Four-parameter equation of state and determination of the thermal and mechanical properties of metals

An Equation of State for Metals at High Temperature and Pressure in Compressed and Expanded Volume Regions

“…Results of such analyses are then used in semi-empirical expressions. We propose to use a four-parameter model, developed by Li et al [16], which is expressed as:…”

“…The specific volume V c0 is slightly lower than the volume at ambient conditions (T 0 = 300 K and P 0 = 1 bar). In our approach, we adjust the value of V c0 such that the zero-temperature pressure together with thermal pressure of ions and electrons is just one bar at 300 K. The four-parameter model is a refinement over Rose equation [17] and Vinet equation [18], and is found to provide quite accurate descriptions of the zero-temperature energy and pressure over compressed volume up to ∼V c0 /2, which corresponds to about 100-150 GPa pressure, for about forty metals [16]. It also provides accurate representation for energy and pressure in the expanded volume up to about ∼2V c0 .…”

“…The factors 1/2 and 2 in Equation 7arise because U(x) is the energy for two atoms; while E cold (x) is the energy per atom. Uncorrected energy E Li (V) for Cu (curve-1) according to the four-parameter model [16] and the zero-temperature energy E cold (x) corrected with QSM model (curve-2) as given in Equation 6. The insert figure shows pressure.…”

“…The positive root gives n = 8.803 and m = 2.901 for Cu. The accuracy of the generalized Lennard-Jones model can be assessed by comparing it with the four-parameter model [16] discussed earlier. In Figure 3A, we compare the repulsive component of the interparticle potential for Cu.…”

“…Figure 3B shows the generalized Lennard-Jones energy and pressure, which compare quite well. Comparison of repulsive part of inter-particle potential for Cu versus scaled inter-particle distance (V/V 0 ) 1/3 , using four-parameter model (curve-1) [16] and generalized Lennard-Jones model (curve-2). (B) Scaled cohesive energy and pressure using four-parameter model (solid lines) [16] and generalized Lennard-Jones model (symbols).…”