Polymorphism of Calcium Orthosilicate

Therecentobservation of orthorhombic α'-Ca₂Si0₄ (bredigite) at all temperatures between about 850° and 1450°C. leads to a rational interpretation of the polymorphism of this substance, which is very satisfactory from the crystal-chemical point of view. The so-called β phase, of as yet unknown, complex structure, exists only meta-stably, and not above but below about 675°C, where γ is the stable phase. The monotropic β phase forms on cooling from α'near 675°C. as the result of the inhibition of the α'→γ inversion, at 850°C. The inhibition is caused by the need for a considerable atomic rearrangement and a 12% volume increase which accompanies the change of the coordinations CaO₂ and CaOlo, in α', to CaO₆, in γ. Among the solid phase equilibria with, Mg₂SiO₄ and Ca₃(PO₄)₂, unlimited solid solubility between γ-Ca₂SiO₄ and Mg₂SiO₄ is predicted, whereas the solubility of Mg₂SiO₄ is a limited one in α'and still more so in a-Ca₂SiO₄, as a result of the substitution, for calcium, of the smaller magnesium.     

The System Zirconia-Scandia

The system zirconia-scandia was investigated using X-ray diffraction analysis, differential thermal analysis, metallographic analysis, and melting point studies. Results reveal the monoclinic α₁ phase (0 to 2 mol% Sc₂O₃), the tetragonal α₂'phase (5 to 8% Sc₂O₃), the rhombohedral β phase (9 to 13% Sc₂O₃), the rhombohedral γ phase (15 to 23% Sc₂O₃), the rhombohedral δ phase (24 to 40% Sc₂O₃), and the cubic % phase (77.5 to 100% Sc₂O₃). The monoclinic α₁ phase and the tetragonal α₂'phase were found to transform to the tetragonal α₂ phase over a wide temperature range depending on composition. The β, γ, and α phases transformed to a cubic phase at temperatures of %600^%, 1100^%, and 1300^%C, respectively. A maximum melting point of %2870^%C was found at %10% Sc₂O₃ and a eutectic at %2400^%C at 55% Sc₂O₃.     

Preferential X-ray line Broadening and Thermal Behavior of γ-Fe2O3

Preferential X-ray line broadenings in γ-Fe₂o₃ samples prepared from γ-FeOOH, α-FeOOH, N₂H₅Fe(N₂H₃-COO)₃-H₂O, FeOOCH₃, and colloidal Fe₃O₄ are compared. Isotropic size and small crystallites are the origin of the uniform and enhanced X-ray line broadening in samples derived from hydrazinate and colloidal Fe₃O₄. Nonuniform line broadening in ex-α-FeOOH and ex-γ-FeOOH is due to an elongated crystallite shape and the presence of stacking faults, respectively. The thermal behavior of samples with low crystallite size and uniform line broadening is characterized by an exothermal recrystallization process simultaneous to the phase transformation γ-Fe₂0₃→α-Fe₂O₃.     

Three Crystalline Polymorphs of KFeSiO4, Potassium Ferrisilicate

Orthorhombic α-KFeSiO₄ ( a =0.5478, b =0.9192, c =0.8580 nm), hexagonal β-KFeSiO₄ ( a =0.5309, c =0.8873 nm), and hexagonal γ-KFeSiO₄ ( a =0.5319, c =0.8815 nm) were synthesized by devitrification of KFeSiO₄ glass. Powder X-ray diffraction data are given for all three polymorphs. Alpha KFeSiO₄, the high-temperature polymorph, melts congruently at 1197°± 2°C. Mössbauer spectroscopy of the α phase indicates that Fe³⁺ occupies two tetrahedral sites in the lattice. Beta KFeSiO₄, the low-temperature polymorph, and γ-KFeSiO₄, a metastable polymorph, appear to be isomorphous with kalsilite, KAISiO₄, and synthetic kaliophilite, KAISiO₄, respectively, and it is proposed that β- and γ -KFeSiO₄ are linked by Si-Fe order-disorder. Beta KFeSiO₄ transforms slowly into α -KFeSi0₄ above 910°C but the transformation was not shown to be reversible in the present dry-heating experiments.     

Calorimetric Study of Nickel Molybdate: Heat Capacity, Enthalpy, and Gibbs Energy of Formation

The thermodynamic properties of the α and β polymorphs of NiMoO₄ were directly investigated by calorimetry. The standard entropies of formation, Δ_f S ° _T , of α and β were determined from measuring the molar heat capacity, C _p,m, from near absolute zero (2 K) to high temperature (1380 K) by a relaxation method and differential scanning calorimetry. The standard enthalpies of formation, Δ_f H ° _T , of α and β were determined by combining C _p,m with the standard enthalpy of formation, Δ_f H °₂₉₈, at 298 K obtained from drop solution calorimetry in molten sodium molybdate at 973 K. The standard Gibbs energies of formation, Δ_f G ° _T , of α and β were determined from their Δ _f S ° _T and Δ _f H ° _T values. The Δ _f G ° _T values indicate that the polymorphic transformation from α to β occurs at 1000 K, consistent with the observed phase transformation at 1000 K.     

Fracture Toughness and Spalling Behavior of High-Al2O3 Refractories

The fracture energies and spalling resistance of high-Al₂O₃ refractories were studied. The fracture energies, γ _WOF and γ _NBT , were measured by the work-of-fracture and the notched-beam-test methods, respectively. Spalling resistance, as measured by the relative strength retained in a water quench, correlated well with the thermal-stress resistance parameter applicable to stable crack propagation under conditions of thermal shock, (γ _WOF /α² E ₀). Many of the refractories exhibited high ratios of γ_WOF to γ_NBT; such high ratios were shown analytically to maximize the parameter ( R ¹¹¹¹= E _0γWOF/S₁²) which describes the resistance to catastrophic spalling. The increase of crack length with increasing quenching temperature difference (Δ T ) was somewhat less than that predicted theoretically; the discrepancy was attributed to an increase of crack density with Δ T . In general, the results show that fracture energy is important in establishing the spalling resistance of high-Al₂O₃ refractories.     

High-Temperature, High-Pressure X-ray Investigation of Dicalcium Silicate

Energy-dispersive X-ray powder diffraction experiments have been investigated at high temperature and room pressure, and at high pressure and room temperature, starting from either γ- or β-Ca₂SiO₄. High-temperature studies were performed up to 1980 K, using a versatile heating cell. The high-temperature phase transformations previously described were reexamined. Volume and linear thermal expansions were measured for each Ca₂SiO₄ polymorph, γ, β, α';_L,α';_H, and α. Volume thermal expansion increases with increasing temperature except for α';_H, whose thermal expansion tends to decrease at elevated temperature. High-pressure investigations were performed in the 0–15 GPa pressure range, using a diamond anvil cell, with silicon oil as the pressure-transmitting medium. The value of the room-pressure bulk modulus K₀ , assuming a second-order BirchMurnaghan equation of state with K'₀= 4, is 140(8) GPa for γ-Ca₂SiO₄. The γ olivine form exhibits anisotropic compression, with the c axis as the most compressible. From such in situ high-pressure X-ray investigations, the γ-→Ca₂SiO₄ phase transformation induced by cold compression is clearly evidenced and extends from 2 to about 5 GPa.     

Studies in the System CaO-Al2O3-SiO2H2O: III, New Data on the Polymorphism of Ca2SiO2 and Its Stability in the System CaO-SiO2- H2O

The nature of the low-temperature inversions γ-α' and α'-β was investigated by various techniques: hydrothermal and "dry" quenching runs, differential thermal analysis at atmospheric and elevated nitrogen pressures, X-ray diffractometer patterns obtained at elevated temperatures, "static" pressure techniques, and infrared absorption spectrometry. A revised energy-temperature diagram is presented for Ca₂SiO₄, with the transition γ' to α' taking place at about 725°C. and the α'-β transition, although not reversible at an exact temperature, taking place at about 670° C. At low water pressures (2000 lb. per sq. in.) the inversion γ-α' was placed at 675°C. Attempts to extrapolate the value obtained at 2000 lb. per sq. in. to obtain a more accurate reversible inversion temperature at atmospheric pressure, although limited in accuracy by the reliability of heat-of-transition data, would indicate a temperature of about 725° C. at atmospheric pressure. Three new compounds, 8CaO.3SiO₂ -3H₂O (X), 6CaO 3SiO₂.H₂O (Y), and 9CaO-6SiO₂ H₂O (Z), were found to be stable above 700°C. at H₂O pressures greater than 7500 lb. per sq. in.     

Structure Change in Strontium Oxide-Doped Dicalcium Silicates

A series of strontium-bearing dicalcium silicate (Ca₂Si0₄ solid solutions (C₂S( ss )), (Sr_χCa_1-χ)₂SiO₄ with 0.02 ≤χ≤ 0.10, was prepared and examined by powder X-ray diffrac-tometry. These crystals, heated in the stable-temperature region of the α phase and then quenched in water, were composed of the β phase, with χ≤ 0.08, and the α'_L and β phases, with χ= 0.10. With increasing x, the unit-cell axes of the β phase expanded and the β angle became small with eventual increase in the unit-cell volume. The Rietveld analysis of the β-C₂S( ss ) with χ= 0.08 showed that the Sr²⁺ ions preferentially occupied the seven-coordinated site rather than the eight-coordinated site. This site preference, which was originally established in the parent α-phase structure, seemed to cause the systematic change in the cell dimensions.     

Preferred Orientation of β-Lead Fluoride Grains Formed within Micropores of Porous Alumina

A PbF₂–Al₂O₃ composite was obtained by reaction between Pb(NO₃)₂ and NH₄F solutions within micropores of a porous alumina pellet. The reaction resulted in the formation of a PbF₂ deposit layer in the interior region of the pellet close to the surface at the Pb(NO₃)₂ solution side, toward which the deposit grew preferentially with time. It suggested that the diffusion of Fusions in the deposit would play an important role in this method because β-PbF₂ is known as a moderate F^- ion conductor at room temperature. The deposit was identified to be †-PbF₂ with the fluorite structure, using both XRD and EPMA, although a small amount of α-PbF₂ with the rutile structure also existed. The β-PbF₂ grains in the initially formed deposit showed essentially no preferred orientation, while the subsequently formed part showed significant preferred orientation with the [ hh O] direction parallel to the growing direction. The degree of preferred orientation increased with distance from the initially formed position and reached a saturated value. The orientation was presumed to be associated with the faster growth rate of the deposited grains along the [ hh O] direction than the others.     

Phase Transformation Kinetics in the System Bismuth Oxide-Zirconia

The effect of ZrO₂ addition on the phase transformation of Bi₂O₃ was studied with powder X-ray diffraction and differential thermal analysis. Samples containing higher than a few mole percent ZrO₂ were obtained as the metastable β phase (tetragonal) at room temperature when they were cooled at 20°C/min from 800°C where the δ phase (fcc) is stable. When the same samples were cooled at the same rate from 1000°C, which is above the solidus, they formed the stable α phase (monoclinic) at room temperature. Evidence for the relatively higher solubility of ZrO₂ in the α phase is discussed to explain this observation.     

Anisotropic Thermal Expansion of β-Ca2SiO4 Monoclinic Crystal

Crystals of β-Ca₂SiO₄ (space group P 12₁/ n 1) were examined by high-temperature powder X-ray diffractometry to determine the change in unit-cell dimensions with temperature up to 645°C. The temperature dependence of the principal expansion coefficients (α_i) found from the matrix algebra analysis was as follows: α₁= 20.492 × 10⁻⁶+ 16.490 × 10⁻⁹ ( T - 25)°C⁻¹, α₂= 7.494 × 10⁻⁶+ 5.168 × 10⁻⁹( T - 25)°C⁻¹, α₃=−0.842 × 10⁻⁶− 1.497 × 10⁻⁹( T - 25)°C⁻¹. The expansion coefficient α₁, nearly along [302] was approximately 3 times α₂ along the b -axis. Very small contraction (α₃) occurred nearly along [     01]. The volume changes upon martensitic transformations of β↔α_L' were very small, and the strain accommodation would be almost complete. This is consistent with the thermoelasticity.     

New Approach to the β→α Polymorphic Transformation in Magnesium-Substituted Tricalcium Phosphate and its Practical Implications

The transformation β→α in Mg-substituted Ca₃(PO₄)₂ was studied. The results obtained showed that, contrary to common belief, there is, in the system Mg₃(PO₄)₂–Ca₃(PO₄)₂, a binary phase field where β+α-Ca₃(PO₄)₂ solid solutions coexist. This binary field lies between the single-phase fields of β- and α-Ca₃(PO₄)₂ solid solution in the Ca₃(PO₄)₂-rich zone of the mentioned system. In the light of the results and the Palatnik–Landau's Contact Rule of Phase Regions, a corrected phase equilibrium diagram has been proposed. The practical implications of these findings with regard to the synthesis of pure α- and β- Mg-substituted Ca₃(PO₄)₂ powders and to the sintering of related bioceramics with improved mechanical properties are pointed out.     

Preparation of Larnthanum β-Alumina with High Surface Area by Coprecipitation

Mixtures of La₂O₃ and Al₂O₃ with various La contents were prepared by co-precipitation from La(NO₃)₃ and Al(NO₃)₃ solutions and calcined at 800° to 1400°C. The addition of small amounts of La₂O₃ (2 to 10 mol%) to Al₂O₃ gives rise to the formation of lanthanum β-alumina (La 2 O₃·11–14Al₂O₃) upon heating to above 1000°C and retards the transformation of γ-Al₂O₃ to α-Al₂O₃ and associated sintering.     

α-Dicalcium Silicate Hydrate: Preparation, Decomposed Phase, and Its Hydration

α-C₂SH can be synthesized by hydrothermal treatment of lime and silicic acid for 2 h at 200°C. When heated to 390–490°C, α-C₂SH dissociates through a two-step process to form an intermediate phase plus some γ-C₂S. This appears to be a new dicalcium silicate different from known dicalcium silicates—α, α'_L, α'_H, β, and γ phase—and is stable until around 900°C. At 920–960°C, all the phases are transformed to the α'_L phase. The intermediate phase has high crystallinity and is stable at room temperature. ²⁹ Si MAS NMR measurements indicate the possibility that it contains both protonated and unprotonated monosilicate anions. The intermediate phase that has passed through the α'phase at higher temperature yields β-C₂S on cooling. The intermediate phase is highly active, and completed its hydration in 1 day ( w/s = 1.0, 25°C). Among the crystalline calcium silicate hydrates with Ca/Si = 2.0, it is hillebrandite that yields β-C₂S at the lowest temperature.     

Phase Diagram of the System BaO-Fe2O3

The phase diagram of the system BaO-Fe₂0₃ was determined by X-ray diffraction, melting-point measurement, and microscopic methods. Since the reduction of Fe³⁺ to Fe²⁺ was observed by chemical analysis in the samples heated at high temperature, especially in molten samples, the samples were heated at 1 atmosphere pressure of oxygen in the temperature region in which the liquid was in equilibrium; 1 atmosphere pressure of oxygen was su5cient to restrain the reduction of Fe³⁺. In the temperature region of solid-solid equilibrium, the dissociation was not observed even when the samples were heated in air. BaO - 6Fe₂O₃ formed a solid solution with BaO.Fe₂0₃. The BaO:Fe₂0₃ ratio of the solid solution was BaO.4.5Fe₂0₃ at 1350°C. and BaO. 5.0Fe₂0_a at 800°C. The precipitation micro-structures of each primary solid solution were observed.     

Determination of Precise Unit-Cell Parameters of the α-Tricalcium Phosphate Ca3(PO4)2 Through High-Resolution Synchrotron Powder Diffraction

Unit-cell parameters of the α-tricalcium phosphate [TCP; Ca₃(PO₄)₂] were investigated using high-resolution synchrotron powder diffraction and the Rietveld method. The diffraction experiment was conducted at 29°C at the BL-15XU experimental station of SPring-8, Japan. Precise unit-cell parameters of the α-TCP were obtained; a =12.87271 (9), b =27.28034(8), c =15.21275(12) Å, α=γ=90°, and β=126.2078(4)°. The calculated density of α-TCP (2.8677 g/cm³) is smaller than that of β-TCP, indicating the "looser" structure of α-TCP.     

Zinc Vanadates in Vanadium Oxide-Doped Zinc Oxide Varistors

Convergent-beam electron diffraction has been used to determine the space groups of β- and γ-Zn₃(VO₄)₂ particles in vanadium oxide-doped zinc oxide varistors. The crystal structure of β-Zn₃(VO₄)₂ has been determined to be monoclinic with space group P 2₁ and lattice parameters of a = 9.80 Å, b = 8.34 Å, c = 10.27 Å, and β= 115.8°, whereas that of γ-Zn₃(VO₄)₂ is monoclinic with space group Cm and a = 10.40 Å, b = 8.59 Å, c = 9.44 Å, and β= 98.8°. Energy-dispersive X-ray microanalysis of these two phases shows significant deviations from their expected stoichiometry. It is apparent that the β-phase is, in fact, the metastable Zn₄V₂O₉ phase, whereas the γ-phase either is a new oxide that consists of zinc, vanadium, and manganese or, more likely, is a zinc vanadate phase with a Zn:V atomic ratio of 1:1 that has the ability to go into solid solution with manganese.     

Effect of Monovalent Cation Additives on the γ-Al2O3-to-α-Al2O3 Phase Transition

The effect of monovalent cation addition on the γ-Al₂O₃-to-α-Al₂O₃ phase transition was investigated by differential thermal analysis, powder X-ray diffractometry, and specific-surface-area measurements. The cations Li⁺, Na⁺, Ag⁺, K⁺, Rb⁺, and Cs⁺ were added by an impregnation method, using the appropriate nitrate solution. β-Al₂O₃ was the crystalline aluminate phase that formed by reaction between these additives and Al₂O₃ in the vicinity of the γ-to-α-Al₂O₃ transition temperature, with the exception of Li⁺. The transition temperature increased as the ionic radii of the additive increased. The change in specific surface area of these samples after heat treatment showed a trend similar to that of the phase-transition temperature. Thus, Cs⁺ was concluded to be the most effective of the present monovalent additives for enhancing the thermal stability of γ-Al₂O₃. Because the order of the phase-transition temperature coincided with that of the formation temperature of β-Al₂O₃ in these samples, suppression of ionic diffusion in γ-Al₂O₃ by the amorphous phase containing the added cations must have played an important role in retarding the transition to α-Al₂O₃. Larger cations suppressed the diffusion reaction more effectively.     

THIRD-ORDER ASYMPTOTIC PROPERTIES OF ESTIMATORS IN GAUSSIAN ARMA PROCESSES WITH UNKNOWN MEAN

Abstract. This paper deals with the third-order asymptotic theory for Gaussian autoregressive moving-average (ARMA) processes with unknown mean μ. We are interested in the estimation of ρ = ( α₁…, α_p, β₁…, β_q ), where α ₁…, α_ρ and β ₁…, β_q are the coefficients of the autoregressive part and the moving-average part, respectively. First, we investigate the third-order asymptotic optimality of the bias adjusted maximum likelihood estimator (MLE) of ρ in the presence of the nuisance parameters μ and ² (innovation variance). Next, for a Gaussian AR(1μ μ, ²), we propose a mean corrected estimator α_c1c2 of the autoregressive coefficient. We make a comparison between the bias adjusted estimator α_c1c2* and the bias adjusted MLE, in terms of their probabilities of concentration around the true value, or equivalently, in terms of their mean squared errors. Finally some numerical studies are provided in order to verify the third-order asymptotic theory.