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 MgH2 (Materials Project id mp-23711)

        99       19       34        0        0        0  
        19       85       32        0        0        0  
        34       32       78        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       36        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48 GPaEV = 80.542 GPaGV = 33 GPaνV = 0.22034
ReussKR = 47.805 GPaER = 77.985 GPaGR = 31.75 GPaνR = 0.22811
HillKH = 47.902 GPaEH = 79.267 GPaGH = 32.375 GPaνH = 0.22421

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 36 GPa 38 GPa 44.701 GPa 72.702 GPa 144.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 58.346 GPa 89.55 GPa 6.2351 TPa–1 7.7673 TPa–1 23.883 GPa 38 GPa0.0600060.40706Value
Anisotropy 1.535 1.2457 1.591 6.7837Anisotropy
Axis 0.0000
0.0000
1.0000
0.8583
-0.0000
0.5131
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.2031
0.6773
0.7071
-0.0000
0.0000
1.0000
-0.0000
1.0000
0.0000
1.0000
-0.0004
-0.0000
Axis
0.2034
0.6772
-0.7071
-0.0000
-1.0000
0.0000
-1.0000
-0.0000
-0.0000
-0.0000
-0.0003
-1.0000
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