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 TiMn2 (Materials Project id mp-1949)

       297      197      147        0        0        0  
       197      297      147        0        0        0  
       147      147      313        0        0        0  
         0        0        0       62        0        0  
         0        0        0        0       62        0  
         0        0        0        0        0       50  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 209.89 GPaEV = 170.65 GPaGV = 62.533 GPaνV = 0.36449
ReussKR = 209.41 GPaER = 163.9 GPaGR = 59.836 GPaνR = 0.36955
HillKH = 209.65 GPaEH = 167.28 GPaGH = 61.184 GPaνH = 0.36701

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
50 GPa 62 GPa 62 GPa 100 GPa 176.77 GPa 630.23 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 155.08 GPa 225.51 GPa 1.4901 TPa–1 1.7953 TPa–1 50 GPa 74.194 GPa0.206020.56133Value
Anisotropy 1.454 1.2048 1.484 2.7246Anisotropy
Axis 0.9266
0.1141
0.3582
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
0.6000
0.3742
0.7071
0.4351
0.9004
0.0000
-0.4142
0.9102
0.0000
Axis
0.0002
1.0000
-0.0000
0.6000
0.3742
-0.7071
0.0000
0.0000
-1.0000
-0.9102
-0.4142
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