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 ErSi (Materials Project id mp-378)

       171       42       77        0        0        0  
        42      203       28        0        0        0  
        77       28      187        0        0        0  
         0        0        0       46        0        0  
         0        0        0        0      107        0  
         0        0        0        0        0       60  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95 GPaEV = 168.98 GPaGV = 70.2 GPaνV = 0.20355
ReussKR = 94.862 GPaER = 155.08 GPaGR = 63.167 GPaνR = 0.22754
HillKH = 94.931 GPaEH = 162.1 GPaGH = 66.683 GPaνH = 0.21541

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
46 GPa 60 GPa 99.823 GPa 107 GPa 175.51 GPa 285.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 120.81 GPa 228.41 GPa 3.3847 TPa–1 3.7555 TPa–1 46 GPa 107 GPa0.0301330.43871Value
Anisotropy 1.891 1.1096 2.326 14.5593Anisotropy
Axis -0.0000
0.6528
0.7576
0.6779
-0.0000
0.7351
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0002
0.0001
1.0000
-0.0000
0.0000
1.0000
-0.7011
0.3767
0.6054
0.0000
0.0000
1.0000
Axis
-0.0000
1.0000
-0.0001
-1.0000
0.0000
-0.0000
-0.7120
-0.3234
-0.6233
1.0000
0.0000
-0.0000
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