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 MgF2 (Materials Project id mp-1249)

       190       60       60        0        0        0  
        60      134       79        0        0        0  
        60       79      134        0        0        0  
         0        0        0       89        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       51  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95.111 GPaEV = 139.32 GPaGV = 55.467 GPaνV = 0.25587
ReussKR = 94.249 GPaER = 123.3 GPaGR = 48.092 GPaνR = 0.28196
HillKH = 94.68 GPaEH = 131.39 GPaGH = 51.779 GPaνH = 0.26872

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 51 GPa 55 GPa 89 GPa 115.87 GPa 287.13 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 83.708 GPa 176.54 GPa 2.7953 TPa–1 3.9074 TPa–1 27.5 GPa 89 GPa-0.00819790.52196Value
Anisotropy 2.109 1.3978 3.236Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
0.0000
0.9239
0.3827
0.0002
0.7071
-0.7071
0.0004
0.0003
1.0000
-0.0000
0.7071
-0.7071
-0.0004
-0.0002
1.0000
Axis
0.0001
-0.7071
-0.7071
0.0000
1.0000
-0.0003
0.0000
0.7071
0.7071
0.0000
1.0000
0.0002
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