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Inorganic Chemistry
Published in Steven L. Hoenig, Basic Chemical Concepts and Tables, 2019
When a crystal lattice forms the ions are arranged in the most efficient way of packing spheres into the smallest possible space. Starting with a single layer as in Figure 2.3a, a second layer can be placed on top of it in the hollows of the first Figure 2.3b. At this point a third layer can be placed. If the third layer is placed directly over the first, Figure 2.3c, the structure is hexagonal close-packed (hcp). The layering in hexagonal close-packed is ABABAB. If the third layer is placed so it is not directly over the first a different arrangement is obtained. This structure is cubic close-packed (ccp). The layering in cubic close-packed is ABCABC, Figure 2.3d. This is identical to a structure with a face-centered cubic (fcc) unit cell.
Mechanical Behavior and Measurement
Published in David W. Richerson, William E. Lee, Modern Ceramic Engineering, 2018
David W. Richerson, William E. Lee
A single dislocation does not result in significant plastic deformation within a material. However, under an applied stress, dislocations can form and multiply. Typical deformed metals contain millions of dislocations per cubic centimeter. The actual slip occurs in bands along preferred crystal planes. The preferred planes are those that require the least applied stress to initiate dislocation movement. The preferred plane for hexagonal close-packed structures is (0001). Slip readily occurs along several families of planes in cubic close-packed structures: {111}, {100}, and {110}.
Introduction
Published in D Sands, Diode Lasers, 2004
Semiconductors, as the term implies, lie somewhere between insulators and metallic conductors, and chemical bonding plays a part in this. In metals the atoms pack together as closely as possible, the most common form being hexagonal close-packed structure. In order to do this the valence electrons from each atom are given up to a general pool of electrons and metals exhibit very high electrical conductivity as a result. In insulators, on the other hand, the electrons tend to be bound tightly to one or other of the constituent atoms, and so require the input of a large amount of energy to overcome the strength of the bond. If that energy is supplied there is no reason why the electrons cannot then move freely through the crystal, as they do in the metal, and contribute to an electrical current. In crystalline insulators the most common form of bonding is the ionic bond, in which one atom gives up one or more of its valence electrons to another atom. Atoms which tend to give up electrons are described as electropositive and those which tend to accept them are described as electro-negative. The driving force for this is stability. The most stable atoms are those that have a full shell of outer electrons, for example helium, neon, argon, etc., and an electro-positive atom that doesn’t possess a full outer shell can form a stable chemical compound with another electro-negative atom which also has a partially filled outer shell of electrons. For example, aluminium, with three valence electrons, can bond with nitrogen, which has five valence electrons, by donating its three electrons to the nitrogen. The nitrogen then has eight electrons (a full shell) and the aluminium has a full lower level of electrons and both are stable. Similarly, two aluminium atoms could bond with three oxygen atoms, each of which would receive two of the valence electrons.
Determination of 3D pore network structure of freeze-dried maltodextrin
Published in Drying Technology, 2022
M. Thomik, S. Gruber, P. Foerst, E. Tsotsas, N. Vorhauer-Huget
The total number of pores and the pore connectivity of the porous domain were estimated based on the binarized images. The results are summarized in Table 2 for the different methods discussed above and a cuboid of size 50 µm × 50 µm × 50 µm. Surprisingly, in relation to the previous assessment, strong differences are observed for the investigated methods, indicating further needs for a deeper assessment of the available image processing options. The computed average coordination number is relatively high and close to the coordination number of the hexagonal close packed structure or cubic face centered crystals (which is 12). A reason for that might be the heterogenous shape of the pores, the segmentation into many smaller objects and the resulting various connections along their length in the 3D structure. High coordination numbers have also been reported in literature regarding the extraction of pore networks from images, e.g. [14,52]. As presented in Table 2, adaptive thresholding with anisotropic diffusion filter resulted in a higher number of pores and higher coordination number compared to Otsu thresholding and anisotropic diffusion filter. This findings are in good agreement with the images in the right column of Figure 10. The images in Figure 10 also indicate that with Otsu thresholding and any filter method as well as adaptive thresholding without filter more isolated pores occur. Also, the pore structure is not as well adapted with these methods compared to adaptive thresholding with previous image filtering.
Constitutive equation for describing true stress–strain curves over a large range of strains
Published in Philosophical Magazine Letters, 2020
Jun Cao, Fuguo Li, Weifeng Ma, Dongfeng Li, Ke Wang, Junjie Ren, Hailiang Nie, Wei Dang
Can the S–V model describe full-range stress–strain curves containing large deformation for all materials? Which constitutive equation is more suitable when the full-range stress–strain curves cannot be described by the S–V model? A combination of the Swift model and a correction function is proposed to describe the full-range stress–strain curve. The correction function could be polynomial since it is easily modified. The correction process needs to be based on a necking type of material. This is an iterative process obtained by adjusting the correction function and weight factor q to make a simulated force-displacement curve that accords with experiment. The constitutive equation is expressed aswhere is a correction function. The power-law type constitutive equation (Swift model) is suitable for body-centred cubic (BCC) metals [21], whereas the exponential-type equation (Voce model) is suitable for most face centred cubic (FCC) metals such as aluminium and copper [22]. Some materials (for example, titanium alloys) have a close-packed hexagonal (HCP) structure. For these materials, the power-law type and exponential-type constitutive equation are not suitable for describing the full-range stress–strain curve. To better describe the full-range stress–strain curve of HCP materials, the correction function is used to modify the shape of the stress–strain curve in the post-necking type; this is a modification for large-deformation behaviour induced by material type.
The effects of yttrium on the {10-12} twinning behaviour in magnesium alloys: a molecular dynamics study
Published in Philosophical Magazine Letters, 2020
Yuchen Dou, Hong Luo, Jing Zhang
Magnesium alloys are hexagonal close packed (HCP) crystals. The most soft deformation modes are basal slip and {10-12} twinning. Lu et al. demonstrated that, in face centre cubic (FCC) crystals, dislocations could be impeded by twin boundaries when the stress is relatively lower [6]. Meanwhile, under higher stress, screw dislocations could cross-slip onto the twin boundaries or traverse across twin boundaries and glide into the next grain. With this mechanism, the stress around a twin boundary is relived and the nucleation of crack is delayed. As a result, twin-structured FCC copper has shown exceptional high strength without severe loss of ductility [6]. In magnesium alloys, it is reported that edge dislocations on the basal plane could dissociate into {10-12} twinning dislocations and facilitate the migration of {10-12} twin boundaries. Meanwhile, screw dislocations on the basal plane could traverse across {10-12} twin boundaries [7–10]. Thus, one can hypothesise that with high density of {10-12} twin boundaries, magnesium alloys might also show exceptional mechanical properties. To achieve this goal, one should promote the nucleation of {10-12} twins and retard the migration of {10-12} twin boundaries.