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 HfN (Materials Project id mp-2828)

       569      114      114        0        0        0  
       114      569      114        0        0        0  
       114      114      569        0        0        0  
         0        0        0      121        0        0  
         0        0        0        0      121        0  
         0        0        0        0        0      121  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 265.67 GPaEV = 407.21 GPaGV = 163.6 GPaνV = 0.24453
ReussKR = 265.67 GPaER = 376.33 GPaGR = 148.88 GPaνR = 0.26391
HillKH = 265.67 GPaEH = 391.89 GPaGH = 156.24 GPaνH = 0.25415

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
121 GPa 121 GPa 121 GPa 455 GPa 455 GPa 797 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 315.15 GPa 530.94 GPa 1.2547 TPa–1 1.2547 TPa–1 121 GPa 227.5 GPa0.110280.44957Value
Anisotropy 1.685 1.0000 1.88 4.0767Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.6533
0.6533
-0.3827
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
0.0004
-0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
-0.0000
0.7071
-0.0005
-0.7071
-0.0002
1.0000
0.0003
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