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 Mg3Sb2 (Materials Project id mp-2646)

        74       37       21       -6        0        0  
        37       74       21        6        0        0  
        21       21       77        0        0        0  
        -6        6        0       15        0        0  
         0        0        0        0       15       -6  
         0        0        0        0       -6       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 42.556 GPaEV = 50.372 GPaGV = 19.333 GPaνV = 0.30272
ReussKR = 42.348 GPaER = 42.564 GPaGR = 15.972 GPaνR = 0.33248
HillKH = 42.452 GPaEH = 46.511 GPaGH = 17.653 GPaνH = 0.3174

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10.315 GPa 12.108 GPa 22.685 GPa 39.892 GPa 59.78 GPa 128.22 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 28.765 GPa 69.054 GPa 7.3059 TPa–1 9.002 TPa–1 10.315 GPa 27.152 GPa-0.0374590.68632Value
Anisotropy 2.401 1.2321 2.632Anisotropy
Axis 0.7065
0.4136
0.5743
0.0000
0.0000
1.0000
-0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.0000
0.6153
0.7883
0.5313
-0.2598
0.8064
-0.4076
0.2321
-0.8832
-0.5034
0.8641
-0.0033
Axis
-1.0000
-0.0001
0.0001
-0.7042
0.3937
0.5909
-0.5002
-0.8659
0.0032
-0.7572
-0.4429
-0.4801
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