Split interstitials

Figure 1. Typical point defects in a binary ordered alloy (a) vacancy ( ) (b) split interstitial (c) bound pair of antisite defects (d) bound triple defect consisting of two vacancies and one antisite atom (e) vacancy-impurity ( ) bound pair (f) unbound wrong pair. Many other types of defects are possible, as will be discussed for example for Bll (CuTi, Section 5.3) and A15 (NbjSn, Section 9.1) compounds...

Figure 13. Configuration and migration of the Cu-Cu split interstitial proposed for ordered CujAu. The labelling I [010] means the dumbbell is oriented along the <010> direction, and centered on the cube face perpendicular to the X axis (From Alamo et at., 1986)...

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

Sauer et al. [185] derived a weak quadmpole interaction from the asymmetry of a poorly resolved Zeeman split spectmm of in W metal versus a Ta metal absorber. They also ascribed the unexpected weak quadmpole effect to deviations from cubic symmetry at the source or absorber atom arising from either interstitial impurities or crystal defects. 

The adequacy of the spin-averaged approach has been confirmed in self-consistent spin-density-functional calculations for H in Si by Van de Walle et al. (1989). The deviation from the spin-averaged results is expected to be largest for H at the tetrahedral interstitial (T) site, where the crystal charge density reaches its lowest value. For neutral H at the T site, it was found that inclusion of spin polarization lowered the total energy of the defect only by 0.1 eV. The defect level was split into a spin-up and a spin-down level, which were separated by 0.4 eV. These results are consistent with spin-polarized linearized-muffin-tin-orbital (LMTO) Green s-function calculations (Beeler, 1986). 

The total volume of the mobile phase in the column VM can be split into two parts the interstitial volume V (external to the pores) and the volumes of the pores VP. V represents the volume of the mobile phase necessary to transport a big molecule, excluded from the pores, and VM= Vi + VP is the volume corresponding to the elution of a small molecule that can enter the pores. The elution volumes VE are thus comprised of V, and VM. For a molecule of intermediate size ... 

Interstitialcy migration depends on the geometry of the interstitial defect. However, an a priori prediction of interstitial defect geometry is not straightforward in real materials. For an f.c.c. crystal, a variety of conceivable interstitial defect candidates are illustrated in Fig. 8.5. The lowest-energy defect will be stable and predominant. For example, in the f.c.c. metal Cu, the stable configuration is the (100) split-dumbbell configuration in Fig. 8.5d [3]. 

The (100) split-dumbbell defect in Fig. 8.5d, while having the lowest energy of all interstitial defects, still has a large formation energy (Ef = 2.2 eV) because of the large amount of distortion and ion-core repulsion required for its insertion into the close-packed Cu crystal. However, once the interstitial defect is present, it persists until it migrates to an interface or dislocation or annihilates with a vacancy. The... 

Figure 8.5 Geometric configurations for a self-interstitial defect atom in an f.c.c. crystal (a) octahedral site, (b) tetrahedral site, (c) (110) crowdion, (d) (100) split, dumbbell, (e) (111) split., (f) (110) split crowdion [2].

Figure 8.6 Diffusiomil migration of a [100] split-dumbbell self-interstitial in an f.e.c.

Diffusion of Self-Interstitial Imperfections by the Interstitialcy Mechanism in the F.C.C. Structure. For f.c.c. copper, self-interstitials have the (100) split-dumbbell configuration shown in Fig. 8.5d and migrate by the interstitialcy mechanism illustrated in Fig. 8.6. The jumping is uncorrelated,8 (f = 1), and a/ /2 is the nearest-neighbor distance, so... 

The preceding analysis provides a powerful method for determining the diffusivities of species that produce an anelastic relaxation, such as the split-dumbbell interstitial point defects. A torsional pendulum can be used to find the frequency, u>p, corresponding to the Debye peak. The relaxation time is then calculated using the relation r = 1/ojp, and the diffusivity is obtained from the known relationships among the relaxation time, the jump frequency, and the diffusivity. For the split-dumbbell interstitials, the relaxation time is related to the jump frequency by Eq. 8.63, and the expression for the diffusivity (i.e., D = ra2/12), is derived in Exercise 8.6. Therefore, D = a2/18r. This method has been used to determine the diffusivities of a wide variety of interstitial species, particularly at low temperatures, where the jump frequency is low but still measurable through use of a torsion pendulum. A particularly important example is the determination of the diffusivity of C in b.c.c. Fe, which is taken up in Exercise 8.22. 

As discussed in Section 8.3.1, the (100) split-dumbbell self-interstitial in the f.c.c. structure can exist with its axis along [100], [010], or [001], Under stress, certain of these orientation states are preferentially populated due to the tetragonality of the defect as a center of dilation. When the stress is suddenly released, the defects repopulate the available states until the populations in the three states become equal. Show that the relaxation time for this repopulation is... 

It is possible to express the diffusivity of the split-dumbbell self-interstitial in an f.c.c. crystal (illustrated in Fig. 8.6) in terms of its total jump frequency, T, and the lattice constant of the crystal, a. Show that the following approaches lead to the same result. 

Solution. Using a torsion pendulum, find the anelastic relaxation time, r, by measuring the frequency of the Debye peak, cup, and applying the relation cupr = 1. Having r, the relationship between r and the C atom jump frequency F is found by using the procedure to find this relationship for the split-dumbbell interstitial point defects in Exercise 8.5. Assume the stress cycle shown in Fig. 8.16 and consider the anelastic relaxation that occurs just after the stress is removed. A C atom in a type 1 site can jump into two possible nearest-neighbor type 2 sites or two possible type 3 sites. Therefore,... 

The magnitudes of J(195Pt- H) and the splitting patterns observed in [Ni9Pt3HB 4(CO)21]" (n = 2,3) suggest that the interstitial hydrides in these... 

Hydrides. Hydrogenation of degassed activated vanadium occurs at —20 to — 60 °C and is complete in 8—10 days forming the cubic hydride VH1-93 whose lattice parameter is a = 4.26 A.362 Two quadrupole-split 2H spectra have been observed363 for the interstitial vanadium deuterides VDX 0.2 x 0.9. 

Figure 5.4a shows the electro-driven elution of alkylbenzenes and polyaromatic hydrocarbons (PAHs) in 80% acetonitrile. Figure 5.4a shows that the 250 mm column (100 pm diameter) produced ca. 40,000 and 35,000 theoretical plates for thiourea and hexylbenzene (k value = 0.8), respectively, at 1.1 mm/s linear velocity. Because of the presence of the very large through-pores at 8-10 pm, low column efficiency would be expected in pressure-driven elution, and this was actually the case. Interstitial voids of that size would be found in a column packed with ca. 30 pm particles. Figure 5.4b shows that the same column produced 5,000 and 6,000 theoretical plates for thiourea and hexylbenzene, respectively, under the pressure-driven conditions, with a split injection HPLC system at a similar linear velocity. The monolithic silica showed much higher performance in CEC than in the pressure-driven mode. 

As explained in Chapter 5, the transport mechanism in dense crystalline materials is generally made up of incessant displacements of mobile atoms because of the so-called vacancy or interstitial mechanisms. In this sense, the solution-diffusion mechanism is the most commonly used physical model to describe gas transport through dense membranes. The solution-diffusion separation mechanism is based on both solubility and mobility of one species in an effective solid barrier [23-25], This mechanism can be described as follows first, a gas molecule is adsorbed, and in some cases dissociated, on the surface of one side of the membrane, it then dissolves in the membrane material, and thereafter diffuses through the membrane. Finally, in some cases it is associated and desorbs, and in other cases, it only desorbs on the other side of the membrane. For example, for hydrogen transport through a dense metal such as Pd, the H2 molecule has to split up after adsorption, and, thereafter, recombine after diffusing through the membrane on the other side (see Section 5.6.1). 

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