Thermodynamic Phase Diagram of Beryllium Using Our Phonon Quasiparticle Approach
Update: 2018-02-24 10:12:48      Author:

Beryllium (Be) has been applied widely in various industry areas, especially for nuclear weapon design. It is also an important material for fundamental research such as plasmonics under high pressure. Therefore, it is important to understand the phase stability of Be under extreme conditions. However, there are controversy and debating about the existence of its bcc phase and the associated hcp → bcc transition both experimentally and theoretically. The phase stability of Be has been extensively studied experimentally. However, in most of experiments, no sign of bcc symmetry was ever captured [PRB 86, 174118 (2012); PRB 72, 094113 (2005); J. Phys. F 14, L1 (1984); J. Phys. F 14, L65 (1984); JPCM 14, 10569 (2002); PRB 65, 172107 (2002); PRB 79, 064106 (2009).]. So far, only three experimental reports declared the observation of bcc phase. Martin and Moore captured bcc Be at 1500 K near the melting temperature (~ 1550 K) at ambient pressure [J. Less-Common Met. 1, 85 (1959)], Abey provided a positive hcp/bcc phase boundary, [NTRL NTIS 198506, 1984]. However, Francois and Contre reported a negative hcp/bcc phase boundary [Proceedings of the Conference Internationale sur la Metallurgie du Beryllium, Grenoble (Presses Universitaires de France, Paris, 1965)]. On the theoretical side, the investigation of bcc Be with traditional methods encounters difficulty. This is because that the stabilization of bcc Be is primarily driven by lattice anharmonicity. Unfortunately, widely used quasi-harmonic approximation (QHA) and Debye model are not able to capture such effect. For this reason, theoretical transition is still missing for P < 11 GPa. When P > 11 GPa, bcc Be is stabilized by pressure and QHA has been extensively employed. Nonetheless, the QHA predicted hcp/bcc boundary shows significantly discrepancy from the experimental revelation. This presumably hints that the anharmonic effect is also pronounced at high pressure [J. Phys. IV France 134, 257 (2006); PRB 82, 104118 (2010); JAP 111, 053503 (2012); PRB 79, 064106 (2009); PRB 71, 214108 (2005); PRB 76, 235109 (2007); RB 75, 035132 (2007)].

Using a novel approach which characterizes phonon quasiparticles from first-principles calculations, the research group led by Dong-Bo Zhang at Beijing Computational Science Research Center carried out a systematic study of phase stability of Be under high pressure and high temperature. The outcomes show that Be exhibits pronounced anharmonic effects in both the bcc and hcp phases. The bcc phase, however, is favorable only in a very narrow temperature range near the melting temperature with a positive Clapeyron slope of ~ 41K/GPa. The temperature range where the bcc phase exists shrinks with increasing pressure and eventually disappears at around 11 GPa. This result agrees well with experiments.


 Fig. 1: Phase diagram of Be. The melting line is dopted from PRB 82, 104118 (2010). The experimental results for the hcp/bcc phase boundary are shown for comparison.



Y. Lu, T. Sun, Ping Zhang, P. Zhang, Dong-Bo Zhang*, and R. M. Wentzcovitch, Pre-melting hcp to bcc Transition in Beryllium, Physical Review Letters 118, 145702 (2017).

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