Materials Characterization 51 (2003) 95–100

Quantitative analysis of Al2O3 particles

in Al3Ti/Al2O3/Al composites

A. Swiderska-Srodaa,*, T. Wejrzanowskib, K.J. Kurzydlowskib,J.W. Wyrzykowskib

aHigh Pressure Research Center, Polish Academy of Sciences, Sokolowska 29/37, PL-01-142 Warsaw, PolandbFaculty of Materials Science and Engineering, Warsaw University of Technology, Woloska 141, 02-507 Warsaw, Poland

Received 24 August 2003; received in revised form 10 October 2003; accepted 14 October 2003

Abstract

This paper concerns the quantitative relation between the microstructure and mechanical properties of Al3Ti/Al2O3/Al

composites fabricated by powder metallurgy. Microhardness measurements and a quantitative evaluation of Al2O3 particles in

composites prepared using different powder consolidation techniques were made. Characterization of the Al2O3 particles was

done in terms of size and volume fraction measured on sections. Voronoi tessellations and a linear covariance method

[T. Wejrzanowski, et al., Image Anal. Stereol. 20 (Suppl. 1) (2001) 71–6] were used for a description of the spatial distribution

of particles. The results revealed differences in the volume fraction of the Al2O3 phase. No significant differences in the size and

size distributions of the particles were detected. The spatial arrangement examinations showed a random distribution of particles

in each composite. Despite this, differences in the homogeneity of the particle dispersion were found. The results prove the

influence of the volume fraction of Al2O3 particles on the microhardness. A significant influence of the homogeneity of the

particle arrangement on the variation of the microhardness was also demonstrated.

D 2003 Elsevier Inc. All rights reserved.

Keywords: Intermetallics; Quantitative description; Image analysis; Homogeneity

1. Introduction to the application of computer systems for image

Fast progress in materials science has brought

about the development of modern materials that are

characterised by complex multiphase microstructures.

Such microstructures can be controlled nowadays due

1044-5803/$ - see front matter D 2003 Elsevier Inc. All rights reserved.

doi:10.1016/j.matchar.2003.10.007

* Corresponding author. Tel.: +48-22-836-44-33; fax: +48-22-

632-42-18.

E-mail address: annas@unipress.waw.pl

(A. Swiderska-Sroda).

analysis, which are useful tools for their quantitative

description. This is especially true for multiphase

composites, where the volume fraction, morphology,

and spatial distribution of the components affect the

composite properties [1].

In the present work a correlation between micro-

structure and microhardness of Al3Ti/Al2O3/Al com-

posites fabricated by powder metallurgy was

investigated. A quantitative description of each

microstructure was obtained from scanning electron

microscopy (SEM) images using a computer system

Table 1

Processing methods of bulk compacts of Al–21at.%Ti alloy

Sample Powder milling Powder sintering

S1 Milling for 5 h (1) Explosive consolidation

at 250 rpm

in argon

(2) Heat treatment at 850 jCfor 2 h in vacuum 10� 3 Pa

S2 Milling for 5 h (1) Preliminary cold pressing

at 250 rpm

in ethyl alcohol

under 103 Pa

(2) Sintering at 1100 jC for 1h

in vacuum 10� 3 Pa

S3 Milling for 5 h (1) Preliminary cold pressing

at 250 rpm in

ethyl alcohol

under 10 MPa

(2) Degassing the compact at

480 jC in vacuum 10� 3 Pa

(3) Hot pressing 830 jC/12MPa/15 min/vacuum 10� 3 Pa

(4) Cooling the compact under

constant pressure and unloading

at 200 jC

A. Swiderska-Sroda et al. / Materials Characterization 51 (2003) 95–10096

for image analysis (MicroMeter) [2]. Characteriza-

tion of the microstructures was done in terms of

size and homogeneity parameters measured on sec-

tions. It was shown that a quantitative description

of the microstructures of these composites allows

one to predict their properties and optimise the

fabrication process.

Fig. 1. S1 composite: SEM image (a), binary (b), influence zones (c).

2. Materials

The composites examined in this work were

produced by powder metallurgy. A cast Al –

21at.%Ti alloy containing Al/Al3Ti phases (accord-

ing to the Ti–Al equilibrium system, the volume

fraction of the intermetallic phase was 83%) was

powdered by mechanical milling in argon or ethyl

alcohol, using a planetary ball mill. Three techni-

ques were subsequently used for powder consolida-

tion: sintering, hot pressing, and heat treatment of

explosively compacted powder. Fabrication details

are given in Table 1. Composites obtained in dif-

ferent consolidation processes possess the same

phase composition (Al3Ti/Al2O3/Al) but differ in

terms of microstructural details. It should be noted

that the presence of the Al2O3 phase in these

composites was due to the oxidation of metallic

Al during the consolidation of powders (for more

details, see Ref. [3]).

3. Experimental method

Images of the microstructures of composites were

obtained using SEM. Binary images revealing ce-

ramic particles were produced via digital processing

of SEM images. The size and volume fractions of

the ceramic particles in composites were determined

by measurements on their sections [4].

Fig. 2. S2 composite: SEM image (a), binary (b), influence zones (c).

Fig. 3. S3 composite: SEM image (a), binary (b), influence zones (c).

A. Swiderska-Sroda et al. / Materials Characterization 51 (2003) 95–100 97

For a description of the distribution of particles,

two methods were used: Voronoi tessellation and

linear covariance methods. The Voronoi tessellation

method is based on a computer-aided technique of

image processing known as skeleton by influence

zone (SKIZ) [5]. These techniques transform the set

of particles into a granular structure. Each ‘‘grain’’

of such a structure defines the zone of influence of

one of the particles. The grain network generated is

subjected to a standard quantitative analysis of grain

size and shape. Examples of microstructural images

and their corresponding ‘‘grain structures’’ are given

in Figs. 1–3.

The linear covariance method is based on the

concept of the linear covariance function defined as

the average probability that the plane P + h, shifted

by distance h with respect to plane P, which

Table 2

Parameters describing volume fraction and size of Al2O3 particles

Sample S1 S2 S3

Volume fraction of particles, VV [%] 2 4 6

Surface area of particles per unit volume,

SV [Am� 1]

0.07 0.18 0.24

Average equivalent diameter, E(d2) [Am] 1.16 1.11 1.25.Standard deviation, S.D. (d2) [Am] 0.48 0.49 0.47.Coefficient of variation, CV (d2) 0.41 0.44 0.37

A. Swiderska-Sroda et al. / Materials Characterization 51 (2003) 95–10098

intersects a given particle, will also intersect this

particle [6]. This condition can be written as

follows:

CðhÞ ¼ E½MesðP \ P þ hÞ�

The covariance is very often determined along

horizontal and vertical directions. The directional

covariance functions are denoted then as C(x) and

C( y).

The measurements of microhardness were made

using a Vickers method under 2 N (HV02). More than

30 measurements were made for each sample.

4. Results

Results of standard image analysis, which include a

determination of the volume fraction, the average size,

and the size variation of ceramic particles and surface

area of particles per unit volume, are given in Table 2.

The results indicate a systematic difference in the

volume fraction of Al2O3 particles. Despite different

fabrication techniques used for each composite, no

significant difference in the average size and the size

variation were detected.

The results of quantitative analysis of spatial

arrangement of Al2O3 particles, obtained by the

Table 3

Parameters obtained by Voronoi tessellation method

Sample Equivalent diameter of influence zones

Average value

E(d2(z)) [Am]

S.D. (d2(z))

[Am]

CV (d2(z))

S1 7.77 2.72 0.35

S2 5.92 1.47 0.25

S3 4.56 1.34 0.29

Voronoi tessellation method, are given in Table 3.

The distribution of equivalent diameters of influence

zones, d2(z), for each composite is lognormal (see

Fig. 4). This result indicates the random spatial

distribution of particles in all of the composites

studied. Nevertheless, statistical parameters describ-

ing the distribution of equivalent diameters (such as

Fig. 4. Distribution of equivalent diameters of influence zones

obtained for Al2O3 particles in composite: S1 (a) S2 (b), S3 (c).

Fig. 5. Linear covariograms obtained for composite S1 (a), S2 (b),

S3 (c).

Fig. 6. Influence of volume fraction of Al2O3 particles on average

microhardness in Al3Ti/Al2O3/Al composites.

Table 4

Microhardness, HV(02), for Al3Ti/Al2O3/Al composites

Sample Microhardness, HV(02)

Average value E(HV02) S.D. (HV02) CV (HV02)

S1 320F 10 37 0.12

S2 520F 10 31 0.06

S3 630F 10 42 0.07

A. Swiderska-Sroda et al. / Materials Characterization 51 (2003) 95–100 99

the coefficient of variation) reveal differences in the

homogeneity of particle dispersion. The data from

Table 3 confirm that the highest homogeneity in the

dispersion of particles occurs in the case of the

composite made by sintering (S2), and the lowest

is in the sample after explosive compaction and heat

treatment (S1). In terms of the values of CV(d2(z)),

the differences in the level of homogeneity reach

50%.

Results of quantitative analysis by the linear

covariance method are shown in Fig. 5. It should

be noted that in the case of ordered arrangement of

particles, the linear covariance diagram reveals

regular peaks. In the case of cluster distributions,

some peaks appear corresponding with the cluster

size and distance between clusters. For a random

spatial arrangement, only a zero peak is observed.

The width of this peak refers to the average size of

particles and the height corresponds with the vol-

ume fraction. The results of microhardness meas-

urements for the composites studied are listed in

Table 4.

Comparing corresponding results of the quantita-

tive description of microstructures and the results of

microhardness measurements, it can be observed that

there is a linear relationship between the volume

fraction of particles and the average microhardness

value (Fig. 6). The dependence of the variation of

microhardness on the degree of uniformity in the

Fig. 7. Influence of inhomogeneity of particle’s arrangement on

variation of microhardness in Al3Ti/Al2O3/Al composites.

A. Swiderska-Sroda et al. / Materials Characterization 51 (2003) 95–100100

arrangement of particles is also observed to be linear,

as illustrated by the plot in Fig. 7.

5. Conclusions

The present work gives a quantitative description

of Al2O3 particles and their influence on microhard-

ness in the case of three Al3Ti/Al2O3/Al composites.

The results of microstructural investigations prove

that the size of the Al2O3 particles remain nearly

constant in each composite. On the other hand, they

differ in volume fraction and spatial distribution. The

influence of the Al2O3 particles on the microhardness

of these composites may be summarized as follows:

The microhardness depends strongly on the

volume fraction of Al2O3 particles. It was found that a linear relationship exists

between the volume fraction of particles and the

average microhardness. A significant influence of the homogeneity of the

particle arrangements on the variation of micro-

hardness measurements was also proved.

These results prove that image analysis techniques

are very useful for structural investigations of poly-

phase materials. The reported correlations between the

quantitative structural parameters and materials prop-

erties give a basis for optimization of fabrication

processes.

Acknowledgements

Financial support from the Polish State Committee

for Scientific Research (KBN), Grant No. PBZ—

KBN-041/T08/02-09, is gratefully acknowledged.

The authors gratefully acknowledge the contribution

to this research of Adam Presz, who helped carry out

the SEM investigations.

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