Antiphases

Figure Bl.13.8. Schematic illustration of (a) an antiphase doublet, (b) an in-phase doublet and (c) a differentially broadened doublet. The splitting between the two lines is in each case equal to J, the indirect spin-spin coupling constant.

M. Porta, C. Frontera, F. Vives, T. Castan. Effect of the vacancy interaction on antiphase domain growth in a two-dimensional binary alloy. Phys Rev B 56 5261, 1997. 

For the phase stability analysis we follow the method given by Kanamori and Kakehashi of geometrical inequalities and compute the antiphase boundary energy defined by... 

Figure 1 (a) The nearest neighbor pair interactions and (b) antiphase boundary energies as functions of energy for Pdj,Vi j, alloys x=0.25, x = 0.5 and x = 0.75 ( from top to bottom). Vertical lines mark the Fermi energy for the three different concentrations. 

Fig. 5 illustrates a peculiar kinetic phenomenon which occurs when an initially disordered alloy is first annealed at temperature T corresponding to area b in Fig. 1 and then quenched to the final temperature T into the spinodal instability area d antiphase boundaries "replicate , generating approximately periodic patterns. This phenomenon reflects the presence of critical, fastest growing concentration waves under the spinodal instability (the Calm waves ). Lowering of the temperature to T < T results in lowering of the minority concentration minimum ("c-well ) within APB, while the expelled solute atoms build the c-bank adjacent to the well . Due to the... 

We studied vacancy segregation near interphase and antiphase boundaries using the MFA and PCA approaches described in Sec. 6 below. For the A-B alloy with vacancies, the stationary distribution of mean vacancy occupations =< > can be explicitly... 

In this Section we use Eqs. (2)-(10) to derive several relations for the free energy F ci of a stationary noiiuniform alloy. These relations can be used to study properties of interphase and antiphase boundaries, nucleation problems, etc. 

ROUGHENING OF AN ANTIPHASE BOUNDARY NEAR A BULK FIRST ORDER TRANSITION... 

Comparison of Ordering After Quenching from above T, with Order-Order Relaxations The Influence of Antiphase Domain Growth... 

R.W Cahn, Antiphase domains, disordered films and the ductility of ordered alloys based on Ni3 Al, Mai. Res. Soc. Symp. Proc. 81 27 (1987)... 

The interatomic interaction is described by an EAM potential specifically developed for NiAl in the B2 structure [12]. Compared to the older potential [16], which was used in most of the previous atomistic studies, our new potential gives considerably higher antiphase boundary (APB) energies = 0.82 J/m, yj pg = 1.06 J/m in good agreement with the APB... 

Using the constructed potentials the y-surface for the (111) plane was calculated. (For more details see Girshick and Vitek 1995). T e lowest energy minimum on this surface corresponds to the ideal Llo structure. However, there are three different metastable stacking fault type defects on (111) the antiphase boundary (APB), the complex stacking fault (CSF) and the superlattice intrinsic stacking fault (SISF). The displacements... 

Antiphase boundary (APB) conservative vacancy segregation at Arrhenius plot Asymmetrical mixtures Atomic-sphere approximation (ASA) ASA-LSDA... 

The recommended Mg-Au phase diagram is that of ref. 3 amended by the addition of several new compounds close to MgAu3 they are a family of close-packed structures modulated both by antiphase boundaries of the superstructure and by a... 

Clearly the extent to which the H nuclei line up along the x -axis (Ild) will depend on the duration of tu which in turn will determine the extent of the antiphase z-magnetization created by the second 90° H pulse. The... 

The experiment just discussed represents a heteronuclear spin system. In a homonuclear case, the separate 90° C pulse necessary in the heteronuclear system is not required, since the second 90° H pulse affects the coupled partner H nucleus as well. The nucleus detected therefore has its two transitions antiphase with respect to each other, corresponding to the states represented in Fig. 2.7, Ilg, Ilh, etc. at detection. 

As mentioned already, the INEPT spectra are typified by the antiphase character of the individual multiplets. The INEPT C-NMR spectrum of 1,2-dibromobutane is shown, along with the normal off-resonance C-NMR spectrum, in Fig. 2.12. Doublets show one peak with positive phase and the other with negative phase. Triplets show the outer two peaks with positive and negative amplitudes and the central peak with a weak positive amplitude. Quartets have the first two peaks with positive amplitudes and the remaining two peaks with negative amplitudes. 

The INEPT experiment can be modified to allow the antiphase magnetization to be precessed for a further time period so that it comes into phase before data acquisition. The pulse sequence for the refocused INEPT experiment (Pegg et al., 1981b) is shown in Fig. 2.13. Another delay, A. is introduced and 180° pulses applied at the center of this delay simultaneously to both the H and the C nuclei. Decoupling during data acquisition allows the carbons to be recorded as singlets. The value of Z), is adjusted to enable the desired type of carbon atoms to be recorded. Thus, with D, set at V4J, the CH carbons are recorded at VsJ, the CH2 carbons are recorded and at VeJ, all protonated carbons are recorded. With D3 at %J, the CH and CH ( carbons appear out of phase from the CH2 carbons. 

The basic INEPT spectrum cannot be recorded with broad-band proton decoupling, since the components of multiplets have antiphase disposition. With an appropriate increase in delay time, the antiphase components of the multiplets appear in phase. In the refocussed INEPT experiment, a suitable refocusing delay is therefore introduced that allows the C spin multiplet components to get back into phase. The pulse sequences and the resulting spectra of podophyllotoxin (Problem 2.21) from the two experiments are given below ... 

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