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 Zr6Al2Ni (Materials Project id mp-13092)

       178       75       67        0        0        0  
        75      178       67        0        0        0  
        67       67      173        0        0        0  
         0        0        0       49        0        0  
         0        0        0        0       49        0  
         0        0        0        0        0       52  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 105.22 GPaEV = 132.46 GPaGV = 51.333 GPaνV = 0.29019
ReussKR = 105.11 GPaER = 132.2 GPaGR = 51.224 GPaνR = 0.29038
HillKH = 105.17 GPaEH = 132.33 GPaGH = 51.279 GPaνH = 0.29029

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
49 GPa 49 GPa 52 GPa 103 GPa 110.15 GPa 315.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 128.32 GPa 137.51 GPa 3.0468 TPa–1 3.4204 TPa–1 49 GPa 54.296 GPa0.263630.3226Value
Anisotropy 1.072 1.1226 1.108 1.2237Anisotropy
Axis 0.7195
-0.0000
0.6945
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
0.0000
1.0000
0.4997
0.5003
0.7071
0.2536
0.2536
-0.9335
1.0000
-0.0002
0.0000
Axis
-0.7660
-0.6428
-0.0000
0.5003
0.4997
-0.7071
-0.7071
0.7071
0.0000
0.0002
1.0000
-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