Reaction diffusion in the Nb-Ge system

Reaction diffusion in the Nb-Ge system was studied in the temperature range 1243 to 1723 K for diffusion couples of (pure solid Nb)-(pure liquid Ge) and (pure solid Nb)-(Ge-37.5wt % Nb liquid alloy). Growth of the NbGe₂, Nb₃Ge₂, Nb₅Ge₃ and Nb₃Ge layers was observed, and the growth rates of all except the Nb₃Ge layer were found to conform to the parabolic law. Growth of the Nb₃Ge layer was observed only along the grain boundaries in the Nb₅Ge₃ layer. Interdiffusion coefficients \(\tilde D\) in the NbGe₂, Nb₃Ge₂ and Nb₅Ge₃ phases were determined by Heumann's method, and the temperature dependence of these was expressed by the Arrhenius equations as follows: $$\tilde D_{{\text{NbGe}}_{\text{2}} } = (6.40_{ - 1.66}^{ + 2.25} \times 10^{ - 6} exp [ - (161 \pm 4) kJ mol^{ - 1} {\text{/RT] m}}^{{\text{2 }}} \sec ^{ - 1} $$ $$\tilde D_{{\text{Nb}}_{\text{3}} {\text{Ge}}_{\text{2}} } = (2.27_{ - 0.60}^{ + 0.82} \times 10^{ - 4} exp [ - (282 \pm 4) kJ mol^{ - 1} {\text{/RT] m}}^{{\text{2 }}} \sec ^{ - 1} $$ and $$\tilde D_{{\text{Nb}}_{\text{5}} {\text{Ge}}_{\text{3}} } = (6.28_{ - 1.93}^{ + 2.78} \times 10^{ - 5} exp [ - (238 \pm 5) kJ mol^{ - 1} {\text{/RT] m}}^{{\text{2 }}} \sec ^{ - 1} $$ In addition to the binary Nb-Ge system, the reaction diffusion of (pure solid Nb)-(Cu-13 wt % Ge liquid alloy) couples was also studied. In this case, only growth of the Nb₅Ge₃ layer containing negligible copper content was observed.     

Surface and grain-boundary energies of cubic zirconia

Using the multiphase equilibration technique for the measurement of contact angles, the surface and grain-boundary energies of polycrystalline cubic ZrO₂ in the temperature range of 1173 to 1523 K were determined. The temperature coefficients of the linear temperature function obtained, are expressed as $$\frac{{{\text{d}}\gamma }}{{{\text{d}}T}}({\text{ZrO}}_{\text{2}} ){\text{ }} = {\text{ }} - 0.431{\text{ }} \times {\text{ }}10^{ - 3} {\text{ }} \pm {\text{ }}0.004{\text{ }} \times {\text{ }}10^{ - 3} {\text{ Jm}}^{ - {\text{2}}} {\text{ K}}^{ - {\text{1}}} $$ and $$\frac{{{\text{d}}\gamma }}{{{\text{d}}T}}({\text{ZrO}}_{\text{2}} - {\text{ZrO}}_{\text{2}} ){\text{ }} = {\text{ }} - 0.392{\text{ }} \times {\text{ }}10^{ - 3} {\text{ }} \pm {\text{ }}0.126{\text{ }} \times {\text{ }}10^{ - 3} {\text{ Jm}}^{ - {\text{2}}} {\text{ K}}^{ - {\text{1}}} $$ respectively. The surface fracture energy obtained with a Vickers microhardness indenter at room temperature is found to be γ _F=3.1 J m^?2.     

Thermodynamic properties of Pt5La,Pt5Ce,Pt5Pr,Pt5Tb and Pt5 Tm intermetallics

The Gibbs’ energies of formation of Pt₅La, Pt₅Ce, Pt₅Pr, Pt₅Tb and Pt₅ Tm intermetallic compounds have been determined in the temperature range 870–1100 K using the solid state cell: $$Ta,M + MF_3 /CaF_2 /Pt_5 M + Pt + MF_3 ,Ta$$ . The reversible emf of the cell is directly related to the Gibbs’ energy of formation of the Pt₅M compound. The results can be summarized by the equations: $$\begin{gathered} \Delta G_f^ \circ \left\langle {Pt_5 La} \right\rangle = - 373,150 + 6 \cdot 60 T\left( { \pm 300} \right)J mol^{ - 1} \hfill \\ \Delta G_f^ \circ \left\langle {Pt_5 Ce} \right\rangle = - 367,070 + 5 \cdot 79 T\left( { \pm 300} \right)J mol^{ - 1} \hfill \\ \Delta G_f^ \circ \left\langle {Pt_5 Pr} \right\rangle = - 370,540 + 4 \cdot 69 T\left( { \pm 300} \right)J mol^{ - 1} \hfill \\ \Delta G_f^ \circ \left\langle {Pt_5 Tb} \right\rangle = - 372,280 + 4 \cdot 11 T\left( { \pm 300} \right)J mol^{ - 1} \hfill \\ \Delta G_f^ \circ \left\langle {Pt_5 Tm} \right\rangle = - 368,230 + 4 \cdot 89 T\left( { \pm 300} \right)J mol^{ - 1} \hfill \\ \end{gathered} $$ relative to the low temperature allotropic form of the lanthanide element and solid platinum as standard states The enthalpies of formation of all the Pt₅M intermetallic compounds obtained in this study are in good agreement with Miedema’s model. The experimental values are more negative than those calculated using the model. The variation of the thermodynamic properties of Pt₅M compounds with atomic number of the lanthanide element is discussed in relation to valence state and molar volume.     

Surface,grain-boundary and interfacial energies in Al2O3 and Al2O3-Sn,Al2O3-Co systems

Using the multiphase equilibrium method for the measurement of contact angles, the surface and grain-boundary energies of polycrystalline Al₂O₃ in the temperature range of 1473 to 1923 K were determined. Linear temperature functions were obtained by extrapolation for both quantities between absolute zero and the melting point of Al₂O₃. The temperature dependence of the surface and grain boundary energies can be expressed as $$\gamma _{{\rm A}l_2 O_3 } = 2.559 - 0.784 \times 10^{ - 3} T(J m^{ - 2} )$$ and $$\gamma _{{\rm A}l_2 O_3 - Al_2 O_3 = } 1.913 - 0.611 \times 10^{ - 3} T(J m^{ - 2} )$$ respectively. The interfacial energies of Al₂O₃ in contact with the molten metals tin and cobalt revealed a linear dependence on temperature.     

Phase relationships in the system Cr-W-O and thermodynamic properties of CrWO4 and Cr2WO6

The phase diagram of the Cr-W-O system at 1000° C was established by metallographic and X-ray identification of the phases present after equilibration in evacuated silica capsules. Two ternary oxide phases, CrWO₄ and Cr₂WO₆ were detected. The oxygen potential over the three-phase mixtures, W+Cr₂O₃ s+CrWO₄, WO_2.90+CrWO₄+Cr₂WO₆ and Cr₂O₃+CrWO₄+Cr₂WO₆, were measured by solid state cells incorporating Y₂O₃ stabilized ZrO₂ electrolyte and Ni+NiO reference electrode. The Gibbs' energies of formation of the two ternary phases can be represented by the following equations $$\begin{gathered} W(s) + \tfrac{1}{2} Cr_2 O_3 (s) + \tfrac{5}{4} O_2 (g) \to CrWO_4 (s) \hfill \\ \Delta G^0 = - 172 047 + 48.725T ( \pm 230) cal mol^{ - 1} \hfill \\ Cr_2 O_3 (s) + WO_3 (s) \to Cr_2 WO_6 (s) \hfill \\ \Delta G^0 = - 3 835 + 0.235{\rm T} ( \pm 500) cal mol^{ - 1} \hfill \\ \end{gathered}$$      

Mechanism of the reduction of carbon/alumina powder mixture in a flowing nitrogen stream

The mechanism of the reduction of carbon/alumina powder mixture in a flowing nitrogen stream was studied. Five steps were found to be involved in the overall reaction. $$\begin{gathered} Al_2 O_{3f} (s) + 2C_f (s)\mathop \to \limits^{k_1 } Al_2 O(g) + 2CO(g) \hfill \\ Al_2 O(g) + solid surface\mathop \rightleftharpoons \limits_{k_2^\prime }^{k_2 } [Al_2 O]_s \hfill \\ [Al_2 O]_s + CO(g) + N_2 (g)\mathop \to \limits^{k_3 } 2AlN(s) + CO_2 (g) \hfill \\ CO_2 (g) + C_f (s)\mathop \rightleftharpoons \limits_{k_4^\prime }^{k_4 } CO(g) + [O]_c \hfill \\ [O]_c \mathop \to \limits^{k_5 } CO(g) \hfill \\ \end{gathered}$$ The consumption rates of Al₂O₃ and carbon, and the production rate of AIN, were determined to be $$\begin{gathered} \frac{{d[Al_2 O_3 ]}}{{dt}} = - 143.88(1 + m)exp( - 290 580/RT) [Al_2 O_3 ][C]^2 / \hfill \\ \left\{ {1 + 5.83 x 10^{14} exp( - 427 497/RT)\frac{{[CO_2 ]}}{{[CO]}}} \right\}^2 kg mol s^{ - 1} m^{ - 3} \hfill \\ \frac{{d[C]}}{{dt}} = - 409.504 exp ( - 254 500/RT) [Al_2 O_3 ][C]^2 / \hfill \\ \left\{ {1 + 5.83 x 10^{14} \exp ( - 427 497/RT)\frac{{[CO_2 ]}}{{[CO]}}} \right\}^2 kg mol s^{ - 1} m^{ - 3} \hfill \\ \frac{{d[AlN]}}{{dt}} = 53.24(1 + m) exp( - 290 580/RT) [Al_2 O_3 ][C]^2 / \hfill \\ \left\{ {1 + 5.83 x 10^{14} exp( - 427 497/RT)\frac{{[CO_2 ]}}{{[CO]}}} \right\}^2 kg mol s^{ - 1} m^{ - 3} \hfill \\ \end{gathered}$$ in the temperature range 1648–1825 K.     

Sublimation study of BiBr3

Steady-state sublimation vapour pressures of anhydrous bismuth tribromide have been measured by the continuous gravimetric Knudsen-effusion method from 369.3 to 478.8 K. Additional effusion measurements have also been made from 435.4 to 478.6 K by the torsion—effusion method. Based on a correlation of Δ_sub H ₂₉₈ ⁰ and Δ_sub S ₂₉₈ ⁰ , a recommended p(T) equation has been obtained for BiBr₃(s) $$\alpha - {\rm B}i{\rm B}r_3 :log{\text{ }}p = - C\alpha /T - 12.294log{\text{ }}T + 5.79112 \times 10^{ - 3} {\text{ }}T + 47.173$$ with Cα=(Δ _subH ₂₉₈ ⁰ +20.6168)/1.9146×10^-2 $$\beta - {\rm B}i{\rm B}r_3 :log{\text{ }}p = - C\beta /T - 23.251log{\text{ }}T + 1.0492 \times 10^{ - 2} {\text{ }}T + 77.116$$ with Cβ=(Δ _subH ₂₉₈ ⁰ +46.2642)/1.9146×10^-2 where p is in Pa, T in Kelvin, Δ _sub H ₂₉₈ ⁰ in kJ mol^?1. Condensation coefficients and their temperature dependence have been derived from the effusion measurements.     

Thermophysical measurements on low carbon 304 stainless steel above 1400 K by a transient (subsecond) technique

Simultaneous measurements, by a subsecond duration transient technique, to determine the specific heat capacity, c _p , the electrical resistivity, ρ, and the hemispherical total emittance in the temperature range 1400–1700 K, and the melting point and the radiance temperature at the melting point, of AISI type 304L stainless steel are described. The results are expressed by the relations: $$c_p = 1127{\text{ }} - {\text{ }}7.265{\text{ }} \times {\text{ }}10^{ - 1} {\text{ }}T{\text{ }} + {\text{ }}2.884{\text{ }} \times {\text{ }}10^{ - 4} {\text{ }}T^2$$ $$\rho = 75.59{\text{ }} + {\text{ }}4.695{\text{ }} \times {\text{ }}10^{ - 2} {\text{ }}T{\text{ }} - {\text{ }}9.592{\text{ }} \times {\text{ }}10^{ - 6} {\text{ }}T^2$$ where c _p is in J · kg^?1 · K^?1, ρ is in ΜΩ · cm, and T is in K. The value of the hemispherical total emittance is 0.37 in the range 1700–1900 K. The melting point and the radiance temperature (at 653 nm) at the melting point are 1707 and 1590 K, respectively, yielding a value of 0.385 for the normal spectral emittance at the melting point. Estimated inaccuracies of the measured properties are: 3% for the specific heat capacity, 2% for electrical resistivity, 5% for hemispherical total emittance, and 8 K for melting point and radiance temperature at the melting point.     

Phase equilibria in the system Sm–Rh–O and thermodynamic and thermal studies on SmRhO3

Using isothermal equilibration, phase relations are established in the system Sm–Rh–O at 1273 K. SmRhO₃ with GdFeO₃-type perovskite structure is found to be the only ternary phase. Solid-state electrochemical cells, containing calcia-stabilized zirconia as an electrolyte, are used to measure the thermodynamic properties of SmRhO₃ formed from their binary component oxides Rh₂O₃ (ortho) and Sm₂O₃ (C-type and B-type) in two different temperature ranges. Results suggest that C-type Sm₂O₃ with cubic structure transforms to B-type Sm₂O₃ with monoclinic structure at 1110 K. The standard Gibbs energy of transformation is $ \Delta_{\text{tr}} G^{\text{o}} ( \pm 87)/{\text{J}}\,{\text{mol}}^{ - 1} = 3763 - 3.39\,(T/{\text{K}}) $ . Standard Gibbs energy of formation of SmRhO₃ from binary component oxides Rh₂O₃ and Sm₂O₃ with B-type rare earth oxide structure can be expressed as $ \Delta_{\text{f(ox)}} G^{\text{o}} ( \pm 75)/{\text{J}}\,{\text{mol}}^{ - 1} = - 64230 + 6.97(T/{\text{K}}) $ . The decomposition temperature of SmRhO₃ estimated from the extrapolation of electrochemical data is 1665 (±2) K in air and 1773 (±3) K in pure oxygen. Temperature-composition diagrams at constant oxygen pressures are constructed for the system Sm–Rh–O. Employing the thermodynamic data for SmRhO₃ from emf measurement and auxiliary data for other phases from the literature, oxygen potential-composition phase diagram and 3-D chemical potential diagram for the system Sm–Rh–O at 1273 K are developed.     

Determination of thermodynamic interactions of poly(l-lactide) and biphasic calcium phosphate/poly(l-lactide) composite by inverse gas chromatography at infinite dilution

Inverse gas chromatography at infinite dilution was applied to determine the thermodynamic interactions of poly(l-lactide) (PLLA) and the composite of biphasic calcium phosphate and PLLA (BCP/PLLA). The specific retention volumes, $ V_{\text{g}}^{0} $ , of 11 organic compounds of different chemical nature and polarity (non-polar, donor or acceptor) were determined in the temperature range of 308–378 K for PLLA and 308–398 K for BCP/PLLA. The weight fraction activity coefficients of test sorbates, $ \Omega_{1}^{\infty } $ , and the Flory–Huggins interaction parameters, $ \chi_{12}^{\infty } $ , were estimated and discussed in terms of interactions of the sorbates with PLLA and BCP/PLLA. Also, the partial molar free energy, $ \Delta G_{1}^{\infty } $ , the partial molar heat of mixing, $ \Delta H_{1}^{\infty } $ , the sorption molar free energy, $ \Delta G_{1}^{\text{S}} $ , the sorption enthalpy, $ \Delta H_{1}^{\text{S}} $ , and the sorption entropy, $ \Delta S_{1}^{\text{S}} $ , were analyzed. A different chromatographic behavior of the two investigated samples, PLLA and BCP/PLLA, was observed. The values of $ \Omega_{1}^{\infty } $ indicated n-alkanes, diethyl ether, tetrahydrofurane (THF), cyclohexane, benzene, dioxane (except for 338 K), and ethyl acetate (EtAc) (except for 338 K) as non-solvents, and chloroform (CHCl₃) as good solvent (except for 378 K) for PLLA. For BCP/PLLA, CHCl₃, EtAc (for 378 K), dioxane (except for 378 K), and THF were indicated as good solvents.     

Thermophysical measurements on tungsten-3 (wt %) rhenium alloy in the range 1500–3600 K by a pulse heating technique

Simultaneous measurements of the specific heat capacity, c _p, electrical resistivity, ρ, and hemispherical total emittance, ε, of tungsten-3 (wt%) rhenium alloy in the temperature range 1500–3600 K by a subsecond-duration pulse heating technique are described. The results are expressed by the relations $$\begin{gathered} c_{\text{P}} = 0.30332 - 2.8727 \times 10^{ - 4} {\text{ }}T + 1.9783 \times 10^{ - 7} {\text{ }}T^2 \hfill \\ {\text{ }} - 5.6672 \times 10^{ - 11} {\text{ }}T^3 + 6.5628 \times 10^{ - 15} {\text{ }}T^4 , \hfill \\ \rho = - 24.261 + 8.1924 \times 10^{ - 2} {\text{ }}T - 3.7656 \times 10^{ - 5} {\text{ }}T^2 \hfill \\ {\text{ + 1}}{\text{.1850}} \times {\text{10}}^{ - 8} {\text{ }}T^3 - 1.3229 \times 10^{ - 12} {\text{ }}T^4 , \hfill \\ \varepsilon = 0.1945 + 5.881 \times 10^{ - 5} {\text{ }}T, \hfill \\ \end{gathered} $$ where T is in K, c_p is in J·g^?1·K^?1, and ρ is in μΩ·cm. The melting temperature (solidus temperature) was also measured and was determined to be 3645 K. Uncertainties of the measured properties are estimated to be not more than ±3 % for specific heat capacity, ±1 % for electrical resistivity, ± 5 % for hemispherical total emittance, and ±20 K for the melting temperature.     

Determination of standard Gibbs energies of formation of ternary oxides in the system Co-Sb-O by solid electrolyte emf method

An isothermal section of the phase diagram of the system Co-Sb-O at 873 K was established by isothermal equilibration and XRD analyses of quenched samples. The following galvanic cells were designed to measure the Gibbs energies of formation of the three ternary oxides namely CoSb₂O₄, Co₇Sb₂O₁₂ and CoSb₂O₆ present in the system.

Surface-diffusion studies on UO2 and MgO

An optical interferometric technique has been used to study the growth of grain boundary grooves and the decay of surface scratches on UO₂ and MgO at temperatures in the range 1100 to 1700° C. The results were interpreted using equations derived by W. W. Mullins and it was found that surface-diffusion was the predominant material transport process for both oxides under the experimental conditions used. Surface-diffusion coefficients and activation energies were calculated, and gave the following equations for the variation of the mass transfer surface-diffusion coefficientD _s with temperature. $$\begin{gathered} UO_{2.005, } {\text{ }}D_s = 1.3 x 10^8 exp^{ - 11000 \pm 15000} /RT[1200{\text{ to }}1{\text{400}}^\circ {\text{ C]}} \hfill \\ MgO, D_s = 8 x 10^4 exp^{ - 88500 \pm 15000} /RT[1200{\text{ to }}15{\text{00}}^\circ {\text{ C]}} \hfill \\ \end{gathered}$$ It was found that for UO₂ the rate of grooving increased markedly as the oxygen content of the oxide increased.     

Surface and grain-boundary energies in yttria-stabilized zirconia (YSZ-8 mol%)

The multiphase equilibration technique has been used to measure the equilibrium angles that develop at the interphase boundaries of a solid-liquid-vapour system after annealing and also the surface (γ_sv)and the grain-boundary, (γ_ss) energies of polycrystalline yttria-stabilized zirconia (8 mol% Y₂O₃). The data was recorded in the temperature range 1573–1873 K. Linear temperature functions were obtained for the surface energy $$\gamma _{SV} (Jm^{ - 2} ) = 1.927 - 0.428x10^{ - 3} T$$ and for the grain-boundary energy $$\gamma _{SS} (Jm^{ - 2} ) = 1.215 - 0.358x10^{ - 3} T$$      

Mixed-mode crack-tip stress fields for orthotropic functionally graded materials

Quasi-static mixed mode stress fields for a crack in orthotropic inhomogeneous medium are developed using asymptotic analysis coupled with Westergaard stress function approach. In the problem formulation, the elastic constants E ₁₁, E ₂₂, G ₁₂, ν ₁₂ are replaced by an effective stiffness ${E=\sqrt {E_{11} E_{22}}}$ , a stiffness ratio ${\delta =\left({{E_{11}}\mathord{\left/ {\vphantom {{E_{11}} {E_{22}}}}\right. \kern-0em} {E_{22}}} \right)}$ , an effective Poisson’s ratio ${\nu =\sqrt {\nu_{12}\nu _{21}} }$ and a shear parameter ${k=\left({E \mathord{\left/ {\vphantom {E {2G_{12}}}}\right. \kern-0em} {2G_{12}}}\right)-\nu }$ . An assumption is made to vary the effective stiffness exponentially along one of the principal axes of orthotropy. The mode-mixity due to the crack orientation with respect to the property gradient is accommodated in the analysis through superposition of opening and shear modes. The expansion of stress fields consisting of the first four terms are derived to explicitly bring out the influence of nonhomogeneity on the structure of the mixed-mode stress field equations. Using the derived mixed-mode stress field equations, the isochromatic fringe contours are developed to understand the variation of stress field around the crack tip as a function of both orthotropic stiffness ratio and non-homogeneous coefficient.     

Synthesis of ZnO single crystals by the flux method

Zinc oxide (ZnO) single crystals have been grown at temperatures ranging from 450–900 °C and for 1–12 h, using hydrous KOH and NaOH melts as fluxes. For a KOH flux, brown ZnO single crystals with diameter 0.5 mm × 7.5 mm were grown under conditions of 500 °C for 20 h and white crystals of diameter 0.5 mm × 7 mm were grown at 800 °C for 20 h, using a small crucible (average 50 ml). When a large crucible (average 400 ml) was used, ZnO single crystals with diameter 0.5 mm × 8 mm were formed at 900 °C for 30 h. When using a KOH + NaOH (1∶1) flux, light-brown and long crystals with diameter 1.0 mm × 18 mm could be grown. The grown ZnO single crystals were bounded with only both p- and m-faces. It seems that crystal qualities were good under conditions of 900 °C for 30 h. The following mechanisms of dissociation and formation of ZnO single crystal from KOH (or NaOH) + ZnO melt seemed to occur $$KOH(or{\text{ NaOH}}){\text{ }} \to {\rm K}^ + {\text{ (or Na}}^{\text{ + }} {\text{) + OH}}^ - $$ $$ZnO{\text{ + 2 OH}}^ - \to {\text{ ZnO}}_{\text{2}}^{{\text{2}} - } {\text{ + H}}_{\text{2}} {\text{O,}}$$ $${\text{ZnO}}_{\text{2}}^{{\text{2}} - } {\text{ }} \to {\text{ ZnO + O}}^{{\text{2}} - } .$$      

Surface mass transport of alumina

The kinetics of thermal grooving at the intersection of rhombohedral twin boundaries with the \((10\bar 10)\) plane in aluminium oxide were measured from 1773 to 2273 K. Analysis of the data using the model of Mullins showed that surface diffusion was the dominant mechanism for mass transport. The results were compared with other similar published work on alumina, and the following equation for surface diffusion was determined: $$D_s (cm^2 sec^{ - 1} ) = 4.05 x 10^5 exp - (452kJ mol^{ - 1} /RT).$$      

Heat capacity and electrical resistivity of POCO AXM-5Q1 graphite in the range 1500–3000 K by a pulse-heating technique

Measurements of the heat capacity and electrical resistivity of POCO AXM-5Q1 graphite in the temperature range 1500–3000 K by a subsecond-duration pulse-heating technique are described. The results for heat capacity may be represented by the relation $$C_{{\text{p }}} = 19.438 + 3.6215 \times {\text{10}}^{{\text{ - 3}}} {\text{ }}T - 4.4426 \times {\text{10}}^{{\text{ - 7}}} {\text{ }}T^2$$ where C _p is in J · mol^?1 · K^?1 and T is in K. The results for electrical resistivity vary with the density (d) of the specimen material and, therefore, are represented by the following relations: for d=1.709, $$\rho = 1084.6 - 1.9940 \times {\text{10}}^{{\text{ - 1}}} {\text{ }}T + 1.6760 \times {\text{10}}^{{\text{ - 4 }}} T^{2{\text{ }}} - 2.0310 \times {\text{10}}^{{\text{ - 8 }}} T^3$$ and for d= 1.744, $$\rho = 943.1 - 1.3836 \times {\text{10}}^{{\text{ - 1}}} {\text{ }}T + 1.3776 \times {\text{10}}^{{\text{ - 4 }}} T^{2{\text{ }}} - 2.0310 \times {\text{10}}^{{\text{ - 8 }}} T^3$$ where ρ is in μΩ · cm, T is in K, and d (at 20°C) is in g · cm ^?3. The maximum uncertainties in the measured properties are estimated to be 3% for heat capacity and 1 % for electrical resistivity.     

Transient interferometric technique for measuring thermal expansion at high temperatures: Thermal expansion of tantalum in the range 1500–3200 K

The design and operational characteristics of an interferometric technique for measuring thermal expansion of metals between room temperature and temperatures in the range 1500 K to their melting points are described. The basic method involves rapidly heating the specimen from room temperature to temperatures above 1500 K in less than 1 s by the passage of an electrical current pulse through it, and simultaneously measuring the specimen expansion by the shift in the fringe pattern produced by a Michelson-type polarized beam interferometer and the specimen temperature by means of a high-speed photoelectric pyrometer. Measurements of linear thermal expansion of tantalum in the temperature range 1500–3200 K are also described. The results are expressed by the relation: $$\begin{gathered} (l - l_0 )/l_0 = 5.141{\text{ x 10}}^{ - {\text{4}}} + 1.445{\text{ x 10}}^{ - {\text{6}}} T + 4.160{\text{ x 10}}^{ - {\text{9}}} T^2 \hfill \\ {\text{ }} - 1.309{\text{ x 10}}^{ - {\text{12}}} T^3 + 1.901{\text{ x 10}}^{ - {\text{16}}} T^4 \hfill \\ \end{gathered}$$ where T is in K and l₀ is the specimen length at 20°C. The maximum error in the reported values of thermal expansion is estimated to be about 1% at 2000 K and not more than 2% at 3000 K.