CHAPTER 3 DIFFUSION and IMPERFECTIONS IN SOLIDS
OUTLINE 1.
TYPES OF DIFFUSIONS 1.1. Interdiffusion 1.2. Selfdiffusion 1.3.Diffusion mechanisms 1.4.Examples
2.
TYPES OF IMPERFECTIONS 2.1.Point Defects 2.2.Line Defects 2.3.Area Defects
3.
METHODS TO SEE DEFECTS 3.1.Optical microscope 3.2.Scanning electron microscope (SEM) 3.3.Transmission electron microscope 3.4.Atomic force microscope
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1.Diffusion
What is diffusion? It is the material transport by atomic motion from high concentration region to low concentration region Why study diffusion? Materials of all types are often heat treated or mixed to improve their properties.During heating or mixing atomic diffusion always exist. To control the diffusion speed and mechanism, one should know the mechanisms and types of diffusion.
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1.1.Interdiffusion(Impurity diffusion)
In a SOLID Alloy Atoms will Move From HIGH Concentration to LOW Concentration REGĐONS
Initial Condition
Cu 100%
0
Ni
100%
Concentration Profiles
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After Time+Temp
0 Concentration Profiles 4
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Alloying a surface
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. Click to animate 5
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1.2.Self-Diffusion
Diffusion in pure elemental solids( also liquids and gases) All Atoms exchanging their positions are the same type.
Label Atoms C A
After Time+Temp C
D
B
B
D
A
How to Label an ATOM?
Use a STABLE ISOTOPE as a tag
e.g.; Label 28Si (92.5% Abundance) with one or both of 29Si 30Si
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→ 4.67% Abundance → 3.10% Abundance 6
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1.3. Diffusion Mechanisms
For an atom to change position: 1.There must be an empty site 2.The atom must have sufficient energy to break the bonds: Vibrational energy increasing with temperature
a) Vacancy diffusion: Host or substitutional impurity atoms replace with vacancies
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Diffusion Mechanism Simulation
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b) Interstitial diffusion: Host or substitutional impurity atoms place between the other atoms. •Applies to interstitial impurities:H,C,N,O small enough to fit into the interstitial positions •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.
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Interstitial Alloy
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Diffusion in Processing: Case1 Example: 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
Shear Resistant
Crack Resistant 11
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Diffusion in Processing:Case2 • Doping Silicon with Phosphorus for n-type semiconductors: 0.5mm • Process: 1. Deposit P rich layers on surface. magnified image of a computer chip
silicon 2. Heat it. 3. Result: Doped semiconductor regions.
silicon 30.07.2007
light regions: Si atoms
light regions: Al atoms 9
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What Do You See?
Polystyrene Beads On A Slide
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Why study imperfections in solids? types of defects arise in solids. defects affect material properties. the number and type of defects can be varied and controlled. defects are sometimes desirable.
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silicon transistors are based on controlled “doping”
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2. Types of Imperfectıons • Vacancy atoms • Interstitial atoms • Substitutional atoms
}
2.1.Point defects
• Dislocations
2.2.Line defects
• Grain Boundaries
2.3.Area defects
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2.1 Point Defects • Vacancies: -vacant atomic sites in a structure. (An empty atomic site)
Vacancy distortion of planes
• Interstitials: -"extra" atoms positioned between atomic sites. An atom somewhere other than an atomic site 1)Self-interstitial 2)Impurity interstitial
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selfinterstitial 16
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Point Defects:Mixing On The Molecular Scale
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How are point defects introduced? Some types are thermally generated Direct result of thermal vibration of the atomic array.The concentration of thermally-produced defects increases exponentially with increasing temperature Doping:Added solutes (impurities or dopants) ordered or disordered solid solution
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Temperature Effect On Vacancies
Click to animate
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Point Defects In Alloys Two outcomes if impurity (B) added to host (A): • Solid solution of B in A (i.e., random dist. of point defects)
OR Substitutional alloy (e.g., Cu in Ni)
Interstitial alloy (e.g., C in Fe)
• Solid solution of B in A plus particles of a new phase (usually for a larger amount of B) Second phase particle --different composition --often different structure. 30.07.2007
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Point Defects In Ceramic Structures • Frenkel Defect --a cation(+ve, metallic ion) is out of place. • Shottky Defect --a paired set of cation and anion(-ve, nonmetallic ion) vacancies. Shottky Defect: Adapted from Fig. 13.20, Callister 5e.
Frenkel Defect
• Equilibrium concentration of defects 30.07.2007
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1.2 Line Defects
Dislocations: are
line defects, cause slip between crystal plane when they move, produce permanent (plastic) deformation.
Schematic of a Zinc bar (HCP): Before
deformation
After Deformation slip steps
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INCREMENTAL SLIP Dislocations slip planes incrementally... The dislocation line (the moving red dot)... ...separates slipped material on the left from unslipped material on the right.
(Courtesy P.M. Anderson)
Simulation of dislocation motion from left to right as a crystal is sheared.
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Dislocation:Incremental Slip
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Carpet Dislocation Anology
Continue to Slide Dislocation with little effort to the End of the Crystal Note
Net Movement at Far End
Di sl
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oc a
tio n
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Edge dislocations
An edge dislocation occurs when there is an extra crystal plane
copper sulphide cactus!
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http://pilot.mse.nthu.edu.tw/tem/gallery/Tem-11.JPG h ttp://www.mse.nthu.edu.tw/jimages/Beuty/
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Bond Breaking And Remaking
Click to animate
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Click to animate
Dislocation motion requires the successive jumping of a half plane of atoms (from left to right here). Bonds across the slipping planes are broken and remade in succession. 28
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Screw dislocation
In screw dislocations, the atom planes look like they have been ‘sheared’
350Å GaN http://www.iap.tuwien.ac.at/www/surface/STM_Gallery/screw_disl_schem.gif http://nano.phys.uwm.edu/li/new_pa4.jpg 29
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Area Defects: Grain Boundaries Grain boundaries: • are boundaries between crystals. • are produced by the solidification process, for example. • have a change in crystal orientation across them.
Metal Ingot ~ 8cm
Schematic
grain boundaries
heat flow Adapted from Callister 6e. 30.07.2007
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Area Defects
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Finally What Do You See?
intersitial
vacancy grain boundary
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Polystyrene Beads On A Slide
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3.Methods To See Defects
Optical microscope
Scanning electron microscope (SEM)
Surface microstructure, analytical chemistry (~50-100 nm)
Transmission electron microscope
surface microstructure (~ 1µm)
Resolve the atomic structure from a very thin foil (30 Ao), (~1 Ao)
Atomic force microscope
3D surface topography, electrical, magnetic scanning (~1 nm) 33
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Optical Microscopy
Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation. microscope
close-packed planes Adapted from Fig. 4.11(b) and (c), Callister 6e. (Fig. 4.11(c) is courtesy of J.E. Burke, General Electric Co.
micrograph of Brass (Cu and Zn)
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0.75mm
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Scannıng Electron Mıcroscopy (SEM)
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Scanning Tuneling Microscopy (Atomic Force Microscope)
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Atoms can be arranged and imaged! Carbon monoxide molecules arranged on a platinum (111) surface.
Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler.IBM 1995. 30.07.2007
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SCANNING TUNNELING MICROSCOPY(2) •
Atoms can be arranged and imaged! Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”.
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Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. IBM1995.
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SCANNING TUNNELING MICROSCOPY
Click to animate
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SUMMARY
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.)
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PROBLEM 1. Using the table given find: a) substitutional solid solution having complete solubility in copper. b) substitutional solid solution of incomplete solubility in copper. c) An interstitial solid solution in copper.
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SOLUTION 1.
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PROBLEM 2. The concentration of silicon in an ironsilicon alloy is 0.25% by mass. What is the concentration in kilograms of silicon per meter cube of alloy. ρSi =2.33 gcm-3 ρFe =7.87 gcm-3
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Solution of Problem 2: cSi = mSi /(VSi + VFe) dSi = mSi / VSi = 2.33 dFe = mFe / VFe = 7.87 VSi = 0.25 / 2.33 = 0.107cm3 VFe = 99.75 / 7.87 = 12.675cm3 cSi = 0.25 /(0.107 + 12.675) = 0.01956 g / cm3 Convert the concentration into kgm-3 30.07.2007
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PROBLEM 3.
Molybdenum forms a substitutional solid solution with tungsten. Compute the number of molybdenum atoms per cubic centimeter for a molybdenum-tungsten alloy that contains 16.4 wt% Mo and 83.6 wt% W. ρMo =10.22 gcm-3 ρW =19.30 gcm-3 Molar mass of Mo=95.94 gmol-1 # of Mo in 1 cm3 = ?
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Solution of Problem 3: cMo = mMo /(VMo + VW ) dMo = mMo / VMo = 10.22 dW = mW / VW = 19.30 VMo = 16.4 / 10.22 = 1.605cm3 VW = 83.6 / 19.30 = 4.332cm3 cMo = 16.4 /(1.605 + 4.332) = 2.762 g / cm3 n = 2.762 / 95.94 = 0.0288mol # of Mo atoms = 0.173x10 23 30.07.2007
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PROBLEM 4.
Germanium forms a substitutional solid solution with silicon. Compute the weight percent of Germanium that must be added to silicon to yield an alloy that contains 2.43 x 1021 Ge atoms per cubic centimeter.
# of Ge in 1 cm3 = 2.43 x 1021 Ge atoms ρGe =5.32 gcm-3 ρSi =2.33 gcm-3 Molar mass of Ge=72.59 gmol-1 Molar mass of Si=28.09 gmol-1
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Solution of Problem 4:
Answer: Ge % by mass= 11.7
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Advanced topic:Calculating Equilibrium Concentration of Point Defects • Equilibrium concentration varies with temperature! No. of defects
Activation energy
−Q ND = D exp kT N
No. of potential Temperature defect sites. Boltzmann's constant (1.38 x 10-23 J/atom K) (8.62 x 10-5 eV/atomK) Each lattice site is a potential vacancy site 30.07.2007
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