es 67 lecture notes

Prepared by: Engr. Jonah L. Gamutan || Reference: Callister- Materials Science and Engineering (Wiley, 2007)

ES 67 Elements of Materials Science – Lecture Notes (1) Classification of Engineering Materials

1. METALS v Composed of one or more metallic elements and often non-metallic elements in relatively

small amounts; May exist in pure (elemental) or alloyed form v eg. Steel = Alloy of iron (Fe) and carbon (C) v Properties: Excellent conductors of both heat and electricity, strong, dense and ductile

2. CERAMICS v Compounds between metallic and non-metallic elements v eg. Oxides (SiO2, Al2O3), Carbides (SiC), Nitrides (Si3N4), glass and cement v Properties: Poor conductors of heat and electricity, strong and hard but extremely brittle

3. POLYMERS v Plastic and rubber materials that are chemically organic in composition (composed of

carbon, hydrogen and other minor elements) v eg. PVC (Polyvinyl chloride), Polyethylene, Polystyrene, Silicone rubber v Properties: Relatively low melting points compared with metals and ceramics, extremely

ductile, and light-weight 4. COMPOSITES

v Combination of two or more individual materials designed to achieve a set of properties not attainable from using only one type of material; incorporates the best characteristics of each of the component material

v eg. Fiberglass = glass fibers embedded in a polymeric material Advance Materials – materials that are utilized in high-tech applications:

a. Semiconductors – possess electrical properties that are intermediate between metals and ceramics; made possible the advent of integrated circuit boards that has totally revolutionized the electronics and computer industries

b. Biomaterials – utilized in medical and surgical operations; implanted into the human body for replacement or support of damaged body parts

Review: ATOMIC AND MOLECULAR STRUCTURE

Components of an atom: Charge Mass Location Proton, p+ +1.6 x 10-19 C 1.67262 x 10-27 kg Nucleus Neutron, n0 0 1.67492 x 10-27 kg Nucleus Electron, e– -1.6 x 10-19 C 9.10938 x 10-31 kg Orbitals

Traditional system of naming of an element:

where: A = mass number = # of p+ + # of n0 Z = atomic number = # of p+

Bohr Atomic Model X = element symbol


Isotopes – atoms of the same elements that have different atomic masses (mass numbers) Avogadro’s number – defines the amount of substance in terms of one mole = 6.023 x 1023 particles QUANTUM MECHANICS

• Stipulates that the energies of electrons are quantized; electrons are permitted to have only specific values of energy. When an electron changes energy, it must either jump to an allowed higher energy level (with the absorption of energy) or to an allowed lower energy level (with a release of energy).

Wave mechanics model of an atom – the electron is considered to behave both as a wave and a particle; its

position is considered to be a probability of it being at various locations around the nucleus Quantum Numbers

1. Principal Quantum Number, n • Defines the distance of an electron from the nucleus and describes the size of the orbital • Has integral values beginning with unity such that n = 1, 2, 3, 4, 5…

2. Angular Momentum Quantum Number, l

• Describes the shape of an electron subshell • Values range from 0 to (n-1)

Value of l Subshell Shape Values for ml

0

s

spherical

ml = 0

1

p

polar

ml = -1, 0, +1

2

d

clover leaf

ml = -2, -1, 0, +1, +2

3. Magnetic Quantum Number, ml

• Defines the number of energy states available for each subshell such that ml ranges from • Range of values for ml = from –l to +l

4. Electron Spin, ms

• Describes the spin of an electron; can only have values of +½ or –½ corresponding with “spin” and “opposite spin”


Order of Orbital Filling

Pauli Exclusion Principle – states that each electron state can only hold a maximum of two electrons, which must have opposite spins; thus the s, p, and d subshells may each accommodate a total of 2, 6, and 10 electrons respectively.

Electron configuration – represents the manner in which the energy

states of an atom are occupied Example: Si (z=14) 1s22s22p63s23p2 Ge (z=32) 1s22s22p63s23p63d104s24p2 Valence electrons – electrons that occupy the outermost shell;

participate in the bonding between atoms.

***Atoms tend to assume the most stable electronic configuration structures, like those of the noble gases, by completely filling its outermost electron shell. This tendency gives rise to the three types of primary bonds. Types of Primary Bonds

1. IONIC – involves the transfer of electrons; found in compounds that are composed of both metallic and non-metallic elements, situated at the horizontal extremities of the periodic table

• eg. NaCl (salt): Na+ - gives up its valence electron à CATION (positively charged ion) Cl- - accepts the valence electron from Na à ANION (negatively charged ion)

2. COVALENT – involves the sharing of electrons; atoms that are covalently bonded will each contribute at least one electron to the bond and the shared electrons may be considered to belong to both atoms

• eg. CH4 (methane):

3. METALLIC – found in metals and their alloys; electrons are delocalized, meaning, they are not bound to any particular atom and are free to move throughout the entire metal as a “sea of electrons”


STRUCTURE OF SOLIDS Solid materials are basically classified according to the regularity with which the atoms or ions are arranged with respect to one another:

Ø Crystalline material – possess atoms that are arranged in a repeating or periodic array over large atomic distances; long-range order exists. Upon solidification, atoms position in a repetitive 3D pattern wherein each atom is bonded to its nearest-neighbor atom.

Ø Amorphous or non-crystalline – characterized by the absence of a long-range atomic order; atoms are arranged in a random order and disorder exists.

Crystal Structure – describes the manner in which atoms or ions are arranged in space; atoms or ions are

thought of as being solid spheres with well-defined diameters, represented in terms of the atomic hard sphere model.

Example of (a) an atomic hard sphere model (b) reduced sphere unit cell or the ball-and-stick model.

Unit cell – basic repeating pattern or unit in a crystal structure; its geometry is completely defined in terms of six lattice parameters (as indicated in the figure on the left):

• Three edge lengths a, b, and c

• Three inter-axial angles αααα, ββββ, and γγγγ ***On this basis, there are seven different possible combinations of a, b, and c; and αααα, ββββ, and γγγγ each of which represents a distinct crystal system.

Seven Crystal Systems:

1. Cubic – possess the greatest degree of symmetry 2. Hexagonal 3. Tetragonal 4. Rhombohedral or Trigonal 5. Orthorhombic 6. Monoclinic 7. Triclinic – possess the least symmetry


Lattice Parameter Relationships and Figures Showing the Unit Cell Geometries for the Seven Crystal Systems


Metallic Crystal Structures Most metallic structures assume relatively large numbers of nearest neighboring atoms and dense atomic packing due to its atomic bonding which is non-directional in nature. Three of the above-mentioned crystal structures are found for most of the common metals:

1. Face-Centered Cubic (FCC) v The unit cell for an FCC crystal structure has a cubic geometry, with atoms located at each of

the corners of the cube and each of the centers of all the cube faces. v eg. Copper (Cu), Aluminum (Al), Silver (Ag) and Gold (Au)

Face-centered cubic crystal structure

2. Body-Centered Cubic (BCC) v The unit cell for a BCC crystal structure also has a cubic geometry with atoms located at all

eight corners of the cube and a single atom at the cube center. v eg. Chromium (Cr), Iron (Fe), and Tungsten (W)

Body-centered cubic crystal structure

3. Hexagonal Close-Packed (HCP) v The unit cell for an HCP crystal structure has a hexagonal symmetry with the top and bottom

faces consisting of six atoms that form regular hexagons surrounding a single atom in the center. Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes.

v eg. Cadmium (Cd), Magnesium (Mg), Titanium (Ti), and Zinc (Zn)


Hexagonal close-packed crystal structure

Factors that influence the 3-D packing of atoms:

a. Coordination Number, CN – corresponds to the number of nearest-neighbor or touching atoms – influenced by the type of bonding present, and by the relative sizes of the atoms

b. Atomic Packing Factor – volume fraction in a crystal structure that is occupied by the atoms – mathematically, equivalent to the sum of the sphere volumes of all atoms within a unit cell divided by the unit cell volume:

�� volume�of�atoms�in�a�unit�cell

total�unit�cell�volume

Crystal Structure Coordination Number

Number of atoms in a Cell

Atomic Packing Factor

FCC 12 4 0.74 BCC 8 2 0.68 HCP 12 6 0.74

Density Computations Knowledge of the crystal structure of a metallic solid permits computation of its theoretical density, ρρρρ, through the relationship:

ρ� � ��

��

where n = number of atoms associated with each unit cell A= atomic weight VC = volume of the unit cell NA = Avogadro’s number


Polymorphism – tendency of a solid material to exist in more than one type of crystal structure; when found in elemental solids, the condition is often termed as allotropy.

– eg. Iron (Fe) has a BCC crystal structure at room temperature and changes to FCC at 912°C. CRYSTALLOGRAPHIC POINTS, DIRECTIONS, AND PLANES

Labeling conventions have been established in which three numbers or indices are used to designate specific point locations, directions and planes within a unit cell. The basis for determining these numbers is the unit cell, with a right-handed coordinate system consisting of three (x, y, and z) axes.

1. Point Coordinates v The position of any point located within a unit cell may be specified in terms of the

generalized coordinates q, r, and s where: q = fractional length along the x-axis r = fractional length along the y-axis s = fractional length along the z-axis Thus, point coordinates for P is given as: q r s **Note: Generally, no punctuation marks, such as commas, are used to separate these coordinates.

2. Crystallographic Directions

v Defined as a line or a vector between two points. v The following steps are utilized in the determination of the three directional indices:

1.) The vector is positioned such that it passes through the origin of the coordinate system. 2.) The length of the vector projection on each of the three axes is determined; these are measured in terms of the unit cell dimensions a, b, and c. 3.) These three numbers are divided by a common factor to reduce them to the smallest integer values. 4.) The three indices, not separated by commas, are enclosed in square brackets: [uvw]. These correspond to the reduced projections along the x, y, and z axes, respectively.

**Note: Negative indices are represented by a bar over the appropriate index.


3. Crystallographic Planes v Orientations of planes in a crystal structure are specified by three Miller Indices as (hkl);

any two planes parallel to each other are equivalent and thus have identical indices. v The steps employed in determining the values of h, k and l are as follows:

1. If a plane passes through the origin, another parallel plane must be constructed by an appropriate translation, or a new origin must be established.

2. The crystallographic plane, at this point, either intersects or parallels each of the three axes; the length of the planar intercept for each axis is determined in terms of the lattice parameters a, b, and c.

3. Reciprocals of these numbers are taken as the indices. A plane parallel to any axis is considered to have an infinite intercept, and, thus, a zero index.

4. These indices are reduced to smallest integers by division with a common factor. 5. Miller Indices, not separated by commas, are enclosed within parentheses: (hkl)

Determination of Miller Indices for Crystallographic Planes

“Family of Planes”

Ø Contains all those planes that are crystallographically equivalent – having the same atomic packing. Ø Designated by indices that are enclosed in braces, such as {111}.

Crystalline Materials can either exist as a:

a) Single Crystal – Exists when the periodic and repeated arrangement of atoms extends throughout the entirety of the specimen without interruption. Single crystals exist in nature but may also be produced artificially in controlled laboratory environments.

b) Polycrystalline Material – Composed of a collection of many small crystals or grains that form during the solidification of a material. Initially, small crystals of random crystallographic orientation are formed and gradually, these grains grow until they impinge on one another as the solidification process is completed.

**Grain boundary – a region of mismatch where two grains meet Anisotropy

v Implies the directionality of the properties of materials associated with the variation of atomic and ionic spacing with crystallographic direction. In contrast, materials which possess properties that are independent of direction are called isotropic.


DETERMINATION OF CRYSTAL STRUCTURES: The X-Ray Diffraction Technique Constructive vs. Destructive Interference Diffraction of a wave occurs when it encounters a series of obstacles that (1) are capable of scattering the wave, and (2) have spacings comparable in magnitude to the wavelength. Two possibilities may result from this event:

Constructive Interference: Two waves remain in phase after a scattering event.

Destructive Interference: Two waves become out of phase after a scattering event.

Bragg’s Law

v When a beam of x-ray impinges on a solid material, part of this beam will be scattered in various directions by the electrons contained within the material. The necessary conditions for constructive interference to occur, according to Bragg’s Law, is as follows:


Constructive interference of the scattered rays occurs at an angle θ if the following is satisfied:

�λλλλ� � �� or

�λλλλ� � �� θθθθ �� θθθθ

�λλλλ� � !�� θθθθ where: n = order of reflection with integer values (1, 2, 3…) λλλλ = wavelength dhkl = interplanar spacing θθθθ = angle of incidence = angle of diffraction **If Bragg’s Law is not satisfied, then the interference will be non-constructive in nature. DEFECTS AND IMPERFECTIONS IN SOLIDS Materials, in reality, do not possess a perfect crystalline structure through its entirety. Imperfections, or defects, basically exist in all materials up to some extent. And in some cases, these imperfections are deliberately fashioned to achieve some desired properties. Types of Crystalline Defects

1. Point Defects – associated with one or two atomic positions a. Vacancy

Ø Indicates a vacant lattice site, one which is normally occupied from which an atom is missing. The presence of vacancies increases the entropy of a material. The equilibrium number of vacancies for a given material varies with temperature according to the following equation:

where N = total number of atomic sites Qv = energy required for the formation of a vacancy T = absolute temperature in Kelvin K = Boltzmann constant = 1.38 x 10-23 J/atom-K

b. Interstitial Ø Occurs when an impurity atom fills the voids or interstices, a position that is normally

unoccupied in the crystal structure. Furthermore, self-interstitial arises when the site is occupied by an atom from its own lattice.

c. Substitutional Ø Substitutional defects arise when impurity atoms replace or substitute the host atoms

occupying the crystal structure. This usually occurs in case of alloys, wherein impurity atoms are intentionally added to a metal to impart specific characteristics.


Illustration of the various types of Point Defects.

2. Linear Defects – one-dimensional region in the lattice characterized by local faults in atomic

arrangements; creates dislocations which allow atoms to slip and slide past one another under applied forces that are much lower than predicted.

a. Edge Dislocation Ø Arises from the insertion of an extra plane of atoms midway through the crystal

structure, distorting the nearby plane of atoms. Causes: i. “Accidents” in the growth process during solidification

ii. Presence of internal stresses associated with other defects in the crystal iii. Interactions between existing dislocations

Ø Burger’s vector is perpendicular to the dislocation line

Schematic representation of an Edge Dislocation

*Burger’s vector – describes the magnitude and direction of a lattice distortion associated with a dislocation

b. Screw Dislocation Ø Burger’s vector is parallel to the dislocation line Ø Formed by a shear stress that shifts the upper front region of the crystal one atomic

distance to the right, relative to the bottom portion. Derived its name from the spiral or helical path that is traced around the dislocation line by the plane of atoms.


Schematic representation of a Screw Dislocation

3. Interfacial or Planar Defects – defects that come in two dimensions and form from normally

separate regions of the material that have different crystal structures and orientations. a. External Surfaces

Ø Contains the surface atoms where the crystal structure terminates. Exist in a higher energy state than the atoms at the interior positions since atoms are not bonded to the maximum number of nearest neighbors.

b. Grain Boundaries Ø An atomic mismatch or separation between two small grains or crystal having different

crystallographic orientations in a polycrystalline material. Also exist in a higher energy state than the internal atoms of the grain and serve as a site for chemical reactions.

c. Twin Boundaries Ø A special type of grain boundary wherein there is specific mirror lattice symmetry; that

is, atoms on one side of the boundary are located in mirror-image positions of the atoms on the other side.

d. Stacking Faults Ø Found in metals when there is an interruption in the stacking sequence of close packed

planes. This occurs due to a collapse of the vacancy cluster or insertion of a cluster of interstitials.

e. Phase Boundaries Ø Exist in multiphase materials across which there is a sudden change in the physical and

chemical characteristics.

es 67 lecture notes

Documents

metals v

nonmetallic elements

minor elements v

cement v properties

carbon c v properties

rubber materials

ceramics v compounds

component material v