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 K (Materials Project id mp-604318)

         6        3        2        0        0        0  
         3        6        2        0        0        0  
         2        2        7        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 3.6667 GPaEV = 3.7258 GPaGV = 1.4 GPaνV = 0.33065
ReussKR = 3.6667 GPaER = 3.3177 GPaGR = 1.2295 GPaνR = 0.3492
HillKH = 3.6667 GPaEH = 3.5232 GPaGH = 1.3148 GPaνH = 0.33986

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 1 GPa 3 GPa 5 GPa 11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.75 GPa 6.1111 GPa 90.909 TPa–1 90.909 TPa–1 1 GPa 2.1429 GPa0.115940.5942Value
Anisotropy 2.222 1.0000 2.143 5.1250Anisotropy
Axis 0.5773
0.5773
0.5774
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.7071
0.0000
-0.7071
0.7071
0.0000
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0005
-0.7071
-0.0004
-0.0004
-1.0000
-0.7071
-0.7071
-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