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-569051)

        98       19       34        0        0        0  
        19       85       32        0        0        0  
        34       32       79        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 = 47.821 GPaER = 78.128 GPaGR = 31.819 GPaνR = 0.22771
HillKH = 47.911 GPaEH = 79.339 GPaGH = 32.409 GPaνH = 0.224

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 36 GPa 38 GPa 45.235 GPa 72.242 GPa 144.52 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 59.265 GPa 89.116 GPa 6.3437 TPa–1 7.7983 TPa–1 24.154 GPa 38 GPa0.0627090.40098Value
Anisotropy 1.504 1.2293 1.573 6.3944Anisotropy
Axis 0.0000
0.0000
1.0000
0.8504
0.0000
0.5262
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.2279
0.6694
-0.7071
-0.0000
0.0000
1.0000
-0.0000
1.0000
0.0000
1.0000
0.0003
0.0000
Axis
-0.2284
-0.6692
-0.7071
-0.0000
-1.0000
0.0000
-1.0000
-0.0000
-0.0000
0.0000
0.0002
-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