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-7631)

       486      104       51        0        0        0  
       104      486       51        0        0        0  
        51       51      535        0        0        0  
         0        0        0      160        0        0  
         0        0        0        0      160        0  
         0        0        0        0        0      191  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 213.22 GPaEV = 437.56 GPaGV = 188.93 GPaνV = 0.15798
ReussKR = 213.22 GPaER = 429.69 GPaGR = 184.56 GPaνR = 0.16412
HillKH = 213.22 GPaEH = 433.64 GPaGH = 186.74 GPaνH = 0.16104

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
160 GPa 160 GPa 191 GPa 382 GPa 485.31 GPa 639.69 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 398.73 GPa 526.18 GPa 1.559 TPa–1 1.5719 TPa–1 160 GPa 227.29 GPa0.0864410.25127Value
Anisotropy 1.32 1.0083 1.421 2.9069Anisotropy
Axis 0.5204
0.5497
0.6535
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.1221
0.6965
0.7071
0.0000
0.0000
1.0000
0.3617
0.5871
0.7242
Axis
-0.7660
0.6428
-0.0000
0.1221
0.6965
-0.7071
0.1736
0.9848
-0.0000
-0.3798
-0.6166
0.6896
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