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 MgAs4 (Materials Project id mp-7623)

        67       33       26        0        0        0  
        33       67       26        0        0        0  
        26       26       83        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       34  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 43 GPaEV = 64.916 GPaGV = 26 GPaνV = 0.24839
ReussKR = 42.889 GPaER = 62.202 GPaGR = 24.717 GPaνR = 0.25828
HillKH = 42.944 GPaEH = 63.564 GPaGH = 25.358 GPaνH = 0.25331

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 26 GPa 34 GPa 34 GPa 53.761 GPa 129.24 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 48.359 GPa 75.042 GPa 6.9085 TPa–1 8.2038 TPa–1 17 GPa 34 GPa0.103560.42231Value
Anisotropy 1.552 1.1875 2 4.0780Anisotropy
Axis 1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
-0.0000
1.0000
0.0007
-0.0000
-0.7071
0.7071
0.0000
1.0000
-0.0000
-0.0001
Axis
-0.7071
0.7071
0.0001
-0.0007
1.0000
-0.0000
-0.7071
-0.7071
0.0000
0.0000
1.0000
0.0000
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