kubisch flächenzentriert (fcc) hexagonal dichtgepackt (hcp)
kubisch flächenzentriert fcc hexagonal dichtgepackt hcp kubisch raumzentriert bcc
Kubische Kristalle kubisch raumzentriert kubisch flächenzentriert
1 20.38 13.95 1.0079 13.595 H 0.0899 Hydrogen 1s 3 6.939 4 9.01218 1603 5.390 2753 9.320 453.5 1556 0.534 Li 1.87 Lithium 2s Be Beryllium 2s 2 11 22.990 1163.2 5.138 370.95 0.97 Na Sodium 3s 19 1027 336.7 0.86 37 973 311.85 39.09 K Potassium 4s 12 1393 923 1.739 20 4.339 1760 Rb 1.532 Rubidium 5s 55 85.47 1123 1.55 4.176 1643 958 3.893 301.79 1.873 Cs Cesium 6s 87 593 298-132.90 Fr Francium 7s 38 1043 2.6 56 1910 983 3.5 88 1800 973 5 24.305 7.644 Mg Magnesium 3s 2 40.08 6.111 Ca Calcium 4s 2 87.62 5.692 Sr Strontium 5s 2 137.34 5.210 Ba Barium 6s 2 5.277 Ra Radium 7s 2 21 3003 1811 2.99 39 2903 1773 4.5 57 Periodic Table of Elements 44.956 Sc Scandium 3d 4s 2 22 6.54 3503 88.905 6.377 Y Yttrium 4d 5s 2 138.91 1943 4.52 40 3900 2128 6.5 72 47.90 6.83 Ti Titanium 3d 2 4s 2 91.22 6.835 Zr Zirconium 4d 2 5s 2 178.49 23 3673 2003 5.96 41 5173 2773 8.55 3743 5.61 5420 7.0 5670 1193 2495 3270 6.18 La 13.36 Hf 16.6 Lanthanum 5d 6s 2 Hafnium 4f 14 5d 2 6s 2 89 3600 1470-6.9 Ac Actinium 6d 7s 2 58 50.942 V Vanadium 3d 3 4s 2 24 6.74 2913 02.906 6.881 Nb Niobium 4d 4 5s 140.12 59 2173 51.996 6.764 3363 Cr 6.93 Chromium 3d 5 4s 42 5073 2893 10.21 3743 6.54 3290 5.48 1070 1208 6.7 Ce 6.7 Pr Cerium Praseodymium 4f 5d 6s 2 4f 3 6s 2 90 4470 2020 73 7.88 Ta Tantalum 4f 14 5d 3 6s 2 232.04 Th 11.724 Thorium 6d 2 7s 2 180.95 91 4470 1840 15.37 95.94 Mo Molybdenum 4d 5 5s 74 140.91 25 1517 7.2 43 7.10 (4900) 180.95 2520 5770 7.98 5870 3650 3453 19.3 W 20.53 Tungsten 4f 14 5d 4 6s 2 Pa Protactinium 5f 2 6d 7s 2 60 3483 1297 6.9 92 54.938 Mn Manganese 3d 5 4s 2 26 7.432 3008 Tc 11.5 Technetium 4d 5 5s 2 75 144.24 Nd Neodymium 4f 4 6s 2 1808 7.86 44 7.228 4373 Re Rhenium 4f 14 5d 5 6s 2 5.51 3473 238.03 4091 4.0 1405 18.97 U Uranium 5f 3 6d 7s 2 61 2773 12.6 Pm Promethium 4f 5 6s 2 1308-186.2 76 55.847 7.87 Fe Iron 3d 6 4s 2 101.07 Ru Ruthenium 4d 7 5s 27 3153 1765 8.9 45 7.365 4233 190.2 2233 12.4 7.87 4670 8.7 4620 2970 2716 22.48 Os 22.42 Osmium 4f 14 5d 6 6s 2 93 4175 912 20.45 Np Neptunium 5f 4 6d 7s 2 62 1943 1345 7.5 T boil T melt 94 3503 912.6 77 mass 5.6 Sm Samarium 4f 6 6s 2 58.933 7.86 Co Cobalt 3d 7 4s 2 102.9 7.461 Rh Rhodium 4d 8 5s 9.2 Ir Iridium 4f 14 5d 7 6s 2 150.35 Pu 19.737 Plutonium 5f 6 7s 2 IP name electrons 192.2 63 1703 1099 5.245 95 2880 1267 13.67 28 3073 1726 8.9 46 3473 1825 11.4 78 58.71 7.633 Ni Nickel 3d 8 4s 2 151.96 Eu Europium 4f 7 6s 2 106.4 Pd Palladium 4d 10 64 5.67 3070 29 2863 1356 8.92 47 8.33 2473 195.09 1585 1234 10.5 79 Gd 7.96 Gadolinium 4f 7 5d 6s 2 63.54 7.724 Cu Copper 3d 10 4s 107.87 7.574 Ag Silver 4d 10 5s 157.25 196.97 65 6.16 2750 1629 8.25 30 1180.2 65.37 9.391 Zn Zinc 3d 10 4s 2 692.66 7.14 48 4570 8.88 2970 9.22 629.73 2042.5 1336.2 234.28 21.450 Pt 19.29 Au 13.546 Platinum 4f 14 5d 8 6s 2 Gold 4f 14 5d 10 6s Am Americium 4f 7 7s 2 96 1610 13.51 Cm Curium 5f 7 6d 7s 2 bcc fcc n! Xx hcp 97 112.40 5 10.811 4173 8.296 2303 2.34 B Boron 2s 2 2p 13 2723 933.3 26.98154 Al 2.702 Aluminium 3s 2 3p 31 6 4623 3923 2.24 14 5.984 2628 69.72 1693 2.42 32 2503 6.00 3103 302.93 1232 5.910 Ga 5.35 Gallium 3d 10 4s 2 4p 49 114.82 1038 8.991 2323 5.785 2963 594.18 429.76 505.06 8.65 Cd 7.362 In 5.750 Cadmium 4d 10 5s 2 Indium 4d 10 5s 2 5p 80 158.92 6.74 Tb Terbium 4f 9 6s 2 Bk Berkelium 5f 8 6d 7s 2 200.59 Hg Mercury 4f 14 5d 10 6s 2 10.434 1731 66 2600 1680 8.45 98 81 6.106 576.7 11.85 Tl Thallium 4f 14 5d 10 6s 2 6p 162.50 Dy Dysprosium 4f 10 6s 2 Cf Californium 5f 9 6d 7s 2 204.37 67 6.82 2760 1734 8.76 99 12.011 11.256 C Carbon 2s 2 2p 2 28.086 8.149 Si Silicon 3s 2 3p 2 72.59 Ge Germanium 3d 10 4s 2 4p 2 50 7.342 Sn Tin 4d 10 5s 2 5p 2 82 164.93 Ho Holmium 4f 11 6s 2 7 77.35 63.15 0.81 15 14.0067 14.545 N Nitrogen 2s 2 2p 3 553.2w 317.2w 1.82w 33 30.97376 P Phosphorus 3s 2 3p 3 8 90.18 54.36 1.14 16 10.484 717.75 74.922 392.2 1.96 34 7.88 889 9.81 958 490.6 5.72 As 4.82 Arsenic 3d 10 4s 2 4p 3 118.69 207.19 2023 7.415 600.5 11.34 Pb Lead 4f 14 5d 10 6s 2 6p 2 Es Einsteinium 5f 10 6d 7s 2 68 2690 1770 9.05 100 51 121.75 1910 8.639 1263 903.7 723 6.69 Sb 6.25 Antimony 4d 10 5s 2 5p 3 83 1833 7.287 544.4 9.8 Bi Bismuth 4f 14 5d 10 6s 2 6p 3 167.28 Er Erbium 4f 12 6s 2 Fm Fermium 5f 11 6d 7s 2 208.98 69 1990 1818 9.29 101 15.999 13.614 O Oxygen 2s 2 2p 4 32.064 10.357 S Sulphur 3s 2 3p 4 78.96 9.75 Se Selenium 3d 10 4s 2 4p 4 52 127.60 9.01 Te Tellurium 4d 10 5s 2 5p 4 84 1235 8.43 527 - Po Polonium 4f 14 5d 10 6s 2 6p 4 168.93 Tm Thulium 4f 13 6s 2 Md Mendelevium 70 1590 1097 7.0 9 85.05 53.55 1.505 17 239.1 172.2 1.56 35 18.9984 17.418 F Fluorine 2s 2 2p 5 35.453 13.01 Cl Chlorine 3s 2 3p 5 79.909 331.93 11.84 265.95 3.12 Br Bromine 3d 10 4s 2 4p 5 53 126.90 2 4.0026 4.1 24.581 3.3 0.126 He Helium 1s 2 10 27.07 24.54 1.20 18 87.29 83.77 1.784 36 456 10.454 165.03 386.8 161.4 4.93 I 5.897 Iodine 4d 10 5s 2 5p 5 85 650 570 - At Astatine 4f 14 5d 10 6s 2 6p 5 173.04 6.22 Yb Ytterbium 4f 14 6s 2 102 No Nobelium 71 3270 20.183 21.559 Ne Neon 2s 2 2p 6 39.948 15.755 Ar Argon 3s 2 3p 6 83.80 119.75 13.996 115.98 3.744 Kr Krypton 3d 10 4s 2 4p 6 54 6.15 Lu Lutetium 4f 14 5d 6s 2 1925 9.82 103 131.30 12.127 Xe Xenon 4d 10 5s 2 5p 6 86 211 10.745 202 - Rn Radon 4f 14 5d 10 6s 2 6p 6 174.97 Lr Lawrencium
Dichtgepackte Strukturen kubisch flächenzentriert fcc hexagonal dichtgepackt hcp kubisch raumzentriert bcc
Diamantstruktur
PC IV Grenzflächen WS 2011/12 (111) (110) (100) fcc single crystal : different surface terminations from BALSAC, K. Hermann siehe auch: http://www.phchem.uni-due.de/photochem/crystal faces.pdf
Rekonstruktion Pt(100) reconstructed
Missing row reconstruction fcc(110)-(2x1)
Si(111)-(7x7)
Si(111)-(7x7)
PC IV Grenzflächen WS 2011/12 (335) steps ( 11 13 19 ) kinks from BALSAC, K. Hermann High Miller indexed fcc surface with steps / kinks BALSAC plot
Edge Vacancy Edge Atom Surface Vacancy Adatom Kink Atom Edge Adatom Surface Atom
BINDING ENERGY (NN BONDS) 0 1 2 3 4 5 6 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
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
fcc(110) + c(2x2)-ad fcc(100)+p(2x2)-ad; ; ~+c(4x2)-ad
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 (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 011 0.2 013 014 0o 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 0.6 017 0.8 Ru(001) Ertl & co, Surf. Sci. 342, 134 (1995)
Metall, Halbleiter und Isolator Metall Halbleiter Isolator E Vakuum E Fermi Leitungsband Valenzband
Fermi-Verteilung Elektronen sind Spin = ½ Teilchen, sog. Fermionen f(e) = exp E µ k B T Besetzung 1.0 0.8 0.6 0.4 0.2 0.0 0 2 +1 1 Fermi-Dirac Statistic 4 Energie [ev] 6 µ = 5.5 ev T = 0 K 300 K 4000 K 8
Jellium unendlicher großer Kristall positive Ladungsdichte: Fermi Energie effektiver Radius typischer Wert: r s = 0.15 nm +(r) =ne F = 4 rs 3 3 2 2m (3 2 n) 2/3 = n 1
r s & n Werte Element rs [nm] n [10 22 cm -3 ] Li 0.17 4.7 Rb 0.27 1.2 Cu 0.14 8.5 Ag 0.16 5.9 Be 0.10 24.2 Ca 0.17 4.6 Al 0.11 18.1 Pb 0.12 13.2
Bandstruktur ev E 5 0-5 _ K Ag (111) _ Γ A _ Γ _ K _ M 1-10 - 1-12 _ M _ K
E CB VB E g Semiconductor Metal Adsorbat E vac e ΦSB EF p-si Ag NO
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). 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)
Surface Smearing & Fridel Oszillationen Electron density Friedel oscillations Distance Surface Exponential decay into vacuum Oszillationen je größer je größer r s
Fe/Cu(111) Eigler, IBM
Don Eigler, IBM, http://www.almaden.ibm.com/vis/stm/ Fe/Cu(111)
a j -1 j +1 j ξ j -1 ξ j ξ j +1 a
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