Prelim 02 Chemical Bonding and Crystalline Structure PDF

Cagayan State University – Carig Campus College of Engineering and Architecture Department of Electrical Engineering First Semester S.Y. 2024-2025 Atomic Structure, Crystal Structure and Inter Atomic Bonding Engr. Raymond H. Lallabban Subj...

Cagayan State University – Carig Campus College of Engineering and Architecture Department of Electrical Engineering First Semester S.Y. 2024-2025 Atomic Structure, Crystal Structure and Inter Atomic Bonding Engr. Raymond H. Lallabban Subject Instructor Email address: [email protected] Mobile/Viber Number: 0917-771-90390 Cagayan State University – College of Engineering and Architecture S.Y. 2023-2024 Chapter 2: Atomic Structure & Interatomic Bonding ISSUES TO ADDRESS... o What promotes bonding? o What types of bonds are there? o What properties are inferred from bonding? ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2023-2024 Atomic Structure (Freshman Chem.) atom – electrons – 9.11 x 10-31 kg protons } neutrons 1.67 x 10-27 kg atomic number = # of protons in nucleus of atom = # of electrons in neutral species A [=] atomic mass unit = amu = 1/12 mass of 12C Atomic wt = wt of 6.022 x 1023 molecules or atoms 1 amu/atom = 1 g/mol C 12.011 H 1.008 etc. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Atomic Structure Some of the following properties 1) Chemical 2) Electrical 3) Thermal 4) Optical are determined by electronic structure ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Electronic Structure Electrons have wavelike and particulate properties. Two of the wavelike characteristics are electrons are in orbitals defined by a probability. each orbital at discrete energy level is determined by quantum numbers. Quantum # Designation n = principal (energy level-shell) K, L, M, N, O (1, 2, 3, etc.) l = subsidiary (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1) ml = magnetic 1, 3, 5, 7 (-l to +l) ms = spin ½, -½ ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Electron Energy States Electrons... have discrete energy states tend to occupy lowest available energy state. 4d 4p N-shell n = 4 Adapted from Fig. 2.6, Callister & 3d Rethwisch 9e. (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and 4s Engineering, p. 22. Copyright © 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.) Energy 3p M-shell n = 3 3s 2p L-shell n = 2 2s 1s K-shell n = 1 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 SURVEY OF ELEMENTS Most elements: Electron configuration not stable. Element Atomic # Electron configuration Hydrogen 1 1s 1 Helium 2 1s 2 (stable) Lithium 3 1s 2 2s 1 Beryllium 4 1s 2 2s2 Boron 5 1s 2 2s 2 2p 1 Carbon 6 1s 2 2s 2 2p 2...... Neon 10 1s 2 2s 2 2p 6 (stable) Sodium 1 1s 2 2s 2 2p 6 3s 1 Magnesium 12 1 1s 2 2s 2 2p 6 3s 2 Aluminum 13 1s 2 2s 2 2p 6 3s 2 3p 1...... Argon 18 1s 2 2s 2 2p 6 3s 2 3p 6 (stable)......... Adapted from Table 2.2, Callister & Rethwisch 9e. Krypton 36 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable) Why? Valence (outer) shell usually not filled completely. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Electron Configurations Valence electrons – those in unfilled shells Filled shells more stable Valence electrons are most available for bonding and tend to control the chemical properties example: C (atomic number = 6) 1s2 2s2 2p2 valence electrons ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Electronic Configurations ex: Fe - atomic # = 26 1s2 2s2 2p6 3s2 3p6 3d 6 4s2 4d valence 4p N-shell n = 4 electron 3d Rethwisch 9e. s Adapted from Fig. 2.6, Callister & (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and 4s Engineering, p. 22. Copyright © 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.) Energy 3p M-shell n = 3 3s 2p L-shell n = 2 2s 1s K-shell n = 1 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 The Periodic Table Columns: Similar Valence Structure inert gases give up 1e- give up 2e- accept 2e- accept 1e- give up 3e- H He LiB O F Ne e Na Mg Adapted from S Cl Ar Fig. 2.8, K Ca Sc Se Br Kr Callister & Rethwisch 9e. Rb Sr Y T I Xe e Cs B Po At Rn a Fr Ra Electropositive elements: Electronegative elements: Readily give up electrons Readily acquire electrons to become + ions. to become - ions. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Electronegativity Ranges from 0.9 to 4.1, Large values: tendency to acquire electrons. Smaller electronegativity Larger electronegativity ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Ionic bond – metal + nonmetal donates accepts electrons electrons Dissimilar electronegativities ex: MgOMg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4 [Ne] 3s2 Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6 [Ne] [Ne] ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Ionic Bonding Occurs between + and - ions. Requires electron transfer. Large difference in electronegativity required. Example: NaCl Na (metal) Cl (nonmetal) unstable unstable electron Na (cation) + - Cl (anion) stable Coulombic stable Attraction ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Ionic Bonding Energy – minimum energy most stable Energy balance of attractive and repulsive terms A B EN = EA + ER = - + n r r Repulsive energy ER Interatomic separation r Net energy EN Adapted from Fig. 2.10(b), Callister & Rethwisch 9e. Attractive energy EA ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Examples: Ionic Bonding Predominant bonding in Ceramics NaCl MgO CaF 2 CsCl Give up electrons Acquire electrons ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Covalent Bonding similar electronegativity ∴ share electrons bonds determined by valence – s & p orbitals dominate bonding Example: H2 H2 Each H: has 1 valence e-, needs 1 more H H Electronegativities are the same. shared 1s electron shared 1s electron from 1st hydrogen from 2nd hydrogen atom atom Fig. 2.12, Callister & Rethwisch 9e. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Bond Hybrization Carbon can form sp3 hybrid orbitals Fig. 2.14, Callister & Rethwisch 9e. (Adapted from J.E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.) Fig. 2.13, Callister & Rethwisch 9e. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Covalent Bonding: Carbon sp3 Example: CH4 C: has 4 valence e-, needs 4 more H: has 1 valence e-, needs 1 more Electronegativities of C and H are comparable so electrons Fig. 2.15, Callister & Rethwisch 9e. are shared in covalent bonds. (Adapted from J.E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.) ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Primary Bonding Metallic Bond -- delocalized as electron cloud Ionic-Covalent Mixed Bonding % ionic character = x (100%) where XA & XB are Pauling electronegativities Ex: MgO XMg = 1.3 XO = 3.5 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Secondary Bonding Arises from interaction between dipoles Fluctuating dipoles asymmetric electron ex: liquid H 2 clouds H2 H2 + - + - H H H H secondary secondary bonding Adapted from Fig. 2.20, bonding Callister & Rethwisch 9e. Permanent dipoles-molecule induced secondary -general + - bonding + - case: Adapted from Fig. 2.22, Callister & Rethwisch 9e. secondary -ex: liquid HCl H Cl bonding H Cl s ec on -ex: polymer dar y b ondin secondary bonding g ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Summary: Bonding Type Bond Energy Comments Ionic Large! Nondirectional (ceramics) Covalent Variable Directional large-Diamond (semiconductors, ceramics small-Bismuth polymer chains) Metallic Variable large-Tungsten Nondirectional (metals) small-Mercury Secondary smallest Directional inter-chain (polymer) inter-molecular ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Properties From Bonding: Tm Bond length, r Melting Temperature, Tm Energy r Bond energy, Eo ro r Energy smaller Tm unstretched length ro larger Tm r Eo = Tm is larger if Eo is larger. “bond energy” ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Properties From Bonding: α Coefficient of thermal expansion, α length, L o coeff. thermal expansion unheated, T1 ΔL ΔL = α (T2 -T1) heated, T 2 Lo α ~ symmetric at ro Energy unstretched length ro r α is larger if Eo is smaller. Eo larger α Eo smaller α ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Summary: Primary Bonds Ceramics Large bond energy (Ionic & covalent bonding): large Tm large E small α Metals Variable bond energy (Metallic bonding): moderate Tm moderate E moderate α Polymers Directional Properties (Covalent & Secondary): Secondary bonding dominates small Tm s ec on dar y b ondin small E g large α ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 The Structures of Crystalline Solids ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Objectives Describe the difference in atomic / molecular structure between crystalline and non-crystalline materials. Draw unit cells for face-centered cubic, body centered cubic, and hexagonal close-packed crystal structures. Derive relationships between unit cell edge length and atomic radius for face-centered cubic and body centered- cubic crystal structure. Compute the densities of metals having face-centered cubic and body centered- cubic crystal structure between their unit cell dimensions. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Outline Crystal structures Metallic crystal structures Density computations Polymorphism and allotropy Crystal systems Crystalline and non-crystalline materials Anisotrophy ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Atomic / Molecular Structure Atomic structure relates to the number of protons and neutrons in the nucleus of an atom, as well as the number of and probability distributions of the constituent electrons. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Crystal structure pertains to the arrangement of atoms in the Crystal Structures crystalline solid material. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Types of solids 1. Crystalline 2. Amorphous ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Crystalline material ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Crystalline material Atoms self-organize in a periodic or orderly array. 1. Single Crystal Atoms are in a repeating or periodic array over the entire extent of the material. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 SNO SALT W ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 2. Polycrystalline material Comprises of many small crystals or grains. (a) Polycrystalline grains, (b) grains seen under a microscope, the dark lines are the grain boundaries (a) (b) ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Solar Panels ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Amorphous ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Amorphous Lacks a systematic atomic arrangement ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 State of Solid Classified according to the regularity with which atoms or Materials ions are arranged with respect to one another. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 State of Solid Materials Characteristics Crystalline Non-Crystalline / Amorphous Crystal Structure Repeating or periodic array of Random and disordered atomic atoms, ions or molecules in a distribution / complex. Will three dimensional pattern become ordered only with some difficulty Long Range Atomic Order Present Absent State of Matter Solid Resembles that of liquid Types of Material All materials, certain ceramics & Inorganic glass, Polymers polymers ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 State of Solid Materials Sometimes the terms amorphous, glassy and vitreous are used synonymously to non-crystalline materials. Amorphous literally means “without form” or supercooled liquids. A + morphe (form) Polymers may be completely non-crystalline and semi crystalline consisting of varying degrees of crystallinity. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Crystal Structures ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Crystal Structures Crystal structure pertains to the arrangement of atoms in the crystalline solid material. In the study of crystalline structures, atoms are considered as hard spheres. 2D honeycomb crystalline structure 3D crystalline structure. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Atomic Hard-Sphere Model Describing crystalline structures, atoms (or ions) as being solid spheres having well defined diameters. In the hard-sphere model, the shortest distance between two like atoms is one diameter. It is defined in terms of unit cell geometry and the atoms positions within the unit cell. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Lattice The regular geometrical arrangement of points in a crystal space. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Unit Cells Basic structural unit of a crystal structure. It is generally defined in terms of atom (or ion) positions within a parallelepiped volume. Small groups of atoms that form a repetitive pattern which forms the entire crystal. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Unit Cells define the crystal structure by virtue of its geometry and the atom positions within. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Metallic Crystal Structures ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Metallic Crystal Structures Simple crystal structures that are found for most of the common metals: 1. Simple Cubic Crystal Structure 2. Face Centered Cubic Crystal Structure 3. Body Centered Cubic Crystal Structure 4. Hexagonal Closed Pack Crystal Structure ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Simple Cubic Crystal Structure Rare due to poor packing. Only the element Polonium (Po) has this structure Aggregate of many Space Filling Model Reduce sphere unit atoms cell or ball and stick model ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Simple Cubic Crystal Structure Number of atoms 1/8 size of atom at each corner 8 corners 1 atom Coordination Number Number of atomic nearest neighbors 6 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Face Centered Cubic (FCC) Crystal Structure This type of structure has atoms at each corner of the cubic unit cell and center of the cubic faces. Hard sphere model Reduced sphere unit cell model Aggregate of many atoms ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Face Centered Cubic (FCC) Crystal Structure Number of atoms 4 atom Coordination Number 12 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Face Centered Cubic (FCC) Crystal Structure Edge Length, a Consider the atomic radius R a2 + a2 = (4R)2 a = 2R √2 Cell Volume, Vc Vc = a3 Vc = 16R3 √2 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Face Centered Cubic (FCC) Crystal Structure Atomic Packing Factor (APF) Sum of the sphere volumes of all atoms within a unit cell. (assuming the atomic hard-sphere model) divided by the unit cell volume Vs APF = Vc Vs = number of atoms x volume of sphere Vs = 4 x ( 4 ) π R3 3 APF = 0.74 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Body Centered Cubic (BCC) Crystal Structure cubic unit cell with atoms at all eight corners and a single atom at the cube center. Hard sphere model Reduced sphere Aggregate of many unit cell model atoms ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Body Centered Cubic (BCC) Crystal Structure Number of atoms 2 atom Coordination Number 8 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Body Centered Cubic (BCC) Crystal Structure Edge Length, a a2 + a2 + a2 = (4R)2 4R a= √3 Cell Volume, Vc Vc = a3 Vc = 64R3 3√3 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Body Centered Cubic (BCC) Crystal Structure Atomic Packing Factor (APF) Vs APF = Vc APF = 0.68 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Hexagonal Closed Packed (HCP) Crystal Structure The top and bottom faces of the unit cell have six atoms forming a regular hexagon and surrounding a single atom at its center Reduced sphere unit cell model Aggregate of many atoms ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Hexagonal Closed Packed (HCP) Crystal Structure Number of atoms 6 atom Coordination Number 12 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Hexagonal Closed Packed (HCP) Crystal Structure Edge Length, a c a = 1.633 a= C 1.633 Cell Volume, Vc Vc = hexagon area x c A = 3 (2R) (2R √3 ) 2 A = 6 √3 R2 Vc = 6 √3 R2c ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Hexagonal Closed Packed (HCP) Crystal Structure Atomic Packing Factor (APF) Vs APF = Vc C a = 2R a= 1.633 c = 2(1.633)R Vc = 24 √2 R3 APF = 0.74 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example 1 Calculate the volume of the zinc crystal structure unit cell by using the following data: pure zinc has HCP crystal structure with the lattice constants a = 0.2665 nm and c = 0.4947 nm Area of triangle ABC = 0.5a2 sin 60o Ans. 0.0913 nm3 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Table of Atomic Radii and Crystal Structure ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Density Computation ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Density Computations Since the entire crystal can be generated by the repetition of the unit cell, the density of a crystalline material is: Where: ρ – theoretical density of the crystal structure of a metallic solid (g/cm 3) n – number of atoms associated within a unit cell A – atomic weight (g/mol) Vc – volume of unit cell (cm3) Na – avogadro's number (6.022 x 1023 atoms /mol) ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example 1 Chromium has an atomic radius of 0.125nm, with BCC crystal structure and atomic weight of 52.0 g/mol. Compute for its theoretical density and compare it with the measured density. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example 2 Copper has an atomic radius of 0.128nm, an FCC crystal structure with atomic weight of 63.5 g/mol. Compute for its theoretical density and compare it with the measured density. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example 3 Calculate the density and packing factor of FeO, which has a NaCl type structure. Given that: RFE2+ = 0.074nm and R02- = 0.14nm. Atomic weight of Fe = 55.8 and of O = 16 g/mol. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Polymorphism & Allotropy ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Polymorphism The ability of a solid material to exist in more than one form or crystal structure. Most often a modification of the density and other physical properties accompanies a polymorphic transformation. Allotrophy The possibility of the existence of two or more different crystal structures for a substance in an elemental solid. Prevailing crystal structure depends on both the temperature and the external pressure. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example: Iron Iron represents perhaps the best-known example for allotropy in a metal. At atmospheric pressure, there are three allotropic forms of iron: alpha iron (α) a.k.a. ferrite, gamma iron (γ) a.k.a. austenite, and delta iron (δ). At very high pressure, epsilon iron (ε) hexaferrum. Some controversial experimental evidence exists for another high-pressure form that is stable at very high pressures and temperatures. (wiki) ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example: Carbon Graphite is a stable polymorph at ambient conditions. Diamond is formed at extremely high pressures. Fullerenes or buckyballs Nanotubes or buckysheets ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example: Carbon ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example: Carbon ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Example: Carbon ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Crystal Systems A scheme by which crystal structures are classified according to unit cell geometry. Unit Cell Geometry The shape of the appropriate unit cell parallelepiped without regard to the atomic positions in the cell. ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Unit Cell Geometry In this frame work: - xyz coordinate system with the origin at one end of the cell corner - Each of the x, y & z axes coincides with one of the parallelepiped edges that extends from this corner ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Types of Crystal Systems Cubic Hexagonal Tetragonal Rhombohedral Orthorhombic Monoclinic Triclinic ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Types of Crystal Systems Crystal system Axial Interaxial Unit Cell Relationship Angles Geometry Cubic α, β, a = b = c α = β = γ = 900 γ Hexagonal a=b≠c α = β = 900 γ = 1200 ES 011_Materials Science and Engineering Types of Crystal Systems Crystal system Axial Interaxial Unit Cell Relationship Angles Geometry Tetragonal α, β, a=b≠c α = β = γ = 900 γ Rhombohedral a=b=c α=β= γ ≠ 900 (Trigonal) Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Types of Crystal Systems Crystal system Axial Interaxial Unit Cell Relationship Angles Geometry Orthorhombic a≠ b≠c α, β, γ α=β=γ = 900 Monoclinic a≠b≠c α=γ= 900 ≠ β ES 011_Materials Science and Engineering Cagayan State University – College of Engineering and Architecture S.Y. 2024-2025 Types of Crystal Systems Crystal system Axial Interaxial Unit Cell Relationship Angles Geometry α, β, γ Triclinic a≠b≠c α ≠ β ≠ γ ≠ 900 ES 011_Materials Science and Engineering