Coarse-grained simulations of material shock compression: interplay between mechanics, thermals, and chemistry

We present a coarse-graining model that enables the description of pressure-induced, endothermic reactions in a model material. An additional implicit variable (the particle size) is used to describe particles undergoing volume-reducing endothermic reactions via a bistable intra-molecular potential, whereas the dynamics of the center-of-mass motion evolves according to interparticle forces. The equations of motion are derived from a Hamiltonian and the model exhibits two desired features: total energy conservation and Galilean invariance. In this study, we explore a simple model material with pairwise interactions between particles to study pressure-induced chemical reactions under both quasi-static and shock loading conditions. Our results demonstrate that such model can capture the complex mechanical processes arising from the interplay between deformation defects and chemical reactions. Moreover, we explore the feasibility to realize a material with such characteristics that can be used to attenuate the energy in sustained shocks which is of interest in many applications

Finite size scaling for quantum criticality using the finite-element method

Finite size scaling for the Schr\"{o}dinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite element method was shown to be a powerful numerical method for ab initio electronic structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, density functional theory under the local density approximation, and an "exact"' formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.Comment: 15 pages, 19 figures, revision based on suggestions by referee, accepted in Phys. Rev.

Applications of finite-size scaling for atomic and non-equilibrium systems

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations

Coarse grain model for coupled thermo-mechano-chemical processes and its application to pressure-induced endothermic chemical reactions

We extend a thermally accurate model for coarse grain dynamics (Strachan and Holian 2005 Phys. Rev. Lett. 94 014301) to enable the description of stress-induced chemical reactions in the degrees of freedom internal to the mesoparticles. Similar to the breathing sphere model, we introduce an additional variable that describes the internal state of the particles and whose dynamics is governed both by an internal potential energy function and by interparticle forces. The equations of motion of these new variables are derived from a Hamiltonian and the model exhibits two desired features: total energy conservation and Galilean invariance. We use a simple model material with pairwise interactions between particles and study pressure-induced chemical reactions induced by hydrostatic and uniaxial compression. These examples demonstrate the ability of the model to capture non-trivial processes including the interplay between mechanical, thermal and chemical processes of interest in many applications

Mechanisms of Plastic Deformation of Metal–Organic Framework‑5

We use large-scale molecular dynamics simulations to investigate the mechanisms responsible for plastic deformation in metal–organic framework-5 (MOF-5). Simulations of uniaxial compression along [001], [101], and [111] directions reveal that structural collapse of {001} planes is responsible for irreversible deformation. The process involves slip along either one of the two ⟨100⟩ directions on the collapsing plane; this local shear process is due to the flexibility of the connection between of Zn–O clusters and 1,4-benzenedicarboxylate ligands. Thus, the collapse is driven both by compressive and shear stresses, and this fact explains the anisotropy in the mechanical response of this cubic crystal. The development of shear-collapse bands follows a nucleation and growth process with nuclei elongated along the slip direction and their subsequent growth in the directions normal to the slip and at much slower rates. This process is reminiscent of the glide of screw dislocations. Compression along the [101] and [111] directions led to intersection of active shear-collapse bands and the activation of multiple ⟨001⟩{100} systems. We also find that partially collapsed planes reduce the stiffness of the structures, an observation that can explain discrepancies between experimental and theoretical stiffness predictions

Mechanisms of Plastic Deformation of Metal–Organic Framework‑5

We use large-scale molecular dynamics simulations to investigate the mechanisms responsible for plastic deformation in metal–organic framework-5 (MOF-5). Simulations of uniaxial compression along [001], [101], and [111] directions reveal that structural collapse of {001} planes is responsible for irreversible deformation. The process involves slip along either one of the two ⟨100⟩ directions on the collapsing plane; this local shear process is due to the flexibility of the connection between of Zn–O clusters and 1,4-benzenedicarboxylate ligands. Thus, the collapse is driven both by compressive and shear stresses, and this fact explains the anisotropy in the mechanical response of this cubic crystal. The development of shear-collapse bands follows a nucleation and growth process with nuclei elongated along the slip direction and their subsequent growth in the directions normal to the slip and at much slower rates. This process is reminiscent of the glide of screw dislocations. Compression along the [101] and [111] directions led to intersection of active shear-collapse bands and the activation of multiple ⟨001⟩{100} systems. We also find that partially collapsed planes reduce the stiffness of the structures, an observation that can explain discrepancies between experimental and theoretical stiffness predictions