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 MgIn (Materials Project id mp-2313)

        67       28       24        0        0        0  
        28       67       24        0        0        0  
        24       24       72        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 39.778 GPaEV = 42.481 GPaGV = 16.067 GPaνV = 0.32201
ReussKR = 39.776 GPaER = 38.074 GPaGR = 14.202 GPaνR = 0.34046
HillKH = 39.777 GPaEH = 40.293 GPaGH = 15.134 GPaνH = 0.33117

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10 GPa 17 GPa 39 GPa 47.664 GPa 119.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.853 GPa 59.874 GPa 8.263 TPa–1 8.4388 TPa–1 10 GPa 22.578 GPa0.165150.57034Value
Anisotropy 1.941 1.0213 2.258 3.4534Anisotropy
Axis 0.5198
0.5197
-0.6780
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9659
0.2588
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.6313
-0.0000
0.7756
0.6862
0.0001
-0.7275
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
-0.0000
-0.7275
-0.0000
-0.6862
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