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 MgCr (Materials Project id mp-973060)

        66       54       54        0        0        0  
        54       67       55        0        0        0  
        54       55       67        0        0        0  
         0        0        0       55        0        0  
         0        0        0        0       55        0  
         0        0        0        0        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 58.444 GPaEV = 88.498 GPaGV = 35.467 GPaνV = 0.24763
ReussKR = 58.421 GPaER = 36.792 GPaGR = 13.187 GPaνR = 0.39504
HillKH = 58.433 GPaEH = 64.087 GPaGH = 24.327 GPaνH = 0.31721

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12 GPa 12.661 GPa 55 GPa 55 GPa 55 GPa 175.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 17.689 GPa 125.6 GPa 5.4054 TPa–1 6.3063 TPa–1 6 GPa 55 GPa-0.551221.2621Value
Anisotropy 7.1 1.1667 9.167Anisotropy
Axis 0.0000
0.0000
1.0000
0.5748
0.5786
-0.5786
0.0000
0.9659
0.2588
1.0000
0.0000
0.0000
0.0000
0.7071
-0.7071
0.0000
0.0000
1.0000
0.7085
0.0001
-0.7057
-0.7061
0.7081
0.0001
Axis
0.0000
0.7071
0.7071
0.1736
0.9848
-0.0000
-0.7057
-0.0002
-0.7085
0.0002
0.0003
-1.0000
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