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 TiSiRu (Materials Project id mp-11560)

       280      143      151        0        0        0  
       143      346      131        0        0        0  
       151      131      352        0        0        0  
         0        0        0      105        0        0  
         0        0        0        0      116        0  
         0        0        0        0        0      118  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 203.11 GPaEV = 267.97 GPaGV = 104.67 GPaνV = 0.28011
ReussKR = 201.67 GPaER = 261.18 GPaGR = 101.69 GPaνR = 0.28415
HillKH = 202.39 GPaEH = 264.58 GPaGH = 103.18 GPaνH = 0.28212

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
105 GPa 116 GPa 118 GPa 149.16 GPa 218.07 GPa 610.77 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 189.88 GPa 289.02 GPa 1.4009 TPa–1 2.0417 TPa–1 80.08 GPa 118 GPa0.169270.43847Value
Anisotropy 1.522 1.4575 1.474 2.5903Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5625
0.0000
0.8268
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0002
0.7071
1.0000
-0.0000
-0.0000
0.7350
0.6781
-0.0000
0.0000
0.0000
1.0000
Axis
0.7071
-0.0006
-0.7071
0.0000
1.0000
-0.0000
-0.6781
0.7350
-0.0000
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