First Principles Calculation of Elastic Properties of Solid Argon at High Pressures

The density and the elastic stiffness coefficients of fcc solid argon at high pressures from 1 GPa up to 80 GPa are computed by first-principles pseudopotential method with plane-wave basis set and the generalized gradient approximation (GGA). The result is in good agreement with the experimental result recently obtained with the Brillouin spectroscopy by Shimizu et al. [Phys. Rev. Lett. 86, 4568 (2001)]. The Cauchy condition was found to be strongly violated as in the experimental result, indicating large contribution from non-central many-body force. The present result has made it clear that the standard density functional method with periodic boundary conditions can be successfully applied for calculating elastic properties of rare gas solids at high pressures in contrast to those at low pressures where dispersion forces are important.Comment: 4 pages, 5 figures, submitted to PR

quasiharmonic equations of state for dynamically-stabilized soft-mode materials

We introduce a method for treating soft modes within the analytical framework of the quasiharmonic equation of state. The corresponding double-well energy-displacement relation is fitted to a functional form that is harmonic in both the low- and high-energy limits. Using density-functional calculations and statistical physics, we apply the quasiharmonic methodology to solid periclase. We predict the existence of a B1--B2 phase transition at high pressures and temperatures

Two-band second moment model and an interatomic potential for caesium

A semi-empirical formalism is presented for deriving interatomic potentials for materials such as caesium or cerium which exhibit volume collapse phase transitions. It is based on the Finnis-Sinclair second moment tight binding approach, but incorporates two independent bands on each atom. The potential is cast in a form suitable for large-scale molecular dynamics, the computational cost being the evaluation of short ranged pair potentials. Parameters for a model potential for caesium are derived and tested

Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve

{\em Ab initio} techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earth's core. The {\em ab initio} free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the {\em ab initio} system, with thermal averages computed by {\em ab initio} molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated earlier using identical {\em ab initio} techniques to obtain the melting curve and volume and entropy of melting. Comparisons of the calculated melting properties with experimental measurement and with other recent {\em ab initio} predictions are presented. Experiment-theory comparisons are also presented for the pressures at which the solid and liquid Hugoniot curves cross the melting line, and the sound speed and Gr\"{u}neisen parameter along the Hugoniot. Additional comparisons are made with a commonly used equation of state for high-pressure/high-temperature Fe based on experimental data.Comment: 16 pages including 6 figures and 5 table

First-principles study of the structural energetics of PdTi and PtTi

The structural energetics of PdTi and PtTi have been studied using first-principles density-functional theory with pseudopotentials and a plane-wave basis. We predict that in both materials, the experimentally reported orthorhombic $B19$ phase will undergo a low-temperature phase transition to a monoclinic $B19'$ ground state. Within a soft-mode framework, we relate the $B19$ structure to the cubic $B2$ structure, observed at high temperature, and the $B19'$ structure to $B19$ via phonon modes strongly coupled to strain. In contrast to NiTi, the $B19$ structure is extremely close to hcp. We draw on the analogy to the bcc-hcp transition to suggest likely transition mechanisms in the present case.Comment: 8 pages 5 figure

First-principles study of the ferroelastic phase transition in CaCl_2

First-principles density-functional calculations within the local-density approximation and the pseudopotential approach are used to study and characterize the ferroelastic phase transition in calcium chloride (CaCl_2). In accord with experiment, the energy map of CaCl_2 has the typical features of a pseudoproper ferroelastic with an optical instability as ultimate origin of the phase transition. This unstable optic mode is close to a pure rigid unit mode of the framework of chlorine atoms and has a negative Gruneisen parameter. The ab-initio ground state agrees fairly well with the experimental low temperature structure extrapolated at 0K. The calculated energy map around the ground state is interpreted as an extrapolated Landau free-energy and is successfully used to explain some of the observed thermal properties. Higher-order anharmonic couplings between the strain and the unstable optic mode, proposed in previous literature as important terms to explain the soft-phonon temperature behavior, are shown to be irrelevant for this purpose. The LAPW method is shown to reproduce the plane-wave results in CaCl_2 within the precision of the calculations, and is used to analyze the relative stability of different phases in CaCl_2 and the chemically similar compound SrCl_2.Comment: 9 pages, 6 figures, uses RevTeX

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society