Creep that proceeds as grains elongate by atomic diffusion, with a rate proportional to stress. It includes Nabarro–Herring creep by lattice diffusion and Coble creep by grain boundary diffusion.
Japanese name: 拡散クリープ
Diffusion creep appears in 4 practice questions across 1 topic, including High-temperature materials and creep.
At a grain boundary under tensile stress σ, the energy needed to create a vacancy falls by σΩ, where Ω is the volume of one atom; at a boundary under compression it rises. Boundaries under tension therefore have more vacancies nearby and those under compression fewer, so vacancies diffuse from the tensile to the compressive boundaries and atoms diffuse the opposite way. As atoms pile onto the boundaries under tension, the grains lengthen in the direction of the stress. σΩ is small compared with the thermal energy kT: with σ = 10 MPa, Ω ≈ 1.1×10⁻²⁹ m³ (close to the value for Ni) and 1000 K, σΩ/kT ≈ 0.008. The difference in vacancy concentration is therefore proportional to stress.
The rate of diffusion creep depends strongly on the grain size d: it is proportional to 1/d² for Nabarro–Herring creep, with diffusion through the grain interiors, and to 1/d³ for Coble creep, with diffusion along grain boundaries. Increasing the grain size tenfold, from 10 µm to 100 µm, lowers the rates to 1/100 and 1/1000 respectively. Grain boundary diffusion has a lower activation energy than lattice diffusion, so the share of Coble creep grows at lower temperatures and finer grain sizes. In ionic crystals, matter is transported only if both cations and anions move, so the slower ion, moving along its fastest path, controls the overall rate. In fine-grained ceramics, diffusion creep is prominent at high temperature.
If grains lengthened by atomic diffusion alone, gaps or overlaps would form between neighboring grains, so diffusion creep is always accompanied by grain boundary sliding. Conversely, in superplasticity grain boundary sliding is the main deformation and is accommodated by dislocation motion and other processes; slowly pulling a material with fine grains of a few µm at more than half its melting point gives elongations of several hundred percent or more. The stress exponent of superplasticity is about 2, distinguishing it from the value of 1 for diffusion creep. Harper–Dorn creep, with n ≈ 1 but no grain size dependence, has been reported in coarse-grained materials at very low stresses, but its existence and mechanism are debated.
Diffusion creep does not stop even at low stress, so it is a problem for parts exposed to high temperature under low stress for long times. The basic remedy is coarser grains, which is why coarse-grained, columnar-grained and single-crystal materials are used for high-temperature parts. In tungsten filaments for incandescent lamps, a trace of potassium is added to create long interlocking grains that suppress sagging under their own weight by grain boundary sliding. On the other hand, diffusion creep is the main deformation in part of the flow of rock in the Earth's mantle and in the high-temperature deformation of fine-grained ceramics. Its characteristic behavior, with the rate proportional to stress, is close to viscous flow.
Answer: A. About 2.5 times
At the same temperature A and exp(−Q/RT) do not change, so the ratio of the rates is the stress ratio raised to the power n: (1.2)⁵ ≈ 2.49, about 2.5 times. That a mere 20% increase in stress more than doubles the rate is characteristic of dislocation creep (power-law creep), where n is large, about 3 to 8, and a small error in the design stress greatly affects the life. About 6.0 times is the value obtained by multiplying the stress ratio by the exponent n, and about 1.2 times assumes that the rate is proportional to stress (n = 1), which is the case for diffusion creep operating at low stress. Plotting rate against stress on log-log axes gives a slope of n.
Answer: B. Coble creep by diffusion of atoms along grain boundaries
In diffusion creep, atoms diffuse from grain boundaries under tension to those under compression, elongating the grains, and the rate is proportional to stress (n = 1). When the diffusion path runs along the grain boundaries it is called Coble creep, and the rate is inversely proportional to the cube of the grain size. When it is lattice diffusion through the grain interiors it is called Nabarro–Herring creep, and the rate is inversely proportional to the square of the grain size. Grain boundary diffusion has a lower activation energy than lattice diffusion, so Coble creep dominates at relatively low temperatures and fine grain sizes, while the contribution of Nabarro–Herring creep grows at high temperatures near the melting point. Power-law creep by dislocations has a large n of 3 to 8 and hardly depends on grain size.
By the grain size dependence of the rate and the activation energy. If, in specimens of different grain sizes, the rate is proportional to 1/d² and the activation energy is close to that of lattice diffusion, it is Nabarro–Herring creep; if it is proportional to 1/d³ and close to that of grain boundary diffusion, it is Coble creep. In practice both act in parallel and their rates add.
Because the difference in vacancy concentration between grain boundaries is proportional to the ratio of the work done by the stress, σΩ, to the thermal energy kT. Since σΩ is far smaller than kT, the concentration difference is proportional to stress, and so are the resulting vacancy flow and therefore the creep rate.
They share a rate proportional to stress, and diffusion creep behaves much like Newtonian viscous flow. However, viscous flow of glasses and liquids occurs by cooperative rearrangement of atoms, whereas diffusion creep is a change in grain shape by atoms diffusing between grain boundaries, and its rate depends strongly on grain size.
About 6.0 times is the value obtained by multiplying the stress ratio by the exponent n, and about 1.2 times assumes that the rate is proportional to stress (n = 1), which is the case for diffusion creep operating at low stress.
The steady-state creep rate of a heat-resistant alloy follo…In diffusion creep, atoms diffuse from grain boundaries under tension to those under compression, elongating the grains, and the rate is proportional to stress (n = 1).
A fine-grained polycrystalline metal was creep tested at a …Dislocation glide dominates at high stresses close to the ideal strength, power-law creep involving dislocation climb at intermediate stresses and high temperatures, and diffusion creep at low stresses and high temperatures.
Which statement about the deformation mechanism map of Ashb…Diffusion creep (especially Coble creep, inversely proportional to the cube of grain size), grain boundary sliding, and rupture by the nucleation and coalescence of voids on boundaries therefore occur more readily in fine-grained material with many boundaries.
At room temperature, refining the grains raises strength (t…Power-law creep Creep Dislocation Deformation mechanism map Hall–Petch relationship Columnar grains Young's modulus Larson–Miller parameter Nickel-based superalloy Parabolic rate law