thermal expansion behaviour of aluminium/sic …s3.amazonaws.com/zanran_storage/ of metal matrix...

Acta Materialia 51 (2003) 3145–3156www.actamat-journals.com

Thermal expansion behaviour of aluminium/SiC compositeswith bimodal particle distributions

R. Arpon a, J.M. Molinaa, R.A. Saravanana, C. Garcı´a-Cordovillab, E. Louisac,J. Narcisod,∗

a Departamento de Fısica Aplicada, Universidad de Alicante, Apartado 99, E-03080 Alicante, Spainb Centro de Investigacion y Desarrollo, Flat Rolling Products, Alcoa Europe, Apartado 25, E-03080 Alicante, Spain

c Unidad Asociada of the Consejo Superior de Investigaciones Cientıficas, Universidad de Alicante, Apartado 99, E-03080Alicante, Spain

d Departamento de Quımica Inorganica, Universidad de Alicante, Apartado 99, E-03080 Alicante, Spain

Received 25 June 2002; accepted 21 January 2003

Abstract

The thermal response and the coefficient of thermal expansion (CTE) of aluminium matrix composites having highvolume fractions of SiC particulate have been investigated. The composites were produced by infiltrating liquid alu-minium into preforms made either from a single particle size, or by mixing and packing SiC particulate of two largelydifferent average diameters (170 and 16µm, respectively). The experimental results for composites with a single particlesize indicate that the hysteresis in the thermal strain response curves is proportional to the square root of the particlesurface area per unit volume of metal matrix, in agreement with current theories. Instead, no simple relationship isfound between the hysteresis and any of the system parameters for composites with bimodal particle distributions. Onthe other hand, the overall CTE is shown to be mainly determined by the composite compactness or total particlevolume fraction; neither the particle average size nor the particle size distribution seem to affect the overall CTE. Thisresult is in full agreement with published numerical results obtained from finite element analyses of the effective CTEof aluminum matrix composites. Our results also indicate that the CTE varies with particle volume fraction at a pacehigher than predicted by theory. 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Aluminium/SiC composites; Thermal response and thermal expansion coefficient; Infiltration; Bimodal particle distri-butions

1. Introduction

The interest in high volume fraction ceramicreinforced Metal Matrix Composites (MMCs) is

∗ Corresponding author. Fax:+34-96-590-3454.E-mail address: [email protected] (J. Narciso).

1359-6454/03/$30.00 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.doi:10.1016/S1359-6454(03)00126-5

steadily increasing. The efforts are mainlyaddressed to implementing their use in multifunc-tional electronic packaging[1–5]. The key require-ments for this application are a high thermal con-ductivity and a coefficient of thermal expansion(CTE) similar to that of common elements inmicroelectronic systems. Ceramics show an

3146 R. Arpon et al. / Acta Materialia 51 (2003) 3145–3156

admissible CTE, while recent processing develop-ments (particularly in sintering and densification,see [6]) have allowed materials to be producedwith a rather high thermal conductivity. Forinstance, monocrystalline SiC has a thermal con-ductivity around 500 W m�1 K�1 which, althoughdecreasing down to 270 W m�1 K�1 in sinteredpolycrystalline material, is more than enough to beused as an electronic support. However, the mainproblem with ceramic materials is the yet insuf-ficient development of metallization technologies(required in most assembling processes). On theother hand, metal supports have a high CTE thatcan produce unacceptable deformations inmicroelectronic systems, while carbon supports inits turn, having a good thermal conductivity, caninduce large deformations due to an excessivelylow and anisotropic CTE.

High volume fraction MMCs usually show asufficiently high thermal conductivity [7], althoughthe different conduction mechanisms in the twomaterials, mainly phonons in ceramics and elec-trons in metals, lead to thermal conductivity valuesbelow the level one could expect (see [8]). On theother hand, due to the largely different CTE of theceramic particle and the metal matrix, the overallCTE of the composite strongly depends on thereinforcement type and content [7–16]. This opensthe possibility of tailoring the composite CTE tofit the requirements of electronic systems. Besides,MMCs allow net-shape fabrication and easy inte-gration of functional components [7]. Thesecharacteristics make high volume fraction MMCa highly promising material family for electronicpackaging applications. An a priori feasible way toobtain particle volume fractions (Vp) as high asthose required for microelectronic packaging(above 0.6) is to attempt compacting the particlesup to their maximum theoretical density. As thisis, however, unpractical (see, for instance, [17] fora more detailed discussion) most of the activity inthis field is being addressed to investigate the pro-duction of high particle volume fractions by pack-ing particles having different sizes [18–20].Recently, it has been concluded that, in order toachieve large particle volume fractions, particles ofsubstantially different sizes have to be used [19].A ratio between average diameters larger than

seven is usually needed to attain acceptable pack-ing efficiencies [20].

Aluminium based composites having high vol-ume fractions of SiC particulates are one of themost suitable and versatile materials among theclass of metal matrix composites currently beingevaluated for these applications. These materialsare produced mainly by pressure infiltration of theliquid metal into the ceramic preform [17,21–24].The purpose of this article is to discuss the resultsof an investigation of the thermal response and theCTE of aluminium matrix composites obtainedthrough pressure infiltration of liquid aluminiuminto SiC particles preforms having bimodal sizedistributions [25,26]. A size ratio larger than 10was used, which allowed particle volume fractionsas high as 0.74 to be obtained. In order to facilitatethe interpretation of the experimental data com-posites having a single particle size have also beeninvestigated. The experimental results (mainly forthe hysteresis in the thermal response curves andthe CTE) are discussed in the light of currenttheories.

2. Experimental procedures

2.1. Materials and fabrication of the composites

Bimodal particle mixtures were prepared fromSiC particles of 16 and 170 µm average diameters;the latter is around twice the maximum sizereported in [1] as being used in commercial com-posites having at least two different particle sizes.The main characteristics of the particulate aregiven in Table 1, and the two particle size distri-butions depicted in Fig. 1. The spans of the sizedistributions (0.95 and 0.71 for fine and coarse par-ticles, respectively) are in the lower end of therange covered by particulates used in previousstudies [23,24]. Particles are rounded (as classifiedby the supplier) with a low aspect ratio of 1.9, thatwas obtained after averaging over a large numberof particles with the help of Image Analysis. Thetapped pack densities provided by the supplier are1.69 and 1.81 for fine and coarse particles, whichgive particle volume fractions Vp of 0.526 and0.565, both quite close to the values attained in this

3147R. Arpon et al. / Acta Materialia 51 (2003) 3145–3156

Table 1Average diameter D (in µm) of the two SiC particulate used in this work

Particulate D D(10) D(90) Span TPD Purity

Fine particles (fp) 16 8.3 23.5 0.95 1.69 98.5%Coarse particles (cp) 170 112 232 0.71 1.81 98.5%

The corresponding size ratio is r = Dfp /Dcp = 0.094. D(x) is the diameter (also in µm) below which x% of the particles are found.The span of the size distribution is defined as [D(90�D(10)]/D(50). The purity of the particulate is also given. The data concerningparticle size distribution (D, D(10), D(90) and the span) were obtained by means of laser scattering using a Malvern Master Sizer.In the present case the average diameter D and D(50) almost coincide (see [24]). The tapped pack density (TPD), as provided bythe supplier, is also given.

-1 -0.5 0 0.5 1 1.5

(d-D)/D

0

5

10

15

P(d

) in

per

cen

tag

e

Fig. 1. Particle size distribution P(d) in percentage, versus (d�D) /D, where D is the average particle diameter, for the fine andcoarse particles used to prepare the bimodal compacts.

work (the agreement is better for coarse particlesas no strokes were used in preparing the compacts,see below and Table 2). Other particles withcharacteristics similar to those of Table 1 anddiameters in the range 6.5–63 µm, were used toproduce composites with a single particle size.Aluminium of commercial purity (around 99.7%)was used to infiltrate the SiC compacts. In prepar-ing the particle compacts we followed the pro-cedures of [23–27]. The ceramic particles werepacked in quartz tubes (5 mm of inner diameter)to a height of approximately 35 mm. Preforms hav-ing a single particle size were prepared by combin-ing strokes of a weight and vibrations. Packing wascarried out in several steps, adding only small

amounts of particulate in each step. As in the caseof coarse particles breaking occurred profusely(probably due to its very large average diameter,see Table 1), they were packed by applying onlyvibrations. It was checked that the method gavea satisfactory homogeneity and a reasonably highcompactness. In the case of particle mixtures theprocess requires two stages: (i) mixing of the par-ticles, and (ii) packing of the mixtures. Mixing wascarried out in ethanol by means of the methoddescribed in [26]. The mixture was subsequentlydried and packed in the quartz tubes by applyingstrokes of a weight (in order to avoid particle seg-regation in the mixtures, vibrations were notapplied). Following these procedures (discussed in


Table 2Experimental results for the particle volume fraction obtained with particle mixtures made from particles of Table 1, versus theamount of coarse particles. The results for the coefficient of thermal expansion and the hysteresis in the thermal response curve (seetext) obtained on composites produced from those mixtures are also reported

% Coarse Vp ��t (×10�3) CTE50–300 (ppm K�1)

0 0.553 0.161 13.425 0.621 0.143 10.850 0.695 0.118 967 0.742 0.076 7.875 0.719 0.080 8.4100 0.578 0.087 12.7

more detail in [25,26]) several mixtures of coarseand fine particles were prepared (100, 75, 67, 50,25 and 0% of coarse particles).

Infiltration was carried out at a melt temperatureof 1023 ± 2 K. The compacts were preheated for5 min by holding the quartz tube just above themelt; it should be noted that shorter preheatingtimes may lead to depacking. The latter is probablyproduced by the expansion of the compact due toits sudden heating as the tube is introduced in themelt; this is particularly critical in the case of par-ticle mixtures due to their high particle volumefractions. The metal surface was cleaned justbefore introducing the quartz tube into the liquidmetal. A pressure well above threshold [25,26] wasthen applied with nitrogen gas. The infiltrated com-pact was then taken out of the melt, air cooled, andsamples were cut for microstructure evaluation andthermal response studies.

2.2. Measurement of the thermal strain responsecurves

A thermomechanical analyser (TMA 2940, TAInstruments) was used to obtain the thermalresponse curves from which the coefficient of ther-mal expansion, among other data, was derived.Samples of approximately 5 mm in length were cutfrom the infiltrated composites using a low speedsaw, all of them being subsequently polished.Measurements were carried out at an applied forceof 0.05 N, under nitrogen atmosphere, and in thetemperature range 298–573 K (heating and coolingrates were 3.00 K/min). The samples were sub-jected to at least four heating and cooling cycles

to remove large residual stresses, if any, developedduring processing of the composite. It is worth not-ing that the hysteresis in the thermal cycle is highlysensitive to the experimental conditions, parti-cularly to the heating and cooling rates, samplesize and shape, and the period of time elapsedbetween the point at which the maximum tempera-ture was reached and the initiation of cooling. Thelatter was kept close to zero in the present experi-ments.

2.3. Microstructure characterisation

In order to characterise the composite micro-structure, samples were sectioned in directionslongitudinal and transverse to the direction ofinfiltration and polished using standard metallo-graphic techniques. A thorough microstructuralexamination of the infiltrated samples was carriedout by means of optical microscopy (OlympusPME-3).

3. Results and discussion

3.1. The composites and their microstructure

As shown in Table 2, particle volume fractionsabove 0.6 can be easily obtained by means of theprocedures followed in this work. As expected, thecompactness shows a maximum as the relativeamount of the two particles is changed. The mix-ture having 67% of coarse particles shows themaximum compactness, 0.74, a value 30% higherthan those obtained for compacts containing a sin-


Table 3Experimental results for the coefficient of thermal expansion and the hysteresis in the thermal response curve (see text) obtained oncomposites produced from compacts containing a single particle size

D (µm) Vp ��t (×10�3) CTE50–300 (ppm K�1)

6.5 0.527 0.202 14.916 0.553 0.161 13.429 0.577 0.126 12.963 0.589 0.118 12.5170 0.578 0.087 12.7

gle particle size (see also Table 3 where particlevolume fractions for compacts having a single par-ticle size are reported). For a thorough discussionof these results we address the interested readerto [25,26]. The microstructure studies revealed auniform distribution of SiC particles with scarcemicrosegregation of fine particles in the com-posites made from mixtures. Representative micro-structures of composites made from mixtures con-taining 25 and 67% of coarse particles are shownin Fig. 2.

3.2. The thermal strain response curve

Almost all of the samples investigated hereshowed negligible changes in their thermal strainresponse upon successive heating/cooling cycles,which indicates that residual stresses accumulatedduring processing are negligible. A typical curvefor the composite having the largest particle vol-

Fig. 2. Optical micrographs of composites made from a particle mixture containing 25% (a) and 67% (b) of coarse particles, respectively.

ume fraction (67% of coarse particles in themixture) is shown in Fig. 3. Two parameters com-monly used to characterise these curves are shownin the Fig. 3. The first ��t is used to quantify thehysteresis in the curve and is just the largest verti-cal (at a given temperature) difference between thecooling and heating curves. The second �c, usuallyreferred to as cyclic strain, gives an informationequivalent to that provided by the CTE obtainedfrom fittings over the whole temperature range (seebelow) and, therefore, will not be discussed hereany further.

The experimental results for ��t obtained oncomposites having bimodal particle distributionsare reported in Table 2. The data are plotted versusthe percentage of coarse particles in Fig. 4. Nosimple relationship between this variable, and anyof the system parameters was found. This is notthe case, however, for composites made out ofcompacts having a single particle size. The results


0

1

2

3

0 50 100 150 200 250 300 350

TEMPERATURE (ºC)

L/L

0 (

x1

0-3

)

!∀ t ∀ c

Fig. 3. Relative expansion versus temperature obtained in thefirst and fourth heating/cooling cycles, on samples of com-posites made from a particle mixture containing 67% of coarseparticles. The strain parameters that characterise the cyclicstrain (�c) and the hysteresis (��t) are indicated.

0 20 40 60 80 100

% COARSE PARTICLES

0.05

0.07

0.09

0.11

0.13

0.15

0.17

∆εt (1

0-3)

Fig. 4. Experimental data for the hysteresis parameter ��t

obtained on thermal response curves for composites with bimo-dal particle distributions versus the percentage of coarse par-ticles. The continuous line is a guide to the eye.

for coarse and fine particles reported in Table 2 arecomplemented by those of Table 3. It is noted thatthe hysteresis sharply decreases as the particleaverage diameter increases. In order to find a quan-titative relationship between the hysteresis and thesystem parameters we borrow the standard theorydiscussed in [28].

The hysteresis parameter is known to be pro-

portional to the increase in yield strength �sinduced by the difference in CTE between the Aland SiC, namely

�et��s (1)

This increase in yield strength is in its turn givenby,

�s � bmbr1/2 (2)

where b is a geometric constant related to thematrix [29–31] , and, m and b are the shear modu-lus and the Burgers vector of the matrix(aluminium) respectively. Besides, the dislocationdensity ρ can be written as,

r �Beb

Vp

(1�Vp)t(3)

where B is a geometric constant, � the misfit straindue to the above mentioned difference in CTE andt the smallest dimension of the particle. The dislo-cation density can be rewritten in terms of the par-ticle surface area per unit volume of the matrixSp as,

r �eb

Sp (4)

In the case of spherical particles Sp is given by [17]

Sp �6lVp

(1�Vp)D(5)

where l is a parameter introduced to account fordeviations from sphericity. The ratio l/D plays arole equivalent to B/t in Eq. (3).

The experimental results for ��t, obtained oncomposites made out of a single particle size, areplotted in Fig. 5 versus the parameter Vp / [(1�Vp)D]. The data can be satisfactorily fitted bymeans of the straight line,

�et � �0.35� Vp

(1�Vp)D�1/2

� 0.058� � 10�3 (6)

This indicates that the geometric factor in Eq. (5)is similar for all particles here investigated, in linewith the fact that their aspect ratios are all around2 [17]. It is worth noting that in the case of thethreshold pressure for liquid metal infiltration, thegeometric factor l may significantly vary from par-


0.05 0.15 0.25 0.35 0.45

[Vp/{(1-Vp)D}]1/2

0.05

0.1

0.15

0.2

0.25

∆εt (1

0-3)

Fig. 5. Experimental data the hysteresis parameter ��t

obtained on thermal response curves for composites with a par-ticle size plotted as a function of the parameter [Vp /{(1�Vp)D}]1/2 in Eq. (4). The continuous curve is the straight linefitted to the data, namely, �� t = (0.058 + 0.35[Vp /{(1�Vp)D}]1/2) × 10�3, with D in µm.

ticle to particle. This may be a consequence, how-ever, of the important effect that the span of thesize distribution has on the threshold pressure [17].In the present case, the results of Fig. 5 allow usto conclude that the hysteresis is proportional tothe surface area per unit volume of metal matrix.

The main difficulty in applying this theory to thecase of bimodal particle distributions lies upon thedefinition of an effective particle diameter to beinserted in Eq. (5). As remarked above, we havenot found a simple way to do it.

3.3. The thermal expansion coefficient

The results shown in Fig. 3 clearly indicate thatthe thermal expansion is not linearly related withtemperature, at least over the whole range exploredhere. Nonetheless, one can draw qualitative con-clusions from linear fittings over wide temperatureranges. Furthermore, as already pointed out, theslope of those fittings (the CTE) gives an infor-mation identical to that of parameter �c in Fig. 3,commonly used to characterise thermal responsecurves. Tables 2 and 3 and Fig. 6 report results forthe CTE (obtained from fittings in the range 50–300 °C) versus particle volume fraction for com-posites having a single particle size or bimodal par-

0.52 0.58 0.64 0.7 0.76

Vp

6

8

10

12

14

16

CTE

(10-6

K-1

)Fig. 6. Thermal expansion coefficient obtained from a linearfitting of the experimental data for the thermal expansion overthe range 50–300 °C (see Fig. 2) versus particle volume frac-tion. The results correspond to composites having either a singleparticle size (circles) or bimodal particle distributions(triangles). The data can be satisfactorily fitted by the straightlinea = 31.3�32.0Vp 10�6 K�1.

ticle distributions. As shown in the figure the datacan be satisfactorily fitted by means of,

a � 31.3�32.0Vp (7)

Hereafter we shall refer to the coefficient of ther-mal expansion by means of either CTE or a. Thefitting is equally valid for composites having a sin-gle particle size or bimodal particle distributions,reinforcing the conclusion that what matters as faras the CTE is concerned is the global particle vol-ume fraction, in qualitative agreement with mostanalyses of the CTE [3].

These results show no significant effect of theparticle size on the CTE. This is in full agreementwith recent experimental studies of the thermalexpansion behaviour of Al/oxidised SiCp [3] andAl/SiCp [31], in which the average particle sizewas varied either in the range 3–40 µm [3] or 3.5–20 µm. [31]. The authors of [3] noted that the silicalayer produced by the oxidation of SiC was respon-sible for the variation in CTE with particle sizethey had observed, and that no effect should beascribed to the particle size itself. In [32], the slightincrease (less than 10%) in the CTE of Al/TiCcomposites, observed when the particle size was


increased from 0.7 to 4.0 mm, was explained [32]in terms of the lattice distortion at the interfacialzone.

It is worth noting that the numerical calculationsreported in [33] are fully consistent with thepresent experimental results. In [33] it wasremarked that the results revealed no effect of thereinforcement spatial or size distribution. Thisobservation is in complete agreement with theresults of Fig. 6, which indicate that the only rel-evant parameter is the particle volume fraction (nomatter whether the composite has a single particlesize or a bimodal size distribution). Besides, nodependence of the CTE on the particle size wasreported in [33]. On the other hand, the results forthe continuous ductile phase model (surely the onewhich applies in the present case) reported in [31],show an almost linear dependence of the CTE onVp over the range covered in the present work, inagreement with Fig. 6. Larger deviations from lin-earity were instead obtained for the continuousbrittle phase model [33].

The strong dependence of the CTE on particlevolume fraction can be qualitatively understood bytaking account of the largely different thermalproperties of Al and SiC (see Table 4). The sig-nificantly smaller CTE of the ceramic, as comparedto that of Al, explains why it sharply decreaseswith Vp. Several models have been developed aim-ing to quantitatively explain this dependence. Thesimplest approach is the linear rule of mixtures(ROM),

ac � Vpap � (1�Vp)am (8)

where the subscripts m and p denote metal and par-ticle, respectively. More sophisticated treatmentsare all based in thermoelasticity theory. Schapery’s

Table 4Properties of aluminium and SiC used in the calculation of the CTE by means of Eqs (8) and (9)

Material T (°C) G (GPa) K (GPa) CTE (ppm K�1)

Al 50 27.2 68.3 21.8100 26.6 68.6 22.4200 24.7 66.2 23.9300 24.1 59.8 25.9

SiC 50–300 188 222 4.7

model [34,35] gives upper (+) and lower (�)bounds on the CTE. The specific expression for thelatter is,

a(+) � ap � (am�ap)Km(Kp�K(�)

c )K(�)

c (Kp�Km)(9)

where K(�)c is Hashin and Shtrickman’s [36] lower

bound to the bulk modulus of the composite, name-ly,

K(�)c � Km �

Vp

1Kp�Km

�Vm

Km �43mm

(10)

where mm is the shear modulus of the matrix. Theupper bound to the bulk modulus is obtained byinterchanging the subscripts m and p everywherein Eq. (10) and, when inserted in Eq. (9), gives thelower bound on the CTE. As noted by Schapery,the upper bound coincides with the expressionderived by Kerner [35].

These models were used to calculate the CTEof the materials investigated here. The results areplotted in Fig. 7. The data used in the calculationsare given in Table 4. Both the experimental dataand Schapery’s bounds can be fitted by straightlines in the narrow range of Vp explored here. Fig.8 shows these fittings for the experimental data,while all fitted lines are reported in Table 5. Theseresults clearly indicate that the rate at which theexperimental data for the CTE vary with com-pactness is higher than predicted by the two modelsdiscussed above. It can also be readily noted inFig. 7 that the value of Vp above which the dataare bounded by Schapery’s bounds increases withtemperature. As the fitted lines are not probably


0.55 0.6 0.65 0.7 0.75

Vp

6

8

10

12

14

CTE

(10-6

K-1

)

7

9

11

13

Fig. 7. Experimental and theoretical results for the coefficient of thermal expansion versus particle volume fraction, obtained fromlinear fittings of curves such as those of Fig. 2 in the temperature ranges 100–150 °C (a) and 200–250 °C (b). The different curvesand symbols correspond to: experimental (circles) straight line fitted to the data (broken line), upper and lower bounds predicted bySchapery’s model [24] (continuous lines) and linear rule of mixtures (chain line).

valid for Vp close to 1 (the pace at which the CTEvaries with Vp should slow down) and as the lowerbound becomes gradually more accurate as thislimit is approached, it may be concluded that therange of particle volume fraction over which thedata lie in between Schapery’s bounds becomesnarrower as the temperature is increased. We notealso that the slope of the straight lines fitted to boththe experimental data and the theoretical resultsincreases as the temperature range over which thefitting is done, is raised; a result which is in accord-ance with the increase of the CTE of aluminiumwith temperature.

These discrepancies can be qualitatively under-stood by noting that none of those two modelstakes into account the effect of particle size andboth have been developed using thermoelasticity

theory. The great difference between the coef-ficients of thermal expansion of the aluminium andthe SiC particles induces stresses and increases thedislocation density in the metal. As a result, themetal is hardened up to an extent that is greaterthe higher is the reinforcement content. As the pre-vious models do not take into account this harden-ing, one may expect the predicted variation of theCTE with particle volume fraction to be lower thanobserved experimentally.

Fig. 9 depicts the measured variation of CTEwith temperature for pure aluminium and com-posites made from mixtures containing 25%, 67%and 75% of coarse particles. The first feature to benoted is that the CTE increases with temperatureat a pace which is higher for pure aluminium thanfor the composites. Moreover, in the latter case we


0.55 0.6 0.65 0.7 0.75

Vp

6

8

10

12

14

16

CTE

(10-6

K-1

)

Fig. 8. Experimental results for the coefficient of thermalexpansion versus particle volume fraction in composites withbimodal particle distributions. The data were obtained from fit-tings over the following temperature ranges: 50–100 °C (filledsquares), 100–150 °C (empty squares), 150–200 °C (filledcircles), 200–250 °C (empty circles), 250–300 °C (filledtriangles). The fitted straight lines are also shown (given inTable 5).

observe that this pace decreases for the highesttemperatures reported in the figure. These resultscan be easily understood by noting that the CTEfor SiC is almost constant in the temperature rangeexplored here. This behaviour may be of someinterest for the engineering applications of thesematerials.

Table 5Straight lines (in ppm K�1) fitted to the coefficient of thermal expansion (ppm K�1) in several temperature ranges (see Fig. 7) versusparticle volume fraction Vp (regression coefficients better than 0.99)

Range (°C) Experimental data Lower bound Upper bound

50–100 26.5–26.7Vp 15.6–11.7Vp 19.5–15.3Vp

100–150 27.7–27.4Vp 15.8–11.9Vp 19.9–15.7Vp

150–200 30.0–29.7Vp 16.8–13.0Vp 21.4–17.2Vp

200–250 32.3–31.9Vp 17.6–13.6Vp 22.7–18.5Vp

250–300 32.7–32.1Vp 18.6–14.9Vp 24.5–14.9Vp

The results correspond to experimental data for composites with bimodal particle distributions and to lower and upper bounds ofSchapery’s theory [24] as discussed in the text.

50 100 150 200 250 300

TEMPERATURE (oC)

0

10

20

30

CTE

(10-6

K-1

)Fig. 9. Experimental results for the coefficient of thermalexpansion versus temperature for pure aluminium (circles) andcomposites with only fine (diamonds) or coarse (triangles) par-ticles, and a particle mixture containing 67% of coarse particles(squares). The lines are guides to the eye.

4. Conclusions

The following conclusions are drawn from theresults reported in this work:

(a) The hysteresis in the thermal strain responsecurve (��t) of composites containing a singleparticle size is proportional to the square rootof the particle surface area per unit volume ofmetal matrix. This result is in agreement withcurrent theories. Instead, no simple relationshipis found between the hysteresis for composites


having bimodal particle distributions and anyof the system parameters.

(b) The coefficient of thermal expansion calcu-lated over a wide temperature range (50–300°C) turns out to decrease linearly with the par-ticle volume fraction. The results for com-posites with a single particle size or bimodalparticle distributions can be satisfactorily fittedby means of the same straight line, indicatingthat the key parameter is in fact Vp, and thatother characteristics of the composites areeither irrelevant or play a minor role.

(c) The CTE varies with particle volume fractionat a pace higher than predicted by theory.Besides, one may interpret the results byassessing that the range of particle volumefraction over which the data lie in betweenSchapery’s bounds becomes narrower as thetemperature is increased. It is argued that theseresults illustrate the failure of the thermoelas-ticity framework upon which most theoriesare based.

(d) The results show that the CTE varies with tem-perature at a pace that is higher for pure alu-minium than for the composites, a directconsequence of the almost constant (with vary-ing temperature) CTE characteristic of SiC.

(e) As a general conclusion we remark that thethermal properties of these materials seem tobe good enough for its application as supportsin microelectronic systems.

Acknowledgements

Partial support by the Spanish CICYT (grants1FD97-0885 and MAT2001-0529) and the Univer-sidad de Alicante is gratefully acknowledged. C.Garcıa-Cordovilla is thankful to Alcoa Europe forpermission to publish this work, and R.A. Sarav-anan and J.M. Molina to the Spanish “Ministeriode Educacion y Cultura” for financial support.Thanks are also due to the supplier of the SiC par-ticles, NAVARRO S.A., for providing us a detailedaccount of the characteristics of the particulate.

References

[1] Lefranc G, Degischer HP, Sommer KH, Mitic G. In: Mas-sard T, Vautrin A, editors. ICMM-12, Paris. electronicsupport; 1999.

[2] Frear DR. J Metals 1999;51:22.[3] Elomari S, Skibo MD, Sundarrajan A, Richards H. Com-

pos Sci Technol 1998;58:369.[4] Sepulveda JL, Jech DE. In: Bose A, Dowding RJ, editors.

Tungsten refractory metals and alloys 4. Princeton, NJ:Metal Powder Industries Federation; 1997. p. 393.

[5] Jech DE, Sepulveda JL. In: IMAPS Int Symp onMicroelectronics. Philadelphia, PA: InternationalMicroelectronic and Packaging Society; 1997. p. 90.

[6] Watari K, Shinde SL. [see also articles in the same issue]MRS Bulletin 2001;June:400–1.

[7] Occhionero M, Adams R, Fennessy K. Proceedings of theForth Annual Portable by Design Conference, ElectronicsDesign; 1997 Mar 24–27. p. 398–403.

[8] Clyne TW. In: Kelly A, Zweben C, editors. Comprehen-sive composite materials, vol. 3. Elsevier Science Ltd;2000. p. 447–68.

[9] Vogelsang M, Arsenault RJ, Fisher RM. Metall Trans1986;17A:379.

[10] Arsenault RJ, Fisher RM. Scripta metall 1983;17:67.[11] Arsenault RJ, Shi N. Mater Sci Eng 1986;81:175.[12] Kim CT, Lee JK, Plichta MR. Metall Trans

1990;21A:673.[13] Wu SQ, Wei ZS, Tjong SC. Composites Sci Technol

2000;60:2873.[14] Tanihata K, Suganuma K. Key Eng Mater 1999;161-

163:259.[15] Hoffman M, Skirl S, Pompe W, Rodel J. Acta mater

1999;47:565.[16] Lee HS, Jeon KY, Kim HY, Hong SH. J Mater Sci

2000;35:6231.[17] Garcıa-Cordovilla C, Louis E, Narciso J. Acta mater

1999;47:4461.[18] Bideau D, Troadec JP, Lemaitre J, Oger L. In: Boccara N,

Daoud M, editors. Physics of finely divided matter. Berlin:Springer; 1985. p. 76.

[19] Lee JH, Lackey WJ, Benzel J-F. J Mater Res1996;11:2804.

[20] Standish N, Yu AB. Powder Technol 1987;53:69.[21] Asthana R, Rohatgi PK, Tewari SN. Process Adv Mater

1992;2:1.[22] Mortensen A, Jin I. Int Mater Rev 1992;37:101.[23] Alonso, Pamies A, Narciso J, Garcıa-Cordovilla C, Louis

E. Metall Trans 1993;24A:1423.[24] Narciso J, Alonso A, Pamies A, Garcıa-Cordovilla C,

Louis E. Metall Trans 1995;26A:983.[25] Molina JM, Saravanan R, Arpon R, Garcıa-Cordovilla C,

Louis E, Narciso J. Trans JWRI 2001;30:449.[26] Molina JM, Saravanan RA, Arpon R, Garcıa-Cordovilla

C, Louis E, Narciso J. Acta mater 2002;50:247.[27] Narciso J, Garcıa-Cordovilla C, Louis E. Mater Sci Eng

1992;B15:148.


[28] Taya M, Arsenault RJ. Metal Matrix Composites. Thermo-mechanical Behavior. Oxford: Pergamon Press, 1989.

[29] Arsenault RJ, Shi N. Mater Sci Eng 1986;81:175.[30] Hansen N. Acta metall 1977;25:863.[31] Ma Y, Bi J, Lu YX, Gao YX. Effect of SiC particulate

size on properties and fracture behavior of SiCp/2024 Alcomposites. In: Proceedings of the Ninth InternationalConference of Composite Materials (ICCM/9); Madrid;1993 Jul 12–16.

[32] Xu ZR, Chawla KK, Mitra R, Fine ME. Scripta metallmater 1994;31:1525.

[33] Shen Y-L, Needleman A, Suresh S. Metall Mater TransA 1994;25:839.

[34] Schapery RA. J Comp Mater 1968;2:380.[35] Kerner EH. Proc Phys Soc Lond 1956;B69:808.[36] Hashin Z, Shtrickman S. J Mech Phys Solids 1962;10:335.

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