arXiv subjects

Umesh C. Roy

Publications and source records attributed to Umesh C. Roy.

4 recordsLinked to original sources

arXiv2025

First-principles calculation of higher-order elastic constants from divided differences

A method is presented to calculate from first principles the higher-order elastic constants of a solid material. The method relies on finite strain deformations, a density functional theory approach to calculate the Cauchy stress tensor, and a recursive numerical differentiation technique homologous to the divided differences polynomial interpolation algorithm. The method is applicable as is to any material, regardless its symmetry, to calculate elastic constants of, in principle, any order. Here, we introduce conceptual framework and technical details of our method, we discuss sources of errors, we assess convergence trends, and we present selected applications. In particular, our method is used to calculate elastic constants up to the 6$^{th}$ order of two crystalline materials with the cubic symmetry, silicon and gold. To demonstrate general applicability, our method is also used to calculate the elastic constants up to the 5$^{th}$ order of $\alpha$-quartz, a crystalline material belonging to the trigonal crystal system, and the second- and third-order elastic constants of kevlar, a material with an anisotropic bonding network. Higher order elastic constants computed with our method are validated against density functional theory calculations by comparing stress responses to large deformations derived within the continuum approximation.

cond-mat.mtrl-sci↗

arXiv2025

New Methods for Critical Analysis: Revealing the Simultaneous Existence of Universality Classes in Nontrivial Magnetic Systems

In magnetic systems, the microscopic constituents exhibit power law behavior near the paramagnetic transition temperature, $T_C$. The critical exponents (CEs) associated with the physical quantities that demonstrate singular behavior at $T_C$ illustrate the critical behavior, specifically the range and type of exchange interactions emerging in magnetic systems. However, it is realized that the developed methodologies may not yield accurate values of CEs, especially for magnetic systems with competing interactions, referred to as nontrivial magnetic systems. Currently, no comprehensive method effectively addresses the competing effects of the range of magnetic interactions among the constituent entities emerging in such systems. Additionally, there is no definitive explanation for CE values that do not belong to any single universality class. Here, we present new methodologies for critical analysis aimed at determining both the range of exchange interaction(s) and appropriate values of CEs. Using computational and experimental investigations, we analyze the magnetic behavior of trivial Ni and nontrivial Gd. Our findings demonstrate that (i) the critical behavior remains the same on either side of $T_C$, (ii) the critical behavior associated with local electron moments remains unaffected by the magnetic field, and (iii) in Gd, the critical role of competing interactions becomes evident: local electron moments follow a three-dimensional Ising-type short-range interaction, while itinerant electron moments exhibit a mean-field-type long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which weakens under an external magnetic field due to the localization effect on itinerant electrons.

cond-mat.str-el↗

arXiv2021

Ab initio study of the density dependence of the Grüneisen parameter at pressures up to 360 GPa

Ab initio calculations based on the Density Functional Theory are used to show that the Debye frequency is a linear function of density to a high accuracy for several elemental solids at pressures (at least) up to 360 GPa. This implies that the ratio of density over the (Debye-frequency-based) vibrational Grüneisen parameter is a linear function of density in this region. Numerical data from first principles calculations for several systems at temperatures up to 2000K suggest that this is also true for the thermal Grüneisen parameter in the same range of pressure. Our analytical form of the vibrational Grüneisen parameter is applied to an implementation of the Lindemann's melting criterion to obtain a simple extrapolation formula for the melting temperatures of materials at higher densities. This prediction is tested against available experimental and numerical data for several elemental solids.

cond-mat.mtrl-sci↗

arXiv2020

Birch's law at elevated temperatures

Birch's law in high pressure physics postulates a linear relationship between elastic wave speed and density and one of its most well known applications is in investigations into the composition of the inner core of the Earth using the Preliminary Reference Earth Model as the primary source of constraints. However, it has never been subjected to high precision tests even at moderately elevated temperatures. Here we carry out such a test by making use of the Density Functional Theory of electronic structure calculation and the Density Functional Perturbation Theory of calculating the phonon dispersion relation. We show that a recently proposed modification to the Birch's law is consistently satisfied more accurately than its original version. This modified version states that it is the product of elastic wave speed and one-third power of density that should be a linear function of density. We have studied the cases of platinum, palladium, molybdenum and rhodium with cubic unit cell and iron with hexagonal-close-packed unit cell with temperatures up to 1500K and pressures up to about 360 GPa. We also examine the genericity of the validity of a recently proposed extension of the Birch's law according to which elastic wave speed is a linear function of temperature at a given density. Within the error bars of our calculation, we find that this is consistent with our data for the four cubic materials at temperatures up to 3300 K.

cond-mat.mtrl-sci↗