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 C3N4 (Materials Project id mp-2852)

       782      233      233        0        0        0  
       233      782      233        0        0        0  
       233      233      782        0        0        0  
         0        0        0      473        0        0  
         0        0        0        0      473        0  
         0        0        0        0        0      473  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 416 GPaEV = 897.68 GPaGV = 393.6 GPaνV = 0.14035
ReussKR = 416 GPaER = 850.59 GPaGR = 366.88 GPaνR = 0.15922
HillKH = 416 GPaEH = 874.33 GPaGH = 380.24 GPaνH = 0.14971

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
473 GPa 473 GPa 473 GPa 549 GPa 549 GPa 1248 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 675.03 GPa 1029 GPa 0.80128 TPa–1 0.80128 TPa–1 274.5 GPa 473 GPa-0.0383320.30938Value
Anisotropy 1.524 1.0000 1.723Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.4830
0.6294
0.6088
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
0.0001
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