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 Al(FeB)2 (Materials Project id mp-3805)

       424      149      113        0        0        0  
       149      370      126        0        0        0  
       113      126      287        0        0        0  
         0        0        0      129        0        0  
         0        0        0        0      166        0  
         0        0        0        0        0      130  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 206.33 GPaEV = 324.76 GPaGV = 131.2 GPaνV = 0.23767
ReussKR = 199.47 GPaER = 314.31 GPaGR = 127.01 GPaνR = 0.23738
HillKH = 202.9 GPaEH = 319.54 GPaGH = 129.1 GPaνH = 0.23753

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
129 GPa 130 GPa 166 GPa 195.66 GPa 254.87 GPa 630.47 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 233.44 GPa 365.35 GPa 1.2326 TPa–1 2.3873 TPa–1 99.251 GPa 166 GPa0.0283880.35931Value
Anisotropy 1.565 1.9368 1.673 12.6572Anisotropy
Axis 0.0000
0.0000
1.0000
0.8784
0.0000
0.4779
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
0.7071
0.7071
0.0000
0.0000
1.0000
0.7015
-0.0002
0.7127
0.7964
0.0004
0.6048
Axis
0.0001
0.7071
-0.7071
-1.0000
0.0000
0.0000
0.7127
-0.0005
-0.7015
-0.0003
1.0000
-0.0001
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