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 HfC (Materials Project id mp-21075)

       496      106      106        0        0        0  
       106      496      106        0        0        0  
       106      106      496        0        0        0  
         0        0        0      171        0        0  
         0        0        0        0      171        0  
         0        0        0        0        0      171  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 236 GPaEV = 431.68 GPaGV = 180.6 GPaνV = 0.19514
ReussKR = 236 GPaER = 430.26 GPaGR = 179.85 GPaνR = 0.19614
HillKH = 236 GPaEH = 430.97 GPaGH = 180.23 GPaνH = 0.19564

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
171 GPa 171 GPa 171 GPa 390 GPa 390 GPa 708 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 413.2 GPa 458.67 GPa 1.4124 TPa–1 1.4124 TPa–1 171 GPa 195 GPa0.162660.2389Value
Anisotropy 1.11 1.0000 1.14 1.4687Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
-0.3536
0.8536
0.3827
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0000
-0.7071
0.7071
-0.0000
-0.7071
Axis
0.9397
0.3420
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
-0.0000
-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