Entropy of Alloy Phases: A Macroscopic Perspective

This study presents a comprehensive analysis of the entropy of condensed phases, its temperature, pressure, and composition dependence on a macroscopic correlative platform. Two principal contributions to total nonconfiguration entropy (S_T) are outlined. They are: (i) the pure thermal (S_th) contribution arising from the isochoric temperature dependence of Gibbs energy (G_T) and (ii) the elastic contribution (S_el) representing the dilatational volume effects. It is then argued that entropy variation among a group of alloy phases can be exclusively related to molar volume, only when both thermal pressure (p_th) and thermal entropy terms assume common values for all members. This argument is extended to establish a linear relationship between transformation entropy (ΔS_tr) and transformation-induced volumetric strain (ΔV_tr/V). The temperature and pressure dependencies of entropy have been discussed in terms of the complementing roles of S_th and S_el and simple approximations to these effects are suggested. A macroscopic power law relation for systematizing the standard entropy variation using a composite scaling parameter (MV^2/3/T_m) has been proposed, and its validity is demonstrated for both solid and liquid metals. This power law correlation has been exploited to deduce the following outcome: (i) a simple approximation for the initial slope (dp/dT_m) of p–T_m melting curve, (ii) self-consistent correlation of entropy with specific heat and Debye temperature, (iii) estimation of entropy of metastable phases, and (iv) correlating dilute solution entropy with volume effects of alloying.

     

Pressure Induced Phase Transition,Elastic and Thermal Properties of Rare Earth Tellurides

The high pressure phase transition, elastic and thermal properties of rare earth tellurides (RETe; RE = La, Ce, Pr, Sm and Eu) have been investigated by using a suitable inter-ionic potential with modified ionic charge (Z_me) to include Coulomb screening effect. This model is capable of explaining first order phase from B₁ to B₂ structure at high pressure and elastic properties for RETe. The values of lattice constant, phase transition pressure and Bulk modulus agree well with their corresponding experimental data. The calculated values of second order elastic constants (C₁₁, C₄₄) and their variation with pressure are also presented for these compounds. We have also reported the Debye temperature (θ_D) and its variation with pressure.     

Copper-zirconium tungstate composites exhibiting low and negative thermal expansion influenced by reinforcement phase transformations

A fully-dense Cu-75 vol pct ZrW₂O₈ metal matrix composite was fabricated by hot isostatic pressing of Cu-coated ZrW₂O₈ particles. A small amount of the high-pressure γ-ZrW₂O₈ phase was created during the cooldown and depressurization following densification; near complete transformation to γ-ZrW₂O₈ was achieved by subsequent cold isostatic pressing. The thermal expansion behavior of the composite between 25 °C and 325 °C was altered by the cold isostatic pressing treatment, and also depended on the length of time that had passed between thermal cycles. The measured thermal expansion coefficients within specific temperature ranges varied from −6 · 10⁻⁶ K⁻¹ to far above the thermal expansion coefficient of the copper matrix. The complex temperature-dependent expansion/contraction behavior could be justified by considering the evolution of phase transformations taking place in the ZrW₂O₈ phase, which were observed by in-situ synchrotron X-ray diffraction measurements.     

Copper-zirconium tungstate composites exhibiting low and negative thermal expansion influenced by reinforcement phase transformations

A fully-dense Cu-75 vol pct ZrW₂O₈ metal matrix composite was fabricated by hot isostatic pressing of Cu-coated ZrW₂O₈ particles. A small amount of the high-pressure γ-ZrW₂O₈ phase was created during the cooldown and depressurization following densification; near complete transformation to γ-ZrW₂O₈ was achieved by subsequent cold isostatic pressing. The thermal expansion behavior of the composite between 25°C and 325°C was altered by the cold isostatic pressing treatment, and also depended on the length of time that had passed between thermal cycles. The measured thermal expansion coefficients within specific temperature ranges varied from −6·10⁻⁶ K⁻¹ to far above the thermal expansion coefficient of the copper matrix. The complex temperature-dependent expansion/contraction behavior could be justified by considering the evolution of phase transformations taking place in the ZrW₂O₈ phase, which were observed by in-situ synchrotron X-ray diffraction measurements.     

Mechanical properties,thermophysical properties and electronic structure of Yb3+ or Ce4+-doped La2Zr2O7-based TBCs

First-principles calculations based on density functional theory were performed to investigate the cohesive energies, elastic modulus, Debye temperatures, thermal conductivities and density of states of La_2−xYb_xZr₂O₇, La₂Zr_2−xCe_xO₇ and La_2−xYb_xZr_2−xCe_xO₇ (x = 0.00, 0.25, 0.50, 0.75, 1.00) ceramics. The results show that doping Yb³⁺ or Ce⁴⁺ into La₂Zr₂O₇ reduces its elastic modulus, thermal conductivity and Debye temperature. Compared with La_2−xYb_xZr₂O₇ (x ≠ 0.00), La₂Zr_2−xCe_xO₇ compounds have better ductility and lower Debye temperature. The Debye temperature values of La₂Zr_2−xCe_xO₇ (x ≠ 0.00) compounds are in the range of 485.0–511.5 K. Among all components, the fluorite-type La_2−xYb_xZr_2−xCe_xO₇ (x = 0.75, 1.00) compounds exhibit better mechanical and thermophysical properties, and their thermal conductivity values are only 1.213–1.246 W/(m∙K) (1073 K), which are 14.5%–16.7% lower than that of the pure La₂Zr₂O₇. Thus, our findings open an entirely new avenue for TBCs.     

The effect of Nb and W alloying additions to the thermal expansion anisotropy and elastic properties of Mo<Subscript>5</Subscript>Si<Subscript>3</Subscript>

The directional thermal expansion and elastic properties of Mo₅Si₃, (Mo_0.8Nb_0.2)₅Si₃, and (Mo_0.85W_0.15)₅Si₃ have been studied as a function of temperature through the use of single crystals. Thermal expansion anisotropy was reduced by Nb and W alloying. The decrease in thermal expansion anisotropy by Nb alloying was only found to occur at low temperatures, and thermal expansion anisotropy of (Mo_0.8Nb_0.2)₅Si₃ was similar to that for the other two compounds at 800 °C. Values for the polycrystalline Young’s, bulk, and shear moduli calculated from the measured single-crystal elastic constants are reduced by Nb alloying, and increased by W alloying at all temperatures studied. The elastic modulus E was calculated for the orientations between [100]-[001] and [100]-[010]. In contrast to the effects of Nb on thermal expansion anisotropy, Nb alloying increased the E _[001]/E _[100] elastic anisotropy. This article is based on a presentation made in the symposium entitled “Beyond Nickel-Base Superalloys,” which took place March 14–18, 2004, at the TMS Spring meeting in Charlotte, NC, under the auspices of the SMD-Corrosion and Environmental Effects Committee, the SMD-High Temperature Alloys Committee, the SMD-Mechanical Behavior of Materials Committee, and the SMD-Refractory Metals Committee.     

Phase Stability,Elastic,Thermo-physical and Electronic Properties of Hexa-(Mo,Cr,W)2 C from First-principles Calculations

Phase stability,elastic properties,thermo-physical properties,as well as electronic properties of hexa-(Mo,Cr,W)2C carbides were investigated by first-principles calculations.The results indicated that the Mo_8C_4,Mo_7Cr_1C_4,Mo_7W_1C_4,Mo_6W_2C_4,and Mo_6W_1Cr_1C_4 are stable and the stability follows the sequence:Mo_6W_1Cr_1C_4Mo_7W_1C_4Mo_7Cr_1C_4 Mo_6W_2C_4 Mo_8C_4.Mo_6W_1Cr_1C_4 shows the highest stability,deformation resistance and hardness.G/B(shear modulus/bulk modulus)and Poisson′s ratio of the stable hexa-(Mo,Cr,W)_2C are all larger than 1.75 and 0.26,respectively,which indicates that they are all brittle.The anisotropies are mainly due to the different Vogit shear modulus/Reuss shear modulus;the mechanical anisotropy of Mo_7Cr_1C_4 is the largest,and that of Mo_8C_4 is the smallest.Moreover,the obtained Debye temperatureΘDand heat capacity Cpindicate that Mo_6W_2C_4 possesses the best thermal conductivity(Θ_D=497.72K),while Mo_7Cr_1C_4 and Mo_6W_2C_4possess the largest heat capacity when the temperature is in the range of 0-10 Kand larger than 10 K,respectively.From the electronic property analysis,the doped Cr and W atoms can not only participate in orbitals hybridization themselves but also enhance the orbitals hybridization between Mo and C atoms,which can reinforce the interatomic interactions.     

Single-crystal elastic constants of Fe-15Ni-15Cr alloy

Resonant ultrasound spectroscopy (RUS) and pulse-echo (PE) superposition techniques have been used to determine the three independent elastic-stiffness constants C₁₁, C₁₂, and C₄₄ as a function of temperature for single crystals of 70Fe-15Ni-15Cr alloy. The values of the elastic moduli determined using RUS and PE are in very good agreement within the range of uncertainties. This particular ternary composition of Fe, Ni, and Cr undergoes an fcc-bcc structural phase transformation near 190 K resulting in a low-temperature ferromagnetic phase. The Debye characteristic temperature was determined to be 447 K from PE and 451 K from RUS measurements. The Zener elastic anisotropy A=2C₄₄/(C₁₁−C₁₂) is nearly constant: A=3.53±0.16 in Fe-Ni-Cr alloys with similar compositions. For these alloys, only small variations are observed in the Grüneisen parameter, γ≈2.08, and in the Poisson ratio, v _[hkl]=0.293±0.013.     

Mechanical properties,thermal conductivity and defect formation energies of samarium immobilization in Gd2Zr2O7:First-principles study and irradiation experiment

A density functional theory(DFT) study was employed to investigate the mechanical property,thermal conductivity,Debye temperature,electronic structure and defect chemistry of(Gd_1-xSm_x)₂Zr₂O₇.All the(Gd_1-xSm_x)₂Zr₂O₇ compounds exhibit an excellent structural and mechanical stability(Gd_0.25Sm_0.75)₂Zr₂O₇ has the lowest Young’s modulus of...     

Thermal and Mechanical Properties of ACoO3 (R = Sm, Tb, Dy, Ho, and Er)

The thermal and mechanical properties of orthocobaltates, ACoO₃ (A = Sm, Tb, Dy, Ho, and Er), have been investigated using the modified rigid ion model (MRIM) by incorporating the effect of lattice distortions. We have computed the variations of specific heat and thermal expansion coefficient for these orthocobaltates in wide temperature range of 1 K (?272 °C) ≤ T ≤ 1000 K (727 °C). The calculated results of specific heat, thermal expansion, bulk modulus, and other thermal and mechanical properties accord very well with the available experimental data, implying that MRIM represents properly the nature of the perovskite-type rare earth cobaltates. In addition, we have also reported the results on molecular force constant (f), Reststrahlen frequency (υ), cohesive energy (?), Debye temperature (θ _D), and Gruneisen parameter (γ).     

Oxygen pressure dependence of Cu2O-CuO-Gd2O3 phase diagram

The phase diagram of the Gd-Cu-O system has been investigated under various oxygen partial pressures by thermal analysis. In this system, only one ternary compound Gd₂CuO₄ exists stably, depending on the oxygen partial pressure. This compound decomposes to Gd₂O3 and Cu₂O under low oxygen partial pressure at high temperature. The incongruent melting and decomposition temperatures of Gd₂CuO₄ and the temperature of eutectic reaction have been investigated as a function of oxygen partial pressure. The present ternary system includes two invariant reactions:L + Gd₂O₃ ⇆ Gd₂CuO₄ + Cu₂O at 1376 K under 0.07 atm O₂ (7.09 kPa) andL⇆ Gd₂CuO₄ + CuO + Cu₂O at 1321 K under 0.42 atm O₂ (42.56 kPa). The thermodynamic properties of the system have also been considered.     

The thermodynamics of melts in the system VO2−V2O5

Using a gravimetric technique, the oxygen isobars in the liquid phase field of the system VO₂−V₂O₅ have been determined in the temperature range 1020° to 1100°C and in the oxygen pressure range 0.01 to 0.4 atm, and the VO₂ liquidus and solidus curves have been determined in the temperature range 953° to 1081°C. From these results have been calculated the activities of the components VO₂ and VO_2.5 in the system and the standard free energy change for the reaction 2VO_{2 (S)}+1/2O_{2 (g)}=V₂O_{5 (1)}. The latter was determined to be ΔG ^o=−17780+7.64T in the temperature range 1020° to 1100°C.     

Temperature dependence of the refractive index of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-Na<Subscript>2</Subscript>O-SiO<Subscript>2</Subscript> melts: Role of electronic polarizability of oxygon controlled by network structure

Refractive indexes for the Al₂O₃-Na₂O-SiO₂ system have been measured using an ellipsometer for a wavelength of 632.8 nm over a wide temperature range (1100 to 1800 K). Two kinds of sample were used: xAl₂O₃-(40-x)Na₂O-60SiO₂ and yAl₂O₃-yNa₂O-(100-2y)SiO₂, where x ranged between 6 and 20 mol pct and y between 12.5 and 25 mol pct. In the former samples, the temperature coefficient of refractive indexes changed from negative to positive on increasing the concentration of Al₂O₃. In the latter samples, the refractive indexes increased monotonically with decreasing concentration of SiO₂, and the temperature coefficient was always positive. It has been found that the temperature dependence of refractive indexes in these melts is determined by the coefficient of thermal expansion, which would be relevant to the degree of polymerization of the melts. In addition, the electronic polarizability of oxygen derived from the refractive indexes increased with increasing temperature in each melt. This suggests that the basicity of the alumino-silicate melts increases as temperature increases. The positive temperature coefficient of the electronic polarizability of oxygen can be attributed to an increase in the distance between cation and oxygen ion due to thermal expansion. The dependence of the electronic polarizability of oxygen on the concentration of Al₂O₃ has also been discussed in terms of the electronic polarizabilities of three types of oxygen contained in the melts. This article is based on a presentation given in the Mills Symposium entitled “Metals, Slags, Glasses: High Temperature Properties & Phenomena,” which took place at The Institute of Materials in London, England, on August 22–23, 2002.     

First-principles computations of mechanical properties of Ni2Cr and Ni2Mo

Nickel-based alloys are being considered for use as the outer container of the waste package for the disposal of high-level nuclear waste. During fabrication processes and long-term storage, Ni-based alloy outer containers can undergo microstructural changes due to the formation of Ni₂Cr, Ni₂Mo, and Ni₂(Cr, Mo), which are ordered orthorhombic (oI6) phases whose mechanical properties are unknown because of fabrication difficulties. To circumvent the experimental limitation, a first-principles quantum-mechanical code based on the full-potential linearized augmented plane-wave (FLAPW) method was used to compute the elastic constants and the theoretical stress-strain curves of Ni₂Cr and Ni₂Mo. The theoretical mechanical properties were then correlated with charge-density distributions of the stressed oI6 unit cell to identify the critical conditions at the onset of fracture. Using first-principles results as material input, the unstable stacking energy and the Peierls-Nabarro (P-N) barrier energy were computed and used to estimate the tensile ductility and fracture toughness of Ni₂Cr and Ni₂Mo. The influences of the elastic anisotropy and slip vector on dislocation mobility in Ni₂Cr and Ni₂Mo are identified and contrasted to those in MoSi₂ with a tetragonal (tI6) crystal structure. This article is based on a presentation made in the symposium “Computational Aspects of Mechanical Properties of Materials,” which occurred at the 2005 TMS Annual Meeting, February 13–17, 2005, in San Francisco, CA, under the auspices of the MPMD-Computational Materials Science & Engineering (Jt. ASM-MSCTS) Committee.     

Study on bulk Sm2 Fe17 Nx sintered magnets prepared by spark plasma sintering

Abstract

Sm₂Fe₁₇N_x sintered magnets were fabricated by spark plasma sintering (SPS) technique. Effects of sintering pressure, sintering temperature and heating rate on the magnetic properties and crystal structures of the magnets were investigated. The results showed that the density of the magnet was obviously improved with increasing sintering pressure, but the coercivity dropped simultaneously because Sm₂Fe₁₇N_x decomposed into SmN, α-Fe and N₂. The coercivity decreased rapidly when sintering temperature was above 200°C under 1 GPa sintering pressure, which indicated that high pressure promoted the decomposition of Sm₂Fe₁₇N_x even at low temperature. In addition, the decomposition could not be effectively restrained even if the heating rate reached 450°C min^?1.     

A thermal processing technique for TRIP steels

An investigation was made to determine the effect of thermal cycling between martensite and reverted austenite on the structure and mechanical properties of a Fe-24 pct Ni-4 pct Mo-0.3 pct C TRIP steel. Measurements of hardness, tensile properties, X-ray line broadening, and metallographic structure indicate that repetitive cycling both strengthens the austenite and raises theM _D from below room temperature to above room temperature. It is shown that cyclical thermal processing produces mechanical properties essentially comparable with thermomechanical processing in this particular TRIP steel.     

Influence of martensite content and morphology on tensile and impact properties of high-martensite dual-phase steels

A series of dual-phase (DP) steels containing finely dispersed martensite with different volume fractions of martensite (V _m) were produced by intermediate quenching of a boron- and vanadium-containing microalloyed steel. The volume fraction of martensite was varied from 0.3 to 0.8 by changing the intercritical annealing temperature. The tensile and impact properties of these steels were studied and compared to those of step-quenched steels, which showed banded microstructures. The experimental results show that DP steels with finely dispersed microstructures have excellent mechanical properties, including high impact toughness values, with an optimum in properties obtained at ∼0.55 V _m. A further increase in V _m was found to decrease the yield and tensile strengths as well as the impact properties. It was shown that models developed on the basis of a rule of mixtures are inadequate in capturing the tensile properties of DP steels with V _m>0.55. Jaoul-Crussard analyses of the work-hardening behavior of the high-martensite volume fraction DP steels show three distinct stages of plastic deformation.     

Comparative study for physical properties and corrosion mechanism of synthetic and in situ MgAl2O4 spinel formation zero cement refractory castables

Abstract

Magnesium aluminate spinel (MgAl₂O₄) is an excellent castable refractory product due to its high temperature thermal, chemical and mechanical properties. Alumina spinel castables are produced by addition of synthetic spinel or in situ spinel formation during the firing process. In the first part of the experimental studies, alumina rich MgAl₂O₄ spinel castable was produced using a solid state reaction technique. Tabular alumina and sea water magnesia (<100 μm) were used as starting raw materials. In the second part of the experimental studies, commercial synthetic spinel added castables were produced. In order to compare experimental results, both parts of the experimental study involved compositions with the same proportions of MgO. α-500 hydratable alumina was used as binder. Castables were sintered at 1500 and 1600°C. Water absorption, apparent porosity, bulk density and cold crushing strength values were considered and the optimum sintering temperature, proportions of synthetic spinel and sea water magnesia were determined. The XRD patterns confirm the phase formation of MgAl₂O₄. Moreover, the physical properties of the castables were supported by this XRD analysis. Scanning electron microscopy investigations of the fired samples were carried out to compare the effect of synthetic spinel addition and in situ phase formation on the physical properties of the castables. The mechanism of slag penetration to two types of zero cement castables for steel ladles was examined and the penetration layer chemically analysed by energy dispersive X-ray analysis studies.     

Characterization of anisotropie elastic constants of silicon-carbide participate reinforced aluminum metal matrix composites: Part I. Experiment

The anisotropic elastic properties of silicon-carbide particulate (SiC _p ) reinforced Al metal matrix composites were characterized using ultrasonic techniques and microstructural analysis. The composite materials, fabricated by a powder metallurgy extrusion process, included 2124, 6061, and 7091 Al alloys reinforced by 10 to 30 pct ofα-SiC _p by volume. Results were presented for the assumed orthotropic elastic constants obtained from ultrasonic velocities and for the microstructural data on particulate shape, aspect ratio, and orientation distribution. All of the composite samples exhibited a systematic anisotropy: the stiffness in the extrusion direction was the highest, and the stiffness in the out-of-plane direction was the lowest. Microstructural analysis suggested that the observed anisotropy could be attributed to the preferred orientation of SiC _p . The ultrasonic velocity was found to be sensitive to internal defects such as porosity and intermetallic compounds. It has been observed that ultrasonics may be a useful, nondestructive technique for detecting small directional differences in the overall elastic constants of the composites since a good correlation has been noted between the velocity and microstructure and the mechanical test. By incorporating the observed microstructural characteristics, a theoretical model for predicting the anisotropic stiffnesses of the composites has been developed and is presented in a companion article (Part II). Formerly with the Department of Aerospace Engineering and Engineering Mechanics, Iowa State University Formerly with Westinghouse Science & Technology Center     

The dependence of the oxidation state of vanadium on the oxygen pressure in melts of VOx,Na2O-VOx,and CaO-SiO2-VOx

The oxidation state of vanadium has been determined as a function of oxygen pressure in pure VO_x melts at 808 °C to 1000 °C, in Na₂O-VO_x melts with the initial molar ratios Na₂O/V₂O₅ = 0.2, 0.5, and 1.0 at 1000 °C, and in CaO-SiO₂-VO_x melts with the molar ratios CaO/SiO₂ = 0.71, 1.00, and 1.36 at 1600 °C. In the VO_x melts,x is close to 2.5 in the range of oxygen pressure fromP _{O 2} to 0.94 atm. The deviation, δ, from stoichiometric V₂O₅ (δ = 2.5-x) varies approximately proportionally toP _{O 2} ^-1/4, indicating an equilibrium between V⁴⁺ and V⁵⁺ ions. In the Na₂O-VO_x melts, and in the CaO-SiO₂-VO_x melts,x varies with logP _{O 2} according to an S-shaped function, withx approaching 1.5 at low and 2.5 at high oxygen pressures. At given oxygen pressures,x increases with Na₂O or CaO content, respectively. Hence, these oxides stabilize the higher valent vanadium ions. For the CaO-SiO₂-VO_x system, the determinedx-P _{O 2} dependence can be interpreted quantitatively in terms of V⁴⁺/V⁵⁺ and V³⁺/V⁴⁺ equilibria.