ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-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 ThSiAu (Materials Project id mp-9164)

       226       95       81        0        0        0  
        95      226       81        0        0        0  
        81       81      148        0        0        0  
         0        0        0       67        0        0  
         0        0        0        0       67        0  
         0        0        0        0        0       65  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 123.78 GPaEV = 160.85 GPaGV = 62.667 GPaνV = 0.28341
ReussKR = 117.36 GPaER = 155.76 GPaGR = 60.901 GPaνR = 0.2788
HillKH = 120.57 GPaEH = 158.31 GPaGH = 61.784 GPaνH = 0.28116

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
65 GPa 67 GPa 67 GPa 90.958 GPa 131 GPa 378.04 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 107.12 GPa 171.73 GPa 1.9485 TPa–1 4.624 TPa–1 49.889 GPa 67 GPa0.165640.39465Value
Anisotropy 1.603 2.3731 1.343 2.3826Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.9114
-0.4115
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5001
0.4999
0.7071
0.0000
0.0000
1.0000
-0.4665
0.4665
-0.7515
1.0000
0.0002
0.0000
Axis
-0.4999
0.5001
-0.7071
0.7660
0.6428
-0.0000
-0.5314
0.5314
0.6598
-0.0000
0.0002
-1.0000
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane