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 Er(CoB)2 (Materials Project id mp-568509)

       331      108       72        0        0        0  
       108      331       72        0        0        0  
        72       72      194        0        0        0  
         0        0        0      106        0        0  
         0        0        0        0      106        0  
         0        0        0        0        0      160  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 151.11 GPaEV = 274.55 GPaGV = 114.67 GPaνV = 0.19718
ReussKR = 138.77 GPaER = 257.65 GPaGR = 108.21 GPaνR = 0.19056
HillKH = 144.94 GPaEH = 266.11 GPaGH = 111.44 GPaνH = 0.194

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
106 GPa 106 GPa 157.21 GPa 160 GPa 223 GPa 475.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 170.38 GPa 349.73 GPa 1.6311 TPa–1 3.944 TPa–1 88.236 GPa 160 GPa0.0929150.33665Value
Anisotropy 2.053 2.4180 1.813 3.6232Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
-0.0000
0.0000
-0.7071
0.7071
0.0000
0.7071
0.7071
-0.0000
Axis
0.7071
-0.0005
-0.7071
0.0000
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
0.0001
-0.0000
1.0000
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