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Chapter 3-1 CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES Single Xtal Crystalline Poly-Xtal Materials Non-crystalline

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Chapter 3-

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atoms pack in periodic, 3D arrays typical of: 3 Crystalline materials... -metals -many ceramics -some polymers atoms have no periodic packing occurs for: Noncrystalline materials... -complex structures -rapid cooling crystalline SiO 2 noncrystalline SiO 2 "Amorphous" = Noncrystalline Adapted from Fig. 3.18(b), Callister 6e. Adapted from Fig. 3.18(a), Callister 6e. MATERIALS AND PACKING

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Chapter 3-4 tend to be densely packed. have several reasons for dense packing: -Typically, only one element is present, so all atomic radii are the same. -Metallic bonding is not directional. -Nearest neighbor distances tend to be small in order to lower bond energy. have the simplest crystal structures. We will look at three such structures... METALLIC CRYSTALS

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5 Rare due to poor packing (only Po has this structure) Close-packed directions are cube edges. Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson) SIMPLE CUBIC STRUCTURE (SC)

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Chapter 3-6 APF for a simple cubic structure = 0.52 Adapted from Fig. 3.19, Callister 6e. ATOMIC PACKING FACTOR

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Chapter 3- Coordination # = 8 7 Adapted from Fig. 3.2, Callister 6e. (Courtesy P.M. Anderson) Close packed directions are cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. BODY CENTERED CUBIC STRUCTURE (BCC)

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Chapter 3-8 APF for a body-centered cubic structure = 0.68 Adapted from Fig. 3.2, Callister 6e. ATOMIC PACKING FACTOR: BCC

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Chapter 3-9 Coordination # = 12 Adapted from Fig. 3.1(a), Callister 6e. (Courtesy P.M. Anderson) Close packed directions are face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. FACE CENTERED CUBIC STRUCTURE (FCC)

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Chapter 3-10 APF for a body-centered cubic structure = 0.74 Adapted from Fig. 3.1(a), Callister 6e. ATOMIC PACKING FACTOR: FCC

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Chapter 3-11 ABCABC... Stacking Sequence 2D Projection FCC Unit Cell FCC STACKING SEQUENCE

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Chapter 3-12 Coordination # = 12 ABAB... Stacking Sequence APF = 0.74 3D Projection 2D Projection Adapted from Fig. 3.3, Callister 6e. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)

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Chapter 3-13 Compounds: Often have similar close-packed structures. Close-packed directions --along cube edges. Structure of NaCl (Courtesy P.M. Anderson) STRUCTURE OF COMPOUNDS: NaCl

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Chapter 3-14 THEORETICAL DENSITY,

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Chapter 3-14 Example: Copper Data from Table inside front cover of Callister (see next slide): crystal structure = FCC: 4 atoms/unit cell atomic weight = 63.55 g/mol (1 amu = 1 g/mol) atomic radius R = 0.128 nm (1 nm = 10 cm) -7

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Chapter 3-15 Adapted from Table, "Charac- teristics of Selected Elements", inside front cover, Callister 6e. Characteristics of Selected Elements at 20C

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Chapter 3-16 Why? Metals have... close-packing (metallic bonding) large atomic mass Ceramics have... less dense packing (covalent bonding) often lighter elements Polymers have... poor packing (often amorphous) lighter elements (C,H,O) Composites have... intermediate values Data from Table B1, Callister 6e. DENSITIES OF MATERIAL CLASSES

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Chapter 3-17 Some engineering applications require single crystals: Crystal properties reveal features of atomic structure. (Courtesy P.M. Anderson) --Ex: Certain crystal planes in quartz fracture more easily than others. --diamond single crystals for abrasives --turbine blades Fig. 8.30(c), Callister 6e. (Fig. 8.30(c) courtesy of Pratt and Whitney). (Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.) CRYSTALS AS BUILDING BLOCKS

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Chapter 3-

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18 Most engineering materials are polycrystalline. POLYCRYSTALS

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Effect of grain size, an example

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Chapter 3-19 Single Crystals -Properties vary with direction: anisotropic. -Example: the modulus of elasticity (E) in BCC iron: Polycrystals -Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. (E poly iron = 210 GPa) -If grains are textured, anisotropic. 200 m Data from Table 3.3, Callister 6e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.) Adapted from Fig. 4.12(b), Callister 6e. (Fig. 4.12(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) SINGLE VS POLYCRYSTALS

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Chapter 3-

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Bar of Vanadium

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Chapter 3- Growing Crystals https://www.youtube.com/watch?v=l_USYub3djY

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Chapter 3- Lattice Positions Example: cubic system

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Chapter 3- Procedure for finding direction: Select two points on the line End point - Start point Clear fraction Put in [hkl] format Note: negative sign goes above the number

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Chapter 3- Example: Select two points on the line End point - Start point Clear fraction Put in [hkl] format

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Chapter 3- Example: Select two points on the line End point - Start point Clear fraction Put in [hkl] format

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Chapter 3-

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Procedure for finding planes: Find plane’s intercept with X, Y and Z axis Inverse the numbers Clear fraction Put in (hkl) format Note: negative sign goes above the number

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Chapter 3- Find plane’s intercept with X, Y and Z axis Inverse the numbers Clear fraction Put in (hkl) format

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Chapter 3- Find plane’s intercept with X, Y and Z axis Inverse the numbers Clear fraction Put in (hkl) format

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Chapter 3-

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The previous equation of planar spacing is only for CUBIC systems.

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Chapter 3-

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Atomic Linear density, LD = (number of atoms/unit length) Slip Direction (more later) Calculate LD if cube is BCC

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Chapter 3- Calculate LD if cube is FCC

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Chapter 3- Atomic Planar density, PD = (number of atoms/unit area) Slip plane (more later) Calculate PD if cube is BCC

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Chapter 3- Calculate PD if cube is FCC

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Chapter 3- Atomic Volume density, VD = (number of atoms/unit volume) Calculate VD if cube is BCC

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Chapter 3- Atomic Volume density, VD = (number of atoms/unit volume) Calculate VD if cube is FCC

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Chapter 3- Converting from/to cubic to hexagonal, Directions [hkl] and [uvtw] u=n/3(2h-k) v=n/3(2k-h) t=-(u+v) w=nl Example: covert [102] to hexagonal system U=n/3(2-0)=2n/3 V=n/3(0-1)=-n/3 t=-(2n/3-n/3)=-n/3 W=n(2) =2n

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Chapter 3- Converting from/to cubic to hexagonal, plane (hkl) to/from (hkil) i=-(h+k) Example: convert (213) to hexagonal system

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Chapter 3- #atoms/UCa0a0 C.NP.FElements SC12R60.52 BCC280.68Fe, W, Mo, Cr,… FCC4120.74Fe, Cu, Al, Au, Ag, Pb, Ni,.. HCP6a 0 = 2R C 0 = 3.266R 120.74Ti, Mg, Zn, Be, Co, Zr,..

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Chapter 3-

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20 Incoming X-rays diffract from crystal planes. Measurement of: Critical angles, c, for X-rays provide atomic spacing, d. Adapted from Fig. 3.2W, Callister 6e. X-RAYS TO CONFIRM CRYSTAL STRUCTURE

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Watch this video: http://www.theguardian.com/science/video/2013/oct/09/100- years-x-ray-crystallography-video-animation http://www.theguardian.com/science/video/2013/oct/09/100- years-x-ray-crystallography-video-animation

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Chapter 3-

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Graphical Methods

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Chapter 3- X-Ray: Another Method

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Chapter 3- Detection method n = 2dsin( )

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Chapter 3- Figure 3.22 Diffraction pattern for polycrystalline a-iron., a=0.29 nm n =2dsin( ) Example: Find wavelength of the x-ray used to generate the above graph.

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Chapter 3- Pyrite (done with SEM at SSU)

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Chapter 3- Atoms may assemble into crystalline or amorphous structures. We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP). Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but properties are generally non-directional (i.e., they are isotropic) in polycrystals with randomly oriented grains. 23 SUMMARY

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Chapter 3-

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