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 Ti5Sn3 (Materials Project id mp-20847)

       184      108       44        0        0        0  
       108      184       44        0        0        0  
        44       44      205        0        0        0  
         0        0        0       45        0        0  
         0        0        0        0       45        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 107.22 GPaEV = 131.47 GPaGV = 50.733 GPaνV = 0.29565
ReussKR = 106.44 GPaER = 120.75 GPaGR = 46.055 GPaνR = 0.31093
HillKH = 106.83 GPaEH = 126.14 GPaGH = 48.394 GPaνH = 0.30322

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 45 GPa 45 GPa 76 GPa 172.58 GPa 324.42 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 111.96 GPa 191.74 GPa 2.8756 TPa–1 3.6436 TPa–1 38 GPa 65.803 GPa0.093450.56461Value
Anisotropy 1.713 1.2671 1.732 6.0419Anisotropy
Axis 0.8216
0.2288
0.5222
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0008
-0.0000
0.3363
0.6220
0.7071
0.4487
0.8937
-0.0000
1.0000
-0.0008
0.0000
Axis
0.0008
1.0000
-0.0000
0.3363
0.6220
-0.7071
-0.0000
0.0000
-1.0000
0.0008
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