Simple-cubic–simple-hexagonal transition in phosphorus under pressure

Akahama, Yuichi; Kobayashi, Masakazu; Kawamura, Haruki

doi:10.1103/physrevb.59.8520

Cited by 91 publications

(101 citation statements)

References 28 publications

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“…The α' phase is seen to have a smaller zero pressure volume and larger bulk modulus, or incompressibility, than the α phase which we would expect. White phosphorus transformed into orthorhombic black phosphorus at 2.68 ± 0.34 GPa and then transformed into rhombohedral and simple cubic black phosphorus with increasing pressure as expected from previous work [20,25]. On decreasing pressure the sample remained as black phosphorus transforming from simple cubic to rhombohedral and then orthorhombic in which form it remained to ambient pressure.…”

Section: Discussionsupporting

confidence: 50%

“…These are compared with the data of Kikegawa and Iwasaki [20] and Akahama et al [25] in Figure 6. We used the KolmogorovSmirnov test to compare these three datasets with each other.…”

Section: The Stability and Equations Of State Of Black Phosphorusmentioning

confidence: 99%

“…We used the KolmogorovSmirnov test to compare these three datasets with each other. Comparison of the Kikegawa and Iwasaki [20] dataset with the Akahama et al [25] Since these confidence levels are all well above 0.01 it is appropriate to combine these datasets together. A second order Birch-Murnaghan equation was found to be sufficient to fit these data.…”

Section: The Stability and Equations Of State Of Black Phosphorusmentioning

confidence: 99%

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Compressibility of cubic white, orthorhombic black, rhombohedral black, and simple cubic black phosphorus

Clark

Zaug

2010

Phys. Rev. B

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The effect of pressure on the crystal structure of white phosphorus has been studied up to 22.4 GPa. The α phase was found to transform into the α' phase at 0.87 ± 0.04 GPa with a volume change of 0.1 ± 0.3 cc/mol. A fit of a second order BirchMurnaghan equation to the data gave Vo = 16.94 ± 0.08 cc/mol and K o = 6.7 ± 0.5 GPa for the α phase and Vo = 16.4 ± 0.1 cc/mol and K o = 9.1 ± 0.3 GPa for the α' phase. The α' phase was found to transform to the A17 phase of black phosphorus at 2.68 ± 0.34 GPa and then with increasing pressure to the A7 and then simple cubic phase of black phosphorus. A fit of a second order Birch-Murnaghan equation to our data combined with previous measurements gave Vo = 11.43 ± 0.05 cc/mol and K o = 34.7 ± 0.5 GPa for the A17 phase, Vo = 9.62 ± 0.01 cc/mol and K o = 65.0 ± 0.6 GPa for the A7 phase and , Vo = 9.23 ± 0.01 cc/mol and K o = 72.5 ± 0.3 GPa for the simple cubic phase. PACS numbers:Phase transitions, crystallographic aspects of, 61.50.KsHigh-pressure effects, structural properties of materials, 81.40.Vw X-ray diffraction in crystal structure, 61.05.cp

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Section: Discussionsupporting

confidence: 50%

“…These are compared with the data of Kikegawa and Iwasaki [20] and Akahama et al [25] in Figure 6. We used the KolmogorovSmirnov test to compare these three datasets with each other.…”

Section: The Stability and Equations Of State Of Black Phosphorusmentioning

confidence: 99%

Section: The Stability and Equations Of State Of Black Phosphorusmentioning

confidence: 99%

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Compressibility of cubic white, orthorhombic black, rhombohedral black, and simple cubic black phosphorus

Clark

Zaug

2010

Phys. Rev. B

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“…1 Some elements have interesting structures beyond the simple cubic ͑sc͒ lattice at high pressure. Phosphorus has the sc structure ͑P-III͒ from 10 to 107 GPa, 2 which transforms, at 107 GPa, to a complex structure 3 ͑P-IV͒ whose structure has long been unidentified. But it has recently been theoretically predicted 4 and experimentally confirmed 5 to be an incommensurately modulated structure.…”

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confidence: 99%

Theoretical study of the structure of calcium in phases IV and V viaab initiometadynamics simulation

et al. 2008

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We searched for the structure of calcium in phases IV and V by a metadynamics simulation based on ab initio calculations, and found two structures. One is a tetragonal lattice which consists of two helical chains along the c axis. The other is an orthorhombic lattice of four zigzag chains. We have calculated the x-ray diffraction patterns and enthalpies of the two structures discovered by our simulation. From comparisons of the patterns with the experimental x-ray patterns of the phases IV and V and from the pressure dependence of the enthalpies, we conclude that the structure with a helical pattern corresponds to phase IV and the structure with a zigzag pattern to phase V. Studies have revealed that many elements have complex structures with low symmetry at high pressures; McMahon and Nelmes have reviewed complex lattice structures of elements under high pressure. 1 Some elements have interesting structures beyond the simple cubic ͑sc͒ lattice at high pressure. Phosphorus has the sc structure ͑P-III͒ from 10 to 107 GPa, 2 which transforms, at 107 GPa, to a complex structure 3 ͑P-IV͒ whose structure has long been unidentified. But it has recently been theoretically predicted 4 and experimentally confirmed 5 to be an incommensurately modulated structure.Another example is calcium, which shows interesting successive structural phase transitions under pressure, where the transitions are from a closest-packed to a less close-packed structure. The fcc structure at ambient pressure transforms to the bcc at 20 GPa and then to the sc structure ͑Ca-III͒ at 32 GPa. 6 In 2005 Yabuuchi et al. pressurized calcium further and observed new structural phase transitions. 7 The sc transforms to phase IV ͑Ca-IV͒ at 113 GPa and then to phase V ͑Ca-V͒ at 139 GPa. 7 Very recently an increase of the superconducting transition temperature T c in the high-pressure phases has also been reported, i.e., 25 K at 161 GPa in Ca-V, which is the highest recorded for an element. 8 This result has attracted much interest in relation to pressure-induced electronic s-d transfer and the increase of the superconducting T c with pressure, which has been discussed also in Sr and Ba under pressure. [9][10][11] Information about the structures of Ca-IV and Ca-V is crucial for the clarification of the high T c in calcium.In this work, we have explored the crystal structures of Ca-IV and Ca-V using an ab initio metadynamics simulation 12 in which we employed density functional theory in the generalized gradient approximation ͑GGA͒. Metadynamics is a method used to find neighboring local minima by filling the potential wells with an artificial Gaussian potential ͑GP͒. To avoid rigid rotation of the system, we treated only the symmetric part of the cell matrix defined by h = ͑a ជ , b ជ , c ជ͒, where a ជ, b ជ , and c ជ are the lattice vectors. We update the simulation cell by the steepest-descent method with a stepping parameter ␦h: h ij t+1 = h ij t + ␦hF ij t / ͉F ij t ͉, where t is the number of updates of h and F is the driving force for the update. If we...

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“…Observation of the P-IV phase was first reported by Akahama et al [8] in 1999. In the sequence of pressure-induced transformations, the simple cubic (sc) phase (P-III) appears at 10 GPa at low temperature.…”

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confidence: 99%

Determining the Structure of Phosphorus in Phase IV

et al. 2006

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We explore the unknown structure of phosphorus in phase IV (P-IV phase) based on first-principles calculations using the metadynamics simulation method. Starting from the simple cubic structure, we find a new modulated structure of the monoclinic lattice. The modulation is crucial to the stability of the structure. Through refining the structure further by changing the modulation period, we find the structure whose x-ray powder diffraction pattern is in best agreement with the experimental pattern. We expect that the modulation period of the structure in the P-IV phase is very close to that found in this study and probably incommensurate. DOI: 10.1103/PhysRevLett.96.095502 PACS numbers: 61.50.Ah, 62.50.+p, 64.70.Kb Recent progress in high-pressure physics has enhanced our recognition of a wide variety of crystal structures. Development of high-pressure techniques has also enabled the identification of structures that are stabilized only in a narrow pressure range. Interesting structures were found unexpectedly through high-pressure experiments. For instance, modulated structures are often found in the highpressure phases of elements. Lattice modulations have been found in group Vb elements, including As, Sb, and Bi Scarcity of experimental ultrahigh-pressure data restricts high-pressure studies. Thus, researchers often encounter difficulties in the identification of a crystal structure on the basis of experimental data alone. A theoretical approach provides additional information on the same problem. First-principles theory for determining crystal structures is believed to be sufficiently accurate. However, the limitations of computational resources sometimes impede full structure searches.We will focus on the case of phase IV of the phosphorus (P-IV) phase. Observation of the P-IV phase was first reported by Akahama et al. [8] in 1999. In the sequence of pressure-induced transformations, the simple cubic (sc) phase (P-III) appears at 10 GPa at low temperature. Akahama et al. [8] reported the appearance of a simple hexagonal (sh) phase, i.e., the P-V phase, which stabilizes above 137 GPa, and an intermediate phase, i.e., the P-IV phase, between sc and sh on the basis of x-ray diffraction data. At even higher pressures, the bcc structure (P-VI) has been theoretically predicted [9] and later identified in an experiment at 262 GPa [10]. The structure of phase IV, however, has not been identified experimentally. Ordinary Rietveld analysis based on a knowledge of the monoclinic symmetry alone has not been successful, presumably owing to the complexity of the lattice. Thus, we must guess the crystal structure or a pseudocrystal.Several structures have been tested as candidate structures for P-IV. Ahuja considered a structure of space group Imma [11]. Ehlers and Christensen studied relative stability of the Ba-IV structure against sc and sh in the pressure range from 100 to 200 GPa [12]. The Ba-IV structure is a kind of modulated structure. Despite these extensive studies, the structure of P-IV remains unidentifi...

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Simple-cubic–simple-hexagonal transition in phosphorus under pressure

Cited by 91 publications

References 28 publications

Compressibility of cubic white, orthorhombic black, rhombohedral black, and simple cubic black phosphorus

Compressibility of cubic white, orthorhombic black, rhombohedral black, and simple cubic black phosphorus

Theoretical study of the structure of calcium in phases IV and V viaab initiometadynamics simulation

Determining the Structure of Phosphorus in Phase IV

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