November 07 2002

 Curvature of 603 atoms at different temperature levels

According to Dr. Dellago's suggestion, the curvature has been calculated by the distance between two neighbor atoms and the angle between the normal vectors of the flatness on those atoms.

Let the positions of the two atoms be (x1, y1, z1) and (x2,y2,z2), the distance between them is:

L = sqrt( (x2-x1)2 + (y2-y1)2 + (z2-z1)2 )

Let the normal vectors be (nx1, ny1, nz1) and (nx2, ny2, nz2), theta be the angle between them,

cos(theta) = nx1*nx2 + ny1*ny2 + nz1*nz2

The radius of curvature can be calculated as:

r = L / ( 2*sin(theta/2) )

Because

cos(theta) = 1 - 2*sin2(theta /2)

The curvature is then

c = 1/r = sqrt(  2 * ( 1 - nx1*nx2 - ny1*ny2 - nz1*nz2 )  /  ( (x2-x1)2 + (y2-y1)2 + (z2-z1)2 ) )

The histograms include 100 bins.

Averages of curvature


 

Standard deviation of curvature

Comparison of curvature distributions at 100K, 500K, 1000K and 1500K

Curvature distributions at different temperatures

The data files of all temperature levels can be downloaded here to achieve more comparisons on the same plot.

1) 100K

2) 200K

3) 300K

4) 400K

5) 500K

6) 600K

7) 700K

8) 800K

9) 900K

10) 1000K

11) 1500K