X射线光学与成像02

1、X射线光学与成像,郭金川 26538592第2讲,X-rays Bragg Diffraction X-rays Duality X-rays basic properties,History,Rntgen discovered x-rays in 1895 1901 he received the first Nobel Prize in Physics 2004 element 111, previously Unununium, renamed Roentgenium, Rg, in his honor,Wilhelm Conrad Rntgen 1845-19

2、23,Theory,What are x-rays? Electromagnetic radiation of wavelength between 0.01 -10 nm. Produced by high-energy electrons striking a metal target (Cu, W, Mo) in an effect opposite the Photoelectric effect,X- rays Are they Waves?,A way to check: Interference (through a diffraction grating or multiple

3、 slits) For effective interference: Typical slit spacing d But, where to get grating with d 0.1nm?,Crystal Lattice 3D grating,由于间隔、取向不同，存在多种晶面，因此，衍射图案非常复杂。,Transmitter,crystal,receiver,Diffraction of (micro)-waves on a crystal lattice follows Bragg Laws,Wavelength, of a microwave here is 1-2 centime

4、ters,“For their services in the analysis of crystal structure by means of x-rays” 1915年父子俩同获诺奖,Discovered that crystalline solids produced peaks of reflected radiation for specific wavelengths and incident angles in 1913.,1862-1942,1890-1971,NaCl Crystal Lattice 3D grating,100面,111面,Unit cell of NaC

5、l with size a0=282.01pm,Bragg Diffraction of a wave on a crystal,Bragg diffraction conditions,Braggs Theory (two conditions), = constructive interference for incoming wave and the wave scattered by the top plane; 2dsin = n constructive interference of waves scattered by adjacent planes.,Result: Inte

6、rference picture,Diffraction on a single crystal,X-ray Diffraction of a polycrystal,Typical X-ray spectra: Looking at the details:,X-rays, are they just waves?,Classical waves should give smooth broad spectrum slowly dropping to 0 at f Observed spectra have 2 non-classical features: Sharp peaks (cha

7、racteristic X-rays) at fmax, the intensity, I0 for any anode material Non-classical featuresQuantum (particulate) nature of X-rays,Quantum Nature of X-rays:,a) E = hf b) Energy of each photon, E comes from one e- Observed 2 non-classical features: Sharp peaks (characteristic X-rays) （后面讲） at fmax, t

8、he intensity, I0 for any anode material Kinetic energy of e-: Kemax = V0e, where V0 is accelerating voltage, then fmax = E /h = Kemax/h = V0e/h -Duane-Hunt Law (1915年杜伦和宏特发现极限波长与电压成反比） highest f of X-rays for any material for given V0,X-rays Duality,a) Wave properties: Bragg diffraction (smooth enve

9、lope) b) Particle properties: 1) characteristic X-rays 2) same fmax for any material 3) Compton Effect,Compton Effect (=scattering of light by a system of charges),Scattering Classically: Oscillating field of incident light makes charges to oscillate Oscillating charges create secondary waves with t

10、he frequency of scattered wave fscat is the same as the frequency of incident wave f0 , fscat= f0,Would it work Experimentally? fscat = f0 Seems to be working for visible light Does it work for X-rays? No, there is a Compton Shift,Atomic Spectra,Franhofer (1814): certain colors are missing in sunlig

11、ht spectrum. Empirical observations (1850-s): Gases absorb light at characteristic of gas atoms/molecules Heated gas emits light at the same characteristic.,Spectrum of Atomic Hydrogen,Balmer empirical formula: For integer n2 and R=0.011nm-1 Perfect description of visible H-spectrum (!),Atomic Spectra of Hydrogen,Balmer (visible) series,Energy of emitted/absorbed photons by a Hydrogen Atom,莫斯莱