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 TbGa5Co (Materials Project id mp-1025288)

       174       35       42        0        0        0  
        35      174       42        0        0        0  
        42       42      155        0        0        0  
         0        0        0       48        0        0  
         0        0        0        0       48        0  
         0        0        0        0        0       46  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 82.333 GPaEV = 132.94 GPaGV = 54 GPaνV = 0.2309
ReussKR = 82.242 GPaER = 130.24 GPaGR = 52.683 GPaνR = 0.23607
HillKH = 82.288 GPaEH = 131.59 GPaGH = 53.342 GPaνH = 0.23347

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
46 GPa 48 GPa 48 GPa 116.75 GPa 139 GPa 247.25 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 119.1 GPa 159.19 GPa 3.9145 TPa–1 4.3302 TPa–1 46 GPa 69.5 GPa0.142180.3387Value
Anisotropy 1.337 1.1062 1.511 2.3822Anisotropy
Axis -0.5794
0.5794
-0.5732
0.0000
1.0000
0.0000
0.5996
0.8003
-0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
-0.0000
0.7071
0.7071
-0.0000
0.9081
0.0005
0.4187
-0.7071
0.7071
0.0000
Axis
-0.0000
1.0000
-0.0000
-0.7071
0.7071
-0.0000
-0.0003
1.0000
-0.0006
-0.7071
-0.7071
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