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 GaSe (Materials Project id mp-1943)

        79       19        2        0        0        0  
        19       79        2        0        0        0  
         2        2        4        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 23.111 GPaEV = 38.337 GPaGV = 15.667 GPaνV = 0.22353
ReussKR = 3.9184 GPaER = 5.2574 GPaGR = 2.0595 GPaνR = 0.27638
HillKH = 13.515 GPaEH = 21.819 GPaGH = 8.8631 GPaνH = 0.23092

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 3.915 GPa 30 GPa 60 GPa 98.085 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.9865 GPa 73.846 GPa 5.2083 TPa–1 244.79 TPa–1 1 GPa 30 GPa0.0204080.68576Value
Anisotropy 24.73 47.0000 30 33.6024Anisotropy
Axis 0.5699
0.0871
0.8171
0.9914
0.1305
0.0000
0.3553
0.9347
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7139
0.7003
0.0000
0.0000
0.0000
1.0000
-0.3560
0.8597
0.3663
Axis
1.0000
0.0000
-0.0000
-0.7003
0.7139
0.0000
-0.7660
0.6428
0.0000
-0.1399
0.3386
-0.9305
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