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Application of a factorial design to study a chromate-conversion process.

[C] FSCT and OCCA 2008

Abstract Chromate conversion coatings are commonly deposited on plated zinc to improve the corrosion resistance of the substrates, and to increase the adherence of painted films. The coatings' properties depend on the composition and the structure of the conversion films as well as on the process parameters. A fractional factorial design was implemented to optimize the experimental conditions of the chromating process (bath composition, rinses composition, draining, treatment time). Surface analytical techniques such as scanning electron microscopy, glow discharge optical spectroscopy, and atomic absorption spectrometry were used to characterize the chromate conversion coatings.

Keywords Chromate conversion, Fractional factorial design, Zinc coating, GDOES

Introduction

Zinc is widely used in many fields that range from paint, cosmetics, and pharmaceuticals, to storage batteries, electrical equipment, or metallic coating for corrosion protection. It is acknowledged that zinc is a very efficient coating against corrosion for iron-based materials because it has a more negative electrochemical potential than iron. Thus, zinc offers an excellent sacrificial protection in aggressive environments. (1-3) A zinc coating lifetime can be increased if it is passivated in a chromium solution. Chromate coatings are favored due to their barrier and corrosion resistance properties. (4-6) Chromating treatments have several objectives: (1) to act as a passivating layer to prevent rapid zinc dissolution and the appearance of "white rust" on the surfaces, thus providing temporary protection during storage; and (2) to improve the adhesion between the organic coating and the metal surface so that it avoids undercoat corrosion when it is applied before the organic coating. (4-9) In this case, it plays the role of an efficient cathodic inhibitor, thereby lowering the overall oxygen reduction reaction on the metal surface and limiting the tendency toward cathodic delamination.

Up to now, most publications about chromate-conversion have mainly focused on fundamental scientific topics. These papers discussed the formation of the layer and the reactions that occur during the treatment, or are devoted to its corrosion properties. First patented in the 1930s, (10) chromate conversion treatments have performed remarkably well for automobile and aerospace industries. Chromate dip treatment is carried out in a chromic acid bath or an acid solution of hexavalent chromium salts. (4-7) Chromate passivation baths also contain "activators" such as fluoride, sulfate, and acetate, which lead to thicker conversion layers. During immersion, a chemical reaction on the coating surface creates a passivated layer of 10 to 1000-nm thick, containing mixtures of Zn(II), Cr(III), and Cr(VI) oxides and hydroxides. The detailed structure and mechanism of chromate-conversion coatings have been the main subject of interest for 30 years due to the noncrystalline nature of the layer that makes structural characterization difficult. (11-14) However, modern surface analytical techniques (XPS, (15), (16) SIMS, (17) and electron diffraction (18) allow us to analyze the conversion layer and determine the specific details relative to chemical analysis, element distribution, and structure of the conversion.

The characteristics of the chromate conversions depend on the base metal used (electrodeposited, hot dip zinc, or zinc alloys), the formulation of the bath, and the process parameters. To our knowledge, there is little information concerning the influence of the process on the properties of the chromating layer. Hence, the objective of the present work consists of investigating the influence of the process parameters, including the chromating tank and the succeeding rinses and/or drainings, on the composition of the chromate layer on electrodeposited zinc, using chemo-metric techniques. It offers a solid alternative for the optimization of the chemical system and processes.

Numerous factors may be involved in the formation process of the chromium-conversion surface layer on zinc coatings. The conventional approach, which consists of studying the influence of a given parameter while keeping the other variables constant, may be misleading because it implies a partial exploration of the experimental field and ignores possible interactions between variables. Chemometric techniques, on the other hand, use statistical methods to select optimal measurement procedures and experiments. This approach has the advantage of taking into account the combined effects of several input factors, while at the same time requiring only a moderate number of experiments. (19-23) In order to identify the most important, or most influential, technological parameters, a two-level fractional factorial design (FFD) was carried out.

Atomic absorption spectrometry (AAS) allows us to determine the composition of the conversion layer. In addition, the chemical element distribution in the conversion film and its morphology were investigated by glow discharge optical spectroscopy (GDOES) and conventional scanning electron microscopy (SEM).

Materials and methodology

Chromating sequence

The tests were carried out in an industrial pilot plant illustrated in Fig. 1. The zinc-plated items follow the chromating sequence composed of five operations: (1) immersion in the chromatation tank ([Cr(VI)] = C) during a determined time, with TCr equal to 20 or 40 s; (2) first rinsing in a dead-rinse tank ([Cr(VI)] = C/2 or C/100) for 15 or 30 s ([TR.sub.1]); (3) draining over the rinse tank for 15 to 45 s ([TDr.sub.1]); (4) rinsing in a live-rinse tank ([Cr(VI)] = C/200 or C/1000) for 60 or 150 s ([TR.sub.2]); and (5) draining over the rinse tank for 60 to 120 s (TDr.sub.2]). The chromate solutions were prepared using a proprietary concentrated Cr(VI) solution ([CrO.sub.3] (99.7% purity), reagent grade acids, and deionized water.

Methodology

To efficiently find the key variables affecting the response variable(s) being studied, FFD is often employed because a system or process is likely to be driven primarily by some of the main effects and low-order interactions. In order to identify the most important or most influential technological parameters among the eight selected on the chromium content in the chromate layer, a two-level FFD (2 (8-4)) was considered. Because all experiments were carried out using an industrial pilot plant, this planned strategy allowed us to perform a low number of experiments, ensuring that the results were as precise as possible and focusing particularly on main effects. The variables ([U.sub.j]) selected were:

* [U.sub.1]: pH of the chromate solution (mol [L.sup.-1])

* [U.sub.2]: chromating time(s)

* [U.sub.3]: concentration of the Cr(VI) ion (mol [L.sup.-1]) in the first rinse after chromating treatment

* [U.sub.4]: time of the first rinse(s)

* [U.sub.5]: time of the first draining(s)

* [U.sub.6]: concentration of the Cr(VI) ion in the second rinse after chromating treatment (mol [L.sup.-1])

* [U.sub.7]: time of the second rinse(s)

* [U.sub.8]: time of the second draining(s)

[FIGURE 1 OMITTED]

Each independent variable was investigated at a high (+1) and low (-1) level. These two levels were determined so that they frame the technological limits of each factor (see Table 1).
Table 1: Overview of the experimental factors at their corresponding
investigated levels

Factor     Unit of measurement     Value at encoded level

                                      -1           +1

[U.sub.1]        pH u                 1.5           1.8
[U.sub.2]        s                   20            40
[U.sub.3]        g [L.sup.-1]        C/2           C/100
[U.sub.4]        s                   15            30
[U.sub.5]        s                   15            45
[U.sub.6]        mg [L.sup.-1]       C/200         C/1000
[U.sub.7]        s                   60           150
[U.sub.8]        s                   60           120


The [2.sup.(8-4)] FFD was obtained by writing down the complete [2.sup.(4)] factorial as the basic design (with the four basic variables [X.sup.1],[X.sup.2], [X.sup.3], and [X.sup.4]) and then equating the four extra variables [X.sub.5], [X.sub.6], [X.sub.7], and [X.sub.8] to the [X.sup.1][X.sup.2][X.sup.3], [X.sup.1][X.sup.2][Xsup.4], [X.sup.1][X.sup.3][Xsup.4],and [X.sup.2][X.sup.3][Xsup.4] interaction, respectively. This type of design is classified as the "resolution IV" design. It should be noted that the resolution of FFD is a measure of the complexity of a confounding pattern. Therefore, and using the standard notation proposed by Box et al., (19) the independent generators (1) and the corresponding complete defining relation (2) (which was the set of all columns that correspond to the identity column) were:

I = 1235 = 1246 = 1347 = 2348 (1)

I = 1235 = 1246 = 3456 = 1347 = 2457 = 2367 = 1567 = 2348 = 1458 = 1368 = 2568 = 1278 = 3578 = 4678 = 12345678 (2)

For this set of generators, it was possible to develop the complete alias design structure. All main effects were confounded with three-factor interactions. From the principle of the effect sparsity, a system is likely to be driven primarily by main factor and low-order interaction effects. So, effects of the high-order interactions (e.g., order of three or greater) are assumed to be negligible, and therefore this enabled all main effects to be determined by this FFD experiment (resolution TV). Two-factor interactions confounded with each other, making it impossible to determine all of them for all the responses. The 16 selected effects and their aliases, which were estimated from the experimental data, are listed in Table 2. Sixteen experiments were run to determine the influence of the eight variables on the response: Cr content in the chromate layer (mg [m.sup.-2]) noted Y. All experiments were performed in random order to minimize the effects of uncontrolled factors that may introduce a bias on the measurements. Nemrowd software was used for regression, statistical analysis, and graphical analysis of the data obtained. (24)
Table 2: Effects and their aliases

[l.sub.0] =   [l.sub.8]=[b.sub.8]
[b.sub.0]

[l.sub.1] =   [l.sub.12]=[b.sub.12]+[b.sub.35]+[b.sub.46]+[b.sub.78]
[b.sub.1]

[l.sub.2] =   [l.sub.13]=[b.sub.13]+[b.sub.25]+[b.sub.47]+[b.sub.68]
[b.sub.2]

[l.sub.3] =   [l.sub.14]=[b.sub.14]+[b.sub.26]+[b.sub.37]+[b.sub.58]
[b.sub.3]

[l.sub.4] =   [l.sub.23]=[b.sub.23]+[b.sub.15]+[b.sub.48]+[b.sub.67]
[b.sub.4]

[l.sub.5] =   [l.sub.24]=[b.sub.24]+[b.sub.16]+[b.sub.38]+[b.sub.57]
[b.sub.5]

[l.sub.6] =   [l.sub.34]=[b.sub.34]+[b.sub.17]+[b.sub.28]+[b.sub.56]
[b.sub.6]

[l.sub.7] =   [l.sub.1234]=[b.sub.18]+[b.sub.27]+[b.sub.36]+[b.sub.45]
[b.sub.7]


Sample preparation and characterizations

A zinc coating of 10-[micro]m thick was electrodeposited onto mild steel sheets (45 [cm.sup.2] of active area) from an acid chloride bath. After zinc deposition, chromate-conversion coatings were produced by immersion of specimens for selected times in different chromate solutions, as defined by the experimental design. Coated specimens were rinsed, drained, and dried in cool air and finally stored in a dessicator.

Atomic absorption spectrometry

The composition of the coatings was determined by means of AAS after stripping the deposits in HC1 1:3 with hexamethylenetetramine to inhibit dissolution of the steel substrate. Cr content in the chromate layer (sum of Cr(III) and Cr(VI)) was measured with a Varian spectrophotometer (Model A800) using an acetylene-air flame and a lamp with a chromium cathode as the radiation source. Absorption was measured on a wavelength of [lambda] = 357.0 nm.

Scanning electron microscopy

The morphology of the conversion layer was studied from the top using a scanning electron microscope, Jeol JSM-6400F.

Glow discharge optical emission spectroscopy

The distribution of species in the chromium layers was determined by depth-profiling using a LECO GDOES 750A instrument. 700 V and 20 mA were chosen as measurement parameters for the excitation and sputtering process. The analysis area was a 4-mm diameter and the sputtering layer was 0.1-[micro]m thick. The following atomic emission lines were: C = 156.143 nm, Cr = 425.433 nm, Ca = 174.724 nm, Fe = 249.399 nm, S = 180.731 nm, and Zn = 330.294 nm.

Results and discussion

FFD[2.sub.[IV].sup.[8-4]]

Table 3 displays the experimental matrix and the measured response. The main effect of a factor [X.sub.j] ([l.sub.j]) and the aliases of two-factor confounded variables interaction effects ([l.sub.jk]) are estimated by least squares regression (19) (Table 4).
Table 3: Experimental design in coded variables and measured
response

Run      [X.sub.1]  [X.sub.2]  [X.sub.3]  [X.sub.4]  [X.sub.5]

1           +1         +1         +1         +1         +1
2           +1         +1         +1         -1         +1
3           +1         +1         -1         +1         -1
4           +1         +1         -1         -1         -1
5           +1         -1         +1         +1         -1
6           +1         -1         +1         -1         -1
7           +1         -1         -1         +1         +1
8           +1         -1         -1         -1         +1
9           -1         +1         +1         +1         -1
10          -1         +1         +1         -1         -1
11          -1         +1         -1         +1         +1
12          -1         +1         -1         -1         +1
13          -1         -1         +1         +1         +1
14          -1         -1         +1         -1         +1
15          -1         -1         -1         +1         -1
16          -1         -1         -1         -1         -1

Run      [X.sub.6]  [X.sub.7]  [X.sub.8]   Y

1           +1         +1         +1      131
2           -1         -1         -1      160
3           +1         -1         -1      250
4           -1         +1         +1      187
5           -1         +1         -1       84
6           +1         -1         +1       74
7           -1         -1         +1      158
8           +1         +1         -1      132
9           -1         -1         +1      469
10          +1         +1         -1      497
11          -1         +1         -1      592
12          +1         -1         +1      546
13          +1         -1         -1      252
14          -1         +1         +1      225
15          +1         +1         +1      398
16          -1         -1         -1      376


In our case, we have to estimate 16 coefficients with 16 experiments, thus there are no degrees of freedom for the model and it is not possible to calculate the residuals at the points used for the model construction. Consequently, four supplementary experiments in the center of the domain were carried out to estimate the experimental error. Note that these experiments are not used to estimate the coefficients [l.sub.j] or [l.sub.jk]. The four responses of the center points are, respectively, 281, 286, 294, and 289 mg [m.sup.-2]. The estimated error is 29.67. The statistical significance of the model equation is evaluated by the F-test for analysis of variance (ANOVA), which shows that the regression is statistically significant at a 99.9% (p < 0.001) confidence level (see Table 5). (19-23) It is important to point out that the p-values and confidence levels provided in Tables 4 and 5 are an expression of the p-value in percent.
Table 5: ANOVA for the response Y

Source of variation      Sum of square       Degree of freedom

Regression           4.41486 x [10.sup.5]          15
Experimental error   8.90100 x [10.sup.1]           3
Total                4.41575 x [10.sup.5]          18

Source of variation  Mean square           F ratio   p-value

Regression           2.94324 x [10.sup.4]  991.9929  <0.01 ***
Experimental error   2.96700 x [10.sup.1]
Total

*** Highly significant at the level 99.9%


The significance of each coefficient, [l.sub.j] or [j.sub.jk], is determined by t-values and p-values, which are listed in Table 4. It should be noted that the p-value is the probability of getting the displayed value for the coefficient if its true value is zero. In other words, the "null hypothesis" ([H.sub.0] hypothesis) is tested for each [l.sub.j] or [l.sub.jk]. For a determined factor, if the [H.sub.0] hypothesis is verified, this factor is said to be not influent. In practice, a confidence level of 95% is considered; i.e., the alpha-level is set at 5%. The alpha level corresponds to the risk of rejecting the [H.sub.0] hypothesis when this hypothesis is verified. The test of the [H.sub.0] hypothesis is thus rejected, and the factor is considered as influent when p < 0.05. Accordingly, the largest magnitude of the t-test and the smallest value of the p-value indicate the high significance of the corresponding coefficient.
Table 4: Value and statistical analysis of the effects and their
aliases

Effects                                              Estimates

[l.sub.0] = [b.sub.0]                                  283.2

[l.sub.1] = [b.sub.1]                                 -136.2

[l.sub.2] = [b.sub.2]                                   70.8

[l.sub.3] = [b.sub.3]                                  -46.7

[l.sub.4] = [b.sub.4]                                    8.6

[l.sub.5] = [b.sub.5]                                   -8.7

[l.sub.6] = [b.sub.6]                                    1.8

[l.sub.7] = [b.sub.7]                                   -2.4

[l.sub.8] = [b.sub.8]                                   -9.7

[l.sub.12] = [b.sub.12] + [b.sub.35] + [b.sub.46] +    -35.8
[b.sub.78]

[l.sub.13] = [b.sub.13] + [b.sub.25] + [b.sub.47] +     11.9
[b.sub.68]

[l.sub.14] = [b.sub.14] + [b.sub.26] + [b.sub.37] +      0.2
[b.sub.58]

[l.sub.23=  [b.sub.23] + [b.sub.15] + [b.sub.48] +       6.9
[b.sub.67]

[l.sub.24] = [b.sub.24] + [b.sub.16] + [b.sub.38] +     -2.1
[b.sub.57]

[l.sub.34] = [b.sub.34] + [b.sub.17] + [b.sub.28] +    -11.1
[b.sub.56]

[l.sub.1234] = [b.sub.18] + [b.sub.27] + [b.sub.36] +    0.2
[b.sub.45]

Effects                                                 t-test

[l.sub.0] = [b.sub.0]                                   207.96

[l.sub.1] = [b.sub.1]                                  -100.01

[l.sub.2] = [b.sub.2]                                    52.00

[l.sub.3] = [b.sub.3]                                   -34.28

[l.sub.4] = [b.sub.4]                                     6.29

[l.sub.5] = [b.sub.5]                                    -6.38

[l.sub.6] = [b.sub.6]                                     1.33

[l.sub.7] = [b.sub.7]                                    -1.79

[l.sub.8] = [b.sub.8]                                    -7.11

[l.sub.12] = [b.sub.12] + [b.sub.35] + [b.sub.46] +     -26.30
[b.sub.78]

[l.sub.13] = [b.sub.13] + [b.sub.25] + [b.sub.47] +       8.77
[b.sub.68]

[l.sub.14] = [b.sub.14] + [b.sub.26] + [b.sub.37] +       0.14
[b.sub.58]

[l.sub.23]= [b.sub.23] + [b.sub.15] + [b.sub.48] +        5.09
[b.sub.67]

[l.sub.24] = [b.sub.24] + [b.sub.16] + [b.sub.38] +      -1.51
[b.sub.57]

[l.sub.34] = [b.sub.34] + [b.sub.17] + [b.sub.28] +      -8.12
[b.sub.56]

[l.sub.1234] = [b.sub.18] + [b.sub.27] + [b.sub.36] +     0.14
[b.sub.45]

Effects                                                  p-value

[l.sub.0] = [b.sub.0]                                    <0.01 ***

[l.sub.1] = [b.sub.1]                                    <0.01 ***

[l.sub.2] = [b.sub.2]                                    <0.01 ***

[l.sub.3] = [b.sub.3]                                    <0.01 ***

[l.sub.4] = [b.sub.4]                                     0.812 **

[l.sub.5] = [b.sub.5]                                     0.780 **

[l.sub.6] = [b.sub.6]                                    27.5

[l.sub.7] = [b.sub.7]                                    17.1

[l.sub.8] = [b.sub.8]                                     0.572 **

[l.sub.12] = [b.sub.12] + [b.sub.35] + [b.sub.46] +       0.0121 ***
[b.sub.78]

[l.sub.13] = [b.sub.13] + [b.sub.25] + [b.sub.47] +       0.313 **
[b.sub.68]

[l.sub.14] = [b.sub.14] + [b.sub.26] + [b.sub.37] +      89.9
[b.sub.58]

[l.sub.23]= [b.sub.23] + [b.sub.15] + [b.sub.48] +        1.46 *
[b.sub.67]

[l.sub.24] = [b.sub.24] + [b.sub.16] + [b.sub.38] +      22.7
[b.sub.57]

[l.sub.34] = [b.sub.34] + [b.sub.17] + [b.sub.28] +       0.390 **
[b.sub.56]

[l.sub.1234] = [b.sub.18] + [b.sub.27] + [b.sub.36] +    89.9
[b.sub.45]

*** Highly significant at the level 99.9%

** Significant at the lever 99%

* Significant at the level 95%


Data from Table 4 reveal that the factors [X.sub.1], [X.sub.2], and [X.sub.3] are significant at a confidence level of 99.9% (p < 0.001), while [X.sub.4], [X.sub.5], and [X.sub.8] are significant at a confidence level of 99% (p < 0.01). In addition, among the confounded interaction effects, "[l.sub.12] = [b.sub.12] + [b.sub.35] + [b.sub.46] + [b.sub.78]," "[l.sub.13] = [b.sub.13] + [b.sub.25] + [b.sub.47] + [b.sub.68]," and "[l.sub.34] = [b.sub.34] + [b.sub.17] + [b.sub.28] + [b.sub.56]" are found to be significant at a confidence level higher than (or equal to) 99% (p < 0.01), while "[l.sub.23] = [b.sub.23] + [b.sub.15] + [b.sub.48] + [b.sub.67]" is significant at a confidence level of 95% (p < 0.05).

At this point, it is worth noting that the influence of factors cannot be discussed separately due to the great importance of their interactions. If we consider that the interaction effects between the extra factors ([X.sub.5], [X.sub.6], [X.sub.7], and [X.sub.8]) and the basic factors ([X.sub.1], [X.sub.2], [X.sub.3], and [X.sub.4]) are not taken into account in the theoretical analysis due to the hypothesis on the construction of the fractional design, it enables us to simplify the expression of the confounded interaction effects.

For the confounded interaction effect [l.sub.12] (= [b.sub.12] + [b.sub.35] + [b.sub.46] + [b.sub.78]), we can assume that the factor interaction effect [b.sub.12] is the dominant term since pH ([X.sub.1]) and chromating time ([X.sub.2]) have the greatest effects on the response, as emphasized in the literature.

The confounded interaction effect [l.sub.13] (= [b.sub.13] + [b.sub.25] + [b.sub.47] + [b.sub.68]) corresponds to [b.sub.13]. This interaction is to be expected. In fact, the conversion can continue during the first rinse if its concentration is sufficiently high. These data clearly indicate that the interaction effect tends to increase the Cr content of the layer when the reactions are carried out at a low pH ([X.sub.1]) and a high concentration of Cr(VT) content in the first rinse ([X.sub 3])

Considering the confounded interaction effect [l.sub.34] (= [b.sub.34] + [b.sub.17] + [b.sub.28] + [b.sub.56]), we can assume that [b.sub.34] (interaction between concentration of Cr(VI) content in the first rinse ([X.sub.3]) and time of first rinse ([X.sub.4])) is the dominating term since the interaction between the chromating time ([X.sub.2]) and the time of the second draining ([X.sub.8]) is highly improbable. It is important, however, to point out that this result clearly shows the great impact of the first rinse operating conditions on the conversion growth.

For the confounded interaction [l.sub.23], we think that the interaction [b.sub.48] could be omitted for the same reasons stated above for [b.sub.25]. Moreover, it is difficult to imagine a relationship between the pH of the chromation solution ([X.sub.1]) and the time of the first draining ([X.sub.5]), so the interaction [b.sub.15] can be reasonably omitted. Finally, [l.sub.23] is equal to [b.sub23]--the interaction between the chromating time ([X.sub.2]) and the Cr(VI) content of the first rinse ([X.sub.3]).

From the foregoing analysis, it follows that the aliases of two confounded variables' interaction effect ([l.sub.12], [l.sub.13], [l.sub.34], and [l.sub.23]) correspond to the factor interaction effect [b.sub.12], [b.sub.13], [b.sub.34], [b.sub.23], respectively. According to the empirical model obtained, we can assume that Cr content in the chromate layer (Y) is represented by the following equation:

Y = 283.2 - 136.2[X.sub.1] + 70.8[X.sub.2] - 46.7[X.sub.3] + 8.6[X.sub.4] - 8.7[X.sub.5] - 9.7[X.sub.8] - 35.8[X.sub.1][X.sub.2] + [11.9[X.sub.1][X.sub.3] + [6.9[X.sub.2][X.sub.4] - [11.1[X.sub.3][X.sub.4]

Figures 2 through 5 present two-factor interaction diagrams related to the Cr content in the chromate layer response. Their analysis allows us to conclude that the best results are obtained in the low levels of pH ([X.sub.1]) and the concentration of Cr(VI) ions in the first rinse after chromating treatment ([X.sub.3]), with high amounts of chromating time ([X.sub.2]) and the time of the first rising ([X.sub.4]), while maintaining the time of the first draining ([X.sub.5]) and the second draining ([X.sub.8]) at their low levels. Moreover, factors [X.sub.6] and [X.sub.7] could be kept at their low level for economic and/or productivity considerations because their effects are not significant.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Coating morphology

The morphological analysis indicates that the Cr(VI)-based passivation treatment shows a network of "dried riverbed" cracks on the coating surface (Fig. 6). These cracks look like platelets with sharp and well-defined edges. In the preparation of the coating, it was known that the coating was a gel-like structure before drying. (25) During the drying stage, the coating shrank and this phenomenon resulted in the formation of microcracks with "dried riverbed" patterns. As a result, microcracks form tensile stresses. (26) The cracks vary in size and direction. The process parameters affect the Cr(VI) content (e.g., chromate thickness) and, correspondingly, the appearance of the chromate films. Longer time and lower pH in the chromate solution enhances the number of cracks in the chromate coating and thus the internal stress, as mentioned in previous works. (26), (27) Accordingly, the thinner layer is "less cracked" (Fig. 6b) than the thicker one (Fig. 6a).

[FIGURE 6 OMITTED]

The depth-profiling of the chromating layer using GDOES shows a "multilayer" structure (Figs. 7-9). The inner layer, corresponding to the initial stage of the chromating process, is a transition region (Fig. 7; sputtering time range of 7 to 13 s) where the content of metallic zinc increases, and those of metallic chromium and oxygen decrease until a constant composition is reached. The outer layer, which represents the other part of the coating (Fig. 8; sputtering time range of 1 to 7 s), is composed of Cr, Zn, O, H, and S. Previous research indicates that this second stage of growth involves the formation of [Cr.sub.2][O.sub.2], [Cr(OH).sub.3], [Cr(OH)-CrO.sub.4], [Zn.sub.2][(OH).sub.2][CrO.sub.4], and a small amount of absorbed [H.sub.2]O. (28)

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

As mentioned above, the thickness of the layer, and indirectly its chromium content, depends on the process parameters. If the chromating composition modifies the layer thickness, it is worth noting that the rinses play an important role in layer formation and affect the layer's morphology. As a matter of fact, the "dead-rinsing" ([Cr(VI)] - C/2) involves a thickening of the chromating layer, and forms a second chromate layer on the chromate-conversion coating that is elaborated after the immersion in the chromating bath (Fig. 9). The composition of this new layer is different from the first chromating layer. The content of chromium is low, and that of carbon and oxygen very high. This phenomenon can be interesting if we consider the corrosion properties of the chromate coating.

[FIGURE 9 OMITTED]

Conclusion

To achieve the best conditions for Cr(VI) conversion on zinc-coated steel, a [2.sup.(8-4)] factorial experimental design was used. Of the eight variables considered, the best results were obtained with low pH levels and a concentration of the Cr(VI) ion in the first rinse after the chromating treatment, with high levels of chromating time and time of first rinsing, while maintaining the time of the first draining and that of the second draining at a low level. Moreover, the concentration of the Cr(VT) ion in the second rinse after chromating treatment and the time of the second rinse could be kept at their low levels for economic and/or productivity considerations. The design of experiment methodology has provided an efficient approach to the general problem of dealing with the many interacting process parameters inherent in surface treatment manufacturing. Chromate films were characterized using SEM and GDOES techniques showing continuous microcracks and changes in the chromate structure and consequent product performances with modifications in the chromating process (bath composition and rinses composition).

Acknowledgment The authors would thank Mr J. Evershed for his assistance.

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S. Wery, M. De Petris-Wery

LCMI, Universite de Franche-Comte, Route de Gray, 25030 Besancon, Cedex, France

S. Wery, M. Feki, H. F. Ayedi

Unite de Recherche Chimie Industrielle et Materiaux, Ecole Nationale d'lngenieurs de Sfax, BP W 1173-3038 Sfax, Tunisia

M. De Petris-Wery (*)

IUT d'Orsay, Universite Paris XI, Plateau du Moulon, 91400 Orsay, France

e-mail: martine.wary@u-psud.fr
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