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 PbSe2 (Materials Project id mp-982261)

        17       -1       13        0        0        0  
        -1       17       13        0        0        0  
        13       13       26        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 12.222 GPaEV = 29.009 GPaGV = 13.133 GPaνV = 0.10442
ReussKR = 4.875 GPaER = 9.5872 GPaGR = 4.0893 GPaνR = 0.17223
HillKH = 8.5486 GPaEH = 19.34 GPaGH = 8.6113 GPaνH = 0.12294

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1.9474 GPa 14 GPa 18 GPa 20 GPa 20 GPa 40.053 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4.875 GPa 37.847 GPa -128.21 TPa–1 166.67 TPa–1 1.3644 GPa 20 GPa-1.10791.3014Value
Anisotropy 7.764 14.66Anisotropy
Axis 0.0000
0.0000
1.0000
0.5076
0.5076
0.6962
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
-0.6028
0.6029
-0.5226
-0.0000
0.5796
0.8149
Axis
-0.7071
-0.0002
-0.7071
-0.5000
0.8660
-0.0000
-0.7071
-0.7071
-0.0000
-1.0000
-0.0000
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