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Acta Materialia 55 (2007) 285–293

Evolution of pore morphology and distribution duringthe homogenization of direct chill cast Al–Mg alloys

A. Chaijaruwanich a, P.D. Lee a,*, R.J. Dashwood a, Y.M. Youssef a, H. Nagaumi b

a Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, UKb Nippon Light Metal Company Ltd., Nikkei Research & Development Centre, 1-34-1 Kambara, Japan

Received 10 October 2005; received in revised form 23 June 2006; accepted 21 August 2006Available online 23 October 2006

Abstract

The evolution of porosity during homogenization heat treatment of direct chill (DC) cast Al–Mg alloys was studied. Homogenizationheat treatment was performed at 530 �C for various holding times (0, 1, 10 and 100 h). The evolution of porosity was quantified usingtwo-dimensional metallography and three-dimensional X-ray microtomography (XMT) techniques. The metallographic data suggestedthat the mean pore size, maximum Feret length and percentage porosity all increased during homogenization, which might be explainedby classical inter-pore Ostwald ripening. However, the pore number density also increased, which is not expected when inter-pore coars-ening is the controlling mechanism. XMT was performed to elucidate this apparent contradiction. XMT data revealed that the tortu-ousity of the pore networks formed in DC casting was very complex and that there was no increase in maximum pore length duringhomogenization. Instead, intra-pore Ostwald ripening of the tortuous pore networks was the key mechanism driving the evolution ofpore morphology, with coarsening of both the asperities and interconnects being driven by their high local curvatures. A one-dimen-sional simulation of vacancy diffusion was developed and corroborated this conclusion.� 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Homogenization; Porosity; X-ray tomography; DC casting

1. Introduction

DC (direct chill) casting is the most common methodused for producing an aluminum alloy ingot for subsequentthermomechanical processing (TMP) such as rolling andextrusion. Casting defects such as microsegregation andporosity are usually present in the as-cast microstructureand can lead to the deterioration of mechanical properties.Many studies have shown the detrimental effect of porosityon fatigue properties for materials used in the as-cast orheat-treated form [1–3].

Microsegregation is successfully reduced during homog-enization heat treatment through extended holding at hightemperature, which accelerates solid-state diffusion andconsequently the segregation effect is reduced. Porosity is

1359-6454/$30.00 � 2006 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2006.08.023

* Corresponding author. Tel.: +44 20 7594 6801; fax: +44 20 7594 6758.E-mail address: [email protected] (P.D. Lee).

likely to be eliminated during the subsequent thermome-chanical processing. However, in applications such as thickplate for high vacuum systems, some porosity has beenfound to remain. Therefore understanding the evolutionof pore morphology and size during homogenization andany subsequent thermomechanical processing may be crit-ical when predicting the final mechanical properties. Thishas been well demonstrated in shape castings both experi-mentally and using mathematical models [4,5].

The two main controlling parameters in the homogeniza-tion process are temperature and time. The homogenizationtemperature is usually selected to lie in the single-phase alu-minum solid solution region and is limited by a maximumtemperature, which should be lower than the solidus tem-perature. As a result, the homogenization temperature isusually fixed at the optimum temperature whereas timebecomes the more flexible and controllable parameter. Thetime required is normally estimated from the relationship

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286 A. Chaijaruwanich et al. / Acta Materialia 55 (2007) 285–293

between the diffusion time, the diffusion coefficient and thediffusion distance, which is approximated to the secondarydendrite arm spacing. The homogenization process ismainly concerned with the reduction of microsegregationand does not take into account the effect on porosity.

Porosity is usually formed during the casting processdue to both dissolved gas (hydrogen for aluminum) andvolumetric shrinkage [6]. Hydrogen is over 10 times moresoluble in liquid than solid aluminum [7] and hence isrejected from the solid into the interdendritic/granularliquid during solidification. Gas pores form when sufficientsupersaturation of hydrogen in the liquid occurs [8]. Thepercentage and size of porosity increase with increasing ini-tial hydrogen content [9–11].

Alloy composition [9,12] and solidification conditionsalso influence pore formation during solidification [13].Chen and Engler [12] found that the percentage porosityincreased with increasing magnesium content from 0 to5 wt.%, but decreased above 9 wt.% Mg for sand cast bars[12]. They also found that increasing hydrogen increasedthe percentage porosity for the full range of alloys tested.Lee et al. [11] found that increasing the magnesium contentfrom 2 to 6 wt.% significantly increased the percentageporosity in DC cast ingots, with the increase attributed toboth increasing magnesium and hydrogen contents. Theseauthors, like several prior studies [14], found that magne-sium increased the uptake of hydrogen in molten alumi-num, which was not reduced despite the use of in-linerotary degassing.

The second cause of pore formation is incomplete feed-ing of solidification shrinkage. In aluminum–magnesiumalloys, the solidification range increases from 10 to 49 �Cas Mg increases from 2 to 6 wt.%. With increasing solidifi-cation range, liquid feeding becomes increasingly more dif-ficult [15]. Therefore, porosity is unavoidable in DC castaluminum–magnesium ingots.

For pore nucleation, one theory suggests that poresgrow from gas entrapped in pre-existing oxide bi-films,with the pore growth also aided by the reduced surface ten-sion due to the presence of the oxide at the liquid–gas sur-face [15,16]. In Al–Mg alloys the formation of a complexAl–Mg oxide has been suggested to be particularly detri-mental [17,18].

Recently, there have been many studies trying to predictthe formation of porosity during casting (e.g. see reviewsby Lee et al. [19] or Stefanescu [20]) with the eventualaim of predicting final component properties. However,most components, even if shape cast, are heat treatedbefore entering service. The change in size and morphologyof porosity during heat treatment must therefore be knownbefore final component properties can be predicted as afunction of processing, alloying, etc. Unfortunately, therehave only been a few prior studies on the influence ofany form of heat treatment upon porosity in aluminumalloys.

Jordan et al. [21] studied the effect of heat treatment onboth the percentage porosity and hydrogen content of lab-

oratory-cast DC Al–4.5wt.% Cu–0.7wt.% Mg ingots. Theyconcluded that the hydrogen content increase was signifi-cant during heat treatment (neither temperature or timewas given), but the percentage porosity increase was onlyminor, going from immeasurable to �0.05% in a lowhydrogen ingot (�0.1 ml/100 g STP) and from �0.75% to�0.85% in a high hydrogen ingot (�0.5 ml/100 g STP).

Talbot and Granger [22] reported that the porosity inDC cast commercial purity aluminum increased from zeroto about 0.08% throughout the ingot thickness after a 12 hheat treatment at 580 �C, with a decrease in hydrogen con-tent. The porosity formed at the grain boundaries, leadingthem to suggest that the pores were caused by vacancy coa-lescence. Talbot and Granger [22] also heat treated samplesof rolled plate and extruded bar and found that poresformed. They suggested that the pores formed during ingotcasting/heat treatment were closed during TMP and thenreopened in subsequent heat treatment.

Grishkovets et al. [23] observed an increase in both poresize and porosity percentage in an Al–Mg alloy (AMG6)for homogenization temperatures between 480 and520 �C and times ranging from 6 to 24 h.

The most recent study was by Anyalebechi and Hogarth[24], who investigated the effect of heat treatments abovethe eutectic temperature in DC aluminum alloy 2014. Inlow hydrogen ingots (�0.05 ml/100 g STP) heat treatedfor approximately 30 h at 540 �C (multi-step) they founda significant increase in porosity (�0.1–0.4%) at the centreof the ingot. They attributed the formation of porosity toboth the growth of existing pores and the nucleation ofnew pores in regions of incipient melted eutectic.

Although these studies all agree that porosity is affectedby heat treatment, increasing in percentage, there is no con-sensus upon the magnitude of the effect. Different mecha-nisms by which the porosity increases were hypothesized,including vacancy coalescence and solidification shrinkageof incipient melted eutectic, but not proven. The aim of thispresent study is to provide a quantitative investigation ofthe effect of homogenization on the morphology and sizedistribution of porosity in DC cast Al–Mg alloys. For thefirst time both metallography and X-ray microtomography(XMT) were used, allowing both two and three dimensionfeature characterization. Three-dimensional (3D) charac-terization proved to be critical for determining the mecha-nism governing pore evolution.

2. Experimental methods

DC cast ingots with a cross-section of 250 · 400 mm ofAl–Mg alloys containing 2, 4 and 6 wt.% Mg (see Table 1for chemical composition and initial hydrogen content)were produced by Nippon Light Metal (NLM) CompanyLtd. The details of the casting conditions are given else-where [25]. The ingots were sectioned to obtain samplesfor microstructural characterization, hydrogen analysisand subsequent homogenization treatment. Samples weretaken from the central region of the ingots (100–120 mm

l

Vacancy Flux ( J)

dp

Dp

Table 1Nominal compositions and initial hydrogen contents of the alloys used in this study

Alloy Composition (wt.%) Hydrogen

Mg Si Fe Cu Ti Mn Cr Al ml/100 g STP

Al–2Mg 1.99 0.02 0.02 <0.01 <0.01 <0.01 <0.01 Bal. 0.29Al–4Mg 4.06 0.02 0.02 <0.01 <0.01 <0.01 <0.01 Bal. 0.41Al–6Mg 6.16 0.02 0.02 <0.01 <0.01 <0.01 <0.01 Bal. 0.60

A. Chaijaruwanich et al. / Acta Materialia 55 (2007) 285–293 287

from the chill surface), where the percentage porosity wasexpected to be consistently high [25]. Five separate condi-tions were examined, as-cast (F) and homogenized for 0,1, 10 and 100 h, denoted as H0, H1, H10 and H100, respec-tively. The samples were ramped at 50 �C/h to 530 �C andthen held for the specified time, followed by quenching forH0 and furnace cooling at 35 �C/h for the rest. The H10condition is typical of industrial practice for DC castAl–Mg alloys. The heat treatment was carried out in thelaboratory on 20 · 20 · 50 mm specimens wrapped instainless steel foil and half industrial length ingots for onlythe H10 and H100 conditions. The samples heat treatedindustrially are denoted with a subscript ‘i’. Porosity char-acterization (using optical microscopy and X-ray microto-mography) was performed on as-cast and homogenizedconditions and hydrogen analysis (LECO sub-fusion) onas-cast condition only.

Samples were sectioned at the mid-plane and this surfacewas prepared for metallographic observation using a stan-dard grinding procedure using SiC paper down to 4000 gritfollowed by OPS (colloidal silica suspension) polishing.Pore size, percentage and pore number density were mea-sured on a Neophot 21 optical microscope equipped withKS400 image analysis software (Carl Zeiss AG, Oberko-chen, Germany). Measurements were taken over sufficientcontiguous frames to examine approximately 100 mm2 atmagnification of (�50·), providing pixel resolutions of2.7 lm. A JEOL T200 scanning electron microscope wasused to examine detailed pore morphology.

XMT was performed on 2.5 mm diameter rodsmachined from the as-cast and industrially heat-treatedingots. A 1 mm high region in the centre of each rod wasscanned using a commercial XMT unit (PhoenixjX-raySystems + Services GmbH, Wunstorf, Germany) with avoltage of 80 kV and a current of 120 mA. A total of 720images were captured on a detector of 1024 · 512 pixelsover one revolution and then reconstructed with a voxelsize of 3 lm. Image processing and porosity analysis wereperformed using VGStudio Max 1.2.1 A 3 · 3 · 3 medianfilter was applied to reduce the noise. This threshold valuewas individually determined for each sample and thenapplied in a defect detection algorithm to quantify theporosity (volume, number density and percentage). A min-imum detectable pore size of 8 voxels (equivalent diameterof 7 lm) was used.

1 VGStudio Max 1.2 : Volume Graphics GmbH, Heidelberg, Germany.

3. Model theory

A one-dimension finite difference (FD) model simulatingthe vacancy diffusion between small (diameter dp) and large(Dp) spherical pores during homogenization was developed(Fig. 1). The volume of the small pore was allowed tochange as a function of net vacancy flux whilst the largepore was assumed to be of constant volume.

The concentration of vacancies in equilibrium at the sur-face Cv(r) of a pore of radius r is given by the Gibbs–Thompson equation:

CvðrÞ ¼ Cev exp

2rv=AlV Al

RT� 1

r

� �ð1Þ

where rv/Al is the surface tension of the pore, VAl is the mo-lar volume, R is the gas constant, T is absolute temperatureand Ce

v is the equilibrium matrix concentration of vacanciesgiven by:

Cev ¼

exp�Ef

kT

� �V atom

ð2Þ

where Ef is the activation energy for vacancy formation, k

is the Boltzmann constant and Vatom is atomic volume ofaluminum.

The vacancy flux (J) was calculated using Fick’s firstlaw:

J ¼ �DoCox

ð3Þ

where D is the self-diffusion of the aluminum and C is va-cancy concentration.

An explicit finite difference scheme was employed todetermine the vacancy concentration profiles as a functionof time (t) by numerically solving Fick’s second law:

oCot¼ D

o2Cox2

ð4Þ

Both cartesian and spherical coordinate system formula-tions were implemented for the purpose of comparison.

Small pore Large pore

Fig. 1. Schematic of the assumptions used in the model.


4. Results and discussion

The typical porosity observed metallographically inboth the as-cast and homogenized (H10) conditions forthe three alloys are given in Fig. 2. The percentage andsize of porosity increased with increasing magnesium con-tent. This has been observed by previous authors [11,12]and was attributed to the increased hydrogen pick upand solidification range with increasing magnesium con-tent. In these samples the hydrogen content doubled inthe Al–6Mg alloy as compared with the Al–2Mg alloy(Table 1). As the magnesium content increased, theamount of eutectic formed increased, producing moredendritic primary phase morphology with increased inter-granular and interdendritic liquid in the final stages ofsolidification. In the Al–6Mg alloy both increased hydro-gen and eutectic has a significant influence upon the poremorphology (Fig. 2c). Much more tortuous pores areformed, nucleating as spheres and then growing along

Fig. 2. Micrographs of porosity in Al–2, 4 and 6M

the intergranular regions and expanding into the interden-dritic spaces within each grain.

The effect of homogenization upon the as-cast porosityis shown in Fig. 2. Pore coarsening appears to haveoccurred, increasing the size and/or roundness of the pores.The changes in metallographically measured mean equiva-lent diameter for the Al–4Mg and Al–6Mg alloys areshown in Fig. 3. The very small percentage and size ofthe porosity in the Al–2Mg alloy precluded statisticallyvalid quantitative analysis. The mean equivalent porediameter increases during homogenization. There is alsoan apparent increase in the percentage porosity (Fig. 4)and pore number density (Fig. 5). The increase in percent-age porosity agrees with the observations of prior authors[21–23]; number density was not measured in these priorstudies. Comparing the Al–4Mg to Al–6Mg results in Figs.3–6, the image analysis supports the visual conclusion fromFig. 2 that the as-cast porosity increases with increasingmagnesium content.

g alloys in: (a)–(c) F and (d–f) H10 conditions.

0.0

0.5

1.0

1.5

F H0 H1 H10 H100i

Condition

Per

cent

age

poro

sity

(%

)

Al-6Mg

Al-4Mg

Fig. 4. Percentage porosity during homogenization in Al–4Mg andAl–6Mg alloys (metallography).

0

5

10

F H0 H1 H10 H100i

Condition

Por

e nu

mbe

r de

nsit

y (m

m-2

)

Al-6Mg

Al-4Mg

Fig. 5. Pore number density during homogenization in Al–4Mg andAl–6Mg alloys (metallography).

a

b

0

1

2

3

4

10 100DM (µm)

NM

(mm

-2)

Al-6Mg_F

H1

H10

0.0

0.5

1.0

1.5

2.0

10 100DM (µm)

NM

(mm

-2)

Al-4Mg_F

H1

H10

Fig. 6. Pore size distribution during homogenization in (a) Al–4Mg and(b) Al–6Mg alloys (metallography).

15

20

25

30

35

F H0 H1 H10 H100 i

Condition

Mea

n eq

uiva

lent

por

e di

amet

er (

µm)

Al-6Mg

Al-4Mg

Fig. 3. Pore size during homogenization in Al–4Mg and Al–6Mg alloys(metallography).


In terms of the pore size distribution, similar trends wereobserved for both the Al–4Mg and Al–6Mg alloys (Fig. 6).For both alloys it would appear that the number of poresand mean size increased after heat treatment. This increasein mean size could be attributed to classical inter-pore Ost-wald ripening. However, associated with this should be asignificant decrease in the number of smaller pores, which

was not observed. This lack of reduction in the numberof smaller pores could be attributed to the fact that onlypores greater than 10 lm were considered. Closer examina-tion of typical individual pores in the Al–6Mg alloy (Fig. 7)suggests another possible explanation for this anomaly.This figure shows that there are two distinct types of pores.Barely visible are a number of small (<5 lm) round pores.In addition, there are much larger pores. In the as-cast con-dition these large pores are complex networks, increasingand decreasing in width as they grew between the grainsand dendrites within each grain. What was not clear fromthe low magnification images of the as-cast material(Fig. 2a) is that the asperities contain extremely high curva-tures, almost forming sharp points at the tips (Fig. 7a).What is evident from the SEM images of the homogenizedmaterial (Fig. 7b and c) is that the curvature of these asper-ities decreases dramatically with increasing homogeniza-tion time. Ostwald ripening is occurring, but these imageswould suggest that it might only be at a local scale withineach individual pore, termed intra-pore coarsening.

To elucidate the pore evolution during homogenization,XMT was performed on samples of the F, H10 and H100conditions. Typical individual pores from the as-cast con-dition for each of the Al–2Mg, Al–4Mg and Al–6Mg alloysare shown in Fig. 8. These figures illustrate that the tortu-ousity of the pore networks is even more complex than sug-gested by metallography (Fig. 2) and how the network sizeincreases dramatically with increasing magnesium content.

Fig. 7. SEM micrographs of porosity of Al–6Mg alloy in: (a) F; (b) H10i

and (c) H100i conditions.


Fig. 9 shows typical pores for the as-cast and twohomogenization conditions for Al–6Mg. This figure clearlyillustrates the intra-pore Ostwald ripening hypothesizedearlier with both the asperities and interconnects coarsen-ing. One can imagine how planar sections through any ofthese pores could lead to a single pore being misinterpretedas a number of smaller pores. This is illustrated by compar-ing Fig. 9 with 2D planar sections of the 3D tomographicdata given in Fig. 10.

Three-dimensional renderings of the entire scans foreach of the three conditions are shown in Fig. 11 for

Al–6Mg. The main observations are that the percentageand density of observable pores dramatically increase duringhomogenization. These data were quantified and the distri-bution of equivalent pore diameter is given in Fig. 12. Thetrends in the data are similar to those observed metallo-graphically (Fig. 6b), the number and mean size increaseduring homogenization. However, pore distributions shouldbe log-normal, suggesting only the larger portion of thesedistributions were resolved by the combination of tomogra-phy and image analysis. If the pores consist of mostly fineinterconnects, these will not be well resolved. A good exam-ple of this is the three-pointed-star-shaped pore in the bot-tom left-hand corner of Fig. 7a. Although this pore has anoverall length of over 30 lm, the maximum width of anyindividual feature is less than 5 lm. This pore would not beresolved by XMT. However, during homogenization intra-pore ripening will spheroidize this pore, making it resolvable.This explains the apparent increase in number densityobserved in Fig. 11 and quantified in Fig. 12.

The change in volume averaged pore shape factor dur-ing homogenization is shown in Fig. 13. The pore shapefactor is the ratio of the measured surface area to the sur-face area of an equivalent volume sphere. The pore shapefactor is equal to one for a spherical pore. As homogeniza-tion progresses the shape factor decreases significantly,indicating that spheroidization of the pores has occurred,providing further quantitative support for intra-pore ripen-ing. Whilst the pore shape factor has reduced after 100 h ofhomogenization, it is still far from spherical (4.8 instead of1), illustrating that the coarsening is highly localized,spheroidizing only the arms, not the entire pore (shownvisually in Fig. 9c). This is supported by measurement ofthe maximum pore dimension, which remains unchangedat 1130 ± 140 lm in all conditions. However, the maxi-mum Feret length measured metallographically increasesfrom 225 lm in the as-cast condition to 365 lm after100 h of homogenization. This trend suggests the poresgrow longer, which the XMT results prove does not hap-pen; instead, the networks become thicker and hence a pla-nar slice captures more of the pore.

A 1D model of vacancy diffusion was developed todetermine the relative time scales for intra- and inter-porecoarsening. The resulting time required for a small porewith an initial diameter dp to reduce in size by 90% is givenin Fig. 14. It was assumed that coarsening occurred byvacancy diffusion between the small pore and a large porewith a constant radius of 10 lm for a series of different dis-tances between the pores. A typical bulk vacancy diffusioncoefficient of 1 · 10�9 m2/s was assumed (Table 2). Previ-ously it was noted that there are two distinct types of poresin the as-cast material, small rounded pores (diame-ter < 5 lm) and large pore networks (see Fig. 7a). Examin-ing the small pores first, these had a diameter ofapproximately 2 lm and a mean spacing derived from thenumber density (assuming an even distribution) of approx-imately 80 lm. From Fig. 14 it can be seen that pores withan initial diameter of 2 lm will dissolve within a homoge-

Fig. 9. Pore morphology during homogenization in Al–6Mg alloy: (a) F; (b) H10i and (c) H100i conditions.

Fig. 10. XMT 2D slices of porosity in Al–6Mg alloy: (a) F; (b) H10i and (c) H100i conditions.

Fig. 8. XMT rendering of single pores in as-cast: (a) Al–2Mg; (b) Al–4Mg and (c) Al–6Mg alloys.


nization time of 50–200 h. However, the pores are concen-trated in the interdendritic spaces and can be seen to beseparated by about 10 lm, and will dissolve in between10 and 50 h. This would suggest that these small porescan dissolve during homogenization through classicalinter-pore ripening. Examination of the H100 conditionAl–6Mg SEM micrograph (Fig. 7c) shows that the smallpores are no longer in evidence.

For larger pores, extrapolating the predictions fromFig. 14, it is evident that pores with a diameter of greaterthan 5 lm could not dissolve within 100 h via inter-pore

coarsening. However, intra-pore coarsening, where thevacancies only need to move locally around the tip of thesharp asperities (1 lm radii and diffusion distances of lessthan 5 lm) will occur in under 10 h. This process will befaster if enhanced diffusion occurs along the pore surfaceor along grain boundaries. Complete spheroidization ofthe pores, where diffusion must happen between asperities(a distance of approximately 30 lm), will only happen fortimes longer than 1000 h. This explains why the pores wereobserved to only reach a volume-averaged shape factor of4.8 rather than 1 (spherical).

Fig. 11. XMT rendering of porosity in Al–6Mg: (a) F; (b) H10i and(c) H100i conditions.

0

200

400

600

800

1000

10 100DX (µm)

NX

(mm

-3)

F

H10

H100

Fig. 12. Pore size distribution during homogenization in Al–6Mg alloy(XMT).

4

5

6

7

8

F H10 H100Condition

Shap

e fa

ctor

Fig. 13. Volume averaged pore shape factor during homogenization inAl–6Mg alloy (XMT).

0.01

0.1

1

10

100

1000

0.1 1 10d p (µm)

t 90%

(hrs

)

100 µm (Cart.)100 µm (Sph.) 5 µm (Cart.)5 µm (Sph.)

Fig. 14. Model calculations showing the effect of initial pore size on thetime required for pore closure (t90%) for different pore separationdistances; Cart. and Sph. refer to Cartesian or spherical coordinateformulation, respectively.

Table 2The constants used in the model

rv/Al (Nm�1) VAl (m3) Ef (J) Vatom T (K) D (m2/s)

1 10�5 1.17 · 10�19 1.66 · 10�29 803 10�9


5. Conclusions

Pore evolution during homogenization of DC cast alu-minum–magnesium alloys was quantified using 2D metal-lography and 3D XMT techniques.

Metallographic observations suggested that the meanpore size increased during homogenization, which would

indicate that classical inter-pore Ostwald ripening hadtaken place. However, an apparent increase in number den-sity was also observed, contradicting this hypothesis.

XMT was employed to resolve this contradiction. Thistechnique revealed that the tortuosity of the pore networksis even more complex than suggested by metallography andthat the pore network size dramatically increases withincreasing magnesium content. XMT analysis clearly illus-trated that intra-pore Ostwald ripening occurred, with boththe asperities and interconnects coarsening, driven by thehigh curvatures of pores developed as they grew betweendendrite arms. However, the XMT analysis concurred withthe metallographic observation that both mean pore sizeand number density increased during homogenization.


SEM observations indicated that very small round poresof diameter less than 5 lm were present in the as-cast mate-rial. Three-pointed-star-shaped pores were also observed.These pores had overall lengths of �30 lm but the maxi-mum width of any individual feature was less than 5 lm.Both pore types were not quantifiable with the metallo-graphic or XMT resolutions used. The very small roundpores were not in evidence after homogenization, suggest-ing that they dissolved via classical inter-pore coarsening.It was proposed that the star-shaped pores spheroidizedduring homogenization via intra-pore ripening, explainingthe increase in number density observed.

A one-dimensional simulation of vacancy diffusion wasdeveloped and the predicted times required for intra- andinter-pore coarsening corroborated the explanations pro-posed above.

Acknowledgements

The authors wish to acknowledge the support of theEPSRC (grant GR/T26344) and one of the authors(A.C.) would like to thank the Thai government for finan-cial support.

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