Inert markers

If samples of two metals widr polished faces are placed in contact then it is clear that atomic transport must occur in both directions until finally an alloy can be formed which has a composition showing die relative numbers of gram-atoms in each section. It is vety unlikely that the diffusion coefficients, of A in B and of B in A, will be equal. Therefore there will be formation of an increasingly substantial vacancy concentration in the metal in which diffusion occurs more rapidly. In fact, if chemically inert marker wires were placed at the original interface, they would be found to move progressively in the direction of slowest diffusion widr a parabolic relationship between the displacement distance and time. 

Oxide movements are determined by the positioning of inert markers on the surface of the oxideAt various intervals of time their position can be observed relative to, say, the centreline of the metal as seen in metal-lographic cross-section. In the case of cation diffusion the metal-interface-marker distance remains constant and the marker moves towards the centreline when the anion diffuses, the marker moves away from both the metal-oxide interface and the centreline of the metal. In the more usual observation the position of the marker is determined relative to the oxide/ gas interface. It can be appreciated from Fig. 1.81 that when anions diffuse the marker remains on the surface, but when cations move the marker translates at a rate equivalent to the total amount of new oxide formed. Bruckman recently has re-emphasised the care that is necessary in the interpretation of marker movements in the oxidation of lower to higher oxides. 

The periodate-permanganate method used was based on a method described previously [105], but three changes from the original published procedure were found to be necessary. A sample size of 50 mg was taken for all oxidations. The same quantities of oxidant, potassium carbonate, and sodium bisulfite (26 ml, 45 mg, 1.06 g, respectively) were used for all samples. An inert marker (5 mg) of methyl palmite or stearate was added to all samples prior to oxidation to serve as a rough check on the completeness of oxidation and the recovery of fragments. 

Inert markers have been used to obtain additional information regarding the mechanism of spinel formation. A thin platinum wire is placed at the boundary between the two reactants before the reaction starts. The location of the marker after the reaction has proceeded to a considerable extent is supposed to throw light on the mechanism of diffusion. While the interpretation of marker experiments is straightforward in metallic systems, giving the desired information, in ionic systems the interpretation is more complicated because the diffusion is restricted mainly to the cation sublattice and it is not clear to which sublattice the markers are attached. The use of natural markers such as pores in the reactants has supported the counterdiffusion of cations in oxide spinel formation reactions. A treatment of the kinetics of solid-solid reactions becomes more complicated when the product is partly soluble in the reactants and also when there is more than one product. 

Let us analyze these results one step further and ask about a quantitative measure of the Kirkendall effect. This effect had been detected by placing inert markers in the interdiffusion zone. Thus, the lattice shift was believed to be observable for an external observer. If we assume that Vm does not depend on concentration and local defect equilibrium is established, the lattice site number density remains constant during interdiffusion. Let us designate rv as the production (annihilation) rate of the vacancies. We can derive from cA+cB+cv = l/Vm and jA +/ B +./v = 0 that... 

In the Kirkendall effect, the difference in the fluxes of the two substitutional species requires a net flux of vacancies. The net vacancy flux requires continuous net vacancy generation on one side of the markers and vacancy destruction on the other side (mechanisms of vacancy generation are discussed in Section 11.4). Vacancy creation and destruction can occur by means of dislocation climb and is illustrated in Fig. 3.36 for edge dislocations. Vacancy destruction occurs when atoms from the extra planes associated with these dislocations fill the incoming vacancies and the extra planes shrink (i.e., the dislocations climb as on the left side in Fig. 3.36 toward which the marker is moving). Creation occurs by the reverse process, where the extra planes expand as atoms are added to them in order to form vacancies, as on the right side of Fig. 3.36. This contraction and expansion causes a mass flow that is revealed by the motion of embedded inert markers, as indicated in Fig. 3.3 [4]. 

Equation 3.23 for the velocity of a local C-frame with respect to the E-frame is therefore the velocity of any inert marker with respect to the E-frame. The assumptions that fli and il2 are each constant throughout the material, and thus that there are no changes in overall specimen volume during diffusion, permit the use of Eq. 3.19 to derive the unique choice of the E-frame. 

Equation 3.23 gives the velocity of the local C-frame with respect to the V-frame (i.e., the velocity of local mass flow measured by the velocity of an embedded inert marker relative to the ends of a diffusion couple such as in Figs. 3.3 and 3.4). The measurement of and D at the same concentration in a diffusion experiment thus produces two relationships involving Di and D2 and allows their determination. In the V-frame, the diffusional flux of each component is given by a simple Fick s-law expression where the factor that multiplies the concentration gradient is the interdiffusivity D. In this frame, the interdiffusion is specified completely by one diffusivity. 

The Kirkendall effect can be studied by embedding an inert marker in the original step-function interface (x = 0) of the diffusion couple illustrated in Fig. 3.4. Show that this marker will move in the F-frame or, equivalently, with respect to the nondiffused ends of the specimen, according to... 

The tracer atoms will spread out as they would in the absence of current however, they will also be translated bodily by the distance Ax = (VA)t relative to an embedded inert marker as illustrated in Fig. 5.9. 

Note that this process will cause the boundary to move relative to inert markers embedded in either crystal adjoining the boundary. 

This could be measured by observing the separation of inert markers buried in each crystal opposite one another across the boundary. 

The symbol designates an inert marker inside the ApBq layer. An increase in layer thickness takes place only at the A-ApBq interface. Not on scale in fact, dx i x. 

The specimen, most suitable for such measurements, is shown schematically in Fig. 1.8. The upper part of the specimen is used for comparison. To prevent the interaction of components A and B in this part, a thin barrier layer of some substance which does not react with both A and B under chosen experimental conditions is deposited. The position of the layer interfaces is measured at certain moments of time relative to the inert markers located at the initial interface between substances A and B and/or inside the ApBq layer. Microhardness indentations onto the specimen cross-section surface, thin wires and strips of chemically inert materials, bubbles of inert gases, etc., can serve as the markers (for more detail, see for example Refs 35, 124). 

Besides measuring the total thickness of the Cu6Sn5 layer, K.N. Tu and R.D. Thompson also determined the distance from inert markers located in the intermetallic layer to its interfaces with copper and tin (see Fig. 1.12). Discontinuous tungsten stripes deposited onto the copper surface prior to the deposition of tin served as markers. In one series of experiments, the distance, xSni, from the Cu-Cu6Sn5 interface to a tungsten marker was found to be around 60 nm, while the distance, xCu2, from this marker to the Cu6Sn5-Sn interface was equal to 185 nm. Hence,... 

The compound layer thickness was determined using a conventional microhardness tester and an optical microscope. The microhardness tester was also used to put inert markers onto the surfaces of the phases involved in the interaction before each anneal of the Ni-Bi couples, except the first one when the intermetallic layer was still too thin. The microhardness indentations are known to possess advantages over other markers (inert... 

It should be noted that kinetic data must necessarily be supplemented by measurements of the displacement of phase interfaces relative to inert markers located within the bulks of growing ApBq and ArBs layers (Fig. 2.4). Otherwise, it is impossible to find all four chemical constants, kom, k 0A2, k 0B2 and k0A3, from the system (2.30) containing only two equations. 

It should be noted that the separate determination of the chemical constants is yet terra incognita because of experimental difficulties associated with putting inert markers and measuring layer thicknesses in very thin films (some tens to some hundreds of nanometres thick). Much work is still to be done in this field. 

Evidently, in the course of layer formation the plane of inert markers cannot coincide with the initial interface between substances A and B. It would mean that compound layers could grow at the expense of one component. Chemically, this is impossible since any binary compound consists of two components. Position of the layers relative to the initial interface is mainly dependent upon the stoichiometry of chemical compounds, if both ends of a couple are equally free to move. Coincidence of initial and marker planes provides evidence for the lack of contact between reacting phases at that place. 

This binary system is worth further investigation, especially in the region of non-parabolic layer-growth kinetics. Marker experiments are also desirable, with inert markers embedded in both intermetallic layers. 

The ApBq layer grows only at interface 2 at the expense of diffusion of component A. At interface 1 its thickness does not increase because of the lack of diffusing B atoms. The AB layer grows only at interface 3 at the expense of diffusion of component B. At interface 4 its thickness does not increase because of the lack of diffusing A atoms. The ArBs layer having no source of both A and B atoms cannot grow at all and therefore is consumed until full disappearance. The symbol designates an inert marker. 

The Pt Sb layer is extremely thin. The letter M designates inert markers. Experimental data from the work by S.L. Markovski el al237 Photograph kindly provided by Dr. A. A. Kodentsov. 

To visualise the diffusing species, inert markers are to be embedded in each of compound layers. From Figs 3.2 and 3.6, it must be quite clear that one marker is insufficient to make far-reaching conclusions regarding the diffusing species in multiple layers. 

One inert marker only indicates the diffusing species in that compound layer in which it is embedded or with which it borders. If this layer grows under conditions of diffusion control, then the very presence of other compound layers provides in itself evidence that another component is diffusing across their bulks. 

Although in the case under consideration only component A diffuses across the bulk of the ArBs layer, the thickness of this layer nevertheless increases at its both interfaces. The final result is thus similar to that which would be observed if both components diffused simultaneously. This should be taken into account when interpreting the experimental data on diffusional contributions of components A and B in the growth process of any chemical compound layer, obtained using inert markers. In the case of reaction couples of the ApBq- B type, their interpretation is not always unambiguous. 

Indeed, if an inert marker is initially placed at the interface between A2B and B and the movement of the A2B AB and ABB interfaces during growth of the AB layer is then followed, it will be found that the distances from the marker to those interfaces gradually increase with passing time and remain equal to one another. On the basis of these observations, from a diffusional viewpoint, the researcher might have concluded that (/) both components A and B are diffusing across the AB layer in the opposite direction and (//) the rates of their diffusion are equal. In fact, however, component B does not diffuse in the AB layer at all. 

O. Thomas, L. Stolt, P. Buaud, J.S. Poler, F.M. d Heurle. Oxidation and formation mechanisms in dicilicides VSi2 and CrSi2, inert marker experiments interpretation // J.Appl.Phys.- 1990.- V.68, No. 12.- P.6213-6223. 

Now, we describe the Kirkendall effect [9], The flux, as well as the diffusion coefficient, has to be chosen relative to a frame of reference. In Figure 5.4, the laboratory frame of reference, X, which is the observer frame of reference, and the moving frame of reference, x, which moves with the inert markers, are shown. 

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