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 Tb2Al3Si2 (Materials Project id mp-3194)

       175       52       32        0        1        0  
        52      159       60        0        4        0  
        32       60      153        0        3        0  
         0        0        0       85        0        5  
         1        4        3        0       65        0  
         0        0        0        5        0       63  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 86.111 GPaEV = 156.69 GPaGV = 65.467 GPaνV = 0.19673
ReussKR = 85.614 GPaER = 151.61 GPaGR = 62.918 GPaνR = 0.20485
HillKH = 85.862 GPaEH = 154.16 GPaGH = 64.193 GPaνH = 0.20076

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
61.917 GPa 64.808 GPa 86.083 GPa 92.939 GPa 135.11 GPa 259.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 126.11 GPa 184.99 GPa 3.3572 TPa–1 4.5038 TPa–1 47.417 GPa 86.083 GPa0.0744590.36388Value
Anisotropy 1.467 1.3415 1.815 4.8871Anisotropy
Axis 0.0000
1.0000
0.0000
0.2006
0.6924
0.6931
0.0000
1.0000
0.0000
0.3698
0.0000
-0.9291
0.0001
0.7071
-0.7071
-0.2117
-0.0000
-0.9773
0.2662
-0.0000
0.9639
0.3807
-0.0002
0.9247
Axis
0.0002
-0.7071
-0.7071
0.0000
-1.0000
0.0000
0.9639
-0.0000
-0.2662
0.0001
1.0000
0.0002
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