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 TiFeCoGe (Materials Project id mp-1018012)

       272      194      194        0        0        0  
       194      272      194        0        0        0  
       194      194      272        0        0        0  
         0        0        0      111        0        0  
         0        0        0        0      111        0  
         0        0        0        0        0      111  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 220 GPaEV = 219.29 GPaGV = 82.2 GPaνV = 0.33387
ReussKR = 220 GPaER = 174.65 GPaGR = 63.85 GPaνR = 0.36769
HillKH = 220 GPaEH = 197.25 GPaGH = 73.025 GPaνH = 0.35057

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
78 GPa 78 GPa 111 GPa 111 GPa 111 GPa 660 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 110.47 GPa 285.06 GPa 1.5152 TPa–1 1.5152 TPa–1 39 GPa 111 GPa-0.0795970.77001Value
Anisotropy 2.58 1.0000 2.846Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.4330
0.7500
0.5000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.9397
0.3420
0.0000
-0.7071
-0.0002
-0.7071
-1.0000
-0.0001
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