Segregation enthalpy

The compositional profiles of C, O, and Si in polycrystalline silicon were reported by Pizzlni et al. [167], who used the secondary ion mass spectrometry (SIMS) to determine the interfacial segregations. The segregation enthalpies and entropies for C and O in polycrystalline silicon have been estimated and listed in Table 13.1. The calculated C and O segregations (solid lines) are compared with the measured values and shown in Fig. 13.28. 

Table 13.1. Estimated polycrystalline Si segregation enthalpies and entropies for...

Fig. 4. Plot of enthalpies of complex formation in the gas phase of CpNi complexes (Cp = cyclopentadienyl) vs those for the corresponding Mn complexes. The ligands are segregated into correlations for soft (O) (N and S donors) and hard (oxygen donors) ( ). Energies are in kcal mol-1. Redrawn after Ref. (14). 

Fig. 8. Correlation between Pearson s hardness parameter (7P) derived from gas-phase enthalpies of formation of halide compounds of Lewis acids (19), and the hardness parameter in aqueous solution (/A), derived from formation constants of fluoride and hydroxide complexes in aqueous solution (17). The Lewis acids are segregated by charge into separate correlations for monopositive ( ), dipositive (O), and tripositive ( ) cations, with a single tetrapositive ion (Zr4+, ). The /P value for Tl3+ was not reported, but the point is included in parentheses to show the relative ionicity of Tl(III) to ligand bonds. 

The adsorption of gases on solids can be classified into physical and chemical adsorption. Physical adsorption is accompanied by a low enthalpy of adsorption, and the adsorption is reversible. The adsorption/desorption characteristics are in these cases often described by adsorption isotherms. On the other hand, chemical adsorption or segregation involves significantly larger enthalpies and is generally irreversible at low temperatures. It is also often accompanied by reconstruction of the surface due to the formation of strong ionic or covalent bonds. 

For such free surfaces with no energetic preference of the surface for one of the components (because of the arbitrary choice of a purely symmetric choice of interactions, UAA=UBB ) the surface enrichment effects are typically rather weak (Fig. 16b), even if one considers asymmetry of chain lengths. Even for %=0 the shorter chains are then attracted to the surface, but this purely entropic effect is particularly weak. For the enthalpy is less effective near the free surface in comparison with the entropy of mixing, and this effect is for small volume fraction < >A b of the minority component nearly independent of the asymmetry in chain length (Fig. 16b) i.e., even if the minority chains are much longer (NA= 2Nb) they segregate to the surface, contrary to the non-interacting case. 

The excellent enthalpy-entropy compensation plot, obtained by using AA// R and AAS R values, confirms that the enantiodifferentiation mechanisi is not altered by a change in solvent [37,38]. Judging from the clearly segregal activation parameters obtained in polar solvents (positive AA// R and AA5 and nonpolar solvents (negative AA// R and AAS R), this unprecedented so]... 

Fig.3. Schematics of the evolution of equilibrium segregation with temperature in alloys with order-segregation competition (a) dominant surface segregation tendency (Langmuir-McLean behaviour), (b) dominant ordering tendency. Signs of enthalpy and entropy of segregation are indicated.

Eq.6 with these parameters together with the apparent segregation excess enthalpy =-38.5 kJ/mol and segregation excess entropy ASg g =36.1... 

This approach can be applied to segregation phenomena in other two-phase alloys, such as reported recently for polycrystalline Fe99Pdi with a small fraction of ordered FePd nuclei [86]. Positive entropy and enthalpy characterize the observed increase in segregation level with temperature. 

In general, for an alloy AB, the phenomenon of segregation is controlled by a range of parameters including the differences in bond strengths A-A, B-B and A-B, atomic size, enthalpies of sublimation and surface energies, temperature, the exposed crystal plane, and metal particle size. 

Simple criteria for surface segregation in alloys (relative melting points, enthalpies of sublimation, metal atom radii, surface free energies of the pure metals) all indicate that surface segregation of titanium should occur on Pt/Ti alloys in vacuo. However, this is inadequate because of the large departures from ideality in Pt/Ti alloys. Analysis (11) of a broken bond model of the system, especially with the use of data directly determined with Pt/Ti alloys, gives a more reliable result. 

AZ is the difference in effective coordination number of a bulk site and a surface site, GptT, is the nearest-neighbour bond strength between Pt and Ti atoms (expressed as free energy, not enthalpy) and GptPti that between Pt atoms. With values derived from pure platinum and from PtgTi, the calculated values (13) of the segregation ratio (ie the ratio of surface and bulk concentration) vary between 2 x 10-7 for the (110) face to lO- for the (111) face at 800 K, and 5 x 10-12 to 2 x 10-7 for the same faces at 500 K. 

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