CHAPTER 6 OUTLINE. DIFFUSION and IMPERFECTIONS IN SOLIDS

Transcription

1 CHAPTER 6 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 2 1

2 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 Interdiffusion(Impurity diffusion) In a SOLID Alloy Atoms will Move From HIGH Concentration to LOW Concentration REGĐONS Initial Condition After Time+Temp 100% Cu Ni 100% 0 Concentration Profiles 0 Concentration Profiles 4 2

3 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 Self-Diffusion Diffusion in pure elemental solids( also liquids and gases) All Atoms exchanging their positions are the same type. Label Atoms C A D B After Time+Temp C D A B How to Label an ATOM? Use a STABLE ISOTOPE as a tag e.g.; Label 28 Si (92.5% Abundance) with one or both of 29 Si 4.67% Abundance 30 Si 3.10% Abundance 6 3

4 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 increasing elapsed time 7 Diffusion Mechanism Simulation 8 4

5 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. 9 Interstitial Alloy 10 5

6 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 Diffusion in Processing:Case2 Doping Silicon with Phosphorus for n-type semiconductors: 0.5mm Process: 1. Deposit P rich layers on surface. 2. Heat it. silicon 3. Result: Doped semiconductor regions. magnified image of a computer chip light regions: Si atoms silicon light regions: Al atoms

7 What Do You See? Polystyrene Beads On A Slide 13 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. silicon transistors are based on controlled doping 14 7

8 2. Types of Imperfectıons Vacancy atoms Interstitial atoms Substitutional atoms Dislocations Grain Boundaries } 2.1.Point defects 2.2.Line defects 2.3.Area defects Point Defects Vacancies: -vacant atomic sites in a structure. (An empty atomic site) distortion of planes Vacancy Interstitials: -"extra" atoms positioned between atomic sites. An atom somewhere other than an atomic site 1)Self-interstitial 2)Impurity interstitial distortion of planes selfinterstitial 16 8

9 Point Defects:Mixing On The Molecular Scale 9 17 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 18 9

10 Temperature Effect On Vacancies Click to animate 19 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

11 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 , Callister 5e. Frenkel Defect Equilibrium concentration of defects

12 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 23 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. Click to animate 24 12

13 Dislocation:Incremental Slip 25 Carpet Dislocation Anology Continue to Slide Dislocation with little effort to the End of the Crystal Note Net Movement at Far End Dislocation 26 13

14 Edge dislocations An edge dislocation occurs when there is an extra crystal plane cactus! copper sulphide h ttp:// 27 Bond Breaking And Remaking Click to animate 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

15 Screw dislocation In screw dislocations, the atom planes look like they have been sheared 350Å GaN 29 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. Schematic Metal Ingot ~ 8cm grain boundaries Adapted from Callister 6e. heat flow 30 15

16 Area Defects 31 Finally What Do You See? intersitial vacancy grain boundary Polystyrene Beads On A Slide 32 16

17 3.Methods To See Defects Optical microscope surface microstructure (~ 1µm) Scanning electron microscope (SEM) Surface microstructure, analytical chemistry (~ nm) Transmission electron microscope Resolve the atomic structure from a very thin foil (30 A o ), (~1 A o ) Atomic force microscope 3D surface topography, electrical, magnetic scanning (~1 nm) 33 Optical Microscopy Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation. microscope Adapted from Fig. 4.11(b) and (c), Callister 6e. (Fig. 4.11(c) is courtesy of J.E. Burke, General Electric Co. close-packed planes micrograph of Brass (Cu and Zn) 0.75mm 34 17

18 Scannıng Electron Mıcroscopy (SEM) 35 Scanning Tuneling Microscopy (Atomic Force Microscope) 36 18

19 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 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. Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. IBM

20 SCANNING TUNNELING MICROSCOPY Click to animate 39 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.) 40 20

21 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. 41 SOLUTION

22 43 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. ρ Si =2.33 gcm -3 ρ Fe =7.87 gcm

23 Solution of Problem 2: c d d V V c Si Si Fe Si Fe Si = m = m Si Si /( V / V Si Si + V Fe = 2.33 = mfe / VFe= 7.87 = 0.25 / 2.33= 0.107cm3 = / 7.87= cm3 ) = 0.25/( ) = g / cm3 Convert the concentration into kgm 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. ρ Mo =10.22 gcm -3 ρ W =19.30 gcm -3 Molar mass of Mo=95.94 gmol -1 # of Mo in 1 cm 3 =? 46 23

24 Solution of Problem 3: c d d V V c Mo Mo W Mo W Mo n= # of = m = m = m Mo Mo W /( V / V / V W Mo Mo = 16.4 /10.22= 1.605cm3 = 83.6 /19.30= 4.332cm3 = 16.4 /( ) = 2.762g / cm / V W = = = mol Mo atoms= 0.173x10 ) 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 Ge atoms per cubic centimeter. # of Ge in 1 cm 3 = 2.43 x Ge atoms ρ Ge =5.32 gcm -3 ρ Si =2.33 gcm -3 Molar mass of Ge=72.59 gmol -1 Molar mass of Si=28.09 gmol

25 Solution of Problem 4: Answer: Ge % by mass= Advanced topic:calculating Equilibrium Concentration of Point Defects Equilibrium concentration varies with temperature! No. of defects N D N = exp Q D kt No. of potential Temperature defect sites. Boltzmann's constant Each lattice site is a potential vacancy site Activation energy (1.38 x J/atom K) (8.62 x 10-5 ev/atomk)