CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES

Transcription

1 CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES ISSUES TO ADDRESS... How do atoms assemble into solid structures? (for now, focus on metals) How does the density of a material depend on its structure? When do material properties vary with the sample (i.e., part) orientation? 1

2 Crystal Structure Motivation: Many of the properties of materials (especially mechanical) are determined by the arrangement of the atoms. This arrangement is called the material s crystal structure. An important distinction Atomic structure relates to the number of protons and neutrons in the nucleus of an atom, as well as the number and probability distributions of the electrons. Crystal structure pertains to the arrangement of atoms in the crystalline solid material.

3 Atoms can be arranged either in a regular, periodic array (i.e., long-range order) or completely disordered (amorphous). We need a way to specify crystallographic directions and planes. c To illustrate the concept of crystal structure and lattice systems, we first identify a coordinate system (x, y, z): a x z y b We can t specify directions or planes without knowing what the reference system is.

4 The unit cell is the smallest group of atoms which can generate the entire crystal by translation. What is the Unit Cell? Definition: the length of each unit cell axis is called a lattice parameter. In cubic systems, all three orthogonal lattice parameters are equal Lattice parameters are typically on the order of a few Angstroms (or a few tenths of a nanometer)

5 ENERGY AND PACKING Non dense, random packing Energy typical neighbor bond length typical neighbor bond energy r Dense, regular packing Energy typical neighbor bond length typical neighbor bond energy Dense, regular-packed structures tend to have lower energy. r 2

6 MATERIALS AND PACKING Crystalline materials... atoms pack in periodic, 3D arrays typical of: -metals -many ceramics -some polymers Noncrystalline materials... atoms have no periodic packing occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline Si crystalline SiO2 Adapted from Fig. 3.18(a), Callister 6e. Oxygen noncrystalline SiO2 Adapted from Fig. 3.18(b), Callister 6e. 3

7 METALLIC CRYSTALS 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... 4

8 SIMPLE CUBIC STRUCTURE (SC) Rare due to poor packing (only Po has this structure) Close-packed directions are cube edges. In terms of the hard sphere model we say the atoms are touching in the close-packed directions! Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson) 5

9 ATOMIC PACKING FACTOR APF = Volume of atoms in unit cell* Volume of unit cell *assume hard spheres APF for a simple cubic structure = 0.52 a R=0.5a close-packed directions contains 8 x 1/8 = 1 atom/unit cell Adapted from Fig. 3.19, Callister 6e. atoms unit cell APF = volume 4 atom 3 π (0.5a)3 a 3 1 volume unit cell 6

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

11 ATOMIC PACKING FACTOR: BCC APF for a body-centered cubic structure = 0.68 Adapted from Fig. 3.2, Callister 6e. R a atoms unit cell APF = Close-packed directions: length = 4R = 3 a Unit cell contains: x 1/8 = 2 atoms/unit cell π ( 3a/4)3 a 3 volume unit cell volume atom 8

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

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

14 FCC STACKING SEQUENCE ABCABC... Stacking Sequence 2D Projection A B B C A A sites B B B C C B sites C sites B B FCC Unit Cell A B C close-packed plane of atoms 11

15 HEXAGONAL CLOSE-PACKED STRUCTURE (HCP) ABAB... Stacking Sequence 3D Projection 2D Projection A sites B sites A sites Top layer Middle layer Bottom layer Adapted from Fig. 3.3, Callister 6e. Coordination # = 12 APF =

16 THEORETICAL DENSITY, ρ # atoms/unit cell Atomic weight (g/mol) Volume/unit cell (cm 3 /unit cell) Example: Copper ρ= n A V c N A Avogadro's number (6.023 x atoms/mol) Data from Table inside front cover of Callister (see next slide): crystal structure = FCC: 4 atoms/unit cell atomic weight = g/mol (1 amu = 1 g/mol) atomic radius R = nm (1 nm = 10-7cm) Vc = a 3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x cm 3 Result: theoretical ρcu = 8.89 g/cm 3 Compare to actual: ρcu = 8.94 g/cm 3 14

17 Characteristics of Selected Elements at 20 C Element Aluminum Argon Barium Beryllium Boron Bromine Cadmium Calcium Carbon Cesium Chlorine Chromium Cobalt Copper Flourine Gallium Germanium Gold Helium Hydrogen Symbol Al Ar Ba Be B Br Cd Ca C Cs Cl Cr Co Cu F Ga Ge Au He H At. Weight (amu) Density (g/cm 3 ) Crystal Structure FCC BCC HCP Rhomb HCP FCC Hex BCC BCC HCP FCC Ortho. Dia. cubic FCC Atomic radius (nm) Adapted from Table, "Characteristics of Selected Elements", inside front cover, Callister 6e. 15

18 Polymorphism and allotropy Carbon is a good example of allotropy, it has 3 crystal structures with very different properties.

19 From Principles of Electronic Materials and Devices 2 nd Ed., S.O. Kasap, McGraw-Hill

20 DENSITIES OF MATERIAL CLASSES ρ metals > ρ ceramics >ρ polymers Why? Metals have... close-packing (metallic bonding) large atomic mass Ceramics have... less dense packing (covalent bonding) often lighter elements ρ (g/cm 3 ) Polymers have... poor packing (often amorphous) lighter elements (C,H,O) Composites have Metals/ Alloys Platinum Gold, W Tantalum Silver, Mo Cu,Ni Steels Tin, Zinc Titanium Aluminum Magnesium Graphite/ Ceramics/ Semicond Polymers Composites/ fibers Based on data in Table B1, Callister *GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers in an epoxy matrix). Zirconia Al oxide Diamond Si nitride Glass-soda Concrete Silicon Graphite intermediate values Data from Table B1, Callister 6e. PTFE Silicone PVC PET PC HDPE, PS PP, LDPE Glass fibers GFRE* Carbon fibers CFRE* Aramid fibers AFRE* Wood 16

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

22 Single crystals of fluorite Fluorite is a ceramic with a unit cell made up of 8 cubes

23 POLYCRYSTALS Most engineering materials are polycrystals. 1 mm Adapted from Fig. K, color inset pages of Callister 6e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany) Nb-Hf-W plate with an electron beam weld. Each "grain" is a single crystal. If crystals are randomly oriented, overall component properties are not directional. Crystal sizes typ. range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers). 18

24 Solidification of a polycrystalline material

25 SINGLE VS POLYCRYSTALS 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. E (diagonal) = 273 GPa E (edge) = 125 GPa 200 μm 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].) 19

26 X-RAYS TO CONFIRM CRYSTAL STRUCTURE Incoming X-rays diffract from crystal planes. 1 incoming X-rays 2 extra distance travelled by wave 2 θ θ outgoing X-rays detector 1 λ d 2 reflections must be in phase to detect signal spacing between planes Adapted from Fig. 3.2W, Callister 6e. Measurement of: Critical angles, θc, for X-rays provide atomic spacing, d. x-ray intensity (from detector) Read more about this subject in the text book. Learn how to use Bragg s Law. d=nλ/2sinθc θc θ 20

27 SCANNING TUNNELING MICROSCOPY Atoms can be arranged and imaged! Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright Carbon monoxide molecules arranged on a platinum (111) surface. Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word atom. 21

28 DEMO: HEATING AND COOLING OF AN IRON WIRE Demonstrates "polymorphism" Temperature, C The same atoms can have more than one crystal structure Liquid BCC Stable longer 914 Tc 768 FCC Stable BCC Stable heat up cool down shorter! longer! magnet falls off shorter 22

29 SUMMARY 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