11.4 Electrical and Chemical Properties of Materials

11.4 Electrical and Chemical Properties of Materials

Two NCEES Materials sub-topics are covered here: "Electrical properties of materials" and "Chemical properties of materials." Both are tested as material-selection knowledge rather than as circuit analysis or reaction stoichiometry — the question is which material behaves how, and why.

Electrical Resistivity and Conductivity

$R = \frac{\rho L}{A}, \qquad \sigma = \frac{1}{\rho}$

The span from copper to fused quartz is 26 orders of magnitude — the widest range of any engineering property, which is why the conductor/semiconductor/insulator classification is qualitative rather than a matter of degree.

Why aluminum is used for transmission lines despite worse resistivity. Copper conducts about 58% better per unit volume, but aluminum's density is 2{,}700 kg/m³ against copper's 8{,}960. Per unit mass, aluminum conducts roughly twice as well — and for a suspended conductor, mass is what sets tower spacing and cost. This is a material-selection judgment where the raw property table gives the wrong answer.

Temperature Dependence: The Sign Distinguishes the Class

$\rho_T = \rho_0\left[1 + \alpha_T(T - T_0)\right]$

For copper, $\alpha_T \approx 0.00393$/°C. A copper winding heating from 20 °C to 120 °C gains:

$\frac{\rho_{120}}{\rho_{20}} = 1 + 0.00393(100) = 1.393$

39% more resistance — which is why motor and transformer windings are tested for resistance to infer their temperature, and why $I^2R$ losses grow as equipment heats.

Exam discriminator: if resistance rises with temperature the material is a metal; if it falls, a semiconductor. A thermistor's steeply negative coefficient is what makes it a temperature sensor (see the Instrumentation chapter), while a platinum RTD's positive, highly linear coefficient is what makes it a precision one.

Semiconductors and Doping

Intrinsic silicon has a band gap of 1.11 eV (germanium 0.67 eV, gallium arsenide 1.42 eV). Doping adds carriers:

Silicon has 4 valence electrons; a group V atom contributes a fifth that is loosely bound and free to conduct, while a group III atom leaves a vacancy — a hole — that conducts by accepting electrons. Doping at parts per million can raise conductivity by six orders of magnitude, which is the entire basis of the semiconductor industry.

Dielectric Properties

$C = \frac{\varepsilon_r\varepsilon_0 A}{d}$

Chemical Properties: Corrosion and Chemical Resistance

The Materials sub-topic "Chemical properties of materials" is tested mainly through corrosion behavior — a material-selection question rather than the electrochemical calculation covered in the Chemistry chapter.

The Galvanic Series

When two dissimilar metals are electrically coupled in an electrolyte, the more active (anodic) metal corrodes preferentially and the more noble (cathodic) one is protected. Ordered from active to noble in seawater:

Two consequences drive real designs:

1. Sacrificial anodes. Bolting a magnesium or zinc block to a steel hull makes the block the anode; it corrodes and the steel does not. Galvanizing applies the same principle as a coating — zinc protects steel even where the coating is scratched through, because the exposed steel becomes the cathode.
2. Cathodic protection. Impressing a current makes the protected structure the cathode, used for buried pipelines and tanks.

The Area Ratio Effect

The single most useful corrosion design rule: corrosion rate depends on current density at the anode, not total current. So:

$\text{Small anode + large cathode} = \textbf{rapid, penetrating attack}$ $\text{Large anode + small cathode} = \text{slow, distributed attack}$

Steel bolts in a copper plate fail quickly — a small steel anode carries the entire galvanic current from a large copper cathode, concentrating attack at the fasteners. Copper bolts in a steel plate are far safer: the large steel anode spreads the same total current thinly.

The general rule for fasteners follows directly: always make the fastener the more noble member, because the fastener is the small-area component and its failure is disproportionately consequential.

Passivation

Some metals form a thin, adherent, self-healing oxide that protects the bulk:

The oxygen paradox. Passive films need oxygen to re-form. In an oxygen-starved crevice — under a gasket, beneath a deposit, inside a lap joint — the film cannot heal, and stainless steel suffers crevice corrosion and pitting precisely where it is least accessible. This is why stainless is unreliable in stagnant chloride service despite excellent general corrosion resistance, and why designs avoid crevices and dead legs. Chlorides specifically break down the chromium oxide film, which is the mechanism behind chloride stress corrosion cracking of austenitic stainless steels.

Chemical Resistance of Polymers

Polymer "corrosion" is fundamentally different from metal corrosion — it proceeds by swelling, solvation, plasticization, and chain scission rather than electrochemistry, so a polymer often fails by losing stiffness and dimensional stability rather than by losing mass.

Worked Example: Fastener Selection

A stainless steel (304) plate assembly in a marine environment requires bolts. Two options: carbon steel bolts or 316 stainless bolts. Evaluate.

Carbon steel bolts: carbon steel is anodic to stainless steel. The bolts are the small anode, the plate the large cathode — the worst possible area ratio. The entire galvanic current concentrates on the bolt shanks, and they fail rapidly by loss of section.

316 stainless bolts: 316 is very close to 304 in the galvanic series, so the driving potential is nearly zero and galvanic attack is negligible. The added molybdenum in 316 also improves chloride pitting resistance, which matters in seawater.

Select 316 stainless. The reasoning combines both rules — minimize the galvanic potential difference, and never make the small-area component the anode.

Trap: "use the cheapest bolt and add a coating." A coating defect on a small anode makes matters worse, because the entire galvanic current now concentrates on the pinhole, producing a far higher local current density than an uncoated bolt would experience.