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 CeO2 (Materials Project id mp-20194)

       335       97       97        0        0        0  
        97      335       97        0        0        0  
        97       97      335        0        0        0  
         0        0        0       51        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       51  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 176.33 GPaEV = 204.39 GPaGV = 78.2 GPaνV = 0.30682
ReussKR = 176.33 GPaER = 176.3 GPaGR = 66.111 GPaνR = 0.33336
HillKH = 176.33 GPaEH = 190.48 GPaGH = 72.156 GPaνH = 0.31996

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 51 GPa 51 GPa 238 GPa 238 GPa 529 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 139.55 GPa 291.44 GPa 1.8904 TPa–1 1.8904 TPa–1 51 GPa 119 GPa0.123620.57307Value
Anisotropy 2.088 1.0000 2.333 4.6357Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
1.0000
0.0000
0.5880
0.7663
0.2588
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
0.0000
-0.7072
0.7071
-0.0000
-0.7071
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-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