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-8062)

       382      126      126        0        0        0  
       126      382      126        0        0        0  
       126      126      382        0        0        0  
         0        0        0      241        0        0  
         0        0        0        0      241        0  
         0        0        0        0        0      241  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 211.33 GPaEV = 448.8 GPaGV = 195.8 GPaνV = 0.14606
ReussKR = 211.33 GPaER = 417.14 GPaGR = 178.11 GPaνR = 0.17103
HillKH = 211.33 GPaEH = 433.14 GPaGH = 186.95 GPaνH = 0.15841

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
241 GPa 241 GPa 241 GPa 256 GPa 256 GPa 634 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 319.5 GPa 523.87 GPa 1.5773 TPa–1 1.5773 TPa–1 128 GPa 241 GPa-0.0629860.35062Value
Anisotropy 1.64 1.0000 1.883Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.8660
0.0000
0.5000
0.4619
0.8001
0.3827
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0005
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0004
1.0000
0.0004
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