June 2, 1950

To: David Shoemaker

From: Linus Pauling

Subject: The sigma phase

I think that I have worked out a structure of the sigma phase. It is based on the orthorhombic unit proposed by Mr. Paul Pietrokowsky as reported in your communication of May 12, 1950. This is an orthorhombic cell with dimensions a_o = 8.661, b_o = 6.214, and c_o = 5.199 kx with 12 atoms in the unit cell. You mention that the hko’s are present only with h even. I am not sure that this is compatible with my structure.

With these units, the parameters of the 12 atoms are the following: [List of x, y and z parameters]

Your communication to me said that there were 12 FeCr in the unit cell; that is, 24 atoms. The other 12 atoms are to be centered around ½ ½ ½ in the same way that these are located around 000. A glide plane is necessary in order to preserve orthorhombic symmetry; but the glide plane must transfer a point at 000 into a point at ½ ½ ½. I judge that it must be a diagonal glide.

Would you determine the coordinates of the other 12 atoms, by introducing a suitable symmetry element, in such a way that no 2 atoms are closer than about 2.5 Å. Would you also evaluate all interatomic distances - I have not carried out this part of the work in detail.

This seems to me to be a very nice structure. In fact, it looks so good to me that I feel reasonably sure that Pietrokowsky’s unit is the correct one. I think that the next thing to do, after you have checked the structure, is to calculate intensities. However, I would like to see the coordinates of all of the atoms. I think it would be a good idea to have a model made – perhaps you could put one together, using the technique of stringing small wooden balls on vertical rods. It may be that we should change the parameters a little bit from the values that I have calculated as the first set.

If this does turn out to be the right structure I shall be pretty pleased.

Linus Pauling:W

cc: Mr. Bergman