Extrinsic-intrinsic diffusion

Experimentally, intrinsic diffusion may be distinguished from extrinsic diffusion because in the intrinsic regime, diffusion is a function of P and T only and is independent of any chemical activities. In the extrinsic regime, diffusion is a function of some chemical potentials in addition to P and T. 

There is no recorded case of true intrinsic diffusion in any silicate so far. The classic example of Buening and Buseck (1973) is not intrinsic at high T, as has been claimed, because they show D dependent on /02 both above and below the kink in the Arrhenius plot, which violates condition (1). There are, however, many examples of intrinsic-extrinsic transition among the oxides. 

Frequently, adsorption proceeds via a mobile precursor, in which the adsorbate diffuses over the surface in a physisorbed state before finding a free site. In such cases the rate of adsorption and the sticking coefficient are constant until a relatively high coverage is reached, after which the sticking probability declines rapidly. If the precursor resides only on empty surface sites it is called an intrinsic precursor, while if it exits on already occupied sites it is called extrinsic. Here we simply note such effects, without further discussion. 

The first four chapters introduce basic concepts that are developed to build up a framework for understanding defect chemistry and physics. Thereafter, chapters focus rather more on properties related to applications. Chapter 5 describes diffusion in solids Chapter 6, ionic conductivity Chapters 7 and 8 the important topics of electronic conductivity, both intrinsic (Chapter 7) and extrinsic (Chapter 8). The final chapter gives a selected account of magnetic and optical defects. 

When the point defect relaxation is diffusion controlled, we can use Eqn. (5.89) to determine k. After setting rAB = aAX (= unit cell dimension), it is found that at even moderate temperatures (= 100°C), x is on the order of a millisecond or less. This r is many orders of magnitude shorter than relaxation times for nonstoichiometric compounds where the point defect pairs equilibrate at external surfaces (Section 5.3.2). In other words, intrinsic defects equilibrate much faster than extrinsic defects if, during the defect equilibration, the number of lattice sites is conserved. 

For example, the self-diffusivity of K in KC1 depends on the population of both extrinsic and intrinsic cation-site vacancies. Extrinsic cation-site vacancies can be created by incorporation of Ca++ by doping KC1 with CaC and can be considered a two-step process. First, two cation vacancies and two anion vacancies form as illustrated in Fig. 8.12.11 Second, the single Ca++ cation and two Cl anions from CaCl2 are inserted into the cation and anion vacancies, respectively electric neutrality requires that each substitutional divalent cation impurity in KC1 be balanced... 

The expected Arrhenius plot for cation self-diffusion in KC1 doped with Ca++ is shown in Fig. 8.13. The two-part curve reflects the intrinsic behavior at high temperatures and extrinsic behavior at low temperatures. 

An Arrhenius plot of the cation self-diffusivity will then possess two linear regions. In the high-temperature intrinsic regime, the slope will be — Hg/3 + Hm)/k in the low-temperature extrinsic regime, the slope will be simply Hm/k, where Hm is the migration enthalpy of a cation vacancy. 

For chromophores that are part of small molecules, or that are located flexibly on large molecules, the depolarization is complete—i.e., P = 0. A protein of Mr = 25 kDa, however, has a rotational diffusion coefficient such that only limited rotation occurs before emission of fluorescence and only partial depolarization occurs, measured as 1 > P > 0. The depolarization can therefore provide access to the rotational diffusion coefficient and hence the asymmetry and/or degree of expansion of the protein molecule, its state of association, and its major conformational changes. This holds provided that the chromo-phore is firmly bound within the protein and not able to rotate independently. Chromophores can be either intrinsic—e.g., tryptophan—or extrinsic covalently bound fluorophores—e.g., the dansyl (5-dimethylamino-1-naphthalenesulfonyl) group. More detailed information can be obtained from time-resolved measurements of depolarization, in which the kinetics of rotation, rather than the average degree of rotation, are measured. For further details, see Lakowicz (1983) and Campbell and Dwek (1984). 

Figure 7. Donor impurity diffusion coefficient (Di) vs. electron concentration (electrons per cm3) showing regions of intrinsic and extrinsic diffusion. (Reproduced with permisssion from reference 119. Copyright 1981 Academic...

This dimensionless rate constant contains typical parameters of the process (i.e., the heterogeneous rate constant k°, the diffusion coefficient, and the experiment time), thus reflecting that the behavior of the process is the result of a combination of intrinsic (kinetics and diffusion) and extrinsic (time window) effects. The effect of Kplane in the voltammograms obtained when both species (a) or only oxidized species O (b) are initially present can be seen in Fig. 3.3. 

The gastrointestinal epithelium forms an extrinsic and an intrinsic barrier against diffusion of toxins and pathogens. The extrinsic barrier is characterized by secretion of mucus, which hinders colonization and accelerates clearance of pathogenic organisms. The importance of mucus as a barrier to drug absorption is discussed in Chapter 2 of this book. In addition, the intestinal immune... 

Fig. 2.19 Diagram of the plasma membrane showing its integral proteins (fluid mosaic model) (adapted from S.J. Singer et af, 1972 and H. Knufermann, 1976). 1 external aqueous milieu, 2 internal aqueous milieu, 3 fracture plane of the apolar membrane layer, 4 externally orientated intrinsic protein (ectoprotein), 5 internally orientated intrinsic protein (endoprotein), 6 external extrinsic protein, 7 internal intrinsic protein, 8, 9 membrane-penetrating proteins with hydrophobic interactions in the inside of the membrane (P = polar region), 10 membrane pervaded by glycoprotein with sugar residues (, 11 lateral diffusion (A) and flip-flop (B), 12 hydrophilic region (A) and hydrophobic region (B) of the bilayer membrane...

Computer simulation methods have been extensively used to probe the structural behavior of ionically conducting solids, with particular emphasis on the preferred diffusion mechanisms and the nature of intrinsic (thermally induced) and extrinsic (generated by chemical doping) defects. As discussed elsewhere [6], these techniques can broadly be divided into three categories ... 

The modem view of biomembrane structure is that it consists of an asymmetric Upid bilayer having proteins, both intrinsic and extrinsic, associated with it. The intrinsic proteins are embedded within and can span the bilayer [1-5]. Associated with this view of biomembrane structure is the idea that in many cases the Upid matrix can be in a fluid condition where the Upids are essentially above their transition temperatures (7J.) and able to diffuse within the bilayer matrix. An additional feature of certain biomembrane systems is the presence of cholesterol. 

Among nonisotopic techniques, fluorescence (both intrinsic and extrinsic) offers a convenient mode of detection, and the sensitivity of some fluorescent labels is comparable to that of radiolabeled iodine. Recent innovations include the use of polarized light for excitation, such that the degree of polarization of the emission as well as its intensity can provide information about the concentration and size-related behavior (e.g., rotational diffusion) of the fluorescent-labeled molecule. One disadvantage of steady-state fluorescence techniques is that many analytical samples either autofluoresce or quench the fluorescence of the substance of interest. A recent development that circumvents this problem utilizes long-lived fluorophores such as the lanthanide metal ions as labels. Detection is time resolved and data are collected after the decay of spurious or otherwise unwanted fluorescence, i.e., after 100-200 psec. 

Disproportionation of intermetallics is indicated by the changes in the shape of the isotherms and associated loss in the hydrogen capacity [20]. This phenomenon may be attributed to short-range diffusion of the atoms, the thermodynamic stability of one of the elemental species from an elemental hydride, and dissociation of the non-hydride former second atom as a metal. Note that it is not necessary for all the binary intermetallic hydride to completely dissociate into elemental hydrides. Many variants of AB5 alloys have been used for hydrogen storage over the years and these hydrides were tested for intrinsic and extrinsic degradation, mainly LaNis and FeTi-type hydrides these hydrides exhibit a propensity for disproportionation. A hydride that would hydride/dehydride really well during the first few cycles may not... 

Since the data were obtained in the transition region where intrinsic and extrinsic defects are contributing to the total defect concentration, the calculation of an enthalpy of motion cannot be made in a simple way because the temperature dependence of the Frenkel constant is not known. However, Ail. probably increases with temperature while the extrinsic defect concentration decreases with temperature. If, to a first approximation, these two trends cancel, then the enthalpy of motion is just the experimentally determined activation energy. Using this value from (16) and the defect concentration shown in Table VII, the preexponential constant Dq and hence the diffusion coefficient can be determined. 

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