INTRODUINTRODUÇÇÃO A CIÊNCIA DOS MATERIAISÃO A CIÊNCIA DOS MATERIAIS

Prof. Aguinaldo M. SeverinoLaboratório de Magnetismo e Materiais Magnéticos – UFSM

© Adalberto Fazzio – IF USP (2005-2007) NOTAS DE AULA

© WILLIAM D CALLISTER JR. Ciência e Engenharia dos Materiais: Uma Introdução

seminários: quintas-feiras (13h30min às 15h30min)

Bibliografia Principal•HUMMEL, Rolf. E., Understanding Materials Science 2a ed.,

New York, Springer Verlag, 2004, ISBN: 0-387-20939-5

CALLISTER JR., WILLIAM D., Ciência e Engenharia dos

Materiais: Uma Introdução, 1a ed., Rio de Janeiro, LTC, 2002,

ISBN: 85-216-2188-5

Bibliografia Auxiliar•VAN VLACK, LAWRENCE H., Princípios de Ciência e Tecnologia de Materiais, 1a ed., São Paulo, Editora Campus, 1994, ISBN: 85-700-1480-5•WHITE, Mary A., Properties of Materials, 1a ed., New York, Oxford University Press, 1999, ISBN: 0-19-511331-4•CALLISTER JR., WILLIAM D., Fundamentos da Ciência e Engenharia dos Materiais, 2a ed., Rio de Janeiro, LTC, 2006, ISBN: 85-216-1515-9

Materials are...

engineered structures...not blackboxes!

Structure...has many dimensions...

Structural feature Dimension (m)

atomic bonding

missing/extra atoms

crystals (ordered atoms)

second phase particles

crystal texturing

< 10 -10

10-10

10-8-10-1

10-8-10-4

> 10-6

1

CHAPTER 1: MATERIALS SCIENCE

& ENGINEERING

• Use the right material for the job.

• Understand the relation between properties,

structure, and processing.

• Recognize new design opportunities offered

by materials selection.

Course Goals:

9

SUMMARY

• What promotes bonding?

• What types of bonds are there?

• What properties are inferred from

bonding?

1

CHAPTER 2:

BONDING AND PROPERTIES

14

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large!

Variablelarge-Diamondsmall-Bismuth

Variablelarge-Tungstensmall-Mercury

smallest

Comments

Nondirectional (ceramics)

Directional

semiconductors, ceramicspolymer chains)

Nondirectional (metals)

Directionalinter-chain (polymer)

inter-molecular

SUMMARY: BONDING

18

Ceramics

(Ionic & covalent bonding):

Metals

(Metallic bonding):

Polymers(Covalent & Secondary):

secondary bonding

Large bond energylarge Tm

large E

small α

Variable bond energymoderate Tm

moderate E

moderate α

Directional PropertiesSecondary bonding dominates

small T

small E

large α

SUMMARY: PRIMARY BONDS

ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...

• How do atoms assemble into solid structures?

(for now, focus on metals)

• How does the density of a material depend on

its structure?

• When do material properties vary with the

sample (i.e., part) orientation?

1

CHAPTER 3: CRYSTAL

STRUCTURES & PROPERTIES

• Atoms may assemble into crystalline or

amorphous structures.

• We can predict the density of a material,

provided we know the atomic weight, atomic

radius, and crystal geometry (e.g., FCC,

BCC, HCP).

• Material properties generally vary with single

crystal orientation (i.e., they are anisotropic),

but properties are generally non-directional

(i.e., they are isotropic) in polycrystals with

randomly oriented grains.

23

SUMMARY

i

READING SCHEDULE

2212Economic & Environmental Issues; Materials Selection

20 e 2111Magnetic & Optical Properties

17, 18 e 1910Corrosion; Electrical & Thermal Properties

15 e 169Structure, Properties, Process of Polymers and Composites

12 e 138Structure, Properties, Process and Applications of Ceramics

117Processing & Applications of Metals

106Kinetics & Phase Transformations

95Phase Diagrams

7 e 84Strengthening Mechanisms; Failure

5 e 63Diffusion; Mechanical Properties

3 e 42Crystalline Structure; Imperfections

1 e 21General Introduction Atomic Bonding

-0Introduction

chapterweekReading Schedule

CALLISTER JR., WILLIAM D., Ciência e Engenharia dos Materiais: Uma

Introdução, 1a ed., Rio de Janeiro, LTC, 2002, ISBN: 85-216-2188-5

ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...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?

1

• Are defects undesirable?

CHAPTER 4:

IMPERFECTIONS IN SOLIDS

2

• Vacancy atoms

• Interstitial atoms

• Substitutional atoms

• Dislocations

• Grain Boundaries

Point defects

Line defects

Area defects

TYPES OF IMPERFECTIONS

3

• Vacancies:-vacant atomic sites in a structure.

Vacancydistortion of planes

• Self-Interstitials:-"extra" atoms positioned between atomic sites.

self-interstitialdistortion

of planes

POINT DEFECTS

Boltzmann's constant

(1.38 x 10-23 J/atom K)

(8.62 x 10-5 eV/atom K)

ND

N= exp

−QD

kT

No. of defects

No. of potential defect sites.

Activation energy

Temperature

Each lattice site is a potential vacancy site

4

• Equilibrium concentration varies with temperature!

EQUIL. CONCENTRATION:

POINT DEFECTS

5

• We can get Q from

an experiment. ND

N= exp

−QD

kT

• Measure this... • Replot it...

1/T

N

NDln

1

-QD/k

slopeND

N

T

exponential dependence!

defect concentration

MEASURING ACTIVATION ENERGY

6

• Find the equil. # of vacancies in 1m of Cu at 1000C.

• Given:

3

ACu = 63.5g/molρ = 8.4 g/cm3

QV = 0.9eV/atom NA = 6.02 x 1023 atoms/mole

8.62 x 10-5 eV/atom-K

0.9eV/atom

1273K

ND

N= exp

−QD

kT

For 1m3, N =NA

ACuρ x x 1m3 = 8.0 x 1028 sites

= 2.7 · 10-4

• Answer:

ND = 2.7 · 10-4 · 8.0 x 1028 sites = 2.2x 1025 vacancies

ESTIMATING VACANCY CONC.

7

• Low energy electron

microscope view of

a (110) surface of NiAl.

• Increasing T causes

surface island of

atoms to grow.

• Why? The equil. vacancyconc. increases via atom

motion from the crystal

to the surface, where

they join the island.

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

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 µm by 5.75 µm.) Copyright (2001) Macmillan

Publishers, Ltd.

OBSERVING EQUIL. VACANCY CONC.

8

Two outcomes if impurity (B) added to host (A):• Solid solution of B in A (i.e., random dist. of point defects)

• Solid solution of B in A plus particles of a new

phase (usually for a larger amount of B)

OR

Substitutional alloy

(e.g., Cu in Ni)

Interstitial alloy

(e.g., C in Fe)

Second phase particle

--different composition

--often different structure.

POINT DEFECTS IN ALLOYS

9

• Low energy electron

microscope view of

a (111) surface of Cu.

• Sn islands move along

the surface and "alloy"

the Cu with Sn atoms,

to make "bronze".

• The islands continually

move into "unalloyed"

regions and leave tiny

bronze particles in

their wake.

• Eventually, the islands

disappear.

Reprinted with permission from: A.K. Schmid,

N.C. Bartelt, and R.Q. Hwang, "Alloying at

Surfaces by the Migration of Reactive Two-

Dimensional Islands", Science, Vol. 290, No.

5496, pp. 1561-64 (2000). Field of view is 1.5

µm and the temperature is 290K.

ALLOYING A SURFACE

10

Definition: Amount of impurity (B) and host (A)

in the system.

• Weight %

Two descriptions:

• Atom %

CB = mass of B

total massx 100 C'B =

# atoms of B

total # atomsx 100

• Conversion between wt % and at% in an A-B alloy:

CB = C'BAB

C'AAA + C'BABx 100 C'B =

CB/AB

CA/AA + CB/AB

• Basis for conversion:

mass of B = moles of B x AB

atomic weight of B

mass of A = moles of A x AA

atomic weight of A

COMPOSITION

11

• are line defects,

• cause slip between crystal plane when they move,

• produce permanent (plastic) deformation.

Dislocations:

Schematic of a Zinc (HCP):

• before deformation • after tensile elongation

slip steps

LINE DEFECTS

12

• Dislocations slip planes incrementally...• The dislocation line (the moving red dot)......separates slipped material on the left

from unslipped material on the right.

Simulation of dislocation

motion from left to right

as a crystal is sheared.

(animação 4_.avi)

(Courtesy P.M. Anderson)

INCREMENTAL SLIP

13

• 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)

BOND BREAKING AND REMAKING

14

• Structure: close-packed

planes & directions

are preferred.

• Comparison among crystal structures:FCC: many close-packed planes/directions;

HCP: only one plane, 3 directions;

BCC: none

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

close-packed directions

Mg (HCP)

Al (FCC)

tensile direction

• Results of tensile

testing.

view onto two

close-packed

planes.

DISLOCATIONS & CRYSTAL STRUCTURE

15

Grain boundaries:• are boundaries between crystals.

• are produced by the solidification process, for example.

• have a change in crystal orientation across them.

• impede dislocation motion.

grain boundaries

heat flow

Schematic

Adapted from Fig. 4.7, Callister 6e.Adapted from Fig. 4.10, Callister 6e.

(Fig. 4.10 is from Metals Handbook, Vol. 9, 9th edition, Metallography and Microstructures, Am. Society for Metals, Metals Park, OH, 1985.)

~ 8cmMetal Ingot

AREA DEFECTS: GRAIN BOUNDARIES

16

• Useful up to 2000X magnification.

• Polishing removes surface features (e.g., scratches)

• Etching changes reflectance, depending on crystal

orientation.microscope

close-packed planes

micrograph of

Brass (Cu and Zn)

Adapted from Fig. 4.11(b) and (c),

Callister 6e. (Fig. 4.11(c) is courtesy

of J.E. Burke, General Electric Co.

0.75mm

OPTICAL MICROSCOPY (1)

Fe-Cr alloy

microscope

grain boundary

surface groove

polished surface

17

Grain boundaries...

• are imperfections,

• are more susceptible

to etching,

• may be revealed as

dark lines,

• change direction in a

polycrystal.Adapted from Fig. 4.12(a)

and (b), Callister 6e.(Fig. 4.12(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].)

ASTM grain size number

N = 2n-1

no. grains/in2 at 100x magnification

OPTICAL MICROSCOPY (2)

18

• Point, Line, and Area defects arise 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

ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...

• How does diffusion occur?

• Why is it an important part of processing?

• How can the rate of diffusion be predicted for

some simple cases?

1

• How does diffusion depend on structure

and temperature?

CHAPTER 5:

DIFFUSION IN SOLIDS

2

• Glass tube filled with water.

• At time t = 0, add some drops of ink to one end

of the tube.

• Measure the diffusion distance, x, over some time.

• Compare the results with theory.

to

t1

t2

t3

xo x1 x2 x3time (s)

x (mm)

DIFFUSION DEMO

100%

Concentration Profiles0

Cu Ni

3

• Interdiffusion: In an alloy, atoms tend to migratefrom regions of large concentration.

Initially After some time

100%

Concentration Profiles0

Adapted

from Figs.

5.1 and 5.2,

Callister 6e.

DIFFUSION: THE PHENOMENA (1)

4

• Self-diffusion: In an elemental solid, atomsalso migrate.

Label some atoms After some time

A

B

C

DA

B

C

D

DIFFUSION: THE PHENOMENA (2)

5

Substitutional Diffusion:

• applies to substitutional impurities

• atoms exchange with vacancies

• rate depends on:

--number of vacancies

--activation energy to exchange.

increasing elapsed time

DIFFUSION MECHANISMS

6

• Simulation of

interdiffusion

across an interface:

• Rate of substitutional

diffusion depends on:--vacancy concentration

--frequency of jumping.

(Courtesy P.M. Anderson)

(animação 5_6.avi)

DIFFUSION SIMULATION

7

(Courtesy P.M. Anderson)

(animação 5_7.avi)

• Applies to interstitial

impurities.

• More rapid than

vacancy diffusion.

• Simulation:--shows the jumping of a

smaller atom (gray) from

one interstitial site to

another in a BCC

structure. The

interstitial sites

considered here are

at midpoints along the

unit cell edges.

INTERSTITIAL SIMULATION

• Case Hardening:--Diffuse carbon atoms

into the host iron atoms

at the surface.

--Example of interstitial

diffusion is a case

hardened gear.

• Result: The "Case" is--hard to deform: C atoms

"lock" planes from shearing.

--hard to crack: C atoms put

the surface in compression.

8

Fig. 5.0,

Callister 6e.(Fig. 5.0 is

courtesy of

Surface

Division,

Midland-

Ross.)

PROCESSING USING DIFFUSION (1)

• Doping Silicon with P for n-type semiconductors:

• Process:

9

1. Deposit P rich

layers on surface.

2. Heat it.

3. Result: Doped

semiconductor

regions.

silicon

silicon

magnified image of a computer chip

0.5mm

light regions: Si atoms

light regions: Al atoms

Fig. 18.0,

Callister 6e.

PROCESSING USING DIFFUSION (2)

• Flux:

10

J =

1

A

dM

dt⇒

kg

m2s

or

atoms

m2s

• Directional Quantity

• Flux can be measured for:--vacancies

--host (A) atoms

--impurity (B) atoms

Jx

Jy

Jz x

y

z

x-direction

Unit area A through which atoms move.

MODELING DIFFUSION: FLUX

• Concentration Profile, C(x): [kg/m3]

11

• Fick's First Law:

Concentration

of Cu [kg/m3]

Concentration

of Ni [kg/m3]

Position, x

Cu flux Ni flux

• The steeper the concentration profile,

the greater the flux!

Adapted

from Fig.

5.2(c),

Callister 6e.

Jx = −D

dC

dx

Diffusion coefficient [m2/s]

concentration

gradient [kg/m4]

flux in x-dir.

[kg/m2-s]

CONCENTRATION PROFILES & FLUX

• Steady State: the concentration profile doesn't change with time.

12

• Apply Fick's First Law:

• Result: the slope, dC/dx, must be constant

(i.e., slope doesn't vary with position)!

Jx(left) = Jx(right)

Steady State:

Concentration, C, in the box doesn’t change w/time.

Jx(right)Jx(left)

x

Jx = −D

dC

dx

dC

dx

left

=dC

dx

right

• If Jx)left = Jx)right , then

STEADY STATE DIFFUSION

• Steel plate at

700C with

geometry

shown:

13

• Q: How much

carbon transfers

from the rich to

the deficient side?J = −D

C2 −C1

x2 − x1= 2.4 ×10

−9 kg

m2s

Adapted

from Fig.

5.4,

Callister 6e.

C1 = 1.2

kg/m3

C2 = 0.8

kg/m3

Carbon rich gas

10mm

Carbon deficient

gas

x1 x205mm

D=3x10-11m2/s

Steady State = straight line!

EX: STEADY STATE DIFFUSION

• Concentration profile,

C(x), changes

w/ time.

14

• To conserve matter: • Fick's First Law:

• Governing Eqn.:

Concentration, C, in the box

J(right)J(left)

dx

dC

dt=D

d2C

dx2

−

dx= −

dC

dtJ = −D

dC

dxor

J(left)J(right)

dJ

dx

= −dC

dt

dJ

dx

= −Dd2C

dx2

(if D does not vary with x)

equate

NON STEADY STATE DIFFUSION

• Copper diffuses into a bar of aluminum.

15

• General solution:

"error function"

Values calibrated in Table 5.1, Callister 6e.

C(x,t) −Co

Cs −Co

= 1− erfx

2 Dt

pre-existing conc., Co of copper atoms

Surface conc., Cs of Cu atoms

bar

Co

Cs

position, x

C(x,t)

tot1

t2t3 Adapted from

Fig. 5.5,

Callister 6e.

EX: NON STEADY STATE

DIFFUSION

• Copper diffuses into a bar of aluminum.

• 10 hours at 600C gives desired C(x).

• How many hours would it take to get the same C(x)

if we processed at 500C?

16

(Dt)500ºC =(Dt)600ºC

s

C(x,t)−Co

C − Co

= 1−erfx

2Dt

• Result: Dt should be held constant.

• Answer:Note: values

of D are

provided here.

Key point 1: C(x,t500C) = C(x,t600C).

Key point 2: Both cases have the same Co and Cs.

t500

=(Dt)

600

D500

= 110hr

4.8x10-14m2/s

5.3x10-13m2/s 10hrs

PROCESSING QUESTION

17

• The experiment: we recorded combinations oft and x that kept C constant.

to

t1

t2

t3

x o x 1 x 2 x3

• Diffusion depth given by:

xi ∝ Dti

C(xi, t i ) − Co

Cs − Co= 1− erf

xi

2 Dt i

= (constant here)

DIFFUSION DEMO: ANALYSIS

• Experimental result: x ~ t0.58

• Theory predicts x ~ t0.50

• Reasonable agreement!

18

BBBBBBBBBBBB

B

B

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3

ln[t(min)]

Linear regression fit to data:ln[x(mm)] = 0.58ln[t(min)] + 2.2

R2 = 0.999

DATA FROM DIFFUSION DEMO

• Diffusivity increases with T.

• Experimental Data:

1000K/T

D (m2/s) C in α-Fe

C in γ-Fe

Al in Al

Cu in Cu

Zn in

Cu

Fe in α-Fe

Fe in γ-F

e

0.5 1.0 1.5 2.010-20

10-14

10-8T(C)1

500

1000

600

300

D has exp. dependence on T

Recall: Vacancy does also!

19

pre-exponential [m2/s] (see Table 5.2, Callister 6e)activation energy

gas constant [8.31J/mol-K]

D= Doexp −Qd

RT

diffusivity[J/mol],[eV/mol] (see Table 5.2, Callister 6e)

Dinterstitial >> Dsubstitutional

C in α-FeC in γ-Fe Al in Al

Cu in Cu

Zn in Cu

Fe in α-FeFe in γ-Fe

Adapted from Fig. 5.7, Callister 6e. (Date for Fig. 5.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992.)

DIFFUSION AND TEMPERATURE

20

Diffusion FASTER for...

• open crystal structures

• lower melting T materials

• materials w/secondary

bonding

• smaller diffusing atoms

• cations

• lower density materials

Diffusion SLOWER for...

• close-packed structures

• higher melting T materials

• materials w/covalent

bonding

• larger diffusing atoms

• anions

• higher density materials

SUMMARY:

STRUCTURE & DIFFUSION

Até aqui, tudo bem

Obrigado !

Prof. Aguinaldo M Severino

MATERIAIS

Revolução industrial Revolução da informação

FORÇAS TÉCNOLÓGICAS REVOLUCIONÁRIAS

Têxt

il

Ferr

oviá

ria

Aut

omot

iva

Com

puta

dor

Nan

otec

nolo

gia

Introdução da tecnologia

Ampla utilização

Final do crescimento rápido

Ref: Milunovich S. and Roy J.M.A.: The Next Small Thing RC 30224705Merril Lynch, 4 September, 2001

© SIEMENS AG, CT, Manfred Weick Montag 1, Marz 2004

Grundlagen und State of he Art der Nanotehnologie.ppt