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 VIr (Materials Project id mp-569250)

       413      242      175        0        0        0  
       242      411      167        0        0        0  
       175      167      465        0        0        0  
         0        0        0      164        0        0  
         0        0        0        0       88        0  
         0        0        0        0        0      111  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 273 GPaEV = 313.08 GPaGV = 119.6 GPaνV = 0.30886
ReussKR = 272.89 GPaER = 294.01 GPaGR = 111.33 GPaνR = 0.32043
HillKH = 272.94 GPaEH = 303.59 GPaGH = 115.47 GPaνH = 0.31462

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
88 GPa 111 GPa 164 GPa 169.85 GPa 299.99 GPa 819.16 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 236.65 GPa 380.76 GPa 1.1599 TPa–1 1.2709 TPa–1 84.962 GPa 164 GPa0.0737270.52171Value
Anisotropy 1.609 1.0958 1.93 7.0763Anisotropy
Axis 0.8308
-0.0000
0.5566
0.0000
0.3845
0.9231
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.0000
-0.0000
1.0000
0.0000
0.7267
0.6870
-0.0000
0.9185
0.3954
Axis
-0.7071
0.7071
0.0000
-0.0000
-1.0000
-0.0000
-0.0000
0.6870
-0.7267
-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