Effect of sintering parameters using the central composite design method, electronic structure and physical properties of yttria-partially stabilized ZrO₂ commercial ceramics

The central composite design fits a quadratic model (second order) for a system with k controllable variables, each ranging between two levels (maximum and minimum) [40]. The number of runs by the CCD method is given by: [2^k+2k + n_c], where 2^k refers to the full factorial design, 2k are the axial points and nc are the central points (usually three to five points are used) [41].

The levels are expressed in the form of encoded variables (±1 for the factorial points, ±α to the axial points, 0 (zero) to the center points). The value of α depends on the value of k according to equation 1[40]: α<!-- a -->=(2)k/4 $$\alpha=(2)^{k/4} $$ (1)Equation 2 is a quadratic expression which correlates the factors and the responses of the system: y^<!-- ^ -->=a0+∑<!-- ? -->i=1kaixi+∑<!-- ? -->i=1kaiixi2+∑<!-- ? -->i=1k∑<!-- ? -->j><!-- > -->1kaijxixj $$\hat y = a_0+\displaystyle\sum\limits_{i=1}^{k}\, a_ix_i+\sum\limits_{i=1}^{k}a_{ii}x_i^2+\sum\limits_{i=1}^{k} \sum\limits_{j\gt 1}^{k}\, a_{ij}x_ix_j $$ (2) i = 1, 2, 3, …, k; j = 1, 2, 3, …, k ; i ≠ j

In this expression, x is the response, x_i and x_j are the coded values of the factors; a₀ is a constant, a_i, a_j and a_ij are the linear, quadratic and interaction coefficients, respectively. The response surfaces can be plotted from the obtained equations.

Commercial 3Y-PSZ ceramics powders from Tosoh, Japan (99.9 % purity) were used in this study. All samples were uniaxially pressed at 390 MPa and then isostatically pressed at 150 MPa. Sintering was performed in air in a conventional furnace (EDG F1600-Sinter-10P). The heating rate was kept constant at 2 °C/min for all samples.

The factors (temperature and time) were evaluated in two factorial levels (−1 and +1), two axial levels (−α and +α → −1.41 and +1.41, for k = 2) and three central points (0) used to estimate the experimental error. Thus, 2²+ 2 × 2 + 3 = 11 (eleven) experiments were performed.

The levels for each factor were obtained as follows: the maximum capacity of our furnace was 1600 °C, so we chose 1550 °C to represent the temperature level (+1). Studies by Badwal et al. [42] presented sintering at low temperature (1350 °C for 4 h). Therefore, we decided to 1350 °C as the temperature level (−1) and 4 h as the time level (−1). Casellas et al. [43] presented the results for sintering of 3Y-PSZ ceramics at 1650 °C for 10 h. Thus, extrapolating this time value, we assumed 12 h as the time level (+1). Temperature and time level (0) are the average between levels (−1) and (+1). Levels (−1.41) and (+1.41) were obtained by extrapolation of the values shown above.

The software Statistica was used to provide the necessary combinations of the levels to achieve the CCD. These combinations are shown in Table 1 under coded and uncoded variables.

Table 1

Coded and uncoded values of levels for sintering temperature and time and its execution order.

The experiments were performed for different combinations of the levels. In order to reduce the error caused by the experimental procedure, the order of experiments was randomized [40]. As it can be observed in Table 1, the presented data are in good agreement with previous results reported in the literature [42, 43].

The commercial powder 3Y-PSZ and sintered bodies were structurally characterized by XRD using a XRD-7000 diffractometer (Shimadzu, Japan) with CuKα radiation (λ = 1.5406 Å) in the 2θ range from 20° to 80° at a scanning rate of 2°·min⁻¹ (exposure time of 30 min). The Rietveld routines were performed in the 2θ range from 20° to 80° at a scanning rate of 1°·min⁻¹ (exposure time of 60 min). The shapes and average grain sizes of 3Y-PSZ ceramics sintered bodies were observed by FE-SEM using a Supra 35-VP microscope (Carl Zeiss, Germany) operated at 10 kV. Vickers hardness investigation was performed according to ASTM C1327-08 [44]. Ten indents were made on each sample using a load of 0.5 kgf for a holding time of 15 s, each.

The volumetric shrinkage was calculated by equation 3: VS(%)=(Vi−<!-- - -->Vf)Vix100 $$VS(\text %) = \displaystyle\frac{(V_i-V_f)}{V_i} x 100 $$ (3) where VS (%) represents the percentage of volumetric shrinkage, V_i is the volume of the samples before sintering, V_f is the volume after sintering. V_i and V_f were measured with a profile projector (PH-A14, Mitutoyo).

Fig. 1 (I to XII) shows the XRD patterns of 3Y-PSZ ceramics: as received commercial powder or non-sintered ceramics and ceramics sintered at different temperatures and times, respectively.

As it can be noted, in Fig. 1a (I) and Fig. 1b, the 3Y-PSZ non-sintered and sintered ceramics reveal the presence of two phases related to tetragonal (•) and monoclinic (♦) structures. The others samples illustrated in Fig. 1a (II to VIII) present some small peaks relating to the presence of residual ZrO₂, corresponding to monoclinic structure, while in Fig. 1a (IX to XII) the presence of the phase related to monoclinic structure cannot be detected in the diffraction peaks. Moreover, the diffraction peaks can be used to evaluate the structural order at long range or periodicity of the material. The ZrO₂ phases were confirmed by the comparison of the XRD patterns with the respective files of Inorganic Crystal Structure Database (ICDS) No. 18190 referring to monoclinic structure and files No. 66782 and No. 86603 referring to tetragonal structure [45–47]. Therefore, all the 3Y-PSZ non-sintered and sintered ceramics exhibited characteristic diffraction peaks corresponding to an ordered structure at a long range. In Fig. 1b, the 3Y-PSZ non-sintered ceramics exhibited characteristic diffraction peaks relating to the presence of two phases; the main phase with the highest percentage is ascribed to tetragonal structure and the second phase is related to monoclinic structure. However, it can be verified in Fig. 1c that the increase of temperature (1550 °C) and time (12 h) promotes a raise in sintering and formation of monophasic ZrO₂ ceramics with tetragonal structure, which can be indexed by both ICSD files No. 66782 or No. 86603 [46, 47]. Finally, in Fig. 1c, it is noted that all the diffraction peaks are in good agreement with those reported for monophasic ZrO₂ in respect ICSD file No. 66782 [46].

To verify and confirm if the structures of 3Y-PSZ non-sintered and sintered ceramics are monoclinic and tetragonal, a structural refinement by the Rietveld method was performed. The Rietveld method is a least squares refinement procedure where the experimental step-scanned values are adapted to the calculated ones. The profiles are considered to be known, and a model for a crystal structure available [48]. This structural refinement method presents several advantages over conventional quantitative analysis methods. As the method uses a whole pattern fitting algorithm, all lines for each phase are explicitly considered, and even severely overlapped lines are usually not a problem. Thus, it is not necessary to decompose patterns into separate Bragg peaks, as is often the case for traditional methods. The use of all reflections in a pattern rather than just the strongest ones minimizes both the uncertainty in the derived weight fractions and the effects of preferred orientation, primary extinction, and nonlinear detection systems [49].

The experimental lattice parameters, unit cell volumes, length of the chemical bonds, and bond angles between (O1−Zr−O2) and (O1−Zr−O1) were obtained and calculated by the Rietveld refinement method [48] using the ReX Program version 0.8.0 [50]. The structural refinement results for 3Y-PSZ non-sintered ceramics and ceramics sintered at 1550 °C for 12 h are illustrated in Fig. 2, and the refinement results are presented in Table 2.

The results obtained from the Rietveld refinement method show a good agreement between the observed XRD patterns and theoretical results (Fig. 2). Moreover, the profiles of XRD patterns experimentally observed and theoretically calculated display small, near zero, differences on the intensity scale as illustrated by the (Y_Observed – Y_Calculated) line. Fig. 2a shows the results of the Rietveld refinement obtained from a quantitative phase analysis with two monoclinic and tetragonal structures using a better approximation and indexing of the Crystallographic Information File (CIF) and employing two CIF files No. 18190 and No. 66782 [45, 46]. However, it is possible to observe the presence of singlephase related to tetragonal structure in Fig. 2b. This behavior is due to increased temperature and time of sintering of the 3Y-PSZ ceramics which was indexed with the CIF file No. 66782 [46].

The results in Table 2 obtained from the Rietveld refinement method indicate good agreement between the XRD patterns observed experimentally and calculated theoretically. According to the literature [51, 52], the quality of the data from structural refinement is generally controlled by R_values (R_p, R_exp, R_wp) and the goodness of fit (GoF = R_wp/R_exp).

Fig. 3 illustrates the schematic representations of the monoclinic ZrO₂ and tetragonal ZrO₂ and Y_0.03Zr_0.97O₂ unit cells performed from the Rietveld refinement data.

These unit cells were modeled through the Visualization for Electronic and Structural Analysis (VESTA) version 3.4.0 for 64-bit version of Windows 7 [53] by Rietveld refinement data (lattice parameters and atomic positions) (Table 2). The ZrO₂ crystals belong to the baddeleyite-type monoclinic structure with a space group (P2₁/c) No. 14 in the International Tables of Crystallography, four molecules per unit cell (Z = 4) and point group symmetry (C2h5) $(\text{C}^5_{2\text{h}})$ [45]. As it can be observed in Fig. 3a, some bonds between the O−Zr−O atoms were projected out of the unit cell. In these unit cells the zirconium (Zr) atoms are coordinated to seven oxygens forming a heptahedron-type polyhedron with the configuration of distorted deltahedral [ZrO₇] clusters and the prescence of 7 vertices (V), 9 faces (F) and 14 edges (E) composed of eight triangular faces and one square face [54−56]. These [ZrO₇] clusters form irregular polyhedra in the lattice, and for each ZrO₂ ceramics we have verified, at different temperatures and times, that the deltahedral [ZrO₇] clusters exhibit a particular characteristics related to the differences in the O−Zr−O bond angles [57, 58]. However, in Fig. 3b, it can be noted that ZrO₂ crystal belongs to the tetragonal structure with a space group (P4₂/nmc) No. 137 in the International Tables of Crystallography; two molecules per unit cell (Z = 2) and point group symmetry (D4h15) $(\text{D}^{15}_{4\text{h}})$ [59]. As it can be verified in Fig. 3b and Fig. 3c, some bonds between the O−Zr−O/ O−Y−O atoms were projected out of the unit cell. In these unit cells, the Zr atoms or yttrium (Y) atoms are coordinated to eight oxygens forming a square antiprism-type polyhedron with configuration distorted deltahedral [ZrO₈]/[YO₈] clusters and prescence of V = 8 vertices, F = 10 faces and E = 16 composed of nine triangular faces and one square face [60, 61]. These [ZrO₈] clusters form irregular polyhedra in the lattice and for each ZrO₂ or Y_0.03Zr_0.97O₂ ceramics we have verified, at different temperatures and times, that the deltahedral [ZrO₈]/[YO₈] clusters exhibit a particular characteristics related the differences in the (O−Zr−O/O−Y−O) bond angles [62]. The amount of V, E and F present in the distorted deltahedral [ZrO₇]/[ZrO₈] or [YO₈] clusters, can be confirmed by Euler’s polyhedron formula, described by [V − E + F = 2].

Fig. 4 shows the electron density models at different planes of 3Y-PSZ non-sintered ceramics (Fig. 4a and Fig. 4b) and 3Y-PSZ ceramics (Fig. 4c and Fig. 4d) sintered at 1550 °C for 12 h, respectively.

These electron density models were calculated by Fourier transform of structure factors from the structural parameters and atomic scattering factors of free atoms obtained from Rietveld refinement for the non-sintered 3Y-PSZ (Fig. 4a and Fig. 4b) and 3Y-PSZ ceramics sintered at 1550 °C for 12 h (Fig. 4c and Fig. 4d). These data were used in the VESTA program version 3.4.0 [53] to model the electron density map [63]. In these figures, a color scale on each plane is displayed, which demonstrates the zones with high and low electronic densities. In Fig. 4a, the blue colored regions are related to the absence of electronic charge, while the red colored areas exhibit a high electronic density. Moreover, it is possible to verify the presence of two Zr atoms with high electron density, bonded to two types of O atoms located at different atomic positions. The O1 and O2 atoms exhibit a large atomic displacement, which suggests the existence of distortions in agreement with Fig. 3a. In the (1 4 1) plane shown in Fig. 4b, a large quantity of O atoms are found and a high amount of blue area suggests that ZrO₂ ceramics with monoclinic structure presents oxygen vacancies in the lattice [64]. In Fig. 4c, in (6 3 6) plane it is possible to observe the presence of two Zr atoms with a high electron density, bonded only by one type of O atoms due to sintering process of ZrO₂ ceramics at 1550 °C for 12 h which promotes the phase transformation from monoclinic to tetragonal structure. Moreover, a reduction of blue area related to absence of electronic charge due to presence of O atoms in ZrO₂ ceramics with tetragonal structure can be noted (Fig. 3b nad Fig. 3c). Finally, it is revealed that the (1 2 0) plane, is related to presence of several O atoms that are able to share the same Zr atom with a large bond distance between O−Zr−O, which indicates a minor distortion of the O−Zr−O bonds present in ZrO₂ ceramics with tetragonal structure (Fig. 4d).

Fig. 5 illustrates the FE-SEM images of 3Y-PSZ ceramics sintered at 1350 °C for 4 h, 1350 °C for 12 h, 1550 °C for 4 h and 1550 °C for 12 h, respectively.

A closer examination of the FE-SEM images revealed the effect of processing temperature on the microstructure of the 3Y-PSZ ceramics. As it can be observed in Fig. 5a, when 3Y-PSZ ceramics was sintered at low temperature and short time, a large quantity of pores on the surface could be observed. However, after 12 h sintering (Fig. 5b) a reduction in quantity of pores and increase in average grain size occurred, which was favored by the matter transport mechanism during the sintering process [65, 66]. When these 3Y-PSZ ceramics were submitted to the sintering process performed at 1550 °C for 4 h and 12 h, the movement of atoms or molecules was driven by differences in curvature between the grains in contact [67, 68]. In order to reduce surface free energy, atoms supposedly moved from the grains with smaller radius to those with larger radius. Moreover, it is possible that the matter transport between several aggregated particles and the high anisotropy in the grain boundary energies induced the formation of compact and irregular grains (Fig. 5c and Fig. 5d). Finally, the effect of processing temperature on the intensified shrinkage and densification rates resulting in denser mass of the grains was analyzed [69].

FE-SEM images were also of great importance to evaluate the average grain size distribution of different 3Y-PSZ ceramics sintered at 1350 °C for 4 h, 1350 °C for 12 h, 1550 °C for 4 h and 1550 °C for 12 h, respectively. Hence, the counting of 140 grains was performed to ensure a good statistic response (Fig. 6).

In all cases, the counting of particle sizes was well described by the log-normal distribution as presented in equation 4[70]: y=y0+A2π<!-- p -->wxe−<!-- - -->ln⁡<!-- ? -->xxc/2w2 $$y=y_0+\frac{A}{\sqrt{2\pi wx}}e^-{\left[\ln\frac{x}{x_c}\right]/2w^2} $$ (4) where y₀ is the first value on y-axis, A is the amplitude, w is the width, π is a constant, and x_c is the center value of the distribution curve on x-axis.

The grains of 3Y-PSZ ceramics sintered at 1350 °C for 4 h exhibit an average size distribution in the range of 0.11 μm to 0.37 μm (Fig. 6a). In this system, it was estimated that 42 % of these grains have an average size of approximately 0.18 μm and 0.19 μm. The raise of processing time to 12 h resulted in an increase in the average grain size to about 0.25 μm (23 %) (Fig. 6b)[71]. As can be seen in Fig. 6c, the raise of temperature to 1550 °C at processing time of 4 h promoted a considerable increase in grain size ranging from 0.25 μm to 0.9 μm, while 37 % of these grains have an average size of 0.55 μm. Finally, when the 3Y-PSZ ceramics was sintered at 1550 °C for 12 h, a considerable increase in average grain size in the range from 0.35 μm to 1.25 μm was observed (Fig. 6d) which proves the effect of grain growth and it is associated with a high shrinkage rate.

Table 3 shows the measured values for volumetric shrinkage (VS), average grain size (AGS) and hardness (HV) of the sintered bodies in eleven different combinations of temperature and time.

Table 3

Volumetric shrinkage (VS), average grain size (AGS) and Vickers hardness (VH) for all combinations of sintering temperature and times.

The data shown in Table 3, were obtained using the CCD method which is able to evaluate the volumetric, average grain size and hardness of our 3Y-PSZ sintered ceramics as presented in equation 5, equation 6 and equation 7, respectively. VS=−0.000096385T2+0.3465594T+0.00932161t2+3.55921t−0.00235937Tt−251.158114$$\eqalign{VS = & - 0.000096385T^{2} + 0.3465594T\\ & + 0.0093.55921t\\ &- 0.00235937Tt - 251.158114 }$$(5)AGS=0.000001433T2−0.003428595T+0.000797220t2−0.170456400t+0.00011883Tt+2.265139067$$\eqalign{AGS = & 0.000001433T^{2} - 0.003428595T\\ & + 0.000797220t^{2} - 0.170456400t\\ &+ 0.00011883Tt + 2.265139067 }$$(6)VH=−0.0219377T2+67.69754T−3.66154t2+273.5638t−0.139184Tt−51040.48033$$\eqalign{VH = & - 0.0219377T^{2} + 67.69754T\\ &- 3.66154t^{2} + 273.5638t\\ &- 0.139184Tt - 51040.48033}$$(7) where T is the sintering temperature (°C) and t is the sintering time (h).

Fig. 7 shows the response surfaces for average grain size, hardness and volumetric shrinkage, respectively.

Fig. 7a shows that volumetric shrinkage increases with the increase of both sintering parameters but the temperature has a more significant effect on the response as compared to the time of processing because the most significant variation occurs in the abscissa. Moreover, as can be observed in Fig. 7a, there is a slight enlargement of the zones of the response surface at higher temperature and longer time conditions. This is an indication that the volumetric shrinkage rate reduces at high sintering temperatures and times [72]. On the surface, for average grain size (Fig. 7b), the temperature effect seems to be slightly more significant. There is a narrowing of the zones with increasing temperature and time, contrary to the former case. This is because in the sintering stage, removing of pores occurs before the stage of grain growth and it is associated with a high shrinkage rate [73]. The response surface to the material hardness (Fig. 7c) also indicates a more significant effect of temperature on the changes in material properties. The closer the maximum of hardness value is the combination of temperature and time (within the darker zone), the lower the hardness increasing rate. The hardness shows the nonlinear behavior as a function of sintering parameters. This occurs because the grain that reached the critical grain size (maximum hardness), makes it more difficult to maintain the stabilized tetragonal phase [74]. It is possible to estimate the value for the critical grain size by combination of Fig. 7c with equation 6. Assuming that the center of the darkest ellipse in Fig. 7c represents the value of maximum hardness of 3Y-PSZ ceramics, this point is close to T = 1520 °C for t = 8 h and 30 min. Introducing these values into equation 7, the grain size of 0.509 μm was found. This size is within the range reported in the literature (<0.8) [16, 17], where a critical grain size for 3Y-PSZ ceramics of 0.5 μm was reported. Introducing the parameters of temperature and time for the critical grain size in equation 6, the suggested value of maximum hardness VH = 15.1±2.3 GPa was obtained. According to equation 5, the predicted volumetric shrinkage in these conditions is VS = 53.37±0.08 %. A new sample was sintered at 1520 °C for 8 h and 30 min and its properties were characterized. The sample hardness was VH = 14.6±0.2 GPa, the average grain size was AGS = 0.51±0.13 μm and the volumetric shrinkage was VS = 53.4±1.2 %. These values are in accordance with the range predicted by the CCD method. Moreover, the literature often points out the hardness between 12 GPa to 13 GPa for 3Y-PSZ ceramics [75–77] and critical grain size <0.8 μm [17], what agrees well with our results presented above.