Questions: Point Defects: Vacancies and Interstitials

Question 1

A copper sample is heated to near its melting point, then rapidly quenched to room temperature. Compared to copper slowly cooled to room temperature, the quenched sample will have:

• A. Fewer vacancies, because rapid cooling traps atoms on their lattice sites
• B. The same vacancy concentration, because equilibrium is always maintained
• C. More vacancies, because rapid cooling freezes in the high-temperature equilibrium concentration
• D. No vacancies, because the quench prevents thermally activated defect formation

Answer: (C)

At high temperature the equilibrium vacancy concentration is much higher (n_v/N = exp(−Q_v/kT)). Rapid quenching freezes this supersaturation by preventing vacancies from diffusing to sinks and annihilating before the sample cools. The slowly cooled sample anneals out excess vacancies progressively, approaching the lower room-temperature equilibrium. This quenched-in supersaturation is exactly what engineers exploit in age-hardening alloys.

Question 2

Which statement best explains why adding ~0.3% carbon by weight transforms soft iron into hard steel?

• A. Carbon atoms substitute for iron atoms, increasing the average atomic mass and resistance to deformation
• B. Carbon atoms occupy interstitial sites, distorting the lattice and creating stress fields that impede dislocation motion
• C. Carbon atoms fill vacancies, eliminating the defects that allow atomic planes to slip past one another
• D. Carbon atoms bond strongly to grain boundaries, preventing the grains from rotating under stress

Answer: (B)

Carbon is a small atom that fits into interstitial sites in the iron lattice. This distorts the surrounding lattice elastically, generating stress fields that interact strongly with gliding dislocations — the carriers of plastic deformation. The stress fields pin dislocations, requiring more applied stress to move them, which raises yield strength dramatically. Option C is a common misconception: vacancies enable diffusion, not slip, and carbon does not preferentially fill vacancies.

Question 3

Vacancies cannot be completely eliminated from a crystalline solid at temperatures above absolute zero, no matter how carefully the material is processed.

• T. True
• F. False

Answer: True

Vacancies are thermodynamically inevitable because their formation increases entropy — there are astronomically many ways to arrange even a small number of vacancies among lattice sites. The free energy G = H − TS is minimized at the equilibrium concentration n_v/N = exp(−Q_v/kT), not at zero. Only at absolute zero does the entropic driving force vanish. Any finite-temperature crystal has an equilibrium density of vacancies that no processing step can remove.

Question 4

Interstitial defects in a crystal are generally detrimental to material properties and should be minimized during processing.

• T. True
• F. False

Answer: False

Interstitial solutes are among the most powerful strengthening mechanisms in engineering materials. Carbon atoms in interstitial sites of iron create the martensite and pearlite microstructures that make steel hard and strong; nitrogen interstitials strengthen stainless steels. Self-interstitials in a pure metal do raise energy and can degrade properties, but intentionally introduced interstitial solutes are a designed feature, not a flaw.

Question 5

Why are vacancies essential for atomic diffusion in crystalline solids, and what would happen to diffusion rates if vacancies were somehow eliminated?

Model answer: Vacancies provide the mechanism for diffusion: an atom adjacent to a vacant site can jump into it, and the net effect of billions of such exchanges is the migration of atoms through the crystal. Direct exchange (two adjacent atoms swapping positions) requires far more energy and is negligible. Without vacancies, atomic mobility in a crystal would be essentially zero at practical temperatures — processes like carburization of steel, doping of semiconductors, and recrystallization of cold-worked metals would become impossible.

The diffusion coefficient D = D₀ exp(−Q_d/kT) depends on both the jump attempt frequency and the availability of vacant sites. Both factors have exponential temperature dependences, which is why diffusion is so strongly accelerated by temperature and why rapidly quenching a metal freezes atomic mobility: not only do atoms vibrate less, but the vacancy supersaturation is kinetically locked in place.