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 HfBe2 (Materials Project id mp-2553)

       252       38       90        0        0        0  
        38      252       90        0        0        0  
        90       90      219        0        0        0  
         0        0        0      130        0        0  
         0        0        0        0      130        0  
         0        0        0        0        0      107  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 128.78 GPaEV = 251.5 GPaGV = 107.07 GPaνV = 0.1745
ReussKR = 128.56 GPaER = 236.7 GPaGR = 99.19 GPaνR = 0.19314
HillKH = 128.67 GPaEH = 244.15 GPaGH = 103.13 GPaνH = 0.18374

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
107 GPa 122.36 GPa 130 GPa 130 GPa 214 GPa 386.64 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 163.14 GPa 278.72 GPa 2.3251 TPa–1 2.7267 TPa–1 68.562 GPa 130 GPa0.00471460.40902Value
Anisotropy 1.709 1.1727 1.896 86.7568Anisotropy
Axis 0.0000
0.0000
1.0000
0.3713
0.6851
0.6267
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7134
0.7007
0.0000
-0.5872
0.8094
0.0000
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7007
0.7134
-0.0000
-0.0000
-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