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 ZnTe (Materials Project id mp-571195)

        61       31       31        2       -3       -3  
        31       61       31        3       -2       -3  
        31       31       61        3       -3       -2  
         2        3        3       27        2        2  
        -3       -2       -3        2       27       -2  
        -3       -3       -2        2       -2       27  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 41 GPaEV = 56.417 GPaGV = 22.2 GPaνV = 0.27066
ReussKR = 40.072 GPaER = 51.974 GPaGR = 20.242 GPaνR = 0.28383
HillKH = 40.536 GPaEH = 54.204 GPaGH = 21.221 GPaνH = 0.27714

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22.364 GPa 28.382 GPa 28.382 GPa 30.618 GPa 30.618 GPa 123.64 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 39.747 GPa 67.065 GPa 5.425 TPa–1 9.7649 TPa–1 14.976 GPa 29.036 GPa0.0382640.5178Value
Anisotropy 1.687 1.8000 1.939 13.5325Anisotropy
Axis -0.0509
0.0509
-0.9974
0.6312
0.4507
-0.6312
-0.5774
0.5774
0.5773
0.7071
0.7071
-0.0001
0.7089
0.0188
-0.7051
-0.0356
0.0356
0.9987
0.7071
0.0002
0.7071
-0.0712
0.7053
0.7053
Axis
-0.7046
-0.0278
-0.7091
0.7071
0.7071
0.0000
0.6893
0.2230
-0.6893
-0.9975
-0.0503
-0.0503
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