1 / 22

Unpolarisierte Neutronen- Van Hove Streufunktion S( κ ,ω )

Aufteilung von S: elastische – inelastische Streufunktion. Unpolarisierte Neutronen- Van Hove Streufunktion S( κ ,ω ). A short Excursion to Fourier And Delta Functions. it follows by extending the range of x to more than –L/2 ...L/2 and going to 3 dimensions (v0 the unit cell volume).

berny
Download Presentation

Unpolarisierte Neutronen- Van Hove Streufunktion S( κ ,ω )

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Aufteilung von S: elastische – inelastische Streufunktion Unpolarisierte Neutronen- Van Hove Streufunktion S(κ,ω)

  2. A short Excursion to Fourier And Delta Functions .... it follows by extending the range of x to more than –L/2 ...L/2 and going to 3 dimensions (v0 the unit cell volume)

  3. Gitter G mit Basis B: Gitterfaktor Strukturfaktor unabhängig von κ: „Isotopen-inkoherente-Streuung“ „Spin-inkoherente-Streuung“ ein Element(NB=1): Neutronen – Diffraktion

  4. The Nobel Prize in Physics 1994 Gitterfaktor Strukturfaktor "In simple terms, Clifford G. Shull has helped answer the question of where atoms are, ...“, (Nobel citation)

  5. Scattered Neutron Bragg’s Law in Reciprocal Space (Ewald Sphere) O 2/l a* c* 2q τ q Incoming Neutron

  6. Einkristall-diffraktometrieE2 – HMI, Berlin k τ O

  7. Bragg’s Law in Reciprocal Space (Ewald Sphere) sin OB τ= sin q = O τ /OB = O τ/(2p/l) O sin q = (O τ/2p)l Reflecting Plane 2p/l q q But since τ is a reciprocal lattice point, the length O τ is by definition equal to 2p/dhkl C 2q q τ sin q = (1/2dhkl) l B Neutron 2dhkl sin q= l sin q / l = (1/2dhkl)= (1/2)(1/dhkl) = (1/2)shkl

  8. guide hall n°1, thermal guide H22 monochromator take-off angle 44.22° crystal pyrolytic graphite (002) . wavelength 2.52 Å . flux at sample/n cm-2s-1 6.5 x 106 crystal Germanium (311) . wavelength 1.28 Å . flux at sample/n cm-2s-1 0.4 x 106 max beam size 5 x 2 cm2 angular range 2     -20° ... 144° detector 3He multidetector containing 400 cells angular range 2     80° radius of curvature 1.525 m detector efficiency 60 % at   = 2.52 Å max diameter / mm available around the sample 600 sample environment cryostat 1.7 ... 300 K furnace < 800 °C furnace < 2500 °C by special arr electromagnet 1 T; 22 mm vertical or horizontal gap Pulver- diffraktometrieD1B

  9. 7C2, LLB Saclay SF.. Strukturfaktor L ... Lorentzfaktor (betont kleine Winkel) Einkristall: 1/sin2θ Pulver Zyl.:1/(sin2θ.sinθ) T Transmissionskoeffizient γ Korrektur für Extinktion GdCu2In Pulver-diffraktometrie I(κ) [counts] 0 1 2 3 4 5 6 |κ|[Å-1] 2θ.... Streuwinkel Detektor

  10. Gitterfaktor Strukturfaktor #lambda= 0.58 A #thetamax=18 #nat=4 nonmagnetic atoms in primitive crystallographic unit cell: #[atom number] x[a] y[b] z[c] dr1[r1] dr2[r2] dr3[r3] [Gd] 0 0 0 0 0 0 [Cu] 0.25 0.25 0.25 0.25 0.25 0.25 [Cu] 0.25 0.25 0.75 0.75 0.75 -0.25 [In] 0.5 0.5 0.5 0.5 0.5 0.5 # a=6.62 b=6.62 c=6.62 alpha= 90 beta= 90 gamma= 90 # r1x= 0 r2x= 0.5 r3x= 0.5 # r1y= 0.5 r2y= 0 r3y= 0.5 primitive lattice vectors [a][b][c] # r1z= 0.5 r2z= 0.5 r3z= 0 # nofatoms=1 number of atoms in primitive unit cell GdCu2In h k l d[A] |kappa|[A^-1]2theta Ikern imag itot |sf| lpg } 1.000 1.000 1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 -1.000 -1.000 -1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 -1.000 1.000 1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 1.000 -1.000 -1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 1.000 -1.000 1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 -1.000 1.000 -1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 1.000 1.000 -1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 -1.000 -1.000 1.000 3.82206 1.64389 8.703 11.661 0.000 11.661 24.966 87.101 0.000 2.000 0.000 3.31000 1.89820 10.053 0.025 0.000 0.025 1.336 65.389 0.000 -2.000 0.000 3.31000 1.89820 10.053 0.025 0.000 0.025 1.336 65.389 0.000 0.000 2.000 3.31000 1.89820 10.053 0.025 0.000 0.025 1.336 65.389 0.000 0.000 -2.000 3.31000 1.89820 10.053 0.025 0.000 0.025 1.336 65.389 2.000 0.000 0.000 3.31000 1.89820 10.053 0.025 0.000 0.025 1.336 65.389 -2.000 0.000 0.000 3.31000 1.89820 10.053 0.025 0.000 0.025 1.336 65.389 0.000 2.000 2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 0.000 -2.000 -2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 2.000 2.000 0.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 -2.000 -2.000 0.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 -2.000 0.000 2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 2.000 0.000 -2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 2.000 0.000 2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 -2.000 0.000 -2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 -2.000 2.000 0.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 2.000 -2.000 0.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 0.000 -2.000 2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822 0.000 2.000 -2.000 2.34052 2.68446 14.235 83.558 0.000 83.558 109.804 32.822

  11. Beispiel 2 • In einem elastischen Streuexperiment beträgt die Einfallsenergie 63 meV. Die Gitterkonstante der kubischen Probe beträgt 0.314 nm. Kann der (430) Reflex in diesem Streuexperiment vermessen werden ?

  12. Neutron – PhotonStreuquerschnitte • Vorteile von Neutronen: • Kontrast bei benachbarten Elementen – man sieht z.B. Überstrukturen • Leichte Elemente besser nachweisbar • Isotope können unterschieden werden

  13. Laue Methode • Einkristalle • „weißer“ Strahl • Film oder Flächendetektor hinter • der Probe • schnelles Erkennen der Symmetrie - • wird zum Orientieren von Einkristallen benutzt VIVALDI very-intense vertical-axis Laue diffractometer

  14. 4-Kreismethode φ χ • Einkristalle • monochromatischer Strahl • ein Detektor • EK in beliebige Richtungen orientierbar (Eulerwiege) ω D10 ILL

  15. Flugzeitmethode Det Spallationsquelle (gepulst) 2θ Probe • Streuwinkel fest (Vorteil z.B. bei Druckzellen) • |k| wird variiert (kein Monochromator) über die Zeit (zuerst • kommen die raschen, dann die langsameren Neutronen) • bessere Nutzung der Quelle (keine Monochromator-verluste) • Auflösung umso besser, je größer Abstand zur Quelle (HRPD: 90m)

  16. Time-of-flight Bragg equation - 2dhklsin =  Two basic equations: where m,v = mass, velocity of neutron L = length of flight path t = time of flight of neutron

  17. Time-of-flight equation Combine: L is a constant for the detector, h, m are constants so: t d d-spacings are discriminated by the time of arrival of the neutrons at the detector

  18. The biggest error in the experiment is where the neutrons originate This gives an error in the flight path, L typical value ~5cm Hence as L increases, error in d is reduced - resolution of the instrument is improved e.g. instrument at 10m compared to instrument at 100m 100m = HRPD, currently highest resolution in the world

  19. HRPD, GEM Sample area collimators and detectors on HRPD.  Neutrons enter via the yellow flight tube on the left. GEM General purpose Materials Diffraktometer

  20. p-dichlorobenzene (DCB) refined structure

  21. c/l k h A k h dhkl . b/k f C c * c *)= c *) = c *) a * + k a * + k a b a * + k a a * + k b b a b * + l b * + l b * + l b * + l a/h - C = h k - . . k h shkl = h (h (h (h Thereforeshkl is perpendicular to C . In the same way one can show that it is perpendicular to A, therefore perpendicular to the plane + 0 + 0 – (0 + + 0) = 1 – 1 = 0 C . shkl= ( - ) . h k

  22. |shkl| n = ha* + kb* + lc* a a a ha* + kb* + lc* . cos f = = dhkl = . n = n = h h h |shkl| ha* + kb* + lc* |shkl| 2p |shkl|

More Related