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 MgNi (Materials Project id mp-1018140)

       208      114      135        0        0        0  
       114      208      135        0        0        0  
       135      135      164        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 149.78 GPaEV = 145.73 GPaGV = 54.467 GPaνV = 0.33783
ReussKR = 148.71 GPaER = 114.32 GPaGR = 41.665 GPaνR = 0.37188
HillKH = 149.24 GPaEH = 130.22 GPaGH = 48.066 GPaνH = 0.35458

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36.382 GPa 61 GPa 73 GPa 73 GPa 94 GPa 449.62 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.801 GPa 178.16 GPa 1.7728 TPa–1 3.1789 TPa–1 21.495 GPa 73 GPa-0.100370.90579Value
Anisotropy 3.507 1.7931 3.396Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5776
0.5776
-0.5768
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
0.5000
0.8660
-0.0000
-0.7071
-0.7071
0.0000
0.0001
-0.0000
-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