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 B6O (Materials Project id mp-1346)

       586      124       49       23        0        0  
       124      586       49      -23        0        0  
        49       49      456        0        0        0  
        23      -23        0      178        0        0  
         0        0        0        0      178       23  
         0        0        0        0       23      231  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 230.22 GPaEV = 485.11 GPaGV = 211.13 GPaνV = 0.14881
ReussKR = 223.67 GPaER = 469.7 GPaGR = 204.21 GPaνR = 0.15001
HillKH = 226.95 GPaEH = 477.4 GPaGH = 207.67 GPaνH = 0.1494

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
169.41 GPa 174.32 GPa 239.59 GPa 438.32 GPa 465.68 GPa 727.68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 400.06 GPa 565.61 GPa 1.276 TPa–1 1.9187 TPa–1 169.41 GPa 239.59 GPa0.0370970.24812Value
Anisotropy 1.414 1.5037 1.414 6.6882Anisotropy
Axis 0.0000
0.6773
0.7357
0.8562
0.4944
0.1499
0.9911
0.1332
0.0000
0.0000
0.0000
1.0000
0.3030
0.1749
0.9368
-0.5000
0.8660
0.0000
-0.0000
0.4361
-0.8999
0.5000
0.8660
-0.0000
Axis
-0.5000
0.8660
-0.0000
-0.8113
-0.4684
0.3498
-1.0000
-0.0000
0.0000
-0.7810
0.4509
-0.4320
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