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 CdTe (Materials Project id mp-406)

        47       30       30        0        0        0  
        30       47       30        0        0        0  
        30       30       47        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       19        0  
         0        0        0        0        0       19  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35.667 GPaEV = 39.005 GPaGV = 14.8 GPaνV = 0.31773
ReussKR = 35.667 GPaER = 34.097 GPaGR = 12.717 GPaνR = 0.34067
HillKH = 35.667 GPaEH = 36.572 GPaGH = 13.758 GPaνH = 0.3291

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 19 GPa 19 GPa 19 GPa 107 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 23.623 GPa 48.405 GPa 9.3458 TPa–1 9.3458 TPa–1 8.5 GPa 19 GPa0.0091540.63245Value
Anisotropy 2.049 1.0000 2.235 69.0906Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.4830
0.6294
0.6088
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
-0.7071
0.0002
-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