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 Ag2S (Materials Project id mp-32884)

        43        9       40        0       -0        0  
         9       26       26        0       -0        0  
        40       26       91        0        0        0  
         0        0        0       11        0        0  
        -0       -0        0        0        7        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34.444 GPaEV = 27.02 GPaGV = 9.8667 GPaνV = 0.36926
ReussKR = 18.02 GPaER = 17.437 GPaGR = 6.5127 GPaνR = 0.33872
HillKH = 26.232 GPaEH = 22.253 GPaGH = 8.1897 GPaνH = 0.35861

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 7 GPa 11 GPa 14.433 GPa 24.22 GPa 121.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 9.1119 GPa 40.905 GPa -12.424 TPa–1 41.868 TPa–1 3 GPa 11.957 GPa-0.130770.82112Value
Anisotropy 4.489 3.986Anisotropy
Axis 0.6860
0.7276
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
-0.0001
-0.0000
0.7071
0.6653
0.2395
-1.0000
0.0000
-0.0000
-0.3259
0.2737
-0.9049
Axis
0.0001
1.0000
0.0000
-0.7071
0.6653
0.2395
-0.0000
-1.0000
-0.0000
-0.8252
-0.5494
0.1310
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