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 VCo (Materials Project id mp-1002109)

       269      176      176        0        0        0  
       176      269      176        0        0        0  
       176      176      269        0        0        0  
         0        0        0       94        0        0  
         0        0        0        0       94        0  
         0        0        0        0        0       94  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 207 GPaEV = 200.75 GPaGV = 75 GPaνV = 0.33836
ReussKR = 207 GPaER = 180.77 GPaGR = 66.733 GPaνR = 0.35445
HillKH = 207 GPaEH = 190.82 GPaGH = 70.866 GPaνH = 0.34636

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
93 GPa 93 GPa 94 GPa 94 GPa 94 GPa 621 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 129.78 GPa 244.93 GPa 1.6103 TPa–1 1.6103 TPa–1 46.5 GPa 94 GPa0.0662910.6109Value
Anisotropy 1.887 1.0000 2.022 9.2154Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
-0.2391
0.8924
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
-1.0000
0.0000
-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