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 Mg(HO)2 (Materials Project id mp-30247)

       153       43       10        1        0        0  
        43      153       10       -1        0        0  
        10       10       53        0        0        0  
         1       -1        0       20        0        0  
         0        0        0        0       20        1  
         0        0        0        0        1       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 53.889 GPaEV = 93.741 GPaGV = 38.733 GPaνV = 0.21008
ReussKR = 38.885 GPaER = 71.061 GPaGR = 29.722 GPaνR = 0.19542
HillKH = 46.387 GPaEH = 82.413 GPaGH = 34.228 GPaνH = 0.20389

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
19.971 GPa 19.978 GPa 51.615 GPa 55.029 GPa 110.02 GPa 197.39 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 49.048 GPa 139.97 GPa 4.2207 TPa–1 17.275 TPa–1 19.971 GPa 55.029 GPa0.0471310.36494Value
Anisotropy 2.854 4.0930 2.755 7.7432Anisotropy
Axis -0.0000
0.4831
0.8756
0.8659
0.5000
0.0135
0.9914
0.1309
-0.0000
0.0000
0.0000
1.0000
-0.0247
0.0143
0.9996
-0.5001
0.8660
-0.0000
0.0000
0.2850
-0.9585
-0.6978
0.4029
0.5923
Axis
0.5000
0.8660
0.0000
-0.8656
-0.4999
0.0285
-1.0000
-0.0000
-0.0000
-0.5129
0.2962
-0.8057
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