APPENDICES
APPENDICES
Appendix Summary of Quantum Number Characteristics The energy states of electrons are characterized by four quan- tum numbers.The main quantum number,n,determines the overall energy of the electrons,i.e.,essentially the radius of the electron distribution.It can have any integral value.For exam- ple,the electron of a hydrogen atom in its ground state has n=1. The quantum number,l,is a measure of the angular momen- tum L of the electrons and is determined by L=VI(+1), where I can assume any integral value between 0 and n-1. It is common to specify a given energy state by a symbol which utilizes the n-and I-values.States with I=0 are called s-states; with I=1,p-states;and with I=2,d-states,etc.A 4d-state,for example,is one with n=4 and 1=2. The possible orientations of the angular momentum vector with respect to an external magnetic field are again quantized and are given by the magnetic quantum number m.Only m val- ues between +l and-l are permitted. The electrons of an atom fill the available states starting with the lowest state and obeying the Pauli principle which requires that each state can be filled only with two electrons having op- posite spin (s=).Because of the just-mentioned multiplicity, the maximal number of electrons in the s-states is 2,in the p- states 6,in the d-states 10,and in the f-states 14. The electron bands in solids are named by using the same nomenclature as above,i.e.,a 3d-level in the atomic state widens to a 3d-band in a solid.The electron configurations of some iso- lated atoms are listed on the next page
Appendix I The energy states of electrons are characterized by four quantum numbers. The main quantum number, n, determines the overall energy of the electrons, i.e., essentially the radius of the electron distribution. It can have any integral value. For example, the electron of a hydrogen atom in its ground state has n 1. The quantum number, l, is a measure of the angular momentum L of the electrons and is determined by L , where l can assume any integral value between 0 and n 1. It is common to specify a given energy state by a symbol which utilizes the n- and l-values. States with l 0 are called s-states; with l 1, p-states; and with l 2, d-states, etc. A 4d-state, for example, is one with n 4 and l 2. The possible orientations of the angular momentum vector with respect to an external magnetic field are again quantized and are given by the magnetic quantum number m. Only m values between l and l are permitted. The electrons of an atom fill the available states starting with the lowest state and obeying the Pauli principle which requires that each state can be filled only with two electrons having opposite spin (s * 1 2 ). Because of the just-mentioned multiplicity, the maximal number of electrons in the s-states is 2, in the pstates 6, in the d-states 10, and in the f-states 14. The electron bands in solids are named by using the same nomenclature as above, i.e., a 3d-level in the atomic state widens to a 3d-band in a solid. The electron configurations of some isolated atoms are listed on the next page. l(l 1)' Summary of Quantum Number Characteristics
416 Appendix I.Summary of Quantum Number Characteristics K M Z Element 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 1 H He 12 3 Li Be 5 BC 22222222 6 22 7 89 0 24 10 Ne 26 11 Na 26 1 12 Mg 26 13 26 21 456 26 22 26 23 26 24 718 A v 22222222 26 25 26 26 26 6 26 1 1901234156728901234567890424 6 488E-852828588488226-829e 222222222222222222 666666666666666566 26 235567 12222122221 8 26 26 2 0 23 0 2 261 2610 26 2610 26 2222222 26 2610 26 61666616 2610 261 2610 262 2610 264 2610 265 1222112 2610 265
KL M N O Z Element 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 1H 1 2 He 2 3 Li 2 1 4 Be 2 2 5 B 2 2 1 6 C 2 2 2 7 N 2 2 3 8 O 2 2 4 9 F 2 2 5 10 Ne 2 2 6 11 Na 2 2 6 1 12 Mg 2 2 6 2 13 Al 2 2 6 2 1 14 Si 2 2 6 2 2 15 P 2 2 6 2 3 16 S 2 2 6 2 4 17 Cl 2 2 6 2 5 18 Ar 2 2 6 2 6 19 K 2 2 6 2 6 1 20 Ca 2 2 6 2 6 2 21 Sc 2 2 6 2 6 1 2 22 Ti 2 2 6 2 6 2 2 23 V 2 2 6 2 6 3 2 24 Cr 2 2 6 2 6 5 1 25 Mn 2 2 6 2 6 5 2 26 Fe 2 2 6 2 6 6 2 27 Co 2 2 6 2 6 7 2 28 Ni 2 2 6 2 6 8 2 29 Cu 2 2 6 2 6 10 1 30 Zn 2 2 6 2 6 10 2 31 Ga 2 2 6 2 6 10 2 1 32 Ge 2 2 6 2 6 10 2 2 33 As 2 2 6 2 6 10 2 3 34 Se 2 2 6 2 6 10 2 4 35 Br 2 2 6 2 6 10 2 5 36 Kr 2 2 6 2 6 10 2 6 37 Rb 2 2 6 2 6 10 2 6 1 38 Sr 2 2 6 2 6 10 2 6 2 39 Y 2 2 6 2 6 10 2 6 1 2 40 Zr 2 2 6 2 6 10 2 6 2 2 41 Nb 2 2 6 2 6 10 2 6 4 1 42 Mo 2 2 6 2 6 10 2 6 5 1 43 Tc 2 2 6 2 6 10 2 6 5 2 416 Appendix I • Summary of Quantum Number Characteristics
Appendix Il Tables of Physical Constants The International System of Units (SI or mksA System) In the SI unit system,essentially four base units,the meter,the kilogram(for the mass),the second,and the ampere are defined. Further base units are the Kelvin,the mole (for the amount of substance),and the candela(for the luminous intensity).All other units are derived units as shown in the table below.Even though the use of the SI unit system is highly recommended,other unit systems are still widely used. Expression in terms of Quantity Name Symbol Other SI units SI base units Force Newton N kg·m/s2 Energy,work Joule J Nm=V·A·skgm2s2 Pressure Pascal Pa N/m2 kg/m·s2 El.charge Coulomb C J/V A·s Power Watt W J/s kg·m2s3 El.potential Volt V W/A kg·m2A·s3 El.resistance Ohm V/A kg·m21A2.s3 El.conductance Siemens 心 A/V A2·s3kg·m2 Magn.flux Weber Wb V·s kg·m21A·s2 Magn.induction Tesla T Wb/m2 kgA·s2 Inductance Henry H Wb/A kg·m21A2.s2 Capacitance Farad CIV A2·s4/kg·m2
Appendix II In the SI unit system, essentially four base units, the meter, the kilogram (for the mass), the second, and the ampere are defined. Further base units are the Kelvin, the mole (for the amount of substance), and the candela (for the luminous intensity). All other units are derived units as shown in the table below. Even though the use of the SI unit system is highly recommended, other unit systems are still widely used. Expression in terms of Quantity Name Symbol Other SI units SI base units Force Newton N — kg m/s2 Energy, work Joule J N m V A s kg m2/s2 Pressure Pascal Pa N/m2 kg/m s2 El. charge Coulomb C J/V A s Power Watt W J/s kg m2/s3 El. potential Volt V W/A kg m2/A s3 El. resistance Ohm # V/A kg m2/A2 s3 El. conductance Siemens S A/V A2 s3/kg m2 Magn. flux Weber Wb V s kg m2/A s2 Magn. induction Tesla T Wb/m2 kg/A s2 Inductance Henry H Wb/A kg m2/A2 s2 Capacitance Farad F C/V A2 s4/kg m2 Tables of Physical Constants The International System of Units (SI or mksA System)
418 Appendix ll.Tables of Physical Constants Physical Constants(SI and cgs units) Mass of electron (free electron mass;rest mass) m0=9.109×10-31(kg)=9.109×10-28(g) Charge of electron e=1.602×10-19(C) Velocity of light in vac. c=2.998×108(m/s)=2.998×1010(cm/s) Planck constant h=6.626×10-34(J·s) =6.626×10-27(g·cm21s)=4.136×10-15(eV·s) 九=1.054×10-34(J·s) =1.054×10-27(g·cm2s)=6.582×10-16(eV·s) Avogadro constant No=6.022 x 1023 (atoms/mol) Boltzmann constant kB=1.381×10-23(J/K) =1.381×10-16(ergK)=8.616×10-5(eV/K) Bohr magneton 4B=9.274×10-24(J/T)=A·m2=9.274×10-21(ergG) Gas constant R=8.314(J/mol·K)=1.986(cal/mol·K) Permittivity of empty space o=1/oc2=8.854×10-12(Fm)≡(A·s/V·m)=(NWA2) Permeability of empty space 0=4π×10-7=1.257×10-6(H/m)≡(V·s/A·m) Faraday constant F=9.648×104(C/mol) Useful Conversions 1(eV)=1.602×10-19(J)=1.602×10-12(g·cm2s2)=1.602×10-19(kg·m2s2) =3.829×10-20(cal)=23.04(Kcal/mol) 1(J)=1(kg·m2s2)=107(eg)=107(g·cm2/s2)=2.39×10-1(cal) 1(1/2cm)=9×1011(1/s) 1(1/m)=9×109(1/s) 1(C)=1(A·s)=1(J/W) 1(A)=10-10(m) 1(tor)=133.3(N/m2)≡133.3(Pa)=1(mmHg) 1(bar)=105(N/m2)≡105(Pa) 1(Pa)=1(N/m2)=1.45×10-4(psi) 1(psi)=6.895×103(Pa) 1(cal)=2.6118×1019(eV) 1(mm)(milli)=10-3(m) 1 km (Kilo)=103 m 1(um)(micro)=10-6(m) 1 Mm (Mega)=106 m 1(nm)(nano)=10-9(m) 1 Gm (Giga)=109 m 1(pm)(pico)=10-12(m) 1 Tm (Tera)=1012m 1(m)(femto)=10-15(m) 1 Pm (Peta)=1015 m 1(am)(atto)=10-18(m) 1 Em (Exa)=1018 m
Physical Constants (SI and cgs units) Mass of electron (free electron mass; rest mass) m0 9.109 1031 (kg) 9.109 1028 (g) Charge of electron e 1.602 1019 (C) Velocity of light in vac. c 2.998 108 (m/s) 2.998 1010 (cm/s) Planck constant h 6.626 1034 (J s) 6.626 1027 (g cm2/s) 4.136 1015 (eV s) ' 1.054 1034 (J s) 1.054 1027 (g cm2/s) 6.582 1016 (eV s) Avogadro constant N0 6.022 1023 (atoms/mol) Boltzmann constant kB 1.381 1023 (J/K) 1.381 1016 (erg/K) 8.616 105 (eV/K) Bohr magneton B 9.274 1024 (J/T) A m2 9.274 1021 (erg/G) Gas constant R 8.314 (J/mol K) 1.986 (cal/mol K) Permittivity of empty space 0 1/0c2 8.854 1012 (F/m) (A s/V m) (N/A2) Permeability of empty space 0 4 107 1.257 106 (H/m) (V s/A m) Faraday constant F 9.648 104 (C/mol) Useful Conversions 1 (eV) 1.602 1019 (J) 1.602 1012 (g cm2/s2) 1.602 1019 (kg m2/s2) 3.829 1020 (cal) 23.04 (Kcal/mol) 1 (J) 1 (kg m2/s2) 107 (erg) 107 (g cm2/s2) 2.39 101 (cal) 1 (1/#cm) 9 1011 (1/s) 1 (1/#m) 9 109 (1/s) 1 (C) 1 (A s) 1 (J/V) 1 (Å) 1010 (m) 1 (torr) 133.3 (N/m2) 133.3 (Pa) 1 (mm Hg) 1 (bar) 105 (N/m2) 105 (Pa) 1 (Pa) 1 (N/m2) 1.45 104 (psi) 1 (psi) 6.895 103 (Pa) 1 (cal) 2.6118 1019 (eV) 1 (mm) (milli) 103 (m) 1 km (Kilo) 103 m 1 (m) (micro) 106 (m) 1 Mm (Mega) 106 m 1 (nm) (nano) 109 (m) 1 Gm (Giga) 109 m 1 (pm) (pico) 1012 (m) 1 Tm (Tera) 1012 m 1 (fm) (femto) 1015 (m) 1 Pm (Peta) 1015 m 1 (am) (atto) 1018 (m) 1 Em (Exa) 1018 m 418 Appendix II • Tables of Physical Constants
Appendix Il.Table of Physical Constants 419 Electronic Properties of Some Metals Number of free Fermi electrons,Neff Work function Resistivity energy electrons (photoelectric) p[μncm] Material EF [eV] m3 [ev] at20°C Ag 5.5 6.1×1028 4.7 1.59 11.8 16.7×1028 4.1 2.65 Au 5.5 5.65×1028 4.8 2.35 Be 12.0 3.9 4.0 Ca 3.0 2.7 3.91 Cs 1.6 1.9 20.0 Cu 7.0 6.3×1028 4.5 1.67 Fe 4.7 9.71 K 1.9 2.2 6.15 Li 4.7 2.3 8.55 Na 3.2 2.3 4.20 Ni 5.0 6.84 Zn 11.0 3×1028 4.3 5.91 Electronic Properties of Some Semiconductors Gap Mobility Mobility energy of of Work Eg [eV] Conductivity electrons holes function 1 m27 m2 (photoelectric) Material 0K300K 2·m Vs h V·s 中[ev] C(diamond) 5.48 5.47 10-12 0.18 0.12 4.8 Ge 0.74 0.66 2.2 0.39 0.19 4.6 Element Si 1.17 1.12 9×10-4 0.15 0.045 3.6 Sn(gray) 0.08 106 0.14 0.12 4.4 GaAs 1.52 1.42 10-6 0.85 0.04 InAs 0.42 0.36 104 3.30 0.046 III-V InSb 0.23 0.17 8.00 0.125 GaP 2.34 2.26 0.01 0.007 IV-IV a-SiC 3.03 2.99 0.04 0.005 ZnO 3.42 3.35 0.02 0.018 Ⅱ-VI CdSe 1.85 1.70 0.08
Appendix II • Table of Physical Constants 419 Electronic Properties of Some Metals Fermi Number of free energy electrons, Neff (photoelectric) [# cm] Material EF [eV] elec m tr 3 ons [eV] at 20° C Ag 5.5 6.1 1028 4.7 1.59 Al 11.8 16.7 1028 4.1 2.65 Au 5.5 5.65 1028 4.8 2.35 Be 12.0 3.9 4.00 Ca 3.0 2.7 3.91 Cs 1.6 1.9 20.0 Cu 7.0 6.3 1028 4.5 1.67 Fe 4.7 9.71 K 1.9 2.2 6.15 Li 4.7 2.3 8.55 Na 3.2 2.3 4.20 Ni 5.0 6.84 Zn 11.0 3 1028 4.3 5.91 Electronic Properties of Some Semiconductors Mobility Mobility of of Work Conductivity electrons holes function (photoelectric) Material 0 K 300 K # 1 m e V m 2 s h V m 2 s [eV] C (diamond) 5.48 5.47 1012 0.18 0.12 4.8 Ge 0.74 0.66 2.2 0.39 0.19 4.6 Element Si 1.17 1.12 9 104 0.15 0.045 3.6 Sn (gray) 0.08 106 0.14 0.12 4.4 GaAs 1.52 1.42 106 0.85 0.04 InAs 0.42 0.36 104 3.30 0.046 III–V InSb 0.23 0.17 8.00 0.125 GaP 2.34 2.26 0.01 0.007 IV–IV -SiC 3.03 2.99 0.04 0.005 ZnO 3.42 3.35 0.02 0.018 II–VI CdSe 1.85 1.70 0.08 Gap energy Eg [eV] Work function Resistivity
420 Appendix ll.Tables of Physical Constants Magnetic Units Name Symbol em-cgs units mks(SI)）units Conversions Magnetic H 0e=- gln A field m12.s m 1合0e strength Magnetic B G= gin cm12.s b-kgT 1T=104G induction m s·C Magnetization M Maxwell gin A 1A=4π Maxwells cm2 cm2·s m m103 cm2 Magnetic Maxwell= cm32·g2 中 Wb=kg:m2 =V·s1Wb=108 Maxwells flux s·C Susceptibility X Unitless Unitless Xmks =4TXegs (Relative) L Unitless Unitless Same value permeability Energy product BH kJ MGOe m3 1 102 MGOe Conversions from the SI Unit System into the Gaussian Unit System mks cgs Quantity (SI) (Gaussian) Magnetic induction B B/c Magnetic flux P Pg/c Magnetic field strength H cH/4π Magnetization M cM Magnetic dipole moment m Clm Permittivity constant E0 1/4π Permeability constant 0 4m/c2 Electric displacement D D/4T Note:The equations given in this book can be converted from the SI (mks)system into the cgs (Gaussian)unit system and vice versa by re- placing the symbols in the respective equations with the symbols listed in the following table.Symbols which are not listed here remain un- changed.It is imperative that consistent sets of units are utilized. o=4m×10-7=1.257×10-6(W·s/A·m)≡(Kg·m/C2≡(Hm). 60=8.854×10-12(A·s/W·m)=(Fm
Magnetic Units Name Symbol em-cgs units mks (SI) units Conversions Magnetic H Oe m A 1 m A 1 4 0 3 Oe strength Magnetic B G W m b 2 s k g C T 1 T 104 G Magnetization M cm g 1 1 / / 2 2 s m A 1 m A Ma c x m w 2 ells Magnetic Maxwell Wb V s 1 Wb 108 Maxwells Susceptibility $ Unitless Unitless $mks 4$cgs (Relative) Unitless Unitless Same value permeability Energy product BH MGOe m kJ 3 1 m kJ 3 MGOe Conversions from the SI Unit System into the Gaussian Unit System mks cgs Quantity (SI) (Gaussian) Magnetic induction B B/c Magnetic flux +B +B/c Magnetic field strength H cH/4 Magnetization M cM Magnetic dipole moment m cm Permittivity constant 0 1/4 Permeability constant 0 4/c2 Electric displacement D D/4 Note: The equations given in this book can be converted from the SI (mks) system into the cgs (Gaussian) unit system and vice versa by replacing the symbols in the respective equations with the symbols listed in the following table. Symbols which are not listed here remain unchanged. It is imperative that consistent sets of units are utilized. 0 4 107 1.257 106 (V s/A m) (Kg m/C2) (H/m). 0 8.854 1012 (A s/V m) (F/m). 4 102 kg m2 s C cm3/2 g1/2 s 4 103 Maxwell cm2 g 1/2 cm1/2 s g 1/2 cm1/2 s 420 Appendix II • Tables of Physical Constants field induction flux
9 牙 母 器 s'g Appendix Ill Unq 33 104 PAPERTECH 105 Pa Uns MASc.C.Bello. Une 窖 君达 .n HO 子8 T 33# I The Periodic Table of the Elements 2. i 员的 6式 可：动 2 用用 司3 B尘 n O.9 No 假型线 102 T: o前 子苗 N
Appendix III The Periodic Table of the Elements
Appendix IV Solutions to Selected Problems Chapter 2 2.1.0.77(m) 2.2.75% 2.3.0.114(cm)(Not0.1195cm) 2.4.1.26×104(N) 2.5.36% 2.6.703.1(MPa) 2.7.0.233 2.8.△V=0 2.10.6=10.26% e=10.8% =105.8(MPa) c=95.49(MPa) 2.11.3.998(cm) 2.12.1=1.502(m) g=254.6MPa(<300MPa) 2.13.0.292 2.14.0.5(Disregard squares of small quantities). Chapter 3 3.1.(220) 3.2.Counterclockwise sequence starting with the front plane: (1010):(0110);(1100);(1010):(0110):(1100) 3.3.(a)a=60(equilateral triangles!);B=120 (b)a=109.47° 3.4.2(not6) 3.5.1/3,2/3,1/2 3.6.Hint:Draw two triangles,one vertically between the A and B planes and the other within the B plane. 3.7.[100K100)
Appendix IV 2.1. 0.77 (m) 2.2. 75% 2.3. 0.114 (cm) (Not 0.1195 cm!) 2.4. 1.26 104 (N) 2.5. 36% 2.6. 703.1 (MPa) 2.7. 0.233 2.8. V 0 2.10. t 10.26% 10.8% t 105.8 (MPa) 95.49 (MPa) 2.11. 3.998 (cm) 2.12. l 1.502 (m) 254.6 MPa (300 MPa) 2.13. 0.292 2.14. 0.5 (Disregard squares of small quantities). 3.1. (220) 3.2. Counterclockwise sequence starting with the front plane: (1010); (0110); (1100); (1010); (0110); (1100) 3.3. (a) 60° (equilateral triangles!); 120° (b) 109.47° 3.4. 2 (not 6!) 3.5. 1/3, 2/3, 1/2 3.6. Hint: Draw two triangles, one vertically between the A and B planes and the other within the B plane. 3.7. {100} 100 Chapter 2 Solutions to Selected Problems Chapter 3
Appendix IV.Solutions to Selected Problems 423 3.8.[111]direction(close packed)lies in (110)plane(not close packed) 3.9.CsCl (a)=8;(b)one Cs and one Cl ion(c)ao=2(r+R)/V3 NaCl (a)=6;(b)4 Cl ions and 4 Na ions (c)ao=2(r+R) 3.10.(a)Each Zn ion has four nearest S ions. (b)Four Zn ions and four S ions,that is,eight ions. (c)ao=4(r+R)/V3 3.11.0.34 3.12.(a)0.707;(b)0.866 3.13.(a)0.340;(b)0.907 3.14.8.933(g/cm3) 3.15.[1100] V2 3.16.a 2 Chapter 5 5.1.Liquid:54.5% Solid:45.5% 5.2.Peritectic at 799C: a+L→B Peritectic at756°C: B+L→Y Peritectoid at640°C: y+e→g Eutectic-type (not named)at 640C: y→e+L Peritectoid at 590C: y+→8 Eutectoid at 586C: B→a+y Eutectoid at 582C: g→8+e Eutectoid at520°C: y→a+8 Peritectic at415°C: e+L→7 Eutectoid at350°C: 8→a+e Eutectic at227°C: L→m+B-Sn Peritectoid at189°C: e+→7 Eutectoid at 186C: 7→n'+B-Sn Nonstoichiometric phase e forms at 676C Allotropic transformation from B-Sn-a-Sn at 13.2C Note:Some transformations are hardly discernible in Fig- ure5.17. 5.3.(a)8.8 mass Cu in Ag at 780C (b)8.0 mass Ag in Cu at 780C 5.4.negligible 5.5.a+0 Ca=1.5 mass Cu Co=52 mass Cu 5.6.About850°C 5.7.No 5.8.(a)780°C (b)Ag-28.1 mass Cu (c)About830°C (d)About 6 mass Cu
3.8. [111] direction (close packed) lies in (110) plane (not close packed) 3.9. CsCl (a) 8; (b) one Cs and one Cl ion (c) a0 2(r R)/3 NaCl (a) 6; (b) 4 Cl ions and 4 Na ions (c) a0 2(r R) 3.10. (a) Each Zn ion has four nearest S ions. (b) Four Zn ions and four S ions, that is, eight ions. (c) a0 4(r R)/3 3.11. 0.34 3.12. (a) 0.707; (b) 0.866 3.13. (a) 0.340; (b) 0.907 3.14. 8.933 (g/cm3) 3.15. [1100] 3.16. a 2 2 5.1. Liquid: 54.5% Solid: 45.5% 5.2. Peritectic at 799°C: L Peritectic at 756°C: L Peritectoid at 640°C: Eutectic-type (not named) at 640°C: L Peritectoid at 590°C: Eutectoid at 586°C: Eutectoid at 582°C: Eutectoid at 520°C: Peritectic at 415°C: L Eutectoid at 350°C: Eutectic at 227°C: L -Sn Peritectoid at 189°C: Eutectoid at 186°C: -Sn Nonstoichiometric phase forms at 676°C Allotropic transformation from -Sn -Sn at 13.2°C Note: Some transformations are hardly discernible in Figure 5.17. 5.3. (a) 8.8 mass % Cu in Ag at 780°C (b) 8.0 mass % Ag in Cu at 780°C 5.4. negligible 5.5. C 1.5 mass % Cu C 52 mass % Cu 5.6. About 850°C 5.7. No 5.8. (a) 780°C (b) Ag–28.1 mass % Cu (c) About 830°C (d) About 6 mass % Cu Chapter 5 Appendix IV • Solutions to Selected Problems 423
