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 DyS (Materials Project id mp-2470)

       228       32       32        0        0        0  
        32      228       32        0        0        0  
        32       32      228        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 97.333 GPaEV = 128.07 GPaGV = 50 GPaνV = 0.2807
ReussKR = 97.333 GPaER = 73.458 GPaGR = 26.727 GPaνR = 0.37422
HillKH = 97.333 GPaEH = 101.73 GPaGH = 38.364 GPaνH = 0.32581

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 18 GPa 196 GPa 196 GPa 292 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.865 GPa 220.12 GPa 3.4247 TPa–1 3.4247 TPa–1 18 GPa 98 GPa0.0352080.74914Value
Anisotropy 4.328 1.0000 5.444 21.2778Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.3827
0.0000
0.9239
-0.0795
0.6036
0.7934
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0003
0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
-0.0000
0.7071
-0.0001
-0.7071
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