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 Nb3B4 (Materials Project id mp-10255)

       464      162      170        0        0        0  
       162      529      137        0        0        0  
       170      137      536        0        0        0  
         0        0        0      192        0        0  
         0        0        0        0      235        0  
         0        0        0        0        0      222  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 274.11 GPaEV = 483.53 GPaGV = 200.47 GPaνV = 0.206
ReussKR = 273.71 GPaER = 475.41 GPaGR = 196.37 GPaνR = 0.21051
HillKH = 273.91 GPaEH = 479.48 GPaGH = 198.42 GPaνH = 0.20825

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
192 GPa 222 GPa 235 GPa 310.4 GPa 395.51 GPa 823.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 381.63 GPa 526.6 GPa 1.1425 TPa–1 1.3211 TPa–1 162.88 GPa 235 GPa0.104150.309Value
Anisotropy 1.38 1.1563 1.443 2.9668Anisotropy
Axis 1.0000
0.0000
0.0000
0.6163
0.0000
0.7875
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.3492
0.6149
0.0000
0.0000
1.0000
0.7166
0.2488
0.6516
0.0000
0.0000
1.0000
Axis
-0.7071
-0.3492
-0.6149
-1.0000
0.0000
0.0000
-0.6975
0.2479
0.6724
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