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 CaSiO3 (Materials Project id mp-5733)

       151       60       52        0      -10        0  
        60      189       51        0        3        0  
        52       51      170        0       -5        0  
         0        0        0       43        0       -1  
       -10        3       -5        0       30        0  
         0        0        0       -1        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 92.889 GPaEV = 124.44 GPaGV = 48.733 GPaνV = 0.27673
ReussKR = 91.415 GPaER = 115.51 GPaGR = 44.791 GPaνR = 0.28941
HillKH = 92.152 GPaEH = 119.99 GPaGH = 46.762 GPaνH = 0.28298

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
28.66 GPa 42.917 GPa 55.083 GPa 102.94 GPa 128.09 GPa 280.31 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 74.991 GPa 157.3 GPa 2.8847 TPa–1 4.954 TPa–1 28.777 GPa 64.549 GPa0.0879590.59248Value
Anisotropy 2.098 1.7173 2.243 6.7358Anisotropy
Axis 0.7668
-0.0000
0.6419
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
-0.8048
0.0000
-0.5936
0.0625
-0.0003
0.9980
-0.0872
0.7071
0.7017
0.5765
0.0000
-0.8171
-0.6351
0.0001
0.7725
Axis
0.9980
0.0002
-0.0625
-0.0872
-0.7071
0.7017
0.0000
1.0000
0.0000
-0.7725
0.0000
-0.6351
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