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 Mg2Ga (Materials Project id mp-30650)

        85       28       26        0        0        0  
        28       85       26        0        0        0  
        26       26       79        0        0        0  
         0        0        0       21        0        0  
         0        0        0        0       21        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 45.444 GPaEV = 64.375 GPaGV = 25.467 GPaνV = 0.26391
ReussKR = 45.359 GPaER = 63.145 GPaGR = 24.9 GPaνR = 0.26798
HillKH = 45.402 GPaEH = 63.761 GPaGH = 25.183 GPaνH = 0.26594

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21 GPa 21 GPa 29 GPa 55.491 GPa 57 GPa 136.51 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 57.363 GPa 72.279 GPa 6.9967 TPa–1 8.0528 TPa–1 21 GPa 29 GPa0.196560.3705Value
Anisotropy 1.26 1.1509 1.381 1.8849Anisotropy
Axis 0.6788
-0.0000
0.7344
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
0.0000
0.4798
0.4798
0.7345
0.5131
0.5131
-0.6881
Axis
-0.7660
-0.6428
0.0000
-0.0007
1.0000
0.0000
-0.7071
0.7071
0.0000
-0.4865
-0.4866
-0.7256
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