I . . . n thls d~scussion of Structural Chemistry

in the Nuclear Age, it seems appropriate to emphasize those techniques of structural chemistry which have been directly affected by nuclear technology. I will not, however, discuss all such techniques hut will stick rather closely to my own area of experiencethe study of the solid state by diffraction and scattering techniques. I would be remiss, however, if I did not at least mention some other techniques which make use of nuclear properties in the elucidation of molecular structure.

One of the most important of these is the use of Mossbauer spectroscopy. This technique, although in its infancy, promises to have valuable applications in the studies of bonding in a few classes of inorganic compounds. From the splittings observed for a partic- ular compound we may at least partially answer subtle questions of stereochemistry. Furthermore, some information concerning the dynamics of molecules in the solid state may be obtained. Since the use of the Mi'ssbauer effect in chemical studies is the subject of a separate symposium (1) at this meeting, I will not discuss it further here.

There are probably few chemists today who have not at least indirectly used another nuclear property for the study of the structures of molecules and chemical systems-namely nuclear magnetic resonance. Its applications are well-known and need no reiteration here. The sophistication of the experiments of course grows daily.

Another spin-off from nuclear technology has been the wide availability of pure isotopes of many elements. The use of isotopically-substituted molecules has been of great value in the interpretation of data in the more traditional structural tools of spectroscopy and crystal- lography. An important part of this work has of course been the study of the structural isotope effect itself.

The last half of this paper will he devoted to the applications of neutron diffraction and neutron inelastic scattering to the study of solids and liquids. First, however, I would like to redefine or reinterpret the title of the symposium to read "Chemistry in the Instru- mentation and Computer Age."

Walter C. Hamilton Brookhaven National Laboratory

Upton, New York 11973

The Impact of instrumentation on Structural Chemistry

Structural Chemistry in the Nuclear Age

An ubiquitous characteristic of almost every chemical laboratory that one enters nowadays is the large rack of sophisticated electronic equipment in one corner, the stack of computer output in the other corner-with some miscellaneous chemistry going on between.

Work supported by the U.S. Atomic Energy Commission.

(Even the latter is rare in some laboratories.) I think that most of us applaud this development, for the development of new types of instrumentation has made possible many experiments which were impossible or unthought of twenty-five years ago. The relevance of this to the present symposium is that nuclear chemists have been among the most sophisticated users of instrumentation-forced into this area perhaps by the complexity of their experiments hut also perhaps by the continual shoulder-rubbing with nuclear physicists, who build the largest and most complex scientific instru- ments known to man. In any case, the competence and know-how in the instrumentation field among Amer- ican chemists has been greatly accelerated by the nuclear chemists, and this acceleration has had an enormous impact on the rest of chemistry. Similarly, the rapid growth in the size and speed of our digital computers has greatly expanded the horizons of most areas of chemistry. This development cannot perhaps be traced directly to any contributions in nuclear science, but it poses an interesting question for students of the history of chemistry as to why the most powerful computers and some of the most advanced uses of them have been associated uith laboratories which have been preeminent in nuclear science as well.

It is thus clear to me that the Nuclear Age and the Instrumentation and Computer Age are synouomous, and the developments in one area have gone hand-in- hand uith those in the other. Many other names could he given to our age of course. Another that comes to mind is the "Solid State Age," and I would like to make a few remarks about the present state of the application of instrumentation to solid state chemistry (or the small branch that is crystal structure analysis). The greatest changes in crystal structure analysis have come about because of the rapidity of data collection and the rapidity of structure solution and refinement; both of these are attributable to the developments in computers and instrumentation in the last two decades.

In the area of data collection, photographic film as a recording medium has largely been replaced by quao- tum counters of various sorts. The availability of inexpensive digital computers has made possible the complete automation of the crystal orientation and counting devices, so that it becomes vossible to collect a compfete set of Bragg diffraction data on any inter- esting small molecule in a week's time with little human intervention. A corresponding decrease in the time required to collect data for protein structures has provided a great impetus to work in this field. In the area of protein crystallography, film still offers some advantages in that for any position of the crystal, several Bragg reflections may he possible. A photo-

296 / Journal of Chemical Education

graphic film may record all of these; a single quantum counter in a fixed position may record only one. One of the more active efforts in X-ray instrumentation is in the development of arrays of wunters for the simul- taneous recording of many diffraction maxima at one time--the electronic analog of a photographic film. Such counter arrays are familiar to the nuclear scientist and may create a further minor revolution in X-ray diffraction. One approach is to use an array of solid state counters. As the crystal moves, information regarding the crystal position and the configuration of counts in the array is fed into a small digital computer which processes the data and records the processed results on a suitable output device. A schematic drawing of such an instrument, under development (3) at Brookhaven is shown in Figure 1.

COUNTER ARRAY

SMALL DIGITAL OUTPUT

COMPUTER DEVICE

Figure 1 . Schematic drawing of a parallel X-ray data mllection system under development a t Bmokhoven Nation01 Lobordory by R. Thomor and coworkers. While the crystal is mtoting, diffracted X-rays moy be re- ceived in reverol counters a t approximately the some time. The x,y coordinates of an octive counter ore fed into the computer together with the encoded cvstol position. On the boris of this informotion, the com- puter progrom muigns the count to the intensity of a particular Bmgg reflection.

The development of high-speed digital computers has created the real revolution in crystallography. Not only have the time-consuming refinement procedures been enormously speeded up, but the great speed of these computers has led to the discovery and use of sophisticated numerical mathematical methods which lead to direct determination of satisfactory trial struc- ture for a complex organic molecule within a few weeks of the time that the chemist hands the crystallographer a bottle of material. The refinement of the structure is reduced to minutes, as opposed to the days, months, and even years so common a number of years ago. What is perhaps more important is that ' the ease of computation makes it possible to obtain more detailed analyses of the re- sults and more meaningful presentation of the chemically interesting information. As an example of this, Figure 2 shows a com- puter-produced stereoscopic drawing of an organic molecule that conveys much more information to the eye than pages of words or simple two-dimensional drawings.

Typical of the calculations that are now carried out routinely for small molecules are nonlinear least squares calculations for the determination of 400 parameters from 4000 observations and the evaluation of electron density at 100,000 points in space by the

calculation of Fourier series involving the same 4000 pieces of data as coefficients. Either of these calcula- tions can be done in much less than 10 min now.

The importance of this increased speed in every step of the crystal structure refinement is that it becomes possible for the crystallographer to launch a broad attack on an interesting chemical problem rather than just an isolated molecular structure. He may ask himself, "What is the chemical problem I would like to solve?" In the course of a year he may then deter- mine half a dozen crystal structures that shed some light on this particular problem.

Neutron Diffraction and Neutron Scanering

Nuclear technology has had its most dramatic and direct applications to the study of molecular and solid state structure in the use of the scattering of thermal neutrons. The availability of nuclear reactors with thermal neutron fluxes approaching 1015 neutrons-em-% sec-' has made possible many exciting experiments. The possihle relevance of techniques involving neutron scattering may he appreciated by an examination of Table 1, which gives some of the energy relationships

Table 1. Wave Length, Energy Relationships for Thermal Neutrons (E = Ic T)

T ('K) 77 100 300 500

A (k 3.51 3.08 1.78 1.38 E (ev) 0.007 0.009 0.028 0.043 - \.. --,

mole) 0.15 0.20 0.60 0.99 E (em-') 53 69 224 344 V (crn/sec) 1 .1 X lo6 1 .3 X 10' 2 .2 X lo6 2 . 9 X 106

pertinent to neutrons in the thermal range. The fact that the characteristic wave lengths are of the order of interatomic distances means that beams of thermal neutrons can be used for diffraction studies of crystal structures in the same way as can X-rays of similar wave lengths. That the energies of these neutrons are of the order of magnitude of several cm-' means that there can be a strong interaction with the vibrational modes of solids or liquids in this energy range, and that neutron spectroscopy thus has a very great potential for the investigation of molecular vibrations. The use of neutrons in structural chemical investigations in- cludes the applications listed in Table 2.

We will first consider the results that have become

Figure 2. Stereoscopic view of the molecular structure of 0 mmplex organic compound, Cso02Hla. The picture may be viewed either with the aid of o rmoll stereo viower or by iudiciously uncoupling the eyer so that the left eye view and the right eye view ore super- imposed. The figure war drown by a computer program written by C. K. Johnson of the O a k Ridge Notional Loborotory.

Volume 45, Number 5, May 1968 / 297

Table 2. Applicability of Neutron Scattering Techniques to Structural Chemistry

Elastic Scattering (Diraction) Magnetic structures-spin arrangement and unpaired electron

density Light atom-hemy atom structures-~articdarly hydrogen - ~~-

stom location Accurate thermd vibration parametera and consequent eccu-

rate electron density determination by X-ray diffraction Use of anomalous scatterina for solution of the phase ~rohlem -

in protein structures The structure of liquids

Inelastic Scatle~ing (Spectroscopy) Intermoleoular forces in molecular ervstala Rotation of groups in solids Dynamics of liquids

available by the use of neutron diffraction techniques. The differences between neutron diffraction and X-ray diffraction are both qualitative and quantitative. Some problems are better attacked by one method than the other, and some recent results suggest the importance of parallel use of the two methods to attack a single problem.

X-rays are scattered by the electrons in a molecule; the picture seen by X-ray diffraction is a picture of the electron density of the scattering sample. Each atom has a scattering power that is proportional to the number of electrons in the atom. The scattering of neutrons is largely from the nuclei of the atoms; each atom has a scattering power that is characteristic of its nuclear properties. The pattern of increase with atomic weight is very irregular. Table 3 gives some comparisons of relative scattering powers for a number of common atoms. The fact that the neutron scattering is from the nucleus means that one can determine the nuclear positions by neutron diffraction. Furthermore, the amplitudes of mo- tion of the nuclei in the molecule or crystal lattice may be accu- rately determined.

Magnetism

There is one important exception to the statement that neutron scat- tering is from the nuclei. Namely, if there are unpaired electrons pres- ent, scattering occurs which is char- acteristic of the interaction between the magnetic moment of the neu- tron and that of the electron. The magnitude of the scattering is in fact proportional to the product of the magnetic moments and the cosine of the angle between them. A measurement of the scattering thus gives information regarding the direction of the electron moments in the crystal. Since the scatter- ing is from the unpaired electrons, a Fourier inversion of the magnetic structure factors gives a picture of the unpaired electron density in the crystal just as an ordinary X-ray diffraction experiment gives a pic-

Table 3. Atomic Scattering Amplitudes in lo-'% cm for Thermal Neutrons for Some Representative Nuclei

'H -0.37 '"0 0.58 =H 0.65 I0F

1971 0.55

I'C 0.66 0.52 "N 0.94

ture of the total electron density in the crystal. Some of the earliest notable contributions of neutron

diffraction were the confirmations of postulated spin structures for antiferromagnetic materials. Not all of these are of a simple parallel-antiparallel type; it was neutron diffraction that first led to the discovery of modulated helical spin structures (5) such as those shown in Figure 3. The measurement of spin densities such as those shown in Figure 4 has been of the greatest importance for theories of magnetic materials (4). The magnetic moment of the unpaired electron spin is not localized at a point but is extended in space in an anisotropic way which can lead to the understanding of bonding in crystals of transition metals and their com- pounds.

Light Atom-Heavy A tom Studies

The quantitative differences between X-ray and neutron scattering factors have been of the greatest importance in an area in which I have been rather active in recent years, namely the study of hydrogen-bonded

Figure 3. Vorious types of spin structures occurring in the rare earth metals. These spin arrangements have been determined by neutron diffraction. The orrow* represent the components of the magnetic moment in the c direction of the crystal ond perpendicular to the c direction. Fmm reference 131.

298 / Journal o f Chemical Education

Figure 4. Spin density in the (100) plone of metallic iron. The denrity is not spherical. The total density is shown in la1 left, ond the difference be- Ween the observed totol denrity ond the dewily for a theoretical spherical atom ir shown in (bl right.

materials. For the proper understanding of the ge- ometry of these systems and the energy relationships involved in them, we must determine the positions of the hydrogen atoms and the amplitudes of motion of the hydrogen atoms to a high degree of accuracy. That this is easier with neutron diffraction than with X-ray diffraction is convincingly demonstrated as follows: For a structure composed of N atoms A , with atomic scattering factors St, the relative contribution of atom A to the intensity of an average Bragg reflection is

If we consider a structure which is composed of equal numbers of carbon atoms and hydrogen atoms, the relative contribution of the hydrogen atoms is '/a, for X-rays and '/, for neutrons. Since the accuracy of determination of atomic positions is higher if the measured quantities depend strongly on those positional parameters, it is clear that the accuracy of determina- tion of hydrogen atom positions must be much greater for neutron data than for X-ray data. The same argument applies to the determination of thermal vibntionnl p3ratnrrrrs. .4norher irnportnnr advmnngc of neutron (liffrnctio~~ over X-r:lv d~t in~r t io t~ for the determination of hydrogen atom positions is that one can assume that it is the position of the hydrogen nucleus which is being measured. With X-rays, the electron density is measured, and the distortion of the electron density from that characteristic of a spherically symmetric atom is great enough so that there are sys- tematic errors of large magnitude (0.1 A) in hond lengths involving hydrogen as determined by X-ray diffraction. These effects are of course interesting in themselves and, as we will discuss below, comparison of the X-ray and neutron diffraction results can be especially illuminating.

In any case, by the use of neutron diffraction we can routinely determine the positions of hydrogen atoms to 0.005 A. Furthermore, the thermal vibrational param- eters can he shown to he quite meaningful and in good

agreement with spectroscopic results. I will illustrate these points with a discussion of some recent studies of the potassium acid salt of acetyl-salicylic acid (potas- sium hydrogen diaspirinate).

The acid salts MHAz of many carboxylic acids HA often contain an unusually short 0.. .H. . .O hydrogen bond. The structures consist of isolated cations- typically K+ or Na+-and monovalent anions:

('4.. .H. . .A)-

The hydrogen hond is probably symmetric with the hydrogen atom equidistant from two oxygen atoms in the carboxyl groups of A. These salts have been extensively studied by X-ray diffraction by Speakman and co--workers (6). One of these salts, the potassium acid salt of aspirin (Fig. 5) has been the subject of both an accurate X-ray investigation (6) and an accurate neutron diffraction study (7). The neutron diffraction study was necessary for accurate location of the hydro- gen atoms. A comparison between the results of the two techniques for the aromatic hv- drogen atoms is presented in Table 4. The standard deviations for the C-H bond lengths are an order of magnitude less for the neutron study. Furthermore, the systematic appar- Figure 5. hydrogen diaspirin.te .,,ion. ent shortening in The midpoint of the hydrogen bond lies a t o

the X-ray study ~rystailographi~ center-of-symmetry in the p ~ t a l l i ~ m salt.

which has been con- firmed in many compounds is evident.

That excellent thermal vibration parameters for the hydrogen atoms were obtained is evident from an examination of Figure 6, which is a view of the methyl group from the C-C bond direction. The constant- probability ellipsoids provide a graphic picture of the motion of the methyl group. The hindered rotation of the group is obvious, and the agreement between the

Volume 45, Number 5, May 1968 / 299

Table 4. Aromatic C-H Bond Lengths in Potassium that it is now possible to see the effects of chemical Hydrogen Diaspirinfte as Determined by Neutron and bonding on the electron density. (For those who have X-ray Diffraction (in A; Standard Deviations in Parentheses1 not considered this problem, it is worthwhile pointing

X-ray Neutron out that the changes in electron density on going from an isolated atom to an atom in a molecule are slight.)

C%-Hg 0.93 (0.05) 1.081 (0.006) 1.03 (0.06) 1.083 (0.006)

It is only possible to see these bonding effects by calcu- Cz-HI C~-HI 0.85 (0.04) 1.080 (0.007) lating a so-called difference map which is the difference C s H s 1.01 (0.04) 1.088 (0.005) between the electron density actually observed and Mean 0.95 (0.04) 1.084 (0 002) t,bat calculated for a model with free noninteracting

atoms. This model must include the parameters , describing the thermal vibration of the atoms, and ' these parameters must be accurately known i f the

results are to be meaningful. If these parameters have been determined by a least squares refinement of the X-ray diffraction data itself, they will un- fortunately be systematically in error if isolated spherical atom scattering factors were assumed in the refinement model. Errors due to the latter as- sumption can be partially absorbed in effective vibra- tional warameters.

If we can, however, determine the thermal vibra- parameters from a neutron diffraction ex-

Figure 6. Tho methyl group in pot~rrium hydrogen diaspirinatc. This rtereolsopis periment, these parameters nil1 be unbiased by any

.,iew down the C-c bond the effect of hindered on the correlations with electron density distortions. I t observed ~ i b ~ ~ t i ~ ~ d amplitudes of the hydrogen atoms. is the nuclear motions that are seen. .We may then

take as our model for t,he calculated electron den- vibrational amplitudes for the three hydrogen atoms is sity an assembly of atoms with positions and ther- convincing evidence of the quality of the data, which is mal parameters given by the neutron diffraction typical of neutron diffraction data today. study and with free atom X-ray scattering factors.

The thermal motion of the atoms in the 0. . . H . . .O The difference between this model and the observed bridge of length 2.45 A is shown in Figure 7. The electron density should give us accurate informa- motion of the hydrogen atom has had the lattice mo- tion on bonding effects. This approach has been tion of the molecule subtracted from it so that it rep- vigorously pursued by Coppens (9, lo), and some of resents the motion of a hydrogen atom in the field of his results are illustrated in Figures 9 and 10. In two stationary oxygen atoms. Quantitative examine Figure 9 are shown the differences between the neutron tion of the components of this motion and consideration diffraction and theX-ray diffraction thermal parameters of infrared data have led to the conclusion that the po- for s-triazine. The X-ray parameters are systematically

larger and obviously try to fit the lone-pair and

&----P3 .. bonding electron density in the molecule. In

. . . 1 Figure 10, the bonding electron density ob- tained by consideration of the neutron-deter-

~i~~~~ I. Thermd motion in the 0-H-o bridge in the diospirinote ."ion. ~h~ prob.. mined structural parameters and the X-ray bility for the hydrogen atom has been corrected for the motion of the molecule data as described above is illustrated. The 0% 0 whole and provider evidence far o brood, flat potential governing the hydmgen extra density in the bond and in the lone- atom motion. pair region of the molecule is clearly evident.

tential energy function governing the hydrogen atom Biological Structures motion in this crystal is truly of the symmetric single-minimum typeillustrated in Figure 8 (7, 8). A word or two should be said concerning the appli-

cability of neutron diffraction methods to compo&ds Thermal Parameters and Electron Density of biological interest. I t has occasionally been sug-

It is well known that the Fourier inversion of Bragg gested that it would be important to determine a pro- diffraction data can lead to accurate electron-densit~ tein structure by neutron diffraction in order to deter- functions for crystals. The techniques of measurement mine the hydrogen atom positions. There is some of X-ray diffraction data have been refined enough so

Figure 8. Portdoted potentid for the motion of the hydrogen cltom in I . - the symmetric hydrogen bond in potassium hydrogen diorpirinote. This Figure 9. Differences between ther- quoiitotive ~ ic tv re is bored on orgu- mol motion p ~ r a m e t e n for r-triozine

mentr from the neutmn diffraction as determined by neutron diffraction data and from the infrored spectra and the apparent parameters 0s de-

of related compounds. termined by X-rays. The difference between the two i s due to bonding effects in the electron density dir- 1 tributionr. (Supplied by P. Cap- p e n 4

300 / lovrnal of Chemical Education

0 NITROGEN 0 CARBON

HYDROGEN

Figure 10. Bonding electron density distribution in r-triarine. This is tho difference between the observed electron density and that calculated for spherical atoms la) top, in molecular Ib) bottom, perpendicular to molecular plane along C-N bond. From reference 191.

question about the wisdom of doing this. The study of proteins by X-rays has not in general resulted in struc- tures which resolve individual atoms with any accuracy. The gross structure that is revealed can however he combined with accurate information about geometries and configurational energies of the individual building blocks of the proteins-the amino acids-to obtain an adequate understanding of the structure. It seems unlikely that the accuracy of determination of hydrogen atom positions in a neutron diffraction experiment taking a reasonable time would lead to any valuable new information. If hydrogen atom positions are crucial to a biological argument, it would seem best to

have a set of accurate structure determinations in- cluding hydrogen atom positions for amino acids and enzyme substrates. This information can then be combined with the gross protein structures to make inferences about hydrogen atom positions in the pro- tein.

A more exciting approach to the applicability of neutron diffraction to protein structures is that of using the unusual characteristics of a particular nucleus to aid in the solution of the crystallographic phase problem. One approach that has been suggested (11) is that of using the anomalous scattering of neutrons by heavily absorbing nuclei. The complex scattering amplitudes for these nuclei are sensitive functions of wavelength; thus simply by varying the wavelength, one has available a continuous set of isomorphous replacement "compounds"; the technique of isomor- phous replacement bas of course been the key to the solution of protein structures by X-ray diffraction. Elements useful in this technique are boron, cadmium, and some of the rare earths. Thus, the technique is limited to proteins into which these elements can be incorporated at specific sites.

Another interesting possibility arises because of the fact that the scattering from hydrogen is opposite in sign to that for most other elements. Since the hy- drogen atoms in a protein structure will in general lie on the outside of a core of other atoms and, furthermore, since the protein chains are often surrounded by water molecules with high hydrogen atom densities, a neutron scattering density map from a protein should consist of a core of positive density surrounded by a sea of neg* tive density. The use of this difference in attacking the phase problem is an area which should be carefully explored.

Structure of Liquids

Neutron diffraction can be used as can X-ray diffrac- tion to obtain information regarding the structure of liquids. The experimental data can be analyzed by the calculation of a radial distribution curve which gives the probability of a given interatomic distance being present. One of the difficulties in the application of neutron diffraction to liquid structure in the past has been that the scattering pattern consists of a super- position of elastic and inelastic scattering so that the interpretation of the data has not been straightforward. Neutron fluxes are now sufficient, and energy analysis of the scattered beam is so routine that the elastically scattered neutrons can be separated from the inelasti- cally scattered neutrons to obtain a data set which can be used with confidence to obtain a radial distribution curve. The application of this technique to the problem of the structure of water and ionic solutions seems promising.

Inelastic Scattering

The energy of thermal neutrons is comparable to that of many vibrational energy levels in liquids and solids. When such neutrons exchange energy with the liquid or solid they induce transitions between the en- ergy levels of the sample. A measurement of the energy difference between the incident neutron and the one which has been scattered with a change in energy is a measurement of an energy level difference in the

Volume 45, Number 5, May 1968 / 301

scattering specimen. The cross-sections or probabil- ities of these energy exchanges are large enough to make the experiment feasible, and the consequent technique may be called neutron spectroscopy. The region conveniently available for examination corre- sponds to the far infrared region of the electromagnetic spectrum and is generally limited to transitions with energies below about 1000 em-' or 0.125 ev.

The method offers certain advantages over conven- tional electromagnetic spectroscopy in a number of ways. First of all, all transitions can be observed; there are no selection rules involving dipole moments and polariaabilities as in infrared and Raman spectro- scopic studies. In addition, transitions are possible between energy levels involving excitation of vibrations where all the motions in unit cells of the crystal are not in phase. That is to say, the complete dispersion curve may be measured. Conventional spectroscopy is limited on the other hand to the study of transitions between energy levels where the motions in all unit cells are in phase. For a given mode of vibration, the phase relationship between the motions in different unit cells of the crystal may be expressed in terms of a dispersion curve which gives the frequency as a function of a wave vector j. If the magnitude of the wave vector i f 1 is zero, the motions in all unit cells are in phase. If / f l = a, the motion in one unit cell hes exactly the opposite phase to that in the adjacent unit cell. Some dispersion curves calculated for the inter- molecular modes of anthracene by Pawley (18) are illustrated in Figure 11. The detailed form of these

Figure 11. Dispersion curve. for the intermolecvlor vibrations in anthra- cene as salculoted by Pawley in reference 1121. Only the points on the left end of the curve ore meorvroble by conventional spectroscopic toch- niquel; the entire curve con be measured by neutron spectroscopy.

curves is sensitive to the assumptions regarding the form of the intermolecular potential functions. By measurement of these curves we are in a position to determine the potential functions for intermolecular forces. This is an exciting area of study which is just beginning to open up. A combination of neutron spectroscopic measurements with diffraction measure ments will undoubtedly greatly increase our under- standing of the factors affecting the forces between molecules.

Many of the important chemical results to date in inelastic scattering have been in the application to hydrogen-containing systems. Hydrogen has a large incoherent scattering cross-section for neutrons, and the energy spectmm of the neutrons scattered from a hydrogenous system is dominated by peaks corre- sponding to vibrational modes involving hydrogen motion. The investigation of the methyl benzenes by Rush ( I S ) provides a good example. In Figure 12 are shown some typical spectra for methyl-substituted benzenes. The dominant modes can be associated

Figure 12. Inelortic scattering cross sections for durene or o function of energy tronlfer a t two temperatures. The peak on the left may be mro- ciated with the torsional frequency of a methyl group which hag only one neighboring methyl group. The shoulder at 290 cm-'moy be an overtone.

with the hindered rotation of the methyl groups. Two characteristic vibrational frequences are oh- served-one characteristic of a methyl group which has two methyl groups as neighbors, one characteristic of a methyl group which is only crowded on one side. Some of the results are tabulated in Table 5. One of the more interesting results is that below the second- order transition temperature of 115"K, the barrier hin- dering rotation in hexamethylbenzene is higher than above the transition. It has been suggested that this change is due to a distortion of the heavy atom frame- work of the molecule below the transition, hut confir- mation of this result must await the completion of de-

Table 5 . Torsional Vibrational Frequencies of Methyl Groups in the Methyl Benzenes os Determined b y Rush by

Neutron Inelastic Scattering

----Position of methyl groups---. 1,2 1,2,4,5 1,2,3 1,2,3,4 1,2,3,4,5,6

. High frequency 169 em-' 175 180 167 Low frequency . . . - . . . 95 95 -- - - 121;'i37. -The lower value is observed above the h-~oint transition.

302 / Journal o f Chemical Education

Figure 13. Single crystal goniometer "red for neutron diffroction work at Brookhaven; a liquid helium cryortot capable of orientation in three dimen- rianr may be placed in the la rge circle.

tailed neutron diffraction studies at several tempera- tures.

The size of crystal required for neutron diffraction studies has decreased markedly over the past several years as nuclear reactors providing increased thermal fluxes have come on the scene. Although crystals larger than those necessary for X-ray work are still required, it is possible to rapidly collect a three-dimen- sional set of neutron diffraction data from crystals with a volume as small as 0.1 mrn3. The neutron inelastic scattering experiments, because of the smaller cross sections, require sample sizes of the order of 1 cm3. The latter experiments are thus limited to those sub- stances for which large single crystals can he grown or to polycrystalline materials; most of the work on hy-

drogenous compounds has been on polycrystalline materials. The measurement of dispersion curves of course requires single crystal specimens.

The modern neutron diffractometer is still a bulky object because of the necessity for shielding. The large single crystal goniometer shown in Figure 13 dwarfs the small crystal on the goniometer head; the large size of this goniometer allows the possibility of mounting a liquid helium cryostat in it and thus pro- vides for the convenient collection of three-dimen- sional diffraction data at many temperatures.

Acknowledgment

I would like to thank my colleagues and friends for permission to quote some of their work in this most interesting and exciting field of structural chemistry which has been stimulated by nuclear science.

Literature Cited

(1) Abstmets, ACS Meeting, 164th, Chicago, Ill., September, 1967 ---..

(2) THOMAS, R., KRANER, H. W., AND HAMILTON, W. C., Abstrads Am. Cryst. Assoc. Meeting, Minneapolis, August, 1967, Paper El.

(3) CHILD, H. R., US. Atomic Energy Commission, ORNL- TM-1063 (1965).

(4) SHULL, C. G., AND YAMADA, Y., J . P h y ~ SOC. Japan, 17, Snnnl. R-111. l(1962). - -

SPEAKMAN, J. c., ~ h e m : C~mmun. , 32 (1967). MANOJLOVIC, L., AND SPEAKMAN, J. C., J. Chem. SOC.,

19678,971 (1967). SEQUEIRA, A., BERKEBILE, C. A. AND HAWILTON, W. C.,

J . Mol. Str., 1 , in press. HAMILTON, W. C., AND IBERS, J. A., "Hydrogen Ebnding in

Solids: Methods in Structure Determination." W. A. Benjamin, Inc., N. Y. 1968, pp 108-113.

(9) COPPENS, P., Science, 158, 1577 (1967). (10) COPPENS, P., -4bst. Am. Cryst. Assoc. Meeting, Tucson,

Ark , February, 1968. Paper G3. (11) RAMASESHAN, S., Current Science (India), 35(4), 87 (1966). (12) PAWLEY, G. S., Phys. Stat. Sol., 20,347 (1967). (13) R U S ~ J. J., J . Chem. Phys., 47, 3836(1967). -

Volume 45, Number 5, May 1968 / 303