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 Hf4N3 (Materials Project id mp-32994)

       340      217      130        0        0        0  
       217      340      130        0        0        0  
       130      130      391        0        0        0  
         0        0        0      127        0        0  
         0        0        0        0      127        0  
         0        0        0        0        0       83  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 225 GPaEV = 277.08 GPaGV = 107 GPaνV = 0.29476
ReussKR = 224.65 GPaER = 255.05 GPaGR = 97.288 GPaνR = 0.31078
HillKH = 224.82 GPaEH = 266.13 GPaGH = 102.14 GPaνH = 0.30271

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
83 GPa 123 GPa 127 GPa 127 GPa 272.28 GPa 675.72 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 195.02 GPa 330.32 GPa 1.4186 TPa–1 1.6142 TPa–1 61.5 GPa 127 GPa0.0763370.58555Value
Anisotropy 1.694 1.1379 2.065 7.6706Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0001
0.0000
0.0000
1.0000
0.7424
0.0001
-0.6699
1.0000
-0.0000
-0.0000
Axis
-0.7071
-0.7071
0.0000
0.7660
0.6428
-0.0000
-0.6699
0.0000
-0.7424
0.0000
1.0000
-0.0000
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