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Sintering of dental porcelain: effect of time and temperature on appearance and porosity
dental materials Dental Materials 18 (2002) 163±173
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Sintering of dental porcelain: effect of time and temperature on appearance and porosity K.C. Cheung a, B.W. Darvell b,* a
b
Dental Technology, The Prince Philip Dental Hospital, Hong Kong Dental Materials Science, Faculty of Dentistry, The University of Hong Kong, Hong Kong Received 27 July 2000; accepted 20 February 2001
Abstract Objective: Mechanical condensation of powder-method dental porcelains can only achieve a limited effectÐthe majority of consolidation and porosity elimination is achieved by sintering. However, there is a surprising lack of information on the process in the literature, and the effects of the two basic conditions of sintering, time and temperature, are very poorly described despite theoretical expectations. The present study was to investigate the effects of these conditions on porosity and to consider its relationship to the recognizable ®ring stages of low and high biscuit, and other aspects of appearance, with a view to schedule recommendations. Methods: The variation of appearance, pore form and percentage porosity with sintering time and temperature was studied for ®ve dental dentine porcelains, two aluminous: Alpha (Vita Zahnfabrik, Bad SaÈckingen, Germany) and Vitadur-N (Vita); and three feldspathic: Omega (Vita), VMK68 (Vita) and Carmen (Esprident, Ispringen, Germany). Disc specimens were sintered for 0±1000 min over 750±11008C in a systematic search pattern to establish limits of acceptable appearance (high biscuit to not quite slumped). Porosity was measured using an image analyser on specimens ®red for sintering times of 24 and 30 s; 1, 3, 6 and 30 min; 1, 5, 10, 15 and 20 h; with sintering temperatures from 750 to 9508C for Carmen and 800±10508C for the others, all with 508C increments. Measurements were made on a ground and polished surface (1 mm diamond), ®ve ®elds on each of ®ve specimens per condition. The percentage porosity, pore count, median pore area and pore size distribution were analyzed. Results: The boundaries of the acceptable appearance areas in maps of sintering temperature vs. sintering time were clearly delineated; analysis showed that they may be related to the activation energy of the diffusive processes occurring during sintering. Minimum porosity was obtained at high temperature and short time, close to but not consistently coincident with the manufacturers' recommendations. There is also a conductivity-related minimum sintering time at high temperatures. The theoretical reduction on prolonging sintering at high temperature was not a general result, and porosity increased markedly in the feldspathic porcelains, particularly VMK-68. Signi®cance: The reduction of porosity of dentine porcelain is much more sensitive to temperature than to time. It is possible systematically to identify optimum conditions using the present approach. Detailed study of the effects of formulation on the sintering process may be made by reference to the activation energy. q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. Keywords: Dental porcelain; Sinter; Porosity; Activation energy
1. Introduction The porosity of dental porcelain needs to be minimized to attain the best optical appearance and strength since pores scatter light, decreasing translucency, and can act as crack initiators with high stress concentration, lowering strength in tension and shear. Control of porosity would therefore appear to be a fundamental consideration in the design and processing of a such a porcelain. * Corresponding author: Dental Materials Science, Prince Philip Dental Hospital, 34 Hospital Road, Hong Kong. Tel: 1852-2859-0303; fax: 18522548-9464. E-mail address: [email protected] (B.W. Darvell).
Mechanical vibration and blotting are commonly used in the ®rst instance to reduce the volume fraction of porosity in a powder-method dental porcelain compact, the number and size of voids remaining depending on the particle size distribution [1,2], although the effect of vibration on the reduction of porosity is limited [3,4]. To enable a better simulation of tooth tissue, dental porcelain restorations are commonly built in layers consisting of different frit formulations. However, vibration tends to cause the porcelain compact to slump (shear thinning of a plastic dilatant system). Thus, surface detail is lost and the porcelain layers may alter in position, spoiling the work. Hence, even with an ideal particle size distribution, the use of vibration must be carefully controlled, and
0109-5641/02/$22.00 + 0.00 q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. PII: S 0109-564 1(01)00038-0
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Table 1 Firing schedules for the porcelains studied, and manufacturer's recommended sintering temperatures and times
Alpha Vitadur-N Omega VMK68 Carmen a b
Manufacturer a
Type b
Preheat time/min
Initial temp./8C
Heating rate/8C min 21
Recommended sintering temp./8C
Recommended sintering time/min
Vita Vita Vita Vita Espr.
A A F F F
6 6 6 6 6
600 600 600 600 400
55 55 55 55 53
960 960 930 930 860
1 1 1 1 1
Vita: Vita Zahnfabrik, Bad SaÈckingen, Germany; Espr.: Esprident, Ispringen, Germany. A: aluminous; F: feldspathic.
substantial porosity remains, which is the cause of the ®ring shrinkage. The bulk of the porosity reduction occurs therefore in the sintering process, the purpose of which is to create as far as possible a non-porous solid. Although sintering is often referred to as a solid-state process, here it is driven by surface tension as a result of partial melting of crystalline phases or suf®cient softening of glassy material [5±7], the pores eventually becoming spherical and contracting in volume. This reduction of pore volume depends on sintering time [6±8], temperature [7,8] and atmosphere [9±12], and the viscosity of the melt [5,7,13]. The viscosity of silicate melts is strongly dependent upon temperature [7] and its chemical composition [14]. Although the reduction of porosity is therefore expected to be promoted by longer sintering time or increasing sintering temperature [15], or both, Hodson [16] and Jones and Wilson [10] reported porosity increase with increase in sintering temperature. Minimum porosities of 0.85% [16], 0.47% [10] and 1.6% [15] have been reported. Without any measurement, Olorunfemi [17], observing three specimens per condition under a microscope, estimated that minimum porosity was obtained by sintering for 1 min longer than the recommendation. McLean and Hughes [18] found that a reasonable correlation was obtained between the results of the methods of apparent speci®c gravity, heavy liquid gradient column and microscopic point counting. The ®rst two methods depend upon the assumptions that the pores are closed and that no chemical changes, and therefore no changes in the density of solid phases, have occurred during ®ring. However, there is variation in the density of dental porcelains depending upon shade and ®ring temperature [19]. Clearly, both time and temperature are important factors in the ®ring of such ceramic materials. However, there seems to have been no systematic analysis of the effects of these factors on the porosity of dental porcelains, and what mention there is of porosity is incomplete or contradictory. In addition, some of the methods that have been used do not permit the characteristics of the porosity, such as shape, number of pores, pore size distribution or other statistics to be analyzed. Porosity is de®ned as the ratio of pore volume, Vp, to the
total (bulk) volume Vs of pore and solid together [20]:
e
Vp : Vp 1 Vs
1
The volume of the closed pores of a sintered dental porcelain cannot be measured directly. However, direct measurement of porosity can be done by a method of lower dimensionality, that is, by working on a plane section of an object, the section area of the porosity Ap behaves proportionately with respect to the solid area, As [20]:
e
Ap : Ap 1 As
2
This approach is unaffected by density, the connectedness or otherwise of the porosity, nor does it require calibration. The present study was thus to investigate the effect of sintering time and temperature on the porosity of powdermethod dental porcelains using area counting. The relationship of porosity to the recognizable ®ring stages known as low and high biscuit or bisque, and other aspects of appearance, could then be considered with a view to schedule recommendations. 2. Materials and methods Two aluminous porcelains and three feldspathic porcelains were studied (Table 1), using the corresponding liquid binders: Modelling Liquid MV (Esprident) for Carmen and Modelling Liquid (Vita) for the others. No instructions for ®ring pressure were given. 2.1. Specimen preparation Circular disc specimens, 8 mm diameter and 2 mm thick, were prepared using the vibration and continuous blotting technique for consolidation in a sheet acrylic mould bolted to a baseplate. Moulds were initially over®lled, specimens being levelled by scraping before being ejected with a ¯atended plunger. Powder compacts showing any signs of distortion, cracking or crumbling were rejected. After drying for one hour at room temperature (to avoid disruption of these thicker than normal compacts), ®ring was done in a
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2.3. Porosity
Fig. 1. Schematic diagram of the form of the ®ring schedule used.
programmable vacuum porcelain furnace (Multimat Mach 2, Dentsply DeTrey, Dreieich, Germany) on a mat (Fibrous Pad Firing Support, Vita). The general form of the ®ring schedule is shown in Fig. 1. The pre-heating times, initial temperatures and heating rates followed the manufacturers' recommendations (Table 1). For all ®rings, the pressure of the ®ring chamber was reduced to 50 hPa before the furnace temperature was increased from the initial temperature. The atmospheric pressure was restored when the sintering temperature was reached. The accuracy of the furnace temperature (claimed to be ^28C) was veri®ed by the silver wire fusion test and measurement of D.C. voltage output produced by the furnace thermocouple. Errors of 11 to 128C were found in the range 800±12008C. These were considered to be insigni®cant for the present purposes. Two series of specimens were ®red: the ®rst to determine the ranges of `acceptable ®ring' based on visual inspection, the second for use in image analysis of the porosity. 2.2. Acceptable ®ring Since in practice the assessment of whether a porcelain has been appropriately ®red is based on a visual inspection (and a suitable quantitative approach is unknown), the sintering time and temperature ranges yielding acceptable results were ®rst determined. The criteria for an acceptable result were set as sharp edges with an egg-shell sheen [16] or glossy appearance [21]. A chalky appearance and rounded edges or slumping are obtained for under- and over-®ring respectively. Using a temperature step size of 108C and roughly logarithmically-spaced sintering times from 0 to 20 h, the upper and lower bounds of the `acceptable' ®ring conditions region were traced staircase fashion using single specimens.
With reference to the results of the `acceptable ®ring' series, for each porcelain a group of ®ve specimens was ®red for sintering times of 24 and 30 s; 1, 3, 6 and 30 min; 1, 5, 10, 15 and 20 h at sintering temperatures ranging from 750 to 9508C for Carmen and 800±10508C for the others, all with 508C increments. Specimens were then embedded as a ®ring schedule group in acrylic thermoplastic resin (Resin 3, Struers, Copenhagen, Denmark) in an embedding press (Duplopress1, Struers). To prevent cracking of specimens under pressure in the embedding process, about 0.2 mm was ®rst removed by wet-grinding by hand to leave a ¯at surface. To assist the retention of ¯at and sharp-edged specimens during subsequent grinding and polishing, the resin mounts were edge-hardened by surrounding specimens to their thickness with a mixture of acrylic resin and porcelain powders in a ratio of 60:40% by bulk volume. The processed blocks were wet-ground to a ¯at and smooth surface on 600 and 1200 grit silicon carbide abrasive papers (Carbimet, Buehler, Lake Bluff, IL, USA) on a polishing machine (Vibromet, Buehler), then polished using 3 and 1 mm diamond polishing pastes (Metadi II, Buehler) in sequence on an ultra-short napped cloth (Texmet, Buehler). Blocks were ultrasonically cleaned in deionized water between stages. The grinding and polishing work was directly checked regularly with an incident light microscope (Universal M, Carl Zeiss, Oberkochen, Germany) at a magni®cation of 50 £ . Individual grinding or polishing steps were repeated until the required result was achieved. The quality of the result was judged from sharp pore edges and freedom from visible scratches. At this stage, the shapes of the pores were classi®ed and recorded as continuous, irregular, or circular. Porosity data were collected for ®ve ®elds without overlap on each of the ®ve specimens of a group using computerbased image analysis. The image was captured by a video camera (TK-1080E, JVC, Tokyo, Japan) through an incident light microscope (Orthoplan-pol, Leitz, Wetzlar, Germany) at a nominal magni®cation of 140 £ . Suf®cient grey-scale contrast was present for automatic measurement without further preparation. Pore size and count determinations were done in software (NIH Image 1.60, Rasband W, National Institute of Health, USA) on a personal computer (Macintosh IIci, Apple Computer, Cupertino CA, USA). The smallest recordable pore area was 7.2 mm 2, and the area of a ®eld 2.84 mm 2. The measurement ®elds were no closer than 0.5 mm from the specimen edge; no visually detectable variation in porosity occurred over the whole area, all ®elds being individually representative. In extreme cases, a measurement might fail because of too long a perimeter or too large a pore area, in which case pore area was determined as the complement after image inversion. The volume fraction porosity was calculated from the pore size distribution data according to Eq. (2) for each of the 25
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®elds as the ratio of pore area to ®eld area and a variety of statistics computed. These data were converted to contour plots in sintering time and temperature (SigmaPlot v6, SPSS, Chicago IL, USA). 3. Results 3.1. Acceptable ®ring There were two patterns of acceptable ranges of sintering times and temperatures, corresponding to whether the porcelain was aluminous or feldspathic, viz. the acceptable temperature range was narrow at a given sintering time in the case of the aluminous porcelains, wide for the feldspathic (Fig. 2). Except at very short times for the feldspathic porcelains, two nearly linear (and nearly parallel) plots were obtained for both the highest and the lowest acceptable sintering temperature against logarithm of sintering time over a substantial range of times. For Omega in particular, the lower bound appears to have a different slope for time below 1 min. A clear minimum possible sintering temperature was present in each case, but while the upper bound for the aluminous porcelains seems to intersect this (at around 1000 min), for the feldspathic porcelain it levelled off some 70±908C higher than this minimum, leaving the acceptable region apparently open on the right. 3.2. Porosity topology The maps of sintering times and temperatures used for the porosity specimens are given in Fig. 3, with the acceptable appearance bounds superimposed for reference. At the lowest time and temperature combinations (black spots) a continuous network of pores was present, the specimens being fragile. This corresponded to the upper limit of what is termed the low-biscuit stage of ®ring, and the pore area determination required image inversion. The lower bound of the `acceptable appearance' corresponded very closely to the upper limit of the presence of irregular pores (open diamonds), i.e. an acceptable ®ring on the basis of appearance corresponded to the presence of spherical porosity. This boundary may be identi®ed as representing the high-biscuit condition. At high enough temperatures, and long enough times, specimens melted suf®ciently to cause them to ball up into a shape incapable of permitting the standardized porosity measurement ®elds (open circles) and no data was collected. However, it is clear from the 24 s data that there is a minimum time required for porosity to become spherical, irrespective of the external appearance. 3.3. Porosity The volume percentage porosity contour plots are shown in Fig. 4, again with the acceptable appearance bounds superimposed for reference. Generally, porosity decreased with increase in sintering temperature at a given time, with
rapid changes occurring between the low- and high-biscuit conditions. However, this was not monotonic. At short sintering times there is evidence of a minimum porosity being attained and then increasing again, although this mostly was only a slight effect it is seen very clearly in the case of VMK-68. The turning point appears to occur at a different temperature for each porcelain. Otherwise, within the acceptable appearance bounds, increasing the sintering temperature had only a slight effect on porosity. However, it is clear that for VMK-68 and Carmen there is a distinct tendency to increase porosity with increasing sintering time at a given temperature. There is no evidence of this effect for the aluminous porcelains. In addition, there is evident a dramatic and rapid decrease in porosity on going from 24 to 30 s sintering corresponding to the change in pore topology noted above. 3.4. Other statistics Similar contour plots were inspected for statistics such as median pore size and pore count. However, since all such statistics were highly correlated no further useful information was extractableÐthe pattern of contours was very similar to that of the volumetric measure in each case. Pore size distributions, cumulative porosity and cumulative count plots were also inspected, but no notable features were identi®ed. 4. Discussion 4.1. Method The microscopic method of porosity determination was found to be a high sensitivity, fast, accurate and reproducible method. It has the advantage of being a direct measurement of porosity, and permits a detailed picture of the characteristics of the porosity because all (visible) individual pores are measured, unconfounded by the dimensions and densities of solid phases. The accuracy is, however, contingent on a time-consuming specimen preparation if errors due to curvature or break-out are to be avoided. In particular, preservation of sharp pore edges required careful selection of grinding and polishing media and schedules. Since the porosity of the green compact is expected to be below 50% [18] values over that for a coherent specimen, i.e. one in the low biscuit stage [22] or initial sintering stage [23], were taken to be indicative of the loss of some particles during grinding, polishing and ultrasonic cleaning, since the particles were only weakly joined at the neck formation stage. If it was worthwhile pursuing more detailed data in this region, in®ltration would be necessary, with, for example, liquid epoxy resin, which is to be cured before grinding. The smallest pore area that could be recorded was 7.2 mm 2, although, course, smaller pores must have been present. Although higher magni®cation could be used, this
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Fig. 2. Results of acceptable ®ring conditions tests. Points on left-most boundary represent zero sintering time. (Time on a logarithmic scale.)
167
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Fig. 3. Porosity topology vs. ®ring conditions. Each point represents conditions for which specimens were examined internally for pore shape. Superimposed is the envelope of acceptable ®ring conditions for the corresponding product (from Fig. 2). (Time on a logarithmic scale.)
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169
Fig. 4. Fitted porosity contours (%) for data obtained under ®ring conditions mapped in Fig. 3. Superimposed is the envelope of acceptable ®ring conditions for the corresponding product (from Fig. 2). (Time on a logarithmic scale.)
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would compromise the measurement as more large pores would be intersected at the boundary of a ®eld, and many more ®elds would be required for a representative sample to be obtained. Informal estimates suggested that the present measurements are in error by missing no more than about 2 or 3% of the value of the recorded porosity. 4.2. Acceptable ®ring The high biscuit [22] or ®nal sintering stage [23] can be clearly identi®ed with the ®rst occurrence of an acceptable appearance, corresponding closely to the point at which spherical pores are formed; the correlation apparent from Fig. 3 is very good. Although there is only a limited effect of temperature on the surface tension of silica [24,25], the viscosity of dental porcelain is temperature dependent [26,27], and the attainment of pore sphericity is thus a matter of exposure-time at temperature, driven by the surface energy minimization. Evidently, the over-®red condition, i.e. exceeding the upper acceptable bound, has no internal correlate, but it is certainly of importance as an observational means of determining when ¯ow is excessive. Taken together with the lower bound observation, this suggests that it is a reasonable ®eld-calibration method that may be easily applied by users, that is, to allow for variation in temperature calibration, heating rates, timing and even porcelain, given that state-of-the-art equipment and conditions are not universally available. Even so, it is to be noted that appearance is a super®cial attribute. The process of sintering, as monitored by the change in appearance, is essentially dependent on diffusive processes, ¯ow driven by the surface tension of the matrix material and limited by its viscosity. Because it is diffusive, the overall process is associated with an activation energy. The acceptable appearance limits represent for a given temperature two separate point estimates of the rate at which sintering is occurring. Thus, writing the general Arrhenius equation as: D Ae2Ea =RT
3
where D is the `diffusivity' or diffusion coef®cient, which is expressed as a rate, i.e. m 2 s 21. It is not certain at present how this needs to be scaled, but since it must have the same dimensions as the pre-exponential factor, A, and since the next step eliminates the scaling from consideration, it is of no consequence for the moment. Ea is then the activation energy, T the absolute temperature, and R the molar gas constant, 8.31451 J K 21 mol 21. Thus, taking logs: log D log A 2
Ea RT
4
from which it is seen that a plot of (arbitrarily scaled) log rate vs. 1/T yields a plot of slope 2Ea/R, whence the activation energy is obtained directly. Applying this to the boundary data extracted from Fig. 2, the plots shown in Fig. 5 were obtained, in which, for example, the good linearity of the
high temperature boundary plots for the aluminous porcelains over three orders of magnitude in time is taken as evidence for the underlying applicability of the model. It is also seen in the case of the aluminous porcelains and for Omega and VMK-68 that there are two clearly separate segments to the low-temperature lines in addition to the abrupt change of slope at the low-temperature boundary. Such slope discontinuities are strongly suggestive that they may be correlated with phase changes such as decompositions (as for example, occurs with feldspar, although the temperature for this is too high at 11508C, 0.70 kK 21) and melting, whether of pure substances or eutectics. However, it is not yet possible to make any such assignment, no obvious candidates being identi®able without details of the formulations. Such assignments are implicitly associated with increasing ease of diffusion, presumably by decreasing the connectivity of the glass network. On the other hand, there is no fundamental reason why a reaction should not increase the connectivity, increasing the activation energy for the process, that is, by changing cation concentration, for example. Suggestions that there might be increases in slope in one or two places in the present data are too weak, however, at present to take this further. To put the estimated activation energies in context, comparison might be made with the Si-O bond energy, which is of the order of 368 kJ mol 21 [28]. Hence the present observations are consistent with bond exchange through anionic attack permitting the ¯ow. It may thus be possible to approach the design of dental porcelains for sintering processes, or glasses for in®ltration techniques, by reference to such activation energy and rate data, the advantage being that the proxy observations of appearance are cheap and easy to obtain, requiring no specialized equipment beyond a suitable furnace. Furthermore, the role of various additives in the formulation can be studied in an objective fashion, with direct reference to the chemistry of the processes being possible. 4.3. Porosity Porosity is expected to decrease with sintering time, and with increasing temperature, as trapped gases escape by diffusion through the matrix, driven by the dissolution occurring under the Laplacian excess bubble pressure according to Henry's Law [29], especially as the viscosity of the matrix decreases. This is indeed seen for the region between the formation of a closed pore system, corresponding roughly to the 30% porosity contour (Figs. 3 and 4), and the lower acceptable appearance bound, that is, where the contours slope down to the right (Fig. 4). However, there is no evidence for this process being dominant in the present data in the acceptable appearance region, i.e. above the lower bound, except for Omega, where a distinct minimum is present at about 9508C and 3 min, and similarly for Carmen at 8508C at about the same time. Otherwise the conclusion is that there is little effect, but with the notable
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171
Fig. 5. Relative sintering rate vs. reciprocal temperature. Points plotted are the outermost `acceptable appearance' points from Fig. 2. The slopes of ®tted line segments represent estimates of the activation energy (kJ mol 21) for the corresponding process. (Reciprocal time on a logarithmic scale.)
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exception of VMK-68. Here, there is a steady increase of porosity with time under all `acceptable appearance' conditions, a pattern that starts to appear for Carmen after about 10 min. Porosity could be increased in two different ways during sintering. Bubbles would tend to increase in size on heating due to expansion towards pressure equilibrium, since the viscosity of the porcelain decreases with temperature [9,10], the pressure opposing the surface tension-drivencontraction. This effect must be traded off kinetically against the dissolution of the gas in the matrix. Nevertheless, the viscosity is still high enough, of the order of 3 MPa.s at 10008C [26], to limit the effect of such pressure expansion and only a slight increase in porosity is obtained, if anything, in most cases. A more probable cause is the generation of a gaseous product by a chemical reaction occurring during sintering [11]. It would seem unlikely that carbonates could be included to any extent in the frit formulation, or form by adsorption from the atmosphere during storage, although this is a testable hypothesis. However, where frits are formed by ®rst thermally-shocking a melt or sintered mass by pouring into water, reactions are possible. For example, it is known that silica glasses hydrolyze in contact with atmospheric moisture, leaving hydroxyl groups on the surface [30]. This reaction would presumably occur more readily in water or water vapour at high temperatureÐas during shocking. Thus, on subsequent heating dehydration might be anticipated, generating gas and thus increased porosity. Again, this is testable and clearly would have implications for the manufacturing process or the composition of the frit. Kaolin, of course, is an already hydrous mineral, Al2O3.2SiO2.2H2O, although its decomposition occurs at 4508C, too low to be relevant here even if it is present, and in any case, for all except Carmen, would have occurred during the pre-heat stage (Table 1) and so not be an issue now. Although the porosity is increased by that process, two points may be made. Firstly, there was no evidence of an increase in the number of pores, merely their total volume. This speaks of a slow rather than abrupt process of decomposition at a speci®c temperature, allowing diffusion to bubbles to occur, the partial pressure of the putative water being greater in the matrix than in the bubble, whose Laplacian excess pressure decreases rapidly as 1/r as they swell. Secondly, this effect was only signi®cant for Omega and Carmen at sintering times that must be considered too long to be relevant to practice. Even so, in the case of VMK68 it appears to be operating even at very short times at all temperatures above about 8508C. This cannot be ignored. A further notable feature is the rapid decrease in porosity on increasing the sintering time from 24 to 30 s for all products, at least for the temperatures tested. It is assumed that the principal controlling factor here is the conductivity of the porcelain, it requiring a certain time for the central region to reach the intended temperature. Since the gradient
change in going from 900 to 10008C, say, is of the order of 10% increase only, timing variation will not be readily detectable in this experiment. The implication nevertheless is of a minimum sintering time if the porcelain is to be heated suf®ciently uniformly for the porosity reduction to be effective overall. 4.4. Standards According to the relevant British Standard [31], the maximum tolerable porosity is 3%, presumably re¯ecting what was then considered a reasonable minimum attainable condition. Thus, the region meeting this requirement (see Fig. 4) and meeting the acceptable appearance criteria in Fig. 2 represents the range of appropriate sintering conditions. In all cases, the 3% boundary is seen to be remarkably lax in comparison with the attainable minimum porosity. It should also be remembered that there are other limitations. Porcelain fused to metal requires, in the ®rst instance, that the alloy solidus is above the ®ring temperature (for example, in current alloy ranges, solidus temperatures from 920 to 12908C at least are known), but in addition to this some leeway is required to avoid creep. This should be taken into account in future work. The manufacturers' recommended ®ring conditions are also shown in Fig. 4 (solid circles). It can be seen that in the case of the aluminous porcelains these ®t the limits set by appearance rather exactly and minimize the porosity for the process as studied. For the feldspathic porcelains the situation is less clear. Neither Omega nor Carmen attained minimum porosity for the recommended conditions, although this could be done easily by ®ring for 3 or 2.5 min, respectively instead of 1. For VMK-68 it would appear that better results could be obtained at a slightly lower temperature (say 9108C) and shorter time (say, 40 s). Whether or not there are other issues to consider in setting the ®ring conditions, it would appear from this that a more detailed appraisal is capable of being made and greater accuracy attained in ®nding an optimum. 5. Conclusions The loss of the connectedness of the porosity of the compact corresponds to the low biscuit stage of sintering, while attainment of pore sphericity, the lower boundary of the acceptable appearance region, may be identi®ed as the high biscuit stage. There is a clear minimum temperature for sintering to acceptable appearance, and above this a wide range of sintering times is available. There is also a minimum sintering time even at high temperatures. However, minimum porosity is obtained only under a very narrow range of conditions, essentially high temperature and short sintering time. Some re®nement of the recommended times and temperatures may be made when a system has been systematically mapped.
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References [1] McGeary RK. Mechanical packing of spherical particles. J Amer Ceram Soc 1961;44(10):513±22. [2] Rasmussen ST, Nagaji-Okumu W, Boenke K, O'Brien WJ. Optimum particle size distribution for reduced sintering shrinkage of a dental porcelain. Dent Mater 1997;13(1):43±50. [3] Gill JR. Methods and results in condensation of dental porcelain. J Amer Dent Assoc 1932;19:1147±54. [4] Evans DB, Barghi N, Malloy CM, Windeler AS. The in¯uence of condensation method on porosity and shade of body porcelain. J Prosthet Dent 1990;63(4):380±9. [5] Mackenzie JK, Shuttleworth R. A phenomenological theory of sintering. Proc Phys Soc B 1949;62:833±52. [6] Herring C. Surface tension as a motivation for sintering, Chap. 8. In: Kingston WE, editor. The physics of powder metallurgy: a symposium held at Bayside, 1st ed. New York: McGraw-Hill, 1951. p. 143±79. [7] Frenkel J. Viscous ¯ow of crystalline bodies under the action of surface tension. J Tech Phys 1945;9(5):385±91. [8] Ivensen VA. Theory and technology of sintering, thermal and chemicothermal treatment processes. Powder Metallurgy (USSR) 1970; 4(88):20±25. [9] Vines RF, Semmelman JO, Lee PW, Fonvielle FP. Mechanisms involved in securing dense, vitri®ed ceramics from preshaped partly crystalline bodies. J Amer Ceram Soc 1958;41(8):304±9. [10] Jones DW, Wilson HJ. Porosity in dental ceramics. Brit Dent J 1975;138:16±21. [11] Rosenkranz V, Frischat GH. Shrinking of a gas bubble in a glass melt under microgravity conditions. In: Material Sciences under Microgravity Results of Spacelab-1: Fifth European Symposium Papers. Schloss Elmau, Germany, 1984. p. 353±7. [12] Wilson HJ, Whitehead FIH. Comparison of some physical properties of dental porcelains. Dent Practit 1967;17(10):350±4. [13] Shaler AJ, Wulff J. Mechanism of sintering. J Indust Eng Chem 1948;40(5):838±42. [14] Bottinga Y, Weill DF. The viscosity of magmatic silicate liquids: a model for calculation. Amer J Sci 1972;272:438±75. [15] Anusavice KJ, Lee RB. Effect of ®ring temperature and water
[16] [17] [18] [19] [20]
[21] [22]
[23] [24] [25]
[26] [27] [28] [29] [30] [31]
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exposure on crack propagation in unglazed porcelain. J Dent Res 1989;68(6):1075±81. Hodson JT. Some physical properties of three dental porcelains. J Prosthet Dent 1959;9(2):325±35. Olorunfemi BO. Sintering ¯aws in Flexoceram inlay porcelain. Afri Dent J 1996;10:9±11. McLean JW, Hughes TH. The reinforcement of dental porcelain with ceramic oxides. Brit Dent J 1965;119(6):251±67. Semmelman JO. A method of measuring porosity of porcelain teeth. J Dent Res 1957;36(6):945±9. Haynes JM. Porosity: characteristics and techniques of investigation. In: Bever MB, editor. Encyclopedia of materials science and engineering, vol. 5. Oxford: Pergamon, 1986. p. 3830±9. The VitaVMK Technique: working instructions. Vita Zahnfabrik, H Rauter, Bad SaÈckingen, Germany [undated]. McLean JW. The science and art of dental ceramics I: the nature of dental ceramics and their clinical use. Chicago: Quintessence, 1979. Coble RL. Sintering crystalline solids: I. Intermediate and ®nal state diffusion models. J Appl Phys 1961;32(5):787±92. Kingery WD. Introduction to ceramics. 2nd ed. New York: Wiley, 1976. Cambier F. Vitri®cation, Chap. 15. In: Brook RJ, editor. Materials science and technology, vol. 17B: processing of ceramics Part II. Weinheim: VCH, 1996. p. 123±44. Asaoka K, Kon M, Kuwayama N. Viscosity of dental porcelains in glass transition range. Dent Mater J 1990;9(2):193±202. Bertolotti RL, Shelby JE. Viscosity of dental porcelain as a function of temperature. J Dent Res 1979;58(10):2001±4. Cotton FA, Wilkinson G. Advanced inorganic chemistry. 5th ed. New York: Wiley, 1988. Pitzer KS, Brewer L. Thermodynamics. 2nd ed. New York: McGrawHill, 1961. Charles RJ. Static fatigue of glass I. J Appl Phys 1958;29(11):1549± 53. BS 5612: Speci®cation for dental porcelains for jacket crowns. British Standards Institution, London, 1978.
www.elsevier.com/locate/dental
Sintering of dental porcelain: effect of time and temperature on appearance and porosity K.C. Cheung a, B.W. Darvell b,* a
b
Dental Technology, The Prince Philip Dental Hospital, Hong Kong Dental Materials Science, Faculty of Dentistry, The University of Hong Kong, Hong Kong Received 27 July 2000; accepted 20 February 2001
Abstract Objective: Mechanical condensation of powder-method dental porcelains can only achieve a limited effectÐthe majority of consolidation and porosity elimination is achieved by sintering. However, there is a surprising lack of information on the process in the literature, and the effects of the two basic conditions of sintering, time and temperature, are very poorly described despite theoretical expectations. The present study was to investigate the effects of these conditions on porosity and to consider its relationship to the recognizable ®ring stages of low and high biscuit, and other aspects of appearance, with a view to schedule recommendations. Methods: The variation of appearance, pore form and percentage porosity with sintering time and temperature was studied for ®ve dental dentine porcelains, two aluminous: Alpha (Vita Zahnfabrik, Bad SaÈckingen, Germany) and Vitadur-N (Vita); and three feldspathic: Omega (Vita), VMK68 (Vita) and Carmen (Esprident, Ispringen, Germany). Disc specimens were sintered for 0±1000 min over 750±11008C in a systematic search pattern to establish limits of acceptable appearance (high biscuit to not quite slumped). Porosity was measured using an image analyser on specimens ®red for sintering times of 24 and 30 s; 1, 3, 6 and 30 min; 1, 5, 10, 15 and 20 h; with sintering temperatures from 750 to 9508C for Carmen and 800±10508C for the others, all with 508C increments. Measurements were made on a ground and polished surface (1 mm diamond), ®ve ®elds on each of ®ve specimens per condition. The percentage porosity, pore count, median pore area and pore size distribution were analyzed. Results: The boundaries of the acceptable appearance areas in maps of sintering temperature vs. sintering time were clearly delineated; analysis showed that they may be related to the activation energy of the diffusive processes occurring during sintering. Minimum porosity was obtained at high temperature and short time, close to but not consistently coincident with the manufacturers' recommendations. There is also a conductivity-related minimum sintering time at high temperatures. The theoretical reduction on prolonging sintering at high temperature was not a general result, and porosity increased markedly in the feldspathic porcelains, particularly VMK-68. Signi®cance: The reduction of porosity of dentine porcelain is much more sensitive to temperature than to time. It is possible systematically to identify optimum conditions using the present approach. Detailed study of the effects of formulation on the sintering process may be made by reference to the activation energy. q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. Keywords: Dental porcelain; Sinter; Porosity; Activation energy
1. Introduction The porosity of dental porcelain needs to be minimized to attain the best optical appearance and strength since pores scatter light, decreasing translucency, and can act as crack initiators with high stress concentration, lowering strength in tension and shear. Control of porosity would therefore appear to be a fundamental consideration in the design and processing of a such a porcelain. * Corresponding author: Dental Materials Science, Prince Philip Dental Hospital, 34 Hospital Road, Hong Kong. Tel: 1852-2859-0303; fax: 18522548-9464. E-mail address: [email protected] (B.W. Darvell).
Mechanical vibration and blotting are commonly used in the ®rst instance to reduce the volume fraction of porosity in a powder-method dental porcelain compact, the number and size of voids remaining depending on the particle size distribution [1,2], although the effect of vibration on the reduction of porosity is limited [3,4]. To enable a better simulation of tooth tissue, dental porcelain restorations are commonly built in layers consisting of different frit formulations. However, vibration tends to cause the porcelain compact to slump (shear thinning of a plastic dilatant system). Thus, surface detail is lost and the porcelain layers may alter in position, spoiling the work. Hence, even with an ideal particle size distribution, the use of vibration must be carefully controlled, and
0109-5641/02/$22.00 + 0.00 q 2002 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. PII: S 0109-564 1(01)00038-0
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Table 1 Firing schedules for the porcelains studied, and manufacturer's recommended sintering temperatures and times
Alpha Vitadur-N Omega VMK68 Carmen a b
Manufacturer a
Type b
Preheat time/min
Initial temp./8C
Heating rate/8C min 21
Recommended sintering temp./8C
Recommended sintering time/min
Vita Vita Vita Vita Espr.
A A F F F
6 6 6 6 6
600 600 600 600 400
55 55 55 55 53
960 960 930 930 860
1 1 1 1 1
Vita: Vita Zahnfabrik, Bad SaÈckingen, Germany; Espr.: Esprident, Ispringen, Germany. A: aluminous; F: feldspathic.
substantial porosity remains, which is the cause of the ®ring shrinkage. The bulk of the porosity reduction occurs therefore in the sintering process, the purpose of which is to create as far as possible a non-porous solid. Although sintering is often referred to as a solid-state process, here it is driven by surface tension as a result of partial melting of crystalline phases or suf®cient softening of glassy material [5±7], the pores eventually becoming spherical and contracting in volume. This reduction of pore volume depends on sintering time [6±8], temperature [7,8] and atmosphere [9±12], and the viscosity of the melt [5,7,13]. The viscosity of silicate melts is strongly dependent upon temperature [7] and its chemical composition [14]. Although the reduction of porosity is therefore expected to be promoted by longer sintering time or increasing sintering temperature [15], or both, Hodson [16] and Jones and Wilson [10] reported porosity increase with increase in sintering temperature. Minimum porosities of 0.85% [16], 0.47% [10] and 1.6% [15] have been reported. Without any measurement, Olorunfemi [17], observing three specimens per condition under a microscope, estimated that minimum porosity was obtained by sintering for 1 min longer than the recommendation. McLean and Hughes [18] found that a reasonable correlation was obtained between the results of the methods of apparent speci®c gravity, heavy liquid gradient column and microscopic point counting. The ®rst two methods depend upon the assumptions that the pores are closed and that no chemical changes, and therefore no changes in the density of solid phases, have occurred during ®ring. However, there is variation in the density of dental porcelains depending upon shade and ®ring temperature [19]. Clearly, both time and temperature are important factors in the ®ring of such ceramic materials. However, there seems to have been no systematic analysis of the effects of these factors on the porosity of dental porcelains, and what mention there is of porosity is incomplete or contradictory. In addition, some of the methods that have been used do not permit the characteristics of the porosity, such as shape, number of pores, pore size distribution or other statistics to be analyzed. Porosity is de®ned as the ratio of pore volume, Vp, to the
total (bulk) volume Vs of pore and solid together [20]:
e
Vp : Vp 1 Vs
1
The volume of the closed pores of a sintered dental porcelain cannot be measured directly. However, direct measurement of porosity can be done by a method of lower dimensionality, that is, by working on a plane section of an object, the section area of the porosity Ap behaves proportionately with respect to the solid area, As [20]:
e
Ap : Ap 1 As
2
This approach is unaffected by density, the connectedness or otherwise of the porosity, nor does it require calibration. The present study was thus to investigate the effect of sintering time and temperature on the porosity of powdermethod dental porcelains using area counting. The relationship of porosity to the recognizable ®ring stages known as low and high biscuit or bisque, and other aspects of appearance, could then be considered with a view to schedule recommendations. 2. Materials and methods Two aluminous porcelains and three feldspathic porcelains were studied (Table 1), using the corresponding liquid binders: Modelling Liquid MV (Esprident) for Carmen and Modelling Liquid (Vita) for the others. No instructions for ®ring pressure were given. 2.1. Specimen preparation Circular disc specimens, 8 mm diameter and 2 mm thick, were prepared using the vibration and continuous blotting technique for consolidation in a sheet acrylic mould bolted to a baseplate. Moulds were initially over®lled, specimens being levelled by scraping before being ejected with a ¯atended plunger. Powder compacts showing any signs of distortion, cracking or crumbling were rejected. After drying for one hour at room temperature (to avoid disruption of these thicker than normal compacts), ®ring was done in a
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165
2.3. Porosity
Fig. 1. Schematic diagram of the form of the ®ring schedule used.
programmable vacuum porcelain furnace (Multimat Mach 2, Dentsply DeTrey, Dreieich, Germany) on a mat (Fibrous Pad Firing Support, Vita). The general form of the ®ring schedule is shown in Fig. 1. The pre-heating times, initial temperatures and heating rates followed the manufacturers' recommendations (Table 1). For all ®rings, the pressure of the ®ring chamber was reduced to 50 hPa before the furnace temperature was increased from the initial temperature. The atmospheric pressure was restored when the sintering temperature was reached. The accuracy of the furnace temperature (claimed to be ^28C) was veri®ed by the silver wire fusion test and measurement of D.C. voltage output produced by the furnace thermocouple. Errors of 11 to 128C were found in the range 800±12008C. These were considered to be insigni®cant for the present purposes. Two series of specimens were ®red: the ®rst to determine the ranges of `acceptable ®ring' based on visual inspection, the second for use in image analysis of the porosity. 2.2. Acceptable ®ring Since in practice the assessment of whether a porcelain has been appropriately ®red is based on a visual inspection (and a suitable quantitative approach is unknown), the sintering time and temperature ranges yielding acceptable results were ®rst determined. The criteria for an acceptable result were set as sharp edges with an egg-shell sheen [16] or glossy appearance [21]. A chalky appearance and rounded edges or slumping are obtained for under- and over-®ring respectively. Using a temperature step size of 108C and roughly logarithmically-spaced sintering times from 0 to 20 h, the upper and lower bounds of the `acceptable' ®ring conditions region were traced staircase fashion using single specimens.
With reference to the results of the `acceptable ®ring' series, for each porcelain a group of ®ve specimens was ®red for sintering times of 24 and 30 s; 1, 3, 6 and 30 min; 1, 5, 10, 15 and 20 h at sintering temperatures ranging from 750 to 9508C for Carmen and 800±10508C for the others, all with 508C increments. Specimens were then embedded as a ®ring schedule group in acrylic thermoplastic resin (Resin 3, Struers, Copenhagen, Denmark) in an embedding press (Duplopress1, Struers). To prevent cracking of specimens under pressure in the embedding process, about 0.2 mm was ®rst removed by wet-grinding by hand to leave a ¯at surface. To assist the retention of ¯at and sharp-edged specimens during subsequent grinding and polishing, the resin mounts were edge-hardened by surrounding specimens to their thickness with a mixture of acrylic resin and porcelain powders in a ratio of 60:40% by bulk volume. The processed blocks were wet-ground to a ¯at and smooth surface on 600 and 1200 grit silicon carbide abrasive papers (Carbimet, Buehler, Lake Bluff, IL, USA) on a polishing machine (Vibromet, Buehler), then polished using 3 and 1 mm diamond polishing pastes (Metadi II, Buehler) in sequence on an ultra-short napped cloth (Texmet, Buehler). Blocks were ultrasonically cleaned in deionized water between stages. The grinding and polishing work was directly checked regularly with an incident light microscope (Universal M, Carl Zeiss, Oberkochen, Germany) at a magni®cation of 50 £ . Individual grinding or polishing steps were repeated until the required result was achieved. The quality of the result was judged from sharp pore edges and freedom from visible scratches. At this stage, the shapes of the pores were classi®ed and recorded as continuous, irregular, or circular. Porosity data were collected for ®ve ®elds without overlap on each of the ®ve specimens of a group using computerbased image analysis. The image was captured by a video camera (TK-1080E, JVC, Tokyo, Japan) through an incident light microscope (Orthoplan-pol, Leitz, Wetzlar, Germany) at a nominal magni®cation of 140 £ . Suf®cient grey-scale contrast was present for automatic measurement without further preparation. Pore size and count determinations were done in software (NIH Image 1.60, Rasband W, National Institute of Health, USA) on a personal computer (Macintosh IIci, Apple Computer, Cupertino CA, USA). The smallest recordable pore area was 7.2 mm 2, and the area of a ®eld 2.84 mm 2. The measurement ®elds were no closer than 0.5 mm from the specimen edge; no visually detectable variation in porosity occurred over the whole area, all ®elds being individually representative. In extreme cases, a measurement might fail because of too long a perimeter or too large a pore area, in which case pore area was determined as the complement after image inversion. The volume fraction porosity was calculated from the pore size distribution data according to Eq. (2) for each of the 25
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®elds as the ratio of pore area to ®eld area and a variety of statistics computed. These data were converted to contour plots in sintering time and temperature (SigmaPlot v6, SPSS, Chicago IL, USA). 3. Results 3.1. Acceptable ®ring There were two patterns of acceptable ranges of sintering times and temperatures, corresponding to whether the porcelain was aluminous or feldspathic, viz. the acceptable temperature range was narrow at a given sintering time in the case of the aluminous porcelains, wide for the feldspathic (Fig. 2). Except at very short times for the feldspathic porcelains, two nearly linear (and nearly parallel) plots were obtained for both the highest and the lowest acceptable sintering temperature against logarithm of sintering time over a substantial range of times. For Omega in particular, the lower bound appears to have a different slope for time below 1 min. A clear minimum possible sintering temperature was present in each case, but while the upper bound for the aluminous porcelains seems to intersect this (at around 1000 min), for the feldspathic porcelain it levelled off some 70±908C higher than this minimum, leaving the acceptable region apparently open on the right. 3.2. Porosity topology The maps of sintering times and temperatures used for the porosity specimens are given in Fig. 3, with the acceptable appearance bounds superimposed for reference. At the lowest time and temperature combinations (black spots) a continuous network of pores was present, the specimens being fragile. This corresponded to the upper limit of what is termed the low-biscuit stage of ®ring, and the pore area determination required image inversion. The lower bound of the `acceptable appearance' corresponded very closely to the upper limit of the presence of irregular pores (open diamonds), i.e. an acceptable ®ring on the basis of appearance corresponded to the presence of spherical porosity. This boundary may be identi®ed as representing the high-biscuit condition. At high enough temperatures, and long enough times, specimens melted suf®ciently to cause them to ball up into a shape incapable of permitting the standardized porosity measurement ®elds (open circles) and no data was collected. However, it is clear from the 24 s data that there is a minimum time required for porosity to become spherical, irrespective of the external appearance. 3.3. Porosity The volume percentage porosity contour plots are shown in Fig. 4, again with the acceptable appearance bounds superimposed for reference. Generally, porosity decreased with increase in sintering temperature at a given time, with
rapid changes occurring between the low- and high-biscuit conditions. However, this was not monotonic. At short sintering times there is evidence of a minimum porosity being attained and then increasing again, although this mostly was only a slight effect it is seen very clearly in the case of VMK-68. The turning point appears to occur at a different temperature for each porcelain. Otherwise, within the acceptable appearance bounds, increasing the sintering temperature had only a slight effect on porosity. However, it is clear that for VMK-68 and Carmen there is a distinct tendency to increase porosity with increasing sintering time at a given temperature. There is no evidence of this effect for the aluminous porcelains. In addition, there is evident a dramatic and rapid decrease in porosity on going from 24 to 30 s sintering corresponding to the change in pore topology noted above. 3.4. Other statistics Similar contour plots were inspected for statistics such as median pore size and pore count. However, since all such statistics were highly correlated no further useful information was extractableÐthe pattern of contours was very similar to that of the volumetric measure in each case. Pore size distributions, cumulative porosity and cumulative count plots were also inspected, but no notable features were identi®ed. 4. Discussion 4.1. Method The microscopic method of porosity determination was found to be a high sensitivity, fast, accurate and reproducible method. It has the advantage of being a direct measurement of porosity, and permits a detailed picture of the characteristics of the porosity because all (visible) individual pores are measured, unconfounded by the dimensions and densities of solid phases. The accuracy is, however, contingent on a time-consuming specimen preparation if errors due to curvature or break-out are to be avoided. In particular, preservation of sharp pore edges required careful selection of grinding and polishing media and schedules. Since the porosity of the green compact is expected to be below 50% [18] values over that for a coherent specimen, i.e. one in the low biscuit stage [22] or initial sintering stage [23], were taken to be indicative of the loss of some particles during grinding, polishing and ultrasonic cleaning, since the particles were only weakly joined at the neck formation stage. If it was worthwhile pursuing more detailed data in this region, in®ltration would be necessary, with, for example, liquid epoxy resin, which is to be cured before grinding. The smallest pore area that could be recorded was 7.2 mm 2, although, course, smaller pores must have been present. Although higher magni®cation could be used, this
K.C. Cheung, B.W. Darvell / Dental Materials 18 (2002) 163±173
Fig. 2. Results of acceptable ®ring conditions tests. Points on left-most boundary represent zero sintering time. (Time on a logarithmic scale.)
167
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Fig. 3. Porosity topology vs. ®ring conditions. Each point represents conditions for which specimens were examined internally for pore shape. Superimposed is the envelope of acceptable ®ring conditions for the corresponding product (from Fig. 2). (Time on a logarithmic scale.)
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169
Fig. 4. Fitted porosity contours (%) for data obtained under ®ring conditions mapped in Fig. 3. Superimposed is the envelope of acceptable ®ring conditions for the corresponding product (from Fig. 2). (Time on a logarithmic scale.)
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would compromise the measurement as more large pores would be intersected at the boundary of a ®eld, and many more ®elds would be required for a representative sample to be obtained. Informal estimates suggested that the present measurements are in error by missing no more than about 2 or 3% of the value of the recorded porosity. 4.2. Acceptable ®ring The high biscuit [22] or ®nal sintering stage [23] can be clearly identi®ed with the ®rst occurrence of an acceptable appearance, corresponding closely to the point at which spherical pores are formed; the correlation apparent from Fig. 3 is very good. Although there is only a limited effect of temperature on the surface tension of silica [24,25], the viscosity of dental porcelain is temperature dependent [26,27], and the attainment of pore sphericity is thus a matter of exposure-time at temperature, driven by the surface energy minimization. Evidently, the over-®red condition, i.e. exceeding the upper acceptable bound, has no internal correlate, but it is certainly of importance as an observational means of determining when ¯ow is excessive. Taken together with the lower bound observation, this suggests that it is a reasonable ®eld-calibration method that may be easily applied by users, that is, to allow for variation in temperature calibration, heating rates, timing and even porcelain, given that state-of-the-art equipment and conditions are not universally available. Even so, it is to be noted that appearance is a super®cial attribute. The process of sintering, as monitored by the change in appearance, is essentially dependent on diffusive processes, ¯ow driven by the surface tension of the matrix material and limited by its viscosity. Because it is diffusive, the overall process is associated with an activation energy. The acceptable appearance limits represent for a given temperature two separate point estimates of the rate at which sintering is occurring. Thus, writing the general Arrhenius equation as: D Ae2Ea =RT
3
where D is the `diffusivity' or diffusion coef®cient, which is expressed as a rate, i.e. m 2 s 21. It is not certain at present how this needs to be scaled, but since it must have the same dimensions as the pre-exponential factor, A, and since the next step eliminates the scaling from consideration, it is of no consequence for the moment. Ea is then the activation energy, T the absolute temperature, and R the molar gas constant, 8.31451 J K 21 mol 21. Thus, taking logs: log D log A 2
Ea RT
4
from which it is seen that a plot of (arbitrarily scaled) log rate vs. 1/T yields a plot of slope 2Ea/R, whence the activation energy is obtained directly. Applying this to the boundary data extracted from Fig. 2, the plots shown in Fig. 5 were obtained, in which, for example, the good linearity of the
high temperature boundary plots for the aluminous porcelains over three orders of magnitude in time is taken as evidence for the underlying applicability of the model. It is also seen in the case of the aluminous porcelains and for Omega and VMK-68 that there are two clearly separate segments to the low-temperature lines in addition to the abrupt change of slope at the low-temperature boundary. Such slope discontinuities are strongly suggestive that they may be correlated with phase changes such as decompositions (as for example, occurs with feldspar, although the temperature for this is too high at 11508C, 0.70 kK 21) and melting, whether of pure substances or eutectics. However, it is not yet possible to make any such assignment, no obvious candidates being identi®able without details of the formulations. Such assignments are implicitly associated with increasing ease of diffusion, presumably by decreasing the connectivity of the glass network. On the other hand, there is no fundamental reason why a reaction should not increase the connectivity, increasing the activation energy for the process, that is, by changing cation concentration, for example. Suggestions that there might be increases in slope in one or two places in the present data are too weak, however, at present to take this further. To put the estimated activation energies in context, comparison might be made with the Si-O bond energy, which is of the order of 368 kJ mol 21 [28]. Hence the present observations are consistent with bond exchange through anionic attack permitting the ¯ow. It may thus be possible to approach the design of dental porcelains for sintering processes, or glasses for in®ltration techniques, by reference to such activation energy and rate data, the advantage being that the proxy observations of appearance are cheap and easy to obtain, requiring no specialized equipment beyond a suitable furnace. Furthermore, the role of various additives in the formulation can be studied in an objective fashion, with direct reference to the chemistry of the processes being possible. 4.3. Porosity Porosity is expected to decrease with sintering time, and with increasing temperature, as trapped gases escape by diffusion through the matrix, driven by the dissolution occurring under the Laplacian excess bubble pressure according to Henry's Law [29], especially as the viscosity of the matrix decreases. This is indeed seen for the region between the formation of a closed pore system, corresponding roughly to the 30% porosity contour (Figs. 3 and 4), and the lower acceptable appearance bound, that is, where the contours slope down to the right (Fig. 4). However, there is no evidence for this process being dominant in the present data in the acceptable appearance region, i.e. above the lower bound, except for Omega, where a distinct minimum is present at about 9508C and 3 min, and similarly for Carmen at 8508C at about the same time. Otherwise the conclusion is that there is little effect, but with the notable
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171
Fig. 5. Relative sintering rate vs. reciprocal temperature. Points plotted are the outermost `acceptable appearance' points from Fig. 2. The slopes of ®tted line segments represent estimates of the activation energy (kJ mol 21) for the corresponding process. (Reciprocal time on a logarithmic scale.)
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exception of VMK-68. Here, there is a steady increase of porosity with time under all `acceptable appearance' conditions, a pattern that starts to appear for Carmen after about 10 min. Porosity could be increased in two different ways during sintering. Bubbles would tend to increase in size on heating due to expansion towards pressure equilibrium, since the viscosity of the porcelain decreases with temperature [9,10], the pressure opposing the surface tension-drivencontraction. This effect must be traded off kinetically against the dissolution of the gas in the matrix. Nevertheless, the viscosity is still high enough, of the order of 3 MPa.s at 10008C [26], to limit the effect of such pressure expansion and only a slight increase in porosity is obtained, if anything, in most cases. A more probable cause is the generation of a gaseous product by a chemical reaction occurring during sintering [11]. It would seem unlikely that carbonates could be included to any extent in the frit formulation, or form by adsorption from the atmosphere during storage, although this is a testable hypothesis. However, where frits are formed by ®rst thermally-shocking a melt or sintered mass by pouring into water, reactions are possible. For example, it is known that silica glasses hydrolyze in contact with atmospheric moisture, leaving hydroxyl groups on the surface [30]. This reaction would presumably occur more readily in water or water vapour at high temperatureÐas during shocking. Thus, on subsequent heating dehydration might be anticipated, generating gas and thus increased porosity. Again, this is testable and clearly would have implications for the manufacturing process or the composition of the frit. Kaolin, of course, is an already hydrous mineral, Al2O3.2SiO2.2H2O, although its decomposition occurs at 4508C, too low to be relevant here even if it is present, and in any case, for all except Carmen, would have occurred during the pre-heat stage (Table 1) and so not be an issue now. Although the porosity is increased by that process, two points may be made. Firstly, there was no evidence of an increase in the number of pores, merely their total volume. This speaks of a slow rather than abrupt process of decomposition at a speci®c temperature, allowing diffusion to bubbles to occur, the partial pressure of the putative water being greater in the matrix than in the bubble, whose Laplacian excess pressure decreases rapidly as 1/r as they swell. Secondly, this effect was only signi®cant for Omega and Carmen at sintering times that must be considered too long to be relevant to practice. Even so, in the case of VMK68 it appears to be operating even at very short times at all temperatures above about 8508C. This cannot be ignored. A further notable feature is the rapid decrease in porosity on increasing the sintering time from 24 to 30 s for all products, at least for the temperatures tested. It is assumed that the principal controlling factor here is the conductivity of the porcelain, it requiring a certain time for the central region to reach the intended temperature. Since the gradient
change in going from 900 to 10008C, say, is of the order of 10% increase only, timing variation will not be readily detectable in this experiment. The implication nevertheless is of a minimum sintering time if the porcelain is to be heated suf®ciently uniformly for the porosity reduction to be effective overall. 4.4. Standards According to the relevant British Standard [31], the maximum tolerable porosity is 3%, presumably re¯ecting what was then considered a reasonable minimum attainable condition. Thus, the region meeting this requirement (see Fig. 4) and meeting the acceptable appearance criteria in Fig. 2 represents the range of appropriate sintering conditions. In all cases, the 3% boundary is seen to be remarkably lax in comparison with the attainable minimum porosity. It should also be remembered that there are other limitations. Porcelain fused to metal requires, in the ®rst instance, that the alloy solidus is above the ®ring temperature (for example, in current alloy ranges, solidus temperatures from 920 to 12908C at least are known), but in addition to this some leeway is required to avoid creep. This should be taken into account in future work. The manufacturers' recommended ®ring conditions are also shown in Fig. 4 (solid circles). It can be seen that in the case of the aluminous porcelains these ®t the limits set by appearance rather exactly and minimize the porosity for the process as studied. For the feldspathic porcelains the situation is less clear. Neither Omega nor Carmen attained minimum porosity for the recommended conditions, although this could be done easily by ®ring for 3 or 2.5 min, respectively instead of 1. For VMK-68 it would appear that better results could be obtained at a slightly lower temperature (say 9108C) and shorter time (say, 40 s). Whether or not there are other issues to consider in setting the ®ring conditions, it would appear from this that a more detailed appraisal is capable of being made and greater accuracy attained in ®nding an optimum. 5. Conclusions The loss of the connectedness of the porosity of the compact corresponds to the low biscuit stage of sintering, while attainment of pore sphericity, the lower boundary of the acceptable appearance region, may be identi®ed as the high biscuit stage. There is a clear minimum temperature for sintering to acceptable appearance, and above this a wide range of sintering times is available. There is also a minimum sintering time even at high temperatures. However, minimum porosity is obtained only under a very narrow range of conditions, essentially high temperature and short sintering time. Some re®nement of the recommended times and temperatures may be made when a system has been systematically mapped.
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References [1] McGeary RK. Mechanical packing of spherical particles. J Amer Ceram Soc 1961;44(10):513±22. [2] Rasmussen ST, Nagaji-Okumu W, Boenke K, O'Brien WJ. Optimum particle size distribution for reduced sintering shrinkage of a dental porcelain. Dent Mater 1997;13(1):43±50. [3] Gill JR. Methods and results in condensation of dental porcelain. J Amer Dent Assoc 1932;19:1147±54. [4] Evans DB, Barghi N, Malloy CM, Windeler AS. The in¯uence of condensation method on porosity and shade of body porcelain. J Prosthet Dent 1990;63(4):380±9. [5] Mackenzie JK, Shuttleworth R. A phenomenological theory of sintering. Proc Phys Soc B 1949;62:833±52. [6] Herring C. Surface tension as a motivation for sintering, Chap. 8. In: Kingston WE, editor. The physics of powder metallurgy: a symposium held at Bayside, 1st ed. New York: McGraw-Hill, 1951. p. 143±79. [7] Frenkel J. Viscous ¯ow of crystalline bodies under the action of surface tension. J Tech Phys 1945;9(5):385±91. [8] Ivensen VA. Theory and technology of sintering, thermal and chemicothermal treatment processes. Powder Metallurgy (USSR) 1970; 4(88):20±25. [9] Vines RF, Semmelman JO, Lee PW, Fonvielle FP. Mechanisms involved in securing dense, vitri®ed ceramics from preshaped partly crystalline bodies. J Amer Ceram Soc 1958;41(8):304±9. [10] Jones DW, Wilson HJ. Porosity in dental ceramics. Brit Dent J 1975;138:16±21. [11] Rosenkranz V, Frischat GH. Shrinking of a gas bubble in a glass melt under microgravity conditions. In: Material Sciences under Microgravity Results of Spacelab-1: Fifth European Symposium Papers. Schloss Elmau, Germany, 1984. p. 353±7. [12] Wilson HJ, Whitehead FIH. Comparison of some physical properties of dental porcelains. Dent Practit 1967;17(10):350±4. [13] Shaler AJ, Wulff J. Mechanism of sintering. J Indust Eng Chem 1948;40(5):838±42. [14] Bottinga Y, Weill DF. The viscosity of magmatic silicate liquids: a model for calculation. Amer J Sci 1972;272:438±75. [15] Anusavice KJ, Lee RB. Effect of ®ring temperature and water
[16] [17] [18] [19] [20]
[21] [22]
[23] [24] [25]
[26] [27] [28] [29] [30] [31]
173
exposure on crack propagation in unglazed porcelain. J Dent Res 1989;68(6):1075±81. Hodson JT. Some physical properties of three dental porcelains. J Prosthet Dent 1959;9(2):325±35. Olorunfemi BO. Sintering ¯aws in Flexoceram inlay porcelain. Afri Dent J 1996;10:9±11. McLean JW, Hughes TH. The reinforcement of dental porcelain with ceramic oxides. Brit Dent J 1965;119(6):251±67. Semmelman JO. A method of measuring porosity of porcelain teeth. J Dent Res 1957;36(6):945±9. Haynes JM. Porosity: characteristics and techniques of investigation. In: Bever MB, editor. Encyclopedia of materials science and engineering, vol. 5. Oxford: Pergamon, 1986. p. 3830±9. The VitaVMK Technique: working instructions. Vita Zahnfabrik, H Rauter, Bad SaÈckingen, Germany [undated]. McLean JW. The science and art of dental ceramics I: the nature of dental ceramics and their clinical use. Chicago: Quintessence, 1979. Coble RL. Sintering crystalline solids: I. Intermediate and ®nal state diffusion models. J Appl Phys 1961;32(5):787±92. Kingery WD. Introduction to ceramics. 2nd ed. New York: Wiley, 1976. Cambier F. Vitri®cation, Chap. 15. In: Brook RJ, editor. Materials science and technology, vol. 17B: processing of ceramics Part II. Weinheim: VCH, 1996. p. 123±44. Asaoka K, Kon M, Kuwayama N. Viscosity of dental porcelains in glass transition range. Dent Mater J 1990;9(2):193±202. Bertolotti RL, Shelby JE. Viscosity of dental porcelain as a function of temperature. J Dent Res 1979;58(10):2001±4. Cotton FA, Wilkinson G. Advanced inorganic chemistry. 5th ed. New York: Wiley, 1988. Pitzer KS, Brewer L. Thermodynamics. 2nd ed. New York: McGrawHill, 1961. Charles RJ. Static fatigue of glass I. J Appl Phys 1958;29(11):1549± 53. BS 5612: Speci®cation for dental porcelains for jacket crowns. British Standards Institution, London, 1978.