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 Mg(AlSi)2 (Materials Project id mp-3833)

       128       57       32       -4        0        0  
        57      128       32        4        0        0  
        32       32       93        0        0        0  
        -4        4        0       28        0        0  
         0        0        0        0       28       -4  
         0        0        0        0       -4       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65.667 GPaEV = 86.113 GPaGV = 33.6 GPaνV = 0.28144
ReussKR = 62.374 GPaER = 82.345 GPaGR = 32.167 GPaνR = 0.27997
HillKH = 64.021 GPaEH = 84.229 GPaGH = 32.883 GPaνH = 0.28072

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26.343 GPa 27.268 GPa 37.657 GPa 71.732 GPa 74.471 GPa 203.53 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.262 GPa 101.84 GPa 4.0245 TPa–1 7.9831 TPa–1 26.286 GPa 38.229 GPa0.129040.44234Value
Anisotropy 1.492 1.9836 1.454 3.4278Anisotropy
Axis -0.0000
0.7091
-0.7051
0.8414
0.5166
-0.1585
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
-0.3400
0.1988
-0.9192
-0.4449
0.4723
-0.7609
0.3697
0.2164
-0.9036
1.0000
-0.0006
-0.0001
Axis
-0.5033
-0.8641
-0.0008
-0.6284
0.4407
0.6410
-0.5023
0.8647
0.0016
0.0005
0.9207
-0.3903
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