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 Ce(MnSi)2 (Materials Project id mp-2965)

       188      123       76        0        0        0  
       123      188       76        0        0        0  
        76       76      191        0        0        0  
         0        0        0      100        0        0  
         0        0        0        0      100        0  
         0        0        0        0        0      113  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 124.11 GPaEV = 201.74 GPaGV = 82.067 GPaνV = 0.22909
ReussKR = 123.01 GPaER = 169.05 GPaGR = 66.506 GPaνR = 0.27094
HillKH = 123.56 GPaEH = 185.65 GPaGH = 74.286 GPaνH = 0.24958

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
65 GPa 100 GPa 100 GPa 113 GPa 127.91 GPa 374.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 103.22 GPa 247.22 GPa 2.4034 TPa–1 3.323 TPa–1 32.5 GPa 113 GPa-0.131580.66122Value
Anisotropy 2.395 1.3826 3.477Anisotropy
Axis 1.0000
0.0000
0.0000
0.6304
0.6304
0.4529
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0000
0.0000
0.6930
-0.0002
0.7210
-0.8133
-0.0000
0.5818
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
0.0000
0.7210
-0.0004
-0.6930
0.0000
-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