Materials Science and Engineering Syllabus PDF

VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Course Code : BMEE209L Materials Sc...

VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Course Code : BMEE209L Materials Science and Engineering Dr. U. Narendra Kumar, Professor Manufacturing Division School of Mechanical Engineering, Room – GDN117 School of Mechanical Engineering, VIT - Vellore 1 Objectives and Outcomes VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 2 1  Syllabus VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 3 Syllabus VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 4 2  VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 5 Syllabus VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 6 3  Question Paper Pattern VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT CAT Exams (50 Marks) Total Marks in each Section No. of Questions Marks section Part A 5 10 50 FAT Examination (100 Marks) Total Marks in each Section No. of Questions Marks section Part A 10 (Out of 11) 10 100 School of Mechanical Engineering, VIT - Vellore 7 Materials Science and Engineering Lab VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 8 4  Materials Science and Engineering Lab VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 9 Materials Science and Engineering Lab VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 10 5 VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Course Code : BMEE209L Materials Science and Engineering Dr. U. Narendra Kumar, Professor Manufacturing Division School of Mechanical Engineering, Room – GDN117 School of Mechanical Engineering, VIT - Vellore  Objectives and Outcomes VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Syllabus VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Syllabus VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Syllabus VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Question Paper Pattern VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT CAT Exams (50 Marks) Total Marks in each Section No. of Questions Marks section Part A 5 10 50 FAT Examination (100 Marks) Total Marks in each Section No. of Questions Marks section Part A 10 (Out of 11) 10 100 School of Mechanical Engineering, VIT - Vellore  Materials Science and Engineering Lab VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Materials Science and Engineering Lab VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Materials Science and Engineering Lab VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Introduction VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Everyone of us is surrounded by / with materials We live in a world that is both dependent upon and limited by materials. Everything we see and use is made of materials: cars, airplanes, computers, refrigerators, microwave ovens, TVs, dishes, silverware, athletic equipment of all types, and even biomedical devices such as replacement joints and limbs. All of these require materials specifically tailored for their application World is materialistic, You can’t imagine a world without materials!!! Importance of Study Challenger Disaster the rubber seal or O-ring, had hardened overnight in freezing Titanic Ship Wreck weather and failed when boosters ignited at launch School of Mechanical Engineering, VIT - Vellore 1  Materials Science VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Materials science combines with many areas of science and how materials science draws from chemistry, physics, and engineering to make better, more useful, and more economical and efficient stuff Materials Science – Investigating relationships that exist between the structure and properties of materials Materials Engineering is, on the basis of the structure-property correlations, designing or engineering the structure of a material to produce a pre-determined set of properties Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. School of Mechanical Engineering, VIT - Vellore 2  Materials Engineering & Technology - Tetrahedron VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Materials Science and Engineering is an interdisciplinary field concerned with inventing new materials and improving the previously known or existing materials by developing a deeper understanding Structure – Property - Composition – Synthesis – Processing relationships performance-to- Tetrahedron Details Property cost ratio Composition Chemical make up of the material composition Synthesis Refers to how materials are made from naturally occurring / man-made chemicals synthesis and (i.e.) ores processing microstructure School of Mechanical Engineering, VIT - Vellore 3  Tetrahedron Details VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Structure – Structure refers to the arrangement of a material's components from an atomic to a macro scale. Understanding the structure of a substance is key to understanding the state or condition of a material, information which is then correlated with the processing of the material in tandem with its properties., Macrostructure, Microstructure, Nanostructure, Crystal structure, Atomic structure Processing - refers to the way in which a material is achieved. Solidification Processing - Most metals are formed by creating an alloy in the molten state, where it is relatively easy to mix the components. This process is also utilized for glasses and some polymers Powder Processing - Powder processing involves consolidation, or packing, of particulate to form a `green body'. Densification follows, usually by sintering. Deposition Processing - Deposition processing modifies a surface chemically, usually by depositing a chemical vapor or ions onto a surface. It is used in semiconductor processing and for decorative or protective coating Deformation Processing - One of the most common processes is the deformation of a solid to create a desired shape. School of Mechanical Engineering, VIT - Vellore 4  Tetrahedron Details VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Properties - Does a material need to be strong and heat-resistant, yet lightweight? Is it possible to bring all the properties in one single material? Whether you're talking about a fork or the space shuttle, products have specific requirements which necessitate the use of materials with unique properties Mechanical Properties: Tensile strength, fracture toughness, fatigue strength, creep strength, hardness, shock resistance Electrical Properties: Conductivity or resistivity, ionic conductivity, semiconductor conductivity (mobility of holes and electrons) Magnetic Properties: Magnetic susceptibility, Curie Temperature, Neel Temperature, saturation magnetization Optical and Dielectric Properties: Polarization, capacitance, permittivity, refractive index, absorption Thermal Properties: Coefficient of thermal expansion, heat capacity, thermal conductivity Environmental Related Properties: Corrosion behavior, wear behavior School of Mechanical Engineering, VIT - Vellore 5  Tetrahedron Details - Application 1 VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Application to sheet steels for automotive chassis. Note that the composition, microstructure, and synthesis-processing are all interconnected and affect the performance-to- cost ratio. School of Mechanical Engineering, VIT - Vellore 6  Tetrahedron Details – Application 2 VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT What are the relationships between the structure of polymers and their electrical properties? How can devices be made using these plastics? Will these devices be compatible with existing silicon chip technology? How robust are these devices? How will the performance and cost of these devices compare with traditional devices? These are just a few of the factors that engineers and scientists must consider during the development, design, and manufacture of semiconducting polymer devices School of Mechanical Engineering, VIT - Vellore 7  Classification of Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Generalized Classification 1. metals and alloys; 2. ceramics, glasses & glass-ceramics; 3. polymers (plastics); 4. semiconductors; and 5. composite materials. School of Mechanical Engineering, VIT - Vellore 8  Representative strengths of various categories of materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 9  Metals & Alloys VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Pure metals: are elements which comes from a particular area of the periodic table. Eg., copper in electrical wires and aluminum in cooking foil and beverage cans. Metals are elements that generally have good electrical and thermal conductivity. Many metals have high strength, high stiffness, and have good ductility and shock resistance Some metals, such as iron, cobalt and nickel are magnetic. At extremely low temperatures, some metals and inter-metallic compounds become superconductors. Metal alloys contain more than one metallic element. Their properties can be changed by changing the elements present in the alloy. Eg., stainless steel, alloy of iron, nickel, and chromium; and gold jewelry which usually contains an alloy of gold and nickel, cadmium. Many metals and alloys have high densities and are used in applications which require a high mass-to-volume ratio. Some metal alloys, such as those based on aluminum, have low densities and are used in aerospace applications for fuel economy. School of Mechanical Engineering, VIT - Vellore 10  Ceramics VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT inorganic crystalline materials; naturally occurring materials Outstanding properties : Hard, brittle, high temperature resistance Ceramics are used in the substrates that houses computer chips, capacitors and spark plugs Some ceramics such as silicon based ceramic barrier coatings show great potential for use in advanced, higher efficiency engines – (Source: NASA featured article on technology dated 29/03/11) Traditional ceramics are used to make bricks, refractories / abrasives Advanced ceramics offer higher strength, better wear & corrosion resistance, enhanced thermal shock Ceramics are used to make the cutting tools – Boron Carbide, Boron Nitride; Grinding Wheels – SiC, Alumina Structural clay products (bricks, sewer pipe, roofing and wall tile, flue linings, etc.) White-wares (dinnerware, floor and wall tile, electrical porcelain, etc.) Refractories (brick and monolithic products used in metal, glass, cements, ceramics, energy conversion, petroleum, and chemicals industries School of Mechanical Engineering, VIT - Vellore 11  Ceramics and Advanced Ceramics VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Glasses (flat glass (windows), container glass (bottles), pressed and blown glass (dinnerware), glass fibers (home insulation), and advanced/specialty glass (optical fibers)) Abrasives (natural garnet, diamond, etc.) and synthetic abrasives (silicon carbide, diamond, fused alumina, etc.) are used for grinding, cutting, polishing, lapping, or pressure blasting of materials) Cements (for roads, bridges, buildings, dams, and etc.) Advanced ceramics Structural (wear resistant parts, cutting tools, and engine components) Electrical (capacitors, insulators, substrates, integrated circuit packages, piezo-electrics, magnets and superconductors) Coatings (engine components, cutting tools, and industrial wear parts) School of Mechanical Engineering, VIT - Vellore 12  Composites VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Blending different properties of the material so as to get a single material with unique properties Composite material may be defined as 2 or more materials (phases/constituents) integrated to form a newer one The individual materials that make up composites are called constituents. Most composites have two constituent materials: a binder or matrix, and a reinforcement. The reinforcement is usually much stronger and stiffer than the matrix, and gives the composite its good properties. A common example of a composite is concrete. It consists of a binder (cement) and a reinforcement (gravel). Adding another reinforcement (rebar) transforms concrete into a three-phase composite. The matrix holds the reinforcements in an orderly pattern. Because the reinforcements are usually discontinuous, the matrix also helps to transfer load among the reinforcements; Reinforcements basically come in three forms: particulate, discontinuous fiber, and continuous fiber. School of Mechanical Engineering, VIT - Vellore 13  Composites VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Matrix and Reinforcements: Matrix materials Polymers, Metals, Ceramics and Reinforcement: fibers Glass, Carbon, Organic Boron, Ceramic, Metallic, School of Mechanical Engineering, VIT - Vellore 14  Composites VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Glass reinforced composites are the most desired materials as a result of advanced technology that has gone beyond the design and application Graphite is a widely available economical reinforcement material with high stiffness, high modulus, high strength and high theoretical efficiency The first structural composite aircraft components, which were introduced during 1950-60, were made from glass fibre reinforced plastics. These components included the fin and the rudder of Grumman E-2A, helicopter canopies, frames, radomes, fairings, rotor blades, etc. Due to high strength and stiffness combined with low density, composites like Boron Fibre Reinforced Plastics (BFRP) and Carbon Fibre Reinforced Plastics (CFRP) were preferred instead of aluminium for high performance aircraft structures. For lightly loaded structures, Aramid Fibre Reinforced Plastics (AFRP) which possess low density, have been used in versatile applications School of Mechanical Engineering, VIT - Vellore 15  Polymers VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Polymers are typically organic materials. They have lower strength; but high strength to weight ratio. Not suitable for high temperature applications Many polymers have good resistance to corrosion and good electrical conductivity Polymers have thousands of applications ranging from bullet proof vests, compact discs, ropes and LCDs. Polymers are of two types – Thermosetting & Thermoplastics School of Mechanical Engineering, VIT - Vellore 16  Polymers VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Thermoplastic polymers are normally Thermosetting polymers are normally produced in one step and then made into produced and formed in the same step. products in a subsequent process. Upon heating, thermosetting polymers will They become soft and formable when become soft, but cannot be shaped or heated. When cooled significantly below their formed to any great extent, and will definitely softening point they again become rigid and not flow. usable as a formed article. These forms have very strong bonds This type of polymer can be readily recycled between the different chains. because each time it is reheated it can again This makes it almost impossible for the be reshaped or formed into a new article chains to slide past each other and result in plastics that are both hard and brittle. School of Mechanical Engineering, VIT - Vellore 17  Semiconductors VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT relatively small group of elements and compounds has an important electrical property, semi-conduction, in which they are neither good electrical conductors nor good electrical insulators. Instead, their ability to conduct electricity is intermediate. These materials are called semiconductors, and in general, they do not fit into any of the four structural materials categories based on atomic bonding. Si, Ge, GaAs are the best examples for Semiconductors School of Mechanical Engineering, VIT - Vellore 18  Functional Classification of Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore 19  Functional Classification of Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Aerospace Wood ---- Steel ---- Al alloys ----- Composites NASA’s space shuttle make use of Al powders for booster rockets tiles Al alloys, Plastics, Silica – for making space shuttle tiles Bio-Medical Bones & teeth are made up of naturally occurring ceramic – Hydroxyapaptite Plastics, Ti alloys, Austenitic stainless steels, composites are used for making artificial organs, prosthetic limbs, bone replacement parts, cardiovascular stents etc. Ultrasonic imaging systems make use of PZT (lead zirconium titanate) Magnetic Resonance Imaging (MRI) – makes use of Ni-Sn based superconductor School of Mechanical Engineering, VIT - Vellore 20  Functional Classification of Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Electronic Materials Cu, Al & other metals are used as conductors in power transmission BaTiO3 & Ta2O5 are used for making ceramic capacitors Si, GaAs, Ge, W and other conducting polymers are used as electronic materials Energy & Environmental Nuclear industry make use of materials such as Uranium oxide & Plutonium as fuels Glasses & Stainless Steels are used handling the nuclear radioactive wastages Batteries and fuel cells make use of nany ceramic materials such as Zirconia & Polymers Oil & Petroleum industry widely utilizes Zeolites, Alumina & other materials as catalyst substrates include Pt/Rh, Pt Solar power is generated using materials such as Amorphous Silicon School of Mechanical Engineering, VIT - Vellore 21  Functional Classification of Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Magnetic Computer hard disks & audio-video cassettes make use of a combination of ceramic, metallic and polymeric materials γ-Fe2O3 are deposited on to a polymeric base to make the cassettes Computer hard disks are made up of alloy consist of Co-Pt-Ta-Cr Steels based on Fe & Si are widely used for making transformer cores. Photonic Silica is widely used for making optical fibers YAG & Al2O3 are used for making lasers Amorphous Silicon is used to make Photovoltaic Modules Polymers are used in making LCDs School of Mechanical Engineering, VIT - Vellore 22  Functional Classification of Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Smart Material PZT & Shape memory alloys When properly processed PZT can be subjected to stress, a voltage is generated. This effect can be used to make such devices as spark generators for gas grills & sensors that can detect underwater objects MR Fluids (Magneto-rheological fluids) - are being widely used in the suspension system of the automobiles – Magneto-rheological fluids (MRF) consist of magnetisable solid particles (mostly iron) in a carrier fluid. Upon applying an external magnetic field, the particles are magnetised and form chains along the lines of the magnetic flux. This causes the MRF to change from a liquid to a solid state within milliseconds Automatic dimming mirrors and photo-chromic glasses make use of smart materials School of Mechanical Engineering, VIT - Vellore 23  Examination of Structure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Structure tells the arrangement of material’s components from macro scale to atomic level – Macrostructure – Microstructure – Nanostructure – SRO & LRO – Crystal Structure – Atomic Structure School of Mechanical Engineering, VIT - Vellore 24  Macrostructure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Studies / features contributes this structure include coating thickness, external porosity, flaws and cracks Visual Examination or low magnification microscope with 5x – 20x magnification School of Mechanical Engineering, VIT - Vellore 25  Microstructure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Study of material at its microscopic level ranging in microns to some nanometers Features include grain size, orientation of grains, amount of elements in the matrix Internal morphology of the material can be studied Lower end microscopes – 5x – 200x Higher end microscopes - >500x SEM analysis reveal the date to about 1,00,000 – 5,00,000 x School of Mechanical Engineering, VIT - Vellore 26  Observations from Microstructure studies VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT A grain is the portion of the material within which the arrangement of atoms are nearly identical Length Scale Range – It is the distance between the atoms When a metal solidifies from the molten state, millions of tiny crystals start to grow. The longer the metal takes to cool the larger the crystals grow. These crystals form the grains in the solid metal. Each grain is a distinct crystal with its own orientation. School of Mechanical Engineering, VIT - Vellore 27  Hi Resolution Microscopy VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Coating SEM Fractography - Void Formation Hydrogen Embrittlement Corrosion Attack School of Mechanical Engineering, VIT - Vellore 28  Nanostructure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Nano-crystalline materials are single- or multi-phase polycrystalline solids with a grain size of a few nanometers (10 Å), typically less than 100 nm Nanostructures formed chemically under ambient conditions can also be found in natural biological systems from seashells to bone and teeth in the human body In comparison to the coarse-grained materials, nano-crystalline materials show higher strength and hardness, enhanced diffusivity, and superior soft and hard magnetic properties. It is often stated that as grain size moves to nanoscale, metals get stronger and harder (and more brittle) while ceramics become more ductile (and malleable). This is an approximation and in fact the reality is more complex and dependent on what part of nano-scale the grain sizes are in Nano-crystalline silicon has properties in addition to electroluminescence (of interest for semiconductor laser applications) such as photoluminescence and thermally induced acoustic emission Nano-sized particles (approx. 5nm) of Fe2O3 are used in liquid magnets/ferro-fluids – These are used as cooling medium for loud speakers School of Mechanical Engineering, VIT - Vellore 29  Nanostructure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Nanostructured materials have been synthesized in recent years by methods including inert gas condensation, mechanical alloying, spray conversion processing, severe plastic deformation, electrodeposition from the melt, physical vapor deposition, chemical vapor processing, co-precipitation, sol-gel processing, sliding wear, spark erosion, plasma processing, auto-ignition, laser ablation, hydrothermal pyrolysis, thermophoretic forced flux system, quenching the melt under high pressure, biological templating, sonochemical synthesis, and devitrification of amorphous phases High hardnesses and yield strength values are observed for nanocrystalline materials. Superplasticity has been observed at low temperatures (0.38Tm) for nanocrystalline nickel and nickel aluminide samples. Currently, bulk nanostructured soft magnetic iron based alloys and WC–Co nanocomposites have found industrial uses Nanocrystalline coatings deposited by laser plasma discharge increased the life of ZnS samples more than five times against abrasion/erosion/rain water corrosion/impact damage School of Mechanical Engineering, VIT - Vellore 30  Short Range & Long Range Order VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT If the arrangement of atoms are regular, If the arrangement of atoms are periodic, continuous and in an orderly irregular, discontinuous and in fashion and also if the regularity & disordered fashion, then these materials repeatability is achieved for a longer will have the orderliness only for a short distances, throughout the entire volume distances, these are refereed to as then the materials termed to have long Short range order range order Crystalline materials are usually possessing LRO whereas the amorphous solids possess SRO; Single-crystal materials feature long-range order throughout the entire piece of material while poly-crystalline materials feature long-range order only within limited grains. School of Mechanical Engineering, VIT - Vellore 31  Atomic Structure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Features for how the atomic bonds lead to the different atomic and ionic arrangements It includes all atoms and the way how they are arranged The insights gained by understanding the atomic structure and bonding configuration of atoms/molecules are essential for the selection of engineering materials School of Mechanical Engineering, VIT - Vellore 32  Crystalline Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT A material has LRO if it exhibits the order over long distances throughout its entire volume The bond length will be uniform, repetitive and properly fashioned Crystalline structure is important because it contributes a lot to decide and alter the properties of a material. For example, it is easier for planes of atoms to slide by each other if those planes are closely packed. Crystals can be classified into (i) Single Crystalline and (ii) Poly-crystalline materials School of Mechanical Engineering, VIT - Vellore 33  Single Crystalline Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT A single /mono-crystal is a crystalline solid in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample with no grain boundaries The absence of defects associated with grain boundaries can give mono-crystals with unique properties in terms of mechanical, optical and electrical Typical Uses Mono-crystals of Sapphire & other materials are used for making lasers and non-linear optics Materials used to fabricate single-crystal piezoelectric elements include – lead magnesium niobate / lead titanate (PMN-PT), – lead zirconate niobate /lead titanate (PZN-PT), – lithium niobate (LiNbO3), lithium niobate with dopants, – lithium tetraborate (Li2B4O7 ), and quartz. – Barium titanate (BaTiO3) is a potential non-lead source of piezoelectric crystals for low temperature and room temperature applications School of Mechanical Engineering, VIT - Vellore 34  Single Crystalline Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Other applications for lithium tetraborate crystals include bulk acoustic wave (BAW) devices, pagers, cordless and cellular telephones, and data communication devices. Applications for quartz crystals include timing mechanisms for watches and clocks and delay lines for electrical circuits. The performance of a single-crystal element depends on the direction in which the raw crystal is cut Single Crystals of Cu has better conductivity than the polycrystalline one Mono-crystals of flourite are used in the fabrication of refractory telescopes NASA utilized single crystal superalloys which offer improved stress rupture life, low and high cycle fatigue life; however the mechanical properties of super conducting materials are highly anisotropic School of Mechanical Engineering, VIT - Vellore 35  Typical Application (NASA Source) VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT High Pressure Turbine Blades consist of a 3-part system: The single crystal Ni substrate, The bond coat/environmental barrier, and The thermal barrier coating. The image above shows a high pressure turbine blade (left), structure of the blade (center) and a magnified view of a single crystal alloy (right). Reference : http://www.grc.nasa.gov/StructuresMaterials/AdvMet/research/turbine_blades.html School of Mechanical Engineering, VIT - Vellore 36  Polycrystalline Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT A poly-crystalline material is composed of numerous, tiny crystals called crystallites; usually these have grain boundaries Poly-crystalline materials contain regions where the different grains meet is called as grain boundary Size of the grains can range from nanometer to being visible through naked eye Grain boundaries profoundly affect the mechanical and electrical properties of polycrystalline materials Depending on the size of the grain, the properties will vary Grains are classified based on the size (i) Coarse Grain (ii) Fine grain Grain size is normally quantified by a numbering system. Coarse 1-5 and fine 5-8. The number is derived from the formula n=2N-1 , where n = the number of grains per square inch at 100X magnification, N = ASTM Grain Size number Fine grained materials offer higher tensile strength and ductility under ambient conditions School of Mechanical Engineering, VIT - Vellore 37  Liquid Crystals VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT These are the polymeric materials that have a special type of order LC Polymers behave as amorphous materials (liquid like) in one state. However when an external stimulus (such as an electric field/ a temp. change) is applied, the polymer molecules undergo alignment & forms small regions that are crystalline and hence the name “liquid crystals” School of Mechanical Engineering, VIT - Vellore 38  Amorphous Materials VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT They have short range atomic arrangement of atoms/ions show a particular order relatively for a short distances Amorphous materials are often prepared by rapidly cooling the molten metal (such as glass). The cooling reduces the mobility of material’s molecules before they can pack into a more thermodynamically stable state Amorphous materials can also be produced by additives which interfere with the ability of primary constituents to crystallize Eg. Addition of soda to SiO2 results in window glass & addition of glycols to water into vitrified solid School of Mechanical Engineering, VIT - Vellore 39  Crystal Structures - Fundamental concept VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances; that is, long-range order exists, such that upon solidification. Periodicity is one of the most important properties of crystals. Crystals are highly symmetrical arrays of atoms which substantially simplifies their analysis Some of the properties of crystalline solids depend on the crystal structure of the material, the manner in which atoms, ions, or molecules are spatially arranged. School of Mechanical Engineering, VIT - Vellore  Crystal Lattice VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Crystal lattice is the periodic and systematic arrangement of atoms that are found in crystals with the exception of amorphous solids and gases. In the simplest of terms, the crystal lattice can be considered as the points of intersection between straight lines in a three-dimensional network. The physical properties of crystals like cleavage, electronic band structure and optical transparency are predominantly governed by the crystal lattice. Lattice – Arrangement of atoms/ions Motif/Basis – A group of one /more atoms located in a particular way with respect to each other and associated with lattice point Crystal Structure = Lattice + Motif/Basis School of Mechanical Engineering, VIT - Vellore  Crystal Lattices VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The concept of a lattice is directly related to the idea of translational symmetry. A lattice is a network or array composed of single motif which has been translated and repeated at fixed intervals throughout space. For example, a square which is translated and repeated many times across the plane will produce a planar square lattice. The unit cell of a lattice is the smallest unit which can be repeated in three dimensions in order to construct the lattice. In a crystal, the unit cell consists of a specific group of atoms which are bonded to one another in a set geometrical arrangement. This unit and its constituent atoms are then repeated over and over in order to construct the crystal lattice. The surroundings in any given direction of one corner of a unit cell must be identical to the surroundings in the same direction of all the other corners. The corners of the unit cell therefore serve as points which are repeated to form a lattice array; these points are termed lattice points. The vectors which connect a straight line of equivalent lattice points and delineate the edges of the unit cell are known as the crystallographic axes. School of Mechanical Engineering, VIT - Vellore  Unit Cell VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT represent the symmetry of the crystal structure the basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions within. The unit cell is characterized by its lattice parameters which consist of the length of the cell edges and the angles between them Unit cell is the subdivision of the lattice that still retains the overall characteristics of the entire lattice By stacking identical unit cells, the entire lattice can be constructed Primitive unit cells contain only one lattice point, which is made up from the lattice points at each of the corners. Non-primitive unit cells contain additional lattice points, either on a face of the unit cell or within the unit cell, and so have more than one lattice point per unit cell. Non-Primitive Primitive Symmetry restricts the unit cells to certain shapes so that the entire space is covered without gaps and overlaps School of Mechanical Engineering, VIT - Vellore  Crystal Symmetries VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Crystals possess a regular, repetitive internal structure. The concept of symmetry describes the repetition of structural features. Crystals therefore possess symmetry, and much of the discipline of crystallography is concerned with describing and cataloging different types of symmetry. Two general types of symmetry exist. – Translational symmetry describes the periodic repetition of a structural feature across a length or through an area or volume. – Point symmetry, on the other hand, describes the periodic repetition of a structural feature around a point. Reflection, rotation, and inversion are all point symmetries. Symmetries are most frequently used to classify the different crystal structures. In general one can generate 14 basic crystal structures through symmetries. These are called Bravais lattices. Any crystal structures can be reduced to one of these 14 Bravias lattices. School of Mechanical Engineering, VIT - Vellore  Lattice Parameters VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The physical properties of solids depend entirely upon the arrangement of the atoms that make up the solid and the distances between them. The arrangement of the atoms in a crystal structure is a combination of the size and shape of the unit-cell and the arrangement of atoms inside the unit-cell. The shape of the unit cells is described by the lattice symmetry. Unit cell = 3-dimensional unit that repeats in space The size of the unit-cell is described in terms of its unit-cell parameters. These are the edge lengths and the angles of the unit-cell. The unit cell geometry is defined in terms of six parameters: the three edge lengths a, b, and c, and the three inter-axial angles α, β, and γ indicated in Figure 3.4, and are termed the lattice parameters or lattice constants of a crystal structure Seven possible combinations of a, b, c & α, β, γ resulting in seven crystal systems School of Mechanical Engineering, VIT - Vellore  Bravais Lattice VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT By assigning specific values for axial lengths and inter-axial angles, unit cells of different types can be constructed Crystallographers have shown that only 7 different types of crystal systems are necessary to create and construct all the lattices Bravais showed that there are 14 possible ways of constructing the crystal lattice from seven crystal systems. Seven different crystal Systems Cubic – 3 Hexagonal – 1 0rthorhombic – 4 Tetragonal – 2 Rhombohedral – 1 Monoclinic – 2 Triclinic - 1 School of Mechanical Engineering, VIT - Vellore  Crystal Structures - The 14 Bravais Lattices VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT In 1850, Auguste Bravais showed that crystals could be divided into 14 unit cells, which meet the following criteria. The unit cell is the simplest repeating unit in the crystal. Opposite faces of a unit cell are parallel. The edge of the unit cell connects equivalent points. School of Mechanical Engineering, VIT - Vellore  Crystal Structures - The 14 Bravais Lattices VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT A Bravais lattice is an infinite array of discrete points with an arrangement and orientation that appears exactly the same viewed from any point of the array. A three dimensional Bravais lattice consists of all points with position vectors R of the form: R = n1a1 + n2a2 + n3a3, where the three primitive lattice vectors ai are not all in the same plane, and the n's are integers. one lattice point per unit cell since the points at the eight corners are shared by eight adjacent unit cells. Crystallographers often describe a crystal in terms of a non-primitive unit cell which is larger than the primitive cell. For instance, a body-centered cubic crystal has a non-cubic primitive cell, but it is often described in terms of a cubic conventional cell which is twice the size of the primitive cell. School of Mechanical Engineering, VIT - Vellore  Crystal Systems - Seven VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT 1 2 3 School of Mechanical Engineering, VIT - Vellore  Crystal Systems - Seven VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT 4 5 6 7 School of Mechanical Engineering, VIT - Vellore  Crystal Structures – Metallic Crystals VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT tend to be densely packed. have several reasons for dense packing – Typically, made of heavy element. – Metallic bonding is not directional; i.e., no restrictions as to the number and position of nearest-neighbor atoms – Nearest neighbour distances tend to be small in order to lower potential energy. have the simplest crystal structures Metallic Crystal Structures – Three relatively simple crystal structures are found for most of the common metals: body-centered cubic, face-centered cubic, and hexagonal close-packed. School of Mechanical Engineering, VIT - Vellore  Notations VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Atomic radius – It is defined as half the distance between the centres of the neighboring atoms Coordination Number – The no. of atoms which are directly surrounding the particular atom; it is also defined as the no. of nearest neighbors for that particular atom Atomic Packing fraction – Close packing of atoms in a unit cell of the crystal structure is known as APF Volume of atom per unit cell APF = No. of effective atoms in the unit cell × Volume of unit cell School of Mechanical Engineering, VIT - Vellore  Face-centered cubic (FCC) VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Some of the familiar metals having this crystal structure are copper, aluminum, silver, and gold spheres or ion cores touch one another across a face diagonal; the cube edge length a and the atomic radius R face-diagonal the length = 4R each corner atom is shared among eight unit cells, whereas a face- centered atom belongs to only two Two other important characteristics of a crystal structure – coordination number , and – the atomic packing factor (APF). School of Mechanical Engineering, VIT - Vellore  FCC - Coordination number VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT each atom has the same number of nearest-neighbor or touching atoms, which is the coordination number. For face-centered cubics, the coordination number is 12. – the front face atom has four corner nearest-neighbor atoms surrounding it, – four face atoms that are in contact from behind, and – four other equivalent face atoms residing in the next unit cell to the front School of Mechanical Engineering, VIT - Vellore  FCC - Atomic packing factor (APF) VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The APF is the sum of the sphere volumes of all atoms within a unit cell (assuming the atomic hard-sphere model) divided by the unit cell volume Both the total atom and unit cell volumes may be calculated in terms of the atomic radius R face-diagonal the length = 4R atoms per unit cell Volume = a3 the atomic packing factor is 0.74. School of Mechanical Engineering, VIT - Vellore  Comparison of crystal structures VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Crystal structure coordination # packing factor close packed directions Simple Cubic (SC) 6 0.52 cube edges Body Centered Cubic 8 0.68 body diagonal (BCC) Face Centered Cubic 12 0.74 face diagonal (FCC) Hexagonal Close Pack 12 0.74 hexagonal side (HCP) School of Mechanical Engineering, VIT - Vellore  Crystal Structures VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The Body-Centered Cubic Crystal Structure The Hexagonal Close-Packed Crystal Structure School of Mechanical Engineering, VIT - Vellore  Body Centered Cubic Crystal Structure (BCC Structure) VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The hard spheres touch one another along cube diagonal Eight nearest neighbors surround the central atom hence CN = 8 Effective Number of atoms per unit cell, n = 2 Center atom (1) shared by no other cells: 1 x 1 = 1 and 8 corner atoms shared by eight cells: 8 x 1/8 = 1 Atomic Radius R = √3 a/4 APF = 0.68 Packing Efficiency = 68% Some of the materials that possess BCC structure include lithium, sodium, potassium, barium, vanadium, alpha-iron and tungsten School of Mechanical Engineering, VIT - Vellore  Hexagonal Close Pack Structure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Metals don’t crystallize into simple hexagonal structure since the APF is too low The atoms in the hcp structure are also packed along close-packed planes. It should also be noted that both the FCC and HCP structures are known as close-packed structures with crystallographic planes having the same arrangement of atoms; However, the order of stacking the planes is different. Atoms in the hexagonal close-packed planes (called the basal planes) have the same arrangement as those in the FCC close-packed planes School of Mechanical Engineering, VIT - Vellore  Hexagonal Close Pack Structure VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The coordination number, CN = 12 (same as in FCC) Atomic radius = a/2 Number of atoms per unit cell, n = 6. – 3 mid-plane atoms shared by no other cells: 3 x 1 = 3 – 12 hexagonal corner atoms shared by 6 cells: 12 x 1/6 = 2 – 2 top/bottom plane center atoms shared by 2 cells: 2 x 1/2 = 1 School of Mechanical Engineering, VIT - Vellore  Expression for ideal c/a ratio - HCP VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The atom at point M is midway between the top and bottom faces of the unit cell that is MH= c/2. And, since atoms at points J, K, and M, all touch one another School of Mechanical Engineering, VIT - Vellore  Expression for ideal c/a ratio - HCP VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  HCP Structure - Atomic packing factor VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Crystal Structures - Density computations VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Theoretical density (ρ) for metals mass(m) Density ( ρ ) = volume(v) mass = (number of atoms per unit cell) x (mass of each atom) mass of each atom = atomic weight/Avogadro’s number n = number of atoms associated with each unit cell A = atomic weight (g/mol) VC = volume of the unit cell (cm3 per unit cell) NA = Avogadro’s number (6.022 x 1023 atoms/mol) School of Mechanical Engineering, VIT - Vellore  Theoretical Density Computation for Copper VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Question: 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 and compare the answer with its measured density. Solution : the crystal structure is FCC, n, the number of atoms per unit cell, is 4. Furthermore, the atomic weight ACu is given as 63.5 g/mol. The unit cell volume VC for FCC is where R, the atomic radius, is 0.128 nm. 16R 3 2 School of Mechanical Engineering, VIT - Vellore  Polymorphism and Allotropy VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Polymorphism – Same compound occurring in more than one crystal structure – depends on both the temperature and the external pressure – Eg. calcite, aragonite and vaterite minerals , different forms of calcium carbonate Allotropy – Polymorphism in elemental solids (e.g., carbon) School of Mechanical Engineering, VIT - Vellore  Crystallographic Points, Directions, and Planes VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT When dealing with crystalline materials, it often becomes necessary to specify a particular point within a unit cell, a crystallographic direction, or some crystallographic plane of atoms. Labeling conventions have been established in which three numbers or indices are used to designate point locations, directions, and planes. The basis for determining index values is the unit cell, with a right-handed coordinate system consisting of three (x, y, and z) axes situated at one of the corners and coinciding with the unit cell edges, as shown in Figure. For some crystal systems—namely, hexagonal, rhombohedral, monoclinic, and triclinic- -the three axes are not mutually perpendicular. School of Mechanical Engineering, VIT - Vellore  Point Coordinates VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT The position of any point located within a unit cell may be specified in terms of its coordinates as fractional multiples of the unit cell edge lengths (i.e., in terms of a, b, and c The position of any point located within a unit cell may be specified in terms of its coordinates as fractional multiples of the unit cell edge lengths (i.e., in terms of a, b, and c). To illustrate, consider the unit cell and the point P situated therein as shown in Figure. We specify the position of P in terms of the generalized coordinates q, r, and s where q is some fractional length of a along the x axis, r is some fractional length of b along the y axis, and s is some fractional length of c along the z axis. Thus, the position of P is designated using coordinates q r s with values that are less than or equal to unity. Furthermore, we have chosen not to separate these coordinates by commas or any other punctuation marks (which is the normal convention). School of Mechanical Engineering, VIT - Vellore  Point Coordinates VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Point Coordinates VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Specification of Point Coordinates Specify point coordinates for all atom positions for a BCC unit cell School of Mechanical Engineering, VIT - Vellore  Crystallographic Directions VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT A crystallographic direction is defined as a line between two points, or a vector. Steps used to determine the three directional indices: 1. A vector of convenient length is positioned such that it passes through the origin of the coordinate system. Any vector may be translated throughout the crystal lattice without alteration, if parallelism is maintained. 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 multiplied or 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, thus: [uvw]. The u, v, and w integers correspond to the reduced projections along the x, y, and z axes, respectively. For each of the three axes, there will exist both positive and negative coordinates. Thus The , , and negative indices_are also possible, which are represented by a bar over the appropriate directions within a unit cell. index. Eg. the [111 ] School of Mechanical Engineering, VIT - Vellore  Crystallographic Directions VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Crystallographic Directions VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT School of Mechanical Engineering, VIT - Vellore  Crystallographic Directions - Family VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT For some crystal structures, several nonparallel directions with different indices are crystallographically equivalent; this means that the spacing of atoms along each direction is the same. The directions in a crystal are given by specifying the coordinates (u, v, w) of a point on a vector passing through the origin. It is indicated as [uvw]. For example, the direction lies on a vector whose projection lengths on x and y axes are one unit. Directions of a form or family like , , are written as and family family School of Mechanical Engineering, VIT - Vellore  Hexagonal Crystals VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT VIT Problem – In crystals having hexagonal symmetry, some crystallographic equivalent directions will not have the same set of indices. This is circumvented by utilizing a four-axis, or Miller–Bravais, coordinate system as shown in Figure. The three a1, a2, and a3 axes are all contained within a single plane (called the basal plane) and are at 120° angles to one