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 HfAl3 (Materials Project id mp-2614)

       189       91       49        0        0        0  
        91      189       49        0        0        0  
        49       49      207        0        0        0  
         0        0        0       89        0        0  
         0        0        0        0       89        0  
         0        0        0        0        0      126  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 107 GPaEV = 205.72 GPaGV = 87.2 GPaνV = 0.17957
ReussKR = 106.74 GPaER = 191.06 GPaGR = 79.499 GPaνR = 0.20168
HillKH = 106.87 GPaEH = 198.46 GPaGH = 83.35 GPaνH = 0.19051

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
89 GPa 89 GPa 98 GPa 126 GPa 165.18 GPa 321.82 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 141.86 GPa 254.38 GPa 2.9723 TPa–1 3.4238 TPa–1 49 GPa 126 GPa0.00943770.44758Value
Anisotropy 1.793 1.1519 2.571 47.4245Anisotropy
Axis 0.0000
1.0000
0.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0000
0.0000
0.7071
0.7071
-0.0000
1.0000
0.0000
-0.0000
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.0000
-0.7071
0.7071
0.0000
-0.0000
1.0000
-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