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 ZnCl2 (Materials Project id mp-567279)

        46       -5        2        0        0        0  
        -5       46        2        0        0        0  
         2        2       10        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 11.111 GPaEV = 19.094 GPaGV = 7.8667 GPaνV = 0.21359
ReussKR = 7.5849 GPaER = 5.4385 GPaGR = 1.9698 GPaνR = 0.3805
HillKH = 9.348 GPaEH = 12.553 GPaGH = 4.9182 GPaνH = 0.27619

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 3 GPa 9.744 GPa 41.256 GPa 51 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.3674 GPa 44.961 GPa 19.9 TPa–1 92.04 TPa–1 1 GPa 25.5 GPa-0.118420.81938Value
Anisotropy 13.35 4.6250 25.5Anisotropy
Axis 0.4981
0.4980
0.7099
1.0000
0.0000
0.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
-1.0000
0.0000
-0.0000
0.8420
0.0000
0.5395
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.7071
0.0000
-0.0000
-1.0000
0.0000
0.5395
0.0001
-0.8420
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