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-568656)

       488      104       50        0        0        0  
       104      488       50       -0        0        0  
        50       50      534        0        0        0  
         0       -0        0      159        0        0  
         0        0        0        0      159        0  
         0        0        0        0        0      192  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 213.11 GPaEV = 437.75 GPaGV = 189.07 GPaνV = 0.15765
ReussKR = 213.1 GPaER = 429.48 GPaGR = 184.47 GPaνR = 0.1641
HillKH = 213.11 GPaEH = 433.62 GPaGH = 186.77 GPaνH = 0.16087

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
159 GPa 159 GPa 192 GPa 384 GPa 486.57 GPa 639.43 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 397.39 GPa 525.55 GPa 1.5556 TPa–1 1.5813 TPa–1 159 GPa 228.08 GPa0.0844590.25429Value
Anisotropy 1.323 1.0165 1.434 3.0108Anisotropy
Axis 0.7534
-0.0002
0.6576
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3095
0.6358
0.7071
0.0000
0.0000
1.0000
0.5167
0.4583
-0.7232
Axis
1.0000
0.0002
-0.0000
0.3095
0.6358
-0.7071
0.1736
0.9848
-0.0000
-0.5410
-0.4799
-0.6906
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