Surface segregation ordered alloys

Alloy surface segregation and ordering phenomena recent progress... 

Theoretical and experimental studies of surface segregation equilibrium phenomena in metallic alloys have been focused traditionally on substitutional solid solutions with elemental constituents (and non-metal impurities) assumed to be randomly distributed among the crystal lattice bulk and surface sites. Only in recent years more attention have been paid to the role of compositional order in surface segregation [1]. 

Muller, S., Stohr, M., and Wieckhorst, O. (2006) Structure and stability of binary alloy surfaces segregation, relaxation, and ordering from first-principles calculations. Appl. Phys. A, 82, 415. 

A very important characteristic of the subsurface region is the surface concentration of the atoms. For alloys, it is customary to speak of the surface segregation of the component whose surface concentration exceeds the bulk one. With an increase in the distance from the surface, the local concentrations of the particles tend to their bulk values. This also relates to the other characteristics of particle distribution determining short- and long-range orders, which in the subsurface region can have a great anisotropy. 

The simplest surface specific feature of an ordered phase is the fact that there usually are different truncations of the bulk ordered alloy by the same surface orientation. In this case the problem is to find the stable truncation which, as we will show in this section, is usually directly related to the surface segregation energy of the deposited element to the corresponding surface of the substrate. 

A similar growth of the ordered NisAl alloy is observed experimentally during deposition of A1 on the (100) surface of Ni [46]. Here the formation of a stable c-(2x2) ordered NiAl alloy was found on the surface while the second layer was an almost entirely pure Ni layer and the third layer was enriched by Al. This type of structure corresponds to the NiAl termination of the NisAKlOO) surface, which also has an alternative truncation. The surface segregation energy of Al on the (100) surface of Ni is only about -0.1 eV, and as has been shown [24], the NiAl termination is more stable than Ni termination by approximately half of this value. 

The BFS method has been applied to a variety of problems, ranging from the determination of bulk properties of solid solution fee and bee alloys and the defeet strueture in ordered bee alloys [28] to more speeifie applieations ineluding detailed studies of the strueture and eomposition of alloy surfaees [29], ternary [30] and quaternary alloy surfaees and bulk alloys [31,32], and even the determination of the phase strueture of a 5-element alloy [33]. Previous appheations have foeused on fundamental features in monatomie [26] and alloy surfaces [29] surface energies, reconstructions, surface structure and surface segregation in binary and higher order alloys [34,35] and multilayer relaxations [36,37]. While most of the work deals with metallic systems, the lack of restrictions on the type of system that can be studied translated into the extension of BFS to the study of semiconductors [38]. 

In case < 0, bonding of like atoms is energetically preferred, leading in principle to separation of the alloy into a mixture of A and B rich solid-solution phases, each with nearly homoatomic SRO clusters, compared to short range A-B mixed or heteroatomic clusters in the former case of V >0. In other words, the tendency to order (or phase-separate) is manifested to some, local degree also in most solid solutions, where the distribution of atoms in the crystal is not entirely random, and should be incorporated too in any theoretical quantitative evaluation of surface segregation phenomena. Moreover, many alloys of... 

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.

Compared to SRO effects on surface segregation in solid solutions, the role of LRO should be naturally more prominent and common. Its elucidation requires calculations that take into account various factors contributing to the net segregation characteristics in ordered alloys including the temperature dependence the crystal bulk structure and surface orientation, effective bulk and surface interatomic interactions (NN, non-NN) in relation to segregation driving forces, deviation from exact stoichiometry, possible surface relaxation and reconstruction, atomic vibrations, etc. This section attempts to quantify some of these factors and present several possible scenarios of segregation/order interplay. 

Fig.7. The B2(110) alloy surface average concentration as a function of temperature calculated in the FCEM approximation for model AcB c alloys with stoichiometric (c=0.50) and near-stoichimetric (c=0.49,0.51) bulk concentrations (segregation/order factor r =8.9).

In addition to the segregation/order factor, and depending on its magnitude, the crystal structure and surface orientation can strongly affect the surface composition in ordered alloys. For example, unlike the case of the equiatomic bulk truncated composition of Ll2(100), LRO tends to maintain the Ll2(lll) surface with nominal bulk concentration (0.25). Therefore, the two ordered surfaces are expected to exhibit quite different segregation characteristics for the same r value (Fig. 10). Moreover, SRO causes pronounced changes of surface sublattice and average compositions associated with a considerable reduction of the order-disorder transition temperature (especially in fee alloys). 

These energetic parameters were used in FCEM calculations assuming segregation at the three outmost layers only. As shown in Fig. 15, the segregation tendency prevails only in the B32 ordered alloys and the surface concentration decreases with temperature (entropy-driven monotonous desegregation). This behavior is associated with the distinctly high segregation/order factor (sec. 3.1). On the other hand, ordered bulk truncation with surface concentration very... 

Fig.18. Phase diagram of Al-Ag [81]. Insert schematics of processes pertinent to surface segregation in bi-phase alloys (a - solid solution, S- ordered compound).

While both LRO and SRO effects on segregation are determined largely by the energetic balance as reflected by the magnitude of r, the role of LRO is naturally more prominent, and thus received more attention in this review. Yet, as exemplified for the above mentioned ternary solid solution, SRO associated with appreciable solute-solvent interactions can affect considerably surface compositional phase transitions. Likewise, in ordered fee alloys with both LRO and SRO operative, order-disorder surface phase-transition temperatures are significantly shifted by SRO, thus modifying the individual sub-lattice... 

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