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 CdS (Materials Project id mp-2469)

        66       47       47        0        0        0  
        47       66       47        0        0        0  
        47       47       66        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 53.333 GPaEV = 51.906 GPaGV = 19.4 GPaνV = 0.33779
ReussKR = 53.333 GPaER = 41.998 GPaGR = 15.342 GPaνR = 0.36876
HillKH = 53.333 GPaEH = 47.009 GPaGH = 17.371 GPaνH = 0.3531

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
19 GPa 19 GPa 26 GPa 26 GPa 26 GPa 160 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.903 GPa 67.097 GPa 6.25 TPa–1 6.25 TPa–1 9.5 GPa 26 GPa-0.0605680.75525Value
Anisotropy 2.494 1.0000 2.737Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.2500
0.9330
0.2588
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
0.7071
-0.0005
-0.7071
-1.0000
0.0000
0.0000
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