Equation of state for solids with high accuracy and satisfying the limitation condition at high pressure

Abstract An equation of state (EOS) with high accuracy is proposed to strictly satisfy the Fermi gas limitation condition at high pressure. The EOS (SJX EOS) is a modification of the effective Rydberg (ER2) EOS. Instead of Holzapfel's method to directly modify the ER2 EOS, one modifying term is added to the ER2 EOS to make it not only satisfy the high pressure limitation condition, but also to avoid the disadvantages occurring in the Holzapfel and ‘adapted polynomial expansion of the order 3’ (AP3) EOSs. The two-parameter ER2, Holzapfel, and three-parameter SJX, AP3, Kumari and Dass (KD) EOSs are applied to 50 materials to fit all experimental compression data available. The five EOSs also are applied to 37 of the 50 materials to fit experimental compression data at low-pressure ranges. The results show that for all pressure ranges the AP3 EOS gives the best fitting results; the SJX, ER2, Holzapfel and KD EOSs sequentially give inferior results. Otherwise, it is shown that the values of B 0 , B 0 ′ and B 0 ″ are different for different EOSs and also, within one EOS, for high and low-pressure ranges. The SJX EOS gives the best consistency between the values obtained by fitting all experimental data available, and the experimental data at low-pressure ranges, respectively. The AP3 EOS gives the worst results. The differences of the values of B 0 , B 0 ′ and B 0 ″ obtained for the ER2, Holzapfel and KD EOSs with those obtained for the SJX EOS are large at high-pressure ranges, but decrease at low-pressure ranges. At present, the newest experimental compression data, within the widest compression range, are available for solid n -H 2 . The values of B 0 , B 0 ′ and B 0 ″ fitted by using the SJX EOS are almost in agreement with these experimental data. The ER2 EOS gives inferior values, and other EOSs give fairly bad results. For the predicted compression curves and the cohesive energy, the SJX EOS gives the best results; the AP3 EOS gives the worst results, even for many solids the AP3 EOS cannot give physically correct results for the cohesive energy. The analysis shows that for such solids, the variation of pressure and energy versus compression ratio calculated by using the AP3 EOS would oscillate, physically incorrectly. Although the AP3 EOS has the best fitting ability to the pressures, it has the worst predicting ability, and fails to be a universal EOS. The SJX EOS is recommended and can be taken as a candidate of universal EOSs to predict compression curves of solids in a wide pressure range only using the values of B 0 , B 0 ′ and B 0 ″ obtained from low-pressure data.