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 Si3N4 (Materials Project id mp-2075)

       515      183      183        0        0        0  
       183      515      183        0        0        0  
       183      183      515        0        0        0  
         0        0        0      326        0        0  
         0        0        0        0      326        0  
         0        0        0        0        0      326  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 293.67 GPaEV = 605.83 GPaGV = 262 GPaνV = 0.15617
ReussKR = 293.67 GPaER = 557.08 GPaGR = 235.29 GPaνR = 0.18384
HillKH = 293.67 GPaEH = 581.75 GPaGH = 248.64 GPaνH = 0.16984

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
326 GPa 326 GPa 326 GPa 332 GPa 332 GPa 881 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 419.04 GPa 713.85 GPa 1.1351 TPa–1 1.1351 TPa–1 166 GPa 326 GPa-0.06890.37982Value
Anisotropy 1.704 1.0000 1.964Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.8660
0.0000
0.5000
0.4957
0.8586
-0.1305
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7072
0.0000
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-0.0001
-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