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METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
METALURGIA FÍSICA Primeira Parte: A Relação Estrutura-Propriedade Segunda Parte: A Microestrutura de Materiais
Terceira Parte: Transformações de Fase
Quarta Parte: Deformação Plástica
Quinta Parte: Endurecimento
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Terceira Parte: Transformações de Fase Difusão atômica Diagramas de equilíbrioTransformações de fase
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Difusão
Difusão - transporte de massa por movimento atômico
Mecanismos • Gases & Líquidos – movimento aleatório (Browniano) • Sólidos – difusão por lacunas ou difusão intersticial
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
• Interdiffusion: In an alloy, atoms tend to migrate
from regions of high conc. toregions of low conc.
Initially After some time
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
• Self-diffusion: In an elemental solid, atoms
also migrate.
Label some atoms After some time
C A D B
C
A B D
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Mecanismos de Difusão
Vacancy Diffusion:
• atoms exchange with vacancies • applies to substitutional impurities atoms • ratedepends on: --number of vacancies --activation energy to exchange.
increasing elapsed time
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Simulação da Difusão
• Simulation of interdiffusion across an interface: • Rate of substitutional diffusion depends on:
--vacancy concentration --frequency of jumping.
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Mecanismos de Difusão
•Interstitial diffusion – smaller atoms can diffuse between atoms.
More rapid than vacancy diffusion
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Processos que usam a difusão
• Case Hardening:
--Diffuse carbon atoms into the host iron atoms at the surface. --Example of interstitial diffusion is a case hardened gear.
• Result: The presence of C atoms makes iron (steel) harder. METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
• Doping silicon with phosphorus for n-type semiconductors: 0.5 mm • Process:
1. Deposit P rich layers on surface.
magnified image of a computer chip
silicon
2. Heat it. 3. Result: Doped semiconductor regions.
light regions: Si atoms
silicon
light regions: Al atoms
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Difusão
• How do wequantify the amount or rate of diffusion?
J
Flux
moles (or mass) diffusing surface area time
mol cm s
2
or
kg m2 s
• Measured empirically
– Make thin film (membrane) of known surface area – Impose concentration gradient – Measure how fast atoms or molecules diffuse through the membrane M= mass diffused
J
M At
l dM A dt
J
time
slope
METALURGIA FÍSICA PROF.LEONARDO B. GODEFROID
Difusão Estacionária
Rate of diffusion independent of time
dC Flux proportional to concentration gradient = dx
C1 C1
Fick’s first law of diffusion
C2 x1 x2
C2
J
dC D dx
x
if linear
dC dx
C x
C2 C1 x 2 x1
D
diffusion coefficient
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Exemplo: Revestimento protetivo químico (CPC)
•Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. • If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove? • Data: – diffusion coefficient in butyl rubber: D = 110 x10-8 cm2/s – surface concentrations: C1= 0.44 g/cm3 C2 = 0.02 g/cm3
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Exemplo (cont.)
• Solution – assuming linear conc. gradient
glove C1
tb 2 6D
J
paint remover
skin
C2
dC -D dx
C2 C1 D x 2 x1
Data:
x1 x 2
D = 110 x 10-8 cm2/s C1 = 0.44 g/cm3 C2 = 0.02 g/cm3 x2 – x1 = 0.04 cm
1.16 x 10 -5 g cm2s
J
(110 x 10
-8
(0.02 g/cm 3 0.44 g/cm 3 ) cm...
METALURGIA FÍSICA Primeira Parte: A Relação Estrutura-Propriedade Segunda Parte: A Microestrutura de Materiais
Terceira Parte: Transformações de Fase
Quarta Parte: Deformação Plástica
Quinta Parte: Endurecimento
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Terceira Parte: Transformações de Fase Difusão atômica Diagramas de equilíbrioTransformações de fase
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Difusão
Difusão - transporte de massa por movimento atômico
Mecanismos • Gases & Líquidos – movimento aleatório (Browniano) • Sólidos – difusão por lacunas ou difusão intersticial
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
• Interdiffusion: In an alloy, atoms tend to migrate
from regions of high conc. toregions of low conc.
Initially After some time
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
• Self-diffusion: In an elemental solid, atoms
also migrate.
Label some atoms After some time
C A D B
C
A B D
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Mecanismos de Difusão
Vacancy Diffusion:
• atoms exchange with vacancies • applies to substitutional impurities atoms • ratedepends on: --number of vacancies --activation energy to exchange.
increasing elapsed time
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Simulação da Difusão
• Simulation of interdiffusion across an interface: • Rate of substitutional diffusion depends on:
--vacancy concentration --frequency of jumping.
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Mecanismos de Difusão
•Interstitial diffusion – smaller atoms can diffuse between atoms.
More rapid than vacancy diffusion
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Processos que usam a difusão
• Case Hardening:
--Diffuse carbon atoms into the host iron atoms at the surface. --Example of interstitial diffusion is a case hardened gear.
• Result: The presence of C atoms makes iron (steel) harder. METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
• Doping silicon with phosphorus for n-type semiconductors: 0.5 mm • Process:
1. Deposit P rich layers on surface.
magnified image of a computer chip
silicon
2. Heat it. 3. Result: Doped semiconductor regions.
light regions: Si atoms
silicon
light regions: Al atoms
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Difusão
• How do wequantify the amount or rate of diffusion?
J
Flux
moles (or mass) diffusing surface area time
mol cm s
2
or
kg m2 s
• Measured empirically
– Make thin film (membrane) of known surface area – Impose concentration gradient – Measure how fast atoms or molecules diffuse through the membrane M= mass diffused
J
M At
l dM A dt
J
time
slope
METALURGIA FÍSICA PROF.LEONARDO B. GODEFROID
Difusão Estacionária
Rate of diffusion independent of time
dC Flux proportional to concentration gradient = dx
C1 C1
Fick’s first law of diffusion
C2 x1 x2
C2
J
dC D dx
x
if linear
dC dx
C x
C2 C1 x 2 x1
D
diffusion coefficient
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Exemplo: Revestimento protetivo químico (CPC)
•Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. • If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove? • Data: – diffusion coefficient in butyl rubber: D = 110 x10-8 cm2/s – surface concentrations: C1= 0.44 g/cm3 C2 = 0.02 g/cm3
METALURGIA FÍSICA PROF. LEONARDO B. GODEFROID
Exemplo (cont.)
• Solution – assuming linear conc. gradient
glove C1
tb 2 6D
J
paint remover
skin
C2
dC -D dx
C2 C1 D x 2 x1
Data:
x1 x 2
D = 110 x 10-8 cm2/s C1 = 0.44 g/cm3 C2 = 0.02 g/cm3 x2 – x1 = 0.04 cm
1.16 x 10 -5 g cm2s
J
(110 x 10
-8
(0.02 g/cm 3 0.44 g/cm 3 ) cm...
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