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1 Lect

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1 Lect

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  1. Lecture 1 ________________________________________________________________________ Materials Science and Engineering “Materials Science” involves investigating the relationships that exist between the structures and properties of materials. In contrast, “Materials Engineering” is, on the basis of these structure-property correlations, designing or engineering the structure of a material to produce a predetermined set of properties. From a functional perspective, the role of a materials scientist is to develop or create new materials, whereas a materials engineer is called upon to create new products or systems using existing materials, and/or to develop techniques for processing materials. “Processing” and “Performance” are two other important components, which involved in the science and engineering of materials. With regard to the relationships of these four components, the structure of a material will depend on how it is processed. Furthermore, a material’s performance will be a function of its properties. Thus, the interrelationship between processing, structure, properties, and performance is as illustrate in Figure 1. Figure 1 The four components of the discipline of materials science and engineering and their interrelationship. Classification of Materials The materials may be classified as: 1. Metals and Alloys 2. Ceramics and Glasses 3. Polymers 4. Composite Materials 1

  2. Lecture 1 ________________________________________________________________________ Distinguishing of Metals Elements considered to be metals are distinguished by several characteristic properties: 1. In the solid state they exist in the form of crystals (Crystalline structure – grain structure) 2. High thermal and electrical conductivity; 3. Ability to be deformed plastically; 4. Relatively high reflectivity of light (Metallic lustre). The structure of metals oThe most aspect of any engineering material is its structure, because its properties are closely related to this feature. oA materials engineer must have a good understanding of this relationship between structure and properties. 2

  3. Lecture 1 ________________________________________________________________________ Crystal Structures FUNDAMENTAL CONCEPTS Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another. Therefore, materials can be classified as either 'amorphous' or 'crystalline'. 1. Crystalline oA crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances. oUpon solidification, the atoms will position themselves in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest-neighbor atoms, under normal solidification conditions. oThe crystalline structure consists of atoms arranged according to some regular geometrical pattern. This pattern varies from one substance to another. oAll metals (solid state) are crystalline in nature. oMany ceramic materials, and certain polymers form crystalline structures 2. Non-crystalline (Amorphous) oIn the amorphous state the elementary particles are mixed together in a disorderly manner (No fixed relationship to those of their neighbours). oLack of systematic and regular arrangement of atoms oRelatively large atomic distances oThe amorphous structure is typical of all liquids (atoms or molecules can be moved easily) oThere is no any fixed pattern. The Polycrystalline structure Metals are crystalline when in the solid form. The normal metallic object consists of a group of many very small crystals (polycrystalline). The crystals in these materials are normally referred to as its grain. There is the basic structure inside the grain themselves; that is, the atomic arrangements inside the crystal. This form of structure is logically called the crystal structure. Microstructure is requiring higher magnification (100 – 1000 times) for examination. 3

  4. Lecture 1 ________________________________________________________________________ Grain and Grain boundary A piece of metal consists of a mass of separate crystals irregular in shape. Within each crystal the atoms are regularly spaced with respect to one another. At the crystal boundaries region exists a film of metal (three atoms thick) in which the atoms do not conform to any pattern (Figure 2). This crystal boundary film is in fact of an amorphous nature. The crystal boundary is not necessarily an area of weakness except at high temperatures when inter-atomic distances increase, and so bond strength decreases. Grain GRAIN BOUNDARY (ABOUT 3 ATOMS THICK) Figure 2: Diagram represents the grain and the grain boundary. Definitions Lattice: is a collection of points, called lattice points, which are arranged in a periodic pattern. Lattice used to describe arrangements of atoms. Unit cell: is the subdivision of a lattice that still retains the overall characteristics of the entire lattice (see Figure 3). When describing crystalline structures, atoms (or ions) are thought of as being solid spheres having well-defined diameters. This is termed the atomic hard-sphere model in which spheres representing nearest-neighbor atoms touch one another. 4

  5. Lecture 1 ________________________________________________________________________ Figure 3: For the face centered cubic structure (FCC), (a) a hard sphere unit cell representation, (b) a reduced-sphere unit cell, and (c) an aggregate of many atoms. crystal Crystal Systems There are seven (7) unique arrangements known as Crystal Systems. A total of 14 different arrangements of lattice points are known as the Bravais Lattices, as shown in Table 1. Three relatively simple crystal structures are found for most of the common metals (Figure 3): ►The hexagonal close-packed (HCP) represents the closest packing which is possible with atoms. ►The face-centered cubic (FCC) arrangement is also a close packing of the atoms, ►The body-centered cubic (BCC) is relatively 'open'. When a metal changes its crystalline form as the temperature is raised or lowered, there is a noticeable change in volume of the body of metal. An element which can exist in more than one crystalline form in this way is said to be polymorphic (Allotropic). Lattice parameter: The lattice parameter, which describes the size and shape of the unit cell, include the dimensions of the sides of the unit cell and the angles between the sides. In cubic crystal system, only the length of one of the sides of the cube in necessary to complete describes the cell (angles of 90o are assumed). The length is the lattice parameter (a), which is often given in nanometre (nm) or Angstromq(Ao). 1 nanometre (nm) = 10-9 m = 10-7 cm = 10 Ao 1 angstrom (Ao) = 0.1 nm = 10-10 m = 10-8 cm Where 5

  6. Lecture 1 ______________________________________________________________________ Table 1: Figures Showing Unit Cell Geometries for the Seven Crystal Systems. Table 2 Atomic Radii and Crystal Structures for 16 Metals _________________________________________________________________ 6

  7. Lecture 1 ______________________________________________________________________ Number of Atoms per unit cell When counting the number of lattice points (Atoms) belonging each unit cell, we must recognize that lattice points may be shared by more than one unit cell. 1.Simple cubic lattice (SC): A lattice point at a corner of one unit cell is shared by eight (8) unit cells. 8 atoms are located at the corners of the unit cell Thus, the number of atoms in one unit cell (SC) is determined as;     1 atoms corner      Number of atoms(SC) 8 8 corners cell  1 Atom per unit cell 2.Body centred cubic (BCC): Eight (8) atoms are located at the corners of the unit cell and one (1) atom is located at the centre of the cube.   1         Number of atoms(BCC) 8 corner 1 centre 8  2 Atoms per unit cell 3.Face centred cubic (FCC): Eight (8) atoms are located at the corners of the unit cell and Six (6) atoms are located at the centre of the cube.     1 1           Number of atoms(FCC) 8 corners 6 faces 8 2  4 Atoms per unit cell 7

  8. Lecture 1 ______________________________________________________________________ Atomic radius versus lattice parameter 1. Simple cubic lattice (SC)  2 aSC ( r r r ) a 2. Body centred cubic (BCC)  4 AB r A     2 2 2 2 2 BC a a a a r 2 r   2 2 AB BC AC r a    2 2 2 3 AB a a a B  4 3 r a C 4 r BCC a a ( ) 3 a 3. Face centred cubic (FCC) r 4 AC  r A 2 2   AC AB BC 2r 2 2    AC a a a 2  r 4 a 2 r r 4   a or a r 2 2 C B ( FCC ) ( FCC ) 2 a 8

  9. Lecture 1 ______________________________________________________________________ Atomic Packing Factor The packing factor is the fraction of the space occupied by atoms Volume of atoms in a unit cell  AtomicPack ingFactor ( APF ) Volume of unit cell ( Number of atoms / cell )( Volume of atom )  APF Volume of unit cell 1. Simple cubic lattice (SC)  2 aSC r One atom per unit cell ( ) a  r 2 3 4 4 a 4 a 3 3        Volume of an atom V r ( ) 3 3 2 3 8 3   Volume of unit  cell a 3 4 a        3 8     APF . 0 52 SC ( ) 3 6 a Thus, the fraction of unit cell (SC) occupied by atoms equals 52% of volume, while 48% is a free space. 2. Body centred cubic (BCC) 4r aBCC 2 atoms per unit cell 3    r  4 4 3 3   ( 2 ) r ( 2 ) r 3 3 3   APF ( BCC ) 4 3 a ( ) 3 8 3  r  3 3    . 0 68 # 3 8 64 r 3 3 3. Face centred cubic (FCC) 4 atoms per unit cell 4r aFCC 2      4 4  3 3 ( 4 ) ( 4 ) r r 3 3   APF ( ) FCC 4 r 3 a 3 ( ) 2 16  3 r  2 3 r    . 0 74 # APF ( ) FCC 3 6 64 2 2 9

  10. Lecture 1 ______________________________________________________________________ Theoretical Density The theoretical density of a material can be calculated using the properties of the crystal structure. ?ℎ????????? ??????? (?) = (?????? ??????? ???? ⁄ ????) ∗ (?????? ????) (?????? ?? ???? ????) ∗ (????????′? ??????) where n - number of atoms associated with each unit cell A - atomic weight VC - volume of the unit cell NA - Avogadro’s number (6.022 X 1023 atoms/mol) Example 1 Example 2 Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and an atomic weight of 63.5 g/mol. Compute its theoretical density. 10

  11. Lecture 1 ______________________________________________________________________ The Hexagonal Close-Packed structure (HCP) A special form of the hexagonal structure, where the unit cell is the skewed prism In metal with ideal HCP structure, the a and c axes are related by the ratio c/a = 1.633 c   . 1 633 & 2 a r a ( ) HCP 1.Number of atoms: 8 atoms are located at corners, and one atom is located at centre of prism ?????? ?? ????? (???) = 1 3(4 ?????) + 1 6(4 ?????) = 2 ????? 2.Atomic Packing Factor ( / Volume )( ) Number of atoms cell of atom  ( ) AtomicPack ingFactor APF Volume of unit cell 3 2     Volume of unit cell a c cos 30 , and cos 30 2 2 2 c       . 1 633 c . 1 633 a ( c a ) & a 2 r a 3 2 2 3   2 3 ( )( ) 2 Volume of unit cell a a a 2 3 8 4 4    3 3 3 ( 2 )( ) ( 2 )( ) ( ) r r r 3 3 3 3 r    APF ( ) HCP 3 3 2 ( 2 ) 2 8 2 a r    . 0 74 # APF ( ) HCP   11

  12. Lecture 1 ______________________________________________________________________ Allotropic or Polymorphic Transformations Materials that can have more than one crystal structure are called Allotropic or Polymorphic. The term allotropy is normally reversed for this behaviour in pure elements, while the term polymorphism is used for compounds. Some metals, such as iron (Fe) and titanium (Ti), have more than one crystal structure (see Table 3). At low temperature, iron has BCC structure, but at higher temperatures, iron transforms to FCC structure. Many of ceramic materials, such as Silica (SiO2) and Zirconia (ZrO2), also are polymorphic. A volume change may accompany the transformation during heating or cooling. Table 3: Crystal Structure Characteristic of some metals Atoms per Cell Packing Factor a versus r Structure Example  (Polonium)  Mn Simple cubic (SC) , Po  2 aSC ( r 1 0.52 ) 4r Body centred cubic (BCC) Fe(α), Ti(β), W, Mo, V, Zr, Cr aBCC 2 0.68 3 4r Face centred cubic (FCC) Fe (ɤ), Cu, Au, Pt, Ag, Pb, Ni aFCC 4 0.74 2 Ti (α), Mg, Zn, Co, Cd, Zr  2 aHCP ( r Hexagonal close-packed (HCP) 2 0.74 ) 12

  13. Lecture 1 ______________________________________________________________________ 13

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