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-1018664)

       324      119      119        0        0        0  
       119      133      109        0        0        0  
       119      109      133        0        0        0  
         0        0        0      112        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 = 142.67 GPaEV = 155.56 GPaGV = 59 GPaνV = 0.31828
ReussKR = 120.98 GPaER = 92.396 GPaGR = 33.655 GPaνR = 0.37271
HillKH = 131.82 GPaEH = 124.41 GPaGH = 46.327 GPaνH = 0.34271

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 51 GPa 51 GPa 109.79 GPa 112 GPa 456.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 41.549 GPa 206.97 GPa0.079863 TPa–1 4.093 TPa–1 12 GPa 112 GPa-0.110360.92458Value
Anisotropy 4.981 51.2500 9.333Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
0.7071
0.7071
0.0002
0.0001
1.0000
-0.7537
0.6572
-0.0000
-0.7737
0.6335
0.0001
Axis
0.0001
0.7071
-0.7071
-0.0000
1.0000
-0.0001
-0.6572
-0.7537
0.0000
-0.0002
-0.0002
-1.0000
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