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 DyCd2 (Materials Project id mp-11294)

       117       37       36        0        0        0  
        37      117       36        0        0        0  
        36       36       70        0        0        0  
         0        0        0       25        0        0  
         0        0        0        0       25        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 58 GPaEV = 78.937 GPaGV = 31 GPaνV = 0.27317
ReussKR = 54.587 GPaER = 73.879 GPaGR = 28.985 GPaνR = 0.27443
HillKH = 56.293 GPaEH = 76.408 GPaGH = 29.993 GPaνH = 0.27378

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25 GPa 25 GPa 40 GPa 46 GPa 80 GPa 178 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.169 GPa 95.016 GPa 4.1524 TPa–1 10.015 TPa–1 25 GPa 40 GPa0.18770.41775Value
Anisotropy 1.787 2.4118 1.6 2.2257Anisotropy
Axis 0.0000
0.0000
1.0000
0.5718
0.8204
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.4028
0.9153
0.0000
0.7232
0.6907
-0.0000
0.7813
0.6242
0.0000
Axis
0.1734
0.9849
-0.0000
-0.9153
-0.4028
-0.0000
-0.6907
0.7232
-0.0000
-0.0000
0.0000
1.0000
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