high-temperature creep
/ creep; Nabarro-Herring: nah-BAR-oh HERR-ing /
Load a ceramic at high temperature and, even at a stress far below the one that would fracture it outright, it slowly and permanently sags over time. A furnace shelf droops between its supports over months; a turbine part gradually stretches. That slow, time-dependent, permanent deformation under load and heat is creep, and it is the limit of hot service — the reason a ceramic that is dead rigid at room temperature can quietly deform its way out of tolerance when it is kept hot and stressed for long enough.
Creep is described by a rate equation of the form strain-rate = A times sigma^n times d^(-p) times exp(-Q/RT), where sigma is the applied stress, d the grain size, T the temperature, Q an activation energy, R the gas constant, and n and p exponents that fingerprint the mechanism. The exponential in temperature means creep switches on sharply once you get hot enough — typically above roughly half the melting temperature. The mechanisms fall into families: diffusional creep, where atoms and vacancies simply migrate from compressed boundaries to stretched ones (Nabarro-Herring creep through the lattice with n near 1 and p near 2, or Coble creep along grain boundaries with p near 3), which dominates in fine-grained ceramics at modest stress; grain-boundary sliding, where grains slip past one another; and, at higher stress, power-law creep by dislocation motion with n around 3 to 5. Finer grains creep faster in the diffusional regime, which is why hot-strength design often wants larger grains — the opposite of what you want for room-temperature strength.
The dominant plot twist in real ceramics is the grain boundary itself. Most engineering ceramics are sintered with a thin glassy grain-boundary film, and at high temperature that film softens and lets grains slide and dissolve-and-reprecipitate, so it, not the crystal, controls the creep rate. This is why an impure silicon nitride or alumina creeps far faster than a chemically pure, glass-free version, and why makers of high-temperature ceramics fight so hard to purify grain boundaries or crystallize the glassy phase. Creep sets the real ceiling for turbine blades, furnace fixtures, and the load-bearing life of refractories — the slow-deformation cousin of thermal shock, both faces of what heat does to a stressed ceramic.
Two silicon nitrides fired to the same density can creep at rates differing by orders of magnitude: the one sintered with a large amount of glassy grain-boundary phase deforms steadily at 1200 degrees C, while a version whose boundary glass has been crystallized holds its shape — proof that the boundary film, not the Si3N4 crystal, sets the creep rate.
A softening glassy grain-boundary film usually controls high-temperature creep, so purifying or crystallizing that film is the key to hot strength.
For creep, the usual wish for a fine grain size backfires: diffusional creep speeds up as grains get smaller (rate scales as d to a negative power), so the fine-grained microstructure that gives high room-temperature strength is exactly the wrong one for resisting deformation when hot.