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 Cd (Materials Project id mp-94)

        87       39       28        0        0        0  
        39       87       28        0        0        0  
        28       28       43        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 45.222 GPaEV = 46.109 GPaGV = 17.333 GPaνV = 0.33007
ReussKR = 38.5 GPaER = 39.586 GPaGR = 14.897 GPaνR = 0.32863
HillKH = 41.861 GPaEH = 42.848 GPaGH = 16.115 GPaνH = 0.32941

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 24 GPa 27.139 GPa 48 GPa 141.86 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 29.582 GPa 62.496 GPa 3.8961 TPa–1 18.182 TPa–1 11 GPa 24 GPa0.192620.49205Value
Anisotropy 2.113 4.6667 2.182 2.5545Anisotropy
Axis 0.4182
0.1499
0.8959
0.7934
0.6088
0.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1873
0.9823
0.0000
0.5111
0.4067
-0.7572
0.8374
0.3032
0.4548
Axis
-0.7880
0.6157
-0.0000
-0.9823
-0.1873
-0.0000
-0.6226
0.7825
-0.0000
0.4277
0.1548
-0.8906
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