Enthalpy of Formation of Zircon

Using high-temperature solution calorimetry in molten 2PbO. B₂O₃, the enthalpy of reaction of the formation of zircon, ZrSiO₄, from its constituent oxides has been determined: Δ_r H ₉₇₇(ZrSiO₄) =−27.9 (± 1.9) kJ/mol. With previously reported data for the heat contents of ZrO₂, SiO₂, and ZrSiO₄ and standard-state enthalpies of formation of ZrO₂ and SiO₂, we obtain Δ_f H °₂₉₈· (ZrSiO₄) =−2034.2 (±3.1) kJ/mol and Δ_f G °₂₉₈ (ZrSiO₄) =−1919.8 kJ/ mol. The free energy value is in excellent agreement with a range previously estimated from solid-state reaction equilibria. At higher temperature also the data are in close agreement with existing data, though the data sets diverge somewhat with increasing T . The limitations of the data for predicting the breakdown temperature of zircon into its constituent oxides are discussed.     

Volatility of PuO2 in Nonreducing Atmospheres

The vapor pressure of plutonium dioxide (PuO₂) was investigated in the range 1450° to 1775°C in air, argon, and oxygen atmospheres by a transpiration technique. There were strong indications that PuO₂ can vaporize congruently or as a suboxide species, depending on the atmosphere. The δH°₂₉₈ for vaporization in 1 atm of oxygen is approximately 154,000 cal per mole. The estimated standard free energy of formation (δG°_f) of gaseous PuO₂ is −121,000 + 10.7 T from 1227° to 1827°C.     

Standard Gibbs Energy of Formation of β-Silicon Nitride

Experimental thermochemical data (temperature, pressure) corresponding to the equilibrium conditions between finegrained β-SiC and β-Si₃N₄ for carbon activity a (C) = 1 are presented. Based on these data, the temperature dependence of ΔG°_f(β-Si₃N₄) has been expressed for standard states Si( s ), C( s ), and p(N₂) = 0.1 MPa by the equation ΔA°_f(β-Si₃N₄) = (-995.9 + 0.4547 T/K) kJ mol for T/K ε〈1650; 1968〉.     

Standard Enthalpy of Formation of Lanthanum Zirconate

The enthalpy of formation of lanthanum zirconate, La₂Zr₂O₇, which is shown to have a distorted pyrochlore structure, was determined. High-temperature solution calorimetry in molten lead borate was used to determine the heat of formation from the constituent oxides as −135.8 ± 6.4 kJ/mol at 974 K. Using additional data on the enthalpies of formation of the oxides and heat contents, this value was converted to a standard enthalpy of formation from the elements: Δ_fH°_298.15=−4130.4 ± 6.8 kJ/mol.     

Heat Capacity and Equilibrium Polymerization of Vitreous Se

The contribution to the heat capacity of liquid Se, _p,r, arising from the ring-polymer equilibrium was calculated from the equilibrium polymerization theory of Tobolsky and co-workers. Above the polymerization transition temperature (∼360°K), _p,r∼(1/8)(Θ H₃²/RT²)(M/M_o) , where Θ H ₃ is the enthalpy change for the polymerization propagation step and (M/M₀) is the monomer fraction of Se₈ rings. Below the transition temperature, _p,r is negligibly small. Heat capacities were measured for glassy and liquid Se from 180° to 280°K and from 320° to BOOK, respectively. Using available literature data and the equilibrium polymerization theory, the temperature dependence of the heat capacity of liquid Se was calculated; it agreed within experimental error with the measured temperature dependence.     

Assessment of the Thermodynamic Values for PuO1.5 and High-Temperature Determination of the Values for PuC1.5

Thermodynamic values for PUO_1.5 were assessed using an improved method for estimating fef ° 1.5 and new data for S°₂₉₈ 1.5. Based on the assessment, a value of ΔH°₂₉₈, 1.5=–828 kJ/mol is recommended. Measurements of (CO) pressure over the nominal equilibrium 1.5+ 1.5+ C were performed between 1348 and 1923 K, yielding pressures between 0.644 and 11600 Pa. Second- and third-law analyses were used to obtain a value for ΔH°₂₉₈ 1.5=–93.3°3.3 kJ/mol.     

Vaporization Thermodynamics and Enthalpy of Formation of Aluminum Silicon Carbide

The vaporization thermodynamics of aluminum silicon carbide was investigated using Knudsen effusion mass spectrometry. Vaporization occurred incongruently to give Al( g ), SiC( s ), and graphite as reaction products. The vapor pressure of aluminum above (Al₄SiC₄+ SiC + C) was measured using graphite effusion cells with orifice areas between 1.1 × 10⁻²and 3.9X10⁻⁴ cm². The vapor pressure of aluminum obtained between 1427 and 1784 K using an effusion cell with the smallest orifice area, 3.9X10⁻⁴ cm², is expressed as
log p (Pa) =−(18567 ± 86) ( K/T ) + (12.143 ± 0.054)
The third-law calculation of the enthalpy change for the reaction Al₄SiC₄( s ) = 4Al( g ) + SiC( hex ) + 3C( s ) using the present aluminum pressures gives Δ H °(298.15 K) = (1455 ± 79) kJ·mol⁻¹. The corresponding second-law result is Δ H °(298.15 K) = (1456 ± 47) kJ·mol⁻¹. The standard enthalpy of formation of Al₄SiC₄( s ) from the elements calculated from the present vaporization enthalpy (third-law calculation) and the enthalpies of formation of Al( g ) and hexagonal SiC is Δ H °_f= -(221 ± 85) kJ·mol⁻¹. The standard enthalpy of formation of Al₄SiC₄( s ) from its constituent carbides Al₄C₃( s ) and SiC( c, hex ) is calculated to be Δ H °(298.15 K) = (38 ± 92) KJ·mol⁻¹.     

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.     

Thermochemistry of the Aluminas and Aluminum Trihalides

Consistent standard free energies of formation of gibbsite, bayerite, boehmite, and diaspore; their respective transition aluminas, α-Al₂O₃; and AlF₃, AlCl₃, H₂O₃ HF, and HCl are compiled from 298.16 to 2100 K from literature review, computations, and estimates. Significant adjustments and additions to earlier compilations are included. Revised analysis is made of the gibbsite-to-α-A1₂O₃ transition series and of reactions of appropriate aluminas with HF and HCl, comparing them with experimental data. These updated Δ G ° tables should also yield accurate ΔG° data for many other alumina reactions, e.g. with SiO₂, M₂O, MO, etc.     

Communications of the American Ceramic Society Estimation of Thermochemical Data for Calcium Silicate Hydrate (C-S-H)

Calcium silicate hydrate (C-S-H) can be viewed as a solid solution, 0.833Ca(OH)₂.SiO₂.0.917H₂O-xCa(OH)₂, at equilibrium at 30°C. On this basis, the change in Gibbsfree energy (ΔG_r) in the solid-solution reaction was calculated from solubility duta for C-S-H in water. The change in ΔG_r with real ratio decreased notably for the higher calcium contents (CaO/Si0₂1.7; ×0.867). Thermochemical values for C-S-H (CaO/SiO₂=1.7) were estimated to be ΔH°=-2890 kJ/mol, ΔG°=-2630 kJ/mol, and S°=200 J1/mol.K at 298 K .     

Review of Thermodynamic Properties of the Cr-N System

Existing thermodynamic data for the Cr-N system were analyzed. High-temperature heat contents measured by Sato were reevaluated, and the heat capacity of Cr₂N was determined to be 15.05+6.58×10⁻³ T (°K) and that of CrN 11.10+ 1.58×10³ T . Using these heat capacities and an estimated ΔS°_{298, f} of 20×1 cal/°K-g atom N for the formation of the nitrides, second- and third-law calculations for all available vapor-pressure data were made. The two calculations agreed very well for the data of Mills. The heats of formation of Cr₂N and CrN are -31.8×1.0 and -28.4×1.5 kcal/mol, respectively. A partial phase diagram of the Cr-N system is presented.     

Interpretation of the Parabolic and Nonparabolic Oxidation Behavior of Silicon Oxynitride

The oxidation process of Si₂N₂O, prepared by a hot isostatic pressing technique, has been studied by the thermogravimetric method. The oxidation has been performed in oxygen for 20 h in the temperature range 1300° to 1600°C, producing oxide scales of amorphous SiO₂ and α-cristobalite. The weight gain for T 1350°C does not begin to follow a parabolic rate law, until a certain time, t ₀. The A ₀ parameter in the parabolic rate law, (Δ w / A ₀)²= K _p t + B , represents the cross section area, A , through which the oxygen diffuses; in the derivation of this law A is assumed to be constant during the experiment. If crystallization occurs during the oxidation process, A will decrease with time. A function, A ( t ), describing the time dependence, has been developed and incorporated into the parabolic rate law, yielding a new rate law, which reads Δ W/A ₀= a arctan √ bt + c √ t . This new rate law is valid in the time interval t < t ₀, whereas, for t > t ₀, the oxidation process follows the equation (Δ w/A ₀)²= K °_p t + B ₀. The relation of the latter equation to the common parabolic rate law is described. All of the oxidation curves are described by these equations. The activation energy of the oxygen diffusion (and of the oxidation ( K _p)) is found to be 245 ± 25 kJ/mol, which is consistent with literature values reported for oxygen diffusion.     

Thermodynamic Properties of the System Indium-Oxygen

The free-energy change for the reaction 2In( l )+3NiO( s ) = In₂O₃( s )+3Ni( s ) was determined from 550° to 800°C from emf measurements on solid-oxide galvanic cells. The results were used to develop an equation for the standard molar free energy of formation of In₂O₃, i.e. ΔG°_ln2O₃= -215,550+72.63 T ±450 cal/ mol. The standard molar enthalpy and entropy of formation of In₂O₃ at 298°K were calculated to be -214,000±1500 cal/mol and -69.03±o0.22 eu, respectively, using the available thermo-chemical data. The absolute entropy of In₂O₃ at 298°K was calculated to be 32.23±0.22 eu. The free-energy results of this study were used in conjunction with literature data to calculate partial pressures of the gaseous species over In₂O₃ for different experimental conditions.     

Knudsen Cell Studies of the Vaporization of Gadolinium and Gadolinium Dicarbide

Vapor pressure of gadolinium metal and carbon-rich gadolinium dicarbide was measured by the Knudsen effusion technique using an automatic recording balance. Knudsen pressures calculated on the basis that Gd( g ) is the major gaseous species did not vary significantly as a function of orifice diameter or sample surface area. Corrections were made for a minor gaseous species, GdC₂( g ). The entropy and heat content of GdC₂ were estimated. For the reaction Gd( l ) = Gd( g ) the third-law Δ H °₂₉₈ of 95.2 ± 0.3 kcal/g-atom was in agreement with the second-law value of 97.3 ± 0.8 kcal/g-atom. Third- and second-law Δ H °₂₉₈ were combined to give a value of 125 ± 9 kcal/mole for the reaction GdC₂( s ) = Gd( g ) + 2C( s ). From these values the enthalpy of formation of carbon-rich GdC₂ was calculated to be — 30 ± 9 kcal/mole. Studies of rare earth dicarbide vaporization behavior are briefly reviewed and discussed, and their possible application to a self-purifying, high-temperature nuclear reactor is considered.     

Thermal Expansion of the Hexagonal (6H) Polytype of Silicon Carbide

The thermal expansion of the hexagonal (6H) polytype of α-SiC was measured from 20° to 1000°C by the X-ray diffraction technique. The principal axial coefficients of thermal expansion were determined and can be expressed for that temperature range by second-order polynomials: α¹¹= 3.27 × 10^–6+ 3.25 × 10^–9T – 1.36 × 10^–12 T ² (1/°C), and ş₃₃= 3.18 × 10^–6+ 2.48 × 10^–9 T – 8.51 × 10^–13 T ² (1/°C). The σ₁₁ is larger than α₃₃ over the entire temperature range while the thermal expansion anisotropy, the δş value, increases continuously with increasing temperature from about 0.1 × 10^–6/°C at room temperature to 0.4 × 10^–6/°C at 1000°C. The thermal expansion and thermal expansion anisotropy are compared with previously published results for the (6H) polytype and are discussed relative to the structure.     

Surface Relief Induced by Martensitic Transformation in Phosphorus-Bearing Dicalcium Silicate

Crystals of (Ca_1.955□_0.045)(Si_0.91P_0.09)O₄, where □ denotes a vacancy, have been prepared and examined by XRD, optical microscopy, SEM, and AFM. At 20°C, the crystals are composed of 38%α' _L and 62%β phases. Upon cooling to −185°C, the α' _L - to β-phase transformation occurs, which increases the β-phase composition to 72%. The transformation is also accompanied by the formation of platelike surface reliefs. The surface relief angles have been determined from observations (7.9°± 0.2°) and calculations based on a phenomenological analysis (7.84°). The fair agreement of these values indicates that the transformation is martensitic and mainly governed by a shear mechanism.     

Preparation and Dielectric Properties of Low-Temperature-Sinterable (Zr0.8Sn0.2)TiO4 Powder

Low-temperature-sinterable (Zr_0.8Sn_0.2)TiO₄ powders were prepared using 3 mol% Zn(NO₃)₂ additive and then compared with powders prepared using 3 mol% ZnO additive and no additives. Sintering at 1200°C for 2 h produced a dielectric ceramic with ρ= 98.6% of theoretical density (TD), ɛ_r= 38.4, Q × f (GHz) = 42000, and τ _f =−1 ppm/°C. Sintering at 1250°C resulted in an excellent dielectric with ρ= 99% of TD, epsilon_r= 40.9, Q × f (GHz) = 49000, and τ _f =−2 ppm/°C. Scanning electron microscopy showed a microstructure with grains measuring 0.5 to 1 μm, and transmission electron microscopy revealed secondary phase in the grain boundaries.     

Structure and Microwave Dielectric Characteristics of Ca1+xNd1−xAl1−xTixO4 Ceramics

CaNdAlO₄ microwave dielectric ceramics were modified by Ca/Ti co-substitution, and their dielectric characteristics were evaluated along with their structure and microstructures. Ca_{1+ x} Nd_{1− x} Al_{1− x} Ti _x O₄ ( x =0, 0.025, 0.05, 0.10, 0.15, 0.20) ceramics with the relative density of over 95% theoretical density were obtained by sintering at 1400°–1450°C in air for 3 h, where the K₂NiF₄-type solid solution single phase was determined from the compositions of x <0.20, while a small amount of CaTiO₃ secondary phase was detected for x =0.20. With Ca/Ti co-substitution in CaNdAlO₄ ceramics, the dielectric constant (ɛ_r) increased with increasing x , and the temperature coefficient of resonant frequency (τ_f) was adjusted from negative to positive, while the Q × f ₀ value increased significantly at first and reached an extreme value at x =0.025 and the maximum at x =0.15. The best combination of microwave dielectric characteristics were achieved at x =0.15 (ɛ_r=19.5, Q × f ₀=93 400 GHz, τ_f=−2 ppm/°C). The improvement of the Q × f ₀ value primarily originated from the reduced interlayer polarization with Ca/Ti co-substitution, while the decreased tolerance factor, the subsequent increased interlayer stress, and the appearance of CaTiO₃ secondary phase brought negative effects upon the Q × f ₀ value.     

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.     

Knudsen Cell Studies of the Vaporization of Samarium Dicarbide

The vapor pressure of SmC₂ in equilibrium with graphite was measured by the Mnudsen effusion technique. Rates of weight loss from the cells were measured with an automatic recording balance. The apparent pressures varied with orifice size, and equilibrium pressures were calculated by extrapolation to zero orifice area. This work was combined with other studies to obtain log₁₀ P(atm) = - 13.869 × 10³/T + 3.752 (1300°-2050°K) for the Sm vapor pressure above SmC₂-C. Estimates of S°₂₉₈ and c_p were made for SmC₂, and δH°₂₉₈ was calculated to be 72.0 ± 2 kcal/mol for the reaction SmC₂(s) = Sm(g) + 2C(s). This value combined with δH°_{v, 298}= 48.6 kcal/mol for Sm gives a δ°_f298 for SmC₂ of 23.4 ± 2 kcal/mol.