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How to See Atoms Goals of this lab

To understand the uncertainty relationship and how slit size affects a diffraction pattern. To calculate slit separation based on a diffraction pattern. To distinguish the effects of element structure versus array in a crystal.

Overview In a sense modern physics got underway with the accidental discovery of X-rays. After people got over the thrill of seeing the bones in their own feet, etc., it eventually became clear that X-rays opened a fantastic window onto the structure of matter. Not only could one see directly that matter was made of small particles (remember, at the turn of the century this was still controversial), but one could also see how those objects were stacked together to make solid objects and even look inside them to see the structure of each one. This is not a musty old fact. X-ray crystallography is today a central research tool in fields as diverse as materials science, condensed matter physics, geology, and biochemistry. X-ray crystallography became the foundation of molecular biology through the pioneering efforts of Rosalind Franklin, Max Perutz, and Maurice Wilkins on the structure of hemoglobin and DNA molecules. Almost every research institution has laboratories devoted to X-ray scattering, and multimillion-dollar facilities such as the Advanced Photon Source (Argonne, IL, U.S.A.) or the European Synchrotron Radiation Facility (Grenoble, France) have been built to generate the exceedingly strong X-ray beams required for specialized studies, such as time-resolved structure resolution on the nanosecond time scale. From our point of view, diffraction is important because for over a century it was regarded as the clinching evidence that light was a wave and not a stream of little bullets as Newton had (tentatively) suggested. Later, when Einstein proposed that light could be regarded as lumps after all, it became urgent to reconcile that picture with experiments like this one. In this lab we will just scratch the surface of the subject. Rather than looking at atomic-size objects with X-rays, we will look at objects a hundred thousand times bigger, with ordinary visible light whose wavelength is correspondingly bigger than X-rays. The principle is the same, but this way you can actually see the real object and compare it to the diffraction patterns which come out. Also, the “objects” we’ll study are highly simplified: instead of 3-dimensional arrays of complicated molecules, we’ll use 2-dimensional arrays of lines or dots. This simplifies the mathematics considerably. Later on in another lab you’ll get to do the real thing, with X-rays. But in this lab we have the advantage that we can actually inspect the object that’s doing the diffracting. We want you to see for yourself a number of surprising things about the diffraction of light:

When you shine a parallel beam of light on an object which is not much bigger than the wavelength of light, the image which forms far away is not just a silhouette of that object.

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Instead it’s a diffraction pattern.

If the object is a single thin slit, the light spreads wider than the slit. More generally, light can spread out after passing by an object, even if it was a parallel beam to begin with: light can go around corners.

Moreover it doesn’t spread uniformly: light forms interference patterns.

Smaller objects generate bigger diffraction patterns. For example, slits or bars spaced a distance d apart yield bright lines on the screen separated by distance x D d (1) where is the wavelength of the light and D is the distance to the screen. We’ll ultimately understand the uncertainty principle of quantum mechanics in terms of this simple fact.

Regularly repeated objects build up a single pattern. This is crucial, since you can’t just hold up one atom and shine X-rays on it. Instead you look at large numbers of atoms all at the same time; the fact that they are regularly arranged in a crystal makes them all contribute to a single strong diffraction pattern. In fact, the more objects there are, the sharper the resulting pattern.

The position of the bright spots tells us the arrangement of the objects. You just need to do a little math to decode it.

The overall character of the diffraction pattern tells us about the nature of the individual objects themselves.

More precisely, the packing pattern determines where the spots will be in the diffraction pattern; no matter what objects you’re packing, if they’re in a square array you’ll always get the same spots, which will always be different from those of a triangular array. But the structure of the individual objects comes in when we look at the pattern of strengths of these spots. Some spots will be brighter or dimmer in one pattern than in another. (For example, it was precisely this pattern of spot strengths, which led Franklin and others to deduce the helical structure of DNA). Now it’s time to check these assertions in the real world. We’ll use laser light, but they all remain true for X-ray diffraction, since X-rays are just a form of light. This lab will be mainly qualitative. We want you to examine the various “crystals”, which are actually 35mm slides of various patterns, put them in the laser beam, sketch what you see, and interpret in light of the above points. On the following pages we show blowups of some of the samples, with the actual sizes. Your “crystals” are not perfect, and so neither will be your results, but you should be able to observe all the above features.

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Procedure Like sunlight, the laser light won’t hurt you unless you stare straight into the beam, so don’t do that. Part 1: Warm-up Shine the laser on the screen and look carefully at the spot it forms. You will see a shimmering grainy pattern called laser speckle. This effect is not our main interest (it’s a little complicated). You can ignore this effect in what follows, but take a minute just to explore it now. If you wear glasses, try taking them off and seeing what happens to the speckle. (If you don’t see a difference, try putting somebody else’s glasses on.) Notice that the laser forms a small spot on the wall, and the spot doesn’t get much wider as you move away from the laser: the beam is pretty parallel, as long as it doesn’t encounter any obstruction.

Part 2: Sample slits This is a 35mm slide with nine different fields. Move the beam to the desired field and observe the diffraction pattern. Information on slit width and separation is available in the table on page 5.

(a) Field 1 has many thin slits (14 micrometers) separated by 40 micrometers. Sketch what you see. From the slit separation and the observed diffraction pattern deduce the wavelength of the laser light.

(b) Field 5 has just two thin slits with the same width and spacing. Sketch what you see and explain qualitatively the differences from Field 1.

(c) Field 2 has just one slit. Sketch what you see and explain qualitatively the differences from Fields 1–2.

(d) Just look at Field 4 (thin double slit, but spaced closer) and Field 3 (fat single slit). Don’t write anything, but notice these qualitative features: A fatter slit doesn’t spread light as much as a thin one; a narrower pattern generates more widely spaced spots.

Part 3: Crystals The samples below are all 35mm slides. They are mostly blank; you’ll have to adjust them until the laser beam passes through the interesting pattern. Every slide has a name. Each has been photo-reduced 25 times from the attached originals. Each sample is two-dimensional arrays of dots. To save you from having to count all those little dots we have done it and indicated the numbers of dots in a marked region. Measure the region and apply the photo-reduction factor to

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find out how closely the dots are spaced on the slides. Be sure to keep track of the slide’s orientation (i.e. which is the narrow spacing and which the wide one) so you can relate it to the orientation of the image.

1) Samples squaredotsa–b. Our next pattern is an array of dots on a square grid. We made samples with two different dot spacings. Try rotating the samples. Also try sliding them back and forth without rotating. (e) Sketch what you see and explain it qualitatively.

(f) Measure the original figure (attached) and apply the photo-reduction factor to find

the actual dot spacing. Then measure the diffraction pattern and the lab distances and from these data find the wavelength of the laser light.

(g) A qualitative question: explain in just one sentence why the patterns you got from slits were long and thin, while the patterns you get from grids are all wide in both directions. Hint: think about the uncertainty relation.

2) Sample rectdots. This time our “crystal” has a rectangular, not square, pattern. Sketch

what you see and explain the difference from squaredots.

3) Sample tridots. This pattern is triangular. Sketch what you see.

You may be getting the impression that the diffraction pattern is just a copy of the object: a square grid gave a square grid, a triangular grid gave a triangular grid, etc. Actually this isn’t how it works; we just chose simple examples so far. The next two parts explore more interesting effects.

4) Sample barpairs. First a one-dimensional sample. This slide consists of a regularly-repeated

pair of bars. Each pair is separated by 1/4 the distance to the next pair. Explain what you see.

5) Samples ddotsa–d. ddotsa is again a square arrangement, just like the square pattern squaredotsa. However we have replaced each round dot in squaredotsa by a little square. In other words, our basic unit now has some structure. Similarly in ddotsb our basic unit cell is a small triangle, while in ddotsc it’s a pair of dots, again separated by 1/4 the unit cell spacing. Finally for real drama, in ddotsd we replaced the dots by lines.

(a) Sketch what you see. In sample (c) the pattern is unfortunately a bit hard to see, but

if you know what to expect from barpairs you should be able to recognize it.

(b) As mentioned above, one way to describe what you see is to break it down into the locations of the spots versus the strengths of the various spots. Describe the differences between samples (a,b) and squaredots in this way.

(c) Describe the symmetry of the diffraction pattern and relate it to the symmetry of the

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original object. For example, in the attached blowups you can see that squaredots and ddotsa,d are symmetric under rotations by 90 , and also under reflection in either the x or y directions. Samples ddotsb–c have a bit less symmetry. Relate this to what you see in the corresponding diffraction patterns.

6) Sample mystery. This one is for just for fun. Something happens in this diffraction pattern

which just can’t happen for a regular repeating array of dots.

(a) Describe what you see. Make a sketch if it’s necessary.

(b) The original pattern is different from all of the other crystals you’ve looked at in this lab. Examine and compare the patterns and see if you can deduce the difference.

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Sample Slits Slide Measurements

All measurements are in microns (1.0 x 10^-6 m)

In fields 1, 4, 5, and 6 the first measurement is the slit width and the second is the slit separation.

Asterisked slides have minor defects (mainly in the first field) which should not affect measuremen

Field 1 Field 2 Field 3 Field 4 Field 5 Field 6 Field 7 Field 8 Field 9

0 12/40 12 23 10/30 10/40 11/50 30

1 14/40 14 22 13/30 13/39 12/50 32 43 52

Slide #

2 * 11/40 10 20 12/30 9/40 9/49 30 40 48

3 * 10/40 10 20 10/30 7/40 8/49 28 36 46

4 12/40 12 22 10/30 10/40 10/50 30 40 50

5 * 12/40 12 24 10/30 11/40 11/50 29 38 49

6 12/40 10 20 12/30 10/40 9/50 31 40 48

7 * 10/40 12 21 10/30 10/40 12/50 30 40 50

8 * 10/40 12 22 9/30 9/40 11/49 28 39 50

9 10/40 10 20 10/30 10/40 9/50 29 38 49

10 * 10/40 12 22 10/30 9/40 10/49 28 38 50

11 10/40 11 21 10/30 9/40 10/50 27 38 50

12 * 10/40 10 20 9/30 7/40 8/50 27 36 46

13 * 12/40 10 21 11/30 10/40 10/49 30 40 50

14 * 11/40 10 20 10/30 8/40 8/50 28 36 46

15 * 10/40 9 18 10/30 8/40 7/50 29 38 47

16 * 10/40 9 20 10/30 9/40 10/50 31 41 49

17 11/40 10 20 11/30 9/40 8/50 31 40 49

18 12/40 11 21 12/30 11/40 10/49 32 40 51

19 12/40 10 20 12/30 12/40 12/50 32 42 52

Ideal 10/40 10 20 10/30 10/40 10/50 30 40 50

Design 12/40 12 22 12/30 12/40 12/50 32 42 52

Make 14/40 14 24 14/30 14/40 14/50 34 44 54

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PAH12/12/08 atoms_diffraction.doc