Materials Science and Diffusion: Key Concepts and Calculations

Fe self diffusion (Fe in Fe) is _____1_______ as compared to diffusion of C in Fe because Fe in Fe diffuses by a/an ______2_______ mechanism and C in Fe diffuses by a/an ______3________ mechanism.

slower, vacancy, intersitial

According to Fick's first law, in which direction does net diffusion occur?

From high concentration to low concentration

Why is interstitial diffusion typically faster than vacancy diffusion?

Interstitial diffusion does not require vacancies and involves smaller atoms

With increasing temperature, the diffusion rate increases:

exponetially

How do dislocations affect the mechanical properties of materials?

Dislocations allow plastic deformation to occur, making materials more ductile but reducing yield strength

What is a grain boundary?

An interface between crystals with different orientations

At room temperature, the concentration of vacancies in metals is typically very high (>1%).

false

Which type of defect involves missing atoms from lattice sites?

vacancy defect

Which of the following is a primary bond?

ionic bond

Based on the periodic table, which element would most likely form covalent bonds?

carbcon (c) - 14

In the linear elastic region of a stress-strain curve:

The material follows Hooke's law

The figure below shows the (111) and (110) planes in the FCC crystal structure. Which plane has the highest energy?

The (110) plane because it has the lowest planar packing density.

The coordination number (number of nearest neighbors) for the BCC crystal structure is: ______.

8

Pick the description that best matches the specific bond type listed below.

Primary Bond described by "electron sharing"

Primary Bond described by "electron transfer"

Primary Bond described as a "sea of electrons" or free electrons

Secondary Bond described as "fluctuating dipole"

covalent

ionic

metallic

van der walls

The shared bond shown in the image is an example of which primary bond type: CH4

covalent

Which material would you expect to have the highest melting point based on the cohesive energy given below?

Tungsten (860 kJ/mol) biggest number

Which material below would you expect to have the greatest Young's modulus?

c - the lowest one

A material property needs to be independent of the [x] and [y] of the material.

size, shape

What does Hooke's law state for stress and strain?

Stress is proportional to strain in the elastic region

How are Young's modulus (E), shear modulus (G), and Poisson's ratio (ν) related?

G = E/(2(1 + ν))

Engineering stress is defined as:

Force / Original cross-sectional area

The bond energy of three different metal samples are shown below. Select the sample which you would expect to have the highest melting point.

5.2 the biggest one

What is the definition of engineering strain?

Change in length divided by original length

Diffusion occurs from regions of high concentration to low concentration.

true

Why might we want to diffuse carbon into the surface of a plain carbon steel?

Increase hardness and improve wear resistance

In an FCC crystal structure, atoms touch along the face diagonal. If the atomic radius is R, what is the edge length a in terms of R?

a = 2R√2

Properties that are independent of direction in a material are called:

isotropic

Which of the following is NOT a type of point defect?

edge disolocation

What role do vacancies play in diffusion processes?

Vacancies provide empty sites that atoms can jump into, enabling diffusion

What is the primary difference between vacancy diffusion and interstitial diffusion?

Vacancy diffusion requires empty lattice sites, while interstitial diffusion does not

Interstitial diffusion is typically _______1_______ as compared to vacancy diffusion because interstitial atoms are ______2_______ as compared to atoms diffusing by a vacancy mechanism and interstitial diffusion ______3______ depend upon the presence of a vacancy in order to diffuse. You should have 3 answers

faster, smaller, does not

Which of the following is an application of diffusion in materials processing?

Semiconductor doping, gas permeation through walls, and surface hardening (carburization)

The properties of ________ materials are typically anisotropic.

crystalline

When material properties do not depend on direction i.e. they are the same in all directions, this is called:

isotropy

The figure below shows the (111) and (110) planes in the FCC crystal structure. Which plane has the lowest energy?

the (111)

On an energy-distance plot, what does r₀ represent?

The equilibrium interatomic spacing

Select the two statements below that best describe the role defects play in determining materials properties.

Defects enhance some material properties., Defects degrade some material properties.

How does vacancy concentration change with temperature?

inc. exponentailly

What is the key difference between an interstitial impurity and a substitutional impurity?

Interstitial impurities fit between host atoms, while substitutional impurities replace host atoms

What is the primary characteristic that distinguishes an edge dislocation from a screw dislocation?

Edge dislocations move parallel to the displacement of the crystal, while screw dislocations move perpendicular

Ceramics typically have more complicated structures as compared to metals. For example, the unit cell for CaF2 is shown below. How many atoms are in the unit cell shown below. The Ca2+ ions are the smaller atoms shown and are completely inside this unit cell.

4 Ca2+ + 8 F-

Which material do you expect to be able to bend more easily? One with a stacking sequence of ABCABC or one with the stacking sequence of ABABAB. Why? Select two answers below.

ABCABC Because ABCABC corresponds to the FCC structure.

When carbon exists in different forms (e.g. diamond, graphite, etc), these are known as:

allotropes or isomorphs

Recall Fick's 1st law:

Consider a planar wall of thickness, x, in which a gas is diffusing through. If we double the thickness of this wall the flux of gas through the wall will:

decrease by a factor of 2

Identify the defect type for each defect listed below.

__3__ Grain boundary

__1__ Vacancy

__1__ Interstitial atom

__2__ Edge dislocation

__3__ Twin boundary

When atoms are in their equilibrium positions, the force between atoms is:

zero

Which primary bond type is associated with a "sea of electrons" or "free electrons?"

metallic

What is Poisson's ratio?

The ratio of lateral strain to axial strain (with negative sign)

How do valence electrons guide bond formation?

Atoms gain, lose, or share electrons to achieve 8 valence electrons (noble gas configuration)

Which pair of elements would form the most ionic bond?

Sodium and Chlorine (Δχ ≈ 2.1) highest change in X

Vacancy diffusion is typically _______1_______ than interstitial diffusion because atoms diffusing by a vacancy mechanism are ______2_______ then interstitial atoms and the vacancy mechanism ______3______ upon the presence of a vacancy for diffusion to occur. You should have 3 answers selected.

slower, larger, depends

For steady-state diffusion through a wall, if you double the wall thickness while keeping the concentration difference constant, what happens to the diffusion flux?

flux halves

How does Young's modulus typically change with increasing temperature?

decreases

A direction [uvw] lies on a plane (hkl) when:

hu + kv + lw = 0

Which crystal structure has the higher atomic packing factor (APF)?

FCC (APF ≈ 0.74)

In FCC structures, which plane typically has the highest planar density and lowest surface energy?

(111)

Approximate the number of atoms in a cubic meter of metal?

10^28

A bond with 50% ionic character would be classified as:

polar covalent

What information can you find on the periodic table for each element?

Element symbol, atomic number, and atomic weight

What is the coordination number (number of nearest neighbors) for the FCC (Face-Centered Cubic) crystal structure?

12

When identifying a plane from a unit cell diagram, you should:

Find where the plane intersects the coordinate axes, take reciprocals, and clear fractions

What does a larger Young's modulus indicate about a material?

stiffer

Which plane is shown in the fcc figure below? yellow cube of circles with a green triangle in center

(111)

Indicate the relative energy for each defect below by ordering them 1 to 6 where 1 is the lowest energy and 6 is the highest energy.

vacany, dislocation, twin boundary, higher grain boundary, (110) surface, (100) surface