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-23262)

       134       23       47        0      -12        0  
        23       65       43        0       -2        0  
        47       43       97        0      -10        0  
         0        0        0       39        0       -5  
       -12       -2      -10        0       34        0  
         0        0        0       -5        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 58 GPaEV = 81.087 GPaGV = 32 GPaνV = 0.26699
ReussKR = 51.14 GPaER = 70.814 GPaGR = 27.897 GPaνR = 0.26922
HillKH = 54.57 GPaEH = 75.951 GPaGH = 29.948 GPaνH = 0.26803

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24.299 GPa 29.914 GPa 36.692 GPa 40.701 GPa 79.319 GPa 184.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.692 GPa 119.8 GPa 2.1364 TPa–1 11.728 TPa–1 17.043 GPa 40.701 GPa0.0208160.5857Value
Anisotropy 2.622 5.4897 2.388 28.1368Anisotropy
Axis 0.0000
1.0000
0.0000
-0.9345
0.0000
0.3560
-0.5497
-0.0000
0.8354
0.0000
1.0000
0.0000
-0.1100
0.7071
-0.6985
-0.3220
0.0000
0.9467
0.0000
1.0000
-0.0000
0.2355
-0.0002
-0.9719
Axis
-0.1101
-0.7071
-0.6985
0.0000
-1.0000
0.0000
-0.9956
0.0000
0.0941
0.0001
1.0000
-0.0001
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