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 Mg(AlSi)2 (Materials Project id mp-3833)

       128       57       32       -4        0        0  
        57      128       32        4        0        0  
        32       32       93        0        0        0  
        -4        4        0       28        0        0  
         0        0        0        0       28       -4  
         0        0        0        0       -4       36  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 65.667 GPa	EV = 86.113 GPa	GV = 33.6 GPa	νV = 0.28144
Reuss	KR = 62.374 GPa	ER = 82.345 GPa	GR = 32.167 GPa	νR = 0.27997
Hill	KH = 64.021 GPa	EH = 84.229 GPa	GH = 32.883 GPa	νH = 0.28072

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
26.343 GPa	27.268 GPa	37.657 GPa	71.732 GPa	74.471 GPa	203.53 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	68.262 GPa	101.84 GPa	4.0245 TPa–1	7.9831 TPa–1	26.286 GPa	38.229 GPa	0.12904	0.44234	Value
Anisotropy	1.492		1.9836		1.454		3.4278		Anisotropy
Axis	-0.0000 0.7091 -0.7051	0.8414 0.5166 -0.1585	0.1305 0.9914 0.0000	0.0000 0.0000 1.0000	-0.3400 0.1988 -0.9192	-0.4449 0.4723 -0.7609	0.3697 0.2164 -0.9036	1.0000 -0.0006 -0.0001	Axis
					-0.5033 -0.8641 -0.0008	-0.6284 0.4407 0.6410	-0.5023 0.8647 0.0016	0.0005 0.9207 -0.3903	Second axis

Spatial dependence of Young's modulus

[[128.0, 57.0, 32.0, -4.0, 0.0, 0.0], [57.0, 128.0, 32.0, 4.0, 0.0, 0.0], [32.0, 32.0, 93.0, 0.0, 0.0, 0.0], [-4.0, 4.0, 0.0, 28.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 28.0, -4.0], [0.0, 0.0, 0.0, 0.0, -4.0, 36.0]] Mg(AlSi)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3833" target="_blank">mp-3833</a>) young

Spatial dependence of linear compressibility

[[128.0, 57.0, 32.0, -4.0, 0.0, 0.0], [57.0, 128.0, 32.0, 4.0, 0.0, 0.0], [32.0, 32.0, 93.0, 0.0, 0.0, 0.0], [-4.0, 4.0, 0.0, 28.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 28.0, -4.0], [0.0, 0.0, 0.0, 0.0, -4.0, 36.0]] Mg(AlSi)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3833" target="_blank">mp-3833</a>) lc

Spatial dependence of shear modulus

[[128.0, 57.0, 32.0, -4.0, 0.0, 0.0], [57.0, 128.0, 32.0, 4.0, 0.0, 0.0], [32.0, 32.0, 93.0, 0.0, 0.0, 0.0], [-4.0, 4.0, 0.0, 28.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 28.0, -4.0], [0.0, 0.0, 0.0, 0.0, -4.0, 36.0]] Mg(AlSi)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3833" target="_blank">mp-3833</a>) shear

Spatial dependence of Poisson's ratio

[[128.0, 57.0, 32.0, -4.0, 0.0, 0.0], [57.0, 128.0, 32.0, 4.0, 0.0, 0.0], [32.0, 32.0, 93.0, 0.0, 0.0, 0.0], [-4.0, 4.0, 0.0, 28.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 28.0, -4.0], [0.0, 0.0, 0.0, 0.0, -4.0, 36.0]] Mg(AlSi)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3833" target="_blank">mp-3833</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)