Small Crystal Size

In representing the scattering length density distribution in the crystal in Section 1.7 as 

Suppose the crystal has the shape of a parallelepiped with edges of lengths Lx, Ly, Lz in the x, y, z directions. The Fourier transform of such a shape can be obtained by integrating for x y and z separately, and is given by 

the lattice factor Z(s), which, for an infinite crystal, is an infinite set of delta functions located at the reciprocal lattice points rkkl, is replaced for a finite crystal by 

Z(s) (s), which is a similarly infinite set of slightly broadened peaks E(s) located at the same reciprocal lattice points. The lattice factor Z(s) E(s) 2 that articulates the intensity in (3.27) is a similar set of broadened peaks located at the reciprocal lattice points. The shape of the individual peaks for the intensity function is given by Z,2(s), which has a width, in terms of FWHM, about 1/V2 of that of E(s). 

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Thermodynamic considerations postulate BjH to be a better boron source than BCl, in CVD of TaB2Using reaction (f) at < 1200 K deposits with extremely small crystal sizes are obtained on graphite substrates . They contain amorphous B at deposition temperatures < 873 K and are substoichiometric in B above this T. Carbon from the substrate substitutes for B, thereby stabilizing the diboride structure at high deposition T... 

A model-free method for the analysis of lattice distortions is readily established from Eq. (8.13). It is an extension of Stokes [27] method for deconvolution and has been devised by Warren and Averbach [28,29] (textbooks Warren [97], Sect. 13.4 Guinier [6], p. 241-249 Alexander [7], Chap. 7). For the application to common soft matter it is of moderate value only, because the required accuracy of beam profile measurement is rarely achievable. On the other hand, for application to advanced polymeric materials its applicability has been demonstrated [109], although the classical graphical method suffers from extensive approximations that reduce its value for the typical polymer with small crystal sizes and stronger distortions. 

Given the complex nature of the crystal structure and small crystal size with an anisotropic morphology of UZM-5, the normal X-ray diffraction patterns were not sufficient to deduce an unambiguous structure. Thus a multi-technique approach was required to successfully solve the structure, to explain the adsorption properties and by analogy to the structure of other zeolites in order to assess potential applications. 

Yamamura, M., Chaki, K., Wakatsuki, T., Okado, H., and Fujimoto, K. (1994) Synthesis of ZSM-5 zeolite with small crystal size and its catalytic performance in ethylene oligomerization. Zeolites, 14, 643-650. 

Highly-broadened XRD peaks and electron diffraction patterns indicate that ferrihy-drites are characterized by small crystal size and/or low structural order. TEM shows single spherical particles, ca. 4-6 nm in size (Fig. 4.17). At higher magnification (HRTEM), 6-line ferrihydrite appeared as single crystals with a hexagonal outline and... 

Iron oxides in soils have in common that they are of extremely small crystal size and/or low crystal order. This, in combination with their low concentration (only tens g kg in most soils) explains why soil iron oxides have escaped identification for a long time in spite of their obvious existence as seen from the soil colour. In the past, therefore, Fe oxides in surface environments have been considered to be amorphous to X-rays and often called limonite , which mineralogically, is an obsolete term. Furthermore, in order to identify the clay minerals in soils properly, Fe oxides are usually removed before X-ray diffraction methods are applied (Alexander et al., 1939 Mehra Jackson, 1960). 

Optical absorption spectroscopy is often carried out on CD films to verify that the films have a bandgap expected from the deposited semiconductor. Additionally, since CD films are often nanocrystaUine and the most apparent effect of very small crystal size is the increasing bandgap due to size quantization (the effect is visible to the eye if the bandgap is in the visible region of the spectrum), absorption (or transmission) optical spectroscopy is clearly a fast and simple pointer to crystal size, since bandgap-size correlations have been made for a number of semiconductor colloids and films. 

Electrical resistivity of the films, both PbS and PbSe, has often been reported to be of the order of 10 fl-cm as deposited, with a reduction of about an order of magnitude after annealing in air. However, this can vary considerably from one type of deposition to another. Resistivities greater than 10 fi-cm have been reported in some cases, which invariably drop to the kH-cm range after air annealing. These high-resistivity films are probably those with a very small crystal size (small meaning ca. 10 nm or less). 

Films of materials deposited at or near room temperature (and in this respect 100°C is considered to be near room temperature) tend to have a small crystal size. This is not surprising since high temperatures are normally required to impart sufficient mobility to a freshly deposited species in order for recrystallization to occur. This small crystal size, which at one time was almost universally considered to be a disadvantage, is increasingly considered to be an advantage as interest in nanocrystalline and nanoparticle materials grows. The term nano crystalline usually refers to materials with a crystal size from a nanometer up to hundreds of nanometers (at this upper limit, the term microcrystalline starts to take over). 

No XRD pattern was found for the films, and on this basis they were believed to consist of amorphous HgSe. Based on more recent XRD studies of nanocrystalline materials, the lack of an XRD pattern was likely due to very small crystal size (supported by the increased bandgap see later). Annealing at 200°C crystallized the HgSe to an extent that it was clearly identified by XRD. Optical spectroscopy gave a bandgap value of 1.42 eV. Bulk HgSe is a semimetal with... 

The wide range of very small crystal sizes in these films gives rise to strong blue shifts in their optical spectra due to size quantization [65], This aspect of these films is dealt with in detail in Chapter 10. 

A note of caution is necessary when deahng with these materials. It is not trivial to distinguish between CuInS(Se)2 and some phases of Cu—S(Se). Diffraction and optical properties may be similar. Elemental analysis is particularly important to verify inclusion of indium in the films and in the correct ratio. A fingerprint of the chalcopyrite XRD is the presence of a weak peak at 26 = 17-18°, corresponding to the (101) chalcopyrite reflection. This is often not seen, although this could be either because the deposit is not chalcopyrite or because weak peaks are usually not seen in nanocrystaUine materials with particularly small crystal size. 

This chapter has dealt with true ternary compounds, with the underlying implication that deposition of separate phases is undesirable. However, it needs to be stressed that what is undesirable for one purpose may be preferable for another (examples being small crystal size and a large amount of scattering). So, too, a composite of different phases may be the goal of a particular deposition. This issue does not appear to have been dealt with in CD. 

Annealed films deposited from a A,A-dimethylselenourea/citrate/ammonia bath were shown to exhibit a (0001) XRD reflection at 26 = 13°, a reflection normally forbidden in hexagonal CdSe [the (0002) reflection is the one normally seen] [13]. This was explained by a breaking of the selection rules due to the small crystal size. Interestingly, this peak was very weak in thin films and prominent in... 

In Ref. 31, using CdAci, a blue shift of nearly 0.1 eV (to 2.50 eV) was obtained, compared to films using CdCli. In contrast to the CdCli deposition, where XRD showed sharp peaks, no pattern was observed for the acetate films (amorphous or small crystal size). 

Other studies on Cn-Se where small crystal sizes were measnred and therefore are potential candidates to exhibit size qnantization give crystal sizes between 10 and 20 nm and bandgaps (direct) of ca. 2.2 eV for Cui-j Se and ca. 2.8 eV for CusSei [73,74] a value of 2.37 eV was measured for CD CusSei with a 40-nm crystal size [72]. 

Certain crystals give diffuse X-ray reflections there are various possible causes for this—small crystal size, structural irregularities, or thermal movements. The consideration of these phenomena in Chapter XI leads on to a brief introduction to the interpretation of the very diffuse diffraction patterns given by non-crystalline substances. 

There appear to be two possible explanations for these central peaks in the natural hematite. One is that some of the ferric material is actually not hematite but is bound to clay that might be present. Other workers (11) obained similar results when they prepared samples of iron compounds absorbed on kaolinite or bentonite. The second reason concerns the effect of small crystal size on Mossbauer spectra and perhaps is better illustrated for goethite. 

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