고체물리 중간,기말고사

pdf : https://archive.org/stream/81060415IntroductionToSolidStatePhysics8thEditionByCharlesKittel/81060415-Introduction-to-Solid-State-Physics-8th-Edition-by-Charles-Kittel#mode/2up






solution :
https://www.slideshare.net/amnahnura/kittel-c-introduction-to-solid-state-physics-8-th-edition-solution-manual










1.  다이아몬드의 사면체 결합각은 그림 10 (10페이지) 에 있는 Body-Centered-Cubic의 체대각선 사이의 각도와 같다. 그 크기를 구하여라.

풀이

벡터 내적을 이용하여 사이각을 구했다.








벡터 내적 혹은 외적을 통해 결합각을 구할 수 있다.























2.  Consider the planes with indices (100) and (001) : the lattice is fcc, and the indices refer to the conventional cubic cell. What are the indices of theses planes when referred to the primitive axes of Fig.11 ?


fcc의 primitive 축에 대한 Miller index를 표현하라.

풀이

primitive axes 이
(1,0,0) 평면과 닿게하기


2a1 0 2a3
(2,0,2) >>> (1,0,1)






primitive axes 이
(0,0,1) 평면과 닿게하기


0 2a2 2a3
(0,2,2) >>> (0,1,1)

3.
Show that the c/a ratio for an ideal hexagonal close-packed structure is ~~~.
If c/a is significantly larger than this value , the crystal structure may be thought of as composed of planes of closely packed atoms, the planes being loosely stacked.




hcp = hexagonal close-packed structure

추가 문제
show that a honeycomb structure is not Bravais.
Identify its structure and basis.



lattice : 일정하게 배열된 점(lattice point)들의 집합
Basis : : Lattice에 동일하게 놓여질 원자무리






일단  honeycomb structure 는
two dimensional lattice types 에 포함되는 4가지에 포함되지 않는다.
게다가 honeycomb structure 의 primitive 으로 Lattice space를 가득 채울 수 없다.









참고 영상 : https://www.youtube.com/watch?v=I4VdRFpxLUQ

2장_1_a

2장_1_b

2장_1_C

2장_2_a

2장_2_b

1. ionization energy, cohesive energy

ionization energy : It is energy that required in taking an electron away from an atom.

cohesive energy : Energy required in taking a compound away from a crystal.

a compound (예 : an atom or nacl compound)

Melting temperature or bulk modulus vary roughly as cohesive energies.

2. What kind of binding is responsible for the following materials being a solid?

a. crystalline argon

Van der waals (relatively weak bonding)
Attractive interaction between non-polar molecules.

b. salt

It is ionically bonded solid.

NA+ (cation) , Cl-(anion)

c. sodium

Metallic bond
Delocalized valence electrons > electron gas(cloud) > collective sharing of electrons > close-packed crystal 

d. diamond

Formation of covalent bond(strong bonding) between carbon atoms.

3. Write down the Lennard-Jones potential and explain where each term is from.

The potential energy as a function of interatomic seperation can be modeled by the Lennard-Jones 6-12  potential energy curve.

Bonding occurs when the potential energy is  minimum. Therefore differentiate the Lennard_Jones potential and set it to zero at r=r0, then r0 is the stabilized radius.