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 ErGa3 (Materials Project id mp-398)

       158       70       70        0        0        0  
        70      158       70        0        0        0  
        70       70      158        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 99.333 GPaEV = 96.837 GPaGV = 36.2 GPaνV = 0.33752
ReussKR = 99.333 GPaER = 94.335 GPaGR = 35.155 GPaνR = 0.34172
HillKH = 99.333 GPaEH = 95.588 GPaGH = 35.677 GPaνH = 0.33962

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 31 GPa 31 GPa 88 GPa 88 GPa 298 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 84.237 GPa 115.02 GPa 3.3557 TPa–1 3.3557 TPa–1 31 GPa 44 GPa0.240980.45608Value
Anisotropy 1.365 1.0000 1.419 1.8926Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3536
0.8536
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.0000
-0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
-0.7071
0.0002
-0.7071
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