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 SiC (Materials Project id mp-568619)

       494       98       50      -31        0        0  
        98      494       50       31        0        0  
        50       50      534        0        0        0  
       -31       31        0      159        0        0  
         0        0        0        0      159      -31  
         0        0        0        0      -31      198  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 213.11 GPaEV = 442.02 GPaGV = 191.47 GPaνV = 0.15431
ReussKR = 213.1 GPaER = 424.63 GPaGR = 181.8 GPaνR = 0.16789
HillKH = 213.11 GPaEH = 433.38 GPaGH = 186.63 GPaνH = 0.16106

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
141.88 GPa 151.15 GPa 215.12 GPa 403.85 GPa 486.57 GPa 639.43 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 349.13 GPa 525.55 GPa 1.5556 TPa–1 1.5813 TPa–1 141.88 GPa 234.28 GPa0.00516150.3098Value
Anisotropy 1.505 1.0165 1.651 60.0222Anisotropy
Axis 0.6900
0.3983
0.6044
0.0000
0.0000
1.0000
0.9220
0.3872
0.0000
0.0000
0.0000
1.0000
0.0000
0.4835
0.8753
0.0000
0.6233
0.7820
0.4404
0.2543
-0.8610
0.5313
0.3074
-0.7894
Axis
-1.0000
0.0000
-0.0000
0.0000
0.7820
-0.6233
-0.5000
0.8660
0.0000
-0.6839
-0.3944
-0.6138
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