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 Zr2Cd (Materials Project id mp-1018104)

       143       27       65        0        0        0  
        27      143       65        0        0        0  
        65       65      105        0        0        0  
         0        0        0       49        0        0  
         0        0        0        0       49        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 78.333 GPaEV = 95.004 GPaGV = 36.6 GPaνV = 0.29786
ReussKR = 78.333 GPaER = 55.108 GPaGR = 19.927 GPaνR = 0.38275
HillKH = 78.333 GPaEH = 75.688 GPaGH = 28.264 GPaνH = 0.33896

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 40 GPa 49 GPa 49 GPa 116 GPa 235 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.213 GPa 127.29 GPa 4.2553 TPa–1 4.2553 TPa–1 7 GPa 58 GPa-0.398811.1253Value
Anisotropy 5.257 1.0000 8.286Anisotropy
Axis 0.7071
0.7071
0.0000
0.8314
-0.0000
0.5556
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
1.0000
-0.0002
-0.0000
-0.7071
0.7071
-0.0000
-0.4678
0.4675
-0.7501
0.4876
0.4876
0.7242
Axis
0.0002
1.0000
-0.0000
-0.7071
-0.7071
0.0000
0.5303
-0.5305
-0.6613
-0.7071
0.7071
-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