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 GeS (Materials Project id mp-12910)

       100       -2       43        0        0        0  
        -2       28        1        0        0        0  
        43        1      105        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0       67        0  
         0        0        0        0        0        5  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35.222 GPaEV = 65.148 GPaGV = 27.333 GPaνV = 0.19173
ReussKR = 19.948 GPaER = 10.837 GPaGR = 3.8443 GPaνR = 0.40946
HillKH = 27.585 GPaEH = 39.353 GPaGH = 15.589 GPaνH = 0.26223

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 5 GPa 27.851 GPa 59.573 GPa 67 GPa 145.58 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.8224 GPa 139.55 GPa 5.8128 TPa–1 36.094 TPa–1 1 GPa 67 GPa-1.38431.8697Value
Anisotropy 36.51 6.2094 67Anisotropy
Axis 0.0000
0.7161
0.6980
0.6959
0.0000
0.7181
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.0002
0.0001
1.0000
-0.0000
0.0000
1.0000
0.7772
0.1074
0.6200
0.7796
0.1450
0.6093
Axis
0.0000
-1.0000
0.0001
-1.0000
0.0000
-0.0000
-0.5201
0.6643
0.5368
0.3141
0.7511
-0.5806
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