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 Ti3SiC2 (Materials Project id mp-5659)

       362       90      101        0        0        0  
        90      362      101        0        0        0  
       101      101      350        0        0        0  
         0        0        0      149        0        0  
         0        0        0        0      149        0  
         0        0        0        0        0      136  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 184.22 GPaEV = 333.07 GPaGV = 138.93 GPaνV = 0.19867
ReussKR = 184.22 GPaER = 331.88 GPaGR = 138.31 GPaνR = 0.19975
HillKH = 184.22 GPaEH = 332.48 GPaGH = 138.62 GPaνH = 0.19921

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
136 GPa 149 GPa 149 GPa 249.33 GPa 272 GPa 552.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 304.86 GPa 344.59 GPa 1.807 TPa–1 1.8142 TPa–1 127.32 GPa 149 GPa0.153710.23581Value
Anisotropy 1.13 1.0040 1.17 1.5342Anisotropy
Axis 0.0000
0.0000
1.0000
0.7022
0.2866
0.6517
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
-0.6197
0.3199
0.7167
-0.3605
0.9327
-0.0000
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.6368
0.3289
-0.6974
0.0002
0.0001
-1.0000
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