High-pressure–temperature phase diagram and the equation of state of beryllium

Lazicki, Amy; Dewaele, Agnès; Loubeyre, P.; Mézouar, M.

doi:10.1103/physrevb.86.174118

Cited by 43 publications

(80 citation statements)

References 50 publications

(79 reference statements)

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“…In addition to the disappearance of all Bragg scattering, in many samples we were also able to observe the onset of rapid recrystallisation of the samples at clearly defined temperatures below that of the melting temperature. Similar behaviour has recently been reported in laser-heating diffraction studies of Be, 35 Mo 37 and Fe. 38 This recrystallisation behavior was clearly distin-guishable from the disappearance of the Bragg scattering at higher temperatures that we associated with melting.…”

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confidence: 61%

“…While this is necessary, however, it is not sufficient, and the observation of a diffuse halo of scattering from the liquid is also required for definitive proof of melting. But, for weakly scattering samples such as Li 36 and Be, 35 diffuse scattering from the liquid has not been observed, even in relatively large, resistivelyheated samples. In the current study, we were able to observe the disappearance of all Bragg scattering from the crystalline phases at clearly discernible temperatures, which we have interpreted as the melting temperature.…”

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confidence: 99%

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Equation of state and high-pressure/high-temperature phase diagram of magnesium

et al. 2014

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The phase diagram of magnesium has been investigated to 211 GPa at 300 K, and to 105 GPa at 4500 K, using a combination of x-ray diffraction and resistive and laser heating. The ambient pressure hcp structure is found to start transforming to the bcc structure at ∼45 GPa, with a large region of phase-coexistence that becomes smaller at higher temperatures. The bcc phase is stable to the highest pressures reached. The hcp-bcc phase boundary has been studied on both compression and decompression, and its slope is found to be negative, and steeper than calculations have previously predicted. The laser heating studies extend the melting curve of magnesium to 105 GPa, and suggest that at the highest pressures, the melting temperature increases more rapidly with pressure than previously reported. Finally, we observe some evidence of a new phase in the region of 10 GPa and 1200 K, where previous studies have reported a double-hexagonal closepacked (dhcp) phase. However, the additional diffraction peaks we observe cannot be accounted for by the dhcp phase alone.

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confidence: 61%

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confidence: 99%

Equation of state and high-pressure/high-temperature phase diagram of magnesium

et al. 2014

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“…At P > 11 GPa, bcc Be is dynamically stabilized by pressure and the QHA might, in principle, be applied. However, the hcp/bcc boundary [23][24][25] predicted by the QHA does not agree with experiments [13], suggesting that anharmonic effects still play an important role at higher pressures.In this Letter, we report a new investigation of the phase stability of bcc Be and the associated hcp → bcc phase transition boundary up to 30 GPa and temperatures up to 2,000 K. We have used a recently developed hybrid approach [30,31] that combines first-principles molecular dynamics (MD) and lattice dynamics calculations to address anharmonic effects in the free energy. In this method, the concept of phonon quasiparticles offers a quantitative characterization of the effects of lattice anharmonicity [32,33].…”

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confidence: 51%

“…Near the melting temperature T M (∼ 1, 550 K at 0 GPa), a competing phase with the body-centered cubic symmetry (bcc) seems to emerge [4][5][6]. However, not all experiments [7][8][9][10][11][12][13] have observed this bcc phase, causing confusion and controversies. Be is important for both fundamental research [14][15][16][17] and practical applications.…”

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Premelting hcp to bcc Transition in Beryllium

Sun

Zhang

et al. 2017

Phys. Rev. Lett.

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Beryllium (Be) is an important material with wide applications ranging from aerospace components to X-ray equipments. Yet a precise understanding of its phase diagram remains elusive. We have investigated the phase stability of Be using a recently developed hybrid free energy computation method that accounts for anharmonic effects by invoking phonon quasiparticles. We find that the hcp → bcc transition occurs near the melting curve at 0 < P < 11 GPa with a positive Clapeyron slope of 41 ± 4 K/GPa. The bcc phase exists in a narrow temperature range that shrinks with increasing pressure, explaining the difficulty in observing this phase experimentally. This work also demonstrates the validity of this theoretical framework based on phonon quasiparticle to study structural stability and phase transitions in strongly anharmonic materials.PACS numbers: 63.20. Ry, 81.30.Bx, 61.50.Ks,Elemental solids usually undergo a series of phase transitions from ambient conditions to extreme conditions [1][2][3]. Knowledge of their phase diagrams is a prerequisite for establishing their equations of state (EOS), a fundamental relation for determining thermodynamics properties and processes at high pressures and temperatures (PT). However, resolving phase boundaries is challenging for experiments given the uncertainties from several sources, especially at very high PT. Beryllium (Be) is a typical system whose phase diagram remains an open problem despite intense investigations. It assumes a hexagonal close-packed (hcp) structure at relatively low T [1]. Near the melting temperature T M (∼ 1, 550 K at 0 GPa), a competing phase with the body-centered cubic symmetry (bcc) seems to emerge [4][5][6]. However, not all experiments [7][8][9][10][11][12][13] have observed this bcc phase, causing confusion and controversies. Be is important for both fundamental research [14][15][16][17] and practical applications. Being a strong and light-weight metal, it has been widely used in a broad range of technological applications in harsh environments and extreme PT conditions, e.g., up to T > 4,000 K and P > 200 GPa [18][19][20][21][22].The bcc phase of Be was directly observed [4,5] only at T > 1, 500 K around ambient pressure before melting. Measurements of the temperature dependent resistance suggested that bcc Be is a high pressure phase and the hcp/bcc phase boundary between 0 < P < 6 GPa has a negative Clapeyron slope (−52 ± 8 K/GPa) [6]. However, recent experiments have challenged this conclusion [8,9,[11][12][13]. For example, it was reported that bcc Be was not observed for 8 < P < 205 GPa and 300 < T < 4, 000 K [13]. On the theory side, the study of Be's phase diagram using conventional methods encounters significant difficulties. The lattice dynamics of bcc Be is highly anharmonic, and the widely used quasi-harmonic approximation (QHA) and Debye model are not able to capture such effect [23][24][25][26][27][28][29]. For this reason, bcc Be and the associated hcp/bcc phase transition remain poorly understood for P < 11 GPa (density < 2.1g/...

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“…A temperature induced solid-solid phase transition at high pressure is difficult to find in a diamond anvil cell (DAC) experiment [1]. Moreover, at high pressures and temperatures it is difficult to discriminate a solid-solid phase transition from melting [2,3].…”

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confidence: 99%