matsci final

% crystallinity

% of material that is crystalline/ordered (Chains aligned)

Match the Equilibrium bond length at T = 0K to the appropriate feature of the atomic bonding potential energy curve, E(r), which determines that property or characteristic.

(a) Horizontal axis position at the minima

Which of the following correctly describes a vacancy?

(b) An empty position on the crystal lattice which an atom usually occupies

Simple Cubic (SC) Crystal Structure

-centers of atoms located at the eight corners of a cube -rare due to low packing density (only Po has this structure) -Close packed directions are cube edges

ionic bonding and structure requirements

1. charge neutrality 2. stable structures: maximize the no. of nearest oppositely charged neighbors

Consider a cubic crystal lattice that has an atom at the midpoint of each cube edge. How many unit cells share that atom?

4

Mg2+ has an ionic radius of 0.072 nm. O2- has an ionic radius of 0.140 nm. What should be the coordination number of the cation in MgO?

6

Consider a cubic crystal system (simple cubic, body centered cubic, or face centered cubic). How many unit cells share an atom that is positioned at a corner of the cube?

8

alternating copolymer

A and B alternate in polymer chain

random copolymer

A and B randomly positioned along chain

What is a dislocation?

A line of distorted or incomplete bonds in a crystal.

hexagonal close-packed structure (HCP)

ABAB stacking sequence-close-packed planes of atoms

You know that the melting temperature of alumina, Al2O3, is much greater than that of aluminum. Which of the following is also most likely to be true?

Al2O3 has a larger elastic modulus than aluminum.

If Ca2+ ions are present in ZrO2 as substitutional impurities (substituting for Zr4+), what other defects are required?

An O2- vacancy for every Ca2+ impurity ion

interstitial impurity

An atom occupying a position between normal lattice sites

Which of the following do you expect to exist in higher concentration in an ionic ceramic: (a) Frenkel defect for anions. (b) Frenkel defect for cations. (c) Both types of Frenkel defect will occur in equal concentrations.

Answer: Frenkel defects, wherein an ion vacancy is paired with the same ion species in an interstitial position, will be much more common for the smaller cation than the large anion since it will cause less distortion.

Match Thermal expansion coefficient to the appropriate feature of the atomic bonding potential energy curve, E(r), which determines that property or characteristic.

Asymmetry of the curve

Consider a BCC crystal of an elemental solid. What are the indices of the closest packed plane?

BCC is not a close packed system; there are no planes where each atom touches 6 neighbors on the plane. However, there is still a "closest" packed plane, with the maximum areal density of atoms. This occurs on the (110) planes for BCC, where each atom touches 4 neighbors in the plane.

Why is dislocation motion difficult in ionically bonded materials?

Bringing like charged ions together is energetically unfavorable.

Which material is most likely to form an amorphous (non-crystalline) solid upon solidification? a. an ionically bonded material. b. a covalently bonded material. c. a metal consisting of one type of atom.

Covalently bonded material By definition, ionic bonding heavily favors unlike ions neighboring each other. The energy required to disorder the system and have liked charged neighbors is thus prohibitively large. Metallic cation cores pack together as tightly as possible to most efficiently take advantage of the shared sea of electrons; for a metal with only one atom type, the densest packing is achieved in an ordered structure with 12 nearest neighbors. Furthermore, both metallic and ionic bonds are nondirectional, whereas covalent bonds are directional. The directional nature of the covalent bonds makes it difficult to align many molecules in an orderly fashion, resulting in a tendency to form amorphous, or noncrystalline, solids.

Match minima Young's modulus (the material's stiffness) to the appropriate feature of the atomic bonding potential energy curve, E(r), which determines that property or characteristic.

Curvature of E(r) near the minima

Match Melting temperature to the appropriate feature of the atomic bonding potential energy curve, E(r), which determines that property or characteristic.

Depth of potential energy well (i.e. minimum energy)

Why is dislocation motion difficult in covalently bonded materials?

Distorting directional bonds is energetically unfavorable.

In which case will atoms typically pack together more densely? (Here, density = # atoms/unit volume.)

In metallically bonded materials.

What type of bonding would be expected for Barium Oxide (BaO)

Ionic. Ba has an electronegativity of 0.9, while O has a much larger electronegativity of 3.5. The Ba looses 2e- to become Ba2+, while the O gains 2e- to become O2-

Consider two materials (A and B) with the same crystal structure but different vacancy formation energies, QA > QB. At temperature T1 > 0 K, which material would have a larger equilibrium vacancy concentration?

Material B

Suppose that CaO is present as an impurity in CaCl2. The O2- ion substitutes for Cl- ion(s). Identify the acceptable accompanying defects.

Replacing a Cl- with O2- results in a -1 charge on the crystal. To maintain charge neutrality, we may either: • create one Cl- vacancy for every O2- substitution • add one Ca2+ interstitial for every two O2- substitutions

Suppose that CaO is present as an impurity to Li2O. The Ca2+ ion substitutes for Li+ ion(s). Identify the acceptable accompanying defects.

Replacing a Li+ with Ca2+ results in a +1 charge on the crystal. To maintain charge neutrality, we may either: • create one Li+ vacancy for every Ca2+ substitution • add one O2- interstitial for every two Ca2+ substitutions

screw dislocation

Spiral stacking of crystal planes around the dislocation line, burgers is parallel to dislocation

Consider the following stacking sequence in an FCC metal: ...ABCABCBCABCA... What kind of defect is illustrated by this stacking sequence?

Stacking fault Notice that the pattern is interrupted by a missing A plane, but continues in the same order. This results in HCP-like stacking over 4 planes: ...ABCABCBCABCA...

Consider an FCC crystal of an elemental solid. What are the indices of the close packed plane?

The "close packed plane" is one in which each atom touches 6 neighbors in the plane. For FCC, this occurs on the (111) planes. Note that this is the densest possible packing for atoms of the same radius. That is why we call FCC a close packed system.

At 900 C, the diffusion coefficient for an interstitial impurity atom in alpha-Fe (BCC) is greater than that for the same interstitial impurity in gamma-Fe (FCC). Which of the following contribute to this fact? a. The BCC unit cell is more open than FCC, with larger interstitial sites. b. The FCC unit cell has more interstitial sites than BCC. c. The BCC unit cell has fewer atoms than FCC. d. Alpha-Fe (BCC) is the equilibrium structure below 900 C.

The BCC unit cell is more open than FCC, with larger interstitial sites.

Which of the following factors must be known to determine the diffusion flux of element A in host material B?

The shape of the concentration profile of A The temperature The activation energy for diffusion of A in B ALL OF THE ABOVE

How does bonding change the structure of the atoms involved in the bond?

The valence electron shell of each atom is filled.

Why do atoms form bonds?

To reach a lower energy state.

Consider the following stacking sequence in an FCC metal: ...ABCABCBACBA... What kind of defect is illustrated by this stacking sequence?

Twin Notice that the stacking sequence is mirrored across the second C: ...ABCABCBACBA...

Consider an FCC crystal. Which of the following correctly describes a crystallographic direction in which the atoms touch each other (i.e. the close packed direction)?

[110]

point coordinates

a lattice position in a unit cell

edge dislocation

a line of imperfect bonds at the bottom of an extra half plane; material permanently deforms as dislocation moves through the crystal; bonds break and reform but only along the dislocation line at any point in time, not along the whole plane at once; dislocation line separates slipped and unslipped material

A "material property" is defined as a material's measurable response to a specific imposed stimulus. Which of the following are properties of the material used to make a steel paper clip? (Select all that are appropriate.)

a) It is silver/gray in color. - YES, color is an optical property of the material. b) It is typically a curved piece of wire approx.1 mm in diameter. - NO, shape is not a material property. c) It bends without breaking. - YES, this is related to strength, stiffness, and ductility, which are all mechanical properties of the material. d) It conducts electricity. - YES, electrical conductivity is an electrical property of the material. e) It is mostly iron. - NO, the composition of the material is not a behavior (it relates more to structure).

Which of the following contribute to the (generally) lower density of covalently bonded materials than metallic bonded materials? (Select all that are appropriate.)

a) Metallic bonds are nondirectional. - YES: This enables the atoms to pack together as tightly as possible, maximizing the number of atoms in a given volume. b) Metals share electrons among all atoms in the solid. - NO: While true, this does not contribute directly to the density of the material. c) Covalent bonds are directional. - YES: This limits the ability of the atoms to pack together as tightly as possible, limiting the number of atoms in a given volume. d) Covalent bonding involves fewer electrons than metallic bonding. - NO: While the electrons are localized to a particular pair of atoms, this does not contribute directly to the density of the material.

Which of the following statements are true for covalent bonding? a. Electrons are shared between two atoms. b. Electrons transfer from the atom with the lower electronegativity to the atom with higher electronegativity. c. Bonds are non-directional. d. All of the above. e. Answers b and c.

a. Electrons are shared between the two covalently bonded atoms.

FCC Plane Stacking Sequence

abcabc

family of directions

all directions that are crystallographically equivalent (have the same atomic spacing) - indicated by indices in angle brackets

family of planes

all planes that are crystallographically equivalent (have the same atomic packing) - indicated by indices in braces

composition

amount of impurity and host in the system

Face-centered cubic structure (FCC)

atoms located at 8 cube corners and at the centers of the 6 faces

Body-centered cubic structure (BCC)

atoms located at 8 cube corners with single atom at cube center

reasons for dense packing

bonds between metal atoms are non-directoinal, nearest neighbor distances tend to be small in order to lower bond energy

Which of the following statements are true for metallic bonding? a. Electrons are shared between two atoms. b. Electrons transfer from the atom with the lower electronegativity to the atom with higher electronegativity. c. Bonds are non-directional. d. All of the above. e. Answers b and c.

c. Metallic bonds are non-directional.

molecules form covalent _____ held together by secondary bonds

chains

graft copolymer

chains of b units grafted onto A backbone

What type of bonding would be expected for Aluminum Phosphide (AlP)

covalent (with some ionic character). Al and P have positions on the periodic table that mirror column IVA, and have similar electonegativities (1.5 for Al, 2.1 for P).

What type of bonding would be expected for Along (or within) the polymer (molecular) chains in nylon

covalent. Polymers molecules are made up primarily of carbon (along the backbone) and hydrogen, which have similar electronegativities.

permanent deformation in metals occurs by

crystal planes slipping past each other

crystalline defects

drive most material behaviors, both good and bad

thermoplastics

ductile, little cross linking, reversibly soften with heating (often recyclable), i.e. polyethylene terephthalate (PET), easier to form and recycle

Which of the following statements are true for ionic bonding? a. Electrons are shared between two atoms. b. Electrons transfer from the atom with the lower electronegativity to the atom with higher electronegativity. c. Bonds are non-directional. d. All of the above. e. Answers b and c.

e. Ionic bonds form when electrons transfer from one atomic species with low electronegativity to another with high electronegativity, creating oppositely charged ions. The ions are then attracted to each other in a non-directional manner.

Crystallographic planes

enclosed in parentheses

self-interstitials

extra atom forces in between sites, distortion of planes

polycrystals are isotropic if

grains are randomly oriented

polycrystals are anisotropic if

grains are textured

defects in ceramic structures

impurities: maintain charge neutrality; substitutional cation impurity, substitutional anion impurity

Element A can diffuse through host material B via either a vacancy mechanism or interstitial mechanism. Assuming that the same energy is required for A to jump to a neighboring vacancy or interstitial, which mechanism will result in faster diffusion at a given temperature?(Vacancy diffusion Interstitial diffusion The diffusion rate will be the same for both mechanisms The answer cannot be determined from the information given)

interstitial diffusion

block copolymer

large blocks of A units alternate with large blocks of B units

graphite

layered structure of parallel hexagonal arrays of carbon atoms with weak VDW Forces bw layer, planes slide easily over one another, good for lubricant

polymer

many repeated units; covalently bonded chains, zig zag structure, easily kinked---> crystallization difficult, covalent bonding along the molecule but secondary bonds hold molecules together (secondary bonds dominate many properties)

molecular weight

mass of a moles of chains

Consider three metals. Metal A has a BCC crystal structure. Metal B has an HCP crystal structure. Metal C has an FCC crystal structure. The metals otherwise have identical bonding characteristics (e.g. same bond energy, etc.) Which metal do you expect would be the easiest to deform by dislocation motion?

metal c

What type of bonding would be expected for brass

metallic. Cu and Zn are both metals

Ceramic structures (Ionic)

more complex than metal structures, most based on FCC, HCP, and SC. Anions make up the basic lattice, cations go into interstitial sites

Glass is

non-crystalline solid, amorphous

coordination number

number of nearest-neighbors or touching atoms

impurity addition can cause solid solution alloy of B in A and

particles of a new phase (more likely as concentration of B increases, different composition, often different structure and properties)

burgers vector

perpendicular to dislocation, along direction that lattice moves

frenkel defect

point defect in ionic ceramic: a cation is out of place (cation vacancy/interstitial pair)

schottky defect

point defect in ionic ceramic: a paired set of cation and anion vacancies

functional ceramics

presence of charged ions allows interactions with electric fields/electrons. ionic conduction (diffusion)

isotropy

properties same in any direction

Anisotropy

properties vary with direction (single crystals)

What is true of the average bond length between two atoms, ravg, when the temperature is greater than 0 K but less than the melting temperature of the material? (In the answers below, r0 is the equilibrium bond length.)

ravg > r0

Coordination number increases with

rcation/ranion

atomic packing factor (APF)

relative density of atomic packing in unit cell, assuming atoms are hard spheres

Substitutional impurity

replaces host atom

What type of bonding would be expected for Between the polymer (molecular) chains in nylon

secondary/van der Waals. The molecules have stable electron configurations; weak dipole interactions hold multiple molecules together.

metallic crystals typically form ...

simple (close packed) structure -electron cloud shield cores from each other -"nearest neighbor" distances typically small to lower bond energy -bonding is not directional; stability comes from dense packing

unit cell

small groupings of atoms that can generate the complete crystal structure by repetitive displacement. more than one is possible/multiple ways to group atoms periodically

diamond

tetrahedral bonding of carbon, hardest material known, high thermal conductivity

we can predict the density of a material provided we know

the atomic weight, atomic radius, and crystal structure

primitive cell

the smallest possible unit cell

Under what conditions is Fick's First Law true?

true for all conditions

Under what conditions is Fick's Second Law true?

true for all conditions

copolymers

two or more monomers polymerized together

What are the units of the atomic packing factor?

unitless

Thermosets

usually hard and brittle, large cross linking (10-50% of mers), do not soften with heating (better structural materials), i.e. polyester resin (fiber glass) epoxies, covalent crosslinks bw molecules

Which type of defect do you expect to be more common?(vacancy, self-interstitial, equally common, or cannot be determined)

vacancy

Each lattice site is a potential

vacancy site

vacancy

vacant atomic site. leads to distortion of planes and can also lead to increase in volume, typically in ionic compounds

What type of bonding would be expected for Solid xenon (Xe)

van der Waals. Xe is an inert gas.

APF Formula

volume of atoms in unit cell/volume of unit cell