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 VRu (Materials Project id mp-1395)

       323      217      217        0        0        0  
       217      323      217        0        0        0  
       217      217      324        0        0        0  
         0        0        0       96        0        0  
         0        0        0        0       96        0  
         0        0        0        0        0       96  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 252.44 GPaEV = 214.28 GPaGV = 78.867 GPaνV = 0.35853
ReussKR = 252.44 GPaER = 198.75 GPaGR = 72.603 GPaνR = 0.36878
HillKH = 252.44 GPaEH = 206.55 GPaGH = 75.735 GPaνH = 0.36363

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
96 GPa 96 GPa 96 GPa 106 GPa 106.67 GPa 757.33 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 148.76 GPa 255.6 GPa 1.3122 TPa–1 1.3246 TPa–1 53.25 GPa 96 GPa0.12910.58509Value
Anisotropy 1.718 1.0094 1.803 4.5320Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5771
0.5771
-0.5779
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.7071
-0.0002
0.7071
-0.0000
0.0000
1.0000
0.7073
-0.0002
0.7069
-0.0000
0.7073
0.7069
Axis
0.7071
-0.0006
-0.7071
-0.7660
0.6428
-0.0000
0.7069
-0.0005
-0.7073
-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