《固体化学》课程教学课件（英文讲稿）Chapter 5 Bonding in Soilds and Electronic Properties

Bonding in solids and electronic propertiesINTRODUCTIONIn the first chapter we learned the physicastructure of solids - how their atoms arearranged in space. We now turntoaof thedescriptionbondinginsolids-theelectronicstructureTo illustrate how thissbondingisreflectedinthe of thesolids,propertieswe exploreelectronic properties of various types of solid

Bonding in solids and electronic properties INTRODUCTION In the first chapter we learned the physical structure of solids – how their atoms are arranged in space. We now turn to a description of the bonding in solids-the electronic structure. To illustrate how this bonding is reflected in the properties of the solids, we explore electronic properties of various types of solid

Bonding in solids and electronic propertiesFree electron theoryThe free electron model regards a metal as abox in which electrons are free to roamunaffectedbytheatomicnucleiorbyeachotherThe model assumes that the nuclei stay fixedon their lattice sites surrounded by the inner orcore electrons while the outer orvalenceelectrons travel freely through the solid

Bonding in solids and electronic properties Free electron theory The free electron model regards a metal as a box in which electrons are free to roam unaffected by the atomic nuclei or by each other. The model assumes that the nuclei stay fixed on their lattice sites surrounded by the inner or core electrons while the outer or valence electrons travel freely through the solid

Electronisconfined to a lineof lengtha.V(x)Schrodingereguation-h? d'yd2,-2m.EU(E-V)yy2m。dx?dr?h2Electronisnotallowedoutsidethebox,sothepotential is o outsidethebox.>xO1X=LEnergy is quantized,with quantum numbers n.222h?n?h?nbnnEIn 1d:EIn 3d:22628mc8m.aawhere h is Plank's constant divided by 2T, me is theismass of the electron, V is the el'ctrical potential.the wave function of the electron and E is the energyof an electron with that wave function

where h is Plank’s constant divided by 2π, me is the mass of the electron, V is the electrical potential, is the wave function of the electron and E is the energy of an electron with that wave function

OOnedimentionalx≤0V(x) = 001II0<x<1(I1)V(x)=0V(a)(i)x≥V(x) = 00Schrodinger equation1x0h?d?V(x)y(x) = Ey(x)8元2m dx2In I and Ill area:1 dy(x)y(x)=V(x) = 00dx?8h?d'y(x):(00 - E)y(x) = 00 y(x)-dx?8元my(x) = 0

(I) (II) (III) One dimentional Schrodinger equation 2 2 2 2 ( ) ( ) ( ) 8 h d V x x E x m dx             2 2 2 2 ( ) ( ) ( ) ( ) 8 h d x E x x m dx          V x( )   In I and III area:

In II area:8V(x)= 0h?d?y(x)= Ey(x)8元*m dx2IIV(x)8元mEk2h?dy(x)1+ky(x)=0x0dr2y(x)=Acoskar+BsinkarAcos0+Bsino=0A=0y(0) = 0 B+0sin kl = 0y=0B sin kl=0

In II area:

sinkl=0IIn元V(x)k=(n=0,±1,±2,...n±0n=-1与n=1Samestate10xn元=Bsinx22n元By(x)dx=7dx=l normalizatioKsin2n'h?n元n =1, 2, 3, ...E=sinX8ml2WaveFunctionParticleenergy

y()12y (a)1=4E=16E,n=3E=9En=2E,=4E,h+n=1E8ml0xxn'h?E=n =1, 2, 3..8ml2n'h?(2n+1)h2(n+l)"h2AE=En+1 -E,8ml28ml28ml2

In one dimentional:h22TXE,sinn=1u8ml21122元X4h2sinE2n=22718ml?9h?23n=3E3sin8ml21

In one dimentional:

cCcCCCCCHE元41II4/9E1/9E31111BAh?A:E.=4E.= 48ml2h?22 h2h?8h?2 10B :E+ 2E= 29 8ml29 8ml298m(31)28m(31)2

C C C C C C C C E 1 4/9 E 1 1/9 E 1 4  4 l l l 3 l 2 1 2 4 4 8 a h E E ml   2 2 2 2 2 2 2 2 2 1 2 2 8 10 2 2 8 (3 ) 8 (3 ) 9 8 9 8 9 b h h h h E E m l m l ml ml      A B A ： B ：

Quiz:CH=CHCH=NR2xi+x=b0X福a = 247.8pmb=561.4pm?2k?1?2?3

Quiz： ？ k  1 ？ 2 ？ 3 ？