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 HfTc (Materials Project id mp-11460)

       330      123      123        0        0        0  
       123      330      123        0        0        0  
       123      123      330        0        0        0  
         0        0        0       61        0        0  
         0        0        0        0       61        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 192 GPaEV = 206.09 GPaGV = 78 GPaνV = 0.3211
ReussKR = 192 GPaER = 194.34 GPaGR = 72.988 GPaνR = 0.3313
HillKH = 192 GPaEH = 200.24 GPaGH = 75.494 GPaνH = 0.32618

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
61 GPa 61 GPa 61 GPa 207 GPa 207 GPa 576 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 165.48 GPa 263.21 GPa 1.7361 TPa–1 1.7361 TPa–1 61 GPa 103.5 GPa0.188170.49515Value
Anisotropy 1.591 1.0000 1.697 2.6313Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.8693
0.0000
0.4943
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
-0.0000
0.7071
-0.0005
-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