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 CdP2 (Materials Project id mp-402)

        82       39       39        0        0        0  
        39       94       37        0        0        0  
        39       37       81        0        0        0  
         0        0        0       29        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 54.111 GPaEV = 72.659 GPaGV = 28.467 GPaνV = 0.27621
ReussKR = 53.913 GPaER = 70.597 GPaGR = 27.539 GPaνR = 0.28176
HillKH = 54.012 GPaEH = 71.63 GPaGH = 28.003 GPaνH = 0.27897

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29 GPa 29 GPa 37 GPa 42.418 GPa 51.969 GPa 162.61 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 57.401 GPa 81.13 GPa 5.278 TPa–1 6.8374 TPa–1 21.239 GPa 37 GPa0.0963170.38227Value
Anisotropy 1.413 1.2955 1.742 3.9688Anisotropy
Axis 1.0000
0.0000
0.0000
0.7043
0.0000
0.7099
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.0000
1.0000
0.7074
-0.0003
0.7068
0.0000
0.6588
0.7523
Axis
0.7071
-0.0006
-0.7071
1.0000
0.0000
-0.0000
0.7068
-0.0005
-0.7074
-1.0000
0.0001
-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