Microstructural effects on grain boundary motion in Al-Mn alloys
Erica Anselmino
Invitation
to attend the defence of my
PhD dissertation
Microstructural effects
on grain boundary
motion in Al-Mn alloys
Monday, November 5th 2007at 10.00 h
in the Senaatzaal of the Aula of the
Technische Universiteit Delft
Mekelweg 5, Delft The Netherlands
Prior to the defence (9.30 h)
there will be a short
presentation on the contents of
the thesis
After the ceremony there will
be a small reception
Erica Anselmino
Paranymphs Rias Lok Thim Zuidwijk
dd
1
27
1. Jerkiness is rather common in nature, although it is not always visible; the observation conditions have to be correct. The viewing of smooth movements on an “out of the ordinary” scale can change the observed characteristics of the phenomenon (Chapter 4). 2. Grain boundary velocity during recrystallisation of Al-Mn alloys is not constant. The
movement is jerky (this thesis).
3. With the increasing CO2 emissions, we must focus on the development of alternate energy
sources, especially those that are clean, efficient and renewable such as solar, wind, biomass, geothermal, and fuel cells.
4. The most exciting phrase to hear in science, the one that can herald new discoveries, is not “Eureka!” but “That's funny...” (Isaac Asimov).
5. It is common that during big international venues young students and researchers are shadowed and intimidated by older and more expert participants. Organising companion Young Scientist Meetings, not open to senior scientist, will increase their participation, will result in an effective fringe network between groups and will create real commitment of young scientist to the research program in which their PhD project is embedded (Vir[Fab] Young Scientist program, introduced by Prof. Gunter Gottstein, RWTH-Aachen).
6. Time spent on academic PhD research is appreciated differently by the industrial world of the Netherlands and that of Italy. It is a considered a valuable experience by the first and a waste of time by the latter.
7. For Italian PhD students, young mothers and people with a full time job in an unconnected field, writing a thesis is the literary equivalent of jerky motion.
8. In modern science, hardly any important results can be attributed to just a single individual. Hence when speaking of one’s scientific achievements and results, it is appropriate to use the first person plural pronoun instead of the singular one. However, well accepted rules for most appropriate formulations during job interviews suggest the opposite.
9. The Dutch health system in brief: go home, wait two weeks and make a new appointment. 10. Although steel is easier to polish, aluminium becomes shinier.
1. Schoksgewijze verplaatsingen zijn niet ongebruikelijk, ook al worden ze niet altijd als zodanig herkend. Daarvoor moeten de waarnemenscondities goed gekozen worden. Waarnemingen van “gelijkmatige” verplaatsingen onder ongebruikelijke condities kunnen leiden tot bijstelling van de conclusies aangaande de ware aard van de verplaatsing (hoofdstuk 4).
2. De korrelgrensverplaatsingssnelheid tijdens rekristallisatie van Al-Mn legeringen is niet constant. Het grensvlak verplaatst zich schoksgewijs (dit proefschrift).
3. Gelet op de toenemende CO2 emissies moeten we ons richten op alternatieve energie bronnen,
in het bijzonder de schone en duurzame processen zoals zonneenergie, wind, biomassa, geothermiek en brandstofcellen.
4. De spannendste uitspraak in wetenschap, en een die aan het begin van nieuwe doorbraken kan staan, is niet “Eureka!”, maar “Dit is gek …” (Isaac Asimov).
5. Meestal worden tijdens grotere wetenschappelijke bijeenkomsten promovendi en jonge onderzoekers overvleugeld en gedomineerd door oudere en ervarener wetenschappers. Door complementaire Jonge Onderzoekers Bijeenkomsten te organiseren welke niet toegankelijk zijn voor senior wetenschappers, ontstaat een tweede, informeel, netwerk van wetenschappers en raken de jonge onderzoekers pas echt betrokken bij het onderzoeksprogramma waar hun promotieonderzoek deel van uit maakt (het VIRFAB Young Scientist programma zoals opgezet door Prof. Gunter Gottstein, RWTH-Aachen).
6. De Nederlandse en Italiaanse industrie hebben een duidelijk verschil in appreciatie van de tijd die besteed wordt aan het doen van een promotieonderzoek: de eerste acht het een waardevolle ervaring, de tweede een verspilling van tijd.
7. Voor Italiaanse promovendi, jonge moeders en mensen met een full time baan elders, is schrijven van een proefschrift een schoksgewijs proces.
8. In hedendaags wetenschappelijk onderzoek kunnen belangrijke resultaten zelden toegekend worden aan een enkel individu. Bij het presenteren van resultaten en prestaties is het daarom passend de eerste persoon meervoudsvorm in plaats van de eerste persoon enkelvoudsvorm te gebruiken. Dit staat echter haaks op de adviezen met betrekking tot de te gebruiken formulering tijdens sollicitatiegesprekken.
9. De Nederlandse gezondheidszorg in een notendop: ga naar huis, wacht twee weken en maak een nieuwe afspraak.
10. Staal mag dan wel gemakkelijker te polijsten zijn, aluminium wordt toch glanzender.
Microstructural effects on grain
boundary motion in Al-Mn alloys
PhD thesis
Microstructural effects on grain
boundary motion in Al-Mn alloys
Proefschrift
ter verkrijging van de graad doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof.dr.ir. J.T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op maandag 5 november 2007 om 10:00 uur
door
Erica Anselmino
Laurea di Dottore in Chimica Università degli Studi di Torino (IT)
Samenstelling promotiecommissie: Rector Magnificus, voorzitter
Prof.dr.ir. S. van der Zwaag, Technische Universiteit Delft, promotor Prof.dr. D. Juul Jensen, Risø National Laboratory, Roskilde, Denemark Prof.dr. D. Prior, University of Liverpool, United Kingdom
Prof.dr.ir. C. Vuik, Technische Universiteit Delft Prof.dr.ir. R. Benedictus, Technische Universiteit Delft
Dr.ir. A. Miroux, Netherlands Institute for Metals Research, Delft Dr.ir. M.R. van der Winden, Corus RD&T, Ijmuiden
Digital material supporting this thesis can be found at www.mcmDelft.nl
ISBN 978-90-77172-33-9
Keywords: Aluminum alloys, dispersoids, recrystallisation, jerkiness, in-situ observation
Copyright © 2007 by Erica Anselmino
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission from the author.
Chapter 1 Introduction
1.1 Recrystallisation and grain boundary migration 1
1.2 Scope of the thesis 4
Chapter 2
Dispersoid size analysis 7
2.1 Introduction 7
2.2 Quantification procedure 9
2.2.1 Sample preparation 9
2.2.2 Microscope parameters 9
2.2.3 Image acquisition and sampling 10
2.2.4 Binarisation 11
2.3 From 2-Dimensions to 3-Dimensions 15
2.3.1 The Johnson-Saltikov method 16
2.3.2 In-depth modification 18
2.4 Quantification of dispersoid characteristics 19
2.4.1 Structure of new procedure 19
2.5 Parametric study of method 21
2.5.1 Size distribution in 2 and 3 dimensions 21
2.5.2 Effect of depth information 22
2.5.3 Effect of class definition 23
2.5.4 Statistical considerations 25
2.6 Conclusions 27
Chapter 3
Microchemistry changes during industrial processing of AA3103 31
3.1 Introduction 31
3.2 The VIR[*] project 32
3.3 Industrial processing and sampling 33
3.4 Characterisation techniques 36
3.4.1 Constituent particles 37
3.4.2 Mn solute levels (NIMR) 38
3.6 The alloy mass balance check 49
3.7 Conclusions 51 Chapter 4 In-situ observations of recrystallisation: experimental 55 4.1 Introduction 55 4.2 Technical requirements 59
4.2.1 Optical microscopy 59
4.2.2 Electron microscopy 60
4.2.3 Parameters that effect the in-situ observations 62
4.2.4 Selected experimental conditions 63
4.3 Sample preparation 65
4.4 Data acquisition 68
4.5 Data processing 69
4.5.1 Time step maps 69
4.5.2 Analysis of the time step maps 72 4.5.3 Misorientation and dislocation networks 73 4.6 Ex-situ validation 74
4.7 Material 77
4.7.1 Initial state 77
4.7.2 Deformation 78
4.7.3 Samples for in-situ annealing 82
4.8 Conclusions 83
Chapter 5 In-situ observations of recrystallisation: results 87 5.1 Introduction 87 5.2 Microstructure evolution 88
5.2.1 Pre-recrystallisation phenomena 88
5.2.2 Recrystallisation 91
5.3 Dynamic observations 98
5.3.1 Grain boundary movement 99
5.3.2 Misorientation and dislocation networks 99
5.3.3 Particles and geometrical configurations 102
5.3.4 A detailed analysis of sample TGA-2 seq 2 106
5.3.5 Statistical summary on data of different features 117
Chapter 6
Modelling jerkiness in grain boundary motion 129
6.1 Introduction 129
6.2 Analytical analysis 129
6.2.1 Pinning 131
6.2.2 Unpinning 132
6.3 Monte Carlo model 138
6.3.1 Model description 141
6.3.2 Model parameters and simulation results 146
6.3.3 Jerkiness domain 152
6.3.4 Simulation based on experimental input 155
6.4 Conclusions 159
Appendix A Particle size analysis 165
A.1 Introduction of the problem 165
A.2 Principles of the method 167
A.2.1 Distribution of the raw data in size classes 167
A.3 Johnson-Saltikov parameters 168
A.3.1 Example for class k 170
A.3.2 Construction and use of the Saltikov tables 171
A.4 In-depth modification 173
A.4.1 Calculation of the coefficients in case of “in-depth” modification 175
A.5 Demonstration of the relation between NA(i)% and NV(i)% 177
A.6 Parameters 182
A.6.1 In cross sections – 2D 182
A.6.2 In volume – 3D 183
Appendix B Data on recrystallisation sequences 185
Appendix C
Monte Carlo time step calculation 217
C.1 Grain boundary roughness effect 217
C.2 Calculation of corrected time step 219
Colour plots 221
Summary 227
Samenvatting 231
Curriculum vitae 235
Introduction
1.1
Recrystallisation and grain boundary migration
Plastic deformation of metals alters the regular arrangement of their crystalline structure and results in the production of point defects, dislocations and interfaces. The presence of these crystal defects corresponds to an increase of the free energy of the material and to a thermodynamically unstable system. In metals, the annihilation or re-arrangement to a configuration of lower energy of these defects requires the activation of thermally activated processes as solid state diffusion. These processes are usually very slow at low temperature and heat treatments at higher temperatures are therefore applied to bring the system to a more stable thermodynamic state. This sequence of plastic deformation and annealing results in a drastic change of the microstructure and texture of the metal and consequently in its physical and mechanical properties.
annealing may result in grain growth in which the larger grains grow at the expense of the smaller ones, and the grain boundaries assume a lower energy configuration leading to an even lower excess energy level. Recovery processes by subgrain coarsening and grain growth are both driven by the elimination of high energy boundary area. The driving force for recrystallisation arises from the elimination of the dislocations introduced during deformation.
The energy source for all the property changes that are typical of deformed metals is the stored energy. This energy is a very small part (~1%) of the work expended in deforming a metal and derives from the crystal defects (or interfaces) that are generated during the process. Point defects do not however contribute significantly to the stored energy and it can therefore be assumed that almost all the energy is derived from the accumulation of dislocations.
In the deformed state the newly formed dislocations arrange themselves to create an internal structure, which always involves the creation of boundaries of some sort. Commonly there is the formation of dislocation cells, which are typically equiaxed, micron-sized volumes bounded by dislocation walls. If these walls are well ordered they will be low angle grain boundaries or subgrain boundaries. The geometry of the dislocation network not only depends on the deformation imposed but also on the presence of second phase particles which may influence the network not only upon formation but also during annealing if pinning is strong enough.
The understanding of the ways in which boundaries separating regions of different crystallographic orientation are formed or rearranged and subsequently migrate on annealing is crucial. The mechanism of GB migration depends on several parameters including the boundary structure, which, in a given material, is a function of misorientation and boundary plane. It also depends on the experimental conditions, in particular the temperature and the nature and magnitude of the forces acting on the boundary. The most recent and complete review of grain boundary migration is the book of Gottstein and Shvindlerman [Gottstein, 1999].
Grain boundaries that can be represented by an array of dislocations are usually low angle grain boundaries (LAGB). LAGB migration occurs in certain circumstances during recovery and during the nucleation of recrystallisation. Much less is known on the structure of high angle grain boundaries (HAGB) that migrate during and after recrystallisation. Early theories suggested that the GB consisted of a thin amorphous layer, but it is now known that these boundaries consist of regions of good and bad matching between the two grains [Wolf, 1992].
often exhibit fast growth rates (for example the 40° <111> boundaries in Aluminium [Cook, 1950; Bowles, 1948]).
In metallic alloys, GB migration is also affected by the presence of solute atoms, second phases and their spatial distribution, i.e. microchemistry. The interaction with solutes is due to the free or excess volume associated to the less dense atomic packing at GBs than in perfect crystal. This excess volume depends on the crystallography of the boundary. This interaction results to the formation of a solute atmosphere around the GB which, at low boundary velocities, moves with the boundary and impedes its migration [Dimitrov, 1978]. This phenomenon is commonly called solute drag and can be responsible for reductions of GB mobility by several orders of magnitude [Gottstein, 1999].
The influence of second phases on GB motion has been investigated for a long time [Manohar, 1998] and depends on the second phase characteristics. A dispersion of fine precipitates will exert a retarding force or pressure on both low and high angle GBs and this may have a profound effect on the processes of recovery, recrystallisation and grain growth. The effect is known as Zener drag [Nes, 1985]. The magnitude of this interaction depends on the nature of the particle and interface, and the shape, size, spacing and volume fraction of the particles. It should be noted that when a boundary intersects a particle, the precipitate effectively removes a region of boundary and thus the energy of the system is lowered, and boundaries are therefore attracted to particles. When a deformed and supersaturated alloy is annealed, precipitation can also take place during annealing. The mutual interaction between precipitation and GB motion is a complicated problem, which is only partially understood.
The interaction of vacancies and other point defects with static HAGBs has been extensively investigated [Balluffi, 1980] and it has been shown that boundaries may act as sources and sinks for point defects and that point defects interact with GB dislocations. The effect of point defects on a migrating boundary is less clear, although there is evidence [Hillert, 1978; Smidoda, 1978] that the diffusion coefficient of a moving boundary is several orders of magnitude larger than that of a stationary boundary. The basic concept that the vacancies swept up by a moving GB will increase the free volume of the boundary and therefore aid atom movement across the boundary is plausible [Gordon, 1966]. Such a model implies that the structure of static and moving boundaries will be different and also suggests that the boundary structure and hence mobility may be dependent on the GB velocity.
during diffusion controlled phase transformations). In this case the boundary migrates into highly defective material, leaving perfect crystal behind it. The mechanism by which the boundary removes the defects during recrystallisation is not known, but it is reasonable to suppose that the boundary energies and structures may differ for the cases of grain growth and recrystallisation.
Despite the importance of GB migration during annealing, the details of the process are not well known. This is mainly because boundary migration involves atomistic processes occurring rapidly, at high temperatures, and under conditions that are far from equilibrium. Because of its scientific interest and technological relevance a significant amount of experimental data have been produced during the last decades and is used as a base for the development of theoretical models for recovery, recrystallisation and grain growth. Given the fact that current models do not accurately predict all aspects of microstructural transformations involving grain boundary movement, there is concern regarding the completeness of the experimental data. A critical analysis of recrystallisation experiments reveals there is a remarkable shortage of in-situ observations of GB movement with a spatial resolution of dimensions of the deformation cells, both for pure metals and more importantly for alloys.
1.2
Scope of the thesis
Main scope of this thesis is to study the detailed local grain boundary motion during recrystallisation and its interaction with obstacles in the deformation matrix. The aluminium alloy AA3103 has been chosen as a case study because of its industrial relevance and the presence of a population of variable second phase, which offers the possibility of a detailed investigation of the interaction between precipitation and GB motion.
Given the interest in interaction effects it is very important to have detailed knowledge of the particle type, density and volume fraction in a material before attempting to understand its GB mechanisms. The thesis begins therefore with the presentation of a quantification method for second phase particles. Chapter 2 describes a semiautomatic method devised to accurately count dispersoid particles in aluminium alloys. Appendix A contains the mathematical details of the quantification method.
Since the lack of understanding of recrystallisation mechanisms also lies in the little knowledge of GB migration a set of experimental observations was devised to provide more data on the local movement of boundaries. Chapter 4 presents the experimental set-up and the method used to analyse the results. In-situ FEGSEM observations in orientation contrast, together with EBSD analysis of well selected initial and final transformation stages, was the chosen method and has proved to be effective in delivering valuable experimental data to describe the local GB motion during recrystallisation.
The results of the experimental in-situ observations are presented in chapter 5 and Appendix B. The GB motion is analysed and compared to the structure of the deformed matrix. GB displacement in time is measured and the local velocity is compared to the average value. The movement is also compared against subgrain misorientation, and both primary and secondary phase particles. The GB movement is followed in several examples along average growth lines but also following the local movement in specific paths along its real trajectory. In contrast to all theory the GB movement was found to be jerky and not smooth. The main factors that could influence this stop and release movement are taken into consideration: misorientation and dislocation networks, vacancies and solute drag, curvature and the shape of the GB and particles and solutes. The forces acting on the boundary are divided in two main groups: pinning and driving forces.
References
Balluffi R.W., Grain boundary structure and kinetics, ASM, Ohio, 1980
Bowles J.S., The effect of crystal arrangement on secondary recrystallisation in metals,
Journal of the Institute of Metals, 74, 1948, p.501
Cook M. and Richards T.L., Fundamental aspects of the cold working of metals, Journal
of the Institute of Metals, 78, 1950, p.463
Dimitrov O., Fromageau R. and Dimitrov C., Recrystallization of Metallic Materials,
Riederer-Verlag GMBH, Stuttgart, 1978
Gordon P. and Vandermeer R., Recrystallisation, Grain Growth and Textures, ASM,
Ohio, 1966
Gottstein G. and Shvindlerman L.S., Grain boundary migration in metals, Materials
Science and Technology, CRC, 1999
Graham C.D. and Cahn R.W., Grain growth rates and orientation relationship in the
recrystallization of aluminium single crystals, Transactions AIME, 206, 1956, p.517-521
Hillert M. and Purdy G., Chemically-induced grain boundary migration, Acta
Metallurgica, 26, 1978, p.333-340
Manohar P.A., Ferry M. and Chandra T., Five decades of the Zener equation, Isij
International, 38, 1998, p.913-924
Nes E., Ryum N. and Hunderi O., On the Zener drag, Acta Metallurgica, 33, 1985,
p.11-22
Smidoda K., Gottschalk W. and Gleiter H., Diffusion in migrating interfaces, Acta
Metallurgica, 26, 1978, p.1833-1836
Chapter 2
Dispersoid size analysis
2.1
Introduction
Due to their small size and high number density the dispersoids play an important role in the recrystallisation kinetics of the alloy and in the workability of the final wrought product. In order to be able to model the characteristics of a material in a proper way it is necessary to include the information of the dispersoids and their evolution throughout the industrial processing of the metal. Details, not only on the presence of these particles, but also on their size distribution, volume fraction, density, type and inter-particle spacing after each step of the industrial processing are required.
The need for precise information on particle sizes and their distribution for material modelling is widely recognised. Many results are presented in literature not only for metallurgy [Aksel, 2003; Lee, 2003; Thurm, 2003; Ivanov-Omskii, 2003; Aguiar, 2003] but also for nanotechnology [O'Connor, 2002; Ahn, 2001; da Silva, 2000], biology [Serra, 2002; Krumins, 2001; Balachandran, 2000; Chung, 2000; Brown, 2000; Sanchez, 2000] and environmental science [Mongia, 2000; Hoss, 1997]. While accurate values of average particle sizes are often sufficient, there are examples where the final material behaviour depends on the full particle size distribution [Hashimoto, 2000; Hausch, 1978].
material, and secondary precipitates that form during the following thermomechanical process and which can be redissolved. These secondary particles are of two types: long thin platelets and smaller dispersoids of a range of shapes. Both form inside the grain, but not in the near vicinity of the constituent particles. Their chemical composition is close to either Al6Mn or cubic α-Al(Mn,Fe)Si [Sanders,
1989].
The ideal procedure for analysing small particles in a metal, such as the dispersoids, would involve the use of the Transmission Electron Microscope (TEM). With this method each particle is examined individually at an adjustable magnification. For a particle fully contained within the TEM sample foil, also some 3D information can be obtained. The disadvantages of this method are that the procedure is very slow and time consuming. The areas examined in a sample are limited and cannot be easily selected, hence the result is unavoidably rather qualitative. Any quantification process has to be carried out by hand and the results do not have a high statistical significance [Flores, 2003].
The use of the Scanning Electron Microscopes (SEM) highly improves the quantitative results. The areas examined can be much larger, can be automated and can easily be aimed at the parts of interest in the sample. The particles can be mainly recognised in their 2D structure thus providing information on the visible area of a precipitate, but well established methods can convert the results to 3D values if particles are assumed to belong to a particular class of shapes [Gacsi, 2003; Hashimoto, 2000; Xu, 2003]. Most methods refer to old stereological studies carried out in the 1960’s and refined by S. A. Saltikov [Saltikov, 1967]. This chapter will present the original method and also new features that were incorporated for the examination of dispersoids. An extension of the traditional size classes and a choice between linear and logarithmic division is now possible, but most importantly the effect of the beam penetration depth during SEM observations is now accounted for.
To obtain reasonable statistics and a reliable estimate of the size distribution a large number of particles is necessary and therefore a semi-automated quantification procedure is to be preferred. The use of a software imaging program combined with a SEM is then a very powerful tool for quantification needs.
The system used during the research is the Noran Vantage software on a Field Emission Gun Scanning Electron Microscope (FEGSEM) with acquired micrographs in backscatter mode. A stage automation system allows to collect a very large number of data so that the results are representative of the whole sample and area fractions can be safely calculated. The results obtained not only show that the quantification procedure is successful, but also that it is a valuable tool in characterising the different industrial stages of the thermomechanical processing of an aluminium alloy.
Every sample has its own features and every micrograph session needs to have its own set of conditions. There is no right or wrong procedure and similar results may be obtained with a different series of operations.
This chapter will present and discuss the quantification method in detail for the example of the AA3103. Beginning with an accurate look at the microscope set-up and the choice of parameters to obtain the best micrographs, then the exact binarisation procedure and the image processing will be analysed. The transformation in 3-dimensional results of the acquired data in 2-dimension is a key process of the quantification procedure. The parameters that affect this transformation will be discussed and analysed in depth along with the introduction of the new features to the method. The analysis of the data will be done in the following chapter.
2.2
Quantification procedure
2.2.1 Sample preparation
The aluminium sheet samples are observed in the direction transverse to rolling. They are embedded in conductive resin and after grinding on sandpaper are polished with diamond paste up to ¼ μm and then carefully rinsed. The usual silica suspension for final polishing should not be used in order to avoid contamination of the surface. The silica particles are effectively very similar in size and shape to the dispersoids and even though most of the times the human eye can distinguish them from the particles, not all software has that ability. On the other hand slight scratches on the surface do not influence the particle quantification process. Chemical polishing is to be avoided as it may unintentionally remove the dispersoids.
2.2.2 Microscope parameters
The micrographs of the polished samples are taken with a Jeol JSM 6500F Field Emission Gun Scanning Electron Microscope, at 5 kV acceleration voltage, 8 mm working distance, in backscatter mode with an Autrata below-the-lens detector [Autrata, 1992].
found to be 5 kV acceleration voltage and 8 mm lens-sample distance. This corresponds to an effective working distance of less than 8 mm [Erlandsen, 1999].
The working magnification can also affect the measurement. Of course it is necessary to use the same magnification for samples that need to be compared, but it is also necessary to choose the magnification according to the average size of the particles that need to be measured. In this thesis the minimum determinable size was set to a 3x3 pixel cluster. At 20000 times magnification this corresponds to 360 nm2 thus a particle of equivalent diameter equal to about 20 nm. The dispersoid
sizes typically range from a couple of tens of nanometres to a set limit, which corresponds to the tail of the second peak in the size distribution (related to the broken constituent particles), of 700 nm equivalent diameter.
Two parameters not directly connected to the software procedure but that need to be adjusted in order to obtain a useful grey level profile are the contrast and brightness. The ideal profile, for particles showing up brighter than the matrix, should be similar toFigure 2-2. The first peak, at lower grey levels (grey level varies from 0 for black to 255 for white), represents the values of the background pixels darker than the particles. The whole area from the right tail of the peak to white (255) belongs to the particles. Contrast and brightness should be adjusted so that the background peak is shifted to lower grey levels leaving a relatively large range of values to the pixels belonging to the particles.
2.2.3 Image acquisition and sampling
Even for perfect microscope settings the backscatter image is influenced by factors that can reduce the resolution of the micrograph. These factors involve the electron source, the detector and the general mechanical and optical stability of the microscope, which create a local fluctuation at pixel level. The software can help to overcome these problems and improve the quality of the image.
The software can compose an image (micrograph) as an average of multiple frames of the same field. The single frames can also be acquired with different times of dwelling on each pixel. The longer the dwell time and more frames are averaged the longer the procedure takes, but also the quality of the field micrographs improves drastically. Each pixel then becomes the average of more measurements thus reducing the background noise. The grey level profile curve smoothens and the particle outlines are clearer (Figure 2-3). It is necessary to adjust these two acquisition parameters to obtain the best possible results in a reasonable amount of time. For the micrographs in this work a dwell time of 21 microseconds per pixel and an average of 3 frames per field was used. The acquisition time is then about 2 minutes per micrograph.
for the quantification and the procedure to apply in each point while the software automatically divides the area in smaller fields and maps them (Figure 2-1). The grey level image obtained, after having selected an appropriate threshold value is then transformed to a binary image in which the particles are white and the matrix black. A set of filters is then applied to clean the binary image from background noise. The software is able to determine any chosen parameter that involves the analysis of the white pixels against the black: for example area, length, width, aspect ratio, orientation and shape factor. Extra criteria are also added to discard features that are not the particles being quantified.
2.2.4 Binarisation
The most critical parameter for the whole quantification procedure is the choice of the threshold value that distinguishes between the signal of the matrix and that of the dispersoids [Coster, 2001]. This is the value that allows the transformation of the grey level image to a binary one and corresponds to the maximum loss of information from the micrograph. There is no rule for choosing this value but a general suggestion will be given here.
The ideal threshold level is actually a somewhat personal choice of the operator and so every set of measurements should be done by the same operator that follows his own logic and personal preferences in a consistent manner. The best way to avoid errors in the final results is to treat them as relative values and not absolute ones. The goal in the present work is a comparison between different Figure 2-1: schematic view of the stage automation procedure.
field 1
field 2
field 3
field 4
field 5
field 6
field 7
field 1
field 2
field 3
field 4
field 5
field 6
industrial stages of processing, so absolute values are not needed with high precision.
Basic rules that can be followed are that the threshold should be applicable everywhere in the chosen investigation area (given good microscope stability) and that it should be able to detect the correct morphology for the particles (important to distinguish between different populations of precipitates).
The choice of the threshold value starts by examining the grey level profile. The value should fall directly after the background noise peak, as indicated in Figure 2-2. It is safer to choose a value that slightly overlaps the last part of the background peak’s tail, rather than to miss any of the pixels that are part of the dispersoids. The exceeding background points will be discarded in the final quantification by a series of extra filters. In non-ideal cases the second peak, corresponding to the particles, is not always evident, especially if the particles in the frame are only a small area percentage. Then the background peak should be considered to be symmetrical and the threshold value should be chosen, as in the ideal case, at the tail of the background peak.
The determination of the threshold parameter is critical because it directly affects the quantification results. In particular for small particles a slightly lower or higher value can influence the final area fraction result heavily. This is shown in Figure 2-4 where on the same grey level image there are 3 different outlines of particles recognised by the software with the ideal threshold level (b), one slightly lower (a) and one slightly higher value (c).
Having established the desired threshold value in a small local region, it is then imperative to check that this threshold value applies to the larger region to be examined.
The choice of the threshold value is also connected to the definition of the micrograph. Every pixel in an acquired digital image represents an interaction volume from which the electrons are backscattered rather than just a spot on the surface of the sample [Liu, 2000]. According to a Monte Carlo simulation performed by the Casino Software v.2.42 at 5 kV acceleration voltage, in a substrate of chemical composition similar to that of the AA3103 and the dispersoids, each pixel represents the backscattered electrons originated from a volume that spreads 50 nm around the selected point and almost 100 nm in depth. This is the main reason why the edges between particles and the matrix are never sharp or well defined. The choice of the threshold value should reflect this effect and be chosen in order to fall within the “fuzzy area” of the boundary (Figure 2-4b).
Figure 2-4: theoretical analysis of the effect of threshold on the particle size. The dotted line represents the outline of the recognised particles for the correct threshold value (b), slightly lower (a) and slightly higher (c).
1 frame Average of 10 frames Average of 50 frames
5
μ
m 5μ
m 5μ
m5
μ
m 5 5 5 5μ
μ
μ
μ
mmmm 5 5 5 5μ
μ
μ
μ
mmmmFigure 2-3: effect of a different number of frame averages on the grey level profile and on the final recognition of the outline of the particles.
Figure 2-5: illustration of the binarisation process from the grey level image acquisition to the quantification procedure.
Acquisition
Threshold
Erode
1Template
connect
(dilate to limit)
Close
(dilate
2+ erode)
Hole fill
Quantification
1Erode: transforms to black all pixels that have at least one edge or corner that borders a black pixel 2Dilate: transforms to white all pixels that have at least a white neighbour
Dilates the white pixels to match the shape of the original grey level image.
It restores the original size of the particles but does not restore the small particles that where completely eroded away.
Binarisat
ion
Grey level image
Binary image. The particles are the selected object and are represented by white pixels. The matrix is black.
Disappearance of single white pixels and small clusters. Reduction in size of all particles.
ACTION
RESULT
Smoothes edges and reduces enclosures.
Fills cavities that may have remained within the particles during the procedure.
Size and area percentage distributions.
Acquisition
Threshold
Erode
1Template
connect
(dilate to limit)
Close
(dilate
2+ erode)
Hole fill
Quantification
1Erode: transforms to black all pixels that have at least one edge or corner that borders a black pixel 2Dilate: transforms to white all pixels that have at least a white neighbour
Dilates the white pixels to match the shape of the original grey level image.
It restores the original size of the particles but does not restore the small particles that where completely eroded away.
Binarisat
ion
Grey level image
Binary image. The particles are the selected object and are represented by white pixels. The matrix is black.
Disappearance of single white pixels and small clusters. Reduction in size of all particles.
ACTION
RESULT
Smoothes edges and reduces enclosures.
Fills cavities that may have remained within the particles during the procedure.
Once the threshold value is properly chosen the binary image is easily created by following the procedure indicated in Figure 2-5. An example of the result can be seen in Figure 2-6. During the binarisation procedure additional filters [Wojnar, 1999; ASM, 2000] can be added in order to avoid particles of undesired areas or positions. In this work particles touching an edge of the image are excluded, as well as those smaller than 4 nm2 or larger than 500.000 nm2. Hence large platelets and
constituent particles are excluded from the counting procedure.
2.3
From 2-Dimensions to 3-Dimensions
Results obtained from the quantification procedure described previously are 2-dimensional. The data measured is the area of the cross section of a precipitate in the matrix, from which an equivalent diameter is derived, i.e. the diameter of a circle with the same area. This measured diameter d can be, however, very different from the actual 3-dimensional diameter D of the precipitate.
Considering a volume with spheres of different sizes dispersed within, a random polishing plane that cuts the volume will give rise to random cross sections through the spheres as shown schematically in Figure 2-7. Cross sections with diameter d can then be due to spheres with 3-dimensional diameter D=d, but also from larger spheres that have been sectioned far from their equator. For example particle A and C have the same cross section dA=dC, but DA is bigger than DC. Otherwise particles B and C have the same real diameter DB=DC but different cross sections dB>dC. And although dB is the largest cross section it does not correspond to the particle with the largest real diameter D.
Methods have been proposed to distinguish the respective contribution of particles of bigger 3D size (D>d) to the ensemble of cross sections of equivalent diameter d. For example the process used here is based on the Johnson-Saltikov stereological method although some modifications and adaptations have been made. DC dC DB dB dA DA volume cross section A B C DC DC dC dC DB DB dB dA dA DA volume cross section A B C
Figure 2-7: schematic view of a distribution of spheres in a volume and the cross sections obtained with a random polish plane. The 3-dimensional diameter D can be considerably different from the cross section diameter d.
2.3.1 The Johnson-Saltikov method
The Johnson-Saltikov method is a classical stereological method developed during the second half of the last century [Saltikov, 1967; DeHoff, 1968] and since then often used and refined [Gacsi, 2003; Hashimoto, 2000; Xu, 2003; Bach, 1967].
But while the interest in particle sizes and their distribution has been high for more than a century, obtaining accurate information remains difficoult. The main, obvious, obstacle is that metals are not transparent leaving no direct way of checking the actual volume distributions of precipitates in a sample. While for some specific cases other 3D measuring methods can be used, such as TEM observations of thin foils with precipitates smaller than the thickness of the foil, the best and simplest way seems to remain the 2D observations and the latter conversion to 3D.
All of the stereological methods available at the moment are based on measurements done on a polish plane randomly cutting through the sample that needs to be analysed. The measured data can be the diameter or radii, for spherical particles, of the precipitates, the area or the chord length [DeHoff, 1968]. The following assumptions are commonly used:
• All particles must have the same shape and differ only from one another in size
• The shape of the particles must be such that a random plane can intersect the particle only once
• The distribution of the particles in the sample should be representative of the whole sample
The particles may be mono- or poly-dispersed in the system, that is to say they may be all of the same size or all of different sizes.
The main assumption behind the Saltikov method is that statistically the polish plane will cut through the sample and the particles in a predictable way. In the classical method the polishing plane cuts the particles at random distance from their centre. With the use of pre-calculated factors it is possible to account for the contribution of bigger particles to the count of the smaller ones. For particles of the same size it is assumed that surface fractions are equal to volume fractions.
d1 d2 d3 d4 d5 ½D5 ½D4 ½D3 ½D2 ½D1 d1 d2 d3 d4 d5 ½D5 ½D4 ½D3 ½D2 ½D1
Figure 2-8: schematic illustration of the contribution of spheres with diameters D1 to D5 to the total
number of sections with diameters d1 to d5.
From the data obtained in the 2D measurement, for example in the case of spherical particles the equivalent diameter, the largest value obtained d is assumed to be the real diameter D of the largest particle. With reference to Figure 2-8 if the largest value measured is d5 then it will be assumed that d5=D5. From that value size classes will be defined ([d5,d4], [d4,d3], [d3,d2],…) and all the values of d that are found between d5 and d4 are considered to be originated from particles of size D5.
reported in tables. These factors are used to subtract the contribution of particles of size D5 to class 4 (d3-d4) and also to smaller classes. The procedure is repeated for successive smaller classes. So for an apparent diameter d between d2 and d3 the real diameter D3 will be assigned to all the particles in that class minus the contribution of particles with real D4 and D5.
Assuming that the surface fractions are equal to the volume fractions it is then possible to calculate the volume distribution of particles and consequently their 3D size distribution.
2.3.2 In-depth modification
Because the experimental data was collected from FEGSEM micrographs some modifications to the Saltikov method are necessary.
In the FEGSEM the electron beam can penetrate the surface of a sample to an extent that depends on the material analysed and on the voltage of the beam. The beam penetrates into one single point in the surface and is then diffracted at different angles in the bulk of the sample and emits backscattered electrons that have interacted not only with one point but with a volume of material in the bulk below the examined surface point. The information contained in the backscattered electron represents then not only the surface but the whole diffraction volume.
Particles at surface
Particle below surface
Figure 2-9: example of particles at and below the surface and how the appear due to the penetration depth of the beam. AA3103 Transfer Slab sample acquired in FEGSEM at 15kV.
Figure 2-10 illustrates the situation assuming a penetration depth t. The particles that are cut by the plane of polish above their equatorial line appear to have a bigger diameter than the real cross section diameter. This error must be taken into account in the Saltikov quantification procedure, especially if the penetration depth t is comparable to the mean size of the particles.
measured diameter measured diameter
sample surface detector e -e-beam t Interaction volume
measured diameter measured diameter
sample surface detector e -e-beam t Interaction volume
Figure 2-10: schematic representation of the penetration depth of a beam and its influence on the particles apparent cross section measurement.
2.4 Quantification of dispersoid characteristics
2.4.1 Structure of new procedure
The Saltikov method has been renewed and new developments have been added to take into account the effect of the depth penetration of the FEGSEM beam on the 2D-3D conversion coefficients (equation A8 is used instead of A6 of the Appendix A). The method has also been made more general. The choice of the size classes is not restricted to the original fixed subdivision into classes of the logarithmic scale, but offers several options for the definition of class size (see paragraph 2.5.3).
The data obtained after the quantification procedure, the so called raw data, is the number of pixels that belong to each identified particle. Knowing the pixel size leads to the area and eventually the equivalent diameter of the cross section of a particle. A program routine based on the Saltikov method and running on an excel sheet was created to run the elaboration analysis automatically. Details of the procedure can be found in Appendix A.
used, the type of size class division and the depth of the beam penetration. From the step size the cross section diameter limits for each class are determined and the particles are then distributed into the classes according to their 2D diameter. The cross section diameters are used eventually, together with the depth size information, to obtain the coefficients for determining the contribution of larger particles to the smaller size classes counts. The conversion coefficients are calculated as described in Appendix A.
Following the scheme reported in Figure 2-11 the number of frames analysed is needed to determine the total area measured in 2D and thus calculate:
• NA(i): number of sections in class i per unit area
• AA(i): total area of the sections of the particles in class i per unit area (i.e. area fraction of all the sections whose 2D diameter belongs to class i, compared to the total area observed).
The data obtained from the measurement is used with the conversion coefficients to determine the 3D information:
• NV(i): number of particles in class i per unit volume (i.e. particle size distribution) • VV(i): volume of particles in
class i per unit volume (i.e. volume fraction of all particles whose 3D diameter belongs to class i) the total sums of which give respectively the particle density and fraction. The same size classes are used both in 2D and 3D. 2D to 3D conversion coefficients volume fraction and density For i = k to 1 Calculate VV(i)
using A(i), coefficients, Vj
(eq A6) Calculate NV(i) (eq A7) update Vj NAand AA per class in 2D 2D to 3D conversion coefficients 2D to 3D conversion coefficients volume fraction and density volume fraction and density For i = k to 1 For i = k to 1 Calculate VV(i)
using A(i), coefficients, Vj
(eq A6)
Calculate VV(i)
using A(i), coefficients, Vj
(eq A6) Calculate NV(i) (eq A7) Calculate NV(i) (eq A7) update Vj update Vj NAand AA per class in 2D NAand AA per class in 2D
2.5
Parametric study of method
2.5.1 Size distribution in 2 and 3 dimensions
Application of the classical Saltikov method gives the 2-dimensional size distribution. The difference between the size distribution of a 2D set of data and the same set recalculated in 3D (for spherical particles) is illustrated in Figure 2-12 for the example of AA3103 back annealed. To confront the data sets they were plotted as NA(i)% and NV(i)% that represent the total number of particles in class i normalised to the total number of particles measured in 2D or calculated in 3D.
Figure 2-13: difference between size and volume distribution plot for the AA3103 back annealed sample.
The shape of the size distribution remains unchanged between 2D and 3D. The most frequent diameter remains the same and only the proportions are different. The 2D distribution overestimates the big particle fraction. This is a bit counterintuitive but can be explained mathematically (see Appendix A).
The results are plotted in two different ways: size and volume distribution (Figure 2-13). The size distribution graphs plot NV(i) that is the number of particles per class per unit volume versus the equivalent diameter. In this particular case the distribution is multi peaked, with a dominant peak in the area of the smaller particles and smaller humps. The volume fraction distribution plot of the same data set (VV(i) vs. equivalent diameter) shows the volume fraction of the particles belonging to a certain class. This distribution is multi peaked too but with, logically, a clearer view of the smaller humps in the area of the bigger dispersoids. It is from the comparison of these two types of plots that the multi peak nature of the distribution can be seen making it easier to appreciate how strongly a small amount of big particles can influence the material.
Of course the threshold setting will directly influence the particle size and volume fraction distributions. The effect will be much larger for the distributions at small dimensions than at big particle sizes. The sensitivity depends on the underlying true particle size distribution.
2.5.2 Effect of depth information
The effect of the use of a FEGSEM has been discussed previously and the introduction of the penetration depth t has been justified. The calculated depth t for this series of measurements was estimated to be around 50 nm. Figure 2-14 illustrates how the depth penetration information affects the size distribution.
If the beam penetration is not considered the particle sizes are overestimated for d>100 nm as described in Figure 2-10. Below 100 nm the size of particle is low enough to be largely or completely under the surface of the sample and still be detected by the beam. If t is not taken into account then the particles will be considered to be lying on the observation plain and thus could be originated from larger size dispersoids resulting in an underestimation of the amount of smaller particles.
2.5.3 Effect of class definition
To determine the total distribution the real data values have to be divided in a number of classes. This distribution can be done in several ways for example with a linear or a logarithmic division of classes. Also the number of classes per distribution distinctively affects the outcome.
The original Saltikov method was very rigid and did not allow for many changes. To adapt the method to the best match with the raw data obtained and to make the method more flexible, some modification regarding the size classes were made.
Initially the classes were determined so that the difference between two consecutive classes was given by
1 log(di+ ) log( )= di + or sd i 1 10sd i d d + =
and the step size sd equal to 0.1. This value was chosen to give the best result for a large range of values. But according to the different necessities the spread of values may be broader or narrower and so the option of choosing a different step size was inserted.
The effect of different step sizes for a logarithmic distribution is shown in Figure 2-15. The change from 0.1 to 0.05 gives a much more detailed view of the typical size distribution of dispersoids in the AA3103. The number of classes increases in the critical area around the maximum equivalent diameter allowing a close up view of how the distribution behaves in that particular range. Other values of step sizes can focus on other size ranges and thus be adapted to the particular data set examined.
Also the choice of having a logarithmic distribution of size classes could be limiting in certain size distributions. The possibility of choosing a linear distribution was also inserted and it can be very useful if more details are necessary in the area of the larger size classes. Caution should be taken when analysing the results plotted in linear or logarithmic scale in determining and comparing the average diameter.
Figure 2-16: effect of difference in perception between the same data set of AA3103 transfer slab with classes divided linearly and logarithmically.
the lower density of the particles. The linear distribution results highly scattered in this region for the same reason.
The choice of step size and linear or logarithmic distribution is a compromise between revealing details and statistics. The advantage in this case of the logarithmic distribution gives better statistics for large particles but does not have constant class size.
2.5.4 Statistical considerations
density of the sample, between 500 and almost 2000. This kind of work load can be accomplished easily thanks to the stage automation. This option allows to determine on a sample the desired area for the analysis, along with the magnification, and the program will calculate itself the best matrix and sequence of acquisition to cover the selected area. On each grey level image the binary and the quantification procedure are run according to a predefined schedule. For each measurement the sequence of operations is the same, but the critical value, the threshold, needs to be changed for every microscope session.
The number of micrographs necessary depends on the characteristic of the sample. First of all, in order to have a representative idea of the whole sample, the examined area must include at least a couple of grains, as the dispersoid population is concentrated within a grain and not equally dispersed throughout the sample. Subsequently the number of images necessary also depends on the particle density of the sample. To have a valid area fraction data the precipitate free zones and the constituent particle areas must be included in the total measurement field too.
0 100 200 300 400 500 600
Number of particles counted per subset
P os iti on of peak (nm ) Peak 1 Peak 2
Figure 2-18: values of the first and second peak, in the size distribution graphs for Transfer Slab, according to the number of particles counted. The bubbles are centred on the X value of the peak and their area is proportional to the height of the peak.
In Figure 2-17 there are examples of the kind of errors that arise from a statistically insufficient data set. The examples are from the Transfer Slab material. The line plot is based on 5863 counted particles yielding a total area fraction of 0,24% that is considered as the reference “realistic” value. It is easily seen that considering subsets of the original full data set with fewer particles (subsets of 100, 500, 1000, and 2000 particles) can give errors both in the area fraction but also in the size distribution. In the example for 500 counted particles the area fraction is already close to the final value but this is only a coincidence since the size distribution gives
a clear overestimation for the larger dispersoids. As a general rule the measurements should be continued until the addition of data does not alter the size distribution significantly.
If the particles are inhomogeneously distributed within the sample, like in the material here analysed, the choice of the subsets should be made particularly carefully. In Figure 2-18 it is shown that for 2000 particles the result can be close to the final value if the chosen frames are well representative of the whole sample, but can also be quite different if the frames are less representative.
2.6 Conclusions
A semi-automatic particle quantification method was developed and successfully applied to the AA3103 aluminium alloy. The method was presented in detail and all the set-up parameters, the output data style and the image processing technique were analysed.
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Microchemistry changes during
industrial processing of AA3103
3.1
Introduction
The fabrication of Aluminium alloy rolled sheets requires complex thermo-mechanical processes, involving a succession of metal working and annealing. During this process the microstructure undergoes significant alterations due to the activation of work-hardening, softening and precipitation-dissolution mechanisms. The understanding and control of these physical mechanisms is a permanent challenge for the metallurgical industry and is complicated by the strong interaction that can take place between these mechanisms. Detailed and accurate experimental characterization of microstructure evolution is therefore a prerequisite to any valid model development.
of microchemistry evolution and gives relevant information on its influence on work-hardening and softening.
3.2
The VIR[*] project
Although numerous mathematical-physical material models are readily available, many developments in the metals industry are still based on experience and the use of empirical relationships that relate processing parameters and the final material properties [Gottstein, 2002]. These mathematical models usually focus on one single feature like for instance the final microstructure after casting [Yu, 2002] or the work hardening of alloys due to plastic deformation [Nes, 1997]. However, during the entire production process of aluminium alloys many sequential structural and chemical changes take place, which can influence each other. Therefore, to be able to predict all the changes that occur during processing, it is necessary that all relevant models are coupled in a consistent way for the entire processing route through (preferably) a limited number of physical parameters. Although such integrated modelling approaches may already exist for a number of years within the aluminium industry [Sigli, 1996], examples in the open literature are still limited. Recent examples of multi-model coupling in metallurgy are by Zurob et al. [Zurob, 2002] who connect existing models for precipitation, recovery and recrystallisation to describe the microstructure development of micro-alloyed austenite and by Gandin et al. [Gandin, 2002] who use existing models for solidification, precipitation and precipitate hardening to predict the yield stress of as-cast Al-Cu. Both examples, nevertheless, still represent only parts of the entire process chain for metallic alloy production.
