Uniaxial phase transition in Si:<i>Ab initio</i>calculations

Cheng, Chih‐Chieh

doi:10.1103/physrevb.67.134109

Cited by 16 publications

(14 citation statements)

References 23 publications

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“…The good agreement of our results with the ones of Cheng et al 53,54 confirm the reliability of our method, which provides a larger field of applications. In addition, our method can be extended to, e.g., the β-tin→Imma→sh transitions in Si and Ge.…”

Section: Discussion Of the Resultssupporting

confidence: 90%

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Transition pressures and enthalpy barriers for the cubic diamond→β-tin transition in Si and Ge under nonhydrostatic conditions

Gaál-Nagy

Strauch

2006

Phys. Rev. B

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We present an ab-initio study of the phase transition cd→β-tin in Si and Ge under hydrostatic and non-hydrostatic pressure. For this purpose we have developed a new method to calculate the influence of non-hydrostatic pressure components not only on the transition pressure but also on the enthalpy barriers between the phases. We find good agreement with available experimental and other theoretical data. The calculations have been performed using the plane-wave pseudopotential approach to the density-functional theory within the local-density and the generalized-gradient approximation implemented in VASP.

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Section: Discussion Of the Resultssupporting

confidence: 90%

“…53,54,74,75,76,77 Directly comparable with our results are just the ones from Lee et al 74 and Cheng et al 53,54 Besides the transition pressures also the function p 53,54 restricted themselves to the enthalpy difference between the phases using path integrals, the enthalpy barrier was not accessible to them.…”

Section: Discussion Of the Resultssupporting

confidence: 90%

Transition pressures and enthalpy barriers for the cubic diamond→β-tin transition in Si and Ge under nonhydrostatic conditions

Gaál-Nagy

Strauch

2006

Phys. Rev. B

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“…We observe that ∆E tot is within 0.20-0.45 eV/atom for the sc, sh, and β-tin phases, for both Si and Ge. Our ∆E tot results for the sc, sh, and β-tin phases of Si, and for the β-tin phase of Ge are in good agreement with recent GGA calculations [13,14]. As a further test of the reliability of our calculations, we consider the structural transition from diamond to β-tin, that occurs for both Si and Ge under pressure.…”

supporting

confidence: 86%

Structures of Si and Ge Nanowires in the Subnanometer Range

Kagimura

Rw²,

Chacham³

2005

Phys. Rev. Lett.

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We report an ab-initio investigation of several possible Si and Ge pristine nanowires with diameters between 0.5 and 1.2 nm. We considered nanowires based on the diamond structure, high-density bulk structures, and fullerene-like structures. We find that the diamond structure nanowires are unstable for diameters smaller than 1 nm, and undergo considerable structural transformations towards amorphous-like wires. Such instability is consistent with a continuum model that predicts, for both Si and Ge, a stability crossover between diamond and high-density-structure nanowires for diameters smaller than 1 nm. For diameters between 0.8 nm and 1 nm, filled-fullerene wires are the most stable ones. For even smaller diameters (d ∼ 0.5 nm), we find that a simple hexagonal structure is particularly stable for both Si and Ge. . These nanowires usually depict a crystalline core surrounded by an oxide outer layer. Further removal of the oxide layer by acid treatment may lead to hydrogenpassivated silicon nanowires as thin as one nanometer [4]. Pristine (non-passivated) silicon wires with diameters of a few nanometers have also been produced from Si vapor deposited on graphite [5]. The elongated shape of silicon and germanium clusters of up to a few tens of atoms, determined by mobility measurements [6,7], indicates that even thinner pristine structures, with diameters smaller than 1 nm, can been produced.The growth of such small-diameter structures raises the question of the limit of a bulk-like description of bonding in these nanowires, since for small enough diameters the predominance of surface atoms over inner (bulklike) atoms will eventually lead to bonds (and structures) distinct from those of the bulk system. In the present work, we use first principles calculations to investigate several periodic structures of silicon and germanium pristine nanowires of infinite length, with diameters ranging from 0.45 to 1.25 nm. The nanowire structures considered are based on the diamond structure, fullerene-like structures, and the high-density bulk structures β-tin, simple cubic (sc), and simple hexagonal (sh).Our calculations are performed in the framework of the density functional theory [8], within the generalizedgradient approximation (GGA) [9] for the exchangecorrelation energy functional, and the soft normconserving pseudopotentials of Troullier-Martins [10] in the Kleinman-Bylander factorized form [11]. We use a method [12] in which the one electron wavefunctions are expressed as linear combinations of pseudo-atomic numerical orbitals of finite range. A double-zeta basis set is employed, with polarization orbitals included for all atoms. For the nanowire calculations, we employ supercells that are periodic along the wire axis, and that are wide enough in the perpendicular directions to avoid interaction between periodic images. All the geometries were optimized until residual forces were less than 0.04 eV/Å. Total-energy differences were converged to within 4 meV/atom with respect to orbital range and k-point sampling.Most ...

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“…Nanoindentation studies with various indenter-shapes 2 have shown that non-hydrostatic conditions lower the transformation stress, which is in accordance with theoretical considerations by Gilman (1993a) as well as various atomistic studies (cf. Lee et al, 1997;Cheng et al, 2001;Cheng, 2003;Gaál-Nagy and Strauch, 2006), which suggest a linear relationship between the transformation pressure p and applied von Mises equivalent stress S q := √ 3 /2 S . Transformation events during unloading appear on the force-displacement (P−h) curve (see Fig.…”

Section: Resultsmentioning

confidence: 99%

“…This choice reproduces the experimentally observed phase transition under hydrostatic compression (Hu et al, 1986), without predicting transformations in hydrostatic tension. Further, the linear relationship between equivalent stress S q and pressure p on the limit surface suggested by MD simulations (Cheng et al, 2001;Cheng, 2003;Gaál-Nagy and Strauch, 2006;Lee et al, 1997) can be smoothly approximated with an arbitrary order of accuracy. The corresponding flow potential is also chosen to be a hyperboloid of revolution, albeit not necessary the same one.…”

Section: Ld-si → Hd-simentioning

confidence: 99%