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 ZnSO4 (Materials Project id mp-5126)

        96       44       33        0        0        0  
        44      158       62        0        0        0  
        33       62      109        0        0        0  
         0        0        0       41        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 71.222 GPaEV = 86.055 GPaGV = 33.133 GPaνV = 0.29862
ReussKR = 65.479 GPaER = 79.132 GPaGR = 30.468 GPaνR = 0.29858
HillKH = 68.35 GPaEH = 82.594 GPaGH = 31.801 GPaνH = 0.2986

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 30 GPa 41 GPa 65.975 GPa 73.231 GPa 223.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 57.132 GPa 116.46 GPa 1.9653 TPa–1 7.5302 TPa–1 20 GPa 41 GPa0.161160.45919Value
Anisotropy 2.038 3.8315 2.05 2.8493Anisotropy
Axis 0.7094
-0.0000
0.7048
-0.0000
0.9319
-0.3628
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.0000
1.0000
-0.7502
0.4622
0.4729
-0.5831
0.6302
-0.5127
Axis
1.0000
0.0000
-0.0000
-0.0000
-1.0000
-0.0000
-0.1698
-0.8259
0.5377
-0.7544
-0.1860
0.6295
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