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-672)

        80       45       37        0        0        0  
        45       80       37        0        0        0  
        37       37       85        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       15        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 53.667 GPaEV = 48.084 GPaGV = 17.8 GPaνV = 0.35067
ReussKR = 53.653 GPaER = 46.701 GPaGR = 17.234 GPaνR = 0.35493
HillKH = 53.66 GPaEH = 47.394 GPaGH = 17.517 GPaνH = 0.3528

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 15 GPa 17 GPa 35 GPa 48.982 GPa 161.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.521 GPa 63.096 GPa 6.086 TPa–1 6.4663 TPa–1 15 GPa 22.269 GPa0.233460.46367Value
Anisotropy 1.484 1.0625 1.485 1.9861Anisotropy
Axis -0.5475
0.5475
0.6329
0.0000
0.0000
1.0000
0.9239
0.3827
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.7071
0.0000
-0.7071
0.7071
0.0000
Axis
0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-0.0000
1.0000
-0.7071
-0.7071
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