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 Cu2O (Materials Project id mp-361)

       124      105      105        0        0        0  
       105      124      105        0        0        0  
       105      105      124        0        0        0  
         0        0        0        8        0        0  
         0        0        0        0        8        0  
         0        0        0        0        0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 111.33 GPaEV = 25.152 GPaGV = 8.6 GPaνV = 0.46235
ReussKR = 111.33 GPaER = 24.979 GPaGR = 8.5393 GPaνR = 0.46261
HillKH = 111.33 GPaEH = 25.066 GPaGH = 8.5697 GPaνH = 0.46248

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8 GPa 8 GPa 8 GPa 19 GPa 19 GPa 334 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 23.439 GPa 27.712 GPa 2.994 TPa–1 2.994 TPa–1 8 GPa 9.5 GPa0.403360.52365Value
Anisotropy 1.182 1.0000 1.187 1.2982Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.2500
0.9330
0.2588
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
-0.7071
0.0002
-0.7071
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