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 ZnSe (Materials Project id mp-380)

        92       41       31        0        0        0  
        41       92       31        0        0        0  
        31       31      111        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 55.667 GPaEV = 69.282 GPaGV = 26.8 GPaνV = 0.29257
ReussKR = 55.589 GPaER = 66.792 GPaGR = 25.694 GPaνR = 0.29974
HillKH = 55.628 GPaEH = 68.04 GPaGH = 26.247 GPaνH = 0.29614

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 22 GPa 26 GPa 51 GPa 76.8 GPa 167.2 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.616 GPa 96.549 GPa 5.5292 TPa–1 6.23 TPa–1 22 GPa 34.337 GPa0.17090.4036Value
Anisotropy 1.593 1.1268 1.561 2.3616Anisotropy
Axis 0.7853
0.0000
-0.6191
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.4999
0.5001
-0.7071
1.0000
-0.0004
-0.0000
0.4614
0.4614
-0.7578
Axis
-0.7880
0.6157
-0.0000
-0.5001
-0.4999
-0.7071
-0.0000
-0.0003
-1.0000
0.5358
0.5358
0.6525
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