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 Ti2Zn (Materials Project id mp-1014229)

       156       33       94        0        0        0  
        33      156       94        0        0        0  
        94       94      123        0        0        0  
         0        0        0      112        0        0  
         0        0        0        0      112        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 97.444 GPaEV = 159.66 GPaGV = 65.067 GPaνV = 0.22692
ReussKR = 94.492 GPaER = 78.963 GPaGR = 29.015 GPaνR = 0.36072
HillKH = 95.968 GPaEH = 121.3 GPaGH = 47.041 GPaνH = 0.28933

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
19.029 GPa 30 GPa 112 GPa 112 GPa 123 GPa 292.97 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 29.497 GPa 206.06 GPa 0.17937 TPa–1 5.2018 TPa–1 11.496 GPa 112 GPa-0.462721.1169Value
Anisotropy 6.986 29.0000 9.743Anisotropy
Axis 0.0000
0.0000
1.0000
0.7921
0.0000
-0.6104
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.5001
0.4999
-0.7071
-0.0000
0.0000
1.0000
0.9881
0.0003
0.1538
1.0000
0.0002
0.0000
Axis
-0.5000
-0.5001
-0.7071
-0.5000
0.8660
-0.0000
-0.0003
1.0000
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