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 CrFeP (Materials Project id mp-21495)

       385      133      157        0        0        0  
       133      467      152        0        0        0  
       157      152      413        0        0        0  
         0        0        0      147        0        0  
         0        0        0        0      157        0  
         0        0        0        0        0      139  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 238.78 GPaEV = 358.58 GPaGV = 143.47 GPaνV = 0.24971
ReussKR = 237.59 GPaER = 355.41 GPaGR = 142.09 GPaνR = 0.25069
HillKH = 238.18 GPaEH = 357 GPaGH = 142.78 GPaνH = 0.2502

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
139 GPa 147 GPa 157 GPa 241.17 GPa 305.17 GPa 718.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 311.55 GPa 393.67 GPa 1.2413 TPa–1 1.6184 TPa–1 120.74 GPa 157 GPa0.182990.32758Value
Anisotropy 1.264 1.3038 1.3 1.7902Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
1.0000
0.0006
-0.0000
0.0000
0.0000
1.0000
Axis
0.7071
-0.0005
-0.7071
-1.0000
0.0000
-0.0000
-0.0006
1.0000
-0.0000
1.0000
0.0000
-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