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 MgSbPd (Materials Project id mp-10183)

       112       65       65        0        0        0  
        65      112       65        0        0        0  
        65       65      112        0        0        0  
         0        0        0       33        0        0  
         0        0        0        0       33        0  
         0        0        0        0        0       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 80.667 GPaEV = 78.168 GPaGV = 29.2 GPaνV = 0.3385
ReussKR = 80.667 GPaER = 76.267 GPaGR = 28.407 GPaνR = 0.34242
HillKH = 80.667 GPaEH = 77.219 GPaGH = 28.803 GPaνH = 0.34046

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33 GPa 33 GPa 33 GPa 47 GPa 47 GPa 242 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 64.26 GPa 87.12 GPa 4.1322 TPa–1 4.1322 TPa–1 23.5 GPa 33 GPa0.212190.45721Value
Anisotropy 1.356 1.0000 1.404 2.1547Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.6871
0.3967
0.6088
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0004
-0.7071
Axis
-0.7071
-0.0002
-0.7071
1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
0.0002
1.0000
-0.0003
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