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 CaCuF4 (Materials Project id mp-12266)

       121       66       52        0        0        0  
        66      121       52        0        0        0  
        52       52      111        0        0        0  
         0        0        0       32        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 77 GPaEV = 88 GPaGV = 33.6 GPaνV = 0.30952
ReussKR = 76.363 GPaER = 86.185 GPaGR = 32.847 GPaνR = 0.3119
HillKH = 76.682 GPaEH = 87.093 GPaGH = 33.224 GPaνH = 0.3107

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 32 GPa 43 GPa 55 GPa 66.223 GPa 231.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 78.698 GPa 106.05 GPa 3.8439 TPa–1 5.4075 TPa–1 27.5 GPa 43 GPa0.232560.43088Value
Anisotropy 1.348 1.4068 1.564 1.8527Anisotropy
Axis 1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
1.0000
0.0000
-0.0000
0.6756
0.6756
-0.2952
1.0000
-0.0001
-0.0000
Axis
-0.7071
-0.7071
-0.0000
-0.0000
1.0000
-0.0000
-0.7071
0.7071
-0.0000
0.0001
1.0000
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