ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of LiIn2Ir (Materials Project id mp-31208)

       178       35       35        0        0        0  
        35      178       35        0        0        0  
        35       35      178        0        0        0  
         0        0        0       83        0        0  
         0        0        0        0       83        0  
         0        0        0        0        0       83  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 82.667 GPa	EV = 178.71 GPa	GV = 78.4 GPa	νV = 0.13971
Reuss	KR = 82.667 GPa	ER = 177.98 GPa	GR = 77.983 GPa	νR = 0.14116
Hill	KH = 82.667 GPa	EH = 178.34 GPa	GH = 78.191 GPa	νH = 0.14043

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
83 GPa	83 GPa	83 GPa	143 GPa	143 GPa	248 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	Emin	Emax	βmin	βmax	Gmin	Gmax	νmin	νmax
Value	166.5 GPa	186.56 GPa	4.0323 TPa–1	4.0323 TPa–1	71.5 GPa	83 GPa	0.090999	0.17874	Value
Anisotropy	1.121		1.0000		1.161		1.9642		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5774 0.5773	0.7071 0.0000 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0002 0.7071	0.7071 -0.0000 0.7071	Axis
					0.7071 -0.0005 -0.7071	0.7660 0.6428 -0.0000	0.7071 -0.0006 -0.7071	0.0000 1.0000 0.0000	Second axis

Spatial dependence of Young's modulus

[[178.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 178.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 178.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 83.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 83.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 83.0]] LiIn2Ir (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31208" target="_blank">mp-31208</a>) young

Spatial dependence of linear compressibility

[[178.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 178.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 178.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 83.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 83.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 83.0]] LiIn2Ir (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31208" target="_blank">mp-31208</a>) lc

Spatial dependence of shear modulus

[[178.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 178.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 178.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 83.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 83.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 83.0]] LiIn2Ir (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31208" target="_blank">mp-31208</a>) shear

Spatial dependence of Poisson's ratio

[[178.0, 35.0, 35.0, 0.0, 0.0, 0.0], [35.0, 178.0, 35.0, 0.0, 0.0, 0.0], [35.0, 35.0, 178.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 83.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 83.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 83.0]] LiIn2Ir (Materials Project id <a href="https://www.materialsproject.org/materials/mp-31208" target="_blank">mp-31208</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)