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-555763)

       116       51       39        4        0        0  
        51      116       39       -4        0        0  
        39       39      133        0        0        0  
         4       -4        0       28        0        0  
         0        0        0        0       28        4  
         0        0        0        0        4       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 69.222 GPaEV = 86.169 GPaGV = 33.333 GPaνV = 0.29253
ReussKR = 69.202 GPaER = 82.596 GPaGR = 31.742 GPaνR = 0.30107
HillKH = 69.212 GPaEH = 84.388 GPaGH = 32.537 GPaνH = 0.29679

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25.528 GPa 27.154 GPa 34.472 GPa 65.846 GPa 92.285 GPa 207.71 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.343 GPa 114.78 GPa 4.6429 TPa–1 4.9038 TPa–1 25.528 GPa 42.221 GPa0.148270.44136Value
Anisotropy 1.68 1.0562 1.654 2.9767Anisotropy
Axis -0.6991
0.4110
-0.5851
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.4886
0.8725
0.0000
0.0000
0.5257
-0.8507
0.0005
0.6427
-0.7661
-0.4191
0.2379
0.8762
-0.0002
0.5986
-0.8011
Axis
-1.0000
0.0000
0.0000
-0.0001
-0.7661
-0.6427
-0.4963
-0.8682
-0.0016
-0.0003
-0.8011
-0.5986
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