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![Page 1: STRUCTURE OF METALS Materials Science. The Structure of Metals Figure 1.1 An outline of the topics described in Chapter 1.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f455503460f94c66ba9/html5/thumbnails/1.jpg)
STRUCTURE OF METALS
Materials Science
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The Structure of Metals
Figure 1.1 An outline of the topics described in Chapter 1.
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Why Study Crystal Structure of Materials?
• The properties of materials are directly related to their crystal structures
• Significant property differences exist between crystalline and non-crystalline materials having the same composition, diamond Vs graphite
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Crystalline and Crystal Structure• A crystalline material is one in which the
atoms are situated in a specific order (repeating or periodic array over large atomic distances)
• All metals, many ceramics, and some polymers make crystalline structure
• Some of the properties of crystalline solids depend on the crystal structure (manner in which atoms, ions or molecules are spatially arranged) of the material
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LatticeWhen describing crystalline structures, atoms are considered as being solid spheres having well-defined diameters•Atomic hard sphere model -> in which spheres representing nearest-neighbor atoms touch one another•Lattice is a regularly spaced 3D array of points coinciding with atom positions (or centers)
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Unit Cells
• Unit Cell is the smallest group of atoms whose repetition makes a crystalline solid.
• Unit cells are parallelepipeds or prisms having three sets of parallel faces
• The unit cell is the basic structural unit or building block of the crystal structure
• A unit cell is chosen to represent the symmetry of the crystal structure
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Crystal Structure of Metals
• Body-centered cubic (BCC) - alpha iron, chromium, molybdenum, tantalum, tungsten, and vanadium.
• Face-centered cubic (FCC) - gamma iron, aluminum, copper, nickel, lead, silver, gold and platinum.
• Hexagonal close-packed - beryllium, cadmium, cobalt, magnesium, alpha titanium, zinc and zirconium.
Common crystal structures for metals:
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Crystal Structure of Metals
1. The Face-Centered Cubic Crystal Structure
2. The Body-Centered Cubic Crystal Structure
3. The Hexagonal Close-Packed Crystal Structure
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Face-Centered Cubic Structure (FCC)
• FCC -> a unit cell of cubic geometry, with atoms located at each of the corners and the centers of all the cube faces
• For the fcc crystal structure, each corner atom is shared among eight unit cells, whereas a face-centered atom belongs to only two
• How many atoms in a unit cell? one-eighth of each of the eight corner atoms and one-half of each of the six face atoms, or a total of four whole atoms, may be assigned to a given unit cell
• copper, aluminum, silver, and gold have fcc
• Cell volume= cube volume (generated from the center of atom at corner)
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Face-Centered Cubic Crystal Structure
• Example: Aluminum (Al)
• Moderate strength
• Good ductility
The face-centered cubic (fcc) crystal structure: (a) hard-ball model; (b) unit cell; and (c) single crystal with many unit cells
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FCC – Exercise- 1
• Derive: ; Where a = side length of the unit cell cube
And R = Radius of the atom sphere
From right angle triangle:
Solving for a:
The FCC unit cell volume:
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FCC – Coordination Number and APF
• For metals, each atom has the same number of touching atoms, which is the coordination number
• For fcc, coordination number is 12
• The APF (Atomic Packing Factor) is the sum of the sphere volumes of all atoms within a unit cell divided by the unit cell volume
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Example 3.2—APF for FCC
Considering atom as a sphere:
Volume of cell: Finally,
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Body-Centered Cubic Structure (BCC)
• BCC -> a cubic unit cell with atoms located at all eight corners and a single atom at the cube center
• Center and corner atoms touch one another along cube diagonals
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Body-Centered Cubic Crystal Structure
• Example: Iron (Fe)• Good strength
• Moderate ductility
The body-centered cubic (bcc) crystal structure: (a) hard-ball model; (b) unit cell; and (c) single crystal with many unit cells
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Assignment
• For BCC unit cell, derive that the side length a obeys the relation:
Where a = side length of the unit cell cube
And R = Radius of the atom sphere
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BCC- Cont
• Chromium, iron, tungsten exhibit bcc structure
• No of atoms in BCC unit cell: 2
• The coordination number for the BCC is 8
• the atomic packing factor for BCC lower—0.68 versus 0.74 (FCC)
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Packing Factor – FCC vs BCC
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Prove that APF for BCC unit cell is 0.68
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Hexagonal Close-Packed Crystal (HCP)
• Each of top and bottom faces of the unit cell consist of 6 atoms that form regular hexagons and surround a single atom in the center
• Another plane that provides 3 additional atoms to the unit cell is situated between the top and bottom planes
• The atoms in this mid-plane have as nearest neighbors atoms in both of the adjacent two planes
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Hexagonal Close-Packed Crystal Structure
• Example: Beryllium, Zinc
• Low strength
• Low ductivity
The hexagonal close-packed (hcp) crystal structure: (a) unit cell; and (b) single crystal with many unit cells
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Hexagonal Close-Packed Crystal (HCP)
• The equivalent of six atoms is contained in each unit cell
• If a and c represent, respectively, the short and long unit cell dimensions the c/a ratio should be 1.633
• The coordination number and the APF for the HCP are the same as for FCC: 12 and 0.74, respectively
• The HCP metals include cadmium, magnesium, titanium, and zinc, etc
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Density Computations
• Density of a material can be computed from its crystalline structure
n = number of atoms associated with each unit cell
A = atomic weight
VC = volume of the unit cell
NA = Avogadro’s number (6.023 × 1023 atoms/mol)
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EXAMPLE PROBLEM 3.3
Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and an atomic weight of 63.5g/mol. Compute its theoretical density and compare the answer with its measured density.
Solution:The crystal structure is FCC, n (atoms) = 4ACu = 63.5g/molVC = a3 = [2R(2)1/2]3 (For FCC)= 16R3(2)1/2 ; R (atomic radius) = 0.128nmUsing the equation:
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EXAMPLE PROBLEM 3.
• The literature value for density for Cu is 8.94g/cm3
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Significance of Crystal Structure: Polymorphism and Allotropy
Polymorphism: Some metals and non-metals may have more than one crystal structure . This phenomenon is known as Polymorphism, e.g., Iron has BCC structure at room temperature , but FCC structure till 912C.
Allotropy: When the above phenomenon is found in elemental solids, called Allotropy, e.g., C has two allotropes: Graphite is formed at room temperature and Diamond is formed at high temperature and pressure.
Note the difference in properties due to change in crystal structure of same metal/element
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Crystalline and Non Crystalline Materials
1. Single Crystal
2. Polycrystalline Materials
3. Anisotropy
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1. Single Crystal
• For a crystalline solid, when the repeated arrangement of atoms is perfect or extends throughout the entirety of the specimen without interruption, the result is a single crystal
• If the extremities of a single crystal are permitted to grow without any external constraint, the crystal will assume a regular geometric shape having flat faces
• Within the past few years, single crystals have become extremely important in many of our modern technologies.
Garnet
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2. Polycrystalline Materials
• Most crystalline solids are composed of a collection of many small crystals or grains; such materials are termed polycrystalline
• Initially, small crystals or nuclei form at various positions. These have random crystallographic orientations
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2. Polycrystalline Materials
• Growth of the crystallites; the obstruction of some grains that are adjacent to one another
• Upon completion of solidification, grains having irregular shapes have formed
• The grain structure as it would appear under the microscope; dark lines are the grain boundaries
• there exists some atomic mismatch within the region where two grains meet; this area, called a grain boundary
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3. Anisotropy
• The physical properties of single crystals of some substances depend on the crystallographic direction in which measurements are taken
• This directionality of properties is termed anisotropy
• The extent and magnitude of anisotropic effects in crystalline materials are functions of the symmetry of the crystal structure
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3. Anisotropy
• For many polycrystalline materials, the crystallographic orientations of the individual grains are totally random.
• Under these circumstances, even though each grain may be anisotropic, a specimen composed of the grain aggregate behaves isotropically
• Also, the magnitude of a measured property represents some average of the directional values
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3. Anisotropy
• The magnetic properties of some iron alloys used in transformer cores are anisotropic—that is, grains (or single crystals) magnetize in a <100>-type direction easier than any other crystallographic direction
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Non-crystalline Solids• Non-crystalline solids lack systematic and regular arrangement
of atoms over relatively large atomic distances. Also called amorphous (without form)
• Compare SiO2 . Crystalline structure has ordered atoms while non-crystalline structure has disorder atoms.
• Each Si atom is bonded to 3 O atoms in crystalline as well as non-crystalline structures.
Crystalline Non-Crystalline