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 Hf(CoSi)2 (Materials Project id mp-571367)

       306      132      128        0        0        0  
       132      306      128        0        0        0  
       128      128      327        0        0        0  
         0        0        0      110        0        0  
         0        0        0        0      110        0  
         0        0        0        0        0      129  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 190.56 GPaEV = 269.4 GPaGV = 106.53 GPaνV = 0.26438
ReussKR = 190.44 GPaER = 265.34 GPaGR = 104.65 GPaνR = 0.26779
HillKH = 190.5 GPaEH = 267.37 GPaGH = 105.59 GPaνH = 0.26608

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
110 GPa 110 GPa 129 GPa 174 GPa 193.16 GPa 571.84 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 229.69 GPa 292.69 GPa 1.6477 TPa–1 1.8016 TPa–1 87 GPa 129 GPa0.133930.33954Value
Anisotropy 1.274 1.0934 1.483 2.5353Anisotropy
Axis 1.0000
0.0000
0.0000
0.6886
0.6886
0.2273
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0002
0.0001
0.7071
0.7071
-0.0000
0.7732
0.0003
0.6342
Axis
-0.7071
-0.7071
0.0000
0.0002
1.0000
-0.0000
-0.7071
0.7071
-0.0000
-0.0000
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