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 Ho2C (Materials Project id mp-1640)

       153       44       23       -2        0        0  
        44      153       23        2        0        0  
        23       23      109        0        0        0  
        -2        2        0       15        0        0  
         0        0        0        0       15       -2  
         0        0        0        0       -2       54  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 66.111 GPaEV = 96.654 GPaGV = 38.467 GPaνV = 0.25633
ReussKR = 63.204 GPaER = 69.175 GPaGR = 26.251 GPaνR = 0.31759
HillKH = 64.658 GPaEH = 83.197 GPaGH = 32.359 GPaνH = 0.28554

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.898 GPa 14.915 GPa 54.102 GPa 98.283 GPa 109.09 GPa 207.72 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.503 GPa 137.47 GPa 4.2126 TPa–1 7.3965 TPa–1 14.898 GPa 54.601 GPa0.0427740.66148Value
Anisotropy 2.894 1.7558 3.665 15.4644Anisotropy
Axis 0.6042
0.3517
0.7150
0.9449
0.3267
-0.0207
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0511
0.9987
0.7071
0.7062
0.0357
-0.0000
0.5945
0.8041
-0.0000
0.7307
0.6827
Axis
1.0000
-0.0000
-0.0000
-0.7071
0.7062
0.0357
-1.0000
0.0000
-0.0000
-0.0000
0.6827
-0.7307
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