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 SrTiN2 (Materials Project id mp-9517)

       180      151       67        0        0        0  
       151      180       67        0        0        0  
        67       67      181        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       53        0  
         0        0        0        0        0      119  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 123.44 GPaEV = 159.47 GPaGV = 62.067 GPaνV = 0.28469
ReussKR = 119.84 GPaER = 104.49 GPaGR = 38.566 GPaνR = 0.35468
HillKH = 121.64 GPaEH = 132.66 GPaGH = 50.317 GPaνH = 0.31824

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29 GPa 53 GPa 53 GPa 119 GPa 135.16 GPa 376.84 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 52.581 GPa 257.89 GPa 2.2382 TPa–1 3.8678 TPa–1 14.5 GPa 119 GPa-0.0999040.84325Value
Anisotropy 4.905 1.7281 8.207Anisotropy
Axis 1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
1.0000
0.0000
-0.0000
0.6623
-0.0000
-0.7492
0.0000
0.8541
-0.5201
Axis
-0.7071
-0.7071
-0.0000
-0.0000
1.0000
0.0000
-0.7492
0.0001
-0.6623
-1.0000
0.0000
-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