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 CaH2 (Materials Project id mp-23713)

        87       23       19        0        0        0  
        23       96       30        0        0        0  
        19       30       94        0        0        0  
         0        0        0       27        0        0  
         0        0        0        0       33        0  
         0        0        0        0        0       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46.778 GPaEV = 79.495 GPaGV = 32.667 GPaνV = 0.21676
ReussKR = 46.443 GPaER = 78.65 GPaGR = 32.293 GPaνR = 0.21776
HillKH = 46.61 GPaEH = 79.073 GPaGH = 32.48 GPaνH = 0.21726

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
27 GPa 33 GPa 35 GPa 64.313 GPa 71.366 GPa 141.32 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.463 GPa 83.344 GPa 6.2471 TPa–1 8.3222 TPa–1 27 GPa 35.609 GPa0.139590.36042Value
Anisotropy 1.134 1.3322 1.319 2.5821Anisotropy
Axis 0.0000
0.7066
0.7076
0.4910
0.8712
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.0003
-0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
0.0000
-0.0000
-0.0003
0.7074
-0.7068
Axis
0.0000
1.0000
0.0000
0.7071
-0.0005
-0.7071
-0.0000
0.0002
-1.0000
-0.0003
-0.7068
-0.7074
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