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 HfCo (Materials Project id mp-2027)

       230      114      114        0        0        0  
       114      230      114        0        0        0  
       114      114      230        0        0        0  
         0        0        0       55        0        0  
         0        0        0        0       55        0  
         0        0        0        0        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 152.67 GPaEV = 150.17 GPaGV = 56.2 GPaνV = 0.33606
ReussKR = 152.67 GPaER = 150.08 GPaGR = 56.162 GPaνR = 0.33615
HillKH = 152.67 GPaEH = 150.13 GPaGH = 56.181 GPaνH = 0.33611

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55 GPa 55 GPa 55 GPa 116 GPa 116 GPa 458 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 147.31 GPa 154.44 GPa 2.1834 TPa–1 2.1834 TPa–1 55 GPa 58 GPa0.319780.35482Value
Anisotropy 1.048 1.0000 1.055 1.1096Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.2241
0.8365
0.5000
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
0.0004
-0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
-0.0000
-0.7071
-0.0002
-0.7071
-0.0003
1.0000
0.0003
-0.7071
0.0002
-0.7071
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