고체 내의 결함(Imperfections in...

Chapter 4 - 1

ISSUES TO ADDRESS...

• What types of defects arise in solids?

• Can the number and type of defects be varied

and controlled?

• How do defects affect material properties?

• Are defects undesirable?

Chapter 4:

고체 내의 결함(Imperfections in Solids)

• What are the solidification mechanisms?

Chapter 4 - 2

학습목표...

1. 공공과 자기 침입형 결정 결함의 분석

2. 어떤 특정한 온도에서 재료의 공공의 평형 상수 계산

3. 두 고용체 형태의 명명과 각각의 짧은 정의와 도식적 그림

4. 합금에서 두 가지 또는 다른 요소들의 질량과 원자 무게가

주어질 때, 각 요소의 질량 비율과 원자 비율의 계산

5. 각 칼날, 나선, 합쳐진 전위에서 (a) 전위의 제도와 분석

(b) 전위선의 위치

(c) 전위선의 연장에 따른 방향 지시

6. (a) 결정립계와 (b) 쌍정 경계 근처의 원자 구조 분석

Chapter 4 - 3

• 응고(Solidification)- result of casting of molten material

– 2단계(steps)

• 핵의 생성(Nuclei form )

• 핵의 성장에 의한 결정의 생성(Nuclei grow to form crystals – grain structure)

• 융액으로부터 시작(Start with a molten material – all liquid)

고체 내의 결함(Imperfections in Solids)

• 결정의 성장(Crystals grow until they meet each other)

Adapted from Fig. 4.14(b), Callister & Rethwisch 8e.

grain structure crystals growing nuclei liquid

Chapter 4 - 4

다결정 재료(Polycrystalline Materials)

결정립계(Grain Boundaries)

• 2개의 결정립 사이에

존재하는 경계면

• 2개의 결정립 사이에

약간의 원자배열 상의

불일치가 존재

• 낮은 밀도

– 높은 이동도(high mobility)

– 높은 확산(high diffusivity)

– 높은 화학 반응성(high

chemical reactivity)

Adapted from Fig. 4.7,

Callister & Rethwisch 8e.

Chapter 4 - 5

응고(Solidification)

Columnar in

area with less

undercooling

Shell of

equiaxed grains

due to rapid

cooling (greater

T) near wall

Grain Refiner - added to make smaller, more uniform, equiaxed grains.

heat

flow

결정 – 등축 [equiaxed (roughly same size in all directions)]

– 주형 [columnar (elongated grains)]

Adapted from Fig. 5.17,

Callister & Rethwisch 3e.

~ 8 cm

Chapter 4 - 6

고체 내의 결함(Imperfections in Solids)

There is no such thing as a perfect crystal.

• What are these imperfections?

• Why are they important?

Many of the important properties of

materials are due to the presence of

imperfections.

Chapter 4 - 7

• 공공(Vacancy atoms)

• 침입형(Interstitial atoms)

• 치환형(Substitutional atoms)

점결함(Point defects)

결함의 종류(Types of Imperfections)

• 전위(Dislocations) 선결함(Line defects)

• 결정입계(Grain Boundaries) 면결함(Area defects)

Chapter 4 - 8

• 공공(Vacancies): -결정 내의 빈 격자점(vacant atomic sites in a structure).

• 자기 침입형(Self-Interstitials): -결정 원자가 침입형 자리로 이동

"extra" atoms positioned between atomic sites.

점결함(Point Defects in Metals)

Vacancy

distortion

of planes

self- interstitial

distortion of planes

Chapter 4 -

9

Boltzmann's constant

(1.38 x 10 -23

J/atom-K)

(8.62 x 10 -5

eV/atom-K)

N v

N = exp

Q v

k T

No. of defects

No. of potential defect sites

Activation energy

Temperature

Each lattice site is a potential vacancy site

• 평형 농도는 온도에 의존

(Equilibrium concentration varies with temperature!)

평형 농도(Equilibrium Concentration):

점 결함(Point Defects)

Chapter 4 - 10

• 실험에 의한 Qv 의 측정 N v

N = exp

Q v

k T

활성화 에너지 측정

(Measuring Activation Energy)

• 측정...

N v

N

T

exponential dependence!

defect concentration

• Replot it...

1/ T

N

N v ln

- Q v /k

slope

Chapter 4 - 11

• 1000C에서 1 m3 당 구리의 공공의 평형 개수 계산.

• 주어진 값: A Cu = 63.5 g/mol r = 8.4 g / cm 3

Q v = 0.9 eV/atom N A = 6.02 x 1023 atoms/mol

평형 공공 농도 계산

( Estimating Vacancy Concentration)

1 m3 당 , N = N

A

A Cu

r x x 1 m3 = 8.0 x 1028 sites/m3

= 2.7 x 10-4

8.62 x 10-5 eV/atom-K

0.9 eV/atom

1273 K

N v

N = exp

Q v

k T

• 정답:

N v = (2.7 x 10-4)(8.0 x 1028) sites/m3

= 2.2 x 1025 vacancies/m3

Chapter 4 - 12

• Low energy electron

microscope view of

a (110) surface of NiAl.

• Increasing temperature

causes surface island of

atoms to grow.

• Why? The equil. vacancy

conc. increases via atom

motion from the crystal

to the surface, where

they join the island. Reprinted with permission from Nature (K.F. McCarty,

J.A. Nobel, and N.C. Bartelt, "Vacancies in

Solids and the Stability of Surface Morphology",

Nature, Vol. 412, pp. 622-625 (2001). Image is

5.75 mm by 5.75 mm.) Copyright (2001) Macmillan

Publishers, Ltd.

평형 공공 농도의 관찰 (Observing Equilibrium Vacancy Conc.)

I sland grows/shrinks to maintain equil. vancancy conc. in the bulk.

Click once on image to start animation

Chapter 4 - 13

불순물(B)를 기지(A)에 첨가에 따른 2가지 결과물: • 고용체(Solid solution) of B in A (i.e., random dist. of point

defects)

• Solid solution of B in A + 제2상 (usually for a larger amount of

B)

OR

치환형 고용체

[Substitutional solid soln.

(e.g., Cu in Ni)]

침입형 고용체

[Interstitial solid soln.

(e.g., C in Fe)]

Second phase particle

-- different composition

-- often different structure.

금속 결함[Imperfections in Metals (i)]

Chapter 4 - 14

금속 결함[Imperfections in Metals (ii)]

치환형 고용체 결정 조건

• W. Hume – Rothery rule

– 1. 원자의 크기: r (atomic radius) < 15%

– 2. 전기 음성도(Proximity in periodic table)

• 전기 음성도 차가 작아야 함(i.e., similar electronegativities)

– 3. 결정 구조: 같은 결정 구조(Same crystal

structure)

– 4. 원자가(Valency)

• 위의 모든 요소가 동일하다면 금속은 낮은 원자가를 갖는

금속보다는 높은 원자가를 갖는 금속에 더 많이 용해

Chapter 4 - 15

금속결함[Imperfections in Metals (iii)]

Hume–Rothery 규칙의 응용 – 고용체

1. Would you predict

more Al or Ag

to dissolve in Zn?

2. More Zn or Al

in Cu?

Table on p. 118, Callister & Rethwisch 8e.

Element Atomic Crystal Electro- Valence

Radius Structure nega-

(nm) tivity

Cu 0.1278 FCC 1.9 +2

C 0.071

H 0.046

O 0.060

Ag 0.1445 FCC 1.9 +1

Al 0.1431 FCC 1.5 +3

Co 0.1253 HCP 1.8 +2

Cr 0.1249 BCC 1.6 +3

Fe 0.1241 BCC 1.8 +2

Ni 0.1246 FCC 1.8 +2

Pd 0.1376 FCC 2.2 +2

Zn 0.1332 HCP 1.6 +2

Chapter 4 - 16

고체 내의 불순물(Impurities in Solids)

• 조성의 표기

– 무게비(weight percent)

100x 21

11

mm

mC

=

m1 = 원소 1의 무게(mass of component 1)

100x 21

1'

1

mm

m

nn

nC

=

nm1 = 원소 1의 일정 무게의 몰수(number of moles of component 1)

– 원자비(atom percent)

Chapter 4 - 17

• 선결함,

• 전위의 이동에 따른 결정면 간 슬립(slip between crystal

planes result when dislocations move),

• 영구(소성)변형[permanent (plastic) deformation]

전위(Dislocations):

예) Zinc (HCP):

• 변형 전 • 인장 연신(tensile elongation) 후

slip steps

선 결함 (Line Defects)

Chapter 4 - 18

고체 내의 결함(Imperfections in Solids)

선 결함[Linear Defects (Dislocations)] – 일부 원자들의 정렬이 어긋난 선 결함 또는 1차원 결함

• 칼날 전위(Edge dislocation): – 잉여의 원자면 또는 반평면이 결정 내에 존재

– 버거스 벡터(b)는 전위선과 수직 ()

• 나선 전위(Screw dislocation): – 전단 변형에 의해 야기되는 뒤틀림

– b와 전위선은 평행 ()

Burger’s vector, b: 격자 변형의 크기와 방향을 나타냄

Chapter 4 - 19

고체 내의 결함(Imperfections in Solids)

Fig. 4.3, Callister & Rethwisch 8e.

칼날 전위(Edge Dislocation)

Chapter 4 - 20

• Dislocation motion requires the successive bumping

of a half plane of atoms (from left to right here).

• Bonds across the slipping planes are broken and

remade in succession.

Atomic view of edge

dislocation motion from

left to right as a crystal

is sheared.

(Courtesy P.M. Anderson)

칼날 전위의 이동(Motion of Edge Dislocation)

Click once on image to start animation

Chapter 4 - 21

Chapter 4 - 22

고체 내의 결함(Imperfections in Solids)

Screw Dislocation

Adapted from Fig. 4.4, Callister & Rethwisch 8e.

Burgers vector b

Dislocation

line

b

(a)

(b)

나선 전위(Screw Dislocation)

Chapter 4 - 23

Chapter 4 -

VMSE: Screw Dislocation

• In VMSE: – a region of crystal containing a dislocation can be rotated in 3D

– dislocation motion may be animated

24

Front View Top View VMSE Screen Shots

http://higheredbcs.wiley.com/legacy/college/callister/0470419970/vsme_gold/dislocations.htm

Chapter 4 - 25

Edge, Screw, and Mixed Dislocations

Adapted from Fig. 4.5, Callister & Rethwisch 8e.

Edge

Screw

Mixed

Chapter 4 - 26

고체 내의 결함(Imperfections in Solids)

투과 전자 현미경 사진(전위 선의 관찰)

Fig. 4.6, Callister & Rethwisch 8e.

Chapter 4 - 27

전위와 결정 구조(Dislocations & Crystal Structures)

• Structure: 조밀 면과 방향

(close-packed planes &

directions are preferred)

view onto two

close-packed

planes.

close-packed plane (bottom) close-packed plane (top)

close-packed directions

• 결정 구조 비교: FCC: 많은 조밀 면과 방향;

HCP: 오진 1면, 3 방향;

BCC: none

• 인장시험 Mg (HCP)

Al (FCC)

tensile direction

Chapter 4 - 28

고체의 면 결함(Planar Defects in Solids)

• 쌍정립계[twin boundary (plane)] – 입계 한쪽 면의 원자는 반대편 원자와 거울면(twin plane) 과 같은 대칭적인 위치.

• 적층 결함(Stacking faults) – FCC metals의 경우 ABCABC 적층의 순서에 결함

– Ex: ABCABABC

Adapted from Fig. 4.9,

Callister & Rethwisch 8e.

Chapter 4 - 29

촉매와 표면 결함(Catalysts and Surface Defects)

• 촉매(catalyst) 는 반응에

직접적인 반응물로

참여하지는 않지만, 화학

반응의 속도를

가속시키는 물질

• 촉매의 흡착은 보통 표면

원자들이 관여하는 결함

사이트에서 발생

Fig. 4.10, Callister & Rethwisch 8e.

Fig. 4.11, Callister & Rethwisch 8e.

Single crystals of

(Ce0.5Zr0.5)O2

used in an automotive

catalytic converter

Chapter 4 - 30

현미경관찰 (Microscopic Examination)

• 결정과 결정립계[Crystallites (grains) and grain boundaries.]

다양한 크기(Vary considerably in size. Can be quite large.)

– ex: Large single crystal of quartz or diamond or Si

– ex: Aluminum light post or garbage can - see the

individual grains

• 결정의 크기 : 수 mm 혹은 그 이하 –

광학현미경을 이용한 관찰 [Crystallites (grains) can be

quite small (mm or less) – necessary to observe with a microscope.]

Chapter 4 - 31

• 최대 2000배

• 표면을 거울 면과 같은 미세 연마

• 식각 : 결정의 화학적 반응은 결정학적 방위에 따라 차이 (Etching changes reflectance, depending on crystal orientation.)

Micrograph of

brass (a Cu-Zn alloy)

0.75mm

광학현미경(Optical Microscopy)

Adapted from Fig. 4.13(b) and (c), Callister

& Rethwisch 8e. (Fig. 4.13(c) is courtesy

of J.E. Burke, General Electric Co.)

crystallographic planes

Chapter 4 - 32

결정립계(Grain boundaries...)

• 결함 (are imperfections,)

• 쉽게 식각 (are more susceptible

to etching,)

• 검은 선 (may be revealed as

dark lines,)

• 결정립계- 결정의 위상 차

(change in crystal orientation

across boundary.) Adapted from Fig. 4.14(a)

and (b), Callister &

Rethwisch 8e.

(Fig. 4.14(b) is courtesy

of L.C. Smith and C. Brady,

the National Bureau of

Standards, Washington, DC

[now the National Institute of

Standards and Technology,

Gaithersburg, MD].)

광학현미경(Optical Microscopy)

ASTM grain size number

N = 2 n -1

number of grains/in2 at 100x magnification

Fe-Cr alloy (b)

grain boundary

surface groove

polished surface

(a)

Chapter 4 - 33

광학현미경(Optical Microscopy)

• 편광(Polarized light)

– metallographic scopes often use polarized

light to increase contrast

– Also used for transparent samples such as

polymers

Chapter 4 - 34

Microscopy

광학 분해능 (Optical resolution)

ca. 10-7 m = 0.1 mm = 100 nm

고해상도 – 높은 주파수

(For higher resolution need higher frequency)

– X-Rays? Difficult to focus

– Electrons

• wavelengths ca. 3 pm (0.003 nm)

– (Magnification - 1,000,000X)

• Atomic resolution possible

• Electron beam focused by magnetic lenses.

Chapter 4 - 35

• Atoms can be arranged and imaged!

Carbon monoxide

molecules arranged

on a platinum (111)

surface.

Photos produced from

the work of C.P. Lutz,

Zeppenfeld, and D.M.

Eigler. Reprinted with

permission from

International Business

Machines Corporation,

copyright 1995.

Iron atoms arranged

on a copper (111)

surface. These Kanji

characters represent

the word “atom”.

주사 탐침 현미경 [Scanning Tunneling Microscopy, (STM)]

Chapter 4 - 36

• Point, Line, and Area defects exist in solids.

• The number and type of defects can be varied

and controlled (e.g., T controls vacancy conc.)

• Defects affect material properties (e.g., grain

boundaries control crystal slip).

• Defects may be desirable or undesirable (e.g., dislocations may be good or bad, depending

on whether plastic deformation is desirable or not.)

Summary

Chapter 4 - 37

Core Problems:

Self-help Problems:

ANNOUNCEMENTS

Reading: