Polycrystalline functionality

Measurement of Residual Stress and Strain. The displacement of the 2 -value of a particular line in a diffraction pattern from its nominal, nonstressed position gives a measure of the amount of stress retained in the crystaUites during the crystallization process. Thus metals prepared in certain ways (eg, cold rolling) have stress in their polycrystalline form. Strain is a function of peak width, but the peak shape is different than that due to crystaUite size. Usually the two properties, crystaUite size and strain, are deterrnined together by a computer program. 

A summary of physical and chemical constants for beryUium is compUed ia Table 1 (3—7). One of the more important characteristics of beryUium is its pronounced anisotropy resulting from the close-packed hexagonal crystal stmcture. This factor must be considered for any property that is known or suspected to be stmcture sensitive. As an example, the thermal expansion coefficient at 273 K of siagle-crystal beryUium was measured (8) as 10.6 x 10 paraUel to the i -axis and 7.7 x 10 paraUel to the i -axis. The actual expansion of polycrystalline metal then becomes a function of the degree of preferred orientation present and the direction of measurement ia wrought beryUium. 

A typical shock-compression wave-profile measurement consists of particle velocity as a function of time at some material point within or on the surface of the sample. These measurements are commonly made by means of laser interferometry as discussed in Chapter 3 of this book. A typical wave profile as a function of position in the sample is shown in Fig. 7.2. Each portion of the wave profile contains information about the microstructure in the form of the product of and v. The decaying elastic wave has been an important source of indirect information on micromechanics of shock-induced plastic deformation. Taylor [9] used measurements of the decaying elastic precursor to determine parameters for polycrystalline Armco iron. He showed that the rate of decay of the elastic precursor in Fig. 7.2 is given by (Appendix)... 

Thermodynamically, an average work function can be defined for a polycrystalline surface3,6 ... 

Figure 14. Plot of the potential of zero charge, Ea=0 (from Table 26), against the work function,

Thus far, Ft has never found a definite position in Ea vs. correlations, more for the uncertainty in the reliability of its pzc than for its work function. On the other hand, Pt is a highly heterogeneous metal and the fact that only polycrystalline surfaces have been used in double-layer studies has not helped remove suspicions. According to Frumkin s data,10,14 the pzc ofpc-Pt is around 0.2 V(SHE) (in acidic solution). If this value is introduced into Fig. 14 (the 0 of pc-Pt is around 5.5 eV),22,65 343,856 865,866 the point of Pt would fall far distant from the line of mercurylike metals and near the line of d-metals. 

Figure 4.19. Experimental work function values, for the 3d, 4d and 5d series including the alkali, alkaline-earth, and noble metals for polycrystalline surfaces (open circles) and for single crystal surfaces (filled circles).53 Reprinted with permission from the American Physical Society.

The quantities jXe, pe >

bulk properties of the metal. The quantities O, and of course F, are surface properties which can vary on a metal surface from one crystallographic plane to the other. Such variations are typically on the order of 0.1 eV but can be as high as 0.5 V. The measured work function , of a polycrystalline metal is an average of the d> values on different crystallographic planes. 

The electrochemically induced creation of the Pt(lll)-(12xl2)-Na adlayer, manifest by STM at low Na coverages, is strongly corroborated by the corresponding catalyst potential Uwr and work function O response to galvanostatic transients in electrochemical promotion experiments utilizing polycrystalline Pt films exposed to air and deposited on (T -AbCb. 3637 Early exploratory STM studies had shown that the surface of these films is largely composed of low Miller index Pt(lll) planes.5... 

Figure 8.14. Turnover frequency for methanol synthesis from H2 and CO2 at 18 bar and 523 K as a function ofZn coverage on polycrystalline copper. [From j. Nakamura, I. Nakamura,...

In anisotropic crystals, the amplitudes of the atomic vibrations are essentially a function of the vibrational direction. As has been shown theoretically by Karyagin [72] and proved experimentally by Goldanskii et al. [48], this is accompanied by an anisotropic Lamb-Mossbauer factor/which in turn causes an asymmetry in quadra-pole split Mossbauer spectra, for example, in the case of 4 = 3/2, f = 1/2 nuclear transitions in polycrystalline absorbers. A detailed description of this phenomenon, called the Goldanskii-Karyagin effect, is given in [73]. The Lamb-Mossbauer factor is given by... 

Fig. 5.17 Comparison of the experimental PVDOS determined from NIS measurements on Fe (TPP)(NO) (upper panel) with the PVDOS predicted on the basis of DFT calculations using the B3LYP (center panel) and BP86 (lower panel) functionals. Blue traces represent the PPVDOS Dp (v)for oriented crystals (see Appendix 2, Part III, 3 of CD-ROM), scaled by a factor of 3 for comparison with the total PVDOS Dpe(v)of unoriented polycrystalline powder (red traces). Since the X-ray beam direction k lies 6° from the porphyrin plane, modes involving Fe motion in the plane of the porphyrin are enhanced, and modes with Fe motion primarily normal to the plane are suppressed, in the scaled oriented crystal PVDOS relative to the powder PVDOS. In-plane Fe modes dominate the 200-500 cm range of the data, while Fe motion in modes observed at 74, 128, and 539 cm is predominantly out-of-plane. Crosshatching in the upper panel indicates the area attributable to acoustic modes. In the lower two panels, the Fe-NO bend/stretch modes predicted at 386 and 623 cm , have been artificially shifted to the observed 539 cm frequency to facilitate comparison with the experimental results. Predicted PVDOS are convolved with a 10 cm Gaussian (taken from [101])...

Quasielastic (Rayleigh) scattering of the 46.5 keV Mossbauer radiation was used to examine the liquid dynamics of glycerol [245, 246] and the harmonic vibrations of the nonhydrogen atoms in polycrystalline myoglobin [247] as a function of temperature. The y-quanta emitted by the Mossbauer source are... 

We used polycrystalline films of ZnO and Sn02 as adsorbents. The films were deposited from the water suspension of respective oxides on quartz substrates. These substrates contained initially sintered contacts made of platinum paste. The gap between contacts was of about lO" cm. All samples were initially heated in air during one hour at T 500 C. We used purified molecular oxygen an acceptor particle gas. H and Zn atoms as well as molecules of CO were used as donor particles. We monitored both the kinetics of the change of ohmic electric conductivity and the tangent of inclination angle of pre-relaxation VAC caused by adsorption of above gases and the dependence of stationary values of characteristics in question as functions of concentrations of active particles. 

Fig. 7. Photoelectric work function for Au, Pt and Ag electrodes emersed from 0.1 M HC104 at different potentials. Work function was measured by means of UPS (He 1). Arrows indicate work functions of clean polycrystalline surfaces. After [20].

More than a decade ago, Hamond and Winograd used XPS for the study of UPD Ag and Cu on polycrystalline platinum electrodes [11,12]. This study revealed a clear correlation between the amount of UPD metal on the electrode surface after emersion and in the electrolyte under controlled potential before emersion. Thereby, it was demonstrated that ex situ measurements on electrode surfaces provide relevant information about the electrochemical interface, (see Section 2.7). In view of the importance of UPD for electrocatalysis and metal deposition [132,133], knowledge of the oxidation state of the adatom in terms of chemical shifts, of the influence of the adatom on local work functions and knowledge of the distribution of electronic states in the valence band is highly desirable. The results of XPS and UPS studies on UPD metal layers will be discussed in the following chapter. Finally the poisoning effect of UPD on the H2 evolution reaction will be briefly mentioned. 

The idea is simple consider a polycrystalline material that is subjected to locally varying strain. Then every crystal is probing its local strain by small compression or expansion of the lattice constant. The superposition of all these dilated lattices makes the observable line profiles - and as a function of order their breadth has to increase linearly. According to Kochendorfer the polycrystalline material becomes inhomogeneous or heterogeneous . 

Polycrystalline films deposited on amorphous substrates are of lower crystallographic surface heterogeneity the higher the temperature of annealing subsequent to deposition or the higher the substrate temperature during deposition again, photoelectric work-function data serve to emphasize the point (9,10, 12,18). 

It is particularly helpful that we can take the Cu-Ni system as an example of the use of successive deposition for preparing alloy films where a miscibility gap exists, and one component can diffuse readily, because this alloy system is also historically important in discussing catalysis by metals. The rate of migration of the copper atoms is much higher than that of the nickel atoms (there is a pronounced Kirkendall effect) and, with polycrystalline specimens, surface diffusion of copper over the nickel crystallites requires a lower activation energy than diffusion into the bulk of the crystallites. Hence, the following model was proposed for the location of the phases in Cu-Ni films (S3), prepared by annealing successively deposited layers at 200°C in vacuum, which was consistent with the experimental data on the work function. 

Silane decomposes to its elements at above 400°C. Process (1) is known as direct thermal decomposition, and produces either amorphous or polycrystalline Si (function of reaction temperature and other processing parameters), and is commonly used, for instance, in the solar cell industry to reduce silane to silicon. 

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