Marker Method in Studying the Defect Structure in Products of the Oxidation of Highly Disordered Substrates

Introduction

Marker method has been applied for the first time by Pfeil [1] about 80 years ago in studying the mechanism of scale formation on iron and this method is continuously used not only in studying the high temperature corrosion, but also in determining the predominant disorder in oxides and sulphides of transition metals. This method consists in the deposition of a small amount of substance on the substrate surface, called marker, which does not react with the oxidant and substrate as well as with reaction product and after terminating the oxidation reaction to determine its location in the system substrate–product. If the marker is found at the substrate–product interface (in the case of metal oxidation, it is metal–scale interface), such a location of the marker means univocally that the reaction product was growing by the outward diffusion of cations and consequently that the cation sublattice is predominantly disordered. If, in turn, the marker is located on the surface of reaction product, it means that the product layer was growing by the inward diffusion of the oxidant. If, finally, the marker is found in the interior of the reaction product layer, it suggests that both sublattices of the compound forming the reaction product are disordered to a comparable degree. However, from an energetic point of view such a situation is found very rarely, because predominant disorder is generally observed in one sublattice only, and most frequently, this is cation sublattice. A specific situation is observed in the case when a marker is found in the interior of the scale but the inner layer, showing the same phase composition as the outer one, is porous. In this particular case, the location of the marker does not indicate that both sublattices are disordered, but that the formation of the inner porous layer beneath the marker is a result of secondary processes, the mechanism of which is described in the literature as “dissociative mechanism of scale growth” [2–8].

Theoretical considerations

A separate and important problem constitutes the application of marker method in studying the type of dominating defects in higher oxides and sulphides of transition metals, the formation of which proceeds not on the metal surface, but on the surface of lower oxides or sulphides [9, 10]. The application of marker method in this particular case is much more difficult and needs separate interpretation. These difficulties constitute the main reason of scant information in the literature concerning defect structure, and in particular predominant disorder in higher oxides and sulphides of transition metals.

If in the discussed case the markers are deposited not on the surface of metal, but on the surface of lower oxide or sulphide (Me_aX_b) and after terminating the reaction they are found on the surface of reaction product (Me_cX_d), it clearly suggests that – like in the case of pure metal oxidation – the reaction product was growing owing to the inward diffusion of oxidant X (Figure 1(a)). If, on the other hand, the reaction product is being formed as a result of the outward diffusion of cations, the markers – in contrast to the case of pure metal oxidation – will be found not at the substrate–product interface, but in the interior of the reaction product layer (Figure 1(b)), because this layer is formed not only on the outer surface, but also at the substrate–product interface due to the substrate decomposition. The formation of the product (Me_cX_d) beneath the markers, as a result of substrate (Me_aX_b) decomposition, may be described by the following equation:

Figure 1

Marker position in the higher oxide layer (Me_cX_d), grown on the surface of the lower oxide (Me_aX_b) as a result of (a) inward diffusion of oxidant; (b) outward diffusion of oxidant

It follows from this formula that for 1 mole of reaction product being formed as a result of substrate decomposition the appropriate number of cations liberated in this process diffuses outwards to the outer surface, where they react with oxidant. This second reaction can be demonstrated as follows:

From these two relationships the ratio (f) of both product layers formed in decomposition process and outward diffusion of cations can be calculated:

The ratio f results from dividing the coefficient before the chemical formula of reaction product forming the outer layer by the coefficient located before the chemical formula of reaction product forming the inner layer (e.i. by 1).

There are a number of cases in which the substrate (oxide or sulphide) is highly disordered. Such a situation is observed among others during the formation of the product of sulphidation of several metals as well as of oxidation of iron to form wustite, Fe_1-yO [11, 12], and cobalt, to form Co_1-yO [13, 14]. The approach to this problem needs specific treatment, both in experimental procedure and in the interpretation of the marker results. These aspects are discussed in the present paper.

The aim of the experimental part of this work was the explanation of the predominant disorder in the higher cobalt sulphide, CoS₂, growing on the surface of the lower cobalt sulphide, Co_1-yS, as well as in the higher nickel sulphide, NiS₂, growing on the surface of the lower nickel sulphide, Ni_1-yS, characterized by extremely high deviation from stoichiometry, y, and thereby point defect concentration, of the order of 0.1 mole of defects per 1 mole of the sulphide [15, 16]. Analogous high deviations from stoichiometry are observed in iron sulphide [17] and oxide [11, 12] (Fe_1-yS and Fe_1-yO), copper sulphide (Cu_2-yS) [18], etc.

Materials and experimental procedure

Substrates in the present study constitute flat, rectangular samples of Co_1-yS and Ni_1-yS sulphides, obtained as a result of completely sulphidized metal samples (15 mm × 10 mm × 0.5 mm) at sulphur pressures lower than the dissociation pressure of CoS₂ and NiS₂, respectively. High-purity cobalt and nickel have been used as starting materials, containing trace amounts of impurities summarized in Table 1.

In order to get homogeneous Co_1-yS and Ni_1-yS sulphides, the sulphidation of pure metals has been carried out in the apparatus described elsewhere [19]. Experimental conditions have been chosen in such a way that only the Co_1-yS or Ni_1-yS sulphides were thermodynamically stable. These conditions have been marked in Figures 2 and 3, describing the fragment of phase diagrams of Co-S and Ni-S systems. Because of very high concentration of defects (cation vacancies) in Co_1-yS and Ni_1-yS, the sulphidation process of both metals proceeded very quickly and consequently after about 24 hours the metal samples were completely sulphidized. However, the most important problem consists in having homogeneous distribution (without gradient) of the defect concentration in the whole sulphide specimen. The homogenization process of such specimens has been carried out during about 24 hours for a number of different sulphur vapour pressures and temperatures in order to get different defect concentration in homogenized specimens. The aim of this procedure will be explained in the next paragraph.

Figure 2

The part of phase diagram of the Co-S system, illustrating temperature–pressure ranges of both: Co_1-yS pretreatment (A) and CoS₂ formation during marker experiments (B)

Figure 3

The part of phase diagram of the Ni-S system, illustrating temperature–pressure ranges of both: Ni_1-yS pretreatment (A) and NiS₂ formation during marker experiments (B)

The samples obtained in this way have been marked by gold. As the sulphidation rate of Co_1-yS and Ni_1-yS substrates proceeds very slowly, the thickness of CoS₂ and Ni_1-yS products is even after hundreds of hours extremely thin. As the markers have to be at least one order of magnitude thinner than the sulphidation product layer, the gold marker film was vacuum evaporated onto the surface of the Co_1-yS and Ni_1-yS substrates through the copper mesh. Consequently, small islands of gold were obtained, spread over the specimen surface. The samples marked in this way were then treated at temperatures presented in Figures 2 and 3 by grey (A) polygon during 24 hours, under sulphur vapour pressure lower than the dissociation pressures of CoS₂ or NiS₂. In the next step, the marked samples were sulphidized under conditions illustrated in Figures 2 and 3 by grey (B) polygon to form CoS₂ or NiS₂, respectively. After terminating these reactions, a part of the specimens has been electrochemically covered by nickel in order to prevent the spallation of the sample during metallographic procedure. Subsequently, the cross section of the samples has been made in order to determine the position of the marker islands in the interior of CoS₂ orNiS₂ layers, using scanning electron microscope.

Results and discussion

All transition metal oxides and sulphides show deviations from stoichiometry, resulting from easiness of cation valency changes. A number of transition metal sulphides, and in particular Co_1-yS, Ni_1-yS, Fe_1-yS, show dramatically high deviations from stoichiometry, y, resulting from the presence of cation vacancies of the order of 0.1 mole of cation vacancies per mole of the sulphide. If such a high concentration of point defects is not taken into account in marker experiments, it may be a reason for erroneous conclusions. In contrast to metals, the marker experiment in the case of the oxidation of the lower oxides and sulphide, showing high nonstoichiometry, it is necessary to homogenize the substrate in order to establish homogeneous distribution of point defects, without their concentration gradient. This homogenization process may be carried out under different oxidant pressures, being however always lower or equal to the dissociation pressure of the higher oxide. As a result of homogenization at different oxidant pressures, the concentration of point defects in the substrate becomes different, assuming that the thermodynamic equilibrium has been reached during homogenization. Substrate samples prepared in this way have been marked by gold using the procedure described previously. The oxidation or sulphidation process of the marked substrate, homogenized under lower oxidant pressure, begins to oxidize after raising the oxidant pressure above the dissociation pressure of the reaction product. In the very beginning of the reaction, extremely thin product of the higher oxide starts to develop, but in the same time substrate sample is “oxidized”, resulting from increase of the defect concentration. This process in the case of CoS and NiS monosulphides can be described using Kröger–Vink notation of defects [20] by the following quasi-chemical equations:

It follows from these relationships that the reactions of these monosulphides with sulphur result not only in the increase in the defect concentration (i.e. doubly ionized cation vacancies and electron holes) but also in the increase of the mass of the sample. These processes proceed orders of magnitude faster than the formation of higher sulphides. As the substrate layer is growing by the outward diffusion of cations, the marker located before the reaction on the surface of the specimen becomes overgrown by the substrate sulphide, as shown in Figure 4. The thickness of the layer above the marker depends on the substrate thickness and on the difference between the sulphur pressures under which the substrate has been homogenized and that of the sulphidation reaction. The higher is this difference and the initial substrate thickness, the thicker is the substrate layer above the marker. As the time of oxidation increases, the thickness of this layer reaches a constant value. This constant value depends on the difference of defect concentration corresponding to the dissociation pressure of the product and oxidant pressure applied during homogenization and on the initial thickness of the specimen substrate. The layer of the higher sulphide, growing extremely slowly, proceeds as a result of the consumption of the substrate layer (lower sulphide) above the marker. Thus, with longer and longer sulphidation time, the thickness of the lower sulphide layer (MeX) above the markers is decreasing due to its sulphidation and finally this layer disappears completely, as schematically shown in Figure 5. Consequently, the markers will be found at the substrate–product interface. Further sulphidation will result in the formation of the product above and below the marker, because the outward diffusion of cations will result on the one hand on the formation of the product due to the decomposition of the substrate (eq. (1)) and on the other hand on the formation of the product at the outer surface (eq. (2)). Thus, markers will be found in the interior of the higher oxide (sulphide) layer, as schematically depicted in Figure 5.

Figure 4

The influence of homogenization of Co_1-yS sulphide at T = 973 K and under sulphur vapour pressure pS2 = 10² Pa on the location of markers after sulphidation during 5 minutes at T = 973 K and pS2 = 10⁴ Pa

Figure 5

Schematic representation of the positions of markers in the highly nonstoichiometric MeX substrate, homogenized under oxidant pressure much lower than the dissociation pressure of higher oxide MeX₂ (where t₁, t₂ and t₃ denote reaction times)

From these considerations it follows that if the marker experiment is carried out with substrate homogenized under sulphur pressure lower than the dissociation pressure of the product of its sulphidation, the position of the markers will depend on the number of factors described above, and consequently, any rational conclusions concerning the mechanism of the formation of the higher sulphide cannot be formulated.

Taking into account the above conclusion, the marker experiment must be carried out with the substrate homogenized under sulphur pressure equal to the dissociation pressure of the higher sulphide. In this situation, namely, after introducing the sulphur to the reaction chamber, the substrate does not consume oxidant to change nonstoichiometry, because the concentration of defects (and thereby the nonstoichiometry) has already reached the maximum value during the homogenization process (Figure 6). Thus, on the surface of marked substrate only the higher sulphide layer begins to grow. If the product is growing by the outward diffusion of cations, the markers will be found in the interior of the higher sulphide layer in the position described by eq. (3) (Figure 1(b)). On the other hand, if the oxidation product is growing by the inward diffusion of sulphur, markers will be located at the outer surface of the product layer (Figure 1(a)).

Figure 6

The influence of homogenization of Co_1-yS sulphide at T = 973 K and under sulphur vapour pressure pS2 = 5 × 10³ Pa on the location of markers after sulphidation during 5 minutes at T = 973 K and pS2 = 10⁴ Pa

It follows from these remarks that rational results of marker experiment can only be obtained if the markers before the reaction are located on the lower sulphide (or oxide) surface, homogenized at the dissociation pressure of the product. The homogenization of substrate at oxidant pressure exactly equal to the dissociation pressure of the higher sulphide (or oxide) constitutes a rather difficult experimental problem. This requirement is particularly difficult to be realized in the case of sulphides, because to get the sulphur partial pressure on strictly defined level is not an easy experimental problem. These difficulties can be overcome by the homogenization of given lower sulphide or oxide substrates at oxidant pressure slightly higher than the dissociation pressure of the reaction product. Under these conditions, the higher sulphide (or oxide) starts to develop as a rule very slowly and after a short period of time a substrate will be homogenized under dissociation pressure of higher sulphide (or oxide). During this period of time, the thickness of the outer sulphide layer is extremely small, which may not be taken into account in marker experiments. The surface of the sample prepared in this way may then be marked and after long period of sulphidation, when the product layer thickness is at least two orders of magnitude higher than the initial thickness developed before marker deposition, the marker position is determined. The above described procedure makes the homogenization much more simple, assuring in the same time the concentration of defects in the substrate on maximal constant level.

Considering different aspects of marker experiments in studying the defect structure in higher oxides and sulphides, it is necessary to take into account the influence of nonstoichiometry on the location of marker in the interior of the reaction product. This situation is well illustrated by microphotograph, showing the cross section of Ni_1-yS substrate, after sulphidation at sulphur vapour pressure higher than the dissociation pressure of NiS₂ disulphide (Figure 7). As can be seen, a compact NiS₂ layer is formed on the surface of Ni_1-yS substrate (marked before the reaction by gold). The position of the markers in the reaction product is clearly visible, but not exactly in the middle of the thickness of the NiS₂ product, which is expected from theoretical analysis of eqs (1)–(3). There may be two reasons of such a location of markers in NiS₂ product. First, thicker inner layer of NiS₂ beneath the markers may be the result of small participation of inward diffusion of sulphur through point defects or grain boundaries of the reaction product. This conclusion can be a priori ruled out, because the NiS₂ product is coarse grained and the sulphidation experiments carried out with the use of radioactive sulphur isotope ³⁵S have demonstrated [21, 22] that the inward grain boundary and lattice diffusion of sulphur does not participate in the formation of the sulphide scale on this metal. The second possibility of the explanation of such position of markers is as follows. If, namely, NiS₂ sulphide would grow on the surface of strictly stoichiometric NiS by the outward diffusion of cations only, the markers should be found exactly in the middle of NiS₂ product (see Figure 1(b)). This conclusion follows directly from the application of eqs (1)–(3) to the process of NiS₂ formation on strictly stoichiometric NiS substrate:

Figure 7

Microphotograph of metallographic cross section of NiS₂ layer, formed on NiS surface during sulphidation of NiS “marked” by gold islands

Such a situation would be observed in the case if the nonstoichiometry of the substrate could be neglected. In reality, nickel sulphide, Ni_1-yS, shows extremely high deviation from stoichiometry, y, equal to 0.15 at the NiS/NiS₂ interface. Considering this fact, the general equations (1)–(3) assume the following form:

From these relationships it follows that during decomposition of 2 mole of Ni_0.85S, under the marker 1 mole of NiS₂ is formed and owing to the outward diffusion of cations above the markers 0.7 mole of NiS₂ develops. It is then obvious that in this case, the markers will not be located in the middle of NiS₂ layer but closer to the outer surface of NiS₂, in agreement with microphotograph presented in Figure 7. It should finally be pointed out that if the markers would be found at the surface of the reaction product layer, it suggests univocally that the product has been growing by the inward lattice or intergranular diffusion. In this particular case, the nonstoichiometry and thereby defect concentration has not any relation with the matter transport through the reaction product.

Conclusions

From the above discussion it follows clearly that the rational results of marker experiments in the case of the formation of the higher sulphide (or oxide) on lower ones need a number of introductory experiments in order to get rational explanation of defect structure. In particular, the problem of homogenization of the starting material is extremely important. In fact, the homogenization process of the substrate must be made under oxidant pressure equal or slightly higher than the dissociation pressure of the higher oxide to be formed. In addition, the nonstoichiometry of the substrate, as well as the product must carefully be taken into account in order to foresee the rational location of markers in the interior of the product layer. Under these conditions only, the position of the markers in the reaction product allows rational conclusions to be formulated.