F. Peter Boer and Truman H. Jordan Harvard University Cambridge. Massachusetts
I
I
X-ray Crystallography "Experiment" Powder patterns for alkali halides
For the past 30 years the determination of molecular stmctures by X-ray crystallography has been largely a specialty in the area of physical chemistry. However, recent technological advances have made fairly routine the structure determinations of a reasonably broad range of chemical compounds, and as a result crystallographic methods have become increasingly practical for non-specialists.' These technical improvements have come in two main areas, the collection of data and the determination of the molecular structure from the data. Automatic diffractometers may now be obtained commercially. These instnlments are proportional or scint,illation counters which are designed to measure automatically the intensity of the Bragg reflections according to programed instructions. They reduce to a matter of days the months previously required to gather the reflections photographically and to estimate their intensities visually. The process of analyzing the reflection data to obtain a structure in terms of an electron density map has also become much more routine. Programs for modern high speed computers are available to handle most of the important stages in the solution of structural problems, and these also provide a variety of approaches that can be tailored to the special features of the problem. While an understanding of the fundamentals of crystallography is still very essential, the problem is often reduced to choosing which of a number of very powerful programed mathematical methods is most appropriate a t each point of the solution process. However, we must emphasize that for a variety of reasons not all structure determinations are routine or even feasible, and unfortunately large molecules without heavy atoms pose especially serious problems. Still, these advances give both organic and inorganic chemists the clear advantage of being able to obtain the complete molecular structure of a compound within a few months of its synthesis and in the laboratory where it was synthesized. For the undergraduate chemistry major a powder experiment can serve as an introduction to the techniques and principles of an increasingly important research method that is one of the most complete and powerful ways of elucidating n~olecularstructure available. I n this article we discuss what powder techniques can and cannot do, describe briefly the objectives and methods of an experiment performed in the undergraduate physical chemistry laboratory a t Haward 1 Similar points have also been made recently with special emphasis on organic and biological problems by MACINTYRE, W. M., THIS JOURNAL, 41,526 (1964).
76
/
Journal o f Chemical Education
University, and provide "dry data" in the form of densitometer traces of actual powder photographs that may be copied and used in courses where X-ray photography may not be safe or economically feasible. The Powder Method in Perspective
While modern crystallographic practice relies almost exclusively on single crystal methods for molecular structure determination, these techniques are unfortunately too complex and varied to fit conveniently into a week or two of an undergraduate course. The powder method has the advantage of simplicity, especially when applied to very small molecules. However, when a crystal is ground into powder, information is inevitably lost, with a concomitant loss of access to some of the important principles of structure determination. Thus, to be in proper perspective with respect to single crystal methods, the pomder experiment should have as an objective the determination of what type of information is accessible to the student and what is not. The information most readily obtained from powder work consists of the lattice type and cell dimensions, although in crystals of low symmetry even these must be obtained from single crystals. Also available but less readily obtainable by the undergraduate are the relative intensities of the powder lines. For some crystals, notably those of elements and of binary compounds, these limitations are not too formidable, since their structures can be solved from limited powder data vith the additional help of chemical information about the elements and the stoichiometry. Single crystal methods theoretically do not require chemical information, helpful as it may be. Rather they seek the structure by measuring the intensities of the reflections and use mathematical methods to obtain their phases. Essentially, the heart of the experimentally obtainable information is data on the intensity of the scattered radiation. The positions on a photographic plate of powder lines or single crystal reflections relate only to the lattice type and length of unit cell edge. Comparisons of different powder photographs can illustrate the close relationship between electron distribution and lme intensity. For example, NaI and KBr have the same lattice type and very similar cell dimensions so their powder lines fall a t the same relative positions on a film. Yet their electron densities are quite different and consequently the relative intensities of the sets of lines are unlike. Furthermore, a series of chemically related compounds can often give considerable "intuition" with regard to intensities. Thus certain lines which are strong in CsCl are weak in CsBr
and virtually extinct in CsI. This result is the consequence of the fact that the primitive lattice appears to be body-centered because Cs+ and I- are virtually indistinguishable to the X-ray beam. The extinction of these lines can be explained qualitatively in terms of constructive and destructive interference from various lattice planes or by mathematical arguments of no great conceptual diffi~ulty.~The next step is the concept of partial destructive interference, which causes lines extinct in CsI to appear weakly in CsBr and more strongly in CsC1. Thus a powder experiment can clarify the concept that the electron density is functionally related to the intensity of the scattered radiation. But it is not so clear u-hy the determination of the phases of the scattered radiation is necessary to the solution of the structure. I n the cubic binary compounds discussed in the following section, the phase problem is circumvented by a combination of symmetry and chemical arguments. The chief limitation of this powder experiment is that it ignores a central problem of X-ray crystallography because it has no need to deal with it. While the phase problem may he solved formally from the intensities of powder lines, this approach is probably within the scope of only the most talented students.
C3, are provided. The first six compounds have facecentered lattices and the last three are primitive (sinple cubic). However, due to the isoelectronic nature of their respective positive and negative ions, KC1 is pseudoprimitive and CsI is pseudobody-centered; so all three cubic Bravais lattices are encountered. The details of the experimental technique adhere closely to those described very adequately elsewhere3 so we shall mention only the general outlines. The samples are finely pulverized by lnortar and pestle and packed into glass capillaries of 0.5 mm diameter. Three powder cameras of 57.3 mm diameter are employed, and an X-ray unit with two portsprovides the Cu radiation. The CuI
