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 Ti2N (Materials Project id mp-7790)

       372      126       87        0        0        0  
       126      372       87        0        0        0  
        87       87      287        0        0        0  
         0        0        0      109        0        0  
         0        0        0        0      109        0  
         0        0        0        0        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 181.22 GPaEV = 266.81 GPaGV = 106.33 GPaνV = 0.25462
ReussKR = 176.5 GPaER = 255.47 GPaGR = 101.47 GPaνR = 0.25877
HillKH = 178.86 GPaEH = 261.14 GPaGH = 103.9 GPaνH = 0.25666

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
70 GPa 109 GPa 109 GPa 230.43 GPa 246 GPa 554.57 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 213.02 GPa 316.91 GPa 1.5651 TPa–1 2.5354 TPa–1 70 GPa 123 GPa0.117750.52158Value
Anisotropy 1.488 1.6200 1.757 4.4294Anisotropy
Axis -0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
0.7071
0.7071
-0.0000
-0.5334
0.5327
0.6570
-0.7071
0.7071
-0.0000
Axis
0.0002
1.0000
0.0000
-0.7071
0.7071
-0.0000
-0.4642
0.4651
-0.7539
-0.7071
-0.7071
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