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 Tl3V (Materials Project id mp-981210)

       131       84       79        0        0        0  
        84      131       79        0        0        0  
        79       79      174        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       27  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 102.22 GPaEV = 74.783 GPaGV = 27.133 GPaνV = 0.37807
ReussKR = 100.92 GPaER = 70.883 GPaGR = 25.627 GPaνR = 0.38294
HillKH = 101.57 GPaEH = 72.836 GPaGH = 26.38 GPaνH = 0.38049

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 22 GPa 27 GPa 47 GPa 80.912 GPa 308.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 62.774 GPa 115.94 GPa 2.2866 TPa–1 3.811 TPa–1 22 GPa 36.085 GPa0.224310.51135Value
Anisotropy 1.847 1.6667 1.64 2.2797Anisotropy
Axis 0.8174
-0.0000
-0.5760
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.5000
0.5000
-0.7071
1.0000
0.0002
0.0000
0.4350
0.4349
0.7884
Axis
-0.7880
0.6157
-0.0000
-0.5000
-0.5000
-0.7071
-0.0000
0.0002
-1.0000
0.5574
0.5575
-0.6151
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