The divergence in functional forms of ZBL screened potential

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1

Hi, all

In LAMMPS manual of command pair_style zbl, the denominator of parameter a is (Zi^0.23+Zj^0.23), and J.F. Ziegler, J. P. Biersack and U. Littmark, “The Stopping and Range of Ions in Matter,” Volume 1, Pergamon, 1985 is cited. But I found in early Ziegler’s thesis (Nuclear Instruments and Methods 194 (1982) 93-100), this denominator is taken as (sqrt(Zi)+sqrt(Zj))^2/3. What’s more, in some more recent articles dealing with potential fitting, that denominator always taken as (Zi^(2/3)+Zj^(2/3)).

I’m not sure which form should i taken when tabulating potentials, since they are obviously not equivalent to each other. Can anyone explain this to me ?

2

Aidan can comment.

Steve

3

Hi Peter,

The problem is surprisingly complex and there is a lot of wrong ZBL in the literature, mainly because the ZBL85 book is hard to get.

However, the form of (Zi^0.23+Zj^0.23) is correct [ZBL85]. There is a small issue of the third exponent in phi. On page 48, Eq. (2-61) it is -0.4028 and on page 49 in Fig. (2-17) it is -0.4029. Usually the value from the figure is taken. Anyway, the actual numerical difference is small.

To add complexity, there is an older article with a similar potential [ZB82]. This one has the form of (sqrt(Zi)+sqrt(Zj))^2/3, but completely different formula for phi.

Then in an article [Ackland97] containing widely used Iron potential a mixture of phi from [ZBL85] and Z scaling from [ZB82] i.e. (sqrt(Zi)+sqrt(Zj))^2/3 appeared. Since then the mistake has been repeated many times, as this article is popular and easily accessible.

The ZBL85 and ZB82 formulas are close to each other. The mixed formula of Ackland97 is a bit off, if I remember well [Fikar07]. I've personally pointed out this issue to D.J. Bacon and I would recommend the ZBL85.

Hope this clears a bit the ZBL issue.
Jan

References:

[ZB82] J. P. Biersack and J.F. Ziegler, Nuclear Instruments and Methods 194 (1982) 93-100.

[ZBL85] J.F. Ziegler, J. P. Biersack and U. Littmark, “The Stopping and Range of Ions in Matter,” Volume 1, Pergamon, 1985.

[Ackland97] G.J. Ackland, D.J. Bacon, A.F. Calder, and T. Harry, Philosophical Magazine A (1997), Vol 75, No 3, 713-732.

[Fikar07] J. Fikar, R. Schaeublin, Nucl. Instrum. and Meth. B 255 (2007) 27.

zbl85.pdf (516 KB)