Thermodynamic properties and structural phase transition of cerium under high pressure

Toward better understanding of the high-pressure structural transformation in beryllium by the statistical moment method

“…33 Having the SMM at hand, Masuda-Jindo et al 27 successfully explained the anharmonically stabilized mechanism of transition metals in the IV-B group. Hung et al 28,29 investigated the phase relations of rare-earth metals and achieved a good agreement with experimental data. Cuong et al 30,31 quantitatively captured the melting process of minerals in deep-planetary interiors by combining the SMM with the work-heat equivalence principle (WHEP).…”

“…Applying the above approach to the latest DFT outputs of Wu et al 20 yieldswhere R i and N i indicate the average radius and the coordination number of the i th neighboring cell, respectively. Similar to Masuda-Jindo et al 32 and Hung et al , 28,29 we set i max = 4 for hcp beryllium and i max = 5 for its bcc counterpart. Our fitted values of b 1 , b 2 , and b 3 are reported in Table 1.…”

“…The hcp-bcc transition takes place when DG is equal to zero. [27][28][29] We begin with the low-temperature regime. Fig.…”

“…Apart from DFT, the statistical moment method (SMM) has recently emerged as a viable solution for the phase-transition problem. [27][28][29][30][31] Fundamentally, the SMM enables a direct connection between the first-order moment of the atomic displacement and its high-order counterparts via the quantum density matrix. 32 Thus, the vibrational free energy and the equation of state (EOS) can be readily computed under various thermodynamic conditions.…”