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 YB2Ru3 (Materials Project id mp-4382)

       369      170      138        0        0        0  
       170      369      138        0        0        0  
       138      138      395        0        0        0  
         0        0        0      118        0        0  
         0        0        0        0      118        0  
         0        0        0        0        0       99  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 225 GPaEV = 289.95 GPaGV = 112.8 GPaνV = 0.28522
ReussKR = 224.99 GPaER = 287.19 GPaGR = 111.55 GPaνR = 0.28726
HillKH = 224.99 GPaEH = 288.57 GPaGH = 112.18 GPaνH = 0.28624

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
99 GPa 118 GPa 118 GPa 199 GPa 258.98 GPa 675.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 273.6 GPa 324.34 GPa 1.4701 TPa–1 1.5044 TPa–1 99 GPa 120.42 GPa0.215980.38181Value
Anisotropy 1.185 1.0233 1.216 1.7678Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.9659
0.2588
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
0.7071
-0.0003
0.7071
0.7071
0.7071
0.0000
-0.7071
0.7071
0.0000
Axis
0.0002
1.0000
-0.0000
0.7071
-0.0005
-0.7071
-0.0000
-0.0000
1.0000
-0.7071
-0.7071
-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