Materials Chemistry and Physics 108 (2008) 296–305
Optimization of mechanical and chemical properties of sulphuricanodized aluminium using statistical experimental methods
W. Bensalah a, K. Elleuch b, M. Feki a, M. Wery c, M.P. Gigandet d, H.F. Ayedi a,∗a Unite de recherche de Chimie Industrielle et Materiaux (URCIM), ENIS, B.P.W. Sfax, Tunisie
b Laboratoire des Systemes Electromecaniques (LASEM), ENIS, B.P.W. Sfax, Tunisiec IUT Mesures Physiques d’Orsay, Plateau du Moulon, 91400 Orsay, France
d LCMI-Corrosion et Traitements de surface 16, Route de Gray, 25030 Besancon Cedex, France
Received 21 September 2006; received in revised form 4 September 2007; accepted 29 September 2007
bstract
We described a three-step strategy to achieve simultaneous optimization of mechanical and chemical properties of an anodic aluminium oxideayer elaborated in a sulphuric acid solution. In the first two steps, a Doehlert design was carried out and then the canonical analysis has beenonducted to study the four fitted models of the responses, namely: dissolution rate, Vickers microhardness, weight loss after abrasion and deflectiont failure of the anodic oxide layer. Canonical analysis showed that the experimental conditions where the optima are found for each individual
esponse are just opposite, so it is required to look for a certain compromise, which was achieved using the desirability function, in the last step.
The morphology and the composition of “optimum” layer was examined by scanning electron microscopy (SEM), atomic force microscopyAFM) and glow-discharge optical emission spectroscopy (GDOES). 2007 Elsevier B.V. All rights reserved.
; Micr
adofsitsobacaw
eywords: Sulphuric anodization; Experimental design and canonical analysis
. Introduction
The use of aluminium alloys in industry has increased in theast few decades due to its exceptional properties (low-specific
ass, good thermal and electrical conductivities, good corrosionesistance, etc.).
Aluminium and its alloys are naturally protected by an oxidelm when they are exposed to air. However, this natural oxide
s thin and heterogeneous and it does not offer sufficient pro-ection against aggressive environments. Moreover, the frictionehaviour of aluminium alloys is mediocre. In order to enhancehe surface properties and mechanical strength of aluminium,nodizing has been used [1–9]. This treatment, which is an elec-rochemical process, consists on converting aluminium into itsxide by appropriate selection of the electrolyte and the anodiz-
ng conditions, such as current density, voltage, temperature,tc.
Performances of sulphuric acid bath and properties ofnodic oxide have been intensively developed during the pastecades [10–16]. In general, the investigations on aluminiumr dilute aluminium alloys focused on the characteristics of theormed oxide layers (e.g. thickness, density, hardness, corro-ion resistance, morphology, etc.). These previous works havenvestigated the influence of each anodizing parameter one at aime while keeping the others constant. This traditional step-by-tep approach for optimization purposes involves a large numberf independent runs and does not take into account the possi-le interactions between factors. To avoid these disadvantages,n experimental design is the most efficient means to reachonclusions with a minimum of trials. The use of multivari-te experimental design techniques is becoming increasinglyidespread in several research fields. Multivariate designs,hich allow the simultaneous optimisation of several controlariables of a process, are faster to implement and more cost-ffective than traditional univariate approaches [17–21]. In the
resent work, the Doehlert experimental design [22,23] was usedo establish the effect of the input factors: bath temperature,nodic current density and sulphuric acid concentration, andheir interactions on some properties of the aluminium oxide
with the ASTM B 680-80 specifications: 35 mL L 85% H3PO4 + 20 g LCrO3 at 38 ◦C. Fig. 3 shows a general evolution of the weight loss versusimmersion time. As can be seen, the weight loss increased linearly with theimmersion time up to a critical value. After that, no increase of the weight losswas observed, indicating that the oxide layer was completely dissolved. The
W. Bensalah et al. / Materials Chem
ayer. In addition, the canonical analysis has been employedo study the response fitted models namely: dissolution rate,ickers microhardness, weight loss after abrasion and deflec-
ion at failure of the anodic oxide layer. In order to find outhe best experimental conditions, which lead to maximize theardness and deflection and to minimize the dissolution ratend the abrasion, an optimization of the process under study haseen achieved using the desirability function [24,25]. Finally, thebtained aluminium oxide layer under the optimum conditionsas examined by scanning electron microscopy (SEM), atomic
orce microscopy (AFM) and glow-discharge optical emissionpectroscopy (GDOES).
. Experimental
.1. Materials and procedures
Parrallelipedic coupons 100 mm × 25 mm × 3 mm of Al were used as theubstrate for anodic conversion treatment. The composition of Al was given inable 1.
The substrates were mechanically ground to P1000 grade paper. Prior tonodizing, the specimens were treated as follows: (a) chemical polishing in15:85 (v/v) mixture of concentrated HNO3 and H3PO4 at 85 ◦C for 2 min,
b) cold water rinsing, (c) etching in 1 M NaOH solution at room temperatureor 1 min, (d) cold water rinsing, (e) chemical pickling in 30% (v/v) HNO3
olution at room temperature for 30 s and (f) deionised water rinsing and drying.fterwards, the specimens (exposed area 85 mm × 25 mm) were anodized inigorously stirred sulphuric acid solution maintained within ±0.1 ◦C of the setemperature for 90 min then washed in deionised water and dried.
The used cathodes were also aluminium sheets, with larger size than thepecimens. Sulphuric, nitric and phosphoric acids are analytical grade chemicals.
.2. Testing methods
In order to characterize the anodic oxide layer the following tests were carriedut.
.2.1. Thickness measurementThe thickness of the anodic oxide layer was measured using ELCOME-
ER 355 Top Thickness Gauge equipped with eddy current probe. The averagehickness of 30 measuring points evenly distributed on both sides was taken.
.2.2. Microhardness measurement
The Vickers microhardness of the anodic film was determined using a Vickers
icrohardness tester DELTALAB HVS-1000, a 200 g load and a loading timef 15 s. The results represented the average of approximately 20 measurementsor each sample.
able 1hemical composition of the used aluminium (wt%)
lements Wt%
i 0.11n <0.005u <0.005i 0.014n 0.009e 0.37b 0.006g <0.005l Balance
F
Fig. 1. Schematic diagram of used pin-on-disc machine.
.2.3. Abrasion testIn order to characterize the tribological properties of the anodic oxide, abra-
ion resistance was carried out on a pin-on-disc machine (Fig. 1).Anodized samples with dimensions of 20 mm × 20 mm × 3 mm were
rought into contact with 320 grit SiC paper, fixed on a rotating disc with aonstant speed of 20 rpm. The applied normal load was 5 N and the test durationas 1 min. Abrasion tests were carried out in water lubrication. For each speci-en a new abrasive paper was used. An analytical balance with an accuracy of
.1 mg was used to measure the weight of the samples before and after each test.
.2.4. Flexure testMeasurements of deflection at failure of the anodic oxide films on aluminium
ere made by performing three-points flexure test on parrallelipedic samples00 mm × 25 mm × 3 mm at room temperature. A universal machine (Lloydnstruments LR 50KN) was used for this purpose. Loading speed was fixed atmm min−1 and the calibrated distance was 50 mm. Load-deflection response
s then recorded using NEXYGEN software program. The deflection at failureDf) is then deduced as shown in Fig. 2.
.2.5. Acid dissolution testingAcid dissolution tests of the anodized samples were achieved in accordance
−1 −1
ig. 2. General load-deflection curve of an anodized aluminium specimen.
298 W. Bensalah et al. / Materials Chemistry and Physics 108 (2008) 296–305
Fd
su
2
ta5
u
2
d4i3t
2
2
ec
Table 2Study domain
Variables Number of levels Centre Uj(0) Variation step �Uj
U1 (◦C) 5 14 11UU
Taifhtt
•••
fi
mfie
wce
w
TD
N
1111111
ig. 3. General weight loss vs. immersion time of an anodized specimen duringissolution test in the mixed acid solution.
lope of the linear part represents the value of the dissolution rate (per surfacenit).
.2.6. Surface characterizationAFM, performed using model Digital instrument-Nanoscope probe II (con-
act mode), was used to examine and to determine the roughness of thenodized surfaces. Surface topography was recorded over scanned areas of0 �m × 50 �m.
The morphology of the oxide layer was studied from the topside of the layersing a scanning electron microscope (Jeol JSM-6400F).
.2.7. Glow-discharge optical emission spectroscopy (GDOES)The distribution of species in the anodic oxide layer was determined by
epth profiling using a Jobin Yvon GD Profiler instrument equipped with amm diameter anode and operating at pressure of 800 Pa and power 600 W
n an argon atmosphere. The relevant wavelengths (nm) were as follows: Al,96.15; O, 130.22; S, 181.73 and C, 156.14. The sputtering layer was 6 �mhick.
.3. Methodology of experimental design
.3.1. Doehlert experimental designThe Doehlert experimental design [22] was performed to establish the
ffect of the bath temperature, anodic current density and sulphuric acid con-entration, and their interactions on some properties of the aluminium oxide.
Ioitt
able 3oehlert experimental design in coded variables and the obtained responses Yi
he choice of Doehlert design is justified by a number of advantages suchs: (i) its spherical experimental domain with an uniformity in space fill-ng, (ii) its ability to explore the whole of the domain and (iii) its potentialor sequentially where the experiments can be re-used when the boundariesave not been well chosen at first. It is important to point out that an impor-ant property of Doehlert design regards the number of levels that each factorakes.
The factors Uj selected were:
U1: the anodizing temperature (◦C),U2: the current density (A dm−2),U3: the sulphuric acid concentration (g L−1).
As currently used in experimental design, natural variables Uj were trans-ormed into coded variables Xj [17–22]. For the Doehlert design construction,ts centre and its variation step (Table 2) defined the study domain.
Four responses were studied: Y1: dissolution rate (g m−2 min−1), Y2: Vickersicrohardness (Hv), Y3: weight loss by abrasion (mg) and Y4: deflection at
ailure of the anodic oxide (mm). A full quadratic model with 10 coefficients,ncluding interaction terms, was assumed to describe the relationship betweenach response Yi and experimental factors Xj:
Yi = b0 + b1X1 + b2X2 + b3X3 + b11X21 + b22X
22 + b33X
23
+b12X1X2 + b13X1X3 + b23X2X3 + e
here b0 is the constant of the model, bj the first degree coefficients, bjk theross-products coefficients, bjj the quadratic coefficients and e is the randomxperimental error.
Doehlert design requires an experiment number according to N = k2 + k + N0,here k is the number of the factors and N0 the number of centre points.
n our case, the N value was fixed at 4 so with three factors the total
0
f points of Doehlert matrix was 16. All experiments were performedn randomized order to transform potential systematic errors of uncon-rolled factors into random errors and then to be able to apply statisticalests.
Replicates at the central level of the variables were carried out inrder to estimate the pure error variance. This ensures independent esti-ates of the model parameters. Using the F-test, a statistical test of theodel fit was made by comparing the variance due to lack of fit to the
ure error variance. The fitted model is considered adequate if the vari-nce due to the lack of fit is not significantly different from the pure errorariance.
.3.2. Canonical analysisThe response functions may be analyzed by canonical analysis [17–20], a
ethod of rewriting a fitted second-degree equation in a form nicely describeshe nature of the stationary point and the nature of the system around the sta-ionary point (in which it can be more readily understood). This is accomplishedy a rotation of axes that remove all cross-product terms. If desired, this may beccompanied by a change of origin to remove first-order terms. Using this newoordinate system, the second-order model equations are simplified and its geo-etrical nature becomes apparent. The equation developed by the transformation
alled the canonical form of the model is:
= Ys +j=3∑j=1
λjW2j
here Wj (j = 1, 2, 3) denotes the transformed independent variables or theanonical variables.
The λj is the eigen values which will describe the curvature of the
esponse. The constant Ys is the calculated response value at the station-ry point. The algebraic signs of the eigen values provide an idea about theature of its stationary point. If the values are all negative, it is a maximum;f all positive, it is a minimum, and if the signs are mixed it is a saddleoint.
3
r
able 4NOVA table for the responses Y1, Y2, Y3 and Y4
ources of variation Sum of squares Degrees of freedom
ˆ1
Regression 6.6969 9Residual 0.3125 6Lack of fit 0.1050 3Pure error 0.2075 3Total variation 7.0094 15
ˆ2
Regression 2.79804105 9Residual 1.75901104 6Lack of fit 1.57953104 3Pure error 1.79475103 3Total variation 2.97394105 15
ˆ3
Regression 1.20271103 9Residual 3.13275101 6Lack of fit 1.93575101 3Pure error 1.19700101 3Total variation 1.23404103 15
ˆ4
Regression 13.8377 9Residual 2.1398 6Lack of fit 1.8123 3Pure error 0.3275 3Total variation 15.9775 15
he significance in the table is the probability (between 0 and 1) of obtaining a rationventional manner: ***<0.001, **<0.01 and *<0.05 [27].
and Physics 108 (2008) 296–305 299
.3.3. Desirability functionAs one might expect, the optimum values (maxima or minima) for the
esponses do not occur at the same operating conditions but rather at widelyeparated points in the studied domain. This means that one must look for aompromise between conflicting criteria.
In this study, the desirability function approach, as proposed by Derringernd Suich [24], was employed to optimize, simultaneously, the four responses.riefly, the i measured responses, i = 1, 2, 3 and 4, are transformed to a dimen-
ionless desirability scale, di, defined as partial desirability function whosecale ranges between di = 0, for a completely undesired response, and di = 1or fully desired response above which further improvements would have nomportance. It is worth noting that each individual desirability function, di
i = 1–4) is a continuous function chosen from among a family of linear or expo-ential functions. Once the function di is defined for each of the responses,hey are combined into an overall desirability function, D, that weighs theesponses together, with one single criterion. A calculation algorithm is thenpplied to the D function in order to determine the set of factors that max-mizes it as close as possible to 100%. The values of D computed from thebserved responses allow locating a near-optimum region. The value of D isighest at conditions where combination of the different criteria is globallyptimal.
In this work, we used NEMROD W software [26] for data calculation andreatment.
. Results and discussion
.1. Response models and validation
Table 3 displays the experimental matrix and the measuredesponses. Fitted to 16 responses values, the second-order mod-
nalysis of variance (ANOVA) is performed on each responseeparately (Table 4). As can be seen the regression sum ofquares is statistically significant (their p-value are less than.05). On the other hand, none of the four models has a lack oft (p-value >0.05).
For the responses Y1, Y2, Y3 and Y4, the multiple correlationoefficient R2 are respectively 0.96, 0.94, 0.98 and 0.88. Thisndicates that the each regression model correlates well with thexperimental data. It should be noted that the multiple correla-ion coefficient is the proportion of the variability in the responsexplained by the deliberate variation of the factors in the coursef experiments. From overall results, we can conclude that eachecond-order model is adequate to describe each response andan be used as a prediction equation in the studied domain.
.2. Canonical analysis
The purpose of the following paragraph is to examine theverall shape of the response and the nature (maximum, min-mum or saddle) and uniqueness of the stationary point. Theanonical form of the four fitted models is represented by theollowing equations:
Y1 = 4.17 + 1.18W21 − 0.50W2
2 − 1.00W23
Y2 = 488.3 + 113.4W21 − 249.6W2
2 − 280.0W23
Y3 = 5.85 + 8.42W21 + 0.22W2
2 − 4.49W23
Y4 = 8.26 + 0.46W21 − 0.17W2
2 − 0.33W23
he mixed or the different eigen value signs indicate that theour responses at the stationary points are shaped like a saddle.he coordinates of the stationary point are
S1
⎛⎜⎝
−0.047
+0.530
+0.096
⎞⎟⎠ ; S2
⎛⎜⎝
−0.126
−0.026
+0.332
⎞⎟⎠ ; S3
⎛⎜⎝
−2.027
+6.387
−3.192
⎞⎟⎠ ;
S4
⎛⎜⎝
+0.391
+2.465
+0.926
⎞⎟⎠ .
t can easily seen that the stationary points corresponding toˆ1 and Y2 are inside the study domain whereas those corre-ponding to Y3 and Y4 are outside the study domain. Underuch circumstances, the response surface around the stationaryoint does not represent any real phenomenon. Accordingly, we
hoose to conduct the canonical analysis taking into accountnly a unique rotation of the co-ordinate system (withoutranslation), which removes the cross-product terms bjkXjXkrom the model while keeping the initial origin at the cen-re point. Zj was used to denote the axes of such rotated
Y
Fot
y and Physics 108 (2008) 296–305
94X23 − 0.81X1X2 + 0.04X1X3 + 0.31X2X3
+ 22.9X23 − 75.1X1X2 + 258.6X1X3 − 192.9X2X3
3.55X23 + 3.46X1X2 + 1.71X1X3 − 3.46X2X3
17X23 + 0.12X1X2 + 0.27X1X3 − 0.08X2X3
ystem. This yielded a canonical model of the form:
= Ys +j=4∑j=1
bjZj +j=4∑j=1
λjZ2j
he λj will describe the curvature of the response while the linearoefficient bj will describe the slope of the ridge in the corre-ponding direction. The constant Ys is the calculated responsealue at the stationary point. The interpretation would be easiery analysing each response along every Zj-axis separately. Theanonical analysis is only detailed for the first response i.e. theissolution rate Y1. For the three responses Y2, Y3 and Y4, onlyhe final results are given.
.2.1. Study of the dissolution rate (response Y1)The variable transformations:
X1 = 0.971Z1 + 0.230Z2 − 0.072Z3
X2 = −0.241Z1 + 0.915Z2 − 0.323Z3
X3 = −0.008Z2 + 0.331Z2 + 0.943Z3
nd
Z1 = 0.971X1 − 0.241X2 − 0.008X3
Z2 = 0.230X1 + 0.915X2 + 0.331X3
Z3 = −0.072X1 − 0.323X2 + 0.943X3
ead to the following canonical form of the model:
ˆ1 = 4.07 + 0.41Z1 + 0.51Z2 − 0.15Z3 + 1.18Z21
−0.50Z22 − 1.00Z2
3
hese data allow us to determine the features of the responseurface in each direction of the study domain (Fig. 4).
.2.1.1. Analysis along the OZ1 direction. The equation of Y1esponse is reduced to:
ˆ1 = 4.07 + 0.41Z1 + 1.18Z21
he corresponding curve is represented in Fig. 4(1). The min-mization of Y1 can be obtained for Z1 = −0.1. Because theZ1-axis is almost parallel to OX1-axis, Y1 should be optimizedy choosing X1 = −0.1.
.2.1.2. Analysis along the OZ2 direction:. The equation of Y1esponse is reduced to:
ˆ1 = 4.07 + 0.51Z2 − 0.50Z22
ig. 4(2) shows that the minimization of Y1 requires a low levelf Z2. According to the equations of the variable transformations,his can be achieved by choosing the low level (−1) for X2.
W. Bensalah et al. / Materials Chemistry and Physics 108 (2008) 296–305 301
3r
Y
FbOb
3
a
t
Y
Tis
•••
3
a
T
Y
The curvatures of the Y3 response along the OZj are given inFig. 6. As mentioned above, we can deduce that the response Y3should be minimized by:
Fig. 4. Curvature of Y1 response vs. Zj.
.2.1.3. Analysis along the OZ3 direction:. The equation of Y1esponse is reduced to
ˆ1 = 4.07 − 0.15Z3 − 1.00Z33
rom Fig. 4(3), one can see that that the minimization of Y1 cane obtained either at a high or a low level of Z3. Because theZ3-axis is almost parallel to OX3-axis, Y1 should be optimizedy choosing either a high or a low level of X3.
.2.2. Study of the Vickers microhardness (response Y2)Using the variable transformations:
X1 = 0.405Z1 + 0.909Z2 − 0.099Z3
X2 = −0.274Z1 + 0.224Z2 + 0.935Z3
X3 = 0.872Z1 − 0.352Z2 + 0.340Z3
nd
Z1 = 0.405X1 − 0.274X2 + 0.872X3
Z2 = 0.909X1 + 0.224X2 − 0.352X3
Z3 = −0.099X1 + 0.935X2 + 0.340X3
he canonical form of the model is represented by:
ˆ2 = 478.3 − 55.7Z1 − 118.2Z2 + 56.6Z3
+113.4Z21 − 249.6Z2
2 − 280.0Z23
he corresponding curves along the three axes are representedn Fig. 5. Following the same analysis as above, the response Y2hould be maximized by:
choosing a level for X1 between 0 and −0.1,choosing a level for X2 between 0 and 0.1,either increasing or decreasing X3: (+1) or (−1).
Fig. 5. Curvature of Y2 response vs. Zj.
.2.3. Study of the weight loss by abrasion (response Y3)By the transformations:
X1 = 0.982Z1 − 0.148Z2 − 0.120Z3
X2 = 0.185Z1 + 0.886Z2 + 0.426Z3
X3 = 0.043Z1 − 0.440Z2 + 0.897Z3
nd
Z1 = 0.982X1 + 0.185X2 + 0.043X3
Z2 = −0.148X1 + 0.886X2 − 0.440X3
Z3 = −0.120X1 + 0.426X2 + 0.897X3
he second-order model of Y3 becomes:
ˆ3 = 25.35 + 15.89Z1 − 3.27Z2 + 0.90Z3 + 8.42Z21
+0.22Z22 − 4.49Z2
3
Fig. 6. Curvature of Y3 response vs. Zj.
3 emistry and Physics 108 (2008) 296–305
•••
3(
a
t
Y
TFm
t
t
oombr
3
02 W. Bensalah et al. / Materials Ch
decreasing X1 (−1),increasing X2 (+1),either increasing or decreasing X3: (+1) or (−1).
.2.4. Study of the deflection at failure of the anodic oxideresponse Y4)
Taking into account the transformations:
X1 = 0.977Z1 − 0.169Z2 − 0.130Z3
X2 = 0.063Z1 − 0.357Z2 + 0.932Z3
X3 = 0.204Z1 + 0.919Z2 + 0.338Z3
nd
Z1 = 0.977X1 + 0.063X2 + 0.204X3
Z2 = −0.169X1 − 0.357X2 + 0.919X3
Z3 = −0.130X1 + 0.932X2 + 0.338X3
he expression of the model of Y4 is:
ˆ4 = 6.33 − 0.66Z1 − 0.03Z2 + 1.70Z3
+0.46Z21 − 0.17Z2
2 − 0.33Z23
he curvatures of the Y4 response along the OZj are given inig. 7.As above, we can deduce that the response Y4 should beaximized by fixing X1 at (−1), X2 at (+1) and X3 at (0).
Table 5 summarizes the experimental conditions, leading to
he optimization of the four separately taken responses.The examination of all the results obtained by means of
he canonical analysis, allows us to conclude that it is notuS
Fig. 8. Evolution of elementa
Fig. 7. Curvature of Y4 response vs. Zj.
bvious how one can find experimental conditions that canptimize the four responses simultaneously. Accordingly, aulticriteria methodology that looks for a certain compromise
The optimization of the four responses was performed bysing the desirability functions as proposed by Derringer anduich [26]. In our case, one-sized transformation was chosen
ry desirability di vs. Yi.
W. Bensalah et al. / Materials Chemistry and Physics 108 (2008) 296–305 303
Table 5Overall results of the canonical analysis
X1 X2 X3
Y1 (g m−2 min−1) −0.1 −1 (+1) or (−1)Y2 (Hv) 0–(−0.1) (0)–(0.1) (+1) or (−1)Y3 (mg) −1 +1 (+1) or (−1)Y4 (mm) −1 +1 0
Table 6Optimal conditions
Xj Uj
The anodizing temperature (◦C) −0.039671 13.6The current density (A dm−2) 0.217253 2.2T
ft
rsfriTt
e
aYcrtYw
Fo
acflnbvc
3o
ssmooth.
Fm
he sulphuric acid concentration (g L−1) 0.978730 199
or the four responses (Fig. 8). The undesirable responses andhe fully desired responses are also reported on Fig. 8.
Taking into account all the requirements for the fouresponses, we choose to compute an overall desirability mea-ure D as a weighted geometric mean of the desirability valuesor individual parameters. Equal weights were given for the fouresponses. Therefore, the function D, over the studied domain,s calculated by using the following equation: D = (d1d2d3d4)1/4.he value of D is highest at conditions where a combination of
he different criteria is globally optimal.After calculation by NEMROD W software, the optimal
xperimental conditions are obtained (Table 6).Under these conditions, the estimated response values
re 3.3 g m−2 min−1, 464 Hv, 23.4 mg and 6.9 mm for Y1,2, Y3 and Y4, respectively. In order to validate the cal-ulated optimal conditions, an additional experiment wasun with the levels of the optimum. The experimen-
−2 −1
al responses (Y1 = 3.1 ± 0.3 g m min , Y2 = 458 ± 24 Hv,3 = 22.5 ± 2.0 mg and Y4 = 6.7 ± 0.3 mm) are in agreementith the predicted ones.
id
ig. 9. Graphical representation of the overall desirability function D: (a) X2 is ploaintaining U1 at 13.6 ◦C.
ig. 10. AFM contact mode images of the anodic film surface obtained underptimal conditions.
The resulting contour plots from modelling the overall desir-bility function can be seen in Fig. 9. It can be noted that the areaorresponding to the optimal conditions (D = 1.00) was ratherat. This would imply that the values of the four responsesear this point are stable. Hence, the maximum can be said toe insensitive to small variations in the studied experimentalariables and represents the robustness of the predicted optimalonditions.
.4. Morphology and composition of the anodic layerbtained under the optimum conditions
Fig. 10 is the three-dimensional AFM image of the anodizedample. As can be seen, the surface is relatively flat and
The oxide layer structure revealed by SEM is illustratedn Fig. 11. The top surface exhibits nano-pores uniformlyistributed, together with some spherical shaped dots, of approx-
tted against X1 maintaining U3 at 199 g L−1 and (b) X3 is plotted against X2
304 W. Bensalah et al. / Materials Chemistr
Fc
itlTd
tpi[atThiim[
Fc
4
ialonbu(ld
A
Ng
R
[
[
ig. 11. Scanning micrograph of anodized surface obtained under the optimalonditions.
mately 20–30 nm in diameter, heterogeneously distributed inhe intervening areas. In addition, the pores are roughly circu-ar in section and gradually merge along domain boundaries.he pore spacing is relatively high compared to the poreiameter.
Fig. 12 shows a depth profile of the oxide layer. The dis-ribution of Al, O and S species are revealed clearly. Theresence of sulphur specie suggests that SO4
2− anions migratenward in the thickening film as reported in the literature28–30]. Its distribution is practically uniform through thenodic oxide coating whereas in the inner layer, adjacent tohe aluminium substrate, the sulphur concentration decreases.his phenomenon has been previously mentioned [29,30] andas been explained by the greater inward mobility of O2−ons relative to SO4
2− ions under the field during anodiz-ng. The presence of Al and O is explained by the outward
igration of Al3+ and the inward migration of O2− ions
29,30].
ig. 12. The GDOES depth profile of the anodic oxide obtained under optimalonditions.
[
[
[
[
[
[
[
[
[
[
[[
[
y and Physics 108 (2008) 296–305
. Conclusion
The achievement of a Doehlert design followed by canon-cal analysis and optimization by using desirability functionllows us to determine the best experimental conditions, whichead to a compromise between studied properties of the anodicxide layer on pure aluminium namely: Vickers microhard-ess, abrasion resistance, oxide film dissolution rate and flexureehaviour. Characterizations of the anodized sample obtainednder optimal conditions by SEM, AFM and GDOES reveal:i) the nano-porous structure of top surface of the anodic oxideayer (ii) and the “homogeneous” distribution of Al, O, S in theepth of the oxide layer.
cknowledgment
The authors would like to thank Mr. Ayadi Hajji (Ecoleationale d’Ingenieurs de Sfax-Tunisie) for his valuable lin-uistic assistance.
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