Optimizing the synthesis of cobalt aluminate pigment using
fractional factorial designCeramics International ] (]]]]) ]]]–]]]
www.elsevier.com/locate/ceramint
Optimizing the synthesis of cobalt aluminate pigment using
fractional factorial design
Y.F. Gomesa,n, P.N. Medeirosa, M.R.D. Bomioa, I.M.G. Santosb, C.A.
Paskocimasa, R.M. Nascimentoa, F.V. Mottaa
aDepartment of Materials Engineering, Federal University of Rio
Grande do Norte, Campus Lagoa Nova, CEP 59078-900, Natal/RN, Brazil
bDepartment of Materials Engineering, Federal University of
Paraíba, Cidade Universitária, CEP 58051-900, João Pessoa/PB,
Brazil
Received 28 April 2014; received in revised form 20 August 2014;
accepted 28 August 2014
Abstract
The increasing use of experimental design techniques comes from the
growing need to optimize products and processes while minimizing
costs and maximizing efficiency, productivity and quality of
products. Ceramic pigments have wide application in ceramic
industries in which the quality and advanced properties of
materials are widely investigated. However, studies are required to
improve the procedure for obtaining cobalt aluminate (CoAl2O4)
using the Complex Polymerization Method (CPM). With the objective
of optimizing this method, a 2(5-2) fractional factorial design was
performed using data from UV–vis spectroscopy analysis as a
response surface. To determine the best conditions for obtaining
(CoAl2O4) in this study, five factors were chosen as input
variables at levels determined for this study: citric acid
concentration (stoichiometric), pyrolysis time (h), temperature
(1C), calcination heating time and rate (1C/min). Through
statistical application in the process of obtaining CoAl2O4, it was
possible to study which of these factors may have greater influence
in optimizing the synthesis. The precursor powders were
characterized using TG/DSC thermogravimetric analysis, and the
calcined powders were analyzed using X-ray diffraction (XRD) and
energy dispersive scanning electron microscopy (SEM/EDS) to confirm
the structural and morphological aspects of CoAl2O4. It was found
that with increased calcination temperature 700 1Co800 1Co900 1C,
the UV–vis bands decreased with increasing absorbance intensity,
and with increasing pyrolysis time (h), there is a proportional
increase in the UV–vis bands. The model was generated with the
conditions proposed in this study due to the determination
coefficient of 99.9%, variance (R2), and satisfactory response
surfaces, thus obtaining optimization of the process according to
the needs and applicability in the ceramic industry of pigments.
& 2014 Elsevier Ltd and Techna Group S.r.l. All rights
reserved.
Keywords: CoAl2O4; Pigment; Optimization; Fractional factorial
design; Complex Polymerization Method (CPM)
1. Introduction
CoAl2O4 has a spinel cubic structure and exhibits an intense blue
color, characteristic of cobalt aluminate, which is a conse- quence
of this type of structure and the existence of a tetrahedral site
for the metal ion that removes the restriction of the Laporte
selection rule present in the octahedral symmetries. The thermal
and chemical stability is due to the location of the Co2þ ion in a
compact packaging arrangement of oxide ions as investigated
by
10.1016/j.ceramint.2014.08.125 14 Elsevier Ltd and Techna Group
S.r.l. All rights reserved.
g author. Tel.: þ55 84 3342 2512; fax: þ55 84 3342 2406. ss:
[email protected] (Y.F. Gomes).
article as: Y.F. Gomes, et al., Optimizing the synthesis of cobalt
x.doi.org/10.1016/j.ceramint.2014.08.125
Meseguer et al. [1] and Akdemir et al. [2]. Currently, cobalt
aluminate (CoAl2O4) has received attention for use in different
applications due to its colorimetric properties, being widely used
for coloring plastics, inks, fibers, paper, rubber, phosphorus,
glass, cement, enamel, ceramic and porcelain bodies, as well as for
TV tubes and as contrast reinforcement for luminescent pigments,
according to Kakihana [3], Cho et al. [4], Kock and Waal [5].
Various chemical methods have been used to synthesize inorganic
pigments, such as the conventional ceramic method as reported by
Costa et al. [6] and Gargori et al. [7], combustion synthesis, co-
precipitation as demonstrated by Mimani, Ghosh [8] and Guna-
widjaja et al. [9], sol-gel method as found that Kakihana et al.
[3]
aluminate pigment using fractional factorial design, Ceramics
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and Yang et al. [10], polymeric precursor as reported by Gaudon et
al. [11] and hydrothermal method as noticed by Lu et al.[12] and
Kim et al. [13].
CoAl2O4 is typically synthesized using inorganic precursors
(primarily nitrate), followed by calcination at high temperature to
obtain the spinel structure. A synthesis route frequently
investigated in the literature for obtaining CoAl2O4 at low
temperatures is the Complex Polymerization Method (CPM) as reported
by Gaudon et al. [11], Lu et al.[12], Gong et al. [14], Chu et al.
[15] and Onfroy et al. [16].
The Complex Polymerization Method (CPM) is based on the Pechini
method and offers the possibility of preparing complexes of good
homogeneity at molecular scale and a good stoichio- metric control.
The temperatures required for the CPM are lower than those in
conventional methods, as in the reactions between materials in the
solid state or decompositions as presented by Gaudon et al. [10].
Many variables can influence the synthesis of oxides via the CPM as
investigated by Ozbay et al. [17], Gunawidjaja et al. [9] and
Jacroux et al. [18].
The most important statistical activity is not data analysis but
rather the planning of experiments in which these data can be
obtained. The essence of good planning is to design an experiment
able to provide exactly the type of information important for the
improvement of the process for obtaining the desired material as
reported by Montgomery [19].
Fractional factorial design is a reliable method to simplify the
process of identifying the most influential preparation variable.
This approach reduces the number of experiments required to
identify the process of variables in a statistically significant
manner as demonstrated by Mason [20] and Nejad et al. [21].
Fractional factorial design was used to optimize the synthesis
process of cobalt aluminate (CoAl2O4) at operating conditions to
determine a means to save time, thus reducing the number of
experiments analyzing the input variables that would influence the
process as noticed by Kavanloui et al. [22].
This study used a factorial planning of variables of the process of
obtaining resin at different citric acid concentrations and
pyrolysis times along with the process of obtaining pigments at
different temperatures, times, and calcination heating rates,
totaling five input variables (k¼5) for the synthesis process for
obtaining the ceramic pigment as discussed by Lu et al. [12],
Llusar et al. [23] and Beal et al. [24].
Table 1 Values and Levels of the Operating Parameters.
Levels
Operating factors 1 0 1 Ccitric acid 2:1 3:1 4:1 time puff (h) 1 2
3 T (1C) 700 800 900 time calcination (h) 2 4 6 Calcination rate
(1C/min) 5 8 11
2. Experimental procedure
Determining the parameter of greater statistical significance in
the preparation of the precursor resins of cobalt aluminate
(CoAl2O4) using the Complex Polymerization Method (CPM) derivative
from the Pechini method was performed in two steps. The study
explored the five main processing parameters in the method.
Subsequently, based on this result, further analysis was designed
using the fractional factorial design. This analysis corresponded
to peaks of higher absorbance intensity in cobalt aluminate.
Thereafter, the fractional factorial design was designed based on
the final optimized factors to confirm that the interaction between
the pyrolysis time (h) and the calcination heating rate
Please cite this article as: Y.F. Gomes, et al., Optimizing the
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(1C/min) has greater statistical significance compared to the other
factors studied.
2.1. Materials and reagents
Aluminum nitrate (Al(NO3)39H2O), cobalt nitrate (CoN2O6
6 H2O), citric acid (C6H8O7) and ethylene glycol (HOCH2- CH2OH)
were used to prepare the precursor resins of cobalt aluminate
(CoAl2O4) as reported in Mimani et al. [8] and Kim et al.
[13].
2.2. Experimental design and characterization of the material
The fractional factorial design used increases the amount of
information obtained and reduces the number of experi- ments. The
designed experiment determines the influence of these parameters on
the syntheses of cobalt aluminate as demonstrated in Meseguer et
al. [1], Akdemir et al. [2], Gong et al. [14], Chu et al. [15],
Onfroy et al. [16] and Pavia et al. [25]. The five factors studied
include citric acid concentrations (Ccitric acid), puff time (time
puff (h)), temperature (T), calcina- tion time (time calcination
(h)), calcination rate (1C/min) and their encoded values (Table 1).
If low and high values were assigned for each of these variables,
there is a 25 factorial design; as a result of the combinations,
there would be 32 experiments to determine the influence of these
five parameters on the synthesis of cobalt aluminate. The syntheses
performed according to scheme are listed in Table 1. According to
the 2(5-2) fractional factorial design, resin was
obtained based on different ratios among the citric acid masses at
concentrations of 2:1, 3:1 and 4:1 and standard ethylene glycol
60/40, with a constant value of approximately 1.5 for the ratio by
weight of citric acid and ethylene glycol. The pyrolysis of the
resin obtained was performed at 350 1C at time intervals of 60 min,
120 min and 180 min with a calcination heating rate of 5 1C/min.
The precursor powders obtained from synthesis were de-agglomerated
using a mill for 90 min, 150 min and 210 min to obtain homogeneous
powder. The calcinations were performed at temperatures of 700 1C,
800 1C and 900 1C in times of 120 min, 240 min and 360 min with
heating rates of 5 1C/min, 8 1C/min and 11 1C/min with cooling to a
temperature of 25 1C. The 2(5-2)¼23 fractional factorial approach
used reduced the
number of experiments to 11, including eight factorial and three
central points as reported by Montgomery [19] and Mason [20].
t aluminate pigment using fractional factorial design, Ceramics
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Y.F. Gomes et al. / Ceramics International ] (]]]]) ]]]–]]] 3
The values of the wavelengths related to higher peak absorbance of
the pigments obtained by analysis of the UV–vis spectroscopy (Y)
are the response variables as demonstrated by Llusar et al. [23].
Based on this analysis in Yahiaoui et al. [26] and Kaladhar et al.
[27], the general equation of the second-order or quadratic model
may be generated, as represented in Eq. (1):
Y ¼ β0þ ∑ k
k
j ¼ 1 βjjx
2 j þε ð1Þ
where Y is the expected response, wavelength (nm), Xi are the
encoded or non-encoded values of factors (citric acid concentra-
tions (Ccitric acid), puff time (time puff (h)), temperature (T),
and calcination time (time calcination (h), and calcination rate
(1C/min)), 0 is a constant, i is the leading coefficient for each
variable, and ij is the effect of the interaction of coefficients
as demonstrated by Ozbay et al. [17], Montgomery et al. [19], Mason
et al. [20] and Raj et al. [28].
The values of polynomial coefficients and the response surface of
the second-order model were obtained using the STATISTICA software
7.0, and the model was validated for the process conditions used in
this study.
The response function (regression model) developed and the response
surface placed over the region around the current selected
conditions can be used to predict the response resulting from any
adjustment of the independent factors as reported by Saravanan et
al. [29].
Table 3 Analysis of Variance (ANOVA) for the Suggested Model.
Source DF SS MS F P
(1)Ccitric acid 1 120.125 120.125 90.094 0.010918 (2)timepuff(h) 1
153.125 153.125 114.844 0.008595 (3)T (1C) 1 1770.125 1770.125
1327.594 0.000752 (4)timecalcination(h) 1 210.125 210.125 157.594
0.0006286 (5)Calcination rate (1C/min) 1 153.125 153.125 114.844
0.008595 2 by 3 1 153.125 153.125 114.844 0.08595 2 by 5 1 136.125
136.125 102.094 0.009653 1n2n4 1 371.095 371.095 278.321 0.003574
Pure error 2 2.667 1.333 Total 10 3069.636
3. Results and discussion
Preliminarily, the identification of the significant factors was
performed by a 2(5-2) fractional factorial design with three
replications at the center point, with preliminary UV–vis
spectroscopy results corresponding to peaks of higher absor- bance
intensity in cobalt aluminate powder as the response surface as
investigated by Kavanloui et al. [22] and Hesse et al. [30].
The experimental results presented in Table 2 were analyzed using
the STATISTICA software and analysis of variance
Table 2 Design Matrix Fractional Factorial 2(5-2) with real, coded
values and the results.
run no. Code of syntheses Coded Values of Parameters
Ccitric acid timepuff(h) T (1C)
1 S1 1 1 1 2 S2 1 1 1 3 S3 1 1 1 4 S4 1 1 1 5 S5 1 1 1 6 S6 1 1 1 7
S7 1 1 1 8 S8 1 1 1 9 S9 0 0 0 10 S10 0 0 0 11 S11 0 0 0
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(ANOVA), which evaluates whether the effect and interaction between
the investigated factors are of significance with regard to the
experimental error. The significance of the main factors and their
interactions was evaluated by the F-test with a confidence level of
95% and the Pareto method as discussed by Montgomery [19] and Mason
[20]. The results of the ANOVA are presented in Table 3 and
indicate that all of the effects and interactions between factors
are significant (po0.05) as discussed by Zolgharnein et al. [31].
The estimated effects and coefficients are listed in Table 4.
The experimental error and the main factors and their interac-
tions were evaluated by the F-test with a confidence level of 95%
as told in Rincón et al. [32]. UV–vis spectra were used to study
the optical properties of the
cobalt aluminate synthesized (Fig. 1). The bands located in the
blue region of the electromagnetic spectrum are 195, 280, 485, 506,
560 and 680 nm, typical of spinel-type cobalt aluminate; with
increasing calcination temperature, the visible bands are more
clearly defined, resulting in a shift of the bands of higher
intensity and thus to a decrease of the absorbed visible bands as
demonstrated in Klockenkamper et al. [33]. Fig. 2(a-c) presents
photographs of cobalt aluminate powders
calcined according to the planning fractional factorial design for
a qualitative analysis of visual denotation of the variation in
the
Absorbance (nm)
timecalcination(h) Calcination rate(1C/min)
1 1 592 1 1 627 1 1 628 1 1 626 1 1 588
1 1 589 1 1 590 1 1 587 0 0 591 0 0 589 0 0 591
aDF ) degree of freedom, SS ) sum of square, MS ) mean square, and
F ) F-test.
aluminate pigment using fractional factorial design, Ceramics
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Table 4 Estimated Effects and Coefficients for the Suggested Design
Matrix Fractional Factorial 2(5-2).
Factor Effect Std.Err T P 95% Cnf.Limt þ95 Cnf.Limt
Mean/ Interc. 590.3333 0.666667 885.5000 0.000001 587.4649 593.2018
(1)Ccitric acid 7.7500 0.816497 9.4918 0.010918 4.2369 11.2631
(2)timepuff(h) 8.7500 0.816497 10.7165 0.008595 5.2369 12.2631 (3)T
(1C) 29.7500 0.816497 36.4362 0.000752 33.2631 26.2369
(4)timecalcination(h) 10.2500 0.816497 12.5536 0.006286 13.7631
6.7369 (5)Calcination rate (1C/min) 8.7500 0.816497 10.7165
0.008595 12.2631 5.2369 2 by 3 8.7500 0.816497 10.7165 0.008595
12.2631 5.2369 2 by 5 8.2500 0.816497 10.1041 0.009653 4.7369
11.7631 1n2n4 26.0833 1.563472 16.6830 0.003574 19.3563
32.8104
Y.F. Gomes et al. / Ceramics International ] (]]]]) ]]]–]]]4
blue hue; the changes in color of blue spinel CoAl2O4 span a total
range from a dark grayish blue (Fig. 2(a)) to an intermediate blue
(Fig. 2(b)) and finally to a clear blue (Fig. 2(c)). These
variations are discussed above and related to the increase or
decrease in the band intensity in the UV–vis spectral range as
reported in Lu et al. [12] and Llusar et al. [23].
Fig. 3(a, b) shows the thermogravimetric analysis and differential
scanning calorimetry curves (TGA/DSC) of the cobalt aluminate
precursor material obtained according to the fractional factorial
design. No mass loss was observed at tempera- tures above 460 1C,
indicating crystallization of the material, and therefore,
calcination can be achieved at temperatures in the range of 700 1C
to 900 1C. Differential scanning calorimetry (DSC) curves exhibit
an exothermic peak in the temperature range from 250 1C to 460 1C
corresponding to the precursor combustion and the removal of carbon
residues corresponding to exothermic peaks at approximately 414 1C,
as reported in Kock et al. [5], Lu et al. [12] and Llusar et al.
[23].
X-ray diffraction was used to verify the crystal structures and
purity of the samples. Fig. 4 presents the X-ray diffractograms of
cobalt aluminate pigments obtained according to the experi- mental
plan, showing its crystallization with the presence of a single
phase of cobalt aluminate (CoAl2O4) with spinel-type cubic
structure of Fd3m (JCPDS 44–0160) geometry. The peaks observed for
CoAl2O4 in 2θ¼31.161, 36.731, 44.731, 48.961, 55.571, 59.191,
65.031, 73.951, and 77.181 are in agreement with JCPDS 44–0160
values, with the peak line d¼2.44 Å in the plane (3 1 1), which is
observed in XRD patterns, in agreement with previous studies
involving cobalt aluminate as told in Lu et al. [12] and
Klockenkamper et al. [33].
SEM images of the CoAl2O4 material of experiments 4, 9 and 7 are
shown in Fig. 5(a-c). The powders were calcined at (a) 700 1C, (b)
800 1C and (c) 900 1C of cobalt aluminate powders obtained from the
proposed experimental plan that had the same configuration among
all syntheses performed. Fig. 5(a-c) shows irregular particles and
clusters, regardless of temperature, puff duration, calcination
heating time and rate, which are input variables to the fractional
factorial design study.
Fig. 6 shows the predicted values versus observed values using the
model equation obtained from the data of the response surface of
UV–vis absorbance. Effects with less than 95% significance
according to the F-test used in this study are not reported.
From the values obtained from response surfaces from UV–vis
spectroscopy analysis, it was possible to obtain an
Please cite this article as: Y.F. Gomes, et al., Optimizing the
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empirical model with first-order interactions that is able to make
predictions within the study range for the five variables under
study. The multiple regression analysis of the resulting empirical
data in the process of obtaining the visible band range for the
cobalt aluminate pigment (CoAl2O4) correspond- ing to the blue hues
obtained led to the following model expressed in Eq. 2:
Y ¼ 590:33¼ ð4:375 tpuf f Þð14:875 Tð 3CÞÞ ð4:375 tpuf f Tð
3CÞÞþð4:125 Tx tpuf f Þ þð13:042 Ccitric acid tpuf f
tcalcinationÞ43:875 ð2Þ
The wavelength model equation is expressed for the following
interval (–1, 0, þ1), i.e., variables of citric acid concentration
(Ccitric acid), puff time (time puff (h)), temperature (T),
calcination time (time calcination (h)), and calcination rate
(1C/min) are valid in the range from –1 to þ1. The equation with
coded values is used for independent variables or interactions
between variables, whereas the response variable (Y) is the
wavelength given in nanometers (nm). Eq. (1) was used to predict
the wavelength in which the
model function is valid for the defined interval, i.e., for the
variables of citric acid concentration (Ccitric acid), puff time
(time puff (h)), temperature (T), calcination time (time
calcination
(h)), and calcination rate (1C/min) in the valid range from –1 to
þ1 for the experimental conditions used in this study, the
determination coefficient of the proposed mathematical model
t aluminate pigment using fractional factorial design, Ceramics
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Fig. 4. X-ray diffraction diagram of powder samples of CoAl2O4
(experiments 4, 9 and 7) prepared by CPM and annealed at: (a) 700
1C, (b) 800 1C and (c) 900 1C.
Fig. 3. TGA (a) and DTA (b) curves of the as-prepared cobalt
aluminate precursor obtained by CPM.
Fig. 2. CoAl2O4 obtained from experiments 4, 9 and 7 heated at: (a)
700oC, (b) 800 1C and (c) 900 1C.
Y.F. Gomes et al. / Ceramics International ] (]]]]) ]]]–]]] 5
can explain approximately 99.9% of the variance (R2) as
demonstrated in Montgomery et al. [19] and Mason et al. [20].
Among the five factors studied, the citric acid concentration alone
has lower statistical significance when compared with the puff time
(h), which is less statistically significant when compared with the
temperature (1C). Furthermore, the tem- perature (1C) has greater
statistical significance than the calcination time, which has lower
statistical significance compared to the calcination heating rate
(h). The relationship between factors studied in ascending
significance order is calcination temperature (1C)4calcination time
(h)4heating rate (1C / min)4puff time (h)4 (Ccitric acid).
The interactions between the factors puff time (h) (or pyrolysis)
interacting with calcination temperature (1C) and calcination
heating rate (1C/min) were found to have statistical significance.
The calcination time (h) has high statistical significance alone
and/or in the interaction with citric acid concentration and puff
time (h) (or pyrolysis).
For the levels studied, the factors were found to be relevant
because the p value was below 5%. The standard deviation values are
smaller than the actual value of effects and parameter, thus
validating the mathematical model proposed as told in Montgomery et
al. [19] and Yahiaoui et al. [26].
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Fig. 7 illustrates the Pareto chart in which the five input
variables with values greater than 10.71 (p¼0.05) at the right of
the line were significant; the calcination temperature (1C) has
greater statistical significance compared to the other
factors
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Fig. 7. Significant interaction graphs. Fig. 6. A comparative plot
between experimental yield and the predicted yield.
Fig. 5. SEM micrographs of the CoAl2O4 powders (experiments 4, 9
and 7): (a) 700 1C, (b) 800 1C and (c) 900 1C.
Y.F. Gomes et al. / Ceramics International ] (]]]]) ]]]–]]]6
studied. The negative value of –36.43 indicates higher values of
the visible band range to the lower level with respect to the
calcination temperature (1C).
The calcination time (h) among the variables studied has the second
highest statistical significance, with a negative value of –12.55,
indicating higher values within the visible range for the shorter
calcination time. The puff time (h) and the calcination heating
rate exhibit the same numerical value of 10.71, and the puff time
(h) with a positive value indicates an increase in the visible band
range when the puff time (h) increases toward its maximum level.
The calcination heating rate (1C/min) with a negative value
indicates higher values in the visible band range toward the lower
level of the heating rate. The citric acid concentration exhibits a
positive numeric value of 9.49, indicating an increase in the
visible band range when the citric acid concentration increases to
its maximum level as reported in Jacroux et al. [18], Kaladhar et
al. [27], Saravanan et al. [29] and Sudhakaran et al. [34].
Fig. 8 shows that the major interactions are between the citric
acid concentration, puff time (h) and calcination time (h), which
exhibit a positive value of 16.68, indicating that the visible band
range will increase if these three variables all go toward the
upper or lower level.
The interaction between puff time (h) and temperature (1C) has a
negative value of –10.71, indicating an increase in the
Please cite this article as: Y.F. Gomes, et al., Optimizing the
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visible band range if the variables go in opposite directions, that
is, a variable toward the upper level and the other toward the
lower level. The interaction between puff time (h) and calcination
heating rate (1C/min) has a positive value of 10.10, indicating an
increase in the visible band range if these variables both go
toward the lower or upper level. Fig. 8(a) shows the relationship
between puff time (or
pyrolysis) and temperature (1C), which provides a better view
through the contour line; it could be inferred that the interaction
between puff time (h) and temperature (1C) leads to an increase in
the response surface in the visible band range when the variables
are moving in opposite directions. For example, if the variable
temperature (1C) is toward the lower level (–1) at 700 1C and the
puff time (h) is toward the upper level (þ1) at 3 h, then there is
a higher value for the response surface in the visible band range
of 610 nm, corresponding to a dark grayish blue as told in Beal et
al. [24] and Rincón et al. [32]. In another situation, in the case
of two variables, temperature (1C) and puff time (h), both going
toward the upper level (þ1) or toward the lower level (–1), there
will be a lower value for the response surface in the visible band
range of 590 nm and 580 nm as demonstrated in Igushi et al. [35],
Cheng et al. [36], Routray et al. [37], Salem et al. [38],
Sirijaruphan et al. [39] and Santos et al. [40]. Increasing the
values of the levels of variables at higher levels (þ1) with
the
t aluminate pigment using fractional factorial design, Ceramics
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Y.F. Gomes et al. / Ceramics International ] (]]]]) ]]]–]]] 7
relationship variables of puff time (h) and temperature (1C)
results in a visible band of approximately 570 nm that is a shade
of lighter blue.
Fig. 8(b) shows the interaction between parameters with respect to
the puff time (h) and calcination heating rate (1C/min). There is
an increase in the visible band range if both variables are in the
same direction, either to the lower or upper level. The variables
puff time (h) and calcination heating rate (1C/min) were observed
to go toward the lower level (–1), with the actual values of 1 h
and 5 1C/min, respectively, and response surface value within the
visible band range of 570 nm, i.e., a grayish blue. In the case of
two variables, the calcination heating rate (1C/min) and puff time
(h), going in opposite directions, if the calcination heating rate
(1C/min) and puff time (h) both are at the upper level (þ1) with
actual values of 11 1C/min and 3 h, respectively, or if the
calcination heating rate (1C/min) and puff time (h) both are at the
lower level (–1) with actual values of 5 1C/min and 1 h,
respectively, there will be a smaller value for the response
surface in the visible band range of 590 nm and 580 nm, obtaining
an intermediate blue color. If the variable puff time (h) and
calcination
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heating rate (1C/min) are toward the upper level (þ1), with their
actual values of 3 h and 11 1C/min, respectively, there will be a
value of 580 nm for the response surface in the visible band range.
Thus according to the RSM, the tonal ranges of grayish blue,
intermediate blue and light blue are defined by the conditions
chosen in the range of temperatures studied 700 1Co800 1Co900
1C.
4. Conclusion
The Complex Polymerization Method is an efficient means for the
single-phase synthesis of cobalt aluminate. The 2(5-2)
fractional factorial design composed of eight factorial points plus
three central points proved the statistical interactions between
input variables and the response surface. The Pareto chart
indicated that the interactions of greater significance for the
formation of response surfaces are pyrolysis time (h) and
temperature (1C), with a negative value of –10.71, which indicated
an increase in the visible band range if the variables are trending
in opposite directions. The interaction between pyrolysis time (h)
and calcination heating rate (1C/min), with a positive value of
10.10, indicated an increase in the visible band range if the two
variables are both trending to the upper or lower level. The
mathematical model generated with the determination coefficients
can explain approximately 99.9% of the variance (R2), with an
empirical model considering first- order interactions able to
predict, within the valid study range (–1) to (þ1), the empirical
results in the visible band range corresponding to the cobalt
aluminate pigment (CoAl2O4). The evaluation of the optimal
conditions for the parameters puff time (h) and temperature (1C)
satisfactorily establish the tonal conditions of grayish blue,
intermediate blue and light blue through the performance of RSM;
the heat treatment condi- tions studied of 700 1Co800 1Co900 1C
allow for these conditions, with the improved performance and
applicability according to the desired traits in the ceramic
industry.
Acknowledgments
The authors thank the financial support of the Brazilian research
financing institutions: CNPq and CAPES.
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International
Introduction
Results and discussion