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-568172)

        87       57       50        0        3        0  
        57      126       29        0        1        0  
        50       29      128        0        2        0  
         0        0        0       17        0       -6  
         3        1        2        0       26        0  
         0        0        0       -6        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 68.111 GPaEV = 86.713 GPaGV = 33.667 GPaνV = 0.28782
ReussKR = 67.444 GPaER = 69.547 GPaGR = 26.182 GPaνR = 0.32814
HillKH = 67.778 GPaEH = 78.256 GPaGH = 29.924 GPaνH = 0.30757

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16.119 GPa 25.762 GPa 38.144 GPa 57.881 GPa 98.343 GPa 204.75 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.496 GPa 129.31 GPa 4.0645 TPa–1 6.5036 TPa–1 16.119 GPa 57.881 GPa-0.0500240.65606Value
Anisotropy 2.723 1.6001 3.591Anisotropy
Axis -0.0861
0.7168
-0.6919
-0.5863
0.8073
0.0675
0.0000
1.0000
0.0000
-0.9584
0.0000
0.2853
0.1452
-0.0000
0.9894
0.9894
-0.0005
-0.1451
-0.7303
0.6549
-0.1941
0.7043
0.5358
0.4657
Axis
0.0000
1.0000
0.0000
0.0005
1.0000
-0.0002
-0.6480
-0.5743
0.5002
0.0393
0.6256
-0.7792
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