{"id":99,"date":"2018-11-30T11:37:45","date_gmt":"2018-11-30T11:37:45","guid":{"rendered":"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=99"},"modified":"2018-11-30T12:18:10","modified_gmt":"2018-11-30T12:18:10","slug":"experimental-techniques","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/chapter\/experimental-techniques\/","title":{"rendered":"Experimental Techniques"},"content":{"raw":"<div>\r\n\r\n<strong>\u00a0 \u00a0 Learning Outcomes<\/strong>\r\n\r\n&nbsp;\r\n\r\nAfter studying this module, you shall be able to\r\n<ul>\r\n \t<li>Learn different techniques of x-ray diffractions.<\/li>\r\n \t<li>Understand the technical requirements for different experimental methods.<\/li>\r\n \t<li>Analyse the real specimen and distinguish between crystalline and amorphous phase<\/li>\r\n \t<li>Find the symmetry of the crystalline specimen<\/li>\r\n<\/ul>\r\n<\/div>\r\n<strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0Introduction:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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. <\/span>Following<span style=\"text-align: initial;font-size: 1em\"> chart in figure 6.1 classify the techniques<\/span><\/p>\r\n\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-103\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52.png\" alt=\"\" width=\"1175\" height=\"507\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\">Figure 6.1 \u2013 Classification of X-ray diffraction based on applications.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">A collomatted beam of continuous spectrum falls upon a fixed single crystal. For each set of planes (<em>hkl<\/em>), 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.<\/p>\r\n&nbsp;\r\n\r\n<strong>Transmission Laue Pattern:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">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<\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-104\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-53.png\" alt=\"\" width=\"737\" height=\"252\" \/>\r\n\r\n&nbsp;\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">Figure 6.2- Left: the geometry of the Laue experiment; right: transmission Laue diffraction pattern of quartz with primary beam parallel to c-axis.<\/span>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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 <\/span>set<span style=\"text-align: initial;font-size: 1em\"> of <\/span>ellipse<span style=\"text-align: initial;font-size: 1em\"> which <\/span>pass<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span><em style=\"text-align: initial;font-size: 1em\">hkl <\/em><span style=\"text-align: initial;font-size: 1em\">which belong to particular zone<\/span><em style=\"text-align: initial;font-size: 1em\"> uvw<\/em><span style=\"text-align: initial;font-size: 1em\">. We define a zone axis <\/span><em style=\"text-align: initial;font-size: 1em\">A<\/em><span style=\"text-align: initial;font-size: 1em\"> = <\/span><em style=\"text-align: initial;font-size: 1em\">ua<\/em><span style=\"text-align: initial;font-size: 1em\">1 + <\/span><em style=\"text-align: initial;font-size: 1em\">va<\/em><span style=\"text-align: initial;font-size: 1em\">2 +<\/span><em style=\"text-align: initial;font-size: 1em\">wa<\/em><span style=\"text-align: initial;font-size: 1em\">3 where<\/span><em style=\"text-align: initial;font-size: 1em\"> uvw <\/em><span style=\"text-align: initial;font-size: 1em\">are\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">integers. All planes <\/span><em style=\"text-align: initial;font-size: 1em\">hkl<\/em><span style=\"text-align: initial;font-size: 1em\"> containing the direction A(<\/span><em style=\"text-align: initial;font-size: 1em\">uvw<\/em><span style=\"text-align: initial;font-size: 1em\">) are said to belong to zone <\/span><em style=\"text-align: initial;font-size: 1em\">uvw<\/em><span style=\"text-align: initial;font-size: 1em\">. Since the planer normal must be perpendicular to the zone axis, H(<\/span><em style=\"text-align: initial;font-size: 1em\">hkl<\/em><span style=\"text-align: initial;font-size: 1em\">)\u0387A(<\/span><em style=\"text-align: initial;font-size: 1em\">uvw<\/em><span style=\"text-align: initial;font-size: 1em\">)=0 and hence the equation for all\u00a0planes hkl belong to the zone uvw is expressed by hu \uf02b kv \uf02b lw \uf03d 0.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The positions of the diffraction spots give the directions of the various diffracted beams, and the corresponding planar normal H (hkl) <\/span>are<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span>projection<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Rotating Crystal Method<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In this <\/span>method<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-105\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-54.png\" alt=\"\" width=\"437\" height=\"358\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\">Figure 6.3 Rotating crystal mount<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">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\u00b0. 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\u00a0<span style=\"text-align: initial;font-size: 1em\">subsequent x-ray analysis of the structure of the crystal is <\/span>most<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Powder Diffraction Method:<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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 <\/span>thin-walled<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span>and<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span>figure<span style=\"text-align: initial;font-size: 1em\"> below.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-107\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-55.png\" alt=\"\" width=\"661\" height=\"346\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\">Figure 6.4 \u2013 A typical diagram of a powder x-ray diffraction.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A sample of some hundreds of crystal (i.e. a powdered sample) <\/span>show<span style=\"text-align: initial;font-size: 1em\"> that the diffracted beam from continuous cones. A circle of <\/span>film<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-108\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-56.png\" alt=\"\" width=\"713\" height=\"422\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">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.<\/p>\r\n&nbsp;\r\n\r\n<strong>Salient features of x-ray diffraction<\/strong>\r\n<ul>\r\n \t<li>Non-destructive technique<\/li>\r\n \t<li>Identify crystalline phases and orientation<\/li>\r\n \t<li>Determine structural properties<\/li>\r\n \t<li style=\"text-align: justify\">To determine lattice parameters, strain, grain size, phase composition, order-disorder transformation, thermal expansion<\/li>\r\n<\/ul>\r\n<img class=\"aligncenter size-full wp-image-109\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-57.png\" alt=\"\" width=\"602\" height=\"418\" \/>\r\n\r\n<\/div>\r\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">Fig. 6.6- A typical x-ray diffraction pattern<\/span><\/p>\r\n\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">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 \u201cfinger print identification\u201d 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.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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 <\/span>parafocusing<span style=\"text-align: initial;font-size: 1em\"> (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.<\/span><\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-110\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-58.png\" alt=\"\" width=\"546\" height=\"447\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\">Figure 6.7: Specimen preparation for powder x-ray diffraction experiment.<\/p>\r\n&nbsp;\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0 Value Addition:<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>Do You Know?<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Laue states in his Nobel Prize Lecture, \u2018On the Discovery of X-ray Interference\u2019, 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\u2019s mind. True, diffraction by a three-dimensional grating had never been considered, but, as he puts it: \u2018my optical intuition told me immediately that under such circumstances spectra must occur.\u2019<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">There is no indication that Laue at that stage made any attempt at consolidating his \u2018optical feeling\u2019 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 \u2018Rest-strahl\u2019 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\u2019s 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 Caf\u00e9 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\u2019s 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\u2019s work, so that it was an easy matter to slip in a few unscheduled runs for Laue\u2019s experiment.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Once the three partners, Laue, Friedrich and Knipping had decided to go ahead, success came swiftly thanks to Friedrich\u2019s 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\u00a0<span style=\"text-align: initial;font-size: 1em\">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 <\/span>crystal<span style=\"text-align: initial;font-size: 1em\">, 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 <\/span>re- flexion<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">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\u2019s 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 \u2018optical feeling\u2019. 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.<\/p>\r\n&nbsp;\r\n\r\n<strong>1.\u00a0<\/strong><strong>Suggested Reading<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>For More Details (on this topic and other topics discussed in Text Module) See<\/strong>\r\n<ol>\r\n \t<li>Neil W. Ashcroft and N. David Mermin, Solid State Physics, Thomson Brooks\/Cole, Eastern Press Bangalore (India) 2005<\/li>\r\n \t<li>Charles Kittel, Introduction to Solid State Physics, John Wiley &amp; Sons, Singapore 1999<\/li>\r\n \t<li>Wikipedia<\/li>\r\n<\/ol>\r\n<strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 Glossary:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">X-ray Tube: <\/strong><span style=\"text-align: initial;font-size: 1em\">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.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Primary Slits: <\/strong><span style=\"text-align: initial;font-size: 1em\">An opening aperture which determines the size of x-ray spot on the sample.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Secondary Slit: <\/strong><span style=\"text-align: initial;font-size: 1em\">A small aperture which defines the solid angle of acceptance at the detector.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Primary Beam: <\/strong><span style=\"text-align: initial;font-size: 1em\">It as a beam of x-rays emanating from <\/span>source<span style=\"text-align: initial;font-size: 1em\"> which falls on the sample under probe.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Collimators: <\/strong><span style=\"text-align: initial;font-size: 1em\">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.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Scattered Beam: <\/strong><span style=\"text-align: initial;font-size: 1em\">X-ray beam emanating after scattering from the sample.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Point detector: <\/strong><span style=\"text-align: initial;font-size: 1em\">It is a NaI scintillator <\/span>solid state detector detector<span style=\"text-align: initial;font-size: 1em\"> with fine slits defining the aperture for diffracted radiation.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Goniometer: <\/strong><span style=\"text-align: initial;font-size: 1em\">A mechanical device which <\/span>rotate<span style=\"text-align: initial;font-size: 1em\"> the sample stage and the detector arm with controlled motorized movement.<\/span><\/p>\r\n\r\n<\/div>","rendered":"<div>\n<p><strong>\u00a0 \u00a0 Learning Outcomes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>After studying this module, you shall be able to<\/p>\n<ul>\n<li>Learn different techniques of x-ray diffractions.<\/li>\n<li>Understand the technical requirements for different experimental methods.<\/li>\n<li>Analyse the real specimen and distinguish between crystalline and amorphous phase<\/li>\n<li>Find the symmetry of the crystalline specimen<\/li>\n<\/ul>\n<\/div>\n<p><strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0Introduction:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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. <\/span>Following<span style=\"text-align: initial;font-size: 1em\"> chart in figure 6.1 classify the techniques<\/span><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-103\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52.png\" alt=\"\" width=\"1175\" height=\"507\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52.png 1175w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52-300x129.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52-768x331.png 768w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52-1024x442.png 1024w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52-65x28.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52-225x97.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-52-350x151.png 350w\" sizes=\"auto, (max-width: 1175px) 100vw, 1175px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\">Figure 6.1 \u2013 Classification of X-ray diffraction based on applications.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A collomatted beam of continuous spectrum falls upon a fixed single crystal. For each set of planes (<em>hkl<\/em>), 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.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Transmission Laue Pattern:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">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<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-104\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-53.png\" alt=\"\" width=\"737\" height=\"252\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-53.png 737w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-53-300x103.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-53-65x22.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-53-225x77.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-53-350x120.png 350w\" sizes=\"auto, (max-width: 737px) 100vw, 737px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">Figure 6.2- Left: the geometry of the Laue experiment; right: transmission Laue diffraction pattern of quartz with primary beam parallel to c-axis.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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 <\/span>set<span style=\"text-align: initial;font-size: 1em\"> of <\/span>ellipse<span style=\"text-align: initial;font-size: 1em\"> which <\/span>pass<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span><em style=\"text-align: initial;font-size: 1em\">hkl <\/em><span style=\"text-align: initial;font-size: 1em\">which belong to particular zone<\/span><em style=\"text-align: initial;font-size: 1em\"> uvw<\/em><span style=\"text-align: initial;font-size: 1em\">. We define a zone axis <\/span><em style=\"text-align: initial;font-size: 1em\">A<\/em><span style=\"text-align: initial;font-size: 1em\"> = <\/span><em style=\"text-align: initial;font-size: 1em\">ua<\/em><span style=\"text-align: initial;font-size: 1em\">1 + <\/span><em style=\"text-align: initial;font-size: 1em\">va<\/em><span style=\"text-align: initial;font-size: 1em\">2 +<\/span><em style=\"text-align: initial;font-size: 1em\">wa<\/em><span style=\"text-align: initial;font-size: 1em\">3 where<\/span><em style=\"text-align: initial;font-size: 1em\"> uvw <\/em><span style=\"text-align: initial;font-size: 1em\">are\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">integers. All planes <\/span><em style=\"text-align: initial;font-size: 1em\">hkl<\/em><span style=\"text-align: initial;font-size: 1em\"> containing the direction A(<\/span><em style=\"text-align: initial;font-size: 1em\">uvw<\/em><span style=\"text-align: initial;font-size: 1em\">) are said to belong to zone <\/span><em style=\"text-align: initial;font-size: 1em\">uvw<\/em><span style=\"text-align: initial;font-size: 1em\">. Since the planer normal must be perpendicular to the zone axis, H(<\/span><em style=\"text-align: initial;font-size: 1em\">hkl<\/em><span style=\"text-align: initial;font-size: 1em\">)\u0387A(<\/span><em style=\"text-align: initial;font-size: 1em\">uvw<\/em><span style=\"text-align: initial;font-size: 1em\">)=0 and hence the equation for all\u00a0planes hkl belong to the zone uvw is expressed by hu \uf02b kv \uf02b lw \uf03d 0.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The positions of the diffraction spots give the directions of the various diffracted beams, and the corresponding planar normal H (hkl) <\/span>are<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span>projection<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Rotating Crystal Method<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In this <\/span>method<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-105\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-54.png\" alt=\"\" width=\"437\" height=\"358\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-54.png 437w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-54-300x246.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-54-65x53.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-54-225x184.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-54-350x287.png 350w\" sizes=\"auto, (max-width: 437px) 100vw, 437px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\">Figure 6.3 Rotating crystal mount<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">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\u00b0. 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\u00a0<span style=\"text-align: initial;font-size: 1em\">subsequent x-ray analysis of the structure of the crystal is <\/span>most<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Powder Diffraction Method:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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 <\/span>thin-walled<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span>and<span style=\"text-align: initial;font-size: 1em\"> 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 <\/span>figure<span style=\"text-align: initial;font-size: 1em\"> below.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-107\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-55.png\" alt=\"\" width=\"661\" height=\"346\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-55.png 661w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-55-300x157.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-55-65x34.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-55-225x118.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-55-350x183.png 350w\" sizes=\"auto, (max-width: 661px) 100vw, 661px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\">Figure 6.4 \u2013 A typical diagram of a powder x-ray diffraction.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A sample of some hundreds of crystal (i.e. a powdered sample) <\/span>show<span style=\"text-align: initial;font-size: 1em\"> that the diffracted beam from continuous cones. A circle of <\/span>film<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-108\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-56.png\" alt=\"\" width=\"713\" height=\"422\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-56.png 713w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-56-300x178.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-56-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-56-225x133.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-56-350x207.png 350w\" sizes=\"auto, (max-width: 713px) 100vw, 713px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">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.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Salient features of x-ray diffraction<\/strong><\/p>\n<ul>\n<li>Non-destructive technique<\/li>\n<li>Identify crystalline phases and orientation<\/li>\n<li>Determine structural properties<\/li>\n<li style=\"text-align: justify\">To determine lattice parameters, strain, grain size, phase composition, order-disorder transformation, thermal expansion<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-109\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-57.png\" alt=\"\" width=\"602\" height=\"418\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-57.png 602w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-57-300x208.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-57-65x45.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-57-225x156.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-57-350x243.png 350w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/p>\n<\/div>\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">Fig. 6.6- A typical x-ray diffraction pattern<\/span><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">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 \u201cfinger print identification\u201d 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.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">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 <\/span>parafocusing<span style=\"text-align: initial;font-size: 1em\"> (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.<\/span><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-110\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-58.png\" alt=\"\" width=\"546\" height=\"447\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-58.png 546w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-58-300x246.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-58-65x53.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-58-225x184.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/11\/Untitled-58-350x287.png 350w\" sizes=\"auto, (max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\">Figure 6.7: Specimen preparation for powder x-ray diffraction experiment.<\/p>\n<p>&nbsp;<\/p>\n<div>\n<p><strong>\u00a0 \u00a0 Value Addition:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Do You Know?<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Laue states in his Nobel Prize Lecture, \u2018On the Discovery of X-ray Interference\u2019, 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\u2019s mind. True, diffraction by a three-dimensional grating had never been considered, but, as he puts it: \u2018my optical intuition told me immediately that under such circumstances spectra must occur.\u2019<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">There is no indication that Laue at that stage made any attempt at consolidating his \u2018optical feeling\u2019 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 \u2018Rest-strahl\u2019 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\u2019s 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 Caf\u00e9 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\u2019s 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\u2019s work, so that it was an easy matter to slip in a few unscheduled runs for Laue\u2019s experiment.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Once the three partners, Laue, Friedrich and Knipping had decided to go ahead, success came swiftly thanks to Friedrich\u2019s 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\u00a0<span style=\"text-align: initial;font-size: 1em\">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 <\/span>crystal<span style=\"text-align: initial;font-size: 1em\">, 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 <\/span>re- flexion<span style=\"text-align: initial;font-size: 1em\"> 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.<\/span><\/p>\n<\/div>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">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\u2019s 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 \u2018optical feeling\u2019. 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.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>1.\u00a0<\/strong><strong>Suggested Reading<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>For More Details (on this topic and other topics discussed in Text Module) See<\/strong><\/p>\n<ol>\n<li>Neil W. Ashcroft and N. David Mermin, Solid State Physics, Thomson Brooks\/Cole, Eastern Press Bangalore (India) 2005<\/li>\n<li>Charles Kittel, Introduction to Solid State Physics, John Wiley &amp; Sons, Singapore 1999<\/li>\n<li>Wikipedia<\/li>\n<\/ol>\n<p><strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 Glossary:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">X-ray Tube: <\/strong><span style=\"text-align: initial;font-size: 1em\">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.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Primary Slits: <\/strong><span style=\"text-align: initial;font-size: 1em\">An opening aperture which determines the size of x-ray spot on the sample.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Secondary Slit: <\/strong><span style=\"text-align: initial;font-size: 1em\">A small aperture which defines the solid angle of acceptance at the detector.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Primary Beam: <\/strong><span style=\"text-align: initial;font-size: 1em\">It as a beam of x-rays emanating from <\/span>source<span style=\"text-align: initial;font-size: 1em\"> which falls on the sample under probe.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Collimators: <\/strong><span style=\"text-align: initial;font-size: 1em\">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.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Scattered Beam: <\/strong><span style=\"text-align: initial;font-size: 1em\">X-ray beam emanating after scattering from the sample.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Point detector: <\/strong><span style=\"text-align: initial;font-size: 1em\">It is a NaI scintillator <\/span>solid state detector detector<span style=\"text-align: initial;font-size: 1em\"> with fine slits defining the aperture for diffracted radiation.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Goniometer: <\/strong><span style=\"text-align: initial;font-size: 1em\">A mechanical device which <\/span>rotate<span style=\"text-align: initial;font-size: 1em\"> the sample stage and the detector arm with controlled motorized movement.<\/span><\/p>\n<\/div>\n","protected":false},"author":3,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["dr-amarjeet-singh"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-99","chapter","type-chapter","status-publish","hentry","contributor-dr-amarjeet-singh"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/99","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":5,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/99\/revisions"}],"predecessor-version":[{"id":111,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/99\/revisions\/111"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/99\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/media?parent=99"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapter-type?post=99"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/contributor?post=99"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/license?post=99"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}