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 PbCl2 (Materials Project id mp-862871)

        46       25       25        0        0        0  
        25       33       28        0        0        0  
        25       28       33        0        0        0  
         0        0        0       27        0        0  
         0        0        0        0        7        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 29.778 GPaEV = 28.107 GPaGV = 10.467 GPaνV = 0.34269
ReussKR = 29.358 GPaER = 16.772 GPaGR = 5.9696 GPaνR = 0.40479
HillKH = 29.568 GPaEH = 22.564 GPaGH = 8.2181 GPaνH = 0.37281

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 7 GPa 7 GPa 17.358 GPa 27 GPa 89.642 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.7122 GPa 41.596 GPa 7.0694 TPa–1 13.496 TPa–1 2.5 GPa 27 GPa-0.22970.7774Value
Anisotropy 4.774 1.9091 10.8Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
0.0000
0.9914
0.1305
0.0002
0.7071
-0.7071
0.0000
-0.0000
1.0000
-0.0000
0.7071
-0.7071
0.5877
0.0002
0.8091
Axis
0.0002
-0.7071
-0.7071
-0.0000
-1.0000
-0.0000
-0.0000
0.7071
0.7071
-0.0003
1.0000
-0.0001
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