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 PbF4 (Materials Project id mp-341)

       199        4        0        0        0        0  
         4      199        0        0        0        0  
         0        0       16        0        0        0  
         0        0        0        9        0        0  
         0        0        0        0        9        0  
         0        0        0        0        0       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46.889 GPaEV = 80.45 GPaGV = 33.133 GPaνV = 0.21404
ReussKR = 13.821 GPaER = 28.27 GPaGR = 12.195 GPaνR = 0.1591
HillKH = 30.355 GPaEH = 54.443 GPaGH = 22.664 GPaνH = 0.20108

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 9 GPa 11 GPa 16 GPa 195 GPa 203 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 16 GPa 198.92 GPa 4.9261 TPa–1 62.5 TPa–1 9 GPa 97.5 GPa00.80444Value
Anisotropy 12.43 12.6875 10.83Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.7071
0.0000
1.0000
0.0000
-0.0000
-0.7071
-0.7071
-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