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 CaF2 (Materials Project id mp-2741)

       151       39       39        0        0        0  
        39      151       39        0        0        0  
        39       39      151        0        0        0  
         0        0        0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.333 GPaEV = 103.02 GPaGV = 40.4 GPaνV = 0.27506
ReussKR = 76.333 GPaER = 95.209 GPaGR = 36.842 GPaνR = 0.29212
HillKH = 76.333 GPaEH = 99.143 GPaGH = 38.621 GPaνH = 0.28353

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 30 GPa 30 GPa 112 GPa 112 GPa 229 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 79.575 GPa 134.99 GPa 4.3668 TPa–1 4.3668 TPa–1 30 GPa 56 GPa0.134840.47793Value
Anisotropy 1.696 1.0000 1.867 3.5444Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
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
0.1736
0.9848
-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