Real crystal face

Similarly, the Miller indices H0 = (h0k0l0) = haQ + kbQ + lcQ denote the unit normal to an imaginary plane in a crystal, or a real crystal face they transform to Hn = (hnknln) as... 

The above considerations show that real crystal faces exhibit different growth patterns depending on degree of perfection and growth conditions. 

The impedance behavior of real crystal faces has been investigated by different authors [5.29, 5.84-5.93]. The results show that the impedance is characterized by various low frequency features (inductive loop and hysteresis) which are related to the non-steady state conditions of the electrochemical crystal growth process. 

These results show that low frequency measurements on growing real crystal faces require a simultaneous in situ microscopic control of the number of screw dislocations and the surface topography in order to obtain reproducible impedance... 

The fifth part deals with growth mechanisms of single crystal faces. The growth by 2D nucleation of quasi-perfect faces as well as the spiral growth mechanism of real crystal faces are discussed. Experimental verification is presented for the case of silver electrocrystallization. 

Acoustic Wave Sensors. Another emerging physical transduction technique involves the use of acoustic waves to detect the accumulation of species in or on a chemically sensitive film. This technique originated with the use of quartz resonators excited into thickness-shear resonance to monitor vacuum deposition of metals (11). The device is operated in an oscillator configuration. Changes in resonant frequency are simply related to the areal mass density accumulated on the crystal face. These sensors, often referred to as quartz crystal microbalances (QCMs), have been coated with chemically sensitive films to produce gas and vapor detectors (12), and have been operated in solution as Hquid-phase microbalances (13). A dual QCM that has one smooth surface and one textured surface can be used to measure both the density and viscosity of many Hquids in real time (14). 

In ordinary diamond (2inc-blende stmcture) the wrinkled sheets He in the (111) or octahedral face planes of the crystal and are stacked in an ABCABC sequence. In real crystals, this ABCABC sequence continues indefinitely, but deviations do occur. For example, two crystals may grow face-to-face as mirror images the mirror is called a twinning plane and the sequence of sheets crossing the mirror mns ABCABCCBACBA. Many unusual sequences may exist in real crystals, but they are not easy to study. 

It is emphasized that the delta L law does not apply when similar crystals are given preferential treatment based on size. It fails also when surface defects or dislocations significantly alter the growth rate of a crystal face. Nevertheless, it is a reasonably accurate generahzation for a surprising number of industrial cases. When it is, it is important because it simphfies the mathematical treatment in modeling real crystallizers and is useful in predicting crystal-size distribution in many types of industrial crystallization equipment. 

The adsorption of aliphatic alcohols, which adsorb on metals with the hydrocarbon tail facing the electrode surface, shows different patterns on real Ag crystal faces440,441 with respect to quasi-perfect single-crystal face electrodes.442-444 This specific point will be discussed in detail in Section III. 

Capacitance data for various crystal faces are available for Bi and Sb.28 As a broad trend, the faces with more negative values of Eam0 show higher values of C. Although this is qualitatively in line with the behavior of real Ag surfaces, the response of Bi and Sb is complicated by their semimetal nature, which gives rise to space-charge effects. For this reason it is not straightforward to compare the absolute values of C and their crystal face sequences with those of metals. 

The equilibrium concentration of each kind of imperfection depends on the biography of the sample and on the temperature. Poltorak lOS, 104) has shown that in real crystals, characterized by non-equilibrium forms of boundary faces, this concentration may be quite considerable corresponding in order of magnitude to the concentration of active centers, as determined from the catalytic data. 

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