Elsevier

Materials Characterization

Volume 90, April 2014, Pages 185-195
Materials Characterization

Particle tracking during Ostwald ripening using time-resolved laboratory X-ray microtomography

https://doi.org/10.1016/j.matchar.2014.01.022Get rights and content

Highlights

  • Ostwald ripening in Al–5 wt.% Cu measured by laboratory X-ray microtomography

  • Time-resolved measurement of individual particle growth

  • Automated segmentation routines developed to close gaps in particle boundary network

  • Particle growth/shrinkage rates deviate from LSW model prediction.

Abstract

Laboratory X-ray microtomography is investigated as a method for obtaining time-resolved images of microstructural coarsening of the semisolid state of Al–5 wt.% Cu samples during Ostwald ripening. Owing to the 3D imaging capability of tomography, this technique uniquely provides access to the growth rates of individual particles, thereby not only allowing a statistical characterization of coarsening—as has long been possible by conventional metallography—but also enabling quantification of the influence of local environment on particle boundary migration. The latter information is crucial to understanding growth kinetics during Ostwald ripening at high volume fractions of the coarsening phase. Automated image processing and segmentation routines were developed to close gaps in the network of particle boundaries and to track individual particles from one annealing step to the next. The particle tracking success rate places an upper bound of only a few percent on the likelihood of segmentation errors for any given particle. The accuracy of particle size trajectories extracted from the time-resolved tomographic reconstructions is correspondingly high. Statistically averaged coarsening data and individual particle growth rates are in excellent agreement with the results of prior experimental studies and with computer simulations of Ostwald ripening.

Introduction

As the resolution of X-ray tomography has improved from the millimeter to the submicrometer range, the scope of applications for this nondestructive 3D imaging technique has broadened from its early use in medical diagnostics to increasingly widespread employment as a tool for characterizing the complex internal microstructures of materials [1], [2]. Tomography is particularly well suited to the study of multiphase materials, as differences in local X-ray absorption can be exploited to map the spatial extent of individual phase regions—even when the latter are interconnected in a complex manner in three dimensions [3], [4]. Previously, such information could be gleaned only from a destructive technique like serial sectioning [5]; however, with the advent of high-resolution X-ray tomography, such studies no longer require cutting open the sample, thereby making it feasible to observe the evolution of phase boundaries during protracted mechanical and/or thermal processing [6], [7], [8], [9], [10].

This in situ 3D imaging capability makes X-ray microtomography ideally suited to the investigation of Ostwald ripening, a coarsening phenomenon first studied more than a century ago [11] and still of technological relevance today because of its prevalence during the synthesis and processing of modern multiphase materials [12], [13], [14], [15]. In the simplest case of particles of one phase dispersed in a matrix of a second phase, Ostwald ripening manifests itself through the growth of larger particles at the expense of smaller ones, leading to an increase in the mean particle size 〈R〉 as the total number of embedded particles decreases (Fig. 1). The driving force for this process is the excess energy of interphase boundaries, the overall area of which is reduced when the volume of the embedded (coarsening) phase is concentrated in fewer particles of larger size.

The first widely accepted analytic model for Ostwald ripening was proposed in 1961 by Lifshitz, Slyozov [16] and Wagner [17]. The so-called LSW model makes three primary predictions regarding the asymptotic kinetics of particle coarsening in a two-phase mixture:

  • (i)

    The cubed mean particle radius 〈R3 of a given phase grows as a linear function of time t.

  • (ii)

    The particle size distribution takes on a time-independent shape when normalized by the corresponding mean particle radius 〈R〉.

  • (iii)

    The quantity R2dR/dt, which is proportional to the instantaneous growth rate of a particle of size R, depends linearly on R/〈R  1, entailing particle shrinkage for R < R〉 and growth when R > R〉.

Strictly speaking, the LSW results were derived in the limit of a vanishing volume fraction of the coarsening phase (i.e. VV  0), which is equivalent to the assumption of no overlap of the concentration depletion zones surrounding the shrinking/growing particles [12], [18], [19]. This assumption leads to discrepancies between theory and experiment at higher, technologically relevant values for VV [20], [21]. Over the past six decades, numerous attempts have been made to extend the LSW model to higher volume fractions by taking particle–particle interactions into account, at least in a mean-field sense [18], [22], [23], [24], [25], [26]. For example, Glicksman et al. [24] and Wang et al. [26] developed a “diffusion screening theory” to describe multiparticle systems in the range 0 < VV < 0.3, and Marsh and Glicksman [23] established the concept of a “statistical field cell” that is valid for volume fractions up to 0.6. At still higher values for VV, however, all current approaches to modeling Ostwald ripening begin to break down [27].

In order to guide the development of analytic models for Ostwald ripening in the high-VV regime, it is necessary to measure the effect of particle–particle interactions on the rate of growth in each particle size class R and to assess their dependence on the overall volume fraction VV of the coarsening phase. Such information can be obtained only from a nondestructive 3D imaging technique that is able to map out the local environment of each particle in a real coarsening system and to deliver relevant data for quantifying the influence of that environment on the particle's growth kinetics. In this work we demonstrate that absorption-contrast X-ray microtomography meets both of these criteria. Moreover, we show that the necessary characterization capabilities are not exclusive to the specialized instrumentation found at synchrotron beamlines: the latest generation of laboratory X-ray tomographs affords sufficient intensity and resolution for performing such studies, as well.

In Section 2, we describe the sample preparation and tomographic characterization protocol that was followed to investigate Ostwald ripening in a two-phase system with VV = 0.74 during both long-term (LT) and short-term (ST) annealing series. By tracking individual particles over several annealing steps, according to the approach presented in Section 3, we extract particle growth/shrinkage trajectories and compare them to statistical measures for the evolution of the ensemble of particles, discussing the results in the context of prior experimental and theoretical studies of Ostwald ripening. Finally, in Section 4 we assess uncertainties in the microstructural data obtained by this approach, considering not only experimental factors but also the consequences of segmentation artifacts on the accurate tracking of particles from one tomographic reconstruction to the next.

Section snippets

Material and Methods

The aggregate state of the phases in a polycrystalline metal undergoing Ostwald ripening can be solid–solid [15] or solid–liquid [21]. Solid–liquid systems offer the advantage of minimizing the interfacial stresses between matrix and coarsening phases [28], thereby eliminating at least one factor having the potential to interfere with conventional coarsening kinetics [20]. Furthermore, ripening occurs faster in solid–liquid systems, owing to the higher rate of atomic diffusion through a liquid

Ostwald Ripening Results and Discussion

Carrying out the image processing and segmentation steps outlined above, we were able to map out more than 2000 particles in the interior regions of each sample in the initial annealing state (1 h at 630 °C). Evolution of the microstructure was then induced via a series of one-hour anneals (Table 1, ST series) or progressively longer heating intervals (Table 1, LT series). From the latter, we investigated the shape of the particle size distribution and the power-law growth of the average particle

Evaluation of Experimental Procedures and Data Analysis

We now assess the accuracy of the microstructural information extracted from tomographic reconstructions of Al–5 wt.% Cu according to the procedures described in the previous sections. After briefly considering the limitations imposed by the ex situ manner in which the data were collected, we discuss the origin of segmentation errors and the extent to which they affect the efficiency of the particle-tracking routine.

Conclusions

In this work, X-ray computed tomography is found to be a powerful tool for the nondestructive investigation of Ostwald ripening at high volume fractions of the coarsening phase. Long-term annealing sequences yielded global measures for microstructural evolution, such as the growth exponent and the particle size distribution, which are in excellent agreement with previous studies of Ostwald ripening in similar systems. From short-term annealing series we gained access to local features of

Acknowledgments

The authors are most grateful to D. Molodov of the Institute of Physical Metallurgy and Metal Physics, RWTH Aachen, for providing all Al–5 wt.% Cu specimens and to the Deutsche Forschungsgemeinschaft for funding through NSF/DFG Materials World Network Project KR 1658/4-1.

References (52)

  • C.K.L. Davies et al.

    The effect of volume fraction of precipitate on Ostwald ripening

    Acta Metall. Mater.

    (1980)
  • S.P. Marsh et al.

    Kinetics of phase coarsening in dense systems

    Acta Mater.

    (1996)
  • M.E. Glicksman et al.

    Diffusional interactions among crystallites

    J. Cryst. Growth

    (2001)
  • M. Aravind et al.

    Formation of Al2Cu and AlCu intermetallics in Al(Cu) alloy matrix composites by reaction sintering

    Mater. Sci. Eng. A

    (2004)
  • S. Annavarapu et al.

    Inhibited coarsening of solid–liquid microstructures in spray casting at high volume fractions of solid

    Acta Metall. Mater.

    (1995)
  • D.J. Rowenhorst et al.

    Three-dimensional analysis of particle coarsening in high volume fraction solid–liquid mixtures

    Acta Mater.

    (2006)
  • W. Bender et al.

    Ostwald ripening of liquid phase sintered Cu–Co dispersions at high volume fractions

    Acta Mater.

    (1998)
  • S.G. Kim

    Large-scale three-dimensional simulation of Ostwald ripening

    Acta Mater.

    (2007)
  • D. Fan et al.

    Phase-field simulation of 2-D Ostwald ripening in the high volume fraction regime

    Acta Mater.

    (2002)
  • K. Wang et al.

    Length scales in phase coarsening: theory, simulation, and experiment

    Comp Mater Sci

    (2005)
  • P.W. Voorhees et al.

    Solution to the multi-particle diffusion problem with applications to Ostwald ripening—II. Computer simulations

    Acta Metall. Mater.

    (1984)
  • P.W. Voorhees et al.

    In situ observation of particle motion and diffusion interactions during coarsening

    Acta Metall. Mater.

    (1987)
  • N. Akaiwa et al.

    The effects of convection on Ostwald ripening in solid–liquid mixtures

    Acta Metall. Mater.

    (1991)
  • O. Pompe et al.

    Microstructural changes during quenching

    J. Cryst. Growth

    (1998)
  • D.J. Rowenhorst et al.

    Measurement of interfacial evolution in three dimensions

    Annu. Rev. Mater. Res.

    (2012)
  • J. Alkemper et al.

    Quantitative serial sectioning analysis

    J. Microsc.

    (2001)
  • Cited by (26)

    • Microstructural changes by controlling austenitizing and tempering conditions on the J-R fracture resistance of SA508 Gr. 1A low alloy steels

      2021, Materials Science and Engineering: A
      Citation Excerpt :

      In contrast, ST1 and ST2, which had the same austenitizing temperature, had similar grain size and phase formation, but the size of the precipitates increased significantly. This is because of the Ostwald Ripening effect, where the surface energy of the particles becomes the driving force, and small particles either dissipate or diffuse into larger particles and grow together [30]. From the tensile test results, all specimens clearly exhibit the discontinuous yielding behaviors at RT.

    • Stochastic modeling of individual grain behavior during Ostwald ripening at ultra-high volume fractions of the coarsening phase

      2016, Computational Materials Science
      Citation Excerpt :

      Colors2 in Fig. 2(b) indicate the values of locally normalized radii, i.e., the grain radii relative to their respective local mean, cf. Section 2.4. Similar as in [19], we consider a local mean radius of the neighborhood for every grain. We define the local mean radius as a weighted mean computed from all radii of adjacent grains.

    • Analytical study of waterlogged ivory from the Bajo de la campana site (Murcia, Spain)

      2016, Microchemical Journal
      Citation Excerpt :

      The alkaline conditions found in seawater could have also contributed to inhibit bioapatite demineralisation, considered a prerequisite for microbial attack [28]. It has been reported that once the organic matrix breaks down, bone crystallites undergo simultaneous dissolution and growth similarly to Ostwald ripening [129], where large crystals grow at the expense of smaller crystallites. This has been supported by the strong relationship between IRSF and organic content reported elsewhere [55].

    View all citing articles on Scopus
    1

    Current address: University of Bern, Institute for Surgical Technology and Biomechanics, Stauffacherstr. 78, 3014 Bern, Switzerland.

    View full text