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 Na2BHO3 (Materials Project id mp-556125)

       131       22       16        0        0        0  
        22      115       23        0        0        0  
        16       23       65        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48.111 GPaEV = 62.761 GPaGV = 24.467 GPaνV = 0.28258
ReussKR = 43.982 GPaER = 40.217 GPaGR = 14.922 GPaνR = 0.3476
HillKH = 46.047 GPaEH = 51.711 GPaGH = 19.694 GPaνH = 0.31283

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 11 GPa 21 GPa 55.301 GPa 101.39 GPa 154.31 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.452 GPa 124.56 GPa 5.2426 TPa–1 12.235 TPa–1 7 GPa 49.929 GPa0.033950.75881Value
Anisotropy 5.094 2.3338 7.133 22.3512Anisotropy
Axis 0.0000
0.6833
0.7301
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.0000
0.7133
-0.7008
-0.0004
0.7773
-0.6292
Axis
-0.0000
1.0000
-0.0000
-0.7071
0.7071
-0.0000
-1.0000
-0.0000
-0.0000
-0.0003
-0.6292
-0.7773
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