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
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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
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