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 Hf3N4 (Materials Project id mp-754434)

       394      202      129       79        0        0  
       202      394      129      -79        0        0  
       129      129      279        0        0        0  
        79      -79        0       98        0        0  
         0        0        0        0       98       79  
         0        0        0        0       79       96  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 220.78 GPaEV = 258.08 GPaGV = 98.867 GPaνV = 0.30518
ReussKR = 208.47 GPaER = 106.79 GPaGR = 37.743 GPaνR = 0.41463
HillKH = 214.62 GPaEH = 185.26 GPaGH = 68.305 GPaνH = 0.35613

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17.994 GPa 23.794 GPa 176.01 GPa 195.83 GPa 266.21 GPa 679.17 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.506 GPa 423.98 GPa 1.1278 TPa–1 2.5413 TPa–1 17.994 GPa 176.01 GPa-0.582261.2167Value
Anisotropy 7.924 2.2533 9.782Anisotropy
Axis 0.0000
0.8489
0.5286
-0.0000
0.8929
-0.4503
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
-0.6162
0.3558
0.7026
0.0000
0.7026
0.7116
0.0000
0.6722
-0.7404
0.5000
0.8660
-0.0000
Axis
-0.5000
-0.8660
-0.0000
-1.0000
-0.0000
0.0000
-1.0000
-0.0000
-0.0000
-0.7289
0.4208
-0.5401
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