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 Pb (Materials Project id mp-20745)

        58       32       32        0        0        0  
        32       58       32        0        0        0  
        32       32       56        0        0        0  
         0        0        0        6        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0       13  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 40.444 GPaEV = 27.886 GPaGV = 10.067 GPaνV = 0.38508
ReussKR = 40.432 GPaER = 24.61 GPaGR = 8.7984 GPaνR = 0.39855
HillKH = 40.438 GPaEH = 26.256 GPaGH = 9.4325 GPaνH = 0.39179

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6 GPa 6 GPa 13 GPa 24.657 GPa 26 GPa 121.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 19.611 GPa 34.978 GPa 8.0214 TPa–1 8.6898 TPa–1 6 GPa 13 GPa0.201620.63456Value
Anisotropy 1.784 1.0833 2.167 3.1473Anisotropy
Axis 0.3260
0.6206
-0.7132
1.0000
0.0000
0.0000
0.6042
0.7968
-0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.6863
0.7273
0.0000
0.5382
0.4747
-0.6965
-0.5752
0.4291
-0.6965
Axis
0.1735
0.9848
-0.0000
-0.7273
-0.6863
0.0000
-0.6615
0.7500
-0.0000
-0.5582
0.4164
0.7176
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