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.     

Thermal expansion of manganese carbonate

Precision lattice parameters of manganese carbonate have been determined at different temperatures by the X-ray powder method in the temperature range 28 to 265° C. The data has been used to evaluate, by a graphical method, the two coefficients of thermal expansion,α _∥ along thec-axis andα _⊥ at right-angles to thec-axis. The temperature-dependence of the coefficients is represented by the following equations: 1 $$\begin{gathered} \alpha _\parallel = 22.942 \times 10^{ - 6} - 5.555 \times 10^{ - 8} T + 3.361 \times 10^{ - 10} T^2 ,{\text{ }}(1) \hfill \\ \alpha _ \bot = 0.740 \times 10^{ - 6} + 2.812 \times 10^{ - 8} T - 6.722 \times 10^{ - 12} T^2 ,{\text{ (2)}} \hfill \\ \end{gathered} $$ whereT is the temperature in ° C.     

Heat capacity and electrical resistivity of nickel in the range 1300–1700 K measured with a pulse heating technique

Measurements of the heat capacity and electrical resistivity of nickel in the temperature range 1300–1700 K by a subsecond duration pulse heating technique are described. The results are expressed by the relations: $$\begin{gathered} C_p = 21.735 + 9.8200 \times 10^{ - 3} T \hfill \\ \rho = 18.908 + 2.3947 \times 10^{ - 2} T \hfill \\ \end{gathered} $$ whereC _p is in J · mol^?1·K^?1,ρ is inμΩ·cm, andT is in K. Estimated maximum uncertainties in the measured properties are 3% for heat capacity and 1% for electrical resistivity.     

Heat capacity of liquid benzene and hexafluorobenzene at atmospheric pressure

Heat capacity, Cp, of benzene and hexafluorbenzene was measured in the liquid phase at atmospheric pressure in the temperature range from 280 K to the boiling point. The results are expressed by the following equations: for C₆H₆, for C₆F₆, $$\begin{gathered} C_p = 1.5194 - 1.299x10^{ - 3} T + 6.927 \times 10^{ - 6} T^2 \hfill \\ for C_6 F_6 \hfill \\ C_p = 1.1913 - 1.072x10^{ - 3} T + 3.589 \times 10^{ - 6} T^2 \hfill \\ \end{gathered} $$ where C _p is in kJ · kg^?1 · K^?1 and T is in K. The limiting error of heat capacity calculated from these equations is 0.23% for benzene and 0.18% for hexafluorobenzene. From the data, equations for specific volume, thermal expansion coefficient, and the quantity (δT/δp)_s were obtained for benzene and hexafluorobenzene.     

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.     

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.     

Thermal expansion of copper,silver, and gold below 30 K

A variable transformer technique has been used to determine the linear thermal expansion coefficients of the noble metals from 4 to 30 K. The precision of the data initially was ±0.04 Å, and this was later increased to ±0.015 Å, resulting in a sensitivity of approximately 2×10^?11 for relative length changes of a 10-cm-long sample. The results agree at all temperatures (to better than 5%) with those of White and Collins who used a differential capacitor technique. The differences are 2% or less above 20 K for Cu, above 8 K for Ag, and at all temperatures for Au. The differences between the two sets of data for the three metals are not systematic (α_WC greater for Cu, less for Ag) and may be due to differences in sample purity since much larger low-temperature anomalies were found within each set for certain samples of Cu and Ag. The resulting electronic Grüneisen parameters γ_e and theT=0 lattice Grüneisen parameters γ₀ are as follows: $$\begin{gathered} copper \gamma _{\text{e}} = 0.91 \pm 0.05 \gamma _{\text{0}} = 1.67 \pm 0.02 \hfill \\ silver \gamma _{\text{e}} = 1.18 \pm 0.15 \gamma _{\text{0}} = 2.29 \pm 0.03 \hfill \\ gold \gamma _{\text{e}} = 1.6 \pm 0.5 \gamma _{\text{0}} = 2.96 \pm 0.04 \hfill \\ \end{gathered} $$ The values of γ₀ are in reasonable (5% at worst) agreement with elastic constant values.     

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.     

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.

Isothermal transformation and decomposition ofβ 1 phase in a CuZnAl alloy

In the present paper, the crystallography of isothermal transformation and decomposition ofβ, phase have been studied by means of transmission electron microscopy and diffraction in the CuZnAl shape memory alloy. It has been proved that the bainite formed inβ ₁, matrix when the samples were transformed isothermally at moderate temperature. The crystallography of the isothermal bainitic transformation is identical to that of martensite in the same system. When the specimens were aged at moderate temperatures for longer time, the bainite and matrix decomposed to equilibrium phases. The decomposition process can be summarized as follows: $$\begin{gathered} bainite (9R) \to 9R + \alpha \left( {fcc} \right) \to \alpha + \beta \left( {bcc} \right) \hfill \\ matrix (B2) \to 2H + B2 \to \beta \left( {bcc} \right) \hfill \\ \end{gathered} $$ There are definite orientation relationships among these phases during the decomposition process and they are shown below: $$\begin{gathered} \left( {111} \right)_\alpha \parallel \left( {001} \right)_B ,\left[ {0\bar 11} \right]_\alpha \parallel \left[ {\bar 110} \right]_B \hfill \\ \left( {111} \right)_\alpha 5^ \circ away from \left( {110} \right)_\beta ,\left[ {0\bar 11} \right]_\alpha \parallel \left[ {1\bar 1\bar 1} \right]_\beta \hfill \\ \left( {110} \right)_M \parallel \left( {001} \right)_{2H} ,\left[ {001} \right]_M \parallel \left[ {010} \right]_{2H} \hfill \\ \end{gathered} $$ Thus, the crystallography of isothermal transformation and decomposition ofβ ₁ phase and the sequence of transitions have been revealed.     

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.     

Thermal expansion of molybdenum in the range 1500–2800 K by a transient interferometric technique

The linear thermal expansion of molybdenum has been measured in the temperature range 1500–2800 K by means of a transient (subsecond) interferometric technique. The molybdenum selected for these measurements was the Standard Reference Material SRM 781 (a high-temperature enthalpy and heat capacity standard). The results are expressed by the relation where T is in K and l ₀ 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 2800 K.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Thermal expansion of tungsten in the range 1500–3600 K by a transient interferometric technique

The linear thermal expansion of tungsten has been measured in the temperature range 1500–3600 K by means of a transient (subsecond) interferometric technique. The tungsten selected for these measurements was the standard reference material SRM 737 (a standard for thermal expansion measurements at temperatures up to 1800 K). The basic method involved rapidly heating the specimen from room temperature up to and through the temperature range of interest in less than 1 s by passing an electrical current pulse through it and simultaneously measuring the specimen temperature by means of a high-speed photoelectric pyrometer and the shift in the fringe pattern produced by a Michelson-type interferometer. The linear thermal expansion was determined from the cumulative shift corresponding to each measured temperature. The results for tungsten may be expressed by the relation $$\begin{gathered} (l - l_0 )/l_0 = 1.3896 \times 10^{ - 3} - 8.2797 \times 10^{ - 7} T + 4.0557 \times 10^{ - 9} T^2 \hfill \\ - 1.2164 \times 10^{ - 12} T^3 + 1.7034 \times 10^{ - 16} T^4 \hfill \\ \end{gathered} $$ whereT is in K andl ₀ 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 approximately 2% at 3600 K.     

The thermodynamic parameters of monomer and dimer molecules of cerium and praseodymium tribromides

The method of high-temperature mass spectrometry is used for studying the composition of saturated vapor over cerium and praseodymium tribromides. Monomer and dimer molecules are found in the temperature ranges of 789–994 K and 804–957 K for cerium and praseodymium, respectively. The partial pressures of vapor components are determined, p(Pa), the temperature dependences of which are approximated by the equations

$\begin{gathered} \log p(CeBr_3 ) = ( - 14.63 \pm 0.08) \times 10^3 /T + (14.54 \pm 0.09), T = 789 - 994 K; \hfill \\ \log p(Ce_2 Br_6 ) = ( - 19.72 \pm 0.61) \times 10^3 /T + (17.60 \pm 0.64), T = 918 - 980 K; \hfill \\ \log p(PrBr_3 ) = ( - 14.13 \pm 0.12) \times 10^3 /T + (14.09 \pm 0.14), T = 804 - 957 K; \hfill \\ \log p(Pr_2 Br_6 ) = ( - 18.90 \pm 0.50) \times 10^3 /T + (17.15 \pm 0.53), T = 903 - 955 K. \hfill \\ \end{gathered} $

The values of pressure of vapor components are used along with literature data for the calculation of enthalpies of sublimation in the form of monomer and dimer molecules by the procedures of the second and third laws of thermodynamics. Based on analysis of the results, thermodynamic parameters of monomer and dimer molecules (in kJ mol^?1) are recommended,

$\begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Delta _s H^0 (CeBr_3 , 298.15) = 305 \pm 5, \Delta _s H^0 (PrBr_3 , 298.15) = 293 \pm 5, \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Delta _s H^0 (Ce_2 Br_6 , 298.15) = 410 \pm 28, \Delta _s H^0 (Pr_2 Br_6 , 298.15) = 403 \pm 28, \hfill \\ \,\,\,\,\,\,\,\Delta _f H^0 (CeBr_3 , gas, 298.15) = - 587 \pm 6, \Delta _f H^0 (PrBr_3 , gas, 298.15) = - 597 \pm 7, \hfill \\ \Delta _f H^0 (Ce_2 Br_6 , gas, 298.15) = - 1372 \pm 28, \Delta _f H^0 (Pr_2 Br_6 , gas, 298.15) = - 1378 \pm 28. \hfill \\ \end{gathered} $

     

The effects of hydrostatic pressure on the ductility of metals and alloys

A law governing the change in the ductility of metals and alloys under pressure is given: $$\begin{gathered} \left( {\frac{P}{{\sigma _n }}} \right) = \tfrac{1}{2}\frac{1}{{\sigma _n }}\frac{{d\sigma }}{{d\varepsilon }}\{ \varepsilon _{local} (P)^{\tfrac{3}{2}} - \varepsilon _{local} (O)^{\tfrac{3}{2}} \} + \tfrac{1}{3}\frac{1}{{\sigma _n }}\frac{{d\sigma }}{{d\varepsilon }}\{ \varepsilon _{local} (P) - \varepsilon _{local} (O)\} + \hfill \\ {\text{ }} + \tfrac{1}{2}\{ \varepsilon _{local} (P)^{\tfrac{1}{2}} - \varepsilon _{local} (O)^{\tfrac{1}{2}} \} \hfill \\ \end{gathered}$$ where P is the hydrostatic pressure, ?_local is the strain accumulated from the start of necking to fracture, σ _n necking stress and (dσ/d?) the coefficient of linear work hardening. This relation is derived from a newly proposed criterion of ductile fracture, viz. “constancy of hydrostatic tensile stress”, which indicates that the change of ductility with pressure obeys a three halves power law. The observed increase in ductility of widely differing metals and alloys under pressure up to 10,000 kg/cm⁴ has confirmed that the proposed criterion is acceptable. It is further shown that the ductilities of some copper alloys with low stacking fault energy, such as Cu-Zn and Cu-Ge alloys, increases with pressure at the beginning but the increase stops at fairly low pressure, i.e. 3,500 ～ 4,000 kg/cm², and their ductilities become almost insensitive to the pressure applied. It is suggested that ductile fracture of metals with low stacking fault energy is dominated by a process which occurs not by the hydrostatic stress component but by shear stress only.     

Thermal expansion of copper,silver, and gold at low temperatures

Improvements have been made in a differential dilatometer using the three-terminal capacitance detector. The dilatometer is of copper and has been calibrated from 1.5–34 K in an extended series of observations using silicon and lithium fluoride as low-expansion reference materials. The expansion of silver and gold samples has been measured relative to the dilatometer, while the calibrations themselves have been used to determine the expansion of copper relative to the reference materials. Analyses of six sets of observations indicate that below 12 K the linear expansion coefficient α of copper is represented by $$10^{10} \alpha = (2.1_5 \pm 0.1){\rm T} + (0.284 \mp 0.005){\rm T}^3 + (5 \pm 3) \times 10^{ - 5} T^5 K^{ - 1} $$ corresponding to respective electronic and lattice Grüneisen parameters γ _e =0.9 ₃ and γ ₀ =γ ₁ =1.78. Measurements on oxygen-free silver yield $$10^{10} \alpha = (1.9 \pm 0.2){\rm T} + (1.14 \mp 0.03){\rm T}^3 + (2 \pm 2) \times 10^{ - 4} T^5 K^{ - 1} $$ below 7 K, whence γ _e ? 0.9 ₇ , γ ₀ =γ ₁ =2.23. By contrast, silver containing ca. 0.02 at. % oxygen showed a much larger expansion at the lowest temperatures: below 7 K, 10 ¹⁰ α ～ 7T+1.19T ³ . We have not been able to obtain an unambiguous representation for gold, but find a reasonable fit below 7 K to be $$10^{10} \alpha \simeq (1 \pm 0.5){\rm T} + (2.44 \mp 0.05){\rm T}^3 - (5 \pm 1) \times 10^{ - 3} T^5 K^{ - 1} $$ with γ ₁ ? 2.94 and γ _e ? 0.7 (free-electron value).     

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 $$\begin{gathered} W(s) + \tfrac{1}{2} Cr_2 O_3 (s) + \tfrac{5}{4} O_2 (g) \to CrWO_4 (s) \hfill \\ \Delta G^0 = - 172 047 + 48.725T ( \pm 230) cal mol^{ - 1} \hfill \\ Cr_2 O_3 (s) + WO_3 (s) \to Cr_2 WO_6 (s) \hfill \\ \Delta G^0 = - 3 835 + 0.235{\rm T} ( \pm 500) cal mol^{ - 1} \hfill \\ \end{gathered}$$      

Carbothermal nitridation synthesis of α-Si3N4 powder from pyrolysed rice hulls

The carbothermal nitridation synthesis of α-Si₃N₄ was studied using a high-temperature tube furnace to react a precursor, comprised of pyrolysed rice hulls (C/SiO₂) and additive “seed” Si₃N₄, with N₂. The experimental design for synthesis was a three-level factorial surface response design for determining the effect of temperature (1300–1380°C) and reaction time (1–5 h) on kinetics. In addition, all precursors were reacted at 1460, 1480 and 1500°G for 5 h in order to ensure high conversion suitable for product powder evaluation (composition and morphology). Following excess carbon removal, the product Si₃N₄ was >95% α-phase and had a surface area of 7.7 m²g^?1 with an oxygen content of 3.6 wt% O. The powder was comprised of a bimodal size distribution of submicrometre solid α-Si₃N₄ crystallites centred at 0.03 and 0.22 μm. No whiskers or high aspect ratio elongated crystallites were found in the powder. The addition of carbon black to the seeded pyrolysed rice hull C/SiO₂ mixture had no significant impact on the reaction rate or product powder properties. The reaction was modelled using a nuclei-growth rate expression as $$\begin{gathered} (kt)^{0.58} = - ln(1 --- X) \hfill \\ k = 1.09 \times 10^{10} exp (--- 50502/T) \hfill \\ \end{gathered} $$ k=1.09×10¹⁰ exp (?50502/T) where (1573 K<T<1653 K), (3600<t<18000 s), (0<X<1), andk=rate in s^?1.     

Mass transport of cobalt and nickel in Incoloy-800

Lattice diffusion of cobalt and nickel in Incoloy-800 has been studied in the temperature range 1070 to 1500K by serial sectioning and residual activity techniques using radioactive tracers⁶⁰Co and⁶³Ni. The lattice diffusion coefficient can be expressed by the relation: