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 TlCl (Materials Project id mp-569639)

        37       12       12        0        0        0  
        12       37       12        0        0        0  
        12       12       37        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0        4  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 20.333 GPaEV = 19.798 GPaGV = 7.4 GPaνV = 0.33772
ReussKR = 20.333 GPaER = 15.121 GPaGR = 5.4945 GPaνR = 0.37605
HillKH = 20.333 GPaEH = 17.493 GPaGH = 6.4473 GPaνH = 0.35662

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4 GPa 4 GPa 4 GPa 25 GPa 25 GPa 61 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 11.262 GPa 31.122 GPa 16.393 TPa–1 16.393 TPa–1 4 GPa 12.5 GPa0.105440.6749Value
Anisotropy 2.764 1.0000 3.125 6.4010Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.6871
0.5272
0.5000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
-0.7071
0.0002
-0.7071
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