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 AuSe (Materials Project id mp-2793)

         3        3        4        0       -0        0  
         3       73       11        0        2        0  
         4       11       26        0       -2        0  
         0        0        0        9        0        1  
        -0        2       -2        0        4        0  
         0        0        0        1        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 15.333 GPaEV = 21.309 GPaGV = 8.4 GPaνV = 0.26838
ReussKR = 2.9476 GPaER = 5.2623 GPaGR = 2.1881 GPaνR = 0.20245
HillKH = 9.1405 GPaEH = 13.312 GPaGH = 5.2941 GPaνH = 0.25727

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.87689 GPa 2.25 GPa 3.7458 GPa 9.1231 GPa 24.326 GPa 75.678 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.2016 GPa 65.746 GPa -17.854 TPa–1 355.05 TPa–1 0.87689 GPa 15.038 GPa-0.531361.4387Value
Anisotropy 29.86 17.15Anisotropy
Axis 0.8940
0.4443
-0.0574
0.0000
1.0000
0.0000
0.0133
-0.0000
0.9999
0.9999
-0.0000
-0.0133
-0.9925
-0.0000
0.1222
-0.1932
0.7071
0.6802
-0.3541
0.3363
0.8726
-0.1329
0.4818
0.8661
Axis
0.0000
-1.0000
-0.0000
-0.1932
-0.7071
0.6802
-0.6317
0.6020
-0.4884
-0.7930
-0.5759
0.1987
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