Solid Solubility and Polymorphism in the System Sr2SiO4-Sr2GeO4-Ba2GeO4-Ba2SiO4

The reciprocal salt pair Sr₂SiO₄-Sr₂GeO₄-Ba₂GeO₄-Ba₂SiO₄ was investigated using X-ray powder diffraction and DTA. Unlimited solubility in the low-K₂SO₄ structure type (α') occurs throughout the system above 85°C. The nonlinear changes of some lattice constants of the solid solutions are discussed. A stable monoclinic low-temperature (β) form of Sr₂SiO₄ was found which converts reversibly to the high-temperature α'-modification at 85°C. The enthalpy of the β-α' transition is 51 cal/mol. In the reciprocal salt pair the β-form solid solutions occur in a very narrow region below 85°C.     

Phases in the System Ba2SiO4-Ca2SiO4

The system Ba₂SiO₄-Ca₂SiO₄ was studied by heating mixtures of Ba₂SiO₄ and Ca₂SiO₄ at 1723 K. Six distinct phases resulted; they were examined by both X-ray diffraction and differential thermal analysis. The phases β -(Ba_0.05Ca_1.95)SiO₄ and α-(Ba_0.15Ca_1.85)SiO₄ are isostructural with corresponding high-temperature modifications of Ca₂SiO₄. The X phase (Ba_0.48Ca_1.52SiO₄) is orthorhombic, is a pure phase rather than a solid solution, and is defined for the first time in the present work. The T phase (Ba_1.31Ca_0.69SiO₄) is hexagonal and interpreted in terms of a unit cell with a doubled c parameter, in contrast with literature data.     

Ionic Conductivity of Li4SiO4, Li4GeO4, and Their Solid Solutions

Conductivity was measured for Li₄SiO₄ and its solid solutions with Li₄GeO₄ over a wide frequency range to separate clearly the effects of electrode polarization, conductance relaxations, etc., and to obtain true "dc" conductivities. The conductivities of all the electrolytes are markedly temperature-dependent, ranging from 10⁻⁸ to 10⁻¹⁰Ω⁻¹ cm⁻¹ at 100°C to 10⁻² to 10¹⁰Ω⁻¹ cm⁻¹ at 700°C. For solid solutions with the Li₄GeO₄ structure, conductivities fit the Arrhenius equation over a wide temperature range, but at higher temperatures a change in activation energy occurs, corresponding to a first-order phase transition. In contrast, solid solutions with the Li₄SiO₄ structure show changes in activation energy which do not correspond to phase transitions, but which appear to indicate changes in the conduction mechanism.     

Thermoelastic Behavior in Ca2SiO4 Solid Solutions

Dicalcium silicate solid solutions (C₂S(ss)) doped with Na₂O, A1₂O₃, and Fe₂O₃ were examined by high-temperature optical microscopy. Surface deformation caused by a possible martensitic transformation between a'_L and β phases was observed in situ under the microscope during temperature changes, indicating that the transformation was thermoelastic. Both the start and finish temperatures of the a'_L-to-β and β-to-a'_L transformations decreased with increased Na:(Na + Ca) ratio. Because of the athermal nature of the a'_L-to-β transformation, the a'_L phase, when cooled below the finish temperature, should have been completely converted to the β phase.     

Activity–Composition Relations in MnCr2O4–CoCr2O4 Solid Solutions and Stabilities of MnCr2O4 and CoCr2O4 at 1300°C

Phase equilibria in the system MnO–CoO–Cr₂O₃ were investigated at 1300°C under controlled oxygen partial pressures by using the gas equilibration technique. The CoO activities in various phase assemblages of the system were measured by determining the partial pressures of oxygen in the gas phase for coexistence with metallic cobalt. The activity data revealed that at 1300°C, MnO–CoO and MnCr₂O₄–CoCr₂O₄ solid solutions exhibit mild positive departures from ideal behavior. The activities in the stoichiometric spinel solutions were found to be in good agreement with those predicted from a model based on cation distribution equilibria. The standard free energy of formation of the compound CoCr₂O₄ from its oxide components at 1300°C was determined as −37 636 J/mol, while that for MnCr₂O₄ was found as −44 316 J/mol.     

Thermodynamic Properties of Fe3O4-FeV2O4 and Fe3O4-FeCr2O4 Spinel Solid Solutions

Solid solutions of Fe304-FeV204 and Fe304-FeCr204 were prepared and equilibrated with Pt under controlled streams of CO/CO, gas mixtures at 1673 K. The concentration of Fe in Pt was used to determine the activity of Fe304 in the solid solutions. The activity of the second component was calculated by Gibbshhem integration. From these data, the Gibbs energy of mixing was derived for both systems. The experimental results and theoretical values which are determined from calculated cation distribution compare favorably in the case of vanadite solid solutions but not in the case of chromite solid solutions. The difference is attributed to a heat term arising from lattice distortion due to cation size difference. The positive heat of mixing will give rise to a miscibility gap in the system Fe304-FeCr204 at lower temperatures.     

Structure Change of Ca2SiO4 Solid Solutions with Ba Concentration

A series of Ba-bearing Ca₂SiO₄ solid solutions (C₂S( ss )), (Ba _x Ca_{1− x} )₂SiO₄ with 0.075 x 0.30, were prepared and examined by X-ray and electron beam diffraction. They are all made up of orthorhombic domains 120° different in orientation around the common c axis of the former α phase. The C₂S solid solution with x = 0.075 shows a superstructure incommensurate along the a axis with λ (modulation wavelength) = 3.5 and commensurate along the c axis with Δ= 3. With x = 0.15, modulation is observed only along the a axis and Δ= 3.4. No evidence of superstructure is found with x = 0.24; the space group and cell dimensions are comparable with those of pure α '_H-C₂S. The C₂S( ss ) with x = 0.30 gives a superlattice with the cell-edge length of 3 b . All the C₂S( ss ), when reheated at 1000°C for 24 h, produced lamellae of the trigonal phase T nearly in parallel with (001) of the host α '_L phase. The crystallographic orientation between the two phases is

This indicates that the above Ba-bearing C₂S( ss ) phases occur as precursors to the thermodynamically more stable two-phase mixtures.     

Phase Stability Study on the Remelting Reaction in Ca2SiO4 Solid Solutions

A pseudobinary phase equilibrium diagram has been established for the P₂O₅-bearing Ca₂SiO₄-CaFe₄O₇ system to confirm the occurrence of remelting reaction in α-Ca₂SiO₄ solid solutions (C₂S(ss)). The reaction started at 1290°C immediately after the α-to-α'_H transition and finished at 1145°C. The reaction products were made up of about 1 wt% of liquid and 99 wt% of solid α'_H-C₂S(ss). The liquid exsolved at 1290°C was rich in Fe₂O₃, consisting of about 30 wt% of Ca₂SiO₄ and 70 wt% of CaFe₄O₇. The liquid coexisting with α-C₂S(ss) precipitated new α'-phase crystals in association with the remelting reaction.     

Dissociation Pressures of Solid Solutions from Fe3O4 to 0.4Fe3O4·0.6CoFe2O4

The dissociation pressures of solid solutions from Fe₃O₄ to 0.4Fe₃O₄·0.6CoFe₂O₄ have been determined as a function of temperature. Within experimental error, solid solutions within this range are thermodynamically ideal.     

Phase Equilibria in the Systems UF4-ThF4 and Li F-UF4-ThF4

As part of a study of materials potentially useful as fluid fuels for high-temperature reactors, equilibrium diagrams for the condensed systems UF₄–ThF₄ and LiF-UF₄–ThF₄ have been determined. Both thermal analysis and quenching techniques were used with phase identification accomplished by microscopic and X-ray dsraction analyses. A complete series of solid solutions without maximum or minimum is formed by UF₄ and ThF₄. Within the system LiF-UF₄–ThF, there occur three invariant points and seven primary phases of which four are ternary solid solutions. Optical properties for all the solid solutions, fractionation paths for the ternary solid solutions, and compatibility triangles for the ternary invariant points have been determined.     

Activity–Composition Relations in NiAl2O4─MnAl2O4 Solid Solutions and Stabilities of NiAl2O4 and MnAl2O4 at 1300° and 1400°C

Activities of NiO were measured in the oxide and spinel solutions of the system MnO–NiO–Al₂O₃ at 1300° and 1400° C with the aim of deriving information on the thermodynamic properties of the spinel phases. Synthetic samples in selected phase assemblages of the system were equilibrated with metallic nickel and a gas phase of known oxygen partial pressures at a total pressure of 1 atm. The data on NiO activities and directions of conjugation lines between coexisting oxide and spinel phases were used to establish the activity–composition relations in spinel solid solutions at 1300° and 1400°C. The MnAl₂O₄–NiAl₂O₄ solid solutions exhibit considerable negative deviations from ideality at these temperatures. The free energy of formation of MnAl₂O₄ from its oxide components (MnO + Al₂O₃) at 1300° and 1400°C is calculated to be −24.97 and −26.56 kJ. mol⁻¹, respectively. The activities determined in the stoichiometric spinel solid solutions are more negative as compared with those predicted from cation distribution models.     

Activity–Composition Relations in FeCr2O4–FeAl2O4 and MnCr2O4–MnAl2O4 Solid Solutions at 1500° and 1600°C

Activity–composition relations of FeCr₂O₄–FeAl₂O₄ and MnCr₂O₄–MnAl₂O₄ solid solutions were derived from activity–composition relations of Cr₂O₃–Al₂O₃ solid solutions and directions of conjugation lines between coexisting spinel and sesquioxide phases in the systems FeO–Cr₂O₃–Al₂O₃ and MnO–Cr₂O₃–Al₂O₃. Moderate positive deviations from ideality were observed.     

Further Consideration of Phases in the System Ba2SiO4–Ca2SiO4

The results of an investigation of the system Ba₂SiO₄–Ca₂SiO₄ by powder X-ray and electron diffraction suggest a greater complexity than supposed hitherto. The previously recognized phases α, α' h α' l , X, T, and the newly reported Y have room-temperature structures that are modulated distortions of hexagonal (or pseudohexagonal) parent structures. Each displays characteristic and distinctive modulations. The phases are more readily distinguished in this way than by their unit-cell dimensions and compositions which, for a given phase, can vary with bulk starting composition and thermal history.     

Thermochemistry of MgAl2O4-Al8/3O4 Defect Spinels

Solution calorimetry of MgAl₂O₄-Al_8/3O₄ solid solutions was performed in a molten 2PbO · B₂O₃ solvent at 975 K. The results indicate small negative heats of mixing, relative to spinel standard states for both end-members. These data were combined with information on the energetics of the α-γ transition in Al₂O₃ and on the MgAl₂O₄-Al_8/3O₄ (MgO-Al₂O₃) subsolidus phase relations to estimate the partial molar entropy of mixing of γ-Al_8/3O₄ in the solid solution. This entropy is much less positive than that calculated from several models for the configurational entropy of mixing of magnesium, aluminum, and vacancies on octahedral and/or tetrahedral sites. The data suggest a good deal of local order to be present in the solid solutions, consistent with negative enthalpies of mixing and entropies of mixing far less than ideal configurational values.     

The Join Ca2SiO4-CaMgSiO4

New data obtained on the join Ca₂SiO₄-CaMgSiO₄ established a limit of crystalline solubility of Mg in α-Ca₂SiO₄ corresponding to the composition Ca_1.90Mg_0.10SiO₄ at 1575°C. The α-α'Ca₂SiO₄ inversion temperature is lowered from 1447° to 1400°C by Mg substitution in the lattice. α'-Ca₂SiO₄ takes Mg into its lattice up to the composition Ca_1.94Mg_0.06SiO₄ at 1400°C and to Ca_1.96Mg_0.04SiO₄ at 900°C. A new phase (T) reported previously by Gutt, with the approximate composition Ca_1.70Mg_0.30SiO₄, was stable between 979° and 1381°C, and should be stable at liquidus temperatures in multicomponent systems involving CaO–MgO–SiO₂.     

Optical Spectra of Synthetic Spinels in the System MgAl2O4–MgCr2O4

Unpolarized optical spectra were measured in the wavelength range 322–1666 nm by the diffuse reflection technique from spinel powders synthesized in the system MgAl₂O₄–MgCr₂O₄. The spectra were interpreted by the crystal-field theory on the basis of trigonally distorted spinel octahedra with D_3d symmetry. For chromium-rich solid solutions, including the MgCr₂O₄ end-member, results after peak fittings showed octahedral D_3d local symmetry around Cr³⁺ ions, identical to the crystallographic site symmetry. For chromium-poor solid solutions, however, octahedral C_3v local symmetry was suggested around Cr³⁺ ions, different from the D_3d crystallographically expected.     

Effect of Nd2O3 Concentration on the Defect Structure of CeO2–Nd2O3 Solid Solution

An extensive X-ray study of CeO₂–Nd₂O₃ solid solutions was performed, and the densities of solid solutions containing various concentrations of NdO_1.5 were measured using several techniques. Solid solutions containing 0–80 mol% NdO_1.5 were synthesized by coprecipitation from Ce(NO₃)₃ and Nd(NO₃)₃ aqueous solutions, and the coprecipitated samples were sintered at 1400°C. A fluorite structure was observed for CeO₂–NdO_1.5 solid solutions with 0–40 mol% NdO_1.5, which changed to a rare earth C-type structure at 45–75 mol% NdO_1.5. The change in the lattice parameters of CeO₂–NdO_1.5 solid solutions, when plotted with respect to the NdO_1.5 concentration, showed that the lattice parameters followed Vegard's law in both the fluorite and rare earth C-type regions. The maximum solubility limit for NdO_1.5 in CeO₂ solid solution was approximately 75 mol%. The relationship between the density and the Nd concentration indicated that the defect structure followed the anion vacancy model over the entire range (0–70 mol% NdO_1.5) of solid solution.     

The System MgO–MgAl2O4

In the determination of the liquidus, solidus, and subsolidus of the system MgO-MgAl₂O₄ the limits of the solid solution of A1 ions in periclase and Mg ions in spinel were measured. By using both X-ray diffraction and optical techniques, the maximum periclase solid solution was found at 82 wt% MgO, 18 wt% A12O3 (9.5% A1³⁺) and maximum spinel solid solution at 39% MgO, 61 % A1203 (6% Mg⁺⁺). Periclase and spinel solid solutions existed stably in easily detectable amounts at temperatures above approximately 1500°C.     

Thermal Expansion of Homogeneous and Gradient Solid Solutions in the System KZr2(PO4)3─KTi2(PO4)3

Low-thermal-expansion ceramics having arbitrary thermal expansion coefficients were synthesized from homogeneous solid solutions in the system KZr₂(PO₄)₃─KTi₂(PO₄)₃ (KZP–KTP). Dense and strong ceramics were fabricated by sintering at 1100° to 1200°C with 2 wt% MgO. The thermal expansion coefficient increased from 0 to +3 × 10⁻⁶/°C with increasing x in KZr_{2 − x}Ti_x (PO₄)₃ (KZTP). In addition, a functionally gradient material with respect to thermal expansion was prepared by forming a series of KZTP solid solutions in a single ceramic body. By heating a pile of KZP and KTP ceramics in contact with each other, KZP and KTP bonded together to form a KZTP gradient solid solution near the interface.