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 ErCdCu4 (Materials Project id mp-12008)

       144       62       62        0        0        0  
        62      144       62        0        0        0  
        62       62      144        0        0        0  
         0        0        0       58        0        0  
         0        0        0        0       58        0  
         0        0        0        0        0       58  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 89.333 GPaEV = 128.96 GPaGV = 51.2 GPaνV = 0.2594
ReussKR = 89.333 GPaER = 125.88 GPaGR = 49.749 GPaνR = 0.26515
HillKH = 89.333 GPaEH = 127.42 GPaGH = 50.474 GPaνH = 0.26227

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
58 GPa 58 GPa 58 GPa 82 GPa 82 GPa 268 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 106.68 GPa 143.04 GPa 3.7313 TPa–1 3.7313 TPa–1 41 GPa 58 GPa0.13630.37187Value
Anisotropy 1.341 1.0000 1.415 2.7284Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.1736
0.9848
-0.0000
0.7071
-0.0006
-0.7071
0.0004
1.0000
0.0004
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