Below the Hall–Petch Limit in Nanocrystalline Ceramics

Abstract

Reducing the grain size of metals and ceramics can significantly increase strength and hardness, a phenomenon described by the Hall-Petch relationship. The many studies on the Hall-Petch relationship in metals reveal that when the grain size is reduced to tens of nanometers, this relationship breaks down. However, experimental data for nanocrystalline ceramics are scarce, and the existence of a breakdown is controversial. Here we show the Hall-Petch breakdown in nanocrystalline ceramics by performing indentation studies on fully dense nanocrystalline ceramics fabricated with grain sizes ranging from 3.6 to 37.5 nm. A maximum hardness occurs at a grain size of 18.4 nm, and a negative (or inverse) Hall-Petch relationship reduces the hardness as the grain size is decreased to around 5 nm. At the smallest grain sizes, the hardness plateaus and becomes insensitive to grain size change. Strain rate studies show that the primary mechanism behind the breakdown, negative, and plateau behavior is not diffusion-based. We find that a decrease in density and an increase in dissipative energy below the breakdown correlate with increasing grain boundary volume fraction as the grain size is reduced. The behavior below the breakdown is consistent with structural changes, such as increasing triple-junction volume fraction. Grain- and indent-size-dependent fracture behavior further supports local structural changes that corroborate current theories of nanocrack formation at triple junctions. The synergistic grain size dependencies of hardness, elasticity, energy dissipation, and nanostructure of nanocrystalline ceramics point to an opportunity to use the grain size to tune the strength and dissipative properties.

Grain boundary strengthening in nanocrystalline zinc aluminate

“…The hardness as a function of grain size is plotted in the form of Hall-Petch equation in Figure 4. Ryou et al 7 have performed a systematic work on various loads during indentation of nanoceramics and noted that when observed in SEM, the high loads lead to spallation and irregular fracture. 14 To allow comparison, data for MgAl 2 O 4 spinel (measured using the similar indentation load, 80 and 40 gf for one of the data points) are also included in the plot (note the data selected was for samples prepared by DP-SPS, not showing Hall-Petch breakdown).…”

“…This is likely due to the lack of plastic yield in large grained samples which is key for the success of the DP-SPS process. 7 The rationale behind the normal Hall-Petch relation has been extensively discussed in the literature, with the most commonly accepted theory attributing it to a decrease in dislocation density and mobility as grain sizes decrease. Several works have been published reporting low grain size limits in the 3-20 nm range below which an inverse Hall-Petch relation is observed in metal alloys.…”

“…Although similar behavior has been observed for both metals and ceramics, in metals the existence of an inverse Hall-Petch relationship, i.e., a low-limiting grain size below which the linear relation is no longer observed, is commonly reported in the literature and attributed to a more dominant role of grain boundary sliding and dislocation interactions when grain sizes are below 20 nm. 6,7 The cause for the inverse relation was linked by Ryou et al to the large fraction of interfacial volume that such small grain size introduces to the system, allowing a large population of triple junctions that can nucleate subsurface cracks during indentation. For instance, MgAl 2 O 4 has been the focus of several works targeting reduction of grain sizes to examine the effect on hardness.…”

“…For instance, MgAl 2 O 4 has been the focus of several works targeting reduction of grain sizes to examine the effect on hardness. 7 On the other hand, an evaluation of the technical aspects of those works points out a difference in the processing of the samples that could be responsible for the observed discrepancies on the breakdown of the Hall-Petch relationship. 6 Ryou et al have reported an increase in hardness with decreasing grain size for the same composition, reaching the maximum at a fairly similar grain size as that reported by Sokol et al,18.4 nm.…”

Size‐induced grain boundary energy increase may cause softening of nanocrystalline yttria‐stabilized zirconia

“…Grain size refinement, with the resulting expansion of the grain boundary network, may act as an additional effective barrier for dislocations, further reducing plasticity and increasing hardness—often referred to as Hall‐Petch relation . In ceramics, this behavior is more pronounced when grain sizes are below 100 nm, but as grain sizes are further reduced, several studies also report, instead, the existence of an inverse relation as grains are refined below a critical size …”