Metalurgia

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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...
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