Solutions Manual for Introduction to Solid State Physics (9th Edition) - Kittel

ALL 22 CHAPTERS COVERED
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SOLUTIONS MANUAL
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,TABLEOFCONTENTS
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Chapter 1 - 1-1
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Chapter 2 - 2-1
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Chapter 3 - 3-1
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Chapter 4 - 4-1
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Chapter 5 - 5-1
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Chapter 6 - 6-1
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Chapter 7 - 7-1
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Chapter 8 - 8-1
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Chapter 9 - 9-1
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Chapter 10 - 10-1
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Chapter 11 - 11-1
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Chapter 12 - 12-1
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Chapter 13 - 13-1
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Chapter 14 - 14-1
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Chapter 15 - 15-1
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Chapter 16 - 16-1
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Chapter 17 - 17-1
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Chapter 18 - 18-1
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Chapter 20 - 20-1
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Chapter 21 - 21-1
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Chapter 22 - 22-1
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, CHAPTERj1

1. Thejvectorsj x̂jjyˆjjzˆj andj xˆjjyˆjjzˆj arejinjthejdirectionsjofjtwojbodyjdiagonalsjofja
cube.j Ifj j isj thej anglej betweenj them,j theirj scalarj productj givesj cosj j =j –1/3,j whence
jjcos11/j3jj90j19j28j'jj109j28j'j.

2. Thej planej (100)j isj normalj toj thej xj axis.j Itj interceptsj thej a'j axisj atj 2a'j andj thej c'j axis
atj 2c'j;j thereforej thej indicesj referredj toj thej primitivej axesj arej (101).j Similarly,j thej plane
(001)jwilljhavejindicesj(011)jwhenjreferredjtojprimitivejaxes.

3. Thejcentraljdotjofjthejfourjisjatjdistance


cosj60j aj
aj jajctnj60jj cosj3
0 3

fromjeachjofjthejotherjthreejdots,jasjprojectedjontojthejbasaljplane.jIfjthej(u
nprojected)jdotsjarejatjthejcenterjofjspheresjinjcontact,jthen
2
j aj 
2
jcj
a 2 j j 
j j jj ,
j

  j2j
3 j



or

2j 2 1j 2 c 8
a j j c ; j1.633.
3 4 a 3




1-1

, CHAPTERj2

1. Thejcrystalj planej withj Millerj indicesj hkAj isj aj planej definedj byj thej pointsj a1/h,j a2/k,j andj a3j/jAj.j (a)
Twojvectorsjthatjliejinjthejplanejmayjbejtakenjasja1/hj–
a2/kjandj a1j/h jja3j/jAj.jButjeachjofjthesejvectorsjgivesjzeroj asjitsj scalarjproductj withj Gjjha1jjka2jjAa3j,jsoj
j

thatjGj mustjbejperpendicularjtojthejplane
hkAj.j (b)j Ifj n̂j isj thej unitj normalj toj thej plane,j thej interplanarj spacingj isj n̂jja1/hj.j Butj n̂j jGj/ | jGj|j,
whencejd(hkA)j jGjja1j/jh|G|jj2j/j|jG|j.j(c)jForjajsimplejcubicjlatticej Gjj(2j/ja )(hx̂ jjkyˆjjAẑ ) j,jwhence

G2 h jjk jjA
2 2 2
1j
j  .
d2 42 a2
1 1j
3a a 0
2 2
1 1j
2. (a)j Cellj volumejaj jaj jaj j j 3a a 0
1 2 3
2 2
0 0 c


1
j 3ja2c.
2

x̂ yˆ zˆ
a2j ja3 1 1j
(b) bj j2  4j3a j 3a a 0
1
|jaj jaj jaj | 2
c 2 2
1 2 3
0 0 c
2j 1ja
j (j x̂jjŷ ), jandjsimilarlyjforjb 2j,jb3.
3

(c) Sixjvectorsjinjthejreciprocaljlatticejarejshownjasjsolidjlines.jThejbrokenjlinesja
rejthejperpendicularjbisectorsjatjthejmidpoints.jThejinscribedjhexagonjformsjthejfi
rstjBrillouinjZone.

3. Byjdefinitionjofjthejprimitivejreciprocaljlatticejvectors
(a2j a 3 j)jj(a3j a 1 j)j(a1jja 2 j)j
V j(2)3j j(2)3j/j|j(aj jaj jaj )j|
BZ
|j(aj ja a j ) j| 3 1 2 3
1 2 3

j(2)3j/jVj .C

Forj thej vectorj identity,j seej G.j A.j Kornj andj T.j M.j Korn,j Mathematicalj handbookj forj scientistsj andjengin
eers,jMcGraw-Hill,j1961,jp.j147.

4. (a)jThisjfollowsjbyjforming




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