Nonmonotonic crystallite-size dependence of the lattice parameter of nanocrystalline nickel

Abstract

A nonmonotonic crystallite-size dependence of the lattice parameter of ultrathin, nanocrystalline Ni films, i.e., lattice contraction followed by lattice expansion with decreasing crystallite size, was observed using in situ x-ray diffraction stress measurements combined with a dedicated thermal treatment called “loop annealing.” The expected lattice contraction with decreasing crystallite size was found for nanocrystalline Cu and nanocrystalline Pd.

Grain-size-dependent non-monotonic lattice parameter variation in nanocrystalline W: The role of non-equilibrium grain boundary structure

“…However, there is an ambiguity in the literature over the dependence of lattice parameters on the grain size of nanocrystalline materials, i.e. both contraction and expansion of the lattice have been reported with the decrease in grain size [10][11][12][13]. Moreover, Divakar and Raghunathan [14] and Birringer et al [15] report both contraction and expansion of the lattice parameter of Pd with a change in grain size.…”

Evolution of crystallite size, lattice parameter and internal strain in Al precipitates during high energy ball milling of partly amorphous Al87Ni8La5 alloy

“…It has been reported that the lattice parameter increases or decreasesas a function of the crystallite size [14,[24][25][26][27].There are several models which describe thecorrelationof the lattice parameter with the crystallite size based on (a) the surface energy [28][29][30], (b) the lack of the outermost bonding of the surface atoms [31],and (c) intra-crystalline pressure [32,33]. According to Qi et al [14] the decrease in the lattice parameter ( ಲ ሺ୲ୀ ሻି ಲ ሺ౪ሻ ಲ ሺ୲ୀ ሻ ൌ ࢤ )of aluminumdepends on the surface energy ࢽ, thecrystallite shape Į(Į=1 for spherical shape), the shear modulusGand the crystallite size D.According to Qi et al [14]the changes of the lattice parameter ( ௱ బ )of Al nanocrystals in ball milled Al 87 Ni 8 La 5 can be described by…”

Nanoparticle Structure by Coherent X-ray Diffraction

“…5) More recently, it has been used to observe the change in lattice parameter of nanopowders by Mittemeijer et al 6) The samples were prepared as small nanocrystalline powders and progressively annealed to higher temperatures in a automated system. On each annealing cycle, the particle diameter D ¼ 2R is given by the width of its in situ X-ray powder diffraction, while the lattice constant is given by the peak position.…”

“…This is what was observed for the smallest nanopowdered Ni samples measured by powder diffraction lineshape analysis. 6) Individual gold nanocrystals were studied by Huang et al using coherent electron diffraction methods. 7,8) Careful model building, achieved on the atomic scale, found a distinct contraction of the outer layers of the crystal, as expected from Eq.…”