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 TaFe2 (Materials Project id mp-568077)

       350      167      157        0        0        1  
       167      349      157        0        0       -0  
       157      157      397        0        0       -0  
         0        0        0       85        0        0  
         0        0        0        0       85        0  
         1       -0       -0        0        0       92  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 228.67 GPaEV = 246.62 GPaGV = 93.4 GPaνV = 0.32025
ReussKR = 228.21 GPaER = 244.02 GPaGR = 92.306 GPaνR = 0.32179
HillKH = 228.44 GPaEH = 245.32 GPaGH = 92.853 GPaνH = 0.32102

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
85 GPa 85 GPa 91.993 GPa 182.5 GPa 226.82 GPa 686.68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 231.3 GPa 301.55 GPa 1.3001 TPa–1 1.5503 TPa–1 85 GPa 107.65 GPa0.250610.38273Value
Anisotropy 1.304 1.1924 1.267 1.5272Anisotropy
Axis -0.7704
0.2307
0.5943
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.5257
0.8507
0.0000
-0.0000
-0.0000
1.0000
0.6015
0.3718
0.7071
0.2879
0.9577
-0.0000
0.5501
0.3400
-0.7627
Axis
0.1727
0.9850
0.0000
0.6015
0.3717
-0.7071
-0.0002
0.0001
-1.0000
0.6488
0.4010
0.6467
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