391 research outputs found
Hexagonal structure of phase III of solid hydrogen
A hexagonal structure of solid molecular hydrogen with symmetry is
calculated to be more stable below about 200 GPa than the monoclinic
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 . The and structures are very
similar and their Raman and infra-red data are in good agreement with
experiment. However, our calculations show that the hexagonal
structure provides better agreement with the available x-ray diffraction data
than the structure at pressures below about 200 GPa. We suggest that two
phase-III-like structures may be formed at high pressures, hexagonal
below about 200 GPa and monoclinic 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 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
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