A nanocrystalline material or nanocrystal (NC) is a polycrystalline nanoparticle with a crystallite size of only a few nanometers. These materials fill the gap between amorphous materials without any long range order and conventional coarse-grained materials. Definitions vary, but nanocrystalline material is commonly defined as a crystallite (grain) size below 100 nm. Grain sizes from 100 to 500 nm are typically considered "ultrafine" grains. The grain size of a NC sample can be estimated using x-ray diffraction. In materials with very small grain sizes, the diffraction peaks will be broadened. This broadening can be related to a crystallite size using the Scherrer equation (applicable up to ~50 nm), a Williamson-Hall plot, or more sophisticated methods such as the Warren-Averbach method or computer modeling of the diffraction pattern. The crystallite size can be measured directly using transmission electron microscopy.
Synthesis Nanocrystalline materials can be prepared in several ways. Methods are typically categorized based on the phase of matter the material transitions through before forming the nanocrystalline final product.
Solid-state processing Solid-state processes do not involve melting or evaporating the material and are typically done at relatively low temperatures. Examples of solid state processes include mechanical alloying using a high-energy ball mill and certain types of severe plastic deformation processes.
Liquid processing Nanocrystalline metals can be produced by rapid solidification from the liquid using a process such as melt spinning. This often produces an amorphous metal, which can be transformed into a nanocrystalline metal by annealing above the crystallization temperature.
Vapor-phase processing Thin films of nanocrystalline materials can be produced using vapor deposition processes such as MOCVD.
Solution processing Some metals, particularly nickel and nickel alloys, can be made into nanocrystalline foils using electrodeposition.
Mechanical properties Nanocrystalline materials show exceptional mechanical properties relative to their coarse-grained varieties. Because the volume fraction of grain boundaries in nanocrystalline materials can be as large as 30%, the mechanical properties of nanocrystalline materials are significantly influenced by this amorphous grain boundary phase. For example, the elastic modulus has been shown to decrease by 30% for nanocrystalline metals and more than 50% for nanocrystalline ionic materials. This is because the amorphous grain boundary regions are less dense than the crystalline grains, and thus have a larger volume per atom, Ω {\displaystyle \Omega } . Assuming the interatomic potential, U ( Ω ) {\displaystyle U(\Omega )} , is the same within the grain boundaries as in the bulk grains, the elastic modulus, E ∝ ∂ 2 U / ∂ Ω 2 {\displaystyle E\propto \partial ^{2}U/\partial \Omega ^{2}} , will be smaller in the grain boundary regions than in the bulk grains. Thus, via the rule of mixtures, a nanocrystalline material will have a lower elastic modulus than its bulk crystalline form.
Nanocrystalline metals The exceptional yield strength of nanocrystalline metals is due to grain boundary strengthening, as grain boundaries are extremely effective at blocking the motion of dislocations. Yielding occurs when the stress due to dislocation pileup at a grain boundary becomes sufficient to activate slip of dislocations in the adjacent grain. This critical stress increases as the grain size decreases, and these physics are empirically captured by the Hall-Petch relationship,
σ y = σ 0 + K d − 1 / 2 , {\displaystyle \sigma _{y}=\sigma _{0}+Kd^{-1/2},}
where σ y {\displaystyle \sigma _{y}} is the yield stress, σ 0 {\displaystyle \sigma _{0}} is a material-specific constant that accounts for the effects of all other strengthening mechanisms, K {\displaystyle K} is a material-specific constant that describes the magnitude of the metal's response to grain size strengthening, and d {\displaystyle d} is the average grain size. Additionally, because nanocrystalline grains are too small to contain a significant number of dislocations, nanocrystalline metals undergo negligible amounts of strain-hardening, and nanocrystalline materials can thus be assumed to behave with perfect plasticity. As the grain size continues to decrease, a critical grain size is reached at which intergranular deformation, i.e. grain boundary sliding, becomes more energetically favorable than intragranular dislocation motion. Below this critical grain size, often referred to as the “reverse” or “inverse” Hall-Petch regime, any further decrease in the grain size weakens the material because an increase in grain boundary area results in increased grain boundary sliding. Chandross & Argibay modeled grain boundary sliding as viscous flow and related the yield strength of the material in this regime to material properties as
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