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 Bi2O3 (Materials Project id mp-1017552)

       179      112       89       25        0        0  
       112      179       89      -25        0        0  
        89       89      137        0        0        0  
        25      -25        0       42        0        0  
         0        0        0        0       42       25  
         0        0        0        0       25       34  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 119.44 GPaEV = 101.27 GPaGV = 37.267 GPaνV = 0.3587
ReussKR = 114.95 GPaER = 63.689 GPaGR = 22.622 GPaνR = 0.40766
HillKH = 117.2 GPaEH = 82.783 GPaGH = 29.944 GPaνH = 0.38228

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12.682 GPa 17 GPa 63.318 GPa 66.45 GPa 92 GPa 361.55 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 37.119 GPa 162.37 GPa 1.9979 TPa–1 4.7034 TPa–1 12.462 GPa 63.161 GPa-0.154020.97306Value
Anisotropy 4.374 2.3542 5.068Anisotropy
Axis 0.0000
0.8690
0.4949
-0.7470
0.4328
0.5046
0.9914
0.1309
0.0000
0.0000
0.0000
1.0000
-0.6595
0.3847
0.6458
-0.5600
0.3222
-0.7633
-0.0000
0.5935
-0.8048
1.0000
0.0002
0.0002
Axis
-0.5085
-0.8610
-0.0064
-0.4986
-0.8668
-0.0001
-1.0000
-0.0000
-0.0000
-0.0003
0.8351
0.5500
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