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 Ca3N2 (Materials Project id mp-568293)

       136       45       39        0        0        0  
        45      112       50        0        0        0  
        39       50      137        0        0        0  
         0        0        0       44        0        0  
         0        0        0        0       33        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72.556 GPaEV = 101.23 GPaGV = 39.933 GPaνV = 0.26747
ReussKR = 72.259 GPaER = 99.302 GPaGR = 39.066 GPaνR = 0.27096
HillKH = 72.407 GPaEH = 100.27 GPaGH = 39.5 GPaνH = 0.26921

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33 GPa 39 GPa 44 GPa 69.188 GPa 97.717 GPa 218.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 86.173 GPa 114.8 GPa 4.099 TPa–1 5.3245 TPa–1 33 GPa 48.684 GPa0.160370.38199Value
Anisotropy 1.332 1.2990 1.475 2.3820Anisotropy
Axis 0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
Axis
-1.0000
0.0000
0.0000
0.7071
-0.0006
-0.7071
-1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
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