Chapter 4 - 1 A (0001) plane for an HCP unit cell is show below. Each of the 6 perimeter atoms in...
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Transcript of Chapter 4 - 1 A (0001) plane for an HCP unit cell is show below. Each of the 6 perimeter atoms in...
Chapter 4 - 1
R2 36R2 3
PD0001 = number of atoms centered on (0001) plane
area of (0001) plane
3 atoms
6R2 3
1
2R2 3
2192
220001 10373.173.13)145.0(32
1
32
1)( mxnm
nmRTiPD
A (0001) plane for an HCP unit cell is show below.
Each of the 6 perimeter atoms in this plane is shared with three other unit cells, whereas the center atom is shared with no other unit cells; this gives rise to three equivalent atoms belonging to this plane.
In terms of the atomic radius R, the area of each of the 6 equilateral triangles that have been drawn is , or the total area of the plane shown is .
. And the planar density for this (0001) plane is equal to
or the total area of the plane shown is
(b) the atomic radius for titanium is 0.145 nm. Therefore, the planar density for the (0001) plane is
Chapter 4 - 2
• Vacancy atoms• Interstitial atoms• Substitutional atoms
• DislocationsEdges, Screws, Mixed
• Grain Boundaries• Stacking Faults• Anti-Phase and Twin Boundaries
Point defects
Line defects
Area/Planar defects
Types of Imperfections
Chapter 4 - 3
Point Defects
Vacancy: a vacant lattice site
Self-interstitial: atom crowded in ‘holes’
It is not possible to create a crystal free of vacancies.About 1 out of 10,000 sites are vacant near melting.
Self-interstitials are much less likely in metals, e.g.,as it is hard to get big atom into small hole - there is
large distortions in lattice required that costs energy.
Thermodynamics (temperature and counting) provides an expression for
Vacancy Concentration: NvN
exp QvkBT
Qv=vacancy formation energykB= 1.38 x 10–23 J/atom-K = 8.62 x 10–5 eV/atom-K
Defects ALWAYS cost energy!
Chapter 4 - 4
Imperfections in Solids
Conditions for substitutional solid solution (S.S.)• W. Hume – Rothery rule
– 1. r (atomic radius) < 15%– 2. Proximity in periodic table
• i.e., similar electronegativities
– 3. Same crystal structure for pure metals– 4. Valency
• All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency
rsolute rsolvent
rsolventx100%
Chapter 4 - 5
Imperfections in SolidsApplication of Hume–Rothery rules – Solid Solutions
1. Would you predictmore Al or Ag to dissolve in Zn?
More Al because size is closer
7.43 % vs 8.48 % – FCC in HCP
and val. Is higher – but not too
Much!
2. More Zn or Al
in Cu?
Surely Zn since size is closer
thus causing lower distortion
(4% vs 12%)
Table on p. 106, Callister 7e.
Element Atomic Crystal Electro- ValenceRadius Structure nega-
(nm) tivity
Cu 0.1278 FCC 1.9 +2C 0.071H 0.046O 0.060Ag 0.1445 FCC 1.9 +1Al 0.1431 FCC 1.5 +3Co 0.1253 HCP 1.8 +2Cr 0.1249 BCC 1.6 +3Fe 0.1241 BCC 1.8 +2Ni 0.1246 FCC 1.8 +2Pd 0.1376 FCC 2.2 +2Zn 0.1332 HCP 1.6 +2
Chapter 4 - 6
Imperfections in Solids
Linear Defects (Dislocations)– Are one-dimensional defects around which atoms are
misaligned
• Edge dislocation:– extra half-plane of atoms inserted in a crystal structure– b to dislocation line
• Screw dislocation:– spiral planar ramp resulting from shear deformation– b to dislocation line
Burger’s vector, b: measure of lattice distortion and is measured as a distance along the close packed directions in the lattice
Chapter 4 - 7
Imperfections in Solids
Edge Dislocation
Chapter 4 -
Burgers Vector.
8
The magnitude and the direction of the displacement are defined by a vector, called the Burgers Vector.
(a), starting from the point P, we go up by 4 steps, then move towards right by 5 steps, move down by 4 steps and finally move towards left by 5 steps to reach the starting point P. Now the Burgers circuit gets closed. When the same operation is performed on the defect crystal (b) we end up at Q instead of the starting point!
So, we have to move an extra step to return to P, in order to close the Burgers circuit.BV= = bQP
((((((((((((((
Chapter 4 - 9
• Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here).• Bonds across the slipping planes are broken and remade in succession.
Atomic view of edgedislocation motion fromleft to right as a crystalis sheared.
(Courtesy P.M. Anderson)
Motion of Edge Dislocation
Chapter 4 - 10
Edge Dislocations Exiting Crystal Form Steps
Shear stress
Burger’sVector = b
The caterpillar or rug-moving analogy
Chapter 4 -
Screw dislocation. The spiral stacking of crystal planes leads to the Burgers vector being parallel to the dislocation
line.
11
Chapter 4 - 12
Imperfections in Solids
Screw Dislocation
Adapted from Fig. 4.4, Callister 7e.
Burgers vector b
Dislocationline
b
(a)(b)
Screw Dislocation
Chapter 4 - 13
Edge, Screw, and Mixed Dislocations
Adapted from Fig. 4.5, Callister 7e.
Edge
Screw
Mixed
Chapter 4 -
Motion – Edge dislocation
Applied shear
14
Chapter 4 -
Motion Screw Dislocation
Apply shear
15
Chapter 4 - 16
Imperfections in Solids
Dislocations are visible in electron micrographs
Adapted from Fig. 4.6, Callister 7e.
Chapter 4 - 17
Dislocations & Crystal Structures
• Structure: close-packed planes & directions are preferred.
view onto twoclose-packedplanes.
close-packed plane (bottom) close-packed plane (top)
close-packed directions
• Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none
• Specimens that were tensile tested.
Mg (HCP)
Al (FCC)tensile direction
Chapter 4 - 18
Planar Defects: Surfaces
All defects cost energy (energy is higher than perfect crystal) Surfaces, grain, interphase and twin boundaries, stacking faults
Planar Defect Energy is Energy per Unit Area (J/m2 or erg/cm2)
• Surfaces: missing or fewer number of optimal or preferred bonds.
surface
Chapter 4 -
SURFACE IMPERFECTIONS
Surface imperfections arise from a change in the stacking of atomic planes on or across a boundary.
The change may be one of the orientations or of the stacking sequence of atomic planes.
In geometric concept, surface imperfections are two- dimensional. They are of two types external and internal surface imperfections.
19
Chapter 4 -
EXTERNAL SURFACE IMPERFECTIONS
20
They are the imperfections represented by a boundary. At the boundary the atomic bonds are terminated.
The atoms on the surface cannot be compared with the atoms within the crystal. The reason is that the surface atoms have neighbors on one side only. Where as the atoms inside the crystal have neighbors on either sides. This is shown in figure. Since these surface atoms are not surrounded by others, they possess higher energy than that of internal atoms.
For most metals, the energy of the surface atoms is of the order of 1J/m2.
Chapter 4 - 15
Grain boundaries: • are boundaries between crystals. • are produced by the solidification process, for example. • have a change in crystal orientation across them. • impede dislocation motion.
grain boundaries
heat flow
Adapted from Fig. 4.7, Callister 6e.
Adapted from Fig. 4.10, Callister 6e. (Fig. 4.10 is from Metals Handbook, Vol. 9, 9th edition, Metallography and Microstructures, Am. Society for Metals, Metals Park, OH, 1985.)
~ 8cmMetal Ingot
AREA DEFECTS: GRAIN BOUNDARIES
21
Chapter 4 - 22
Planar Defects in Solids• One case is a twin boundary (plane)
– Essentially a reflection of atom positions across the twin plane.
• Stacking faults– For FCC metals an error in ABCABC packing sequence– Ex: ABCABABC
Adapted from Fig. 4.9, Callister 7e.
Chapter 4 -
STACKING FAULTS
Whenever the stacking of atomic planes is not in a proper sequence throughout the crystal, the fault caused is known as stacking fault.
For example, the stacking sequence in an ideal FCC crystal may be described as A-B-C-A-B-C- A-B-C-……. But the stacking fault may change the sequence to A-B-C-A-B-A-B-A-B-C. The region in which the stacking fault occurs (A-B-A-B) forms a thin region and it becomes HCP.
This thin region is a surface imperfection and is called a stacking fault.
23
Chapter 4 - 24
Microscopic Examination
• Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite large– ex: Large single crystal of quartz or diamond or Si– ex: Aluminum light post or garbage can - see the
individual grains
• Crystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.
Chapter 4 -
MACROSCOPIC EXAMINATION: The shape and average size ordiameter of the grains for a polycrystalline specimen are large enough to observe with the unaided eye.
25
Chapter 4 -
MICROSCOPIC EXAMINATION
Applications
• To Examine the structural elements and defects that influence the properties of materials.
• Ensure that the associations between the properties and structure (and defects) are properly understood.
• Predict the properties of materials once these relationships have been established.
Structural elements exist in ‘macroscopic’ and ‘microscopic’ dimensions
26
Chapter 4 - 27
Optical Microscopy
• Polarized light – metallographic scopes often use polarized
light to increase contrast– Also used for transparent samples such as
polymers
Chapter 4 - 28
• Useful up to 2000X magnification.• Polishing removes surface features (e.g., scratches)• Etching changes reflectance, depending on crystal orientation.
Micrograph ofbrass (a Cu-Zn alloy)
0.75mm
Optical Microscopy
Adapted from Fig. 4.13(b) and (c), Callister 7e. (Fig. 4.13(c) is courtesyof J.E. Burke, General Electric Co.
crystallographic planes
Chapter 4 - 29
Grain boundaries...
• are imperfections,• are more susceptible to etching,• may be revealed as dark lines,• change in crystal orientation across boundary.
Adapted from Fig. 4.14(a) and (b), Callister 7e.(Fig. 4.14(b) is courtesyof L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)
Optical Microscopy
Fe-Cr alloy(b)
grain boundary
surface groove
polished surface
(a)
Chapter 4 -
GRAIN SIZE DETERMINATION
The grain size is often determined when the properties of a polycrystalline material are under consideration. The grain size has a significant impact of strength and response to further processing
Linear Intercept method
• Straight lines are drawn through several photomicrographs that show the grain structure.
• The grains intersected by each line segment are counted
• The line length is then divided by an average number of grains intersected.
•The average grain diameter is found by dividing this result by the linear magnification of the photomicrographs. 30
Chapter 4 -
ASTM (American Society for testing and Materials)
VISUAL CHARTS (@100x) each with a number Quick and easy – used for steel
ASTM has prepared several standard comparison charts, all having different average grain sizes. To each is assigned a number from 1 to 10, which is termed the grain size number; the larger this number, the smaller the grains.
N = 2 n-1No. of grains/square inch
Grain size no.
31
Chapter 4 - 32
High resolutions and magnification (50,000x SEM); (TEM 1,000,000x)
Chapter 4 - 33
Chapter 4 - 34
• 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. Reprinted with permission from International Business Machines Corporation, copyright 1995.
Iron atoms arranged on a copper (111)
surface. These Kanji characters represent
the word “atom”.
Scanning Tunneling Microscopy(STM)
Chapter 4 - 35
• Point, Line, and Area defects exist 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.)
Summary
Chapter 4 - 36