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# Exam 1 Study Guide MAT E 273

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This 21 page Study Guide was uploaded by Elena Camp on Tuesday September 29, 2015. The Study Guide belongs to MAT E 273 at Iowa State University taught by Tim Cullinan in Fall 2015. Since its upload, it has received 62 views. For similar materials see Materials Science and Engineering: An Introduction in General Engineering at Iowa State University.

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Date Created: 09/29/15

MatE 273 Materials Engineering Study Guide for Midterm 1 Professor Tim Cullinan Iowa State University Fall 2015 Important Concepts for the Exam Bohr model of the atom hybridization of orbitals chemical bonding electronegativity density and prefixes Crystals structure unit cell and lattices Crystallography naming points directions families and planes Cubic Crystallography structures cube geometry packing efficiency coordinate axes lattice vectors and lattice parameters Theoretical density Bragg s Law and interplanar spacing Defects point defects vacancies ArrheniusThermally activated behavior lattice distortion line defects edge dislocation screw dislocation planarsurface defects and volume defects Diffusion vacancy diffusion selfdiffusion substitutional impurity diffusion interstitial diffusion what causes diffusion Fick s 1st law Fick s 2ncl law diffusivity and carburization The difference between heterogeneous and homogeneous Components phases composition and phase transformation Singlecomponent phase diagrams multicomponent phase diagrams binary isomorphous phase diagrams and lever law Bohr Model Bohr ll odell Example Magnesium Electrons orbit the nucleus within different shells The valence electrons are the electrons in the outermost shell The atomic number is the same number of protons and electrons an atom has Hybridization of Orbitals Hybrid orbitals occur because electrons try to maximize the distance between themselves The directional nature of hybrid orbitals play an important role in determining the structure of many materials such as pure carbon and other carbon based materials There are 4 hybrid orbitals sp sp2 and sp3 3 r 42222 c 0 M 0 s orbtijl p orbital 39l mu 5 hybrid orbitals sp hybrid orbitals shown together large lobes only This is an sp hybrid orbital N One 5 orbital I 0 on y gt 39l39wo p orbitals ef t 4e wiger 1 All 13 Three by hybrid orbitals 5 hybrid orbitals shuwn together large lobes only This is a sp2 hybrid orbital Hybridize to form four sp hybrid orbitals J V 5P 39 39 5 6 a I 5p 53 Shown together large lobes only J v This is a sp3 hybrid orbital Chemical Bonding There are two types of chemical bonding primary and secondary bonds Primary bonds Ionic electrons are transferred resulting in charged ions Covalent electrons are shared binding the atoms Metallic electron sea the valence electrons are free to move about the material Secondary bonds Van der Waals bonds Hydrogen bond permanently polarized molecules containing HN HO or HF bond Everything else this includes fluctuating induced dipole bonds polar molecules induced dipole bonds and permanent dipole bonds Mixed Bonding A bond that has mixed characteristics and is based on the difference in electronegativity between the atoms of interest To determine if a bond is purely covalent mostly covalent or mostly ionic you use the percent ionic character equation IC 1 e03925XAXB2 x 100 X4 and X3 are the electronegativity value for the atoms of interest What value for percent ionic character is what kind of bond IC 0 then the bond is purely covalent IC gt O and IC S 115 then the bond is mostly covalent IC gt 115 and IC S 668 then the bond is mostly ionic Electronegativity Electronegativity is the measure of how well an atom attracts electrons to itself from an atom bond with and is usually represented by X and AX To determine the bond type you can find the change in the electronegativity f AX 0 then the bond is has a nonpolar tendency f AX lt 17 then the bond has a polar covalent or metallic tendency f AX 17 then the bond is has a covalent tendency f AX gt 17 then the bond has an ionic tendency Denshy Density is the ratio of mass to volume and is typically reported in gCm3 The equation for density is m 107 m Nano n 10399 Mirco u 10396 Milli m 10 3 Kilo k 103 Mega M 106 Giga G 109 Crystal Structures Crystals usually fall into 4 categories where the most ordered is a perfect single crystal followed by a textured polycrystal random polycrystal and then the least orderly is a noncrystallineamorphousglass Perfect Single Crystal 39o39oojo39o o o o oo 39b y o39o o 0601 93903 jbb ob o o o39 0 5 9 96 3 quoto o quoto quoto o quoto o O 0 A longrange periodic arrangement of atoms Perfect single crystals are rare in nature and very hard to make Textured Polycrystal 39 vA An aggregate of tiny single crystals that are somewhat aligned Textured polycrystals are rare in nature Random Polycrystal An aggregate of tiny grains that are randomly oriented Random polycrystals are very common and difficult to avoid NoncrystallineAmorphousGlass Noncrystalline is very disordered has no longrange periodicity and is somewhat common Crystal Unit Cells There are 5 types of unit cells square rectangle centeredrectangular hexagonal and oblique Square Rectangle b O C 3 390 O C CenteredRectangular ab 6390 Hexagonal C O C O O O quotquotquot I I Oblique Crystal Lattices A lattice in an infinite arrangement of mathematical points each having identical surroundings There are a total of 14 lattices that can be made in 3 dimensions which belong to 7 different systems called the Bravais lattices 1 Triclinic 2 Monoclinic a 90 at90 Br90 r90 253 Centered 36mph 3 Orthorhombic 3b0 a b c ab c a b c P D C c X c 39 c O o 4 a b a v b a b a v D Simple Base Face Body Centered Centered Centered 4 Rhombohedral a B y at 90 a 5 Tetragonal a c ac c 39 c a a a a Simple Body Centered 6 Hexagonal 7 Cubic or Isometric O V i O 9 Q r 4 l 1 q I I a 39 1 r 39 I J o a o o r 39 a Simple Body Face Centered Centered These are the main ones that we are going to focus on Crystallography Naming Points When naming a point start at the origin then count how far the point is from each axis 239 gin X y g D 3 Point 1 o in 0 1 0 Point 390 1 in D 1 Fm 0 m Crystallography Directions When naming a direction start by placing the origin at the tail of the vector direction then write its coordinates in the lowest integers A direction is indicated by brackets ie hkl Fleduce to lowest intgg ers Fractional Coordinates X y z Direction 1 0 1 0 D l 0 1 0 D 1 r0 0 0 1 D 0 1 l Crystallography Planes When naming a plane start by placing the origin that is not on your plane of interest then write the intersection between the plane and the axes then take the reciprocal 1 of the intersection A plane is indicated by patenthesis ie hkl Reciprocal Z intersections With A i X Z Plaine DO 00 1 U U 391 In this case the plane never intersects i cuts me x or y axes a 111051 intersections are therefore written as no and their reciprocals are zero e 39w X Cuhic Setting p Iquot la lbl IE 1 y900 21 Crystallography Families Here is some of the important families A trick for families is that the plane hkl will be perpendicular to the direction hkl Edges lt1 0 11gt Face Diagonal lt1 1 11gt Baily Diagonal lt1 1 1gt Faces I Squares 1 0 Ramps IWedges 1 1 Eqiuiilateral Triangles 1 1 1 Z Z A A a a N am 11 m i y iv v 1 on I a 7 V a E a F a i l n x 1 Cubic Crystallography Structures The 3 cubic structures that we will be focusing on is Simple Cubic SC BodyCentered Cubic BCC and FaceCentered Cubic FCC Simple Cubic BodyCentered Cubic FaceCentered Cubic FCC Lattice Crystal Structure Cubic Geometry Because crystals form cubic structures most of the math dealing with the crystals also deals with the hypotenuse of a plane Packing Efficiency There are 3 ways to describe how well atoms occupy space Linear Packing Factor LPF Planar Packing Factor PPF and Atomic Packing Factor APF Linear Packing Factor LPF Length Occupied Along Length of Interest Total Length of Interest Planar Packing Factor PPF Area Occupied Within Area of Interest Total Area of Interest Atomic Volume Packing Factor APF Volume Occupied Within Volume of Interest Total Volume of Interest Simple Cubic BodyCentered Cubic FaceCentered Cubic a2R ax3 4R ax2 4R Coordinate Axes Lattice Vectors and Lattice Parameters a b E are lattice vectors a IEI are lattice parameters the magnitude of the lattice vectors Z Tricllliinic Sing 2 ygiubiicje ing a a1 gin lm y I51Ilbll39ci quot a 9 2 900 39 agpy 139 Bl l Theoretical Density For cubic unit cells we have a relationship between a and R thus that we can derive the number of atoms per unit cell n nA m pVNAa3 Bragg s Law Bragg s Law allows you to find where the constructive interference occurs when a light laser etc hits a certain type of crystal and is diffracted off Bragg s Law can also be used to find the Xray diffraction pattern 711 2 Zdhkl 111 6 Where n is the order dhkl is the interplanar spacing and 6 is one half of the diffraction angle w mww Interplanar Spacing To find the distance between parallel lattice planes hkl and hi1 kil lil you want to use a modified distance formula dcubic a W W Point Defects Vacancy a missing atom in the host material Substitutional Impurity an impurity positioned on a lattice site of the host material Interstitial Impurity an impurity within the empty space of a host material SelfInterstitial a host atom that is out of alignment and centered over an interstitial site Vacancies Vacancies are caused by thermal fluctuations and are necessary for selfdiffusion To find the number of vacancies in a material use the following equation Eatom ka E rnole RT NV Noe Noe Where NV is the density of vacancies N0 is the density of atomic sites EV is the energy to form a vacancy kb is Boltzmann s Constant 8616 X 10 5 R is the gas constant 8314 and T is the temperature in kelvin ArrheniusThermally Activated Behavior Many of the phenomenas that are discussed are based off of this equation and the concept that the processes speed up as the temperature increases EIA EA P Poe 167739 Poe RT Lattice Distortion There are two types of lattice distortion or strain vacancy and selfinterstitial Vacancy causes a local tension in which the surrounding atoms are relaxed and slightly separated 39 F 7 31 30 Selfinterstitial causes a local compression in which the surrounding atoms have less room and are more compact Line Defects There are 2 types of line defects edge dislocation and screw dislocation Edge Dislocation is where a portion of the atoms in the plane are missing or have been added II J Dislocation Line Burgers vector Ed 8 l E 11 da 5 dislocgation lll lllw line a as a 0 V l39 f f f Screw dislocation occurs when a plane of shear and form a quothelical ramp or step quotquotquotquotquotI V A 3 IIIIIIIIIIII b Dislocationb Line PlanarSurface Defects There are 2 types of planarsurface defects exposed surfaces and grain boundaries Exposed surface open white spaces could be outer surfaces or even internal porosity the atomic disregistry along the intersection of crystals with different orientations a M t ltgt 00 ltgt 4quot 4 T iii 1 Volume Defects There are 2 types of volume defects porosity and inclusions Porosity large voids that didn t fill during casting this causes holes and makes the part mechanically undesirable Macro Porosity mm Micro Porosity sub mm I I l Inclusions carbon particles that get caught in the casting process and if the material is casted wrong then it causes large clumps of this carbon x quot 1 pig s K I 39 h nd Diffusion Vacancy Diffusion a vacancy and a host atom swap positions SelfDiffusion a vacancy and a host atom swap positions Substitutional Impurity Diffusion an impurity and a host atom swap positions Interstitial Diffusion species that are small enough to fit in the interstitial sites of a crystal are able to diffuse freely thought this connected network of open spaces n 44 0 mum Causes of Diffusion Diffusion is caused by entropy This happens because nature does not like the orderly concentration gradients thus over time diffusion will occur and the species will tend to mix Fick s Laws Fick s 1st Law can be applied to steady state diffusion Constant dt M I At Fick s 2quot l Law can be applied to nonsteady state diffusion M at Constant dt ac D azc at 6x2 Diffusivity Diffusivity measures the mobility of a diffusing species in a host material If diffusivity is high then that means that diffusion is fast Diffusivity can be measured using this equation D Doe Where Do is a temperature independent preexponential and Qd is the activation energy for diffusion Carburization Carburization is technique where a lowcarbon steel part is placed in a very hot furnace than dipped in water or oil to quench or temper the part This causes the steel to harden or carburize For nonsteady state diffusion we ll assume that diffusion occurs through a semiinfinite 1D solid so the solution to Fick s 2ncl Law is Cx Co CS Co 1 erfltZjDt Where C5 is the concentration of carbon at the surface C0 is the uniform carbon concentration Cx is the carbon concentration after some time t and erf stands for inverse error function Heterogeneous v Homogeneous Heterogeneous a system featuring portions that differ in composition and properties Homogeneous a portion of a system that have uniform composition and properties Components The components of a systems are the smallest set of idependently variavle chemical constituents necessary to express the composition of each phase that is present Components are chemically distinct Elements compounds molecules ions etc could be components depending on the specific system of interest Phases Any portion including the whole system that is physically homogeneous within itself and bounded by a surface so that it s mechanically separate from other phases It is not always as easy as distinguishing between solids liquids and gases Composition A measure of the relative amounts of the components in a system If there is one component in multiple phases in a solution then the composition is 100 of that component Phase Transformation A phase transformation involves the changing of the atomic structure in response to various driving forces such as pressure and temperature Here is a phase transformation diagram for Plutonium Phase Diagrams A phase Diagram is a convenient way to graphically represent a material s response to its condition and it describes the equilibrium state of a material as a function of the thermodynamic state variables temperature pressure and composition TPC There are several types of phase diagrams that we will encounter The first type is the single component phase diagram the second type is the multiphase diagram and finally the third type is the binary iosmorphous phase diagram SingleComponent Phase Diagram 1 000 I l l l l I i l I I l I 100 Liquid 10 Sam Melting Points Water 10 Pressure aim 01 001 0001 a A ow 720 0 20 4o gt0 80 100 120 Temperature l C MultiComponent Phase Diagram l u Liquid i NeCl 2H20 2 4 5 an 1m 2 NaCl Binary Isomorphous Phase Diagram A special where there is a complete solid solubility between two components Temperature A solid solulilm of A iln B lB Composition A Lever Law The phase fractions within a multiphase field will vary according to the mathematics of a fulcrum located at the overall composition of interest 1300 licmd Uclm0 zllxuun 1300 s P0 30 39 40 30 V M L InnpumhcniwllNH 1 Draw horizontal lines at the temperature of interest until they interest the nearest phase boundanes 2 Label the levers R and S 3 The weight fraction of a phase is given by the length of the opposite lever over the entrie length of the levers R Q Q fa RS Ca Q 5 cg CO h2R5Q q

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