1 February

1956

Dr. Charles E. Weir

Leather Section

National Bureau of Standards

Washington 25, D.C.

Dear Dr. Weir:

I have read the manuscript sent with your letter of 23 January with interest, and I have several comments to make on it.

On the first page you mention my discussion of effect of radius ratio on properties of alkali halides, and say that no specific details were discussed. I think that the argument about the effect of radius ratio that I gave is complete so far as density is concerned. It is true that I discussed the interatomic distances in detail, in particular giving values of actual interionic distances for alkali halide crystals and values calculated for hypothetical substances with the same radius sums of the alkali halides but with the standard radius ratio. The calculation of the values of the density from the values of interatomic distance is such a simple and straightforward one that anybody could make it. The whole argument about the effect of radius ratio is, I think, fundamental to any discussion of density of these substances, and I feel that unless the effect of radius ratio is taken into consideration in a discussion the conclusions that are reached will be unreliable.

On page 4 you discuss the irregularity found on graphs of density, etc., at atomic number of about 20 for either anion or cation, and on page 5 you say that this behavior has not been described previously. The behavior is, in fact, well known, and has been discussed in greater or less detail many times during the past thirty years. For example, in my paper on the sizes of ions and the structure of ionic crystals published in the Journal of the American Chemical Society in 1927 there is given, as Figure 3, a drawing showing the radii of ions as a function of the atomic number, and on this drawing lines are shown connecting the points for the halogenide ions and also the points for the alkali ions. These lines show the same peculiarity, a pronounced change in slope at atomic number about 20, as the lines in your figures 1 and 2.

The attempt that you make on page 6 and following pages to discuss the lattice spacing in terms of principal quantum numbers and quantum defects seems to me to be likely to be unproductive, because there is no reason to expect the radii of the ions in a sequence to be proportional to the square of an effective quantum number, and, moreover, surely the effect of radius ratio, which is neglected in your treatment, must be taken into consideration.

I cannot see any value in the discussion of a complex energy cycle beginning on page 10 of your manuscript. You are not able to evaluate the quantities E1 and E2 (I refer to the interaction of the nuclei with the surrounding electrons, not the nuclear energy itself, which cancels out, as you mention), and because of this inability you cannot reach any significant conclusions from consideration of this cycle. I cannot see any advantage to your discussion over the ordinary discussion of these ionic crystals, in terms of attraction of ions and repulsion of ions.

In general, I think that there is the possibility of significant progress in the theoretical discussion of essentially ionic crystals, such as the alkali halides; but I think that the methods described in your manuscript are less satisfactory than those that have been used in the past, and that you probably would make more rapid progress by building upon the earlier methods.

Sincerely yours,

Linus Pauling:w