Partial Ordering

Other examples of order-disorder second-order transitions are found in the alloys CuPd and Fe Al. Flowever, not all ordered alloys pass tlirough second-order transitions frequently the partially ordered structure changes to a disordered structure at a first-order transition. 

Fig. 3.52. Normalized back-scattering yields of ions from Pb near the melting point, with the incident beam and scattered beam directed along <101 > crystal axes (double alignment) curve a, 295 K curve b, 506 K curve c, 561 K curve d, 600.5 K curve e, 600.8 K. Spectrum d is fitted by a sum of contributions M, from a liquid surface layer, and I, from a partially ordered transition layer [3.133].

We have studied the fee, bcc, and hep (with ideal eja ratio) phases as completely random alloys, while the a phase for off-stoichiometry compositions has been considered as a partially ordered alloy in the B2 structure with one sub-lattice (Fe for c < 50% and Co for c > 50%) fully occupied by the atoms with largest concentration, and the other sub-lattice randomly occupied by the remaining atoms. 

In summary, we have demonstrated the possibility of calculating the phase stability of a magnetic random alloy from first principles by means of LMTO-CPA theory. Our calculated phase diagram is in good agreement with experiment and shows a transition from the partially ordered a phase to an hep random alloy at 85% Co concentration. 

Experimentally it is found that the Fe-Co and Fe-Ni alloys undergo a structural transformation from the bee structure to the hep or fee structures, respectively, with increasing number of valence electrons, while the Fe-Cu alloy is unstable at most concentrations. In addition to this some of the alloy phases show a partial ordering of the constituting atoms. One may wonder if this structural behaviour can be simply understood from a filling of essentially common bands or if the alloying implies a modification of the electronic structure and as a consequence also the structural stability. In this paper we try to answer this question and reproduce the observed structural behaviour by means of accurate alloy theory and total energy calcul ions. 

We have used the basis set of the Linear-Muffin-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed the Vosko-Wilk-Nusair parametrization for the exchange-correlation energy density and potential. In conjunction with this we have treated the alloying effects for random and partially ordered phases with a multisublattice generalization of the coherent potential approximation (CPA). 

We have considered the fee and bee phases for both random and ordered (partially ordered) alloys. The ordered bee phase is based on the B2 structure. In this structure only the FcsoXso (X = Co, Ni or Cu) alloys can be perfectly ordered. For the off-stoichiometry compositions partially ordered alloys have been considered with one... 

Accept partial delivery Sometimes a supplier can deliver a partial order to keep your project on schedule and complete the delivery later. X X... 

Pake spectrum 26, 38, 44 Paraffin crystals 129 Parallel model 130 Partially ordered systems 27... 

The present appendix represents a detailed derivation of the kinetic equations of the fluctuating liquid cage model in the classical formalism. A natural generalization is done for the case of partially ordered media, e.g. nematic liquid crystals. One of the simplest ways to take into account the back reaction is demonstrated, namely to introduce friction. 

For partially ordered media the stationary solution (A8.10) is an eigenfunction of the integral operator in (A8.10), belonging to the eigen-... 

Zn, Al, Ga, In, Ge, Sn, Sb Structure variants with an extended statistical distribution or with partial ordering... 

The constraint transformation algorithm accepts a network of goals partially ordered by constraints, and generates a constraint network of primitive actions, such that, if there exists a directed path from goal A to goal B (i.e., A must be achieved before B) in the first network, and if OP-A is the primitive action that achieves goal A, and OP-B the action that accomplishes B, then OP-A and OP-B are labels on nodes in the generated network, and there exists a directed path from the node labeled with OP-A to the node labeled with OP-B. 

Definition. A dominance relation, D, is a partial ordering of the partial solutions of the discrete decision processes in X, which satisfies the following three properties for any partial solutions, x and y. 

The morphology of the semicrystalline polyphosphazenes is complex. Table I provides examples of phosphazenes with two first order transitions denoted by T(l) and Tm. The T(l) is an intermediate transition to a partially ordered state. Between T(l)... 

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