Correlation of temperature dependencies of thermal expansion and heat capacity of refractory metal up to the melting point: Molybdenum

Abstract

By the example of molybdenum, the detailed correlation investigation between the volume thermal expansion coefficient, o(T), and the heat capacity, C(T), of the refractory metal is carried out. It is shown that distinct correlation of o(C) takes place not only within the low temperature region where it is linear and is known as the Gruneisen law but also within a much wider temperature region, up to the melting point of the metal. Essential deviation of the o(C) dependency from the low temperature linear behavior takes place when the heat capacity achieves its classical Dulong and Petit limit, 3R

Equation of state of Mo from shock compression experiments on preheated samples

“…The density of Mo at 1673 K was calculated from the reported thermal expansion data. [26][27][28] The difference of specific internal energies of Mo between room-T and 1673 K was calculated from the specific heat at constant pressure. [28][29][30] The uncertainties of density and specific internal energy difference at any particular temperature were evaluated as root-mean square deviations about the average values among the three sources for each quantity, assuming uncorrelated data.…”

“…[26][27][28] The difference of specific internal energies of Mo between room-T and 1673 K was calculated from the specific heat at constant pressure. [28][29][30] The uncertainties of density and specific internal energy difference at any particular temperature were evaluated as root-mean square deviations about the average values among the three sources for each quantity, assuming uncorrelated data. Full uncertainties took into account variations of thermodynamic parameters with the initial temperature, which is known to 63 K. 9 Since this is an unconstrained fit of (U 2 , D 2 ) data without any relationship to (U 1 , D 1 ) data, it is not forced to yield a consistent value of the nominally constant parameter c 0 .…”

“…[40][41][42] Only three sets of cðTÞ data are shown in Figure 4 as reported. [37][38][39] All other cðTÞ curves or discrete data points were recalculated from the reported K s ðTÞ experimental values [40][41][42] or cðVÞ models 3,5,6,36,43,44 using the same aðTÞ [26][27][28] and C p ðTÞ [28][29][30] functions that we applied in constructing our Mo EOS. FIG.…”

Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow

“…Previous work compared averaged experimental values of α and c P and found equality at low T but a linear dependence at high T [ 27 , 28 , 29 , 30 ]. Bodryakov and colleagues [ 27 , 28 , 29 , 30 ] explained the discontinuous behavior on the basis of vibrations being the main energy reservoir in a solid, and did not consider elastic energy. Our derivation of Equation (43) suggests continuous behavior, but we have not yet incorporated the rigidity of solids.…”

“…Previous comparisons of α( T ) to c P ( T ) averaged many data sets [ 27 , 28 , 29 , 30 ], which removes random errors. Because systematic errors also exist, we compare individual data sets in Figure 16 a which should accurately represent each of α( T ) and c P ( T ).…”