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 V2B3 (Materials Project id mp-9208)

       486      132      142        0        0        0  
       132      654      104        0        0        0  
       142      104      639        0        0        0  
         0        0        0      246        0        0  
         0        0        0        0      254        0  
         0        0        0        0        0      228  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 281.67 GPaEV = 558.92 GPaGV = 239 GPaνV = 0.16928
ReussKR = 278.59 GPaER = 550.94 GPaGR = 235.36 GPaνR = 0.1704
HillKH = 280.13 GPaEH = 554.93 GPaGH = 237.18 GPaνH = 0.16984

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
228 GPa 246 GPa 254 GPa 383.07 GPa 543.06 GPa 852.87 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 435.83 GPa 610.98 GPa 1.0653 TPa–1 1.4562 TPa–1 203.68 GPa 271.12 GPa0.105850.26343Value
Anisotropy 1.402 1.3670 1.331 2.4887Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.7071
0.3754
0.5992
0.0000
0.7071
0.7071
0.0000
-0.0000
1.0000
0.0000
0.0000
1.0000
Axis
-0.7071
-0.3754
-0.5992
0.0000
0.7071
-0.7071
-0.0000
-1.0000
-0.0000
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