Origin of the structural phase transition in Li7La3Zr2O12

Garnet-type Li7La3Zr2O12 (LLZO) is a solid electrolyte material with a low-conductivity tetragonal and a high-conductivity cubic phase. Using density-functional theory and variable cell shape molecular dynamics simulations, we show that the tetragonal phase stability is dependent on a simultaneous ordering of the Li ions on the Li sublattice and a volume-preserving tetragonal distortion that relieves internal structural strain. Supervalent doping introduces vacancies into the Li sublattice, increasing the overall entropy and reducing the free energy gain from ordering, eventually stabilizing the cubic phase. We show that the critical temperature for cubic phase stability is lowered as Li vacancy concentration (dopant level) is raised and that an activated hop of Li ions from one crystallographic site to another always accompanies the transition. By identifying the relevant mechanism and critical concentrations for achieving the high conductivity phase, this work shows how targeted synthesis could be used to improve electrolytic performance

From Electrons to Finite Elements: A Concurrent Multiscale Approach for Metals

We present a multiscale modeling approach that concurrently couples quantum mechanical, classical atomistic and continuum mechanics simulations in a unified fashion for metals. This approach is particular useful for systems where chemical interactions in a small region can affect the macroscopic properties of a material. We discuss how the coupling across different scales can be accomplished efficiently, and we apply the method to multiscale simulations of an edge dislocation in aluminum in the absence and presence of H impurities.Comment: 4 page

Moments of spectral functions: Monte Carlo evaluation and verification

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval $(-\beta \hbar / 2, \beta \hbar/2)$. The algorithmic detail that leads to robust numerical approximations is the fact that the path integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is non-linear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed.Comment: 13 pages, 2 figure

Lagrangian particle paths and ortho-normal quaternion frames

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vorticity. The method is applicable to a wide range of Lagrangian flows including the three-dimensional Euler equations and its variants such as ideal MHD. The applicability of the quaterionic frame description to Lagrangian averaged velocity gradient dynamics is also demonstrated.Comment: 9 pages, one figure, revise

Dynamic of a non homogeneously coarse grained system

To study materials phenomena simultaneously at various length scales, descriptions in which matter can be coarse grained to arbitrary levels, are necessary. Attempts to do this in the static regime (i.e. zero temperature) have already been developed. In this letter, we present an approach that leads to a dynamics for such coarse-grained models. This allows us to obtain temperature-dependent and transport properties. Renormalization group theory is used to create new local potentials model between nodes, within the approximation of local thermodynamical equilibrium. Assuming that these potentials give an averaged description of node dynamics, we calculate thermal and mechanical properties. If this method can be sufficiently generalized it may form the basis of a Molecular Dynamics method with time and spatial coarse-graining.Comment: 4 pages, 4 figure

Masculinity as Governance: police, public service and the embodiment of authority, c. 1700-1850

About the book: Public Men offers an introduction to an exciting new field: the history of masculinities in the political domain and will be essential reading for students and specialists alike with interests in gender or political culture. By building upon new work on gender and political culture, these new case studies explore the gendering of the political domain and the masculinities of the men who have historically dominated it. As such, Public Men is a major contribution to our understanding of the history of Britain between the Eighteenth and the Twentieth centuries

Eleanor Davies and the New Jerusalem

Eleanor Davies was a great believer in historical moments. In her first work—A Warning to the Dragon and All His Angels of 1625-she told readers that “The Lord is at the Dore.”1 This immanence of God made her watchful and purposeful, reading the signs in her daily life, counting days, weeks, and years because she believed that Christ would come again. His arrival had been predestined from the beginning of the world: “from the going forth of the Commandement, which is the beginning of the Creation to the building of the New Jerusalem, the second comming of Messiah, the Prince the Sonne of God, it shall be Seaven Weekes or Seaven Moneths.”2 For Davies, time was elastic, but history was absolute. What the biblical prophets (in this case Ezekiel) said would come to pass, really would come to pass, but their promises were oracular; they had complete authority but were also elusive. Davies accepted this. She knew that she was living in the latter days, but when it came to God’s final judgment, “the daye and houre knoweth no man.”3 God could not be known as such and what she called knowledge was a spiritual transformation that took place when “He powreth out his Spirit upon his hand-maidens,” like herself.4 This essay uses A Warning to the Dragon and Davies’ works of the 1630s and 1640s to examine her theology

Effective pair potentials for spherical nanoparticles

An effective description for spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, the effective potential generally has non-analytic points, but for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered, and shown to be related to those for solid nanoparticles. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London-Van der Waals, Morse, Buckingham, and Lennard-Jones potential. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and nonoverlapping particles added, as well as a comparison with an idealized atomic descriptio

Renormalization group approach to multiscale modelling in materials science

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory of the underlying crystallographic anisotropy, and thus is ill-suited for problems involving defects or elasticity. The phase field crystal (PFC) equation-- a conserving analogue of the Hohenberg-Swift equation --is a phase field equation with periodic solutions that represent the atomic density. It can natively model elasticity, the formation of solid phases, and accurately reproduces the nonequilibrium dynamics of phase transitions in real materials. However, the PFC models matter at the atomic scale, rendering it unsuitable for coping with the range of length scales in problems of serious interest. Here, we show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive appropriate coarse-grained coupled phase and amplitude equations, which are suitable for solution by adaptive mesh refinement algorithms

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation