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 ZnS (Materials Project id mp-561258)

       119       51       39        0        0        0  
        51      119       39        0        0        0  
        39       39      130        0        0        0  
         0        0        0       29        0        0  
         0        0        0        0       29        0  
         0        0        0        0        0       34  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 69.556 GPaEV = 88.447 GPaGV = 34.333 GPaνV = 0.28807
ReussKR = 69.555 GPaER = 86.381 GPaGR = 33.403 GPaνR = 0.29301
HillKH = 69.555 GPaEH = 87.416 GPaGH = 33.868 GPaνH = 0.29054

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29 GPa 29 GPa 34 GPa 68 GPa 91.331 GPa 208.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 79.379 GPa 112.11 GPa 4.7749 TPa–1 4.8274 TPa–1 29 GPa 42.058 GPa0.190120.37874Value
Anisotropy 1.412 1.0110 1.45 1.9921Anisotropy
Axis -0.0340
0.7648
0.6434
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
0.4504
0.8928
-0.0000
0.0820
0.6639
-0.7433
Axis
1.0000
0.0000
-0.0000
-0.5291
-0.4692
-0.7071
0.0000
-0.0000
-1.0000
-0.0911
-0.7377
-0.6690
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