dispersoid precipitation and process modelling in

Acta mater. 49 (2001) 599–613www.elsevier.com/locate/actamat

DISPERSOID PRECIPITATION AND PROCESS MODELLING INZIRCONIUM CONTAINING COMMERCIAL ALUMINIUM

ALLOYS

J. D. ROBSON* and P. B. PRANGNELLManchester Materials Science Centre, Grosvenor Street, Manchester M1 7HS, UK

( Received 28 August 2000; received in revised form 16 October 2000; accepted 18 October 2000 )

Abstract—Small dispersoid particles inhibit recrystallisation and are thus critical in controlling the grainstructure of many high strength commercial aluminium alloys. A general, physical model has been developedfor the precipitation of Al3Zr dispersoids in aluminium alloys. The predictions of the model have beencompared with results of an experimental investigation of Al3Zr precipitation in 7050. The model has beenshown to faithfully reproduce the distribution of dispersoids observed in this alloy, correctly predicting disper-soid free zones observed in interdendritic regions and at grain boundaries. Furthermore, the predicted precipi-tation kinetics agree well with experimental observation. The model has been used to study the effects ofhomogenisation conditions and alloy composition on dispersoid formation and has been shown to be a power-ful tool for optimising the dispersoid distribution in 7xxx series aluminium alloys. 2001 Acta MaterialiaInc. Published by Elsevier Science Ltd. All rights reserved.

Keywords:Computer simulation; Aluminium alloys; Nucleation & growth; Kinetics; Recrystallisation &recovery

1. INTRODUCTION

Small additions of zirconium can often improve theproperties of wrought high strength aluminium alloysby forming metastable, coherent Al3Zr dispersoidswhich inhibit recrystallisation. The effectiveness ofthe dispersoids in fulfilling this role depends on theirsize, spacing and distribution [1]. In commercial prac-tice, the dispersoids are precipitated during homogen-isation of the cast billets. The homogenisation con-ditions are usually chosen to dissolve the maximumnumber of unwanted eutectic phases and redistributethe solute, rather than optimise dispersoid precipi-tation. It may therefore be possible to increase theeffectiveness of the dispersoids by refining the hom-ogenisation conditions and zirconium concentration.

The binary Al–Zr system has been extensivelystudied [2–10], particularly in rapidly solidifiedsamples which may have zirconium supersaturationsfar in excess of those obtained in commercial alloys.It is now well established that, for small zirconiumadditions, decomposition of the supersaturated solidoccurs firstly by the formation of a metastable L12

Al3Zr phase [2, 3]. Prolonged heat treatment is usu-ally required before this phase transforms to the equi-

* To whom all correspondence should be addressed. Fax:144-161-200-3586.

1359-6454/01/$20.00 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.PII: S1359-6454(00 )00351-7

librium DO23 Al3Zr phase. Qualitative studies of theprecipitation kinetics of the metastable phase in sim-ple, binary alloys show that the peak transformationrate lies between 400 and 500°C [5–7]. The size ofthe dispersoid particles obtained depends in part onthe heat up rate to the homogenisation temperature,with slower heating rates apparently leading to arefinement in particle size [7, 10]. It has also beennoted that the Al3Zr particles are often inhomo-geneously distributed within individual grains [10].This is not surprising, since the dispersoids are preci-pitating directly from the as-cast state and the initialsupersaturation of zirconium varies strongly withinthe dendritic structure.

A small number of studies have investigated Al3Zrprecipitation in commercial 7xxx alloys. Homogenis-ation of these alloys leads to the precipitation of themetastable L12 Al3Zr phase as fine, spherical particles(typically .20 nm in diameter [11, 12]). Dispersoidfree zones have been observed in these alloys adjac-ent to the grain boundaries [11]. This inhomogeneousdistribution of dispersoid particles is likely to be ofparticular significance, since it implies there will bea lower resistance to recrystallisation in regionsadjacent to grain boundaries, where the presence oflarge primary particles is also known to encouragerecrystallisation [11].

A key aim of the study was to develop a process

600 ROBSON and PRANGNELL: DISPERSOID PRECIPITATION IN Zr CONTAINING ALUMINIUM ALLOYS

model capable of predicting the dispersoid precipi-tation during homogenisation. This is of great techno-logical significance, since in principle it should thenbe possible to determine the optimum compositionand homogenisation conditions required to give animproved dispersoid distribution. A physically basedmodel is most satisfying since the number of fittingparameters is usually smallest. Furthermore, physicalmodels often provide an increased understanding ofthe factors controlling the process. A powerful modelcan be developed by using well established kineticequations to calculate the overall transformation kin-etics in discreet time steps [13]. At each step, newparticles are allowed to nucleate and existing onesgrow or shrink depending on their size. The particlesize distribution and remaining solute supersaturationare then recalculated and used in making predictionsfor the change in particle size and number for the nexttime step. This numerical approach involves trackingthe behaviour of a great many particles simul-taneously and has therefore only become practicalwith the advent of high speed computing. The mainadvantage of this technique is that the traditionalregimes of growth and coarsening arise as a naturalconsequence of changes in composition and drivingforces during precipitation. Models based on thisapproach have been previously applied successfullyto a number of systems, including predicting the pre-cipitation ofh9 in Al–Zn–Mg [14] and calculating theformation of Al3Li in Al–Li [15].

The precipitation of Al3Zr in commercial alu-minium alloys is complicated by the fact that zir-conium segregates during solidification. The Scheilapproximation is a simple and widely used methodfor predicting segregation during casting, which hasbeen shown to give good agreement with experi-mental observation in aluminum alloys [16]. In thiswork, a simple Scheil model for the segregation ofzirconium was coupled with a model for the precipi-tation kinetics to allow the local dispersoid size anddensity to be predicted as a function of positionwithin a grain. This novel combination enables thecombined model to successfully predict the inhom-ogeneities in dispersoid precipitation observed inpractice.

The model has been tested by comparing the pre-dictions with experimental results obtained fromstudying dispersoid precipitation in a commercial7050 alloy. Electron microprobe analysis has beenused to quantify the zirconium distribution in the caststructure. High resolution scanning electronmicroscopy (FEGSEM) and transmission electronmicroscopy (TEM) have been used to study the num-ber, size and distribution of dispersoid particles fol-lowing a range of heat treatments. The advantageusing a FEGSEM is that it enables a much larger areafrom the same sample to be analysed. This hasallowed the relationship between the dispersoid pre-cipitation and zirconium segregation to be seenclearly for the first time.

2. EXPERIMENTAL

Specimens, approximately 1 cm cubed in size,were cut from the centre of a slice of stress relieved,direct-chill cast 7050 ingot, supplied by British Alu-minium Plate. Stress relief was performed by soakingthe ingot for 6 h in a furnace heated to 400°C. Thenominal composition of the alloy is shown in Table 1.

Some of the samples of the cast, stress relievedmaterial were then examined in a Cameca SX-50electron microprobe. Microsegregation of zirconiumand other alloying elements was evaluated by per-forming traverses across 10 grains in each sample,with composition measurements being made at 2µm intervals.

Isothermal heat treatments were performed onsmall samples held at temperatures from 350 to550°C for times ranging from 5 to 100 h. Thermo-couples were attached to each sample and used tomonitor the metal temperature, which after the initialrapid heating period, was maintained to within±1° ofthe target. Following heat treatment, the samples werequenched into cold water.

The heat treated samples were examined in a Phil-ips XL-30 field emission gun FEGSEM. The opti-mum operating voltage for resolving of the disperso-ids was found to be 10 kV using the backscatteredimaging mode, where the atomic number contrast dueto the zirconium made the Al3Zr particles easily vis-ible. It was found that with careful specimen prep-aration and selection of suitable operating conditions,dispersoids as small as 10 nm in radius could beresolved using this instrument.

To investigate the dispersoids formed at short heattreatment times and to enable comparisons to be madebetween the appearance of dispersoids in the FEG-SEM and TEM, thin foils were prepared by electro-polishing at 12 V in a 30% nitric acid, 70% methanolsolution cooled to230°C. These were examined ina Philips CM200 TEM operated at 200 kV.

The compositions of the large intermetallic par-ticles, found in both the cast and heat treated con-dition were measured using energy dispersive X-rayanalysis (EDX) in a Philips 525 SEM.

It was found that the size, fraction and spacing ofdispersoid particles varied significantly dependingupon the position within a grain (see Results). Dueto the high magnifications necessary to resolve thesmall dispersoid particles, only a small fraction of anyone grain was imaged at a time. Therefore, great carewas taken to examine enough grains, and enoughareas within each grain to ensure representative datawere collected. For each sample at least 5 grains wereexamined, and for each grain at least 20 areas wereimaged.

3. RESULTS

3.1. Microstructural analysis

Low and higher magnification backscattered elec-tron FEGSEM images of the cast, stress relieved,

601ROBSON and PRANGNELL: DISPERSOID PRECIPITATION IN Zr CONTAINING ALUMINIUM ALLOYS

Table 1. Nominal composition of the 7050 alloy (wt%) used in the present study

Si Fe Cu Mg Zn Ti Zr

0.03 0.05 2.30 2.30 6.20 0.04 0.13

7050 material are shown in Fig. 1. The grain bound-aries can be seen to be delineated by intermetallicconstituent particles and eutectic components. EDXanalysis has shown that the majority of the intermet-allic particles were closest to Al7Cu2Fe in compo-sition (Table 2). Within the grains, near the grainboundaries, further plate shaped particles can be seen[Fig. 1(b)]. The morphology and composition of theseparticles suggests they areh phase. These particlesprobably precipitate during cooling from the stressrelieving treatment.

Typical results of quantitative compositionmeasurements from a linescan across a grain areshown in Fig. 2. In Fig. 2(a) the data have been scaledto allow the different elements to be plotted on thesame graph. The peaks in Zn, Cu and Mg correspondto measurements made in, or close to, the intermet-allic particles on the grain boundaries. It can be seenthat zirconium segregates in the opposite direction tothe major alloying elements as expected from a con-sideration of the peritectic Al–Zr phase diagram [17,

Fig. 1. (a) Low and (b) high magnification backscattered elec-tron images of the as cast structure.

18] and the lowest concentration of zirconium isfound at the grain boundaries. The measured actualzirconium concentration across the same grain isshown in Fig. 2(b). The fluctuations in zirconiumlevel across the analysed region reflect the underlyingdendritic structure within each grain. The peaks corre-spond to measurements made close to the centres ofthe dendrite arms where the zirconium concentrationexceeds its nominal value of 0.13 wt%. These regionssolidified first during casting and are thus enriched inzirconium. However, a significant fraction of thegrain contains zirconium levels below the nominalvalue. In particular, very low zirconium levels arepresent near the grain boundaries and interdendriticregions.

3.2. Precipitation kinetics

To obtain an approximate estimate of the disper-soid precipitation kinetics across the range of tem-peratures investigated, observations were made todetermine in which of the heat treated samples Al3Zrprecipitates could be detected. As might be expected,a consequence of the microsegregation of zirconiumin the cast material is that the dispersoids were alwaysinhomogeneously distributed within each grain withwide variations in the particle size and spacing. Thisbehaviour is demonstrated for a typical grain in Fig.3. To enable comparisons to be made after differentheat treatments, measurements of the particle sizeswere always made from dispersoids in the regionclose to the centre of the dendrite arms, where theparticle size and spacing was most uniform.

Figure 4 shows small dispersoid particles in a den-drite core after heating for 20 h at 450°C as observedusing FEGSEM and TEM. The particle radii meas-ured using both imaging methods were similar, asshown in Table 3. This table also summarises for eachtreatment the measured mean particle radius forsamples in which dispersoids were observed. Forshort times, where no dispersoids were detected in theFEGSEM, TEM observations were made to verifytheir absence or presence. Of the samples in whichno dispersoids were detected in the FEGSEM, onlythe sample heated for 10 h at 450°C showed evidenceof dispersoid precipitation in the TEM.

These results show that the time taken for the dis-persoids to reach a given size decreases with increas-ing temperature, up to at least 550°C (at this hightemperature some local melting occurs at the grainboundaries). After only 1 h at 500 and 550°C rela-tively large dispersoid particles were already present[Fig. 5(a)]. The spherical morphology suggests theseare still metastable, rather than equilibrium Al3Zr.


Distance / micrometres

Scal

ed C

once

ntra

tion

10050

0

1

0.5

Al

Zr

Mg

Zn

Cu

Distance / micrometres

Zr

Con

cent

rati

on /

wt%

10050

0.1

0.05

0.15

Fig. 2. (a) Scaled variation in the concentrations of Al, Zn, Cu, Mg and Zr across a typical grain. The peaksin Zn, Mg and Cu concentrations correspond to the positions of intermetallic particles at the grain boundaries.

(b) Variation in actual zirconium concentration across the same grain.

Fig. 3. Image of a grain showing a typical non-uniform distribution of dispersoids after isothermal homogenis-ation for 20 h at 500°C. At this magnification the dispersoids appear as small, white dots which can just be

resolved towards the centre of the grain.

After 20 h at 550°C morphological changes weredetected. Many of the dispersoid particles showedorthogonal protrusions [Fig. 5(b)]. These have beennoted elsewhere [19] and attributed to preferentialgrowth alongk100l and k110l crystallographic direc-tions in the metastable phase. Others showed a cuboidmorphology, suggesting transformation to the equilib-

rium D023 Al3Zr phase. These particle morphologieswere not observed at any of the lower temperatures,even after the longest times. This implies that at500°C and below, the metastable phase persists for atleast 100 h. The observation of the metastable Al3Zrphase in this alloy (0.13 wt% Zr) at 550°C confirmsthermodynamic predictions [18] that the solvus tem-


Fig. 4. (a) FEGSEM image of dispersoids after homogenisationat 450°C for 20 h. (b) TEM image of dispersoids in the same

sample.

perature of the metastable phase lies close to that forthe equilibrium Al3Zr phase, which is.590°C at 0.13wt.% Zr).

3.3. Influence of zirconium segregation

It has already been noted that the segregation ofzirconium during casting leads to wide variations inthe dispersoid distribution within each grain. Thereare also regions, particularly close to grain bound-aries, where no dispersoids were observed at all. Asexpected, the regions where no dispersoids wereobserved correlate well with with the occurrence ofthe lowest zirconium levels in the cast structure. Thebinary phase diagram indicates that dispersoid pre-cipitation will only be thermodynamically possible ifthe zirconium concentration is greater than about 0.01wt% at 350°C increasing to over 0.08 wt% at 500°C.With reference to Fig. 2(b), it can therefore be seenthat there is insufficient zirconium in solid solutionfor precipitation of Al3Zr near to the grain boundaries

Fig. 5. (a) Al3Zr dispersoids after homogenisation for 1 h at550°C. (b) A dispersoid particle after homogenisation for 20 h

at 550°C, showing protrusions.

and interdendritic regions at temperatures greaterthan .400°C. Travelling from the grain boundarytowards the centre of a dendrite arm, the zirconiumconcentration and hence the supersaturation,increases. This results in an increasing driving forcefor Al3Zr precipitation. The effect of the localchanges in the driving force for precipitation can beseen in Fig. 6(a) where distinctly different precipi-tation behaviour can be observed depending on thepre-existing solute supersaturation.

Figure 6(a) shows the observed dispersoid distri-bution in an area adjacent to a grain boundary. Threeregions showing different precipitation behaviourmay be identified. Close to the grain boundary [region1, Fig. 6(a)], there are no dispersoids since here thezirconium concentration lies below the solubility limitfor the metastable phase. The zirconium in region 3,close to the centre of the dendrites, has a sufficientlyhigh supersaturation after casting to allow the forma-tion of copious numbers of small, homogeneouslynucleated, Al3Zr particles. The most interestingeffects occur in region 2. Here, the dispersoid par-ticles are considerably larger (typically twice theradius) than those in region 3 and there are also far


Table 2. Measured mean composition (at.%) of the grain boundary intermetallic particles and the plate shaped precipitates within grains in cast(stress relieved) material. The suggested phase identity is also shown

Al Cu Fe Mg Zn Suggested phase

G.B. precipitate 74.8±6.3 15.0±5.0 7.1±2.5 2.2±0.7 0.76±0.74 Al7Cu2FePlates 31.5±7.1 6.3±2.1 0.10±0.10 30.3±3.4 32.7±4.1 h

Table 3. Mean Al3Zr particle radius (nm) and standard deviation after heat treatmenta

1 h 5 h 10 h 20 h 40 h 100 h

550°C 15±3 18±3 — 32±3 — —500°C 10±2 12±3 19±5 20±5 20±5 21±3450°C X X (10±2) 18±2 (20±3) 19±2 25±7400°C X X X X X 10±4350°C X X X X X X

a Diameters shown in brackets were measured using TEM rather than FEGSEM micrographs. (X) indicates no dispersoids were observed. (—)indicates that no measurements were made.

Fig. 6. (a) Pattern of dispersoid precipitation after homogenis-ation for 20 h at 500°C in a region adjacent to a grain boundary.The boundary itself is to the left of the area viewed. Regions1, 2 and 3 are referred to in the text. (b) Higher magnification

image of clusters of dispersoid particles seen in region 2.

fewer of them. Elongated clusters consisting ofgroups of 10 or more spherical dispersoid particlescan be seen. As region 2 is near to the grain boundary,the supersaturation of zirconium is low and thus thedriving force for the precipitation of Al3Zr is small.A consequence of this is that processes which requirea large activation energy will be stifled. However,processes which have smaller energy barriers will stillbe viable. The relatively low number density of dis-

persoids observed in region 2 suggests that here thehomogeneous nucleation rate, which will be verysensitive to the driving force, is drastically reducedand instead heterogeneous nucleation occurs at pre-ferred sites such as dislocations or pre-existing pre-cipitates. Evidence for nucleation on precipitates isprovided by the clusters of dispersoid particles. Thelocation and shape of these clusters correlates wellwith that of theh precipitates seen in the cast, stressrelieved, structure [Fig. 1(b)]. It therefore seemslikely that the dispersoids are nucleating hetero-geneously on these particles, prior to their dissolution.This observation is not surprising, since it is wellknown that the reverse behaviour (Al3Zr acting asheterogeneous nucleation sites forh precipitates)occurs during slow cooling from solution treatment[20, 21]. It is thus apparent that heterogeneous andhomogeneous nucleation are competing, with hetero-geneous nucleation becoming dominant at low solutesupersaturations. This behaviour is, however, depen-dent upon the availability of suitable nucleation sites.

As well as the regions close to grain boundaries,there were also interdendritic regions within thegrains where the zirconium concentration is muchlower than the average level. Figure 7 shows a typical

Fig. 7. A dispersoid free region across an interdendritic regionwithin a grain after homogenisation for 40 h at 500°C.


example of the dispersoid distribution in such aregion. As noted previously, the zirconium concen-tration falls below the level required for dispersoidprecipitation in the interdendritic region and there isthus a dispersoid free band. In contrast with obser-vations made close to grain boundaries, no clusters ofdispersoid particles were observed adjacent to thesebands. Instead there was a low number density oflarge, isolated dispersoids. This lack of dispersoidclusters within the grains arises because theh par-ticles on which they can nucleate were only foundnear the grain boundaries. The large, isolated disper-soids may therefore be the result of homogeneousnucleation with a low nucleation rate, due to the smallzirconium supersaturation. Alternatively they may beheterogeneously nucleated at a feature not yet ident-ified.

The position and width of the dispersoid freeregions discussed above depends on the temperatureof homogenisation. A decrease in homogenisationtemperature will lead to an increased zirconiumsupersaturation at all points. Therefore, at lower tem-peratures a narrower dispersoid free region would beexpected, providing there is sufficient time for com-plete precipitation. Nevertheless, even at the lowesttemperature where dispersoids were observed to pre-cipitate (400°C), the same general pattern of precipi-tation was observed and dispersoid free regions, of asimilar width, were still present.

4. MODELLING DISPERSOID PRECIPITATION

A model has been developed, based on the method-ology of Kampmann and Wagner [13], to predict theinfluence of zirconium concentration and homogenis-ation treatment on the precipitation kinetics and distri-bution of the metastable L12 Al3Zr (a9) particles. Themodel for precipitation kinetics has been coupled withdata for the segregation of zirconium in the cast struc-ture to enable the dispersoid distribution within agrain to also be predicted.

Development of the model required the use of sev-eral simplifying assumptions. These were:

O Metastable Al3Zr has the stoichiometric compo-sition and is the only precipitate in which zir-conium has appreciable solubility. Therefore, itsprecipitation in 7xxx series aluminium alloys maybe adequately modelled by consideration of themetastable phase boundaries in the Al–Zr binarysystem.

O Nucleation occurs homogeneously within thematrix, with the proviso that the nucleation ratewill depend upon the local zirconium concen-tration. Heterogeneous nucleation onh particles,which was observed in narrow regions close tograin boundaries, has been ignored since such par-ticles are likely to be present only in stressrelieved castings.

O The growth of the L12Al3Zr particles is controlled

by diffusion of zirconium to the particle/matrixinterface.

O The overlap of diffusion fields from adjacentgrowing particles (soft impingement) may beadequately represented using the mean fieldapproximation.

Subject to these assumptions, nucleation andgrowth of the Al3Zr dispersoids can be modelled ina rigorous manner [13]. Particle coarsening, whichbecomes most important once precipitation is close tocompletion, arises naturally as a result of the effectof precipitate curvature on the local composition atthe particle/matrix interface.

In order to calculate the precipitation kinetics thecontinuous time evolution is divided up into a discretenumber of small time steps of durationDt. At eachstep, new particles are allowed to nucleate and exist-ing particles grow (or shrink). The size distributionof the particles is updated accordingly and used tocalculate the volume fraction of dispersoids andhence the instantaneous average zirconium concen-tration in the matrix. The updated mean matrix con-centration is then used in calculating the nucleationand growth rates in the next time-step and this pro-cedure is repeated until the desired end-time is reach-ed.

4.1. Nucleation

The classical steady state nucleation equation hasbeen used to describe the nucleation rate. Thenucleation rate is then given by [22]:

J 5 N0

kTh

expS2G∗ 1 Q

kT D (1)

whereJ is the nucleation rate per unit volume.N0 isthe number density of nucleation sites which forhomogeneous nucleation is equal to the number ofzirconium atoms per unit volume.G∗ is the activationenergy barrier for formation of a critically sized clus-ter. Q is the activation energy for diffusion of zir-conium in aluminium.k andh are the Boltzmann andPlanck constants respectively andT is the thermodyn-amic temperature.G∗ is related to the critical radiusand the interfacial energy,s, according to:

G∗ 543pr∗2s (2)

Following Kampman and Wagner, the criticalradius size is calculated using the Gibbs Thomsonequation, an approach which is valid for dilute sol-utions. The critical radius corresponds to a specialcase of this equation, since whenr 5 r∗ the soluteconcentration at the interface is the same as the meanconcentration of the matrix and there is no concen-tration gradient at the interface.r∗ is thus given by:


r∗ 52sVa

kT lncca`

(3)

whereVa is the atomic volume,c is the instantaneousconcentration of zirconium in the matrix andca` is theconcentration of zirconium in the matrix in equilib-rium with Al3Zr assuming a planar interface. Valuesof ca` were obtained from the solvus line calculatedby Saunders [18] for the metastable Al3Zr phase inthe binary Al–Zr system.

The interfacial energy of the L12 Al3Zr particles(s) is unknown and is the only adjustable parameterin the model. This was determined by finding the bestfit between the predicted and experimental results, aswill be discussed in the next section.

At each time-stepr∗ is calculated first (equation 3)and used in conjunction with equations (1) and (2) tocalculate the nucleation rate. If it is assumed that thenew particles can form anywhere in the assembly (i.e.hard impingement may be ignored) then the numberof new particles formed in an intervalDt will simplybe vIDt. The radius of each of the newly formed par-ticles is set to be slightly larger than the critical radiusto enable these particles to grow. FollowingKampmann and Wagner this radius is arbitrarilytaken to be 10% larger thanr∗.

4.2. Precipitate growth

Fortunately the L12 Al3Zr particles have a simplespherical growth morphology. For spherical particles,the growth rate is given by:

drdt

5Dr

c2carca92car

(4)

where D is the diffusion coefficient,r the particleradius,car the concentration of zirconium in the matrixat the interface (including the effect of the curvatureof the interface) andca9 the concentration of zir-conium in the particle.car is calculated fromca` (themean matrix composition) using the Gibbs–Thomp-son equation, which for the general case (rather thanthe special case ofr 5 r∗) may be expressed as:

car 5 ca`expS2sVa

kT1rD (5)

The diffusion coefficient of zirconium in alu-minium was calculated at a given temperature from:

D 5 D0exp2QRT

(6)

whereR is the gas constant. The values forD0 and

Q used were 0.0728 m2 s21 and 242 kJ mol21 respect-ively [23].

4.3. Precipitate coarsening

The radii of particles which nucleate in each timeinterval are tracked separately. As the fraction of sol-ute in the matrix decreases during precipitation, thecritical particle radius increases, reducing thenucleation rate with time. Those particles which havea radius,r∗ will have a negative growth rate accord-ing to equation (4) and will thus shrink. When thesize of a group of particles reaches zero they areremoved from the size distribution. In this way, coars-ening as well as classical growth is accounted forusing these equations.

4.4. Dispersoid distribution within a grain

The experimental observations of dispersoid pre-cipitation demonstrate the strong effect that zirconiumsegregation has on the eventual distribution of disper-soid particles within each grain. It would be useful tobe able to predict this behaviour. Of particular interestis the effect of alloy composition and homogenisationconditions on the width of the dispersoid free zonessince these regions are likely to be particularly sus-ceptible to recrystallisation.

Due to zirconium’s slow diffusion rate, Al3Zr dis-persoids precipitate before there is time for any long-range diffusional redistribution. This can be demon-strated by a simple√Dt estimate of the mean diffusiondistance. For example, even after 24 h at 475°C thezirconium remaining in solid solution will only havediffused .0.3 µm. Therefore, to make the predic-tions, only a knowledge of the variation in zirconiumconcentrationc(x) with distancex prior to homogenis-ation is required. This is available directly from themicroprobe measurements for the 0.13 wt% Zr alloystudied. A simple Scheil model, fitted to microprobedata for the 0.13 wt% Zr alloy, was used to describethe segregation during casting for other zirconiumconcentrations. The Scheil equation gives the zir-conium concentration in the solid (cs) as a functionof the volume fraction solidified (fs) during castingfor one dimensional solidification [24].

cs 5 kc̄(12fs)(k21) (7)

where c̄ is the mean concentration of zirconium andk is the partitioning coefficient. As a first approxi-mation, it was assumed that during solidificationfsincreased linearly from 0 to 1 as each dendrite grewoutward (a 1-dimensional solidification model).fsmay then be replaced byfx in equation (7) wherefxis the fractional distance across the dendrite arm fromthe centre to the edge.

Equation (7) therefore enables composition vs dis-tance profiles to be estimated for any givenc̄. Usingc̄ 5 0.13 wt% for the alloy investigated the predictedprofiles were compared with the microprobe measure-


ments. It was found that good agreement could bereached between microprobe measurements and pre-dicted values if the partition coefficientk was takenas being equal to 1.4 (Fig. 8). This value ofk wasused to predict the composition profile for alloys withother mean zirconium concentrations.

The model for the precipitation kinetics was runrepeatedly, using the local zirconium concentrationspredicted from the Scheil equation as inputs. In thisway, the variation in the mean particle size, numberdensity and volume fraction was predicted as a func-tion of distance from the edge to the centre of the den-drites.

5. DISCUSSION OF PREDICTIONS

5.1. Calibrating the model

The interfacial energy,s, of the Al3Zr dispersoidsis required in both the expressions for nucleation andgrowth. Consistent experimentally measured valuesof this parameter are not available, particularly duringthe early stages of transformation. The value used forthe interfacial energy was therefore found by fittingthe predicted values to the experimental results. At500°C metastable dispersoids were observed after allheat treatment times and thus data from this tempera-ture were used to perform the fitting. The best agree-ment between predicted and measured particle radiiand number density at this temperature was obtainedwith s 5 0.10 Jm22 (Fig. 9). This value was thenverified across a range of temperatures by comparingthe predicted and actual times required for dispersoidobservation. To do this, it was assumed that disperso-ids were first observed when the maximum particleradius exceeded 10 nm (the radius of the smallest par-ticles observed in practice). Figure 10 shows that thepredicted time required for the largest dispersoids toreach this radius is consistent with the observations.The value of 0.1 J m22 for the interfacial energy iswithin the upper limit of.0.2 J m22 expected for afully coherent nucleus [24].

Normalised Distance

Zir

coni

um C

once

ntra

tion

/ w

t%

0 10.5

0

0.1

0.05

0.15

Scheil (k=1.4)

Fig. 8. Zirconium concentration profile from the dendrite edge to the centre predicted by the Scheil modelusing a partition coefficient (k) value of 1.4. Two measured profiles are shown for comparison.

(a)

(b)

Fig. 9. Predicted evolution of (a) dispersoid numberdensity/µm23 (N) and (b) mean particle radius/nm (r) at 500°Cfor a zirconium concentration of 0.13 wt%. Experimental datapoints and associated error bars corresponding to one standard

deviation are shown for comparison.

5.2. Predicted TTT behaviour

The predicted time taken for Al3Zr to reach a givenvolume fraction (0.05%) is shown on a TTT-diagramin Fig. 11(a) for a zirconium concentration of 0.13wt%. It can be seen that the most rapid precipitationkinetics are predicted at 495°C which is within therange expected from previous qualitative studies ofAl3Zr precipitation kinetics [6–8]. It is interesting tocompare this diagram with that in Fig. 10 which givesthe time taken for the dispersoids to reach a certainsize. The differences between the two diagrams arebest explained with reference to Fig. 11(b). This


Time / h

Tem

pera

ture

/ C

-110 010 110 210

400

500

350

450

550

Predicted Detected Not detected

Fig. 10. A plot of the predicted time taken for the maximum dispersoid radius to reach 10 nm for a zirconiumconcentration of 0.13 wt%, which is approximately the critical size required for detection. Also shown are

experimental data points indicating whether any dispersoids were found.

Time / h

Tem

pera

ture

/ C

110 210

400

500

450

550

0.05%

Temperature / C

Gro

wth

or

Nuc

leat

ion

Rat

e (n

orm

alis

ed)

200 300 400 500 600250 350 450 550

0

1

0.5

Nucleation rateGrowth rate

Fig. 11. (a) Predicted TTT diagram for forming a 0.05% volume fraction of Al3Zr for a zirconium concentrationof 0.13 wt%. (b) Variation of the normalized growth and nucleation rates with temperature.

shows how the nucleation and growth rates vary as afunction of temperature at the start of transformation.The peak nucleation rate occurs at 450°C and thepeak growth rate at 555°C. Thus, at 450°C the highestnumber of particles will form, but these will growslowly. At 495°C the optimum balance between thegrowth and nucleation rates is obtained, giving thefastest kinetics. Above this temperature, fewer par-ticles form, but those which do, grow increasinglyrapidly. Therefore the time taken to reach a certainparticle size continues to decrease even though theoverall transformation kinetics are now slower.

5.3. Optimisation of homogenisation

Precipitation of a uniform fine distribution of dis-persoid particles during homogenisation is known tomaximise the resistance to recrystallisation [1]. Thedispersoid size and spacing will clearly be effectedby homogenisation temperature and time. In practice,the range of temperatures and times used are limitedsince the primary requirement of homogenisation isto dissolve as many of the unwanted intermetalliccompounds as possible and redistribute the alloyingelements uniformly. To do this, the temperature for


homogenisation must exceed.470°C. Although thisis predicted to be below the nose of the kinetics “C”curve, it is above the peak in the nucleation rate andis thus not the best temperature for forming the finestdispersoid distribution. In practice, the maximumhomogenisation temperature is also limited to below485°C to avoid liquation of low melting point eutec-tics. This gives a rather narrow temperature windowwithin which alloys such as 7050 can be homogen-ised. Figure 12 shows the predicted evolution of dis-persoid size and number density with time for a 0.13wt% Zr alloy homogenised at 475, 480 and 485°C.Despite the small difference in temperature, there ispredicted to be a significant effect on the particle den-sity. As expected, the mean radius is predicted to beleast and the number density greatest at the lowesttemperature, since here the growth rate is smallest andthe nucleation rate greatest. When considering thelikely effect of a reduction in homogenisation tem-perature on the recrystallisation resistance, theincreased fraction of undissolved large intermetallicparticles at low temperature must also be taken intoaccount. Such particles promote recrystallisation byacting as sites for particle stimulated nucleation ofnew grains [11]. This effect will therefore competewith the increased Zener pinning expected due to arefined dispersoid distribution.

It has previously been reported that slow heatingrates up to the homogenisation temperature lead to a

Time / h

Mea

n P

arti

cle

Rad

ius

/ nm

0 10 205 15

0

10

20

5

15

475480485

Time / h

Num

ber

Den

sity

0 10 205 15

0

10

20

30

40

50

60

475480485

Fig. 12. (a) Predicted evolution of mean radius and (b) dispersoid number density/µm3 with time for threedifferent homogenisation temperatures.

refinement in dispersoid size [7, 10]. In commercialpractice, slow heating will arise naturally due to thethermal mass of the ingot, the centre heating up moreslowly than the surface. The model was used to inves-tigate the effect of heating rate on the dispersoid sizeand number density. Figure 13(a) shows the variationof the predicted mean radius with heating time for ahigh temperature homogenisation treatment of 480°Cfor 24 h at temperature. It can be seen that a modestrefinement in size, from a mean radius of 17 nm toa mean radius of 14 nm is predicted for ramp heatingover 40 h rather than the isothermal treatment. How-ever, the particle number density increases more shar-ply and almost doubles. In Fig. 13 it can be seen thatif even longer heat up times are used, some furtherrefinement is predicted, but the sensitivity to heatingrate drops.

Changing the average zirconium concentration ofthe alloy would be expected to lead to changes in thedispersoid radius and number density. The specifi-cation for alloy 7050 allows for zirconium in therange 0.08–0.15 wt%. The predicted effects of vary-ing the zirconium level in this range on the mean par-ticle size and number density are shown in Fig. 13(b).In commercial practice, it is unlikely that a zirconiumlevel as high 0.15 wt% can be retained in solid sol-ution after casting due to precipitation of primaryAl3Zr. This calculation also only reflects the “aver-age” behaviour since segregation leads to large local


Fig. 13. (a) Predicted effect of heat up time to homogenisation(24 h at 480°C) on the number density/µm3 and mean radiusof the dispersoids. (b) Predicted number density/µm3 and meanparticle radius as a function of zirconium concentration afterhomogenisation for 24 h at 480°C (allowing a 20 h heat up

time).

fluctuation in zirconium concentration. As expected,it is predicted that increasing the zirconium contentleads to a greater number of dispersoid particles, sincethe driving force for nucleation increases. From Fig.13(b) it can be seen that there is a wide variation inthe number density of particles in going from the low-est to the highest zirconium concentration. Thisreflects the large range of zirconium concentrationpermissible in 7050 and the high sensitivity ofnucleation rate to supersaturation. The predicted vari-ation in the mean dispersoid radius shows theopposite trend. This behaviour results from the com-petition for the available solute between growth andnucleation. At higher zirconium levels, the nucleationrate is large and many particles form, each of whichis only able to grow to a small size before exhaustingthe supersaturated zirconium. As the zirconium levelfalls, the nucleation rate falls more sharply than thegrowth rate. Since far fewer particles are forming,each particle can grow to a larger size before exhaust-ing the supersaturated zirconium, despite there beinga lower zirconium concentration. This agrees with theexperimental observations which show an increasedparticle size as the local zirconium concentration fallstowards the edge of the dendrite arms (e.g. Fig. 7).The average grain boundary pinning pressure of thedispersoids in a 0.08 wt% alloy is therefore expected

to be several orders of magnitude smaller than that ina 0.15 wt% Zr alloy.

5.4. Dispersoid distribution within a grain

Experimental observations have shown that the dis-persoids are heterogeneously distributed within eachgrain. This has been attributed to variations in thelocal zirconium concentration resulting from segre-gation during casting. The model was therefore usedto make predictions of the volume fraction, mean par-ticle radius and number density as a function of pos-ition, using the concentration profile fitted with theScheil equation. Figure 14 shows the predicted vari-ation in dispersoid size and number from the edge tothe centre of a dendrite after isothermal homogenis-ation for 20 h at 480°C. The model correctly predictsa dispersoid free region at the dendrite edge. This isfollowed by a transition region with a small numberof particles with a relatively large mean radius. At thehighest zirconium concentrations the particle numberdensity increases and the size decreases. All of thesephenomena are consistent with the experimentalobservations [Fig. 6(a)]. However, heterogeneousnucleation of dispersoids is not accounted for in themodel. Thus, the predicted number density in regionswhere heterogeneous nucleation occurs is likely to bean underestimate.

The dispersoid free regions are likely to recrys-tallize most easily, as has been noted by previousworkers [11]. Therefore, reducing the width of theseregions is expected to lead to a beneficial decrease inthe fraction of recrystallisation. Homogenising at alower temperature will increase the zirconium super-saturation at all points across the grain and thus dis-persoids should form at a lower zirconium level, pro-viding the kinetics of precipitation are sufficientlyrapid at the lower temperature. Increasing the averagezirconium concentration will similarly increase thesupersaturation, although the magnitude of theincrease will also depend on how the zirconium seg-

Fig. 14. Predicted number density/µm3 and mean particle radiusas a function of the normalized distance between dendrite edgeand centre after homogenisation for 24 h at 480°C (allowing

a 20 h heat up time).


regates. Figure 15 shows the predicted effects of hom-ogenisation temperature, average zirconium concen-tration and heating rate (within commercially possibleranges) on the variation in volume fraction of the dis-persoid phase for a standard homogenisation time of24 h. It can be seen from Fig. 15 that changing thehomogenisation temperature has a fairly small effecton the width of the dispersoid free region. This isbecause there are two competing effects at work. Atlower homogenisation temperatures, the supersatu-ration of zirconium is increased and thus precipitationof dispersoids is thermodynamically possible at a

Fig. 15. Prediction of the volume fraction of dispersoids as afunction of the normalized distance between dendrite edge andcentre after 24 h homogenisation. (a) Three homogenisationtemperatures (0.13 wt% Zr, 20 h heat up time). (b) Three meanzirconium levels (480°C homogenisation, 20 h heat up time).(c) Comparing isothermal and ramp heating (0.13 wt% Zr,

480°C homogenisation).

lower zirconium level (i.e. closer to the dendriteedge). However, the kinetics of precipitation areslower at the lower temperature. The model predictsthat the kinetic effect outweighs the thermodynamiceffect; i.e. the dispersoid free region is slightly widerat lower temperature because there is insufficient timefor complete precipitation, despite the increasedsupersaturation. The Scheil model was then used topredict the concentration profiles for mean zirconiumlevels of 0.11 wt% and 0.09 wt%. The predictedeffect of the three zirconium levels on the variationin dispersoid volume fraction is shown in Fig. 15(b).It can be seen that relatively small reductions in theaverage zirconium level are predicted to lead to a sub-stantial increase in the width of the dispersoid freeregion. For example, a decrease in zirconium concen-tration from 0.13 to 0.09 wt% is predicted to doublethis width.

Ramp heating, at a sufficiently slow rate, wouldalso be expected to reduce the width of the dispersoidfree region due to the increased zirconium supersatu-ration and hence enhanced particle nucleation duringheating. The predicted effect of three different ramprates is shown in Fig. 15(c). It can be seen that com-pared with isothermal treatment, ramp heating leadsto a significant decrease in the width of the dispersoidfree region. There is, however, little advantage to begained from use of a heat up time longer than 20 h.

The model was further used to predict the patternof dispersoid precipitation across an interdendriticregion within a grain and compare this with experi-mental observation. In Fig. 16(a), a plot is given ofthe measured zirconium concentration across such aregion prior to homogenisation. Figure 16(b) is a plotof the predicted dispersoid number density and meanradius across the same region following homogenis-ation at 500°C for 40 h. These predictions were com-pared with the observed pattern of dispersoid precipi-tation in the same region after an identical heattreatment (Fig. 6). The model has correctly predictedthat as the zirconium concentration falls, the numberdensity of particles decreases and the mean radiusincreases to reach a peak, resulting in a narrow bandof large particles. On further reduction of the zir-conium, the predicted number density falls to almostzero, corresponding to the dispersoid free region. It isinteresting to note that the observed increase in meanparticle radius in the regions of intermediate zir-conium concentration is predicted to occur even ifnucleation in these regions still occurs homo-geneously. This behaviour is a result of the relativechanges in the growth and nucleation rate with zir-conium concentration, as discussed previously.

6. CONCLUSIONS

The precipitation of metastable Al3Zr dispersoidshas been studied in a commercial aluminium alloy inwhich there is strong microsegregation of zirconium.These results have been compared with a model


Fig. 16. (a) Measured zirconium concentration across an inter-dendritic region within a grain after casting. (b) Predicted andmeasured particle number density and mean dispersoid radiusacross the same region after homogenisation for 40 h at 500°C.

developed in order to optimise the homogenisationtreatment of commercial castings.

1. Strong zirconium segregation towards the dendritecentres occurs during the casting of a commercial7050 aluminium alloy.

2. The pattern of dispersoid precipitation observedwithin a grain after homogenisation treatmentdepends critically on distribution of zirconium. Inlow zirconium regions, the solubility limit is notexceeded and no dispersoids precipitate. At inter-mediate zirconium levels, a low density of largeparticles form, which nucleate heterogeneously ondislocations or h particles where present. Inregions of higher zirconium, a fine distribution ofhomogeneously nucleated dispersoids is observed.

3. A physical model has been developed to describethe kinetics of precipitation and distribution ofmetastable Al3Zr dispersoids. The model has gen-eral applicability and has been shown to reproducethe experimental observations well for a commer-cial 7050 alloy. The model provides a powerfultool in predicting the effects of changes in alloycomposition and homogenisation practice on thedispersoid distribution.

4. Use of a lower homogenisation temperature andramp heating are predicted to lead to a modestreduction in particle size and a significant increasein number density. This is expected to increase theeffectiveness of the dispersoids in pinning grain

boundaries. Large changes in dispersoid size andnumber density (and therefore pinning effect) arepredicted for variations in zirconium concentrationwithin the range allowed for in commercial alloyspecifications.

5. Interdendritic and grain boundary free regions areknown to recrystallise the most readily. It is pre-dicted that the width of the dispersoid free regionsis almost unchanged by altering the homogenis-ation temperature. Use of slow heat up rates tothe homogenisation temperature and an increase inzirconium concentration both reduce the predicteddispersoid free width. The zirconium concen-tration is predicted to have the most potent effect,with a small increase in zirconium concentrationleading to a large reduction in the dispersoidfree width.

6. The predictions imply that to obtain a dispersoiddistribution which leads to a minimum fraction ofrecrystallisation requires a zirconium concen-tration near the upper limit (e.g. 0.13 wt% Zr) andslow heating to the homogenisation temperature,with a heat up time of 20 h being sufficiently long.Since the width of the dispersoid free region ispredicted to be insensitive to small changes inhomogenisation temperature, this should bechosen to fully dissolve the soluble intermetallicparticles.

Acknowledgements—The authors are grateful to The LuxferGroup for funding this work. They also thank J. Newman andS. Khosla of Luxfer for their invaluable help and advice.

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dispersoid precipitation and process modelling in

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