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 P3N5 (Materials Project id mp-567907)

       224      119       86        0       24        0  
       119      200      102        0       12        0  
        86      102      299        0       41        0  
         0        0        0      109        0       30  
        24       12       41        0      117        0  
         0        0        0       30        0      106  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 148.56 GPaEV = 233.15 GPaGV = 94.133 GPaνV = 0.23842
ReussKR = 142.01 GPaER = 201.73 GPaGR = 79.846 GPaνR = 0.26325
HillKH = 145.28 GPaEH = 217.55 GPaGH = 86.99 GPaνH = 0.25043

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
77.463 GPa 85.386 GPa 113.37 GPa 137.54 GPa 186 GPa 455.25 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 124.35 GPa 334.6 GPa 1.4313 TPa–1 2.9881 TPa–1 44.943 GPa 137.54 GPa-0.0573220.65386Value
Anisotropy 2.691 2.0876 3.06Anisotropy
Axis 0.0000
1.0000
0.0000
0.5313
0.4805
0.6977
0.5689
0.0000
0.8224
-0.8224
0.0000
0.5689
-0.6996
0.7071
0.1027
0.6892
-0.0003
0.7246
0.6472
-0.0001
0.7623
0.7112
-0.0005
0.7030
Axis
-0.6996
-0.7071
0.1026
-0.0001
1.0000
0.0005
0.7623
0.0001
-0.6472
0.0003
1.0000
0.0005
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