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-570985)

       488      104       51        1        0        0  
       104      488       51       -1        0        0  
        51       51      534        0        0        0  
         1       -1        0      160        0        0  
         0        0        0        0      160        1  
         0        0        0        0        1      192  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 213.56 GPaEV = 438.43 GPaGV = 189.33 GPaνV = 0.15783
ReussKR = 213.55 GPaER = 430.5 GPaGR = 184.92 GPaνR = 0.16401
HillKH = 213.55 GPaEH = 434.48 GPaGH = 187.13 GPaνH = 0.16091

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
159.97 GPa 159.99 GPa 192.03 GPa 384.01 GPa 485.26 GPa 640.74 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 397.64 GPa 525.21 GPa 1.5534 TPa–1 1.5759 TPa–1 159.97 GPa 227.65 GPa0.08580.25292Value
Anisotropy 1.321 1.0145 1.423 2.9478Anisotropy
Axis -0.6554
0.3784
-0.6536
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0270
0.0156
0.9995
0.6080
0.3549
0.7102
-0.0000
-0.0803
0.9968
0.0001
0.6872
-0.7264
Axis
-0.5000
0.8660
-0.0000
0.6134
0.3579
-0.7040
-1.0000
0.0000
-0.0000
0.0001
-0.7264
-0.6872
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