DIFFUSION IN SOLIDS  FICK’S LAWS  KIRKENDALL EFFECT  ATOMIC MECHANISMS Diffusion in Solids P.G. Shewmon McGraw-Hill, New York (1963)

Slides:



Advertisements
Similar presentations
Lecture on DIFFUSION IN SOLIDS. Applications of Diffusion in Solids
Advertisements

Diffusion (continued)
Lecture 3.
Chapter 6 Diffusion in Solids.
Chapter ISSUES TO ADDRESS... How does diffusion occur? Why is it an important part of processing? How can the rate of diffusion be predicted for.
Chapter 5: Thermally Activated Processes & Diffusion ME 2105 Dr. R. Lindeke.
Chapter ISSUES TO ADDRESS... How does diffusion occur? Why is it an important part of processing? How can the rate of diffusion be predicted for.
Fick’s Laws Combining the continuity equation with the first law, we obtain Fick’s second law:
Diffusion Movement of atoms in a material Thermal Energy = Atom Movement Eliminates concentration differences Important for material processing (heat treating,
Diffusion – And Its Role In Material Property Control
Chapter ISSUES TO ADDRESS... How does diffusion occur? Why is it an important part of processing? How can the rate of diffusion be predicted for.
Chapter 6: Diffusion.
Solid State Diffusion-1
CHAPTER 6: DIFFUSION IN SOLIDS
CHAPTER 5: DIFFUSION IN SOLIDS
Crystalline Arrangement of atoms. Chapter 4 IMPERFECTIONS IN SOLIDS The atomic arrangements in a crystalline lattice is almost always not perfect. The.
CHAPTER 5 Diffusion 5-1.
Diffusion Interdiffusion: In an alloy, atoms tend to migrate from regions of high concentration to regions of low concentration. Initially After some.
Thermally Activated Processes and Diffusion in Solids
Diffusion Diffusion means atoms moving and changing places. This happens in solids and liquids, exactly in the same way that an unpleasant smell moves.
ECE/ChE 4752: Microelectronics Processing Laboratory
THERMODYNAMIC MODELLING OF INTERDIFFUSION IN Fe-Co AND Fe-Ni BONDS Matej Pašák.
Chapter 5 Diffusion Skip Sec. 5-7, 5-8 and Homework No. 6 Problems 4-17, 4-19, 4-32, 4-47, 4-48, 5-9, 5-15, 5- 23, 5-26, 5-60.
ENS 205 Materials Science I Chapter 5: Diffusion
Anandh Subramaniam & Kantesh Balani
Chapter 5- 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.
Chapter 5 - Imperfections in Solids
1 Diffusion Diffusion: Atom and Ion Movements in Materials Applications of Diffusion  Nitriding - Carburization for Surface Hardening of Steels  p-n.
Introduction To Materials Science, Chapter 5, Diffusion University of Virginia, Dept. of Materials Science and Engineering 1 Diffusion  how atoms move.
Materials science I - Metallic materials Metallic materials Solid state atomic structure atomic arrangement microstructure macrostructure Pure materials.
Relative Energy Levels of Defects Information was extracted from: Porter and Easterling, Phase Transformations in Metals and Alloys, 2nd Edition, CRC Press,
Introduction Material transport by atomic motion Diffusion couple:
Diffusion. Diffusion: The motion of atoms through matter Diffusion Couple: An assembly of two materials in such intimate contact that each diffuse into.
V. Diffusion in Solids MECE 3345 Materials Science 1 VI. Diffusion in Solids copyright © 2008 by Li Sun.
Molecular Diffusion in Metal Alloys Aaron Morrison ME 447.
Diffusion videos YouTube: Diffusion posted by smcblackburn
Byeong-Joo Lee Byeong-Joo Lee POSTECH - MSE Diffusion.
CHAPTER 5 Diffusion 5-1. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Atomic Diffusion in Solids Diffusion.
CHE 333 CLASS 20 DIFFUSION.
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 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.
1 CHAPTER 7 Structure and Properties of Materials Defects and Properties : Point Defects and Diffusion.
ENGR-45_Lec-07_Diffusion_Fick-2.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical.
Diffusion (continued)
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?
Chapter 1 Diffusion in Solids. Diffusion - Introduction A phenomenon of material transport by atomic migration The mass transfer in macroscopic level.
Diffusion in interfaces on surfaces and along dislocations Grain Boundary Diffusion : Diffusion along grain boundaries is more rapid than normal lattice.
Lecture 17: Diffusion PHYS 430/603 material Laszlo Takacs UMBC Department of Physics.
Diffusion Chapter 5. Mechanics of Diffusion Primary method by which atoms mix Consider a drop of food coloring in a glass of water.
SURFACE HARDENING HEAVY CROSS SECTION - IMPOSSIBLE TO COOL QUICKLY TO PRODUCE A UNIFORMLY MARTENSITIC STRUCTURE THROUGHOUT A SOFT UNHARDENED CORE DUE TO.
MIT Microstructural Evolution in Materials 6: Substitutional Diffusion Juejun (JJ) Hu
Introduction to Materials Science and Engineering
CHAPTER 5: DIFFUSION IN SOLIDS
Materials Engineering
Diffusion Thermally activated process
5 Atom and Ion Movements in Materials
Chapter 5: Diffusion ISSUES TO ADDRESS... • How does diffusion occur?
Chapter 6 Diffusion.
Diffusion how atoms move in solids
Point Defects in Crystalline Solids
"War is a matter of vital importance to the State;
Chapter 5: Diffusion in Solids
Rate Process and Diffusion
Transport Zuoan Li NorFERM-2008.
CHAPTER 5: DIFFUSION IN SOLIDS
TOPIC 2: Diffusion in Solids
Rate Process and Diffusion
PDT 153 Materials Structure And Properties
Diffusion Chapter 5 9/4/2019 9:52 AM9/4/2019 9:52 AM
Diffusion.
Presentation transcript:

DIFFUSION IN SOLIDS  FICK’S LAWS  KIRKENDALL EFFECT  ATOMIC MECHANISMS Diffusion in Solids P.G. Shewmon McGraw-Hill, New York (1963)

ArH2H2 Movable piston with an orifice H 2 diffusion direction Ar diffusion direction Piston motion Piston moves in the direction of the slower moving species

AB Inert Marker – thin rod of a high melting material which is basically insoluble in A & B Kirkendall effect  Materials A and B welded together with Inert marker and given a diffusion anneal  Usually the lower melting component diffuses faster (say B) Marker motion

Diffusion  Mass flow process by which species change their position relative to their neighbours  Driven by thermal energy and a gradient  Thermal energy → thermal vibrations → Atomic jumps Concentration / chemical potential ElectricGradient Magnetic Stress

 Assume that only B is moving into A  Assume steady state conditions → J  f(x,t) (No accumulation of matter)  Flux (J) (restricted definition) → Flow / area / time [Atoms / m 2 / s]

Fick’s I law No. of atoms crossing area A per unit time Cross-sectional area Concentration gradient Matter transport is down the concentration gradient Diffusion coefficient/ diffusivity A Flow direction  As a first approximation assume D  f(t)

Fick’s first law

 Diffusivity (D) → f(A, B, T) D = f(c) D  f(c) C1C1 C2C2 Steady state diffusion x → Concentration →

Diffusion Steady state J  f(x,t) Non-steady state J = f(x,t) D = f(c) D  f(c)

Fick’s II law JxJx J x+  x xx Fick’s first law D  f(x)

RHS is the curvature of the c vs x curve x → c → x → c → +ve curvature  c ↑ as t ↑  ve curvature  c ↓ as t ↑ LHS is the change is concentration with time

Solution to 2 o de with 2 constants determined from Boundary Conditions and Initial Condition  Erf (  ) = 1  Erf (-  ) = -1  Erf (0) = 0  Erf (-x) = -Erf (x) u → Exp(  u 2 ) → 0  Area

A B Applications based on Fick’s II law x → Concentration → C avg ↑ t t 1 > 0 | c(x,t 1 ) t 2 > t 1 | c(x,t 1 ) t = 0 | c(x,0) A & B welded together and heated to high temperature (kept constant → T 0 ) Flux f(x)| t f(t)| x Non-steady state  If D = f(c)  c(+x,t)  c(-x,t) i.e. asymmetry about y-axis  C(+x, 0) = C 1  C(  x, 0) = C 2 C1C1 C2C2  A = (C 1 + C 2 )/2  B = (C 2 – C 1 )/2 Determination of Diffusivity

Temperature dependence of diffusivity Arrhenius type

Applications based on Fick’s II law Carburization of steel  Surface is often the most important part of the component, which is prone to degradation  Surface hardenting of steel components like gears is done by carburizing or nitriding  Pack carburizing → solid carbon powder used as C source  Gas carburizing → Methane gas CH 4 (g) → 2H 2 (g) + C (diffuses into steel) x → 0 C1C1 CSCS  C(+x, 0) = C 1  C(0, t) = C S  A = C S  B = C S – C 1

Approximate formula for depth of penetration

ATOMIC MODELS OF DIFFUSION 1. Interstitial Mechanism

2. Vacancy Mechanism

3. Interstitialcy Mechanism

4. Direct Interchange and Ring

Interstitial Diffusion HmHm  At T > 0 K vibration of the atoms provides the energy to overcome the energy barrier  H m (enthalpy of motion)  → frequency of vibrations, ’ → number of successful jumps / time

1 2 Vacant site     c = atoms / volume  c = 1 /  3  concentration gradient dc/dx = (  1 /  3 )/  =  1 /  4  Flux = No of atoms / area / time = ’ / area = ’ /  2 On comparison with

Substitutional Diffusion  Probability for a jump  (probability that the site is vacant). (probability that the atom has sufficient energy)   H m → enthalpy of motion of atom  ’ → frequency of successful jumps As derived for interstitial diffusion

Element HfHf HmHm  H f +  H m Q Au Ag Calculated and experimental activation energies for vacancy Diffusion

Interstitial Diffusion Substitutional Diffusion  D (C in FCC Fe at 1000ºC) = 3  10  11 m 2 /s  D (Ni in FCC Fe at 1000ºC) = 2  10  16 m 2 /s

DIFFUSION PATHS WITH LESSER RESISTANCE Q surface < Q grain boundary < Q lattice Experimentally determined activation energies for diffusion  Core of dislocation lines offer paths of lower resistance → PIPE DIFFUSION Lower activation energy automatically implies higher diffusivity  Diffusivity for a given path along with the available cross-section for the path will determine the diffusion rate for that path

Comparison of Diffusivity for self-diffusion of Ag → single crystal vs polycrystal 1/T → Log (D) → Schematic Polycrystal Single crystal ← Increasing Temperature  Q grain boundary = 110 kJ /mole  Q Lattice = 192 kJ /mole