Diffraction (bending) Diffraction grating

Transcription

1 X-ray X-ray iffraction Eectromagnetic wave (f= Hz, E=1eV 1keV (1.9* J), λ< m).1-1keV: soft; 1-1keV: har (high penetration) raiation emitte by the atom ue to eectron transitions (!?) Ionizing raiation (the energy is use to remove (etach) the eectrons from the atoms) Discovere by a german physicist, Wihem Conra Röntgen 8th of November 1895 X-ray (unknown raiation) 191 Nobe Price in Physics raiation emitte by the atom ue to eectron transitions gamma ray: raiation emitte by the atomic nuceus Types of X-ray characteristic x-ray ine spectrum (epens on the matter of the anoe) Chares Gover Barka: Nobe Price in Physics 1917: iscovery of the characteristic x-ray Barka suggeste tha X-ray is eectromagnetic wave X-ray prouction Ejecte eecron M L Incient eectron K Characteristic x-ray (iscrete energy transitions) braking raiation or "eceeration raiation" ( Bremsstrahung ) Continuous spectrum cose interaction (moerate energy) Coision wirh rhe atomic nuceus (maxima energy) istant interaction (ow energy) Interference a physica phenomena two ifferent waves combine in the resutant wave the ispacement at any point is the sum of the ispacements of the iniviua waves constructive or estructive interference Diffraction (bening) s = + 1 = sin + sin = (sin + sin ) s = = (sin + sin ) 1 = sin 1 = sin ange of incience (sin + sin ) = 1 ange of iffraction A B iffraction grating = sin = sin

2 Diffraction (bening) Diffraction grating Ange of incience sin sin Ange of iffraction 8. sin = sin Incient ight Diffracte ight a) b) (sin + sin ) = ange of iffraction () irecty proportiona to the waveegth (λ) inversey proportiona to the attice constant () m: a positive or negative whoe number Spacing between the sits (attice constant) beta (egree) (nm) apha=1 egree amba1=5nm sin = sin sin = sin beta (egree) apha=1 egree amba=nm (nm) apha=1 egree amba1=5nm beta (egree) (nm) apha1=1 egree amba=5nm sin = sin sin = sin beta (egree) apha=5 egree amba=5nm apha1=1 egree amba=5nm Conitions which are require to prouce iffraction: proper ratio of the λ an neee! proper is neee! (nm)

3 Max von Laue ( ) Nobe Laureate (1914) german physicist. X-ray eectromagnetic wave or partice? If wave iffraction! Di not work with optica gratings. The waveength of x-ray is smaer compare to the attice constant of the appie grating!? Crysta-attice? Two stuents, Water Frierich an Pau Kipping compete the experiment (copper-sufate an zinc-sufie). Concusions The x-ray is a wave The crystas have attice structure Determining the waveength of the x-ray X-ray iffraction structura informations (e.g James Watson an Francis Crick etermine the structure of the DNA) Exporing the structure of the crysta-attice Wiiam Henry Bragg an his son Wiiam Lawrence Bragg Estabishe the basics for stuying the structure of the crysta-attice by x-ray Nobe Laureates in Physics 1915 Bragg equation Conitions to get constructive interference: sin Θ = : space between the attice ayers (atomic panes ~ attice constant) Θ: the ange of incience m: an integer number λ: waveength At what Θ vaue wi be the x-ray most efficienty iffracte (refecte) if we know the waveength of the x-ray (λ) an the istance bettween the atomic panes ( ~ attice constant)? Laue-equations sin Θ = ange of incience γ 1 = cosγ 1 = cosγ = cosγ = cosγ γ γ s = 1 = cos γ cos γ = (cos γ cos γ ) s = = (cosγ ) (cosγ ) = 1 γ ange of iffraction

4 cos Laue-equations a (cos cos ) = hλ b (cos cos ) = kλ c (cosγ ) = λ x-, y-, z- components. + cos + cos γ = 1 X-ray iffraction A metho to investigate the structure of materias. To get a goo iffraction pattern, the sampe has to contain a high number of perioicay arrange eements (crystas). It is base on the iffraction an refection of x- ray on matters. Diffraction pattern (interference) spectrum (intensity profie) The waveength of x-ray (Å) ~ atomic sizes Protein crystaography Preparing protein crystas. Choosing the right crystaization conitions (sat, buffer, precipitating agent). Avantages of using crystas: high number of perioicay arrange eements within the crystas the scattering wi be more effective in certain irections. Intensity an phase ata can be use to preict the structure of a sampe. Freezing in iqui nitrogen. Recor x-ray iffraction pattern. X-ray is scattere on the eectrons aroun the nuceus eectron ensity map Diffraction pattern wi be prouce. Phase ata are missing. Labeing the sampe with heavy atoms. Diffraction pattern wi change. Phase shift can be etermine. Recor a new x-ray iffraction pattern. Mathematica anaysis of the ata (Fourier transformation). Moe preiction. The en!

5 Atomic force microscopy Ger Binnig, Heinrich Rohrer, Christoph Gerber és Emun Weibe Scanning probe microscopy Scanning the surface of tne sampe. Resoution nm Scanning piezzoeectric effect (inverse) Repusive force between the tip an the eectron cous within the sampe. The tip is mae of har siica crysta. Diameter is nm. Static or contact moe. Dinamic or non contact operation. The en! Jung SH, Park D, Park JH, Kim YM, Ha KS. Moecuar imaging of membrane proteins an microfiaments using atomic force microscopy. Exp Mo Me. 1 Sep 3;4(9):