Stability and elastic properties of Nb _x C _y compounds

Abstract

Density functional theory (DFT) is applied to investigate the stability and mechanical properties of Nb x C y compounds. The structures of Nb x C y compounds are optimized, and the results are in good agreement with previous work. The calculated results of the cohesive energy and the formation enthalpy of Nb x C y show that they are thermodynamically stable structures, except for Pmc21-Nb 2 C. The mechanical properties such as the bulk modulus, Young's modulus, the shear modulus, and Poisson's ratio are obtained by Voigt-Reuss-Hill approximation. The results show that the Young's modulus and shear modulus of NbC are larger than other Nb x C y compounds. The mechanical anisotropy is characterized by calculating several different anisotropic indexes and factors, such as universal anisotropic index (A U ), shear anisotropic factors (A 1 , A 2 , A 3 ), and percent anisotropy (A B and A G ). The surface constructions of bulk and Young's moduli are illustrated to indicate the mechanical anisotropy. The hardness of Nb x C y compounds is also discussed in this paper. The estimated hardness for all Nb x C y compounds is less than 20 GPa.

Mimetic Gravity: A Review of Recent Developments and Applications to Cosmology and Astrophysics

“…The expression "mimetic dark matter" was first coined in a 2013 paper by Mukhanov and Chamseddine [69] although, as we shall see later, the foundation for mimetic theories had actually been developed a few years earlier in three independent papers [380][381][382]. In [69], the proposed idea is to isolate the conformal degree of freedom of gravity by introducing a parametrization of the physical metric g µν in terms of an auxiliary metricg µν and a scalar field φ, dubbed mimetic field, as follows:…”

Recovering a MOND-like acceleration law in mimetic gravity

“…The term "mimetic dark matter" (later referred to as mimetic gravity) was coined in 2013 by Chamseddine and Mukhanov [43] (see also [44]), although the prototype for mimetic theories had actually been introduced a few years earlier in [47][48][49]. In this approach, the conformal degree of freedom of gravity is isolated covariantly, by parametrizing the physical metric g µν in terms of an auxiliary metricg µν and a scalar field (the "mimetic field") φ, as follows:…”

“…(13). The study of Lagrange multiplier-constrained theories, which represent the prototype for mimetic theories, had been initiated earlier in [47][48][49]. 4 Various aspects of mimetic gravity (including ghost and stability issues, null-energy condition violation, connections to other theories such as Hořava-Lifshitz gravity and the scalar Einstein-aether theory, and various solutions such as static spherically symmetric, cylindrical, stellar ones) and extensions thereof have been discussed at length in the quickly growing literature related to the subject , to which we refer the reader for further details.…”

Mimicking dark matter and dark energy in a mimetic model compatible with GW170817

“…A particularly interesting theory of modified gravity is mimetic gravity, proposed in 2013 by Chamseddine and Mukhanov [45] (see also [46][47][48][49] for related and important earlier work). In the original work, the conformal degree of freedom of gravity was isolated in a covariant way, through a reparametrization of the physical metric g µν in terms of an auxiliary metric g µν and the mimetic scalar field φ:…”