Imperfections in Solid Materials R. Lindeke ENGR 2110

In our pervious Lecture when discussing Crystals we ASSUMED PERFECT ORDER In real materials we find: Crystalline Defects or lattice irregularity Most real materials have one or more “errors in perfection” with dimensions on the order of an atomic diameter to many lattice sites Defects can be classification: 1. according to geometry (point, line or plane) 2. dimensions of the defect

ISSUES TO ADDRESS... What types of defects arise in solids? Can the number and type of defects be varied and controlled? How do defects affect material properties? Are defects always undesirable? What are the solidification mechanisms?

Solidification - result of casting of molten material –2 steps Nuclei form Nuclei grow to form crystals – grain structure Start with a molten material – all liquid Imperfections in Solids Adapted from Fig.4.14 (b), Callister 7e. Crystals grow until they meet each other nuclei crystals growing grain structure liquid

Polycrystalline Materials Grain Boundaries regions between crystals transition from lattice of one region to that of the other ‘slightly’ disordered low density in grain boundaries –high mobility –high diffusivity –high chemical reactivity Adapted from Fig. 4.7, Callister 7e.

Solidification Columnar in area with less undercooling Shell of equiaxed grains due to rapid cooling (greater  T) near wall Grain Refiner - added to make smaller, more uniform, equiaxed grains. heat flow Grains can be- equiaxed (roughly same size in all directions) - columnar (elongated grains) Adapted from Fig. 4.12, Callister 7e. ~ 8 cm

Vacancies: -vacant atomic sites in a structure. Self-Interstitials: -"extra" atoms positioned between atomic sites. Point Defects Vacancy distortion of planes self- interstitial distortion of planes

SELF-INTERSTITIAL: very rare occurrence This defect occurs when an atom from the crystal occupies the small void space (interstitial site) that under ordinary circumstances is not occupied. In metals, a self-interstitial introduces relatively (very!) large distortions in the surrounding lattice.

POINT DEFECTS The simplest of the point defect is a vacancy, or vacant lattice site. All crystalline solids contain vacancies. Principles of thermodynamics is used explain the necessity of the existence of vacancies in crystalline solids. The presence of vacancies increases the entropy (randomness) of the crystal. The equilibrium number of vacancies for a given quantity of material depends on and increases with temperature as follows: N v = N exp(-Q v /kT) Equilibrium no. of vacancies Total no. of atomic sitesEnergy required to form vacancy T = absolute temperature in  Kelvin k = gas or Boltzmann’s constant

We can get Q v from an experiment.  N v N = exp  Q v kT       Measuring Activation Energy Measure this... N v N T exponential dependence! defect concentration Replot it... 1/T N N v ln - Q v /k/k slope

Example Problem 4.1 Calculate the equilibrium number of vacancies per cubic meter for copper at 1000°C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000 ° C) for copper are 63.5 g/mol and 8.4 g/cm 3, respectively. Solution. Use equation 4.1. Find the value of N, number of atomic sites per cubic meter for copper, from its atomic weight A cu, its density, and Avogadro’s number N A.

Continuing: And Note: for MOST MATERIALS just below T m  N v /N = Here: /8 = = 2.75*10 -4

Two outcomes if impurity (B) added to host (A): Solid solution of B in A (i.e., random dist. of point defects) Solid solution of B in A plus particles of a new phase (usually for a larger amount of B) OR Substitutional solid soln. (e.g., Cu in Ni) Interstitial solid soln. (e.g., C in Fe) Second phase particle --different composition --often different structure. Point Defects in Alloys

Imperfections in Solids Conditions for substitutional solid solution (S.S.) Hume – Rothery rules –1.  r (atomic radius) < 15% –2. Proximity in periodic table i.e., similar electronegativities –3. Same crystal structure for pure metals –4. Valency equality All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency (it provides more electrons to the “cloud”)

Imperfections in Solids Application of Hume–Rothery rules – Solid Solutions 1. Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu? Table on p. 106, Callister 7e. ElementAtomicCrystalElectro-Valence Radius Structure nega- (nm) tivity Cu0.1278FCC1.9+2 C0.071 H0.046 O0.060 Ag0.1445FCC1.9+1 Al0.1431FCC1.5+3 Co0.1253HCP1.8+2 Cr0.1249BCC1.6+3 Fe0.1241BCC1.8+2 Ni0.1246FCC1.8+2 Pd0.1376FCC2.2+2 Zn0.1332HCP1.6+2 More Al because size is closer and val. Is higher – but not too much – FCC in HCP Surely Zn since size is closer thus causing lower distortion (4% vs 12%)

Imperfections in Solids Specification of composition –weight percent m 1 = mass of component 1 n m1 = number of moles of component 1 – atom percent

Wt. % and At. % -- An example

Converting Between: (Wt% and At%) Converts from wt% to At% (A i is atomic weight) Converts from at% to wt% (Ai is atomic weight)

Determining Mass of a Species per Volume  i is density of pure element in g/cc Computed this way, gives “concentration” of species i in kg/m 3 of the bulk mixture (alloy)

And: slip between crystal planes result when dislocations move, this motion produces permanent (plastic) deformation. Are called Dislocations: Schematic of Zinc (HCP): before deformation after tensile elongation slip steps which are the physical evidence of large numbers of dislocations slipping along the close packed plane {0001} Line Defects Adapted from Fig. 7.8, Callister 7e.

Linear Defects (Dislocations) –Are one-dimensional defects around which atoms are misaligned Edge dislocation: –extra half-plane of atoms inserted in a crystal structure –b (the berger’s vector) is  (perpendicular) to dislocation line Screw dislocation: –spiral planar ramp resulting from shear deformation –b is  (parallel) to dislocation line Burger’s vector, b: is a measure of lattice distortion and is measured as a distance along the close packed directions in the lattice

Edge Dislocation Fig. 4.3, Callister 7e. Edge Dislocation

Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). Bonds across the slipping planes are broken and remade in succession. Atomic view of edge dislocation motion from left to right as a crystal is sheared. (Courtesy P.M. Anderson) Motion of Edge Dislocation college/callister/CL_E WSTU01031_S/vmse /dislocations.htm

Screw Dislocations Adapted from Fig. 4.4, Callister 7e. Burgers vector b Dislocation line b (a) (b)

Edge, Screw, and Mixed Dislocations Adapted from Fig. 4.5, Callister 7e. Edge Screw Mixed

Imperfections in Solids Dislocations are visible in (T) electron micrographs Adapted from Fig. 4.6, Callister 7e.

Dislocations & Crystal Structures Structure: close-packed planes & directions are preferred. view onto two close-packed planes. close-packed plane (bottom)close-packed plane (top) close-packed directions Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none “super-close” many “near close” Specimens that were tensile tested. Mg (HCP) Al (FCC) tensile direction

Planar Defects in Solids One case is a twin boundary (plane) –Essentially a reflection of atom positions across the twinning plane. Stacking faults –For FCC metals an error in ABCABC packing sequence –Ex: ABCABABC Adapted from Fig. 4.9, Callister 7e.

MICROSCOPIC EXAMINATION Applications To Examine the structural elements and defects that influence the properties of materials. Ensure that the associations between the properties and structure (and defects) are properly understood. Predict the properties of materials once these relationships have been established. Structural elements exist in ‘macroscopic’ and ‘microscopic’ dimensions

MACROSCOPIC EXAMINATION: The shape and average size or diameter of the grains for a polycrystalline specimen are large enough to observe with the unaided eye.

Useful up to  2000X magnification (?). Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation since different Xtal planes have different reactivity. Micrograph of brass (a Cu-Zn alloy) 0.75mm Optical Microscopy Adapted from Fig. 4.13(b) and (c), Callister 7e. (Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co. crystallographic planes

Grain boundaries... are planer imperfections, are more susceptible to etching, may be revealed as dark lines, relate change in crystal orientation across boundary. Adapted from Fig. 4.14(a) and (b), Callister 7e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) Optical Microscopy ASTM grain size number N = 2 n number of grains/in 2 at 100x magnification Fe-Cr alloy (b) grain boundary surface groove polished surface (a)

GRAIN SIZE DETERMINATION The grain size is often determined when the properties of a polycrystalline material are under consideration. The grain size has a significant impact of strength and response to further processing Linear Intercept method Straight lines are drawn through several photomicrographs that show the grain structure. The grains intersected by each line segment are counted The line length is then divided by an average number of grains intersected. The average grain diameter is found by dividing this result by the linear magnification of the photomicrographs.

ASTM (American Society for testing and Materials) VISUAL CHARTS each with a number Quick and easy – used for steel ASTM has prepared several standard comparison charts, all having different average grain sizes. To each is assigned a number from 1 to 10, which is termed the grain size number; the larger this number, the smaller the grains. N = 2 n-1 No. of grains/square inch Grain size no. NOTE: The ASTM grain size is related (or relates) a grain area AT 100x MAGNIFICATION

Determining Grain Size, using a micrograph taken at 300x We count 14 grains in a 1 in 2 area on the image The report ASTM grain size we need N at 100x not 300x We need a conversion method!

For this same material, how many Grains would I expect /in 2 at 100x?

At 100x

Electron Microscopes  beam of electrons of shorter wave-length (0.003nm) (when accelerated across large voltage drop) Image formed with Magnetic lenses High resolutions and magnification (up to 50,000x SEM); (TEM up to 1,000,000x)

Uses a moveable Probe of very small diameter to move over a surface Atoms can be arranged and imaged! Carbon monoxide molecules arranged on a platinum (111) surface. Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”. Scanning Tunneling Microscopy (STM)

Summary Point, Line, and Area defects exist in solids. The number and type of defects can be varied and controlled –T controls vacancy conc. –amount of plastic deformation controls # of dislocations –Weight of charge materials determine concentration of substitutional or interstitial point ‘defects’ Defects affect material properties (e.g., grain boundaries control crystal slip). Defects may be desirable or undesirable –e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not. –Inclusions can be intention for alloy development