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 CaMgSiO4 (Materials Project id mp-6493)

       175       70       66        0        0        0  
        70      144       55        0        0        0  
        66       55      215        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       57        0  
         0        0        0        0        0       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 101.78 GPaEV = 140.39 GPaGV = 55.267 GPaνV = 0.27011
ReussKR = 99.504 GPaER = 136.57 GPaGR = 53.713 GPaνR = 0.27125
HillKH = 100.64 GPaEH = 138.48 GPaGH = 54.49 GPaνH = 0.27067

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48 GPa 57 GPa 57 GPa 87.772 GPa 136.85 GPa 309.38 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 111.7 GPa 183.06 GPa 2.5944 TPa–1 4.5328 TPa–1 44.216 GPa 62.676 GPa0.150440.40881Value
Anisotropy 1.639 1.7471 1.418 2.7174Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.7071
0.7071
0.0000
-0.6343
0.3125
0.7071
-0.0000
1.0000
-0.0000
1.0000
-0.0001
0.0000
Axis
-0.7071
0.7071
-0.0000
-0.6342
0.3128
-0.7071
0.0001
-0.0000
-1.0000
0.0001
1.0000
0.0000
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