arXiv subjects

M. P. Gururajan

Publications and source records attributed to M. P. Gururajan.

10 recordsLinked to original sources

arXiv2025

Theoretical issues in the accurate computation of the electron-phonon interaction contribution to the total energy

We report the computation of the Standard Hamiltonian of a coupled electron-phonon system by accurately computing the electron-phonon interaction (EPI) contribution to the total energy. This gives the most accurate ab initio total energy till date. However, our results show that the per-atom EPI energy is unit-cell-size dependent due to the partial-Fan-Migdal term that arises from the antisymmetric nature of the crystal wavefunction. Due to this, only energy differences between polytypes, in supercells with identical number of atoms, are meaningful, rather than per-atom total energy. This violates our understanding of Quantum Mechanics applied to periodic solids and raises serious theoretical questions. In his original (1951) paper, Fan suggested, without specifying any reason, that second-order perturbation theory applied to the whole crystal is of questionable validity. Our results support Fan's suggestion for the reason that the partial-FM term makes the per-atom total energy unit-cell-size dependent. This leads to a new fundamental problem in condensed matter physics, viz. second-order perturbation theory is invalid for whole crystals, an entire class. It is essential to resolve this problem, especially because it causes the standard Hamiltonian, the starting point of EPI studies and the most accurate ab initio total energy, to be of questionable validity.

cond-mat.mtrl-sci↗

arXiv2024

Extracting Rates and Activation Free Energies of Martensitic Transitions Using Nanomechanical Force Statistics: Theory, Models, and Analysis

Nanomechanical responses (force-time profiles) of crystal lattices under deformation exhibit random critical jumps, reflecting the underlying structural transition processes. Despite extensive data collection, interpreting dynamic critical responses and their underlying mechanisms remains a significant challenge. This study explores a microscopic theoretical approach to analyse critical force fluctuations in martensitic transitions. Extensive sampling of the critical forces was performed using nonequilibrium molecular dynamics simulations of an atomic model of single-crystalline titanium nickel. We demonstrate that a framework of nonequilibrium statistical mechanics offers a principled explanation of the relationship between strain rate and the critical force distribution as well as its mean. The martensitic transition is represented on a free energy landscape, taking into account the thermally activated evolution of atomic arrangements over a barrier during its time-dependent deformation. The framework enables consistent inference of the relevant fundamental properties (e.g., intrinsic rate, activation free energy) that define the rate process of structural transition. The study demonstrates how the statistical characterisation of nanomechanical response-stimulus patterns can offer microscopic insights into the deformation behaviours of crystalline materials.

cond-mat.mtrl-sci↗

arXiv2024

MICROSIM: A high performance phase-field solver based on CPU and GPU implementations

The phase-field method has become a useful tool for the simulation of classical metallurgical phase transformations as well as other phenomena related to materials science. The thermodynamic consistency that forms the basis of these formulations lends to its strong predictive capabilities and utility. However, a strong impediment to the usage of the method for typical applied problems of industrial and academic relevance is the significant overhead with regard to the code development and know-how required for quantitative model formulations. In this paper, we report the development of an open-source phase-field software stack that contains generic formulations for the simulation of multi-phase and multi-component phase transformations. The solvers incorporate thermodynamic coupling that allows the realization of simulations with real alloys in scenarios directly relevant to the materials industry. Further, the solvers utilize parallelization strategies using either multiple CPUs or GPUs to provide cross-platform portability and usability on available supercomputing machines. Finally, the solver stack also contains a graphical user interface to gradually introduce the usage of the software. The user interface also provides a collection of post-processing tools that allow the estimation of useful metrics related to microstructural evolution.

cond-mat.mtrl-sci↗

arXiv2023

Electron-phonon interaction contribution to the total energy of group IV semiconductor polymorphs: evaluation and implications

In density functional theory (DFT) based total energy studies, the van der Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are included to obtain energy differences between polymorphs. We propose and compute a new correction term to the total energy, due to electron-phonon interactions (EPI). We rely on Allen's general formalism, which goes beyond the Quasi-Harmonic Approximation (QHA), to include the free energy contributions due to quasiparticle interactions. We show that, for semiconductors and insulators, the EPI contributions to the free energies of electrons and phonons are the corresponding zero-point energy contributions. Using an approximate version of Allen's formalism in combination with the Allen-Heine theory for EPI corrections, we calculate the zero-point EPI corrections to the total energy for cubic and hexagonal polytypes of Carbon, Silicon and Silicon Carbide. The EPI corrections alter the energy differences between polytypes. In SiC polytypes, the EPI correction term is more sensitive to crystal structure than the vdW and ZPVE terms and is thus essential in determining their energy differences. It clearly establishes that the cubic SiC-3C is metastable and hexagonal SiC-4H is the stable polytype. Our results are consistent with the experimental results of Kleykamp. Our study enables the inclusion of EPI corrections as a separate term in the free energy expression. This opens the way to go beyond the QHA by including the contribution of EPI on all thermodynamic properties.

cond-mat.mtrl-sci↗

arXiv2022

Critical role of electron-phonon interactions in determining the relative stability of Boron Nitride polymorphs

Despite several first principles studies, the relative stability of BN polymorphs remains controversial. The stable polymorph varies between the cubic (c-BN) and hexagonal (h-BN) depending on the van der Waals (vdW) dispersion approximation used. These studies are unable to explain the main experimental results, c-BN is stable, the relative stability order and the large energy difference between h-BN and c-BN (greater than 150 meV/formula unit). In this study, we introduce contributions from electron-phonon interactions (EPI) to the total energy of BN polymorphs. This clearly establishes c-BN is the stable polymorph irrespective of the vdW approximation. Only by including EPI contributions do the ab initio results match, for the first time, the main experimental results mentioned above. The EPI contribution to the total energy is strongly sensitive to chemical bonding (approximately twice in $sp^2$-bonded layered over $sp^3$-bonded polymorphs) and to crystal structure. The crucial role of EPI contributions is seen in $sp^2$-bonded layered BN polymorphs where it is greater than the vdW contribution. Given that h-BN is a prototype layered material, in bulk or 2D form, our results have a broader relevance, that is, including EPI correction, along with vdW approximation, is vital for the study of energetics in layered materials.

cond-mat.mtrl-sci↗

arXiv2018

Finite temperature electronic structure of Diamond and Silicon

The electron-phonon interaction contribution to the electronic energies is included in density functional total energy calculations with ab initio pseudopotentials via the Allen formalism [Phys. Rev. B 18, 5217 (1978)] to obtain temperature dependent electronic structure of diamond and silicon. This method allows us to obtain the thermally-averaged ab initio electronic structure in a straightforward and computationally inexpensive way. Our investigations on the finite temperature electronic structure of diamond and silicon lead to a new criterion, temperature transferability, which is required in the ab initio pseudopotentials for temperature dependent studies. The temperature transferability of the Troullier-Martins pseudopotentials used in this work is strongly dependent on the cut-off radius and the inclusion of the unbound 3d$^0$ state. The finite temperature indirect band gaps are highly sensitive to the choice of cut-off radius used in the pseudopotentials. The finite temperature band structures and density of states show that thermal vibrations affect the electron energies throughout the valence and conduction band. We compare our results on the band gap shifts with that due to the Debye-Waller term in the Allen-Heine theory and discuss the observed differences in the zero point and high temperature band gap shifts. Although, the electron energy shifts in the highest occupied valence band and lowest unoccupied conduction band enable to obtain the changes in the indirect and direct band gaps at finite temperatures, the shifts in other electronic levels with temperature enable investigations into the finite temperature valence charge distribution in the bonding region. Thus, we demonstrate that the Allen theory provides a simple and theoretically justified formalism to obtain finite temperature valence electron charge densities that go beyond the rigid pseudo-atom approximation.

cond-mat.mtrl-sci↗

arXiv2017

Effect of stacking fault energy on nucleation limited plasticity in Cu-Al alloys

We study the effect of Stacking Fault Energy (SFE) on the deformation behaviour of copper and copper-aluminium alloys using Molecular Dynamics (MD) simulation. We find that both yield stress and the magnitude of stress drop at yield decrease with increasing Al content. This "anomalous" softening behaviour is explained on the basis of nucleation controlled yielding behaviour. Further, the decrease in stress drop is rationalised in terms of the stored energy available at yielding - we show that this decreases with increasing Al. As a result, the maximum dislocation density is found to decrease with increasing Al content. Finally, we show that the yield stress calculated using a continuum model of homogeneous nucleation of partial loops agrees well with the yield stress seen in the simulations.

cond-mat.mtrl-sci↗

arXiv2015

Finite temperature external potential in crystalline solids

Thermal vibrations alter the external potential. Allen (Phys. Rev. B 18 (1978) 5217) proved that at finite temperatures the pseudopotential form factors are corrected by a Debye-Waller Factor (DWF). We generalize this result to the crystal potential. (The generalization to the all-electron case of the nuclear potential fails due to the breakdown of the rigid-atom approximation.) This finite temperature formalism only gives thermal-averaged properties and no dynamical information can be obtained. Hence, it is labeled the Quasi Ab Initio formalism. Analogous to the use of experimental lattice parameters in ab initio studies, experimental DWF can also be used. The justification is identical; the experimental parameters can be validated by separate ab initio studies. Our work transforms, forty years later, Kasowski's empirical study (Phys. Rev. B. 8 (1973) 1378) into the first ab initio finite temperature band structure calculation. This formalism opens the way to obtain ab initio finite temperature thermal-averaged properties from a single calculation.

cond-mat.mtrl-sci↗

arXiv2014

On the incorporation of cubic and hexagonal interfacial energy anisotropy in phase field models using higher order tensor terms

In this paper, we show how to incorporate cubic and hexagonal anisotropies in interfacial energies in phase field models; this incorporation is achieved by including upto sixth rank tensor terms in the free energy expansion, assuming that the free energy is only a function of coarse grained composition, its gradient, curvature and aberration. We derive the number of non-zero and independent components of these tensors. Further, by demanding that the resultant interfacial energy is positive definite for inclusion of each of the tensor terms individually, we identify the constraints imposed on the independent components of these tensors. The existing results in the invariant group theory literature can be used to simplify the process of construction of some (but not all) of the higher order tensors. Finally, we derive the relevant phase field evolution equations.

cond-mat.mtrl-sci↗

arXiv2013

Effect of Epitaxial Strain on Phase Separation in Thin Films

We examine the role of an imposed epitaxial strain e in enhancing or depressing the spinodal instability of an alloy thin film. Since the alloy film starts with an imposed strain, phase separation offers a mechanism to relieve it, but only when the film is elastically inhomogeneous. With composition-dependence of elastic modulus given by y, and that of lattice parameter by η, our simulations using the Cahn-Hilliard model show (and analytical results for early stages confirm) that, for (ey/η) > 0, the imposed strain adds to the driving force for phase separation, decreases the maximally growing wave length, and expands the coherent spinodal in the phase diagram. Further, when (ey/η) > 0.372, it expands to even outside of chemical spinodal. Phase separation produces islands of elastically softer (harder) phase with (without) a favorable imposed strain. These results are in agreement with experimental results in GeSi thin films on Si and Ge substrates, as well as in InGaAs films on GaAs substrates.

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