Density gradients and the expansion–shrinkage transition during sintering

Acta Materialia 52 (2004) 2057–2066 www.actamat-journals.com

Density gradients and the expansion–shrinkage transition during sintering Peizhen K. Lu, Wenxia Li *, John J. Lannutti Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, OH 43210, USA Received 17 July 2003; received in revised form 22 December 2003; accepted 23 December 2003

Abstract Links between density gradients, internal microstructure and in situ sintering shrinkage in compacts formed from spray-dried alumina powder are established using a laser dilatometer and X-ray computed tomography (CT). All samples initially have the same overall density but different internal structures. An expansion–shrinkage transition occurs between 1000 and 1100 °C. Forming conditions appear to play a role: the samples compacted at 25% RH (Relative Humidity) shrank more rapidly than those compacted at 98% RH below 1300 °C; above 1300 °C, however, the specimen formed at 98% RH shrank more rapidly. CT examination following sintering showed both preservation and exaggeration of the original density gradients. Microstructural connectivity apparently contributes to both the observed macroscopic expansion and the onset of shrinkage. Discrete element modeling clearly suggests that the effective ÔtransmissionÕ of particle-level behavior to the macroscopic level is controlled both by internal agglomerate density and initial agglomerate bonding. Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Firing; SEM; Mesostructure; Simulation; Laser dilatometry; DEM

1. Introduction Inorganic components formed by the compaction of powder undergo the majority of their sintering shrinkage in the intermediate ÔstagesÕ [1,2] of thermally driven sintering; logically, then, dimensionality should be most sensitive to microstructural factors during this period. Intermediate/initial stage sintering models typically focus only on the global effects of particle surface area, surface or bulk diffusion and particle/pore size on shrinkage [3–7]. Density gradients, a universal result of compaction processes, should be included. In addition, ultimate inorganic particles are deliberately agglomerated by spray-drying to both enhance their ability to flow and minimize process variability. Therefore, the contribution (if any) of agglomeration also needs to be established. Binder distribution in these agglomerates is inhomogeneous; a binder-rich shell [8] can exist at the outer surface and increases in thickness with increasing *

Corresponding author. Tel.: +1-6146883182; fax: +1-6142921537. E-mail address: [email protected] (W. Li).

binder content [8–10]. The physical state of these binders is sometimes affected by the absorption of ambient moisture [11]. Higher compact densities can be obtained at high humidities [12] at the cost of decreased uniformity [13]. The initial microstructural features of green compacts formed from these binder-influenced agglomerates should govern both microstructural development and dimensional behavior during sintering. Inherently multiscalar sub-micron particles are present within much larger agglomerates; this structure undergoes localized shrinkage which is not always directly transmitted to the macro-scale [14,15]. It is known that individual agglomerates more easily sinter to high densities while the pores between agglomerates require considerably greater thermal exposure to achieve elimination [14–16]. Internal connectivity between particles and primary grains must necessarily play a dominant role [17,18] in determining the final exterior dimensions. One of the main technical challenges facing this field involves the accurate prediction of the macroscopic shrinkage of these multi-scalar structures following

1359-6454/$30.00 Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.12.044

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various stages of sintering. Density gradients at the microscopic level may or may not fully control net macroscopic dimensional variations. Over the past few years [16,19–21], a non-contact laser dilatometer has been used to establish the effects of density variation on external dimensions post-compaction. SEM can be used to connect these changes to specific structural features that developed during compaction [12,13]. In addition, our previous studies [22,23] demonstrated that CT (Xray computed tomography) can be used to provide critical quantification of density gradients/distribution. Discrete element modeling (DEM), employed previously to examine the effects of filling [24,25], the early stages of compaction [24,25] and particle modulus [26] is used to provide conceptual connections between these variations, agglomerate packing and thermal expansion. This combination of investigational tools – CT, SEM, laser dilatometry and DEM – are used to examine a set of samples that initially have the same overall density but different internal structures. This approach provides answers to the general question: ‘‘what is the effect of agglomerate-level factors on dimensional change independent of overall initial density?’’ Subsequent internal evolution is then connected to macroscopic expansion/ shrinkage observed in situ. Local differences in the ÔtransmissionÕ of particle-level events and internal density variations to the surface are quantified and rationalized in terms of the agglomerate mesostructure. The observed phenomena occur within a system typifying classical solid-state sintering and the subsequent interpretations should be applicable to a wide range of materials formed by the compaction of spray-dried agglomerates.

2. Materials and methods Calcined A16-SG alumina powder (Alcoa Chemicals, Pittsburgh, PA) having an average particle size of 0.7 lm was spray-dried (Model DL-41, Yamato, Orangeburg, NY) courtesy of Nalco Chemical Co. (Naperville, IL) with 1 wt.% PEG and 1 wt.% PVA (both from Air Products, Inc. Allentown, PA) added as binder. The Mw Õs of the PVA and PEG are 31,000–50,000 and 3400, respectively. The average agglomerate size was approximately 35 lm. The powder was weighed under ambient conditions and placed into a humidity chamber (Model THJr SPL, Tenney Environmental, Union, NJ) at specified humidities for 24 h. 25% and 98% RH (relative humidity) were chosen for equilibration prior to compaction to generate ÔhardÕ and ÔsoftÕ particles having industrially relevant elasto-plastic properties. The die used consisted of 12.85 mm diameter hardened steel tubes and rams. All samples were uniaxially compacted (Model 1322, Instron Corp., Canton, MA) to 50% of the theoretical density of alumina and a length/diameter

ratio of 2.0 by calculating the desired sample height and controlling the displacement of the upper punch. The pressing speed was held constant at 1 mm/s. 2.1. Laser dilatometry The use of a transmission laser to monitor compact dimensions during sintering (as opposed to post-sintering [16]) provides a number of advantages. Non-contact measurement overcomes two problems intrinsic to LVDT-based dilatometry: (1) a contact force must be applied and (2) dimensional change can only be reported as a single value measurement that does not describe the differential shape change of an area [19]. A positioning motor (Model Zeta 6104, Parker Hannifin Corp., Wadsworth, OH) was used to control sample vertical position within the horizontal beam. By connecting this with the laser micrometer output, compact dimensions at different positions can be accurately measured. For the He-Ne laser, the repeatability of the system is listed as 0.0005 mm. More detailed descriptions of the technique have been published previously [19]. All the samples were positioned so that the high density (HD) zone was oriented upwards to reduce setter drag effects [16]. The samples were heated in air in the laser dilatometer at 5 °C/min to 400 °C and held there for 1 h to complete binder removal. They were then heated to 1400 °C at 5 °C/min and held there for another hour. The dimensions were measured by the laser dilatometer at specific temperatures and recorded by a computer. 2.2. X-ray computed tomography The CT facility used in our study is a secondgeneration ARACOR scanner functioning on a translate-rotate premise. By rotating the sample between the X-ray source and the detector, the attenuation of a finely collimated fan beam is reconstructed using mathematical algorithms into a two-dimensional map that can be converted into a quantitative density distribution [22,23]. From its first use to examine compaction by Sawicka and Palmer [27], we have since utilized this experimental tool rather heavily [13,14,16,19,22,23,25]. As before, SEM is used to compare structural features within specific zones of density to their subsequent thermal evolution at 500, 900, and 1100 °C. The compacts were first fractured along the longitudinal direction. These fragments were then fractured in diametral cross section at positions corresponding to the HD and LD zones and mounted on aluminum stubs covered with conductive carbon adhesive prior to gold coating. 2.3. Discrete element modeling We have previously employed discrete element modeling to examine key concepts inherent to compaction

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3. Results 3.1. Laser dilatometry: non-uniform expansion and the expansion–shrinkage transition

Dimensional change (d-d0)*100/d0

During heating, only thermal expansion was observed below 1000 °C (Fig. 1). Samples from ÔsoftÕ (pre-conditioned at 25% RH) or ÔhardÕ agglomerates (pre-conditioned at 98% RH) exhibited similar behavior: the higher the initial zone density, the greater the thermal expansion of that zone. Generally, the samples composed of hard agglomerates displayed greater thermal expansion than those made up of soft agglomerates. Both samples display dimensional decreases between 1000 and 1100 °C (Fig. 1). The hard agglomerate sample exhibits a more rapid transition to shrinkage than the soft agglomerate sample. The other unique observation is that all samples now exhibit uniform dimensional change between the HD and the LD zones following this

98%RH

500˚C

700˚C

1000˚C

1100˚C

25%RH

500˚C

700˚C

1000˚C

1100˚C

0.0 -0.12 -1.0 -0.13 -2.0 -0.14 -3.0

-0.15

-4.0

-5.0 0.0

-0.16

Absolute dimensional change (mm)

-0.11

Dimensional change (d-d0)*100/d0

[24,26]. In this work, we use it to generate conceptual connections between agglomerate-level factors, localized density and thermal expansion. As before [24], a cylindrical die is created and filled with particles to a specific desired density. Agglomerates are then created by removing the particles outside the boundaries of spherical assemblies within this die. In an extension of the capabilities of the technique, we simulated dimensional changes caused by thermal expansion by increasing the radii of the ultimate particles making up these ÔagglomeratesÕ to evaluate the potential transmission of particle-level events (expansion) up through the density gradients (quantified by CT) to the macroscopic level (quantified by laser dilatometry).

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-0.17 4.0

8.0

12.0

16.0

20.0

24.0

Distance from LD end (mm) 25% RH 98% RH

1100˚C 1100˚C

1200˚C 1200˚C

1300˚C 1300˚C

Fig. 2. Dimensional change (the minus sign represents shrinkage) along the longitudinal direction. Faster shrinkage occurs in the HD zone rather than in the LD zone. The disconnected marks represent the relative shrinkage. The continuous line illustrates the absolute dimensional change between the green and the 1200 °C state for the soft agglomerate sample.

transition (1100 °C) even though the samples are now larger than their initial states (Fig. 1). Following the expansion–shrinkage transition, densification continues between 1100 and 1300 °C for all samples (Fig. 2). The HD zone now shrinks faster than the LD zone; the hard agglomerate sample appears to undergo greater overall shrinkage. At higher temperatures (1300–1400 °C), these shrinkage trends are reversed in the soft agglomerate samples (Table 1). The HD zone densification rate is slightly less than that of the LD zone. The LD zone experiences greater shrinkage after 1 h of sintering at 1400 °C. For the hard agglomerate sample, the shrinkage of the LD zone is smaller than that of the HD zone. The sample formed from hard agglomerates exhibits both a smaller rate of shrinkage and less total shrinkage (Table 1).

0.55 0.50

3.2. X-ray CT: density distributions following compaction and sintering

0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.0

4.0

8.0 12.0 16.0 Distance from LD end (mm)

20.0

24.0

Fig. 1. Thermal expansion of both samples at different temperatures. Each data point is the average of three different specimens and all three exhibit the same behavior. The HD zone expands more rapidly than the LD zone. The 1000 °C line of sample formed from hard agglomerates displays the onset of shrinkage in the HD zone. d: diameter at an elevated temperature; d0 : diameter at room temperature.

As expected, both compaction conditions lead to density gradients (Fig. 3). The sample formed from soft agglomerates shows larger density gradients from the HD to the LD end as observed previously [13]. The linear cross-sectional density is similar in both the HD zones but varies significantly between the LD zones. The sample formed from hard agglomerates exhibits a higher density near the fixed punch. However, the overall density distribution of the sample formed from hard agglomerates is slightly wider as shown in Fig. 4 due to a larger lower density ÔtailÕ. CT examination of the sintered samples provides information regarding internal uniformity following these

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Table 1 Dimensional variation at high temperature and after cooling following different initial compaction conditions Sample

HD

LD

Shrinkage (%)

Absolute shrinkage (mm)

Shrinkage (%)

Absolute shrinkage (mm)

98% RH

1400 °C, 1 h Post-sintering

12.92 14.12

1.66 1.82

13.18 14.39

1.70 1.85

25% RH

1400 °C, 1 h Post-sintering

12.66 13.90

1.60 1.78

12.45 13.86

1.63 1.79

Thermal shrinkage during cooling boosts the absolute final shrinkage.

0.83 98%RH

Relative density (%)

0.81 0.79 25%RH

0.77 0.75 0.73 0.71 0.69 0.67 0.0

4.0

8.0

12.0

16.0

20.0

24.0

Distance from LD end (mm) Fig. 3. Density variations along the length of the samples resulting from different initial humidity conditions. In these CT images, densities are in descending order of white, red, yellow, and green [13,22,23]. As before, density increases almost linearly [16] from the fixed to the moving punch. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Average cross section density values for samples compacted under different levels of relative humidity after sintering.

0.07

Normalized Frequency

0.10 25%RH

0.08

98%RH 0.06 0.04

0.05

25%RH 98% RH

0.04 0.03 0.02 0.01 0 0.55

0.02 0.00 0.35

Normalized Frequency

0.06

0.65

0.75

0.85

0.95

Fraction Theoretical Density (%)

0.40

0.45 0.50 0.55 0.60 Fraction Theoretical Density

0.65

Fig. 4. Green compact density distribution following compaction at 25% and 98% RH.

extended thermal exposures. The average value of cross sectional density along the length of the sample (Fig. 5) and the density distribution (Fig. 6) show that the initial density differences do not decrease but continue to widen. The sample formed from soft agglomerates does not experience an overall improvement in uniformity versus the green state in spite of the greater shrinkage experienced by the LD zone. However, the sample formed from soft agglomerates shows a higher sintered

Fig. 6. Widened density distribution following sintering for samples produced under different initial compaction conditions.

density than the sample formed from hard agglomerates in spite of its relatively lower initial density (Fig. 3). After sintering, the average overall densities are approximately 77% and 75% for the specimens formed from the soft and hard agglomerates, respectively. 3.3. Scanning electron microscopy In the green state, SEM shows that the HD zone (Figs. 7(a) and (b)) exhibits a more dense agglomeratelevel (as opposed to ultimate particle-level) packing than

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the corresponding LD zone (Figs. 7(c) and (d)) [13]. A larger degree of agglomerate–agglomerate contact area exists in the HD zones. The sample formed from soft agglomerates (Fig. 7(a)) shows that green state fracture primarily occurs in a trans-agglomerate mode in the HD zones, indicating that agglomerate–agglomerate joining is stronger than particle–particle bonding inside the agglomerate. In contrast, the agglomerates in the LD zone are relatively less deformed. Much larger interagglomerate pores exist in this zone as a result of the

Fig. 7. SEM micrographs taken from zones of different density. (a) 98% RH, HD zone, (b) 25% RH, HD zone, (c) 98% RH, LD zone, and (d) 25% RH, LD zone.

Fig. 8. SEM micrographs of HD zone fracture surfaces showing changes in inter-agglomerate bonding as temperature increases: (a) 500 °C, 98% RH; (b) 500 °C, 25% RH; (c) 900 °C, 98% RH; (d) 900 °C, 25% RH; (e) 1100 °C, 98% RH; and (f) 1100 °C, 25% RH. The differences in fracture mode between the specimens formed from soft and hard agglomerates are fairly obvious.

Fig. 9. Changes in the morphology of ultimate particles within a compact formed from soft agglomerates following exposure to: (a) 500, (b) 900 and (c) 1100 °C.

P.K. Lu et al. / Acta Materialia 52 (2004) 2057–2066 0.8 HD zone 0.6 Shrinkage (%)

relatively loose agglomerate packing; the primary absorption of compaction pressure is by the agglomerates in the HD zone. At 500 °C, SEM of the HD zone fracture of compacted soft agglomerates (Fig. 8(a)) reveals an interesting phenomenon: more fracture now occurs along agglomerate interfaces rather than through the agglomerates. For the hard agglomerate sample, such inter-agglomerate fracture (Fig. 8(b)) is common. The soft agglomerate sample exhibits inter-agglomerate fracture surfaces that are slightly rougher (Figs. 8(a) and (b)) resulting from better inter-agglomerate joining during compaction. At 900 °C, both samples show increasing levels of trans-agglomerate fracture driven by sintering (Figs. 8(c) and (d)). The ultimate particle level structure was also examined over the same thermal range. Ultimate particle growth and necking are clearly visible (Fig. 9) coinciding with the observed thermal expansion. Following the 1100 °C exposure, SEM detects two levels of distinct microstructural change: increasing inter-agglomerate joining (visible as an increase in transagglomerate fracture in Figs. 8(e) and (f)) and the absorption of nanometer-sized particles and minimization of surface area (Fig. 9(c)). The degree of trans-agglomerate fracture appears more severe in the soft agglomerate sample.

LD zone classical

0.4 0.2 0 -0.2

pre-sintering

-0.4 -0.6 0

200

(a)

400

600

800

1000

1200

Temperature (˚C) 2

intermediate

initial

0 -2 Shrinkage (%)

2062

-4 HD zone

-6

LD zone -8

classical

-10 -12 950

(b)

1050

1150

1250

1350

1450

Temperature (˚C)

Fig. 10. Schematic illustration of the expansion–shrinkage behavior versus initial zone density and temperature. (a) Low temperature portion and (b) high temperature portion.

4. Discussion First and foremost, it is necessary to point out that our work concludes near the end of the intermediate stage of sintering. This choice is deliberate as this marks the end of high-rate shrinkage during which deviation away from net shape is most likely. This is a key difference between our work and investigations that focus only on net shrinkage at/near the end of final stage sintering. Instead of a single sintering curve that attempts to completely characterize overall dimensional change, differential expansion/shrinkage of the HD and LD zones, a logical consequence of the presence of density gradients, was discovered (Fig. 10). This is a novel observation illustrating the value of both laser dilatometry and the importance of detecting/quantifying density gradients. 4.1. Expansion in the presence of density gradients Upon heating, all specimens exhibit only expansion below 1000 °C (Fig. 10). At no point along the length of the compact is shrinkage evident until the sintering temperature exceeds 1000 °C (Figs. 1 and 2). Dorey et al [7] recently observed similar behavior and proved that it is not an effect of residual stress release. We have observed similar behavior for nanozirconia compacts below 400 °C [20].

Internally, there are clear variations in the degree of joining within the HD and LD zones. Different elastoplastic agglomerate properties can result in variable compaction/densification behavior for individual agglomerates at the local scale [14]. At the level of the ultimate particles, HD zone agglomerates possess more dense packing due to locally higher compaction pressures. Not surprisingly, this leads to variations in the effective ÔtransmissionÕ of ultimate particle expansion to the macroscopic scale; the body is inhomogeneous not only from the macroscopic standpoint of HD and LD zones but also at the level of the agglomerates within these zones. Macroscopic expansion associated with the LD zone must be moderated by relatively larger amounts of inter-particle and inter-agglomerate porosity. Stated differently, the inter-particle and inter-agglomerate connectivity is poorer in the LD zone and this decreases macroscopic expansion. Due to the complex relationship between agglomerate packing and the coexistence of inter- and intra-agglomerate pores, discrete element modeling was utilized to better illustrate how thermal expansion transfers to the exterior of the agglomerates and, eventually, to the surface of the compact. The simulation in Fig. 11 plots the overall linear thermal expansion of a simple threeagglomerate chain versus agglomerate density. Initial

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Fig. 11. Simulation of the effect of initial agglomerate density on the thermal expansion of a chain of agglomerates having identical, constant contact configurations. Each agglomerate is composed of approximately 220 particles and each particle is then expanded to 105% of the initial radius. The overall dimensional change of the chain is then plotted to approximate the expansion of a compact.

agglomerate density appears to be critical as expansion is initiated only once a critical value (
57% in this simulation) is reached. At lower densities, no macroscopic thermal expansion occurs as the particles simply expand into the empty space within each agglomerate. After a threshold density is reached, overall thermal expansion increases as the initial density increases. If we instead hold the agglomerate density constant and vary the center-to-center distance of the agglomerates (i.e., agglomerate connectivity) for the same ultimate particle expansion, the ÔexternalÕ dimensions increase linearly with increased connectivity (Fig. 12). It is reasonable to conclude that agglomerate connectivity controls overall thermal expansion. Better connectivity produces larger rates of thermal expansion. Although more sophisticated DEM will undoubtedly be conducted, these simple simulations provide fundamental insight into how elasto-plastic agglomerate characteristics during compaction at room temperature

Fig. 12. Simulation of the effect of agglomerate connectivity on thermal expansion at a constant agglomerate density. At various center-tocenter agglomerate distances, each particle is expanded to 105% of the initial radius and the overall dimensional change of the chain approximates the expansion of a compact.

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can influence sintering well after the binder has been removed. The obvious consequence is that the LD zone consistently shows less thermal expansion than the corresponding HD zone (Figs. 1 and 2) regardless of the compaction condition. The overall expansion rate of the hard agglomerate sample is greater than that of the soft agglomerate sample due to its more uniform density (Fig. 3) resulting from the more efficient transmission of compaction force [14,16]. Internal agglomerate density cannot be overlooked, however. The soft agglomerate sample shows less thermal expansion than the corresponding hard agglomerate sample at the same HD zone value suggesting that the 25% RH sample has higher agglomerate densities, consistent with previous experimental observations [23].

4.2. Expansion–shrinkage transition and the initial stage of sintering The detection of subtle dimensional anisotropies during heating (Fig. 10) has significant practical implications. The ability to track the thermal behavior of a compact, especially the detection of such spatially and temporally variable transitions, is crucial in predicting the final shape and dimensions of any green body. Moreover, this suggests that specific changes in green microstructure will be necessary to achieve a targeted dimensional behavior such as adherence to net shape. The observed transition from expansion to shrinkage is important in that the existing structure must display self-consistent behavior on both sides of the transition. Structural features that lead to macroscopic expansion at low temperatures should also be influential in triggering shrinkage. Likely neck formation at relatively low temperatures [28–31] corresponds to the observed macroscopic change suggesting that, taken globally, the formation of small sinter necks [32,33] overcomes the continuing thermal expansion of the particles. The subsequent macroscopic result is a dimensional decrease due to repacking [34]. Since the hard agglomerate sample HD zone is more likely to exhibit higher agglomerate densities and more agglomerate contacts, its transition to shrinkage is faster. Surface area minimization polygonizes and smoothes ultimate particles (Fig. 9). Small ÔspacerÕ particles between grains are consumed via grain growth providing additional shrinkage. These nanoscaled features constitute contact points that could inhibit smaller center-to-center distances between relatively large particles [24]. There is little difference, energetically, between the surface smoothing of a nanometer-sized peak and the surface consumption of a nanometer-sized particle. Via the elimination of pinning fine particles [24], surface diffusion can result in densification in real systems containing a polydisperse range of particle sizes.

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During this portion of the shrinkage curve, more densely packed, better-connected agglomerates appear to undergo considerably greater shrinkage (Fig. 10). In a reassuring display of self-consistency, those zones that were expanding more rapidly now reverse their behavior and contract more rapidly. Thus, net dimensional change along the length of the sample following the expansion–shrinkage transition is also reversed and all samples trend back toward the ideal ‘‘net shape’’ for the body. 4.3. Shrinkage rate in intermediate sintering and barriers to full density The shrinkage of the sample formed from soft agglomerates between 1100 and 1400 °C differs from the classic curve [1] (Fig. 10) due to the existence of density gradients. The HD zone initially shrinks more rapidly but this slows while the LD zone initially shrinks more slowly and then accelerates. For the sample formed from hard agglomerates, the HD zone shrinks more rapidly all the way through to the final state. Although the hard agglomerate sample shrinks more quickly than the soft agglomerate sample between 1100 and 1300 °C, its shrinkage rate decreases above 1300 °C. The final overall shrinkage/density is smaller than that of the soft agglomerate sample after 1h at 1400 °C. This can again be explained in terms of the microstructure of the agglomerates and their connectivity. 4.3.1. Preferential HD zone initial shrinkage In previous studies of spray-dried powder compacts [15,29,35], sintering has been assumed to occur in two steps specific to intra- and inter-agglomerate regions. Intra-agglomerate particle packing units densify and undergo grain growth as sintering initiates. In contrast, the inter-agglomerate pores remain unchanged or possibly enlarge as sintering continues [14,36–39]. That sintering shrinkage in spray-dried powder compacts is related to both the individual particle packing units and the connections between these units has long been recognized [3,4]. However, the associated connection to spatially varying compact density has only recently been proven [16]. Initially, the HD zone contains denser agglomerate packing relative to the LD zone (Fig. 7). HD zone interagglomerate boundaries are more likely to contain pores having coordination numbers less than a critical value [40]. In the extreme case, these pores can be easily eliminated as intra-agglomerate pores. Increasing transagglomerate fracture (Fig. 8) versus heating provides evidence supporting this conclusion. When both intraagglomerate and, potentially, inter-agglomerate sintering are taken into account, the higher compressive sintering forces in the HD zone promote additional inter-agglomerate shrinkage and larger overall shrink-

age. In the LD zone, on the other hand, the agglomerates are more constrained in their effects on their neighbors by the larger amount of free space separating them. As an individual agglomerate sinters, its shrinkage cannot be efficiently transferred into macroscopic shrinkage. As a result, the HD zone shrinks faster even though the ultimate particles are identical in both zones. 4.3.2. Trend reversal at elevated temperatures As sintering proceeds toward the end of intermediate stage, the HD zone of the soft agglomerate sample now shrinks more slowly than the LD zone (Table 1). At this point, the HD zone inter-agglomerate porosity could experience less densification as the microstructure approaches the densely sintered state. In the LD zone, however, individual agglomerate pores can reassume a coordination number smaller than the critical value and undergo shrinkage [40]. Eventually, the overall shrinkage trend in the longitudinal direction reverses to finally reflect the initial distribution of matter: the LD zone now shrinks more rapidly than the HD zone. Due to its greater porosity, however, the total shrinkage of the LD zone will be determined by how easily the porosity can be eliminated. A similar line of reasoning explains the sintering behavior above 1300 °C: the hard agglomerate sample shrinks more slowly than the soft agglomerate sample due to the higher initial overall density and greater number of contacts within or between the agglomerates. However, these more rigid, less deformable agglomerates should tend to fracture rather than deform during compaction [13,41,42], resulting in more non-uniform density distributions within each agglomerate. The smaller density ÔtailÕ in Fig. 4 and the cracks observed in the hard agglomerates under SEM (Figs. 7(b) and (d)) suggest the existence of these low density locations. Weaker inter-agglomerate bonding is suggested by the larger percentage of trans-agglomerate fracture in the soft agglomerate sample (Fig. 8). Less favorable agglomerate bonding or more internal agglomerate fractures could result in either large gaps along the interagglomerate interface or within the agglomerates themselves [14,42] as sintering proceeds. As this largerscale porosity begins to influence overall shrinkage at high temperatures, the hard agglomerate sample exhibits less favorable intra-and inter-agglomerate densification at the same sintering temperatures. 4.3.3. Density distribution widening As was readily observed, intra-agglomerate particles sinter preferentially while inter-agglomerate sintering is controlled by the initial degree of association of neighboring elements. In these L=D ¼ 2:0 compacts, densification is typically more efficient in the HD zone as has been observed previously [13]. In the LD zone, far less

P.K. Lu et al. / Acta Materialia 52 (2004) 2057–2066

inter-agglomerate contact exists. The net result is an increase in the width of the density distribution. To better understand the effects of these agglomerate characteristics we can view any compact as an array of agglomerates connected via highly variable contacts. Each agglomerate sinters internally while the interagglomerate sintering response depends on the ÔstrengthÕ of the contact. At inter-agglomerate boundaries having pore coordination numbers less than a critical value, ultimate particles become better connected and provide more contact area as sintering continues. Since the driving force for densification appears only at the particle contacts, these new contacts introduce additional driving forces. This trend continues until the inter-agglomerate boundary attains a configuration similar to that found within an agglomerate. LD zone shrinkage is slower and continues for a longer period due to its lower initial compacted density or the existence of substantially more porous inter-agglomerate boundaries. Interagglomerate ÔsinterabilityÕ decreases from the HD to the LD zone. These HD and LD zone differences are substantial and the larger pores and more loosely packed structure of the LD zone are simply not eliminated as quickly [23] and overall differences in density become exaggerated. The persistence of the LD zone (Fig. 6) provides evidence of this sintering barrier.

5. Conclusions The dimensional behavior of dry-pressed compacts during sintering reflects both the characteristics of the initial agglomerates and their response to compaction. Governing characteristics include the relative magnitude of the HD and LD zones, the internal density/connectivity of the agglomerates, and the particle level microstructure. 1. All of these alumina samples exhibit only expansion prior to 1100 °C. The higher the initial density, the greater the corresponding expansion. At temperatures around 1100 °C, net expansion finally ceases and net sintering shrinkage begins. 2. The same HD zones that more efficiently transferred particle-level expansion to macroscopic growth now more efficiently transfer sintering driven particle-level shrinkage to the macroscopic level. The sample then trends back toward uniform dimensions due to this non-uniform dimensional interplay. 3. The samples preserve and exaggerate their original density gradients following sintering at 1400 °C. 4. Both internal density variations and the degree of connection between the agglomerates control expansion, the onset of shrinkage and the subsequent shrinkage rate. HD zone shrinkage slows likely depending on the initial connectivity along the inter-agglomerate boundary. Final shrinkage is a combined

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result of both the local structure of the primary particles and the agglomerates in which they exist. Acknowledgements We would like to thank the Edward Orton Jr. Ceramic Foundation and the Edison Materials Technology Center (EMTEC) for the financial support of this project. We also express our appreciation to the Wright Laboratory/Materials Directorate at Wright-Patterson Air Force Base for generous donations of CT scanner time. We acknowledge Kevin Moeggenborg of the Nalco Chemical Company for providing us with spraydried alumina. References [1] Reed JS. In: Principles of ceramic processing. 2nd ed. New York: Wiley; 1995. p. 594–7. [2] German RM. In: Sintering theory and practice. New York: Wiley; 1996. p. 12. [3] Kingery WD. J Appl Phys 1959;30:301. [4] Coble RL. J Appl Phys 1961;32:787. [5] Chu M, Rahaman MN, DeJonghe LC. J Am Ceram Soc 1991;74:1217. [6] German RM, Bulger M. Int J Powder Metall 1992;28:301. [7] Dorey RA, Yeomans JA, Smith PA, Pan J. Acta Mater 2001;49:519. [8] Masters K. In: Spray-drying handbook. 5th ed. New York: Halsted Press; 1991. p. 309–42. [9] Kamyia H, Isomura K, Jimbo G. J Am Ceram Soc 1995;78:49. [10] Baklouti S, Chartier T, Boumard JF. J Am Ceram Soc 1997;80:1992. [11] DiMilia RA, Reed JS. Am Ceram Soc Bull 1983;62:484. [12] Brewer JA, Moore RH, Reed JS. J Am Ceram Soc 1981;60:212. [13] Deis TA, Lannutti JJ. J Am Ceram Soc 1998;81:1237. [14] Lannutti JJ. M R S Bull 1997;22:38. [15] Pampuch R, Haberko K. Agglomerates in ceramic micropowders and their behavior on cold pressing and sintering. In: Vincenzini P, editor. Ceramic powders. Amsterdam: Elsevier; 1983. p. 623– 34. [16] Lu PK, Lannutti JJ. J Am Ceram Soc 2000;83:1393. [17] Chu M, DeJonghe LC, Lin MFK, Lin FJT. J Am Ceram Soc 1991;74:2902. [18] Long GG, Krueger S, Page RA. J Am Ceram Soc 1991;74:1578. [19] Lu PK, Lannutti JJ. J Am Ceram Soc 2000;83:2536. [20] Li W, Lannutti JJ. J Mater Res 2002;17:2794. [21] Nam J, Li W, Lannutti J. Powder Tech 2003;133:23. [22] Phillips DH, Lannutti JJ. NDT&E Int 1997;30:339. [23] Lu PK, Lannutti JJ, Klobes P, Meyer K. J Am Ceram Soc 2000;83:518. [24] Kong CM, Lannutti JJ. J Am Ceram Soc 2000;83:2183. [25] Kong CM, Lannutti JJ. J Am Ceram Soc 2000;83:685. [26] Li W, Nam J, Lannutti J. Metall Mater Trans A 2002;33:165. [27] Sawicka BD, Palmer BJF. Nucl Instr Meth A 1988;A263:525. [28] Zheng J, Reed JS. J Am Ceram Soc 1989;72:810. [29] Lange FF. J Am Ceram Soc 1984;67:83. [30] Lin FJT, DeJonghe LC. J Am Ceram Soc 1997;80:2267. [31] Wu SJ, DeJonghe LC. J Am Ceram Soc 1996;79:2207. [32] Rankin J, Sheldon BW. Mater Sci Eng A 1995;204:48. [33] Petzow G, Exner HE. Particle rearrangement in solid state sintering. In: Somyia S, Moriyoshi Y, editors. Sintering key papers. New York: Elsevier; 1990. p. 639–55.

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