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 ThAg2 (Materials Project id mp-309)

       136       56       43        0        0        0  
        56      136       43        0        0        0  
        43       43       99        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72.778 GPaEV = 91.975 GPaGV = 35.667 GPaνV = 0.28937
ReussKR = 70.229 GPaER = 89.944 GPaGR = 34.956 GPaνR = 0.28655
HillKH = 71.504 GPaEH = 90.96 GPaGH = 35.311 GPaνH = 0.28798

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 31 GPa 40 GPa 68.948 GPa 80 GPa 222.05 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 78.911 GPa 105.45 GPa 3.6577 TPa–1 6.9236 TPa–1 31 GPa 40 GPa0.223960.33262Value
Anisotropy 1.336 1.8929 1.29 1.4852Anisotropy
Axis 0.2507
0.3256
0.9117
1.0000
0.0002
0.0000
0.8660
0.5000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0836
0.9965
0.0000
0.0000
0.0000
1.0000
-0.4069
0.7067
-0.5788
Axis
1.0000
0.0002
-0.0000
-0.9965
-0.0836
-0.0000
-0.9394
0.3428
0.0000
-0.2888
0.5016
0.8155
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