Source-linked AI summary
ELATE: An open-source online application for analysis and visualization of elastic tensors
Romain Gaillac, Pluton Pullumbi, François-Xavier Coudert
TL;DR
ELATE addresses the scarcity and usability challenges of elastic-tensor analysis as computational databases expand and directional properties become important for anisotropic materials. It combines an open-source Python module with a standalone online application that computes conventional and directional elastic properties, visualizes them interactively, and connects to the Materials Project. The paper presents this integrated analysis and visualization workflow, while noting a typographical issue in a referenced derivation.
Problem
Elastic constants are experimentally scarce and existing tensor-analysis tools are technically difficult, locally installed, noninteractive, or tied to proprietary software, limiting accessible directional analysis.
Method
ELATE combines an open-source Python tensor-analysis module with a standalone online application that computes averaged, stable-system directional, extrema, and anisotropy properties and renders interactive plots.
Results
ELATE provides routine elastic-tensor analysis, interactive 2D and 3D visualizations, and Materials Project integration through a web application and simple API.
Takeaways & Limitations
ELATE makes directional elastic-property analysis available through an online interface and supports links from materials databases to detailed visualizations.
Takeaways & Limitations
The implementation relies on a referenced theoretical derivation containing a reported typo in the expression for b in Eq. 6 of Ref..
Abstract
from arXiv · showhide
We report on the implementation of a tool for the analysis of second-order elastic stiffness tensors, provided with both an open-source Python module and a standalone online application providing visualization tools of anisotropic mechanical properties. After describing the software features, how we compute the conventional elastic constants and how we represent them graphically, we explain our technical choices for the implementation. In particular, we focus on why a Python module is used to generate the HTML web page with embedded Javascript for dynamical plots.
1. Introduction
ELATE addresses the limited availability and usability of elastic-tensor analysis by combining an open-source Python module with a standalone online application for routine analysis and visualization. It targets directional properties needed to identify anomalous mechanical behavior and integrates with growing computational elastic-constant databases.
- Motivation: Measured second-order elastic constants remain scarce because experiments require large single crystals and precise measurements, especially for low-symmetry crystals.Routine ab initio calculations now make predictions from crystalline structures feasible on high-performance computing infrastructures.
- Computational context: Automated elastic-tensor calculations and high-throughput databases have expanded the supply of computed elastic properties for systematic materials characterization.The Materials Project database contained 1181 inorganic compounds at publication in March 2015 and 2111 at the stated later date.
- Motivation: Directional analysis of Young’s modulus, linear compressibility, shear modulus, and Poisson’s ratio is needed for anisotropic materials and targeted or anomalous responses.Examples include negative linear compressibility, negative Poisson’s ratio, and highly anisotropic elastic moduli.
- Existing tools: Available software is limited by local compilation and noninteractive output in ElAM or dependence on proprietary Mathematica software for interactive analysis.ElAM is implemented in Fortran 90 and produces PostScript and VRML outputs, whereas the earlier Mathematica implementation is restricted to that software suite.
- Contribution: ELATE provides an open-source Python module and standalone online application for manipulating and routinely analyzing elastic tensors without local installation.The online application also exposes an API and can import elastic data from the Materials Project through the Materials API.
2. Software description and features
ELATE converts elastic tensors into conventional averages, stability checks, directional visualizations, extrema, and anisotropy measures, while using a browser-based architecture for interactive plots and database integration. Its displays cover both single-direction properties and two-direction properties such as shear modulus and Poisson’s ratio.
- Tensor analysis: ELATE accepts a symmetric 6 × 6 Voigt elastic-constant matrix in GPa and computes bulk, Young’s, shear, and Poisson’s moduli using Voigt, Reuss, and Hill averages.It also computes six eigenvalues and stops with an error when any negative eigenvalue indicates mechanical instability.
- Directional properties: Young’s modulus and linear compressibility are functions of one unit vector and can be visualized as 3D parametric surfaces or 2D projections.The directional coordinates use spherical angles with 0 ≤ θ ≤ π and 0 ≤ ϕ ≤ 2π.
- Directional properties: Linear-compressibility plots separate positive directions in green from negative directions in red, illustrated for trigonal Ag3Co(CN)6.Both 3D surfaces and 2D curves are provided.
- Directional properties: Shear modulus and Poisson’s ratio depend on orthogonal stress and measurement directions, so ELATE plots their minimum and maximum over the remaining angular coordinate.For each spherical coordinate pair, the outer surface represents the maximum and the inner surface the minimum.
- Quantitative analysis: ELATE reports directional extrema, the directions where they occur, and an anisotropy measure for each modulus to identify properties not aligned with crystallographic axes.Marked anisotropy is associated with anomalous behavior including negative linear or area compressibility and possible large-scale structural transitions.
- Implementation: Server-side Python computations support interactive browser graphs, with JSXGraph for 2D plots and plotly.js for dynamic 3D surfaces.Users can zoom, rotate, pan, and inspect values at points of interest without lag.
- Database integration: ELATE interfaces with Materials Project elastic tensors for more than 2,000 crystalline inorganic materials and provides a URL-based API for linked visualizations.Other databases could be integrated in the future.
3. Perspectives
As computational materials databases expand in size and scope, tools are needed to analyze and visualize their growing property data. ELATE addresses this need for second-order elastic tensors while planning broader database integration and tensor analysis.
- Growing computational materials databases now include properties beyond structures and formation energies.
- ELATE analyzes and visualizes second-order elastic tensors through a Python module and online application with Materials Project integration.
- The project plans interfaces with additional mechanical-property databases and a unified API rather than incompatible protocols.
- Future extensions aim to cover other tensorial properties, including piezoelectric and photoelastic tensors.