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 PbS (Materials Project id mp-21276)

       121       18       18        0        0        0  
        18      121       18        0        0        0  
        18       18      121        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 52.333 GPaEV = 80.984 GPaGV = 32.6 GPaνV = 0.24209
ReussKR = 52.333 GPaER = 67.971 GPaGR = 26.478 GPaνR = 0.28353
HillKH = 52.333 GPaEH = 74.584 GPaGH = 29.539 GPaνH = 0.26247

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 20 GPa 20 GPa 103 GPa 103 GPa 157 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.22 GPa 116.34 GPa 6.3694 TPa–1 6.3694 TPa–1 20 GPa 51.5 GPa0.0685360.53929Value
Anisotropy 2.186 1.0000 2.575 7.8687Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
-0.2330
0.5624
0.7934
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
-0.7660
0.6428
-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