suggests that the ternary oxide is Pseudobrookiteil 692 + 2"C stabilized at high temperatures by a positive entropy of formation and should becomeunstable relative to FerTiOu was prepared by ignition of a stoi- the binary oxides at low temepratures. Such decom- chiometricmixture of dried BakerAnalyzed Reagent position has indeed been found by Haggerty and FerO, (hematite) and TiO, (rutile) for a total of Lindsley (1970),with an equilibrium temperatureof 72 hours in platinum a cruciblein air at 1350.C, 565 + 15"C. We can calculatethe entropy of the for- with four intermediategrindings of the sample.At mation reaction since at 838 K its free energy change the end of eachfiring, the samplewas cooled relative- is zero. ly rapidly in air. The powder X-ray diffraction +=tllo pattern of the product showedit to be singlephase ASo: : +2.4 cal K-' mol-' (2) pseudobrookite. 838 The high temperatureCalvet-type twin micro- The free energy of formation of FerTiOu from calorimeter and the sample assemblyfor measur- FerO, and TiO, is then given by the equation: ing the heat of solutionof a solid oxide samplein a molten oxide solvent have been describedpre- AGo: + 1990- 2.4T (T inK) (3) viously (Navrotskyand Kleppa, 1968).Navrotsky and Kleppa(1967a,1968) have shown that a sodium Thisequation gives AG' with an estimatederror of t molybdatemelt of thecomposition 3NarO-4MoO, is 300cal in the range700-1200 K, sincethe difference a suitable solvent for the calorimetricstudy of in heat capacity between reactantsand products anatase,rutile, Tia+-containingspinels, FerOr, and shouldbe small at high temperaturesand one can ZnFerOn.A similar calorimeterand essentiallyiden- neglect any changes in cation distribution with tical conditionswere usedin the presentwork. In temperature.To our knowledge,no enthalpyor free eachsolution experiment, 50-100 mg of solutewas energy of formation data have been reported for dissolvedin l0- I 5 g of solventat 692L 2oC.Two ex- FerTiOr. Heat content and standardentropy values periments each on a-Fe2Osand TiO, (rutile) fell aretabulated by Robieand Waldbaum (1968) and by within experimentalerror of the valuesof the heatof Kelley(1960). From thesetabulations, the entropyof solution of these oxides reported previously by formation of pseudobrookitefrom hematite and Navrotsky and Kleppa (1968).Accordingly, those rutile is given in Table 2. The agreementwith our values,*2.38 kcal mol-l and -0.49 + 0.05 kcal value at 858 K is excellentbut, we believe,may be mol-'were used in the presentwork for the fortuitous. The heat capacityand heat contentdata enthalpiesof solution of rutile and hematite,respec- are to be questionedon two counts. First, the tively.rNo difficulty wasencountered in the solution calculatedentropy of formation of pseudobrookite varies rather strongly with temperature,which is somewhatsurprising. If this is a real effect,it may be I Throughoutthis paper,heat effects are given in calories,where relatedto the anomalouslysmall thermal expansion I cal = 4.184ioule. coefficientsreported for pseudobrookite-typecom- FORMATION OF PSEUDOBROOKITES AND FeTizOu-TisOuSOLID SOLUTIONS 251 pounds(Bayer, l97l), or to changesin thecation dis- Trsts 2. Lattice Entropies(Calorimetric Entropies) of FezTiO,and MgTirOufrom the Oxides tribution (seebelow). The datafor MgTirOu(Table 2) Formationof no anomaly,though the valuesof AS" show such -'-2 otgo" Ferore FerTlora MeTtrOrb scattersomewhat. In addition, the tabulatedvalues c ^o -o -o TK -T -T -T -Tco -"7 si os; do not include any contribution for the con- o figurationalentropy arising from an "inverse"or par- tially disorderedcation distributionof Fe3+and Tia+ 298 r2.o4 6.44 20.89 37.40 +4.47 30.40 -0,12 800 27.85 15.98 5r.64 81.75 +2.26 7L.65 -1.03 over nonequivalent octahedral sites. Waldbaum 1200 34.98 27.93 56.59 LO2,45 +0.78 91.33 -0.56 1600 40.24 25.53 76.52 117.60 +0.84 105.71 -O.70 (1973)has discussed this point. If the cationdistribu- tion in FerTiO,is indeedinverse as Lind and Housley a, source of date, R, A. Roble and D. R. Waldbes, U's. Geol. suney Bull. 1259 (1968); (1972) suggest,then, as Waldbaum (1973) rec- Soc. 71' 4569 b. Data f or ugTt ro< f r@ s. s. Todd, J. Aner. Ch6. ommends,one should add 2Rln2 : 2.76 cal K-r (1952) and x..-ll orr and J. P. CouthllE, J. Amer' Ch@. soc. 21' 3186 G952), mol-' to the standardentropy of pseudobrookite. cal K-I
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