PC IV Grenzflächen WS 2011/12

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1 kubisch flächenzentriert (fcc) hexagonal dichtgepackt (hcp)

2 kubisch flächenzentriert fcc hexagonal dichtgepackt hcp kubisch raumzentriert bcc

3 Kubische Kristalle kubisch raumzentriert kubisch flächenzentriert

4 H Hydrogen 1s Li 1.87 Lithium 2s Be Beryllium 2s Na Sodium 3s K Potassium 4s Rb Rubidium 5s Cs Cesium 6s Fr Francium 7s Mg Magnesium 3s Ca Calcium 4s Sr Strontium 5s Ba Barium 6s Ra Radium 7s Periodic Table of Elements Sc Scandium 3d 4s Y Yttrium 4d 5s Ti Titanium 3d 2 4s Zr Zirconium 4d 2 5s La Hf 16.6 Lanthanum 5d 6s 2 Hafnium 4f 14 5d 2 6s Ac Actinium 6d 7s V Vanadium 3d 3 4s Nb Niobium 4d 4 5s Cr 6.93 Chromium 3d 5 4s Ce 6.7 Pr Cerium Praseodymium 4f 5d 6s 2 4f 3 6s Ta Tantalum 4f 14 5d 3 6s Th Thorium 6d 2 7s Mo Molybdenum 4d 5 5s (4900) W Tungsten 4f 14 5d 4 6s 2 Pa Protactinium 5f 2 6d 7s Mn Manganese 3d 5 4s Tc 11.5 Technetium 4d 5 5s Nd Neodymium 4f 4 6s Re Rhenium 4f 14 5d 5 6s U Uranium 5f 3 6d 7s Pm Promethium 4f 5 6s Fe Iron 3d 6 4s Ru Ruthenium 4d 7 5s Os Osmium 4f 14 5d 6 6s Np Neptunium 5f 4 6d 7s T boil T melt mass 5.6 Sm Samarium 4f 6 6s Co Cobalt 3d 7 4s Rh Rhodium 4d 8 5s 9.2 Ir Iridium 4f 14 5d 7 6s Pu Plutonium 5f 6 7s 2 IP name electrons Ni Nickel 3d 8 4s Eu Europium 4f 7 6s Pd Palladium 4d Gd 7.96 Gadolinium 4f 7 5d 6s Cu Copper 3d 10 4s Ag Silver 4d 10 5s Zn Zinc 3d 10 4s Pt Au Platinum 4f 14 5d 8 6s 2 Gold 4f 14 5d 10 6s Am Americium 4f 7 7s Cm Curium 5f 7 6d 7s 2 bcc fcc n! Xx hcp B Boron 2s 2 2p Al Aluminium 3s 2 3p Ga 5.35 Gallium 3d 10 4s 2 4p Cd In Cadmium 4d 10 5s 2 Indium 4d 10 5s 2 5p Tb Terbium 4f 9 6s 2 Bk Berkelium 5f 8 6d 7s Hg Mercury 4f 14 5d 10 6s Tl Thallium 4f 14 5d 10 6s 2 6p Dy Dysprosium 4f 10 6s 2 Cf Californium 5f 9 6d 7s C Carbon 2s 2 2p Si Silicon 3s 2 3p Ge Germanium 3d 10 4s 2 4p Sn Tin 4d 10 5s 2 5p Ho Holmium 4f 11 6s N Nitrogen 2s 2 2p w 317.2w 1.82w P Phosphorus 3s 2 3p As 4.82 Arsenic 3d 10 4s 2 4p Pb Lead 4f 14 5d 10 6s 2 6p 2 Es Einsteinium 5f 10 6d 7s Sb 6.25 Antimony 4d 10 5s 2 5p Bi Bismuth 4f 14 5d 10 6s 2 6p Er Erbium 4f 12 6s 2 Fm Fermium 5f 11 6d 7s O Oxygen 2s 2 2p S Sulphur 3s 2 3p Se Selenium 3d 10 4s 2 4p Te Tellurium 4d 10 5s 2 5p Po Polonium 4f 14 5d 10 6s 2 6p Tm Thulium 4f 13 6s 2 Md Mendelevium F Fluorine 2s 2 2p Cl Chlorine 3s 2 3p Br Bromine 3d 10 4s 2 4p He Helium 1s I Iodine 4d 10 5s 2 5p At Astatine 4f 14 5d 10 6s 2 6p Yb Ytterbium 4f 14 6s No Nobelium Ne Neon 2s 2 2p Ar Argon 3s 2 3p Kr Krypton 3d 10 4s 2 4p Lu Lutetium 4f 14 5d 6s Xe Xenon 4d 10 5s 2 5p Rn Radon 4f 14 5d 10 6s 2 6p Lr Lawrencium

5 Dichtgepackte Strukturen kubisch flächenzentriert fcc hexagonal dichtgepackt hcp kubisch raumzentriert bcc

6 Diamantstruktur

7 PC IV Grenzflächen WS 2011/12 (111) (110) (100) fcc single crystal : different surface terminations from BALSAC, K. Hermann siehe auch: faces.pdf

8 Rekonstruktion Pt(100) reconstructed

9 Missing row reconstruction fcc(110)-(2x1)

10 Si(111)-(7x7)

11 Si(111)-(7x7)

12 PC IV Grenzflächen WS 2011/12 (335) steps ( ) kinks from BALSAC, K. Hermann High Miller indexed fcc surface with steps / kinks BALSAC plot

13 Edge Vacancy Edge Atom Surface Vacancy Adatom Kink Atom Edge Adatom Surface Atom

14 BINDING ENERGY (NN BONDS) free atom in vapor adatom, W A ledge adatom, W LA kink atom, W K ledge atom, W L surface atom, W T bulk atom

15 Oberflächengitter a 2s a 1s a 1s γ γ a 1s a 2s γ square a 1s a 2s γ = 90 a 1s = a 2s γ = 90 γ rectangular centred rectangular hexagonal oblique a 1s = a 2s γ = 120 a 1s a 2s γ 90 a 1s a 2s a 2s a 2s a 1s γ

16 fcc(110) + c(2x2)-ad fcc(100)+p(2x2)-ad; ; ~+c(4x2)-ad

17 Adsorbate

Surface Crystallography 0.35-0.30 0.25 0.20 0.15 0.13 0.O w~"/3 I,,31 i, Ocs- O o -phase diagram. i weak "/ 3 +di ~ffu se (2x2) ~I I I I ~3 ~, 12~I

18 Surface Crystallography O w~"/3 I,,31 i, Ocs- O o -phase diagram. i weak "/ 3 +di ~ffu se (2x2) ~I I I I ~3 ~, 12~I (2x2) = I [diffuse) I [snlitl x I ~ r2x2~! 12~.,) "= I i (diffuse / (diffuse) (2x2)) 2q3 t [ l I '(2x21 I spi t I 1 ~39 `/39 diffuse (2x~) [ ",~39 I I I weak) ring! diffuse ring I B [ ring i diffuse ring I I I I ii (z~l I I dif.se ring I (2x2) ] Idifftls e I I o l l I I ) [ -421 (3x2-~a)iffu I ~-- ~. d-- se)-ld I diffuse 1"17 D. I diffuse [ "/7 I D, I I I I dllffuse J `/7 [diffuse 47 l I I ~7 I diffuse q7 I --q~ "~'7 idtffuse "/7 I `]7 lldifusel ~ I `/7 I P I o15 [ diffuse ~ I I Ru(001) Ertl & co, Surf. Sci. 342, 134 (1995)

19 Metall, Halbleiter und Isolator Metall Halbleiter Isolator E Vakuum E Fermi Leitungsband Valenzband

20 Fermi-Verteilung Elektronen sind Spin = ½ Teilchen, sog. Fermionen f(e) = exp E µ k B T Besetzung Fermi-Dirac Statistic 4 Energie [ev] 6 µ = 5.5 ev T = 0 K 300 K 4000 K 8

21 Jellium unendlicher großer Kristall positive Ladungsdichte: Fermi Energie effektiver Radius typischer Wert: r s = 0.15 nm +(r) =ne F = 4 rs m (3 2 n) 2/3 = n 1

22 r s & n Werte Element rs [nm] n [10 22 cm -3 ] Li Rb Cu Ag Be Ca Al Pb

23 Bandstruktur ev E _ K Ag (111) _ Γ A _ Γ _ K _ M _ M _ K

24 E CB VB E g Semiconductor Metal Adsorbat E vac e ΦSB EF p-si Ag NO

25 Smoluchowski smoothing (+) (-) Stufenkante

Strom e - FIG. 1. (a) Constant current image of a Cu(111) step edge: 280 Å 3 138 Å, V 1.4 V, I 7 na. (b) di dv image taken simultaneously with (a) by lock-in technique (DV 135 mv).

26 Strom e - FIG. 1. (a) Constant current image of a Cu(111) step edge: 280 Å Å, V 1.4 V, I 7 na. (b) di dv image taken simultaneously with (a) by lock-in technique (DV 135 mv). Standing wave patterns at static scatterers as steps and impurities are clearly visible. y x FIG. 2. (a) Typical di dv data perpendicular to a descending Cu(111) step obtained by averaging over several line scans of a di dv image as shown in Fig. 1(b). The data at 1 and 2 ev were taken with a stabilizing current of 5 and 10 na and a DV of 119 and 156 mv, respectively. The solid lines depict the fits with Eqs. (4) and (5). The significance of the deduced L f is demonstrated by the dashed line: neglecting inelastic processes by setting L f ` leads to a much slower decay rate than observed. (b) Comparison between the full calculation of di dv with Eqs. (1) and (3) and the result obtained by setting T constant (T! 0, L f! `, typical Cu(111) parameters: W s W t 4.5 ev, r 0.5 [23]). Bürgi et al., Phys. Rev. Lett. 82, 4516 (1999)

27 Surface Smearing & Fridel Oszillationen Electron density Friedel oscillations Distance Surface Exponential decay into vacuum Oszillationen je größer je größer r s

28 Fe/Cu(111) Eigler, IBM

29 Don Eigler, IBM, Fe/Cu(111)

31 a j -1 j +1 j ξ j -1 ξ j ξ j +1 a

32 Debye Temperatur Debye Frequenz, ωd, ist ein Maß für die Steifheit des Gitters der Atome Die Debye Frequenz der Oberfläche ist meist niedriger als die im Volumen z.b. für Pt(100): 110 K Die Vibrationsamplituden an der Oberfläche sind 1.4 bis 2.6 mal so groß wie im Volumen D = D k B Element θd [K] Ag 225 Au 165 C (Diamand) 2230 C (Graphit) 760 Ge 385 Pt 240 Si 645 W 400

This resource contains three different versions of the periodic table, including a blank one for colouring!

Teaching notes This resource contains three different versions of the periodic table, including a blank one for colouring! It also contains tables of the Group 0, 1 and 7 elements with a few columns for