Fred's father, John Kasper, is well known in the field of crystallography, for his ground-breaking work. For many years he was a research scientist at General Electric, in Schenectady, New York. He is now retired and lives in Scotia, New York. The following are excerpts from a biographical memoir on David Harker by Herbert Hauptman. Included are comments by Harker recalling the incidents surrounding John Kasper's groundbreaking work. Also, there is quoted a letter written at the request of Herbert Hauptman by John Kasper, Fred's father. This is his own account, as dictated to his wife Charlys, also a scientist, and working with him at the time. There is a short appendation by her as well, recalling the discovery. For the complete article on David Harker go to: David Harker memoir THE HARKER-KASPER INEQUALITIES

David Harker's academic career in crystallography began as a graduate student at Caltech, in Pasadena, in 1933. Harker at CALTECH(1933-36) In 1933 (the depth of the Depression) Dave lost his job. He returned to California with his wife and child, borrowed some money from an old friend of his parents, and entered the graduate school of the California Institute of Technology. There, under the supervision of Linus Pauling, he began to work on the determination of crystal structures using the technique of X-ray diffraction. THE FOCUS OF DAVE Harker's life, around which all his thoughts and actions revolved, was the science of crystallography, which he dearly loved. To crystallography he gave everything–his time, his energy, his total devotion. So complete was his dedication to this science and so fundamental and many faceted were his contributions that he influenced forever the course of its development. To this day, the Harker section and the Harker construction play essential roles in the determination of the structures of very large molecules. The Harker-Kasper inequalities provided the inspiration for a new branch of X-ray crystallography, the so-called direct methods of phase determination.


In 1941 Dave received an offer from W. D. Coolidge to work in the famous research laboratory of the General Electric Company and after some hesitation he accepted it. He became a member of the metallurgy division at General Electric and proceeded to learn properties of metals using X-ray diffraction and other crystallographic methods. Owing to the liberal policy of the General Electric research laboratory in those days, Dave was not compelled to work exclusively on metals, although he did publish several papers on solid state reactions characteristic of them, including a paper on grain shape and grain growth, another on order-disorder reaction, and several others.

Although Dave is known primarily for his contributions to X-ray crystallography, his metallurgical papers had a considerable impact on the physical metallurgical community. One of these, in particular, was primarily concerned with the microstructural subtleties associated with the ordering reaction in the alloy AuCu in which there is a change in unit cell from cubic to tetragonal. His theoretical analysis of the complex microstructures, which are to be expected as a means for the material to avoid long-range internal stresses, was far ahead of its time and had considerable influence on the research concerned with ordering reactions in alloys.

During his years at General Electric, Dave also developed an X-ray method for finding the orientation of quartz fragments, so that oscillator plates could be cut from them. In addition, he did several pieces of crystallographic work for other divisions of the laboratory. He also started work on the design of X-ray diffraction equipment with which the diffracted intensity would be measured with a Geiger-Müller or other particle counter.

It was during Dave's tenure at General Electric that he and his collaborator John S. Kasper produced their paper on the inequalities among the crystal structure factors, the famous Harker-Kasper inequalities. Because these inequalities constitute the first contribution to the direct methods of phase determination, which now (1997) has a fifty-year history and which continues to be a subject of intense interest, activity, and importance, it is appropriate to describe in some detail the circumstances surrounding their discovery. We are fortunate to have first-hand accounts by the authors. First, Dave's account:

One problem in particular fascinated us: the determination of the crystal structure of decaborane, B10H14. This turned out to be surprisingly difficult. It was borne in upon Dr. John S. Kasper and me that a structure which could not easily be guessed at approximately from known stereochemical principles, could not be solved by the traditional trial and error methods. Some twenty structures for the B10H14 molecule had been published, but none could be made to fit the X-ray diffraction data from the crystals.

One day John Kasper was sitting at his desk staring gloomily at a lot of algebra he had been writing down. I looked over his shoulder and said something like, "What on earth is that?" and he replied "Schwartz's Inequality for a structure factor, but it doesn't seem to help." He then kept on writing, while I looked on. I said, "Oh, well, let's expand those squares of cosines into functions of double angles." So we did. Then it hit us both, I think, at the same time. "Say! We can get the signs of some structure factors from this!" Then we went madly to work, and in a couple of weeks we had enough algebraic apparatus assembled "unitary" structure factors, sum and difference inequalities, etc. To be useful. Kasper applied this schema to the decaborane data and came out with a preliminary model which explained the diffracted intensities from one zone, and, after another couple of months, the complete structure emerged. Thus was born the subject of "sign determination" from intensities. This was in 1947.

At my request John Kasper sent me his account, with a postscript by his wife Charlys:

Here is my version of the origin of the sign-determining inequalities. First, I would like to give you some background information that may be of interest to you. At the 1946 meeting of ASXRED (American Society for X-ray and Electron Diffraction) at Lake George, N.Y., a method of attacking the phase problem was presented by A. Booth, namely, the method of steepest descent. While this did not turn out to be a viable method, considerable discussion of the phase problem ensued. Nothing useful resulted, however, and there was a consensus that nothing could be done about obtaining phases and that it was a waste of time to think about it. Among the minority were Dave Harker, Buerger, and Fankuchen, although no convincing evidence could be given to justify the optimistic viewpoint. For Dave and myself the phase problem was on our minds although we were quite busy with other problems at G. E.

I became intrigued with the fact that the straightforward squaring of a real structure factor, Fhkl (with cosine terms) contained, in part, the sum of modified cosine squared terms. These latter could be rewritten, by virtue of the relation 2 cos2A=1+cos 2A as components of F2h,2k,2l. A relation then exists between F2hkl and F2h,2k,2l, but also with the summation of cross terms. I did not know what to do with the cross terms and so I put the thing aside. Some days later (in 1947) it occurred to me that Schwartz's inequality would deal only with the desirable summation of cosine2 terms. Accordingly, one morning at work I wrote down the relationship between F2hkl and F2h,2k,2l resulting from the application of Schwartz's inequality. No sooner had I written this down, when Dave walked in the office and looked over my shoulder. "What is that?" Dave asked. "That is the result of applying Schwartz's inequality to a structure factor," I replied. After satisfying himself that what I had written was alright, Dave became quite excited and remarked: "You can determine signs with that." "That's right," I replied.

I was unhappy, however, that the treatment so far was only for the case of one kind of atom. Dave said that could be fixed, and in short order he proposed using the unitary atomic structure factor, . This enabled treatment of more general situations.

For the next few weeks Dave was immersed in the applications to various symmetries and space groups, and other ramifications, such as sum and difference formulas. He also produced an elegant write up of the work. I concentrated on its application to the Decaborane problem which was uppermost in our minds.

I realize that my version is not exactly the same as one that Dave has given, but I stand by it. We were in communication in 1989, with the goal of achieving a version that was mutually agreeable, I regret deeply that Dave's illness prevented the completion of that project.

From what you say I wonder if you have the autobiography which was written in 1961, and which Dave sent to me in 1989. It is very interesting reading to anyone who knew Dave. I have little to add to it. I would mention what a good and influential teacher he was. I first knew Dave as a teacher of freshman chemistry at Johns Hopkins. He revolutionized the course with emphasis on basic principles. His approach was adopted by students who subsequently taught chemistry. He only mentions his work in metallurgy, but his contributions were fundamental in the areas of grain growth and recrystallization and in order-disorder phenomena. I would like to add that the single crystal orienter he developed was the first such device for use with a counter.

I hope this is useful to you. I am not able to do many things because I now am legally blind. That is why I am unable to attend the tribute to Dave.

I would appreciate a copy of the Biography when it is done.

John S. Kasper


P.S. I am typing this for John. I was working closely with both John and Dave on the decaborane problem at the time and clearly recall the sequence of events as John has described. I was also working in the office while John was busy working with the relationship of Schwartz's inequality and the structure factors to possibly help determine signs when Dave arrived in the office and became very excited at the possibilities of its use. It was an event one doesn't forget.
Charlys Lucht Kasper

It is appropriate to point out here the mathematical basis of the Harker-Kasper inequalities since this is not mentioned explicitly in their paper. This is simply the non-negativity property of the electron density function, a fact implicitly assumed in their analysis.

After a good deal of prodding on Dave's part, the X-ray department of General Electric was finally persuaded to build its first counter diffractometer for powder patterns, although not before the North American Philips Co. had already put a similar device on the market. Next, Dave set about adapting it to single crystal work. By 1949 he had built several models and had used them successfully, mostly on metallurgical problems.

During his time at General Electric, Dave served as president of the Society for X-ray and Electron Diffraction (1946). He also headed the American delegation to the London conference where the formation of the International Union of Crystallography was proposed and later was established, along with its adhering body in the United States, the U.S. National Committee for Crystallography.

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