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 PbSe (Materials Project id mp-2201)

       117       12       12        0        0        0  
        12      117       12        0        0        0  
        12       12      117        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 47 GPaEV = 76.641 GPaGV = 31.2 GPaνV = 0.22822
ReussKR = 47 GPaER = 59.994 GPaGR = 23.303 GPaνR = 0.28726
HillKH = 47 GPaEH = 68.513 GPaGH = 27.251 GPaνH = 0.25705

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 17 GPa 105 GPa 105 GPa 141 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.513 GPa 114.77 GPa 7.0922 TPa–1 7.0922 TPa–1 17 GPa 52.5 GPa0.0434440.57643Value
Anisotropy 2.522 1.0000 3.088 13.2684Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.7330
0.5624
0.3827
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
-0.1736
0.9848
-0.0000
-0.7071
-0.0002
-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