7 Experimental Techniques

Amarjeet Singh

    Learning Outcomes

After studying this module, you shall be able to

• Learn different techniques of x-ray diffractions.
• Understand the technical requirements for different experimental methods.
• Analyse the real specimen and distinguish between crystalline and amorphous phase
• Find the symmetry of the crystalline specimen

   Introduction:

X-ray diffraction (XRD) is a method of structure determination at atomic length scale. There are three XRD techniques which are popularly used to identify the structure of the materials. Following chart in figure 6.1 classify the techniques

Figure 6.1 – Classification of X-ray diffraction based on applications.

A collomatted beam of continuous spectrum falls upon a fixed single crystal. For each set of planes (hkl), the spacing and the Bragg angle are fixed, a reflected beam will be produced if the correct wavelength which satisfies the Bragg law is contained in the continuous spectrum. The unfiltered radiation from a copper target tube is often used for Laue patterns.

Transmission Laue Pattern:

The experimental arrangement for a transmission Laue pattern is illustrated by Figure 6.2. The collimated continuous spectrum passes through the thin slice of the single crystal. The diffracted beams are registered on a thin film placed perpendicular to the primary beam at distance of about 5 cm from the crystal. If the crystal is symmetrically oriented with respect to the primary beam, the Laue pattern may show a very high symmetry

Figure 6.2- Left: the geometry of the Laue experiment; right: transmission Laue diffraction pattern of quartz with primary beam parallel to c-axis.

In the Laue pattern of quartz shown above, 3-fold symmetry is seen in the pattern. It is evident that the diffraction pattern the spots fall on set of ellipse which pass through the central spot. This is true weather or not the crystal has symmetrical orientation. All spots falling on the ellipse are due to planes hkl which belong to particular zone uvw. We define a zone axis A = ua1 + va2 +wa3 where uvw are integers. All planes hkl containing the direction A(uvw) are said to belong to zone uvw. Since the planer normal must be perpendicular to the zone axis, H(hkl)·A(uvw)=0 and hence the equation for all planes hkl belong to the zone uvw is expressed by hu  kv  lw  0.

The positions of the diffraction spots give the directions of the various diffracted beams, and the corresponding planar normal H (hkl) are readily constructed. The intersections of the planar normal with the plane of the film gives the gnomonic projection of Laue pattern. This projection is readily interpreted as projection of reciprocal lattice. In the early days of structure determination, the gnomonic projection was much used to index Laue patterns, and simple structures were determined by means of transmission Laue patterns.

Rotating Crystal Method

In this method a single crystal is rotated about a fixed axis in a beam of monochromatic x-rays or neutrons. The variation of the angle q brings different atomic planes into position for reflection. The film is mounted in a cylindrical holder concentric with the rotating spindle on which the single crystal specimen is mounted. The dimensions of the crystal usually need to be greater than 1 mm.

Figure 6.3 Rotating crystal mount

The incident x-ray beam is made nearly monochromatic by a filter or by reflection from an earlier crystal. The beam is diffracted from a given crystal plane whenever in the course of rotation the value of q satisfies the Bragg equation. Beams from all planes parallel to the vertical rotation axis will lie in the horizontal plane. Planes with other orientations will reflect in layers above and below horizontal plane. Several variations of the rotating-crystal method are in common use. In oscillating-crystal photographs the crystal is oscillated through a limited angular range, instead of being rotated through 360°. The limited range reduces the possibility of overlapping reflections. The Weissenberg goniometer and also the precession cameras shift the film in synchronism with the oscillation of the crystal. Modern methods use diffractometer in which the scintillation counters or proportional counter tube are used to detect the diffracted radiation. These methods allow automatic collection of data. Nearly all crystals with simple structures were solved by x-ray analysis a long time ago. One present center of interest in x-ray structure analysis is in the determination of the configuration of enzymes with molecular weight between 10,000 and 100,000. The crystallization of an enzyme and the subsequent x-ray analysis of the structure of the crystal is most effective method for the determination of the shape of the molecule. The coordinates of 500 to 5000 atoms in a cell are wanted, so at least these number of x-ray reflection lines are required. Computer programs have enormously simplified the problem of structure determination.

Powder Diffraction Method:

In powder diffraction method the incident monochromatic radiation strikes a finely powdered specimen or a finely grained polycrystalline specimen contained in a thin-walled capillary tube. The distribution of crystalline orientation will be thin-walled capillary tube. The distribution of crystallite orientations will be nearly continuous. Diffracted rays go out from individual crystallites which happen to be oriented with planes making and incident angle q with the beam satisfying the Bragg equation. The Diffracted rays leave the specimen along the generators of cones concentric with the original beam. The generators make the angle 2q with the direction of the original beam, where q is the Bragg angle. The cones intercept the film in a series of concentric rings as shown in figure below.

Figure 6.4 – A typical diagram of a powder x-ray diffraction.

A sample of some hundreds of crystal (i.e. a powdered sample) show that the diffracted beam from continuous cones. A circle of film is used to record the diffraction pattern as shown in the figure. Each cone intersects the film giving diffraction lines. The lines are seen as arcs on the film.

Fig. 6.5- A picture of a modern diffractometer. In this arrangement, the sample is mounted on the center stage which is rotated with angle q and detector arm rotate with 2q whereas x-ray tube remains fixed.

Salient features of x-ray diffraction

• Non-destructive technique
• Identify crystalline phases and orientation
• Determine structural properties
• To determine lattice parameters, strain, grain size, phase composition, order-disorder transformation, thermal expansion

Fig. 6.6- A typical x-ray diffraction pattern

In x-ray diffraction work we normally distinguish between single crystal and polycrystalline or powder applications. The single crystal sample is a perfect (all unit cells aligned in a perfect extended pattern) crystal with a cross section of about 0.3 mm. The single crystal diffractometer and associated computer package is used mainly to elucidate the molecular structure of novel compounds, either natural products or man made molecules. Powder diffraction is mainly used for “finger print identification” of various solid materials, e.g. asbestos, quartz. In powder or polycrystalline diffraction it is important to have a sample with a smooth plane surface. If possible, we normally grind the sample down to particles of about 0.002 mm to 0.005 mm cross section. The ideal sample is homogeneous and the crystallites are randomly distributed (we will later point out problems which will occur if the specimen deviates from this ideal state). The sample is pressed into a sample holder so that we have a smooth flat surface. Ideally we now have a random distribution of all possible h, k, l planes. Only crystallites having reflecting planes (h, k, l) parallel to the specimen surface will contribute to the reflected intensities. If we have a truly random sample, each possible reflection from a given set of h, k, l planes will have an equal number of crystallites contributing to it. We only have to rock the sample through the glancing angle THETA in order to produce all possible reflections.

The mechanical assembly that makes up the sample holder, detector arm and associated gearing is referred to as goniometer. The working principle of a Bragg-Brentano parafocusing (if the sample was curved on the focusing circle we would have a focusing system) reflection goniometer is shown below. The distance from the x-ray focal spot to the sample is the same as from the sample to the detector. If we drive the sample holder and the detector in a 1:2 relationship, the reflected (diffracted) beam will stay focused on the circle of constant radius. The detector moves on this circle.

Figure 6.7: Specimen preparation for powder x-ray diffraction experiment.

    Value Addition:

Do You Know?

Laue states in his Nobel Prize Lecture, ‘On the Discovery of X-ray Interference’, given in Stockholm on 3 June 1920, his question about the fate of short waves in a crystal was prompted by the expectation that if their wave-length is of a similar magnitude as the atomic distances the regular arrangement in a crystal must lead to some kind of diffraction effect. Through his work on the Encyclopedia article the theory not only of the simple diffraction grating but also that of a cross grating was fully present in Laue’s mind. True, diffraction by a three-dimensional grating had never been considered, but, as he puts it: ‘my optical intuition told me immediately that under such circumstances spectra must occur.’

There is no indication that Laue at that stage made any attempt at consolidating his ‘optical feeling’ by seeking to predict the kind of phenomenon that might be expected. Besides, the Easter vacations soon began and during that period a group of physicists traditionally met in the Alps for skiing. Here Laue discussed his idea with Sommerfeld, Wien and others with the result of encountering a strong disbelief in a significant outcome of any diffraction experiment based on the regularity of the internal structure of crystals. It was argued that the inevitable temperature motion of the atoms would impair the regularity of the grating to such an extent that no pronounced diffraction maxima could be expected. This objection may have been checked by a quantitative estimate of the magnitude of the thermal displacements although this would have had to be based on a number of uncertain assumptions seeing that no crystal structure was as yet known. An evaluation of the thermal deformation of the crystal lattice could have been made by comparing the known average thermal energy of an oscillator at room temperature to that of an oscillator of amplitude A and frequency corresponding to a ‘Rest-strahl’ wave- length of, say, 50 microns as for rock salt or KCI. Assuming the mass of the oscillator to equal that of the chlorine atom, amplitude A of about 0.75 A is obtained. This is larger than the X-ray wave-length as given by Wien (0.6 A) or Sommerfeld (0.4 A), and thus the regular phase relations between the individual scattered wavelets, which are essential for the formation of a diffracted beam, would be destroyed. This or similar arguments seem to have weighed so heavily in Sommerfeld’s mind that he was staunchly opposed to cede his newly appointed experimental assistant, Walter Friedrich, to Laue for the experiment. The situation was also discussed by Laue at the Café Lutz physics table, and here the opinion prevailed that experiment was safer than theory and that since the diffraction experiment required no elaborate set-up, it should at least be tried. Paul Knipping, who had just finished his thesis work in Rontgen’s Institute, volunteered to assist, so as to reduce the time Friedrich would be taken off his work for Sommerfeld. The X-ray tube, the induction coil and the Wehnelt electrolytic interrupter had to be set up anyway for Friedrich’s work, so that it was an easy matter to slip in a few unscheduled runs for Laue’s experiment.

Once the three partners, Laue, Friedrich and Knipping had decided to go ahead, success came swiftly thanks to Friedrich’s experience in X-ray experimentation. Led by the exposure times Herweg had required in his experiments on double scattering, Friedrich knew that exposures of several hours would be needed. This in turn meant careful screening of the crystal and photographic plate from the unwanted X-rays which come from the glass walls of the X-ray tube and from the mass of irradiated air. The tubes available at the time had a glass bulb of 10 cm radius and the glass wall acquired a high charge and potential while the tube was running. Any grounded lead diaphragm had to be at least 17 cm from the target in order to avoid a breakdown of the tube. The minimum distance target-crystal thus came to be about 25 cm, and this meant that only a very small fraction of the total output of the tube was used. Friedrich constructed a lead box containing the crystal and the photographic plate. It consisted of a tray of lead sheet about 12 x 7 cm with a turned-up rim, and a cover in the form of an open box about 6 cm high which could be placed with the open side on the tray, and whose side facing the tube had a hole of 3 mm diameter for admitting the X-rays. There may have been a second hole on the opposite side through which the strong primary beam passed out of the box without generating secondary X-rays by hitting on lead. For crystal, a piece of copper sulfate was used as it was found in the laboratory. In fixing the crystal on its holder by means of wax no particular orientation was aimed at. The photographic plate was placed between the X-ray tube and the crystal on the assumption that the crystal would act like a re- flexion grating. The first exposure gave no effect. Thinking this negative result over, Friedrich and Knipping came to the conclusion that better success might be achieved by placing the plate behind the crystal, as for a transmission grating. Knipping insisted on placing plates all around the crystal.

The result of the second attempt was positive. On the plate behind the crystal, surrounding the imprint of the direct or primary ray, rings of fuzzy spots appeared, each spot of elliptical shape with the minor axis pointing to the overexposed and therefore solarized centre of the black area produced by the primary ray. No similar spots were produced on the other plates. Crude as the picture was, it contained an unmistakable proof that some property of X-rays had been found which had escaped all previous investigators. It also gave strong support to the correctness of Laue’s idea of diffraction of X-rays by crystals. Laue learned of this result in Cafe Lutz; he hurried to the Institute and convinced himself of the correctness of his ‘optical feeling’. Going home in deep thoughts he suddenly perceived the theory of the diffraction effect-so suddenly that in his autobiography he mentions the street and house in passing which his illumination occurred.

1. Suggested Reading

For More Details (on this topic and other topics discussed in Text Module) See

1. Neil W. Ashcroft and N. David Mermin, Solid State Physics, Thomson Brooks/Cole, Eastern Press Bangalore (India) 2005
2. Charles Kittel, Introduction to Solid State Physics, John Wiley & Sons, Singapore 1999
3. Wikipedia

    Glossary:

X-ray Tube: It is an x-ray source with filament and target material in a vacuum tube. The electrons are thermally emitted from the filament and are accelerated to hit the target. X-rays are emitted from the target.

Primary Slits: An opening aperture which determines the size of x-ray spot on the sample.

Secondary Slit: A small aperture which defines the solid angle of acceptance at the detector.

Primary Beam: It as a beam of x-rays emanating from source which falls on the sample under probe.

Collimators: X-rays coming out of tube are divergent and the direction is broadly defined. Collimators are used to give direction to the incident beam with a minimal divergence within a precision limit.

Scattered Beam: X-ray beam emanating after scattering from the sample.

Point detector: It is a NaI scintillator solid state detector detector with fine slits defining the aperture for diffracted radiation.

Goniometer: A mechanical device which rotate the sample stage and the detector arm with controlled motorized movement.