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 CaCl2 (Materials Project id mp-23214)

        19       20        9        0        0        0  
        20       39       19        0        0        0  
         9       19       42        0        0        0  
         0        0        0       12        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 21.778 GPaEV = 35.129 GPaGV = 14.267 GPaνV = 0.23116
ReussKR = 16.081 GPaER = 21.81 GPaGR = 8.5601 GPaνR = 0.27395
HillKH = 18.929 GPaEH = 28.51 GPaGH = 11.413 GPaνH = 0.24898

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6.4288 GPa 11 GPa 12 GPa 25.444 GPa 31 GPa 68.127 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.7267 GPa 48.985 GPa -11.935 TPa–1 57.161 TPa–1 3.3445 GPa 31 GPa-0.283920.94402Value
Anisotropy 5.613 9.269Anisotropy
Axis 1.0000
0.0000
0.0000
0.6370
0.7708
-0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
-1.0000
-0.0000
-0.0001
0.5574
0.0001
0.8302
-0.0000
0.9326
0.3608
Axis
-0.7071
-0.7071
0.0000
0.0000
-1.0000
0.0000
0.8302
0.0004
-0.5574
-1.0000
0.0000
-0.0001
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