Miller’s index

In crystals, it is necessary to denote the plane directions and is done conventionally either by Miller s indices or by lattice planes. Directions are given as the lowest vector in referring to the coordinate system, x a), y b) and z c). A vector parallel to the chain axis is denoted [001]. The first plane intersects the origin of the coordinate system. The next plane intersects the three axes at x = ajh, y = b k and z = cll. The task is to find an integral combination of h, k and / that is finally presented in parentheses (hkl). All planes containing the chain axis, i.e. those parallel to the chain, have the general formula (/z, k, 0). The lattice index system indicates not only the orientation of the planes but also the shortest distance between planes. The set of planes denoted (010) is a subset of (020). The orientation of the two sets of planes is the same but the interplane distances d k) are different /qio = b and J020 = bjl. 

Miller s index system is similar to the lattice plane index system but with the difference that the hkl values are the lowest possible integer values. The Miller s index notation for both the sets of planes with the lattice plane indices (010) and (020) is simply (010). Miller s indices thus provide information only about the orientation of the planes and disregard the interplanar distances involved. 

A) Experimental set-up for in situ X-ray diffraction during forced siiking. The spider is fixed by soft tape and mylar bandages to a metai support. The path of the thread from the spinnerets to the motorised reei is schematically indicated. Distance indications (to the spinneret exit) correspond to points where X-ray diffraction data were recorded. (B) Optical image of draw-down of N. edulis spider silk at a drawing speed of 20 mm s T (C) Diffraction pattern obtained at 23.5 +. 5°C. Miller s indices are indicated for selected reflections (for details see ref. 87). 

Figure 13.4 Planes for the hexagonal crystal, corresponding to polar, nonpolar, and semipolar directions and their Miller s indices h k i I), with i= — h + k)...

This flexibility is not without a price, however, as learners need to keep track of where they are and pace themselves. To address this, we examine the situation from the psychological perspective of cognitive load theory. Cognitive load theory is based on the premise that people have a limited working memory capacity and that information must flow through before it can be stored in long-term memory (Sweller 2005). The basis for this is Miller s work, which indicated most people had a working memory capacity of 7 2 items (Miller 1956). 

The work presented here showed that P increased signiticantly for the thin polymer Aims compared with the solution values. A comparison of Hgures of merit indicated that the thin poly-yne films arc competitive with Foster Miller s biaxially-oricntcd PBT film. Development of improved film quality should produce films with figures of merit surpassing those presented at this time. 

Apart from this peculiar way of defining the coordinate system, the calculation of the indices of directions and planes is the same as for the Miller indices. However, the normal vector of a plane does not correspond to the plane s indices. 

There is still no united idea regarding the so-called biogenic iron sulphide as a good indicator of bacterial activity compared to abiotic sulphide films (please also refer to footnote 20 in Chapter 4 regarding Smith and Miller s review). Some researchers have postulated that the presence of mackinawite may be used as an indication of MIC by SRB [26]. On the other hand, others believe that while SRB may affect the crystallisation mode of iron sulphides, they reject the idea that mackinawite is the unique SRB-influenced corrosion product [27]. Thus, until researchers agree on one or another idea, it is not recommended to use sulphide films as the only way to identify MIC. 

Miller s group reported the use of sodium salts, such as sodium arsenate (Gxmter et al., 1995), silica-supported sodium nitrates (Wadley et al., 1997), and a screening of different pore glass-supported alkali hydroxides (Tam et al., 1998). By the use of the Cs, a 49% PD yield was achieved at 280°C, while only 15% was obtained by Tam at 320°C (Tam et al., 1998). Accordingly, FT-IR studies indicated that the formation of alkali lactates via a proton transfer to the counter anion (eg, with the release of HNO3 for nitrates) was the dominant mechanism (Tam et al., 1997). For the supported NasPO/ catalyst, Na9HP04 and sodium lactate were formed (Wadley etal., 1997). 

Lee and Miller (130) have observed a rather large effect (ka/ko = 1.28) on the iodide promoted debromination of sym-tetrabromoetbane-di in methanol. According to Miller s (60) calculations, an effect in this direction, decreasing as it does with temperature, is indicative of a dissociative transition state [Section VA, 2(b)]. The isotope effect is thus taken as evidence against displacement at carbon of bromide by iodide, followed by rapid loss of the latter, and favoring a direct bimolecular elimination ... 

A comparison of experimental data for carbon dioxide absorption obtained oy Hatta anci Katori (op. cit.), Grimley [Trans. Inst. Chem. Eng., 23, 228 (1945)], and Vyazov [Zh. Tekh. Fiz. (U.S.S.R.), 10, 1519 (1940)] and for absorption or oxygen and hydrogen by Hodgson (S. M. thesis, Massachusetts Institute of Technology, 1949), Henley (B.S. thesis. University of Delaware, 1949), Miller (B.S. thesis. University of Delaware, 1949), and Richards (B.S. thesis. University of Delaware, 1950) was made by Shei wood and Pigford (Absorption and Extraction, McGraw-Hill, New York, 1952) and is indicated in Fig. 14-78. 

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