much research (in physics, chemistry, material science, etc.) have been done to understand the difference in materials properties.

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1 1.1: Introduction Material science and engineering Classify common features of structure and properties of different materials in a well-known manner (chemical or biological): * bonding in solids are classified to be one of four categories (metallic, ionic, covalent, or van der Waals), depending on electronic structure and inter-atomic bonding forces. * structure of solids are either internally crystalline or noncrystalline. * Crystalline solids can be subdivided to one of 14 different geometric arrays or lattices, depending on the placement of the atoms. * When properties are considered, materials are either good, intermediate, or poor conductors of electricity, and they are either mechanically brittle or can easily be stretched without fracture, and they are either optically reflective or transparent, etc much research (in physics, chemistry, material science, etc.) have been done to understand the difference in materials properties. Crystal structure: the manner in which atoms, ions, or molecules are spatially arranged. Crystallinity: Repeating or periodic array over large atomic distances. 3-D pattern in which each atom is bonded to its nearest neighbors. 1

2 1. Crystalline Solids 2

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5 Examples of materials having different crystal systems 5

6 In crystal studying, we always refer to what is called planes and directions we need to know what is called Miller indices 6

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8 The interplanar spacing (space between same planes of same miller indices) in a crystal can be calculated as follows a d hkl h k l For example: the interplanar spacing between 111 planes is d111 a 3 The angle between two planes (h 1 k 1 l 1 ) and (h 2 k 2 l 2 ) can be calculated from the relation: cos h 2 1 h h k k 1 k l h l l k 2 2 l 2 2 8

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12 Theoretical Density Example, for Fcc lattice of lattice constant a, Find a) The coordination number b) Number of atoms per unit cell c) The nearest neighbor distance d) Radius of each atom (assume atoms are spheres) e) Volume of each atom f) Packing fraction g) Density of GaN which has an fcc structure, lattice constant (a = 4.5 Å), atomic weight (μga = 69.7 g/mol,μn = 14 g/mol) and Avogadro s number (N A = particles/mole). 12

13 a) Coordination number = 12 b) c) d) e) f) g) 1.3: Defects in solids In bulk materials, Perfect crystal structure is not the usual case. Usually there exist defects that disturb the regularity of the structure like grain boundaries, dislocations and vacancies. In thin crystalline films, the presence of defects in lattice influence many film properties like chemical, electrical, and mechanical properties. 13

14 1.3: Defects in solids Point defects play an important role in all processes related to solidstate diffusion, including recrystallization, grain growth, sintering, and phase transformation 1.3: Defects in solids 14

15 1.3: Defects in solids Line defects (dislocations) are important because they have provided a model to help explain a great variety of mechanical phenomena and properties in all classes of crystalline solids There exist two types of dislocations: Edge dislocation and Screw dislocation 1.3: Defects in solids 15

16 1.3: Defects in solids 1.3: Defects in solids 16

17 1.3: Defects in solids 1.3: Defects in solids 17

18 1.3: Defects in solids surface or area defects (Grain boundaries) are that defects constitute the interface between two single-crystal grains of different crystallographic orientation. 1.3: Defects in solids 18

19 1.3: Defects in solids Grain Boundaries The atomic bonding in grains, terminates at the grain boundary. at grain boundaries, more loosely bound atoms prevail. Like atoms on surfaces are more energetic than those within the grain interior. This causes the grain boundary to be a region where various atomic reactions and processes, are favored or accelerated. Examples of such atomic reactions and processes are solid-state diffusion and phase transformation, precipitation, corrosion, impurity segregation, and mechanical relaxation. In addition, electronic transport in metals is impeded through increased scattering at grain boundaries, which also serve as charge recombination centers in semiconductors. 1.3: Defects in solids 19

20 1.3: Defects in solids 20

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22 Net potential energy 22

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24 Energy bands formation: The electrons of a single, isolated atom occupy atomic orbitals. Each orbital forms at a discrete energy level as shown for Si atom When two atoms are completely isolated from each other, in a way that there s no interaction of electrons, they can have identical electronic structures. When atoms approach to form molecules, Pauli s exclusion principle assumes a fundamental role says that two different electrons can not be described by the same quantum state; so, an unfolding of the isolated atom s discrete energy levels into new corresponding levels to the electron pair occurs Energy bands formation: In order to form a solid, many atoms are brought together. Consequently, the unfolded energy levels form, essentially, continuous energy bands. Energy band As an example, the next picture shows an imaginary Si crystal formation from isolated Si atoms. As the distance between atoms approaches the equilibrium inter-atomic separation of the Si crystal, this band unfolds into two bands separated by an energy gap, E g. 24

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26 The total bonding energy at equilibrium can be calculated as follows: At equilibrium (at r 0 ) E is minimum de/dr 0 = 0. Hence we can find the constant B at r 0 E bond is calculated 26

27 Example Solution to Example : 27

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31 Covalent bond found to exist between some molecules that have hydrogen as one of the constituents like H 2 O hydrogen bond 31

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33 Thermal expansion α is less if E 0 is larger T m larger, α smaller (stiffness) 33

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