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 BiPbClO2 (Materials Project id mp-23084)

       109       21       29        0        0        0  
        21       52       22        0        0        0  
        29       22      126        0        0        0  
         0        0        0        9        0        0  
         0        0        0        0       19        0  
         0        0        0        0        0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 47.889 GPaEV = 56.18 GPaGV = 21.533 GPaνV = 0.30448
ReussKR = 40.609 GPaER = 37.925 GPaGR = 14.106 GPaνR = 0.34435
HillKH = 44.249 GPaEH = 47.132 GPaGH = 17.819 GPaνH = 0.32248

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8 GPa 9 GPa 19 GPa 42.996 GPa 87.538 GPa 156.47 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.163 GPa 112.67 GPa 4.0617 TPa–1 15.445 TPa–1 8 GPa 43.991 GPa0.0636930.67725Value
Anisotropy 4.306 3.8027 5.499 10.6330Anisotropy
Axis -0.5988
0.7374
0.3126
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
-0.0005
0.0001
0.7071
-0.0000
-0.7071
-0.7402
0.6724
0.0001
0.8009
0.5988
-0.0000
Axis
0.0005
1.0000
-0.0001
-0.7071
0.0002
-0.7071
-0.0003
-0.0002
-1.0000
-0.5988
0.8009
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