MATE 2730 exam 1

What are valence electrons?

Electrons in the outermost occupied electron shell; they participate in bonding.

What is electronegativity?

The tendency of an atom to attract shared electrons toward itself.

What type of bond generally forms between a metal and a nonmetal with a large electronegativity difference?

Ionic bonding; electrons are transferred, forming positive and negative ions.

What type of bonding involves sharing electrons?

Covalent bonding.

What type of bonding involves a sea of mobile valence electrons?

Metallic bonding.

Which primary bond is generally non-directional?

Metallic bonding.

Which primary bond is directional?

Covalent bonding.

What happens to potential energy as two atoms approach from a very large separation?

It decreases as attractive interactions become significant, reaching a minimum at the equilibrium separation.

What occurs at the equilibrium interatomic separation?

Attractive and repulsive forces balance, net force is zero, and potential energy is minimum.

What does a deeper potential-energy well generally indicate?

Stronger bonding and generally a higher melting temperature, assuming other factors are comparable.

How many crystal systems exist?

7.

How many Bravais lattices exist?

14.

How many atoms are in a simple cubic unit cell?

1 atom.

How many atoms are in a BCC unit cell?

2 atoms.

How many atoms are in an FCC unit cell?

4 atoms.

How much of a corner atom belongs to one unit cell?

1/8.

How much of a face-centered atom belongs to one unit cell?

1/2.

How much of an edge-centered atom belongs to one unit cell?

1/4.

How much of a body-centered atom belongs to one unit cell?

1.

What is the atomic radius-to-lattice parameter relationship for simple cubic?

a = 2r.

What is the atomic radius-to-lattice parameter relationship for BCC?

4r = √3a; therefore a = 4r/√3.

What is the atomic radius-to-lattice parameter relationship for FCC?

4r = √2a; therefore a = 4r/√2.

Along what feature do atoms touch in BCC?

The body diagonal.

Along what feature do atoms touch in FCC?

The face diagonal.

What is the coordination number of simple cubic?

6.

What is the coordination number of BCC?

8.

What is the coordination number of FCC?

12.

What is the atomic packing factor of simple cubic?

Approximately 0.52.

What is the atomic packing factor of BCC?

Approximately 0.68.

What is the atomic packing factor of FCC?

Approximately 0.74.

Which common cubic crystal structure has the highest atomic packing factor?

FCC, with an APF of approximately 0.74.

What is the formula for atomic packing factor?

APF = volume of atoms in unit cell / total unit-cell volume.

What is the formula for linear packing factor?

LPF = length occupied by atoms along a direction / total direction length.

What is the LPF along the BCC [111] direction in a perfect crystal?

1.000, because atoms touch along the body diagonal.

What is the LPF along the BCC [111] direction if the body-centered atom is missing?

0.500, assuming no lattice distortion.

What is the length of a face diagonal of a cubic unit cell?

√2a.

What is the length of an edge of a cubic unit cell?

a.

What do square brackets [uvw] represent?

A specific crystallographic direction.

What do angle brackets represent?

A family of crystallographically equivalent directions.

What do parentheses (hkl) represent?

A specific crystallographic plane.

What do curly brackets {hkl} represent?

A family of crystallographically equivalent planes.

How do you determine a crystallographic direction?

Determine endpoint minus starting-point coordinates, clear fractions, reduce to the smallest whole numbers, and place in square brackets.

How is a negative crystallographic direction index represented?

With a bar over the number, such as [1̅10].

How do you determine Miller indices for a plane?

Find axis intercepts in lattice parameters, take reciprocals, clear fractions, and reduce to the smallest whole numbers.

What does a zero Miller index mean?

The plane is parallel to that crystallographic axis.

What are the Miller indices for intercepts x = a, y = 2a, z = infinity?

(120).

What are the Miller indices for intercepts x = 2a, y = a, z = infinity?

(210).

What is the difference between [110] and (110)?

[110] is a direction; (110) is a plane.

What is the difference between

What is theoretical density?

The mass of atoms contained in a unit cell divided by the unit-cell volume.

What is the theoretical density equation?

ρ = nA/(VcNA), where n is atoms per unit cell, A is atomic mass, Vc is unit-cell volume, and NA is Avogadro's number.

What is the volume of a cubic unit cell?

Vc = a³.

What is Avogadro's number?

6.022 × 10²³ atoms/mol.

What units are commonly used for theoretical density in materials science?

g/cm³.

If atomic radius is given in nm, what conversion is needed to calculate density in g/cm³?

Convert lattice parameter to cm: 1 nm = 10⁻⁷ cm.

What is a vacancy?

A missing atom at a normal lattice site; a zero-dimensional point defect.

What is an interstitial impurity?

A foreign atom occupying a space between normal lattice sites.

What is a substitutional impurity?

A foreign atom replacing a host atom at a normal lattice site.

If Al atoms are introduced into Cu and replace Cu atoms, what defect forms?

Substitutional impurities.

What is a dislocation?

A one-dimensional line defect in a crystal.

What is a grain boundary?

A two-dimensional boundary separating crystals or grains with different orientations.

What is a twin boundary?

A planar defect across which the crystal structure has a mirror-related orientation.

What is a pore or void?

An empty volume within a material; commonly classified as a three-dimensional defect.

What are the dimensional classifications of vacancy, dislocation, grain boundary, and void?

Vacancy = 0D; dislocation = 1D; grain boundary = 2D; void = 3D.

What is diffusion?

The movement of atoms through a material, generally driven by a concentration gradient.

What is Fick's first law used for?

Steady-state diffusion; J = −D(dC/dx).

What is Fick's second law used for?

Nonsteady-state diffusion, when concentration changes with both position and time.

What is the common solution to Fick's second law for a semi-infinite solid with constant surface concentration?

(Cx − C0)/(Cs − C0) = 1 − erf[x/(2√Dt)].

In the diffusion equation, what does D represent?

Diffusion coefficient, commonly in m²/s.

In the diffusion equation, what does Cs represent?

Surface concentration.

In the diffusion equation, what does C0 represent?

Initial concentration.

In the diffusion equation, what does Cx represent?

Concentration at depth x after time t.

For the same material, temperature, and target concentration, how are diffusion distance and time related?

x²/t is constant; therefore t is proportional to x².

If diffusion distance doubles, how does the required time change for the same concentration?

Time increases by a factor of 4.

If diffusion distance triples, how does the required time change?

Time increases by a factor of 9.

A treatment takes 12.3 h to reach a concentration at 2.4 mm. How long to reach the same concentration at 5.4 mm?

t = 12.3(5.4/2.4)² ≈ 62.3 h.

What is the Arrhenius equation for diffusion?

D = D0 exp(−Qd/RT), or D = D0 exp(−Qd/kBT) when using energy per atom.

What happens to diffusion rate as temperature increases?

Diffusion generally becomes faster because the diffusion coefficient increases.

What is a binary alloy?

An alloy containing two components.

What is a phase?

A physically and chemically homogeneous portion of a material with distinct structure and properties.

What is a component?

A chemically distinct constituent of a system.

How many components are present in a binary alloy?

Two.

What does a single-phase region mean on a phase diagram?

Only one phase is present.

What does a two-phase region mean on a phase diagram?

Two phases coexist in equilibrium.

What is a solubility limit?

The maximum amount of solute that can dissolve in a particular phase at a specified temperature.

What does the solvus line represent?

The solid-state solubility limit separating a single-solid-phase region from a two-solid-phase region.

What does the liquidus line represent?

The boundary above which the alloy is entirely liquid.

What does the solidus line represent?

The boundary below which the alloy is entirely solid.

What is the eutectic reaction during cooling?

Liquid transforms into two solid phases: L → α + β.

What is a eutectic point?

The specific composition and temperature at which liquid transforms into two solid phases during cooling.

What is a tie line?

A horizontal line drawn across a two-phase region at a specified temperature to determine phase compositions.

How do you find the composition of each phase in a two-phase region?

Draw a horizontal tie line and read the compositions at its intersections with the phase boundaries.

In an α + L region, what does the left tie-line endpoint usually give?

The composition of the α phase, Cα.

In an α + L region, what does the right tie-line endpoint usually give?

The liquid composition, CL.

What does C0 represent in the lever rule?

The overall alloy composition.

What is the lever rule equation for the fraction of alpha in an α + L region?

Wα = (CL − C0)/(CL − Cα).

What is the lever rule equation for the fraction of liquid in an α + L region?

WL = (C0 − Cα)/(CL − Cα).

What is the relationship between the fractions of two phases in a two-phase region?

The phase fractions add to 1, or 100%.

A tie line has Cα = 10 wt% Sn, CL = 60 wt% Sn, and C0 = 30 wt% Sn. What is the alpha fraction?

Wα = (60 − 30)/(60 − 10) = 0.60, or 60%.