Chapt 6 x-rays

1. Chapt 6 x-rays

2. 6-1. Discovery of x-ray. Wave like character Discovery of x-ray lX-rays were discovered by Roentgen in 1895 at the University of Wurzburg. The rays were so named because of their unknown nature. l Roentgen was one of a number of physicists who were carefully studying electric discharge in gases at low pressures.

3. lWorking in his laboratory with an ordinary electric discharge tube he noticed that a paper screen which had been painted with fluorescent (荧光的) solution of platinum- barium cyanide (铂-钡 氰化物) glowed with a greenish light at a distance of two meters from the discharge tube. lIn a short time the properties listed below were confirmed by Roentgen and others. 1.X-rays make a fluorescent screen glow with visible light. 2.They blacken a photographic plate (照相底片) .

4. 3.In passing through air or any gas they make the gas a conductor by producing ions（离子） in the gas. 4.They are strongly absorbed by dense substances such as iron or lead. 5.They cast shadows of dense objects on a fluorescent screen and hence must travel in straight lines. 6.They are not deflected (转向) by either electric or magnetic fields.

5. Debate on the nature of x-ray lAlthough properties of x-ray were confirmed by many physicists, their nature was at first vigorously debated. l Some thought x-ray consisted of particles of extremely small dimensions. Others thought them to be a form of extremely penetrating wave motion. l In order to determine why the x-ray showed the common properties of the light Roentgen himself tried to produce reflection (反射) refraction (折射), polarization ( 偏振),and diffraction (衍射). Regretfully, from these experiments he obtained only negative results.

6. lHowever later experiments by means of much more refined methods have detected all these effects and as early as 1902 Brunhes and Blondlot in a serious of experiments had shown the x-rays traveled at approximately the speed of light. lIn 1905 Barkla in England found that the rays could be polarized like visible light waves. Barkla’s experiment is illustrated in Fig.6.1.1. Fig.6.1.1

7. lIt remained for Max von Laue in Germany in 1911 to show that when x-rays were passed though a crystal a diffraction pattern of spots could be obtained. This was the critical experiment which tipped (使倾斜) the scales(天平) in favor of the wave theory of the ray. lAfter that it was generally accepted that the x-ray is a form of electromagnetic wave similar to light waves but with wavelength a thousandth or less than that of a visible light. lHowever, when A.H. Compton studied the scattering of x-rays by matter in 1921 he found that observed effects could be satisfactorily described only if the radiation was assumed to consist of individual quanta or photons.

8. lNow we have realized that the x-rays may exhibit both particle like characteristics and wave-like characteristics just like a visible light.

9. 6-2 The production of x-ray: Characteristic x-rays The production of continuous or general x-rays lX-rays are produced whenever high-speed electrons (cathode rays(阴极射线)) strike a dense target and are suddenly stopped. lThe higher the speed of an electron at the moment it is stopped, and the more suddenly it is stopped, the more penetrating is the x-ray produced.

10. lThe larger the number of electron per second being stopped, the more intense is the x-ray beam. lTungsten(钨) targets are frequently used although less penetrating x-rays can be produced with less dense target . lThe x-ray tube contains two electrodes, the cathode which is the source of electrons ,and an anode (阳极) or target upon which they strike.

11. lIn a modern type of x-ray tube a heated filament (细丝) is used for the cathode, thereby obtaining a luxuriant (丰富的) supply of electron. (Fig 6.2.1)

12. lThe tube is highly evacuated (抽真空),and accelerating potentials as high as 100,000 volts are commonly used. lThe electron current through the tube and in consequence the intensity of the x-rays ,can readily be controlled by adjusting the temperature of the cathode. lThe general x-rays consist of a continuous range of frequencies up to the maximum possible for a given voltage between cathode and anode.

13. lWhen the intensity of these general x-rays is plotted as a function of the frequency there results a curve like that shown in Fig 6.2.2. (Fig 6.2.2)

15. The characteristic x-rays lThe characteristic x-rays were discovered by Barkla and Sadler in 1908, which are produced by a different process. lThe characteristic x-rays produced in an x-ray tube consist of one or more narrow bands of frequency characteristic of the target material ,resulting from disturbances within the atoms of the target by the bombarding electrons. l They would appear as peaks of considerable intensity superposed on the continuous background of general radiation (Fig 6.2.3).

16. (Fig 6.2.3).

17. 6-3 The mechanism of x-ray production Quantum theory of general x-ray production l If we assume x-rays represent energy radiated discontinuously in the form of quanta, then making use of the Planck quantum relation we find the energy of a quantum is lFor the most favorable collision in which the election is stopped so completely and suddenly that all of its kinetic energy Ek = eV (V is the accelerating potential difference) goes into producing a single quantum of radiant energy: (6-3-1)

18. lConsequently the maximum frequency of x-rays produced by electrons of energy eV is (6-3-2) This is the Duane and Hunt law which is an important approximation,since the small amounts of initial energy possessed by an electron emitted from a hot cathode are neglected. lSince any election may not be stopped by a single collision but may be stopped by a sequence of collisions the energy may be radiated as several successive quanta of lower frequencies. lThis accounts for the production of a continuous range of frequencies in the general x-rays below a definite limit.

19. lActually the efficiency of production of x-rays is low and 1 percent or less of the kinetic energy of the electrons striking the target is ordinarily converted into x-ray quanta. The remainder and major part of the energy appears as heat in the target. lThe production of radiation when electrons (or other charges) are decelerated is found not only in an x-rays tube but wherever high-speed charged particles are accelerated. Since the slowing down is somewhat as if a brake had been applied the radiation is sometimes called “braking radiation”. (刹车辐射)

20. Mechanism of characteristic x-ray production lWhile visible spectra are produced by excitation of an atom so that one or other electrons are raised to higher energy states, characteristic x-ray excitation involves the displacement of an inner electron as, for instance, one in what we now call the K or L shells. lSince there are usually no nearby vacant energy levels to which these electrons may be raised, such excitation involves removing them altogether from the atom (ionization). lThis permits transition of a nearby electron to the vacancy thus created in an inner shell.

21. lThe transitions most likely to occur are those in which the vacancy is filled by a nearby electron from a higher energy state. In the transition a characteristic x-ray photon is radiated. lThe vacancy left by this electron is in turn filled by the transition of another electron from a still higher energy state with radiation of a photon of somewhat lower frequency. lThus the displacement of one inner electron may permit a series of transitions, with each emission of radiation occurs. lSince the electrons in the innermost or K shell of an atom are those most tightly bound to the nucleus they require bombardment by higher energy electrons to displace them than do electrons in L or outer shells.

22. lIf displacement of a K electron is followed by transition of an electron from L to K shell, an x-ray quantum is emitted representing the first line of the K series of characteristic x-rays. This is called theKα line . lIf the transition is from the M to the K shell, the emitted quantum represents the second or kβ line of the K series. lSince the energy difference between levels is greater for the latter than for the former transit ion the second line of the series will have a higher frequency, and the K series will be composed of lines of increasing frequency approaching a high- frequency limit.

23. lAs the probability of transition decreases rapidly for the higher frequency members of the series only a few lines of the K and L series can be readily detected except in the elements of high atomic weight. lIn the L, M, and higher shells there are electrons with different j values representing slightly differences in energy. Consequently the characteristic lines may be expected to have a fine structure.

24. 6-4 X-ray crystal diffraction (衍射) von Laue’s method lBy 1911, increased evidence had begun to indicate that x-ray wave lengths might be as short as a few hundred millionths of a centimeter or a few angstrom (β) units. lThis led Max von Laue in Germany to the brilliant idea that they might act to give an effect somewhat similar to crossed diffraction gratings (透射光栅) ,since atomic layers in a crystal usually have spacing of few angstrom units. lVon Laue predicted that if x-rays were passed through such a crystal a diffraction pattern of spots would be found.

25. lThe experiment is shown in Fig. 6.4.1 6.4.1 6.4.2

26. lThe prediction was complicated by the fact that a crystal could not act as a two-dimensional grating, but would constitute a kind of three dimensional grating and furthermore that atomic layers could be thought of as existing in many planes. lHowever at von Laue’s suggestion the experiment was tried by two of his students and it was a notable success. lA typical photograph of von Laue spots is shown in Fig 6.4.2.The large central spot is merely the results of the direct beam of x-rays from which only a relatively small fraction of the rays are diffracted by the crystal. lThe positions of the small spots were close to where von Laue had calculated they would be.

27. lX-rays are confined to a narrow beam by means of blocks of lead (铅) through which a small hole is drilled. lThis pencil (束) of x-rays is allowed to pass through a crystal of some substance such as potassium chloride (氯化钾)。 lThe spots are obtained on a photographic film after an exposure of as much as 30 minutes or more.

28. Bragg’s method lThe way in which the diffraction of x-rays depends upon the wavelength and the crystal spacing is more simply seen from the work of W.H Bragg and his son W.L Bragg. lWhereas von Laue passed the x-rays through a crystal to obtain diffraction, the Braggs reflected the x-rays from the successive planes parallel to the face of a crystal. lThe diffraction pattern thus obtained is much simpler to analyze than the one obtained by von Laue lLet us consider how x-rays would be reflected from the planes of such a crystal lattice according to Bragg’s method.

29. l Fig 6.4.3 represents an x-ray beam incident upon the crystal plane at an angle θ,called the grazing angle (掠射角).Rays reflected at the same angle θ are also indicated. l From the diagram it is seen that the difference in path between rays from successive planes is 2dsinθ, where d is the spacing between the crystal planes. (Fig 6.4.3)

30. lConstructive interference occurs for the emerging beam if the waves are in phase. (同相) This occurs only at those angles for which the path difference is a whole wavelength or an integer number of wave lengths. lA reinforcement spot (or line) then occurs when 2dsinθ= nλ(6-4-1) where n may be integral values 1,2,3,…… . At other angles the waves are out of phase and destructive interference occurs.

31. lThe experimental arrangement is shown in Fig 6.4.4. With a crystal x-ray spectrometer the wavelength of x-rays can be computed if the spacing of the crystal planes is known and if the angle to the observed spot is measured. (Fig 6.4.4.)

32. lOn the other hand, when the wavelength of the x-ray is known, the x-ray spectrometer maybe used to determine the crystal spacing .The crystal spacing have now been accurately measured for many crystals and this is one of the great achievements in the field of x-rays.

33. The powder method lLater, a diffraction method of analyzing crystals was developed by Hull, Debye and Scherrer, in which it is not necessary to use a large single crystal , as in the original Bragg method . lCrystal fragments(碎屑) or fragments in the form of a powder, are effective since they are actually large compared to the x-ray wavelengths . lThese fragments present relatively large crystal planes to the incident rays, just as the single crystal dose in the Bragg method, but they are oriented in nearly all possible directions.

34. lInstead of lines or spots being produced on a photographic film, circles are obtained. The random orientation of crystal fragments causes the spots from a given set of crystal planes to fall on the arc of a circle about the central spot formed by the original beam. (Fig 6.4.5)

35. lFor different grazing angles and for different sets of atomic planes there would be other circles concentric with the first. lIf a strip(条) of photographic film is not wide enough to show the complete circles, it will show the regions as arcs of circles, as in Fig6.4.6. (Fig6.4.6)

36. lForm the radii of the circles and the angles at which they are formed the crystal spacings can be readily determined. lThe convenience of this method has led to its wide spread scientific and industrial adoption in the study of metals and alloys (合金).

37. 6-5. The Compton effect The Compton effect lAn experiment performed by A.H Compton in 1923 showed that when monochromatic (单色的)x-rays are scattered by graphite (石墨) , their frequency decreases. This is called the Compton effect. lAlthough this effect is hard to understand classically, Compton demonstrated that it has a simple explanation in terms of photos.

38. lClassically, the scattering of electromagnetic radiation by matter occurs because the electric field of waves incident at a frequency ν causes charges to oscillate at that frequency. These oscillating charges reradiate electromagnetic waves in various directions at the same frequency, ν. Compton’s solution lCompton’s solution was to treat the scattering(散射) as an elastic collision of a photon and electron, much like the collision of two billiard falls. (Fig.6.5.1)

39. (Fig 6.5.1) lThe energy of an x-ray photon is large compared to the kinetic and potential energies of the electrons in a carbon atom. Thus we can make the approximation that initially the electrons are free and at rest.

40. When a photon collides with one electron and is deflected (转向), the electron recoils (后退) with an energy Eel. • The scattered photon has an energy hν’, where ν’ must be less than ν since energy conservation requires (6-5-1) l On the other hand, for conservation of momentum is the initial direction of the photon. and in a direction at right angle to this

41. lElinimating θ and v from the above three equations, we have • In the non-relativistic case where v<<c , the shift in wavelength is given by 9(9 5-5)4444444 (6-5-5) lThe quantity h/mC in the above equation has the dimension of a length and when written where m0 is the rest mass it is called the Compton wavelength. lWith ordinary light these shifts would be too small to be detectable, but with x-rays the frequency is so high that

42. each photon possesses sufficient energy and momentum to produce a shift which can be measured with a good x-ray crystal spectrometer. lWhen the experiment is performed, scattered photons that have not undergone change in frequency and wavelength are also detected. This is due to the fact that many electrons in a block of carbon are more firmly bound(束缚) to the parent atom to form a more massive object. Photons in collision with then lose little energy and thus the scattering occurs with them lose little energy and thus the scattering occurs with no appreciable shift in wavelength.

43. The End • Thank You for Your Attention!