Distortions and stabilization of simple-cubic calcium at high pressure and low temperature

Mao, Wendy L.; Wang, Lin; Ding, Yang; Yang, Wenge; Liu, Wenjun; Kim, Duck Young; Luo, Wei; Ahuja, Rajeev; Meng, Yue; Sinogeikin, Stanislav V.; Shu, Jinfu; Mao, Ho‐kwang

doi:10.1073/pnas.1005279107

Cited by 40 publications

(46 citation statements)

References 32 publications

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“…Increasing pressure at room temperature, Ca-I transforms to Ca-II with a body-centered cubic (bcc) structure at 20 GPa, to Ca-III with a simple cubic (sc) structure at 32 GPa (1,2,8), to Ca-IV (P4 1 2 1 2) at 119 GPa (3), to Ca-V (Cmca) at 143 GPa (3), to Ca-VI (Pnma) at 158 GPa (4), and to Ca-VII at 210 GPa (5). High-precision X-ray diffraction studies revealed rhombohedral (9) and orthorhombic distortions (4) of the sc structure. However, the distortions are very small.…”

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confidence: 99%

“…Finally, when the sample was warmed up to 299 K, the broad orthorhombic peaks gradually became narrower, indicating a transition from Cmmm to the sc phase, as described in ref. 9.…”

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confidence: 99%

“…The structures of the Cmmm (orthorhombic) and I4 1 ∕amd (tetragonal) phases can both be viewed as a distortion of the sc structure (9,13,14), and they were all observed by exploring the low-temperature areas. Our results indicate that the I4 1 ∕amd and Cmmm structures of Ca only exist in a very small pressure range just above the transition pressure from bcc to sc phase at room temperature.…”

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confidence: 99%

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Calcium with the β-tin structure at high pressure and low temperature

Ding

Yang

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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Using synchrotron high-pressure X-ray diffraction at cryogenic temperatures, we have established the phase diagram for calcium up to 110 GPa and 5-300 K. We discovered the long-sought for theoretically predicted β-tin structured calcium with I4 1 ∕amd symmetry at 35 GPa in a s mall low-temperature range below 10 K, thus resolving the enigma of absence of this lowest enthalpy phase. The stability and relations among various distorted simple-cubic phases in the Ca-III region have also been examined and clarified over a wide range of high pressures and low temperatures.phase transition | structure distortion A t high pressures, calcium (Ca) not only displays very rich structural changes (1-5) but also holds the record for the highest superconducting critical temperature (T c ¼ 26 K) among elemental materials (5-7). Ca is currently one of the most studied elements under high pressure. A series of phase transitions have been observed in previous experiments. Under ambient conditions, Ca crystallizes in a face-centered cubic (fcc) structure (Ca-I). Increasing pressure at room temperature, Ca-I transforms to Ca-II with a body-centered cubic (bcc) structure at 20 GPa, to Ca-III with a simple cubic (sc) structure at 32 GPa (1, 2, 8), to Ca-IV (P4 1 2 1 2) at 119 GPa (3), to Ca-V (Cmca) at 143 GPa (3), to Ca-VI (Pnma) at 158 GPa (4), and to Ca-VII at 210 GPa (5). High-precision X-ray diffraction studies revealed rhombohedral (9) and orthorhombic distortions (4) of the sc structure. However, the distortions are very small. In this paper, we refer these slightly distorted sc structure generally as Ca-III for simplicity.Among the high-pressure phases, the Ca-III phase is particularly intriguing. The pressure-induced electronic transition from a normal metal to a superconductor occurs in the Ca-III phase region above 44 GPa (10, 11), and the T c increases with pressure from 2 K to 10 K within the Ca-III region (6). Ca-III is also a very active test case of modern theories and experiments, where a number of paradoxes arise (12-18). Based on density-functional theory (DFT) calculations, Ca-III with sc structure has imaginary phonon frequencies, indicating dynamic instability (19-21). On the other hand, high-pressure room temperature experiments confirmed that Ca-III adopts the nearly sc structure (8). To overcome this discrepancy, Teweldeberhan et al. (16) (17) provided a detailed analysis of ab initio molecular dynamics simulations that could account for the stability of the sc structure at room temperature. The remaining major discrepancy is that Yao et al. (14) and Oganov et al. (13) predicted that Ca with I4 1 ∕amd symmetry (β-tin structure) has a much lower zero-temperature enthalpy than sc, but in spite of many experimental efforts, the presumably more stable β-tin structured Ca has never been discovered. Here we report the search and discovery of the β-tin structured Ca and establish its stability range.To study the stability of sc Ca at ground state, Mao et al. (9) performed low-temperature experiments and observed an...

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confidence: 99%

“…Finally, when the sample was warmed up to 299 K, the broad orthorhombic peaks gradually became narrower, indicating a transition from Cmmm to the sc phase, as described in ref. 9.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Calcium with the β-tin structure at high pressure and low temperature

Ding

Yang

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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“…[10][11][12][13][14][15][16][17][18][19][20] Ab initio phonon calculations within semi-local approximation (SLA) showed that the SC structure exhibits severely imaginary (unstable) phonons.…”

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confidence: 99%

“…9 Extensive debates have been recently focused on the validity of the observed SC phase. [10][11][12][13][14][15][16][17][18][19][20] Ab initio phonon calculations within semi-local approximation (SLA) showed that the SC structure exhibits severely imaginary (unstable) phonons. 12,13 Subsequently, structure prediction studies 10,21 proposed a body-centered tetragonal I4 1 /amd structure, which is calculated to be energetically more stable than the SC structure within SLA over the entire pressure range of Ca-III.…”

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Hybrid functional study rationalizes the simple cubic phase of calcium at high pressures

Liu

Cui

2012

The Journal of Chemical Physics

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Simple cubic (SC) phase has been long experimentally determined as the high-pressure phase III of elemental calcium (Ca) since 1984. However, recent density functional calculations within semi-local approximation showed that this SC phase is structurally unstable by exhibiting severely imaginary phonons, and is energetically unstable with respect to a theoretical body-centered tetragonal I4 1 /amd structure over the pressure range of phase III. These calculations generated extensive debates on the validity of SC phase. Here we have re-examined the SC structure by performing more precise density functional calculations within hybrid functionals of Heyd-Scuseria-Erhzerhof (HSE) and PBE0. Our calculations were able to rationalize fundamentally the phase stability of SC structure over all other known phases by evidence of its actual energetic stability above 33 GPa and its intrinsically dynamical stability without showing any imaginary phonons in the entire pressure range studied. We further established that the long-thought theoretical I4 1 /amd structure remains stable in a narrow pressure range before entering SC phase and is actually the structure of experimental Ca-III' synthesized recently at low temperature 14 K as supported by the excellent agreement between our simulated X-ray diffraction patterns and the experimental data. Our results shed strong light on the crucial role played by the precise electron exchange energy in a proper description of the potential energy of Ca.PACS numbers: 61.50. Ks, 63.20.dk, 71.20.Dg High-pressure polymorphs of elemental Ca exhibit complicated and somewhat mysterious behaviors. X-ray diffraction (XRD) experiments established that at room temperature Ca transforms from its ambient-pressure face-centered cubic structure (FCC, Ca-I) to the body-centered cubic structure (BCC, Ca-II) at 19 GPa, 1 and then to a simple cubic structure (SC, Ca-III) at 32GPa. [2][3][4][5] This transition sequence is rather unusual as accompanied by a decrease of coordination numbers (12 → 8 → 6). Ca-III remains remarkably stable up to 113 GPa and then transforms to Ca-IV [3]. Several other higher pressure phases of Ca-V, Ca-VI and Ca-VII were also observed at 139, 158 and 210 GPa, respectively. 3,4,6,7 One intriguing physical phenomenon of Ca is the observed superconductivity 8 with T c = 2 K at 44 GPa as the consequence of phase transitions. It is strikingly found that T c increases with pressure, reaching 25 K at 161 GPa, a record high among all known elemental superconductors. 9Extensive debates have been recently focused on the validity of the observed SC phase. [10][11][12][13][14][15][16][17][18][19][20] Ab initio phonon calculations within semi-local approximation (SLA) showed that the SC structure exhibits severely imaginary (unstable) phonons. 12, 13Subsequently, structure prediction studies 10, 21 proposed a body-centered tetragonal I4 1 /amd structure, which is calculated to be energetically more stable than the SC structure within SLA over the entire pressure range of Ca-III. These ca...

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Synchrotron Radiation Experimental Techniques

Tai

Huang

et al. 2018

Synchrotron Radiation in Materials Science

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Distortions and stabilization of simple-cubic calcium at high pressure and low temperature

Cited by 40 publications

References 32 publications

Calcium with the β-tin structure at high pressure and low temperature

Calcium with the β-tin structure at high pressure and low temperature

Hybrid functional study rationalizes the simple cubic phase of calcium at high pressures

Synchrotron Radiation Experimental Techniques

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