Hexagonal structure of phase III of solid hydrogen

A hexagonal structure of solid molecular hydrogen with $P6_122$ symmetry is calculated to be more stable below about 200 GPa than the monoclinic $C2/c$ structure identified previously as the best candidate for phase III. We find that the effects of nuclear quantum and thermal vibrations play a central role in the stabilization of $P6_122$. The $P6_122$ and $C2/c$ structures are very similar and their Raman and infra-red data are in good agreement with experiment. However, our calculations show that the hexagonal $P6_122$ structure provides better agreement with the available x-ray diffraction data than the $C2/c$ structure at pressures below about 200 GPa. We suggest that two phase-III-like structures may be formed at high pressures, hexagonal $P6_122$ below about 200 GPa and monoclinic $C2/c$ at higher pressures.B.M. acknowledges Robinson College, Cambridge, and the Cambridge Philosophical Society for a Henslow Research Fellowship. R.J.N., E.G., and C.J.P. acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom (Grants No. EP/J017639/1, No. EP/J003999/1, and No. EP/K013688/1, respectively). C.J.P. is also supported by the Royal Society through a Royal Society Wolfson Research Merit award. The calculations were performed on the Darwin Supercomputer of the University of Cambridge High Performance Computing Service facility (http://www.hpc.cam.ac.uk/) and the Archer facility of the UK national high performance computing service, for which access was obtained via the UKCP consortium and funded by EPSRC Grant No. EP/K014560/1.This is the author accepted manuscript. The final version is available from the American Physical Society via https://doi.org/10.1103/PhysRevB.94.13410

Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces

Strain effects at solid surfaces near the melting point

We investigate the effects of strain on a crystal surface close to the bulk melting temperature T_m, where surface melting usually sets in. Strain lowers the bulk melting point, so that at a fixed temperature below but close to T_m the thickness of the quasi-liquid film is expected to grow with strain, irrespective of sign. In addition, a strain-induced solid surface free energy increase/decrease takes place, favoring/disfavoring surface melting depending on the sign of strain relative to surface stress. In the latter case one can produce a strain-induced prewetting transition, where for increasing temperature the liquid film suddenly jumps from zero to a finite thickness. This phenomenology is illustrated by a realistic molecular dynamics simulation of strained Al(110).Comment: Acceped for publication on Surface Scienc

Alternative sampling for variational quantum Monte Carlo

Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous publication it has been shown that for the simplest, most commonly applied strategy in continuum Quantum Monte Carlo, the random error in the resulting estimates is not well controlled. At best the Central Limit theorem is valid in its weakest form, and at worst it is invalid and replaced by an alternative Generalised Central Limit theorem and non-Normal random error. In both cases the random error is not controlled. Here we consider a new `residual sampling strategy' that reintroduces the Central Limit Theorem in its strongest form, and provides full control of the random error in estimates. Estimates of the total energy and the variance of the local energy within Variational Monte Carlo are considered in detail, and the approach presented may be generalised to expectation values of other operators, and to other variants of the Quantum Monte Carlo method.Comment: 14 pages, 9 figure

A Geometric Formulation of Quantum Stress Fields

We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the non-unique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity.Comment: 22 pages, 2 figures. Submitted to Physical Review B. This paper supersedes cond-mat/000627

Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions

We investigate Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors which arise in correlated sampling estimations of the energy and its variance. We investigate the numerical stability of the techniques and identify two reasons why variance minimization exhibits superior numerical stability to energy minimization. The characteristics of each method are studied using a non-interacting 64-electron model of crystalline silicon. While our main interest is in solid state systems, the issues investigated are relevant to Monte Carlo studies of atoms, molecules and solids. We identify a robust and efficient variance minimization scheme for optimizing wave functions for large systems.Comment: 14 pages, including 7 figures. To appear in Phys. Rev. B. For related publications see http://www.tcm.phy.cam.ac.uk/Publications/many_body.htm

Surface energy and stability of stress-driven discommensurate surface structures

A method is presented to obtain {\it ab initio} upper and lower bounds to surface energies of stress-driven discommensurate surface structures, possibly non-periodic or exhibiting very large unit cells. The instability of the stressed, commensurate parent of the discommensurate structure sets an upper bound to its surface energy; a lower bound is defined by the surface energy of an ideally commensurate but laterally strained hypothetical surface system. The surface energies of the phases of the Si(111):Ga and Ge(111):Ga systems and the energies of the discommensurations are determined within $\pm 0.2$ eV.Comment: 4 pages RevTeX. 2 Figures not included. Ask for a hard copy (through regular mail) to [email protected]

Observation of nano-indent induced strain fields and dislocation generation in silicon wafers using micro-raman spectroscopy and white beam x-ray topography

In the semiconductor manufacturing industry, wafer handling introduces micro-cracks at the wafer edge. During heat treatment these can produce larger, long-range cracks in the wafer which can cause wafer breakage during manufacture. Two complimentary techniques, micro-Raman spectroscopy (μRS) and White Beam Synchrotron X-ray Topography (WBSXRT) were employed to study both the micro-cracks and the associated strain fields produced by nano-indentations in Si wafers, which were used as a means of introducing controlled strain in the wafers. It is shown that both the spatial lateral and depth distribution of these long range strain fields are relatively isotropic in nature. The Raman spectra suggest the presence of a region under tensile strain beneath the indents, which can indicate a crack beneath the indent and the data strongly suggests that there exists a minimum critical applied load below which cracking will not initiate