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 SrAl2O4 (Materials Project id mp-5492)

       150       70       40        0        0        0  
        70      150       40        0        0        0  
        40       40      123        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       40        0  
         0        0        0        0        0       40  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 80.333 GPa	EV = 107.74 GPa	GV = 42.2 GPa	νV = 0.27648
Reuss	KR = 77.974 GPa	ER = 105.95 GPa	GR = 41.597 GPa	νR = 0.27353
Hill	KH = 79.154 GPa	EH = 106.84 GPa	GH = 41.898 GPa	νH = 0.27503

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
40 GPa	40 GPa	40 GPa	80 GPa	96.987 GPa	246.01 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	100.66 GPa	113.28 GPa	3.4786 TPa–1	5.8676 TPa–1	40 GPa	46.727 GPa	0.18182	0.41602	Value
Anisotropy	1.125		1.6867		1.168		2.2881		Anisotropy
Axis	0.6208 0.2449 0.7447	1.0000 0.0002 0.0000	0.2588 0.9659 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.5955 0.3812 0.7071	0.0000 0.0000 1.0000	0.7704 0.6376 0.0000	Axis
					-0.7660 0.6428 -0.0000	0.5955 0.3812 -0.7071	0.1736 0.9848 -0.0000	-0.6376 0.7704 0.0000	Second axis

Spatial dependence of Young's modulus

[[150.0, 70.0, 40.0, 0.0, 0.0, 0.0], [70.0, 150.0, 40.0, 0.0, 0.0, 0.0], [40.0, 40.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 40.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 40.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 40.0]] SrAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5492" target="_blank">mp-5492</a>) young

Spatial dependence of linear compressibility

[[150.0, 70.0, 40.0, 0.0, 0.0, 0.0], [70.0, 150.0, 40.0, 0.0, 0.0, 0.0], [40.0, 40.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 40.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 40.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 40.0]] SrAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5492" target="_blank">mp-5492</a>) lc

Spatial dependence of shear modulus

[[150.0, 70.0, 40.0, 0.0, 0.0, 0.0], [70.0, 150.0, 40.0, 0.0, 0.0, 0.0], [40.0, 40.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 40.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 40.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 40.0]] SrAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5492" target="_blank">mp-5492</a>) shear

Spatial dependence of Poisson's ratio

[[150.0, 70.0, 40.0, 0.0, 0.0, 0.0], [70.0, 150.0, 40.0, 0.0, 0.0, 0.0], [40.0, 40.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 40.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 40.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 40.0]] SrAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-5492" target="_blank">mp-5492</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)