Grain size effects on lateral islands in hard-sphere crystals

Abstract

-Due to the lateral stacking disorder, random hexagonally closed-packed hard-sphere crystals consist of lateral islands with different lateral positions A, B, and C, and as a consequence, different stacking. We investigate the extent of lateral stacking disorder as a function of grain size, and as a function of the fraction of FCC-stacked particles α by laser scanning confocal microscopy and Monte Carlo simulations. We compare the simulations and microscopy data to relate stacking islands (2D domains with identical stacking type and direction) to lateral islands. Small crystals mainly contain single hexagonal planes, whereas larger crystals consist of a much larger number of lateral islands. Furthermore, the typical stacking island size is related to the FCC fraction. At high α, more FCC islands nucleate, and these are more likely to combine into larger islands than the HCP islands. Copyright c EPLA, 2007Introduction. -Small crystallites are remarkably different from their large counterparts. The amount of particles at the surface is relatively high, which can drastically affect elastic [1], optical [2], electric [3] and magnetic properties [4]. The change in properties is often coupled to a change in particle configuration. It is extremely difficult to study atomic systems on the single-particle level, but colloidal systems are excellent reference systems: they are very similar to atomic systems [5] and enable 3D studies on the single-particle level by confocal microscopy [6-9] due to large particle size and their relative slowness. The phase diagram of colloidal hard spheres is based on excluded-volume interactions only. The free energy difference between face-centered cubic (FCC) and hexagonally closed packed (HCP) structures is tiny for hard sphere crystals [10][11][12]: less than 10 −3 k B T per particle, where k B T is the thermal energy. As a result, a so-called randomhexagonal close-packed (RHCP) crystal structure is often found in experimental hard sphere systems [13][14][15][16][17][18]: the reorganisation from RHCP to FCC structure is expected to take months to years for experimental systems [18,19]. Due to the variety of possible RHCP configurations, an additional gain in entropy can stabilize the RHCP structure for sufficiently small crystals [20]. The RHCP structure is characterized not only by randomly alternating FCC and HCP layers, but also by lateral islands with

Ptychographic X‐Ray Imaging of Colloidal Crystals

“…At the same time, the periodicity in the phase profiles changes only slightly as they cross domain boundaries in Figure c, which are shown as dashed vertical lines. This feature may indicate that the observed defects are partial dislocations . Such dislocations may be described as transition between the stacking sequences of 3 layers with a shift from local fcc via hcp to fcc with different stacking direction: (ABC via ABA to CBA).…”

“…The presence of many differently stacked domains in a close proximity can be attributed to stacking faults and partial dislocations, and has been discussed in detail. [28,58] Interestingly, such fine domain structure was not observed before [53] neither by the optical nor by scanning electron microscopy (SEM). Hard X-ray ptychography, being highly penetrating technique, provides different contrast mechanism [37] in comparison to SEM and reveals complementary features in colloidal crystal samples.…”

“…The presence of many differently stacked domains in a close proximity can be attributed to stacking faults and partial dislocations, and has been discussed in detail . Interestingly, such fine domain structure was not observed before neither by the optical nor by scanning electron microscopy (SEM).…”

“…This feature may indicate that the observed defects are partial dislocations. [28,58] Such dislocations may be described as transition between the stacking sequences of 3 layers with a shift from local fcc via hcp to fcc with different stacking direction: (ABC via ABA to CBA). Clearly, the colloidal crystal studied here contains many of these transitions.…”

Relating microstructure and particle-level stress in colloidal crystals under increased confinement

“…In our system, this reduction in gap produces smaller grain sizes. Such a grain size reduction has been suggested to have a great influence on the microstructure [62], defect density [63,64], and particle diffusivity [65] in polycrystals. More importantly, in atomic nanocrystals, grain size reduction leads to substantially lower yield stress a phenomena known as the inverse Hall-Petch relation [66,67].…”