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1、Chapter 3Crystal Diffraction: Theory3.1Electromagnetic RadiationThe interaction between electromagnetic radiation and material objects allows us to see them. If the objects are too small, our radiation detectors (eyes) are in- capable of sensing the wavelengths of the radiation necessary to visualiz
2、e them directly, and we must resort to indirect methods to create the microscopic images that we are interested in. The interaction of electromagnetic radiation with theregularly repeated arrangement in crystalline solids amplifies the images of smallentities (atoms and molecules) sufficiently for u
3、s to observe them, provided that we can somehow mimic the image formation process that our detectors and complex computers (brains) do automatically for larger objects.3.1.1The Electric Field.Objects with certain properties are able to influence one another when separated inspace. Indeed, we define
4、these properties based on our observations of this influence (it is how we observe them!). One such property is known as charge, and we begin byconsidering how objects with charge influence one another. Qualitatively, objects with the same charge exert a repulsive force on one another, while objects
5、 with opposite charges exert an attractive force.Figure 3.1: The electric field surrounding an object with charge q1exerts a force, F2on an object with charge q2at a distance r12.In order to “explain” the ability of one charged object to influence another weinvoke the notion of an electric field. Co
6、nsider the sphere with charge q1depicted in Fig. 3.1, which we will call the source charge.We envision an electric field181182Electromagnetic Radiationsurrounding the charged sphere which exerts a force on a second sphere withtest charge q2. We now wish to determine the magnitude of the strength of
7、this field that is we seek a number that will indicate how the field resulting from charge q1influences a general charge placed somewhere else in space. In order to do this, we use the force exerted on the sphere with charge q2as a measure of this influence. However, as might be expected, the greate
8、r the magnitude of the test charge, q2, the greater the force: F2 q2. Thus to make the magnitude of the electric field atthe location of the test charge independent of the specific charge, we define it as E = F2/q2. By performing a few experiments, we determine two important properties ofthe electri
9、c field and its ability to influence another charge. First, the force, andtherefore the magnitude of the electric field decreases as the distance, r12, increases in inverse proportion: F 1/r12. Second, the influence is not instantaneous. That is, if the sphere containing the source charge is suddenl
10、y moved toward the sphere with the test charge (we assume here that both charges are negative), thesecond sphere will respond to an additional repulsive force from the first sphere, since they are now closer to one another. However, it will do so only after a time delay of r12/c has occurred, where
11、c is the speed of light. By responding, we meanthat its speed has changed, which means it has gained energy from the first sphere,after we have increased the energy of the first sphere by moving it. Apparently this energy is transmitted from the source charge to the test charge at the speed of light
12、.3.1.2Waves.We now consider a gedanken experiment a thought experiment one that would be impractical to perform, but will allow us to discuss the essential elements of electromagnetic radiation without getting bogged down in experimental details. We make use of a hypothetical generator, a device whi
13、ch alternatively removes electrons from one electrode and moves them to a second electrode making it negative andleaving the first electrode positive, then reverses so that the first electrode becomes positive and the second becomes negative. When switched on, the generator will charge each electrod
14、e in a sinusoidal manner, as depicted in Fig. 3.2. Our generatorFigure 3.2: Hypothetical generator.is an ideal one, subject to no constraints it can shuttle the charges back and forthCrystal Diffraction: Theory183Figure 3.3:Electron velocity at different values of the electric field in the hypo- the
15、tical generator: (A) v = 0. (B) v = +vmax. (C) v = 0. (D) v = vmax.between the two electrodes at any rate (frequency) that we desire. The electrodesare shielded so that the electric field of the charges on the electrodes can only be sensed in the region directly between then.An electron is now place
16、d between the electrodes with the generator turned off. We restrict the electron to “up and down” motion between the electrodes as in a wire or an electron-sized tube (remember, this is a gedanken experiment!). The electron is initially at rest. The generator has been designed so that the electronwill initially be exposed to the maximum value of the electric field.When thegenerator is switched on, the electron is subjected to a force from the electric field, E, between the elect
