Compound layer formation

The second apparent factor influencing the mobility of the atoms and hence the sequence of compound-layer formation is atomic radii of reacting elements. Clearly, the direct juxtaposition of the melting points to decide which compound has a greater chance to occur first is only justified if the atomic radii are identical or close for both elements, as is the case with titanium and aluminium, the atomic radius being 0.146 nm and 0.143 nm, respectively.152 153 Similarly, the juxtaposition, with the same purpose, of the atomic radii is valid only if the melting points of both elements are close. An example of this kind is the Al-Mg binary system already considered in Section 2.8.3 of Chapter 2. 

Thus, looking at the equilibrium phase diagram and knowing the physical-chemical properties of the elemets A and B and their compounds, it is possible to draw certain conclusions concerning the sequence of compound-layer formation in a multiphase binary system. It must be remembered, however, that any predictions based on the above-mentioned or other criteria hitherto proposed are only weak correlations, rather than the precise rules. As both the researcher and technologist are always interested in knowing the sequence of occurrence of chemical compounds in a particular reaction couple, they can hardly be satisfied even with a correlation valid in 99 out of 100 cases, because it remains unknown whether this couple falls in the range of those 99 or is the only exception. Further theoretical work in this direction is badly needed. 

By combining the thermodynamic data with those on the structure of the equilibrium binary phase diagram, R. Pretorius et al 261,262 were able to improve the accuracy of predicting the sequence of compound-layer formation in the transition metal-aluminium systems. For this, they used the values of the standard enthalpies (heats) of formation of the compounds. 

During the whole course of annealing the A-B couple under pressure, contacts between initial and occurring phases may well be lost and renewed several times, giving rise to a hardly tractable microstructure of the A-B transition zone. Thus, in many cases the compound-layer formation actually takes place in a few independent couples. Though in each of those couples no more than two compound layers can grow under conditions of diffusion control, multiple compound layers will ultimately be seen between A and B. Evidently, the newly occurred layers can only grow at the expense of the former ones whose thickness must therefore decrease. 

Let us leave to the specialists in phase equilibria to argue whether these are individual phases or compositional polymorphs of the same phase. The results presented appear to be sufficient for the reader to appreciate how complicated phase relations may be and how careful it is necessary to be when interpreting any experimental data on both phase diagrams and compound-layer formation in diffusion couples, especially in those cases where the two-phase fields are narrow compared to the homogeneity ranges of chemical compounds. 

Since the time of publication of my first papers, I have felt an incessant interest (both negative and positive but equally stimulating and therefore valuable to me) of the researchers, who are involved into the investigation of reaction diffusion and compound-layer formation at phase interfaces, to theoretical results presented in those works. Therefore, I decided to write a new book summarising almost all I presumptuously think I know about the fundamentals of this subject. 

The unjustified neglect of a chemical interaction step in analysing the process of compound-layer formation appears to be the main source of discrepancies between the diffusional theory and the experimental data. The primary aim of this book is, on the basis of physicochemical views regarding solid state reaction kinetics, to attempt... 

This tutorial will not attempt to deal with aU these ion implantation phenomena, although Mossbauer spectroscopy has been used in aU these fields. We wUl give several illustrative examples but we will mainly focus on semiconductors and to rather low implantation fluences where the implanted atoms are still isolated from each other or just start to coalesce and to form precipitates. The phenomena at high fluences and the dynamics of compound layer formation are beyond the scope of this tutorial. The reason for this limitation is that emission Mossbauer spectroscopy on radioactive probe atoms is particularly powerful in this low concentration range and allows to study the more fundamental phenomena of lattice location and defect association at the individual probe level, which is hard to study with other techniques. On the other hand, experience has shown that one has to be extremely careful in drawing conclusions from Mossbauer spectroscopy results only, as the possible interpretation of a particular Mossbauer spectrum is often not unique. Complementary data, e.g. from electron microscopy. X-ray difiEraction, transport measurements, channelUng experiments, are often more than welcome or even crucial for the interpretation of the hyperfine interaction data. 

In the presence of molten solder, the interface reactions include the simultaneous process of base metal dissolution or base metal erosion as well as intermetallic compound layer formation. The extent of dissolution depends upon the composition of the base metal as demonstrated in Fig. 9 for the case of molten 40Pb-60Sn solder and the base metals Au, Ag, Pd, Pt, Ni, and Cu [14]. The dissolution rate of Cu, specifically as a function of temperature for several molten Pb-Sn compositions is shown in Fig. 10 [15]. A lower Sn content reduces the extent of base metal dissolution. 

The observed complexity of the Se(IV) electrochemistry due to adsorption layers, formation of surface compounds, coupled chemical reactions, lack of electroactivity of reduction products, and other interrelated factors has been discussed extensively. Zuman and Somer [31] have provided a thorough literature-based review with almost 170 references on the complex polarographic and voltammetric behavior of Se(-i-IV) (selenous acid), including the acid-base properties, salt and complex formation, chemical reduction and reaction with organic and inorganic... 

According to studies reported in Ref. 738, a multimolecular layer of the product is formed on the metal surface. Since for its formation the presence of metal atoms or ions on the border between liquid and solid phases is needed, a diffusion of metal atoms through the compound layer is a necessary condition for such layer formation. The cavitation processes on the surface contribute to this. Since an energetic barrier should be mastered in the reaction route, a cavitation ultrasonic action has the same importance as triboplasma formed by metal friction [756]. 

FORMATION OF A CHEMICAL COMPOUND LAYER AT THE INTERFACE OF TWO ELEMENTARY SUBSTANCES... 

Consider first the main characteristic features of formation of the layers of chemical compounds, common to solid-solid, solid-liquid and solid-gas systems (Chapters 1 to 4). Then, the effect of dissolution of a solid in the liquid phase of a solid-liquid system or of its evaporation into the gaseous phase of a solid-gas system on the growth kinetics of a chemical compound layer will be analysed in Chapter 5. Thus, under the conditions of occurrence of a chemical reaction its product will be assumed to be solid and to form a continuous compact layer adherent at least to one of the initial phases. 

Reaction diffusion is a physicochemical process resulting in the occurrence of a continuous solid compound layer at the interface between initial substances. The term reaction diffusion reflects the most important feature of the layer-formation mechanism, namely, that the layer growth is due to a continuous alternation of the two consecutive steps ... 

Redistribution of the electronic density of atomic orbitals resulting in the formation of molecules, ions, radicals or other stable groupings of atoms included in a growing compound layer. 

F.M. d Heurle evaluated a specific thickness of the layers (an analogue of the critical radius of nuclei in a homogeneous system for more detail, see Ref. 31) for compounds of the Ni-Si binary system. For Ni2Si, its value was found to be 0.15 nm, i.e. the nucleus does not contain even one lattice unit. Although higher values were obtained for other nickel silicides, they never exceeded 1 nm. Therefore, the nucleation process can hardly play any significant role in the formation of most transition-metal silicides, except in some special cases. This conclusion is likely to be valid for any other chemical compound layer. It should be noted, however, that there is also a different viewpoint.38 132... 

The idea about the summation of the times of consecutive steps of the examined solid-state process is of primary importance for understanding the peculiarities of multiphase growth of compound layers in binary heterogeneous systems. Moreover, even in the case of formation of a single compound layer, this idea makes it possible to reveal a few aspects of reaction... 

On the contrary, at x > x[f, there is a deficit of the B atoms because the reactivity of the A surface exceeds the flux of these atoms across the ApBq layer. Therefore, on reaching interface 1, each B atom is combined at this interface into the ApBq compound. In this case, there are no excessive B atoms for the formation of other compounds enriched in component A. Thus, none of compound layers located between A and ApBq can grow at the expense of diffusion of component B. This almost obvious result following in a natural way from the proposed physicochemical considerations is crucial for understanding the mechanism of formation of multiple compound layers. Perhaps, just its evident character is the main reason, firstly, why many researchers in the field have overlooked it and, secondly,... 

The thickness, x[f, of the ApBq layer is referred to as critical because the growth conditions for the layers of other compounds of a given multiphase system become indeed critical if x xj because all of them lose a source of the B atoms (actually, only substance B is such a source) and their growth at the expense of diffusion of the B atoms is stopped. This problem will be examined in more detail when analysing the process of simultaneous formation of two and multiple chemical compound layers. 

It is usually assumed that AcA is the driving force for the process of formation of a chemical compound layer, i.e. jA AcA. However, if this were the case, the layers of chemical compounds without any homogeneity ranges like A1203 or NiBi3 would not grow at all. Indeed, at AcA — 0, equation (1.70) produces infinitely high values of the diffusion coefficient Da —> oo). 

At the time of E. Kirkendall, his interpretation of the experimental results obtained was severely criticised. Then, as often happens, the situation changed to the contrary. Now, the Kirkendall effect is found even in those cases to which it has no relation. In particular, this is so in the case of formation of chemical compound layers at the interface of initial substances. 

To derive a system of two differential equations describing the rate of formation of two compound layers at the A B interface, it is necessary ... 

Also, formation of a solid solution is often considered to be a prerequisite for the occurrence of a chemical compound layer, with the latter being a result of supersaturation of the former. In fact, however, these are two concurrent, competing processes, if both solid solutions and chemical compounds are present on the phase diagram of a binary system. In any... 

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