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 YSi2 (Materials Project id mp-12769)

       116       79       70        0        0        0  
        79      116       70        0        0        0  
        70       70       99        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       67  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 85.444 GPaEV = 79.768 GPaGV = 29.667 GPaνV = 0.34441
ReussKR = 84.115 GPaER = 64.202 GPaGR = 23.384 GPaνR = 0.37279
HillKH = 84.78 GPaEH = 72.06 GPaGH = 26.525 GPaνH = 0.35834

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 22 GPa 36.982 GPa 37 GPa 67 GPa 257.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 48.744 GPa 111.87 GPa 3.051 TPa–1 5.7864 TPa–1 18.53 GPa 67 GPa-0.165170.82385Value
Anisotropy 2.295 1.8966 3.616Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
1.0000
0.0007
-0.0000
-0.7071
0.7071
0.0000
-0.7071
0.7071
-0.0000
Axis
-0.7071
0.0002
-0.7071
-0.0007
1.0000
0.0001
-0.7071
-0.7071
0.0000
-0.0003
-0.0003
-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