Illustrated Physics
physics, drawn
Concept

Porosity — where it appears

The fraction of a solid's volume occupied by empty space, in pores, voids or gaps between grains. It sets how much fluid a material can hold and, with the pores' size and connectedness, how easily fluid flows through it; in metals it often marks where vacancies have condensed.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Grains that hide their own shadows. The share of the grain surface an observer can see that is also lit, against the angle between the observer's line of sight and the light's direction, for random layers of grains filling 10, 30, 50 per cent of the space, with the light 20° from the vertical. Computed by following sight lines to the first grain they meet and asking whether that point can see the source. At zero phase angle the share is exactly one: every surface the observer sees is lit, because the observer is looking along the light's own path. Away from it shadows come into view, and the share falls to 0.51, 0.63, 0.70 at 40°. The fall is fastest in the loosest layer — half of it is complete by 4.9° — and slowest in the densest, 14.2°, because long shadows between widely spaced grains need only a small change of viewpoint to be seen.

The full moon that is too bright

Half a moon shows half the lit disc, so it ought to be about half as bright as a full one — a little less, allowing for the angle. It is a tenth as bright. In the last few days before full the Moon brightens far faster than its growing area can explain, and the extra light is not reflected any more strongly. It comes from shadows disappearing. The lunar soil is a loose heap of grains, and when the Sun is directly behind the observer every grain hides its own shadow.

optics · Scattering Two metals mixing at unequal speeds. The fraction of the fast-diffusing species A against position across a welded couple, A on the left and B on the right, at three times in the ratio 1 : 4 : 16, when A diffuses 3 times as fast as B, from Darken's equations, in units in which B's diffusivity and the middle time are both one; each profile's marker — an inert wire laid at the original weld — as a dot on it. The profiles spread as the square root of time, and they are lopsided: A pours into B's side faster than B into A's, so the mixed zone extends further into B. The markers do not stay at the weld. They move into A's side — by 0.39, 0.80 and 1.63 units at the three times — because the lattice planes of A's side are being emptied faster than they are filled. That drift, first seen in copper and brass in 1947, is the Kirkendall effect.

The markers that move because atoms are unequal

In 1947 Ernest Kirkendall and Alice Smigelskas wound fine molybdenum wires around a bar of brass, plated it thickly with copper, and heated it for fifty-six days. The wires, which do not dissolve in either metal, ended closer together: the brass inside them had shrunk. Zinc had diffused out of the brass faster than copper diffused in, and the lattice planes of the brass had been taken away along with the zinc. If atoms in a metal moved by swapping places with each other, the two flows would have had to be equal. They were not, and the only way the books balance is if atoms move by jumping into vacancies — empty lattice sites — that flow the other way. The wires were the first direct evidence that diffusion in metals runs on holes.

thermodynamics · Diffusion

Named alongside it

The objects these essays reach for when they reach for this one.

Coherent backscatteringDiffusionFicks lawInterdiffusionKirkendall effectLambertian surfaceLattice defectOpposition effectPhase angleRandom walkRegolithScattering

All concepts