High-throughput in-situ characterization and modeling of precipitation kinetics in compositionally graded alloys
Graphical abstract
Introduction
The process of designing engineering alloys requires finding an optimal point in a chemistry space, subject to relevant constraints of processing. In all major alloy families, the number of alloying elements typically ranges from 5 to 10 and optimizing a composition in such multicomponent space is an extremely challenging task. The traditional approach is to try to decouple the interactions between different solutes and study alloys of discrete compositions. In recent years, considerable efforts have been launched (e.g. the Materials Genome Initiative (MGI) [1] and the Accelerated Metallurgy Project [2]) to develop new alloy design strategies using combinatorial methods in both computational material science and related experimental approaches that accelerate this alloy design process. Materials containing compositional gradients have long been used to map the composition space of alloys. Specifically, diffusion couples or multiples have been used for determining the effect of composition on the material structure (phase diagram identification [3], [4], [5], [6], [7]), on the diffusion of solute species [8], and on various properties related to materials chemistry (e.g. modulus [9], thermal conductivity [10], [11]) and sometimes more complex properties such as shape memory alloy identification [12] or metallic glass formability [13].
However, a key characteristic of engineering metallic alloys is that their main properties depend not only on chemistry, but also on microstructure. Therefore, their optimization with respect to a given property requires an understanding of the effect of chemistry on the kinetic path of microstructure development during thermal or thermo-mechanical treatments. Few studies have actually tried to determine the microstructure development in compositionally graded materials from the point of view of combinatorial experimentation. The community interested in phase transformations in steels have used this approach to study the compositional limits for certain types of phase transformations [14], [15]: the limits for the massive transformation [16], [17], acicular ferrite formation [18] and allotriomorphic ferrite formation [19], [20] have all been examined using specially designed samples containing a macroscopic gradient in either carbon or substitutional solute such as Ni or Mn. Sinclair et al. [21] have even used a sample containing a gradient in Nb content in one direction and a gradient in temperature in an orthogonal direction to simultaneously probe the effect of temperature and Nb content on the recrystallization of Fe. Similar approaches have been used by to study the compositional limits for coherent versus incoherent precipitation [22], order/disorder transformations [22], [23], competition between spinodal decomposition and nucleation and growth [22], nucleation in the vicinity of phase boundaries [22], [24] and the effect of Cu and Mg content on the rapid hardening phenomenon in Al–Mg–Cu alloys [25].
In all of these studies, the alloys were observed ex-situ after a specific heat treatment, which provided a snapshot of the microstructure (and hence of the corresponding potential properties) as a function of chemical composition. However, composition interacts in a complex manner with microstructure development during heat treatments, and an alloy design strategy requires the characterization of the full kinetic path in composition space. If this is to be done, in a combinatorial manner, by exploiting samples containing a macroscopic composition gradient, the characterization strategy requires tools exhibiting the following characteristics:
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Fast, quantitative characterization of the microstructural feature of interest.
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Spatially resolved with a high resolution compared to the size of the composition gradient, yet probing a volume large enough to guarantee sufficiently good statistics on the measured microstructure features.
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Time resolved with a time resolution sufficient so the kinetics can be monitored simultaneously in the desired number of locations within the composition gradient.
For the particular case of strengthening precipitation, the microstructural features of interest are the size, volume fraction and number density of precipitates. In most metallic systems the precipitate radius for maximum strength occurs at the nanoscale (often 2–5 nm). The only experimental technique that satisfies the three conditions above is small-angle X-ray scattering (SAXS). Reviews discussing the manner in which it can be used to provide a fast, quantitative characterization of precipitates can be found in [26], [27], [28], [29], [30]. The spatial resolution of these measurements is equal to the X-ray beam size, which is typically greater than 1 mm for laboratory sources and 100 μm for synchrotron experiments. Several studies have demonstrated the capability of SAXS to map the distribution of nanoscale precipitates in heterogeneous microstructures such as in welds [31], [32], [33]. Furthermore, SAXS is particularly well suited to be performed in-situ during heat treatments, along isothermal or more complex thermal paths (e.g. [34], [35]). Depending on the particular contrast of scattering factors between the precipitates and matrix, acquisition times on synchrotron beamlines can be as low as 1–10 s, which opens the possibility to couple spatially and time-resolved experiments.
The aim of this contribution is to demonstrate the feasibility of in-situ, combinatorial studies of the effect of alloy composition on precipitation kinetics, and to use the acquired database as a tool for assessing the capability of a simple precipitation model in a wide range of compositions and temperatures. For the experimental proof-of-concept study, we have chosen a model system, Cu–Co. This system offers a number of advantages, including:
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This system is relatively dilute (a maximum of 2 wt.%Co is used), and the precipitates formed are almost pure Co [36]. These two conditions will make it possible to apply relatively simple precipitation models.
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At relatively low temperatures, the precipitates form as spherical particles [37], [38], [39], which simplifies the interpretation of the SAXS data;
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Cu–Co has been used several times as a model system (ie. spherical precipitates of pure Co exhibiting negligible strain with the matrix) to assess the capability of classical nucleation theory and more generally to provide a comparison with precipitation models [40], [41].
As will be detailed below, the experiments involved preparing diffusion couples between pure Cu and Cu–2 wt.%Co, performing a solution heat treatment on the composition gradient material, and subsequently performing heat treatments at three temperatures (450, 500 and 550 °C) in-situ at a synchrotron SAXS beamline (BM02 – D2AM at ESRF) while measuring the SAXS signal at different positions along the composition gradient (Fig. 1). Co undergoes an allotropic phase transformation at 422 °C which is below the lowest temperature studied in this work. As a result Co precipitates as fcc particles under all conditions considered in this contribution. Experimental difficulties were yet encountered. They included some loss of Co during diffusion couple preparation that must be accounted for. The grain structure within the sample was such that double Bragg scattering interfered with the measured SAXS signal, and it was necessary to develop a specific methodology to deconvolute the two signals. Finally, a challenge was to link the observed precipitation kinetics to the local alloy composition where the X-ray measurement was made. A specific procedure was used to obtain an in-situ composition measurement with the help of the X-ray beam.
The precipitation kinetics, as a function of time, temperature and solute content has been modeled using the so-called numerical Kampmann–Wagner class model [42], [43]. In relatively simple systems, such as that studied here, this model has been shown to provide a robust and efficient framework which compares satisfactorily with experimental results [43], [44], [45], [46]. One advantage of this modeling technique is its good computational efficiency, which makes it possible to apply to a large set of experimental conditions with varying temperature and alloy composition, so that the results can be compared to the full dataset that is produced from the combinatorial experiment shown in Fig. 1. One of the interests here is to assess the limitations (and therefore the robustness) of this model when applied to situations where all parameters (e.g. diffusivity, driving force) vary widely.
Section snippets
Materials and preparation of the diffusion couple
The diffusion couples were prepared from pieces of Pure Cu and Cu–2.0Co (wt.%) produced by AMES Laboratory and contained impurity levels below 0.01%, as measured by ICP-AES. Pieces of pure Cu and Cu–2Co were first sectioned into cubes ∼14 mm × 14 mm × 14 mm. To help the bonding between the alloys, pieces of each alloy were held together for ∼10 min at ∼500 °C using a hot compression machine before being encapsulated in a quartz tube and transferred to a tube furnace for 15 days at 1000 °C (above the
Characterization of the composition gradient
Due to the small size of the diffusion zone in the samples (1–3 mm), and the uncertainty regarding the alignment of the samples relative to the X-ray beam, it is challenging to ascertain precisely at which position in the composition gradient the X-ray beam is aiming. It is therefore desirable to use the beam itself to measure the local concentration of Co in the samples after they have been mounted in the furnace. This can be achieved by monitoring the change in transmitted beam intensity as a
SAXS data processing
All of the SAXS images collected in this investigation contained streaks (e.g. Fig. 6a) which varied in number and intensity with the sample position. Generally, the number of streaks appeared to increase towards the pure Cu end of the diffusion couples. This observation, combined with the high purity and large grain size of the Cu foils, suggests that the streaks are multiple-diffraction effects. As the samples were heated in-situ, the position and intensity of the streaks were observed to
Precipitation kinetics: in situ SAXS measurements
The SAXS patterns were fitted to the theoretical scattering of an assembly of spherical precipitates of concentration 90% Co, which is close to experimental reports [36]. To account for the Laue scattering of the solid solution as well as for the contribution of the remaining streak features on the scattering pattern, we considered a background contribution of the form [47], [48]:with the Porod exponent n being typically between 3.5 and 4. The total intensity for a given SAXS pattern
Precipitation kinetics: modeling
This large experimental data set can now be compared to a precipitation model. It represents a challenge for the robustness of such a model, since it covers the complete precipitation kinetics (nucleation, growth and coarsening) at 3 different temperatures over a significant concentration range. A classical numerical Kampmann–Wagner class model approach was used, the details of which can be found in [43]. We simply recall here that the model uses the classical equations for homogeneous
Summary
This investigation has demonstrated that it is possible to study precipitation kinetics in-situ in a composition gradient. It has highlighted some of the technical challenges faced when performing such an experiment, particularly on the preparation of the diffusion couples (obtaining a smoothly varying concentration gradient along an adequate distance) and its proper positioning relative to the X-ray beam during the in-situ SAXS experiments. This latter issue could be handled through the design
Acknowledgements
The beamtime for this experiment was awarded by the ESRF through experiment MA-1443 and was realized on the French CRG beamline “BM02 – D2AM”. The authors would like to thank the D2AM staff for their technical assistance and particularly Dr. J.F. Berar for his help concerning the local composition measurement through transmission below and above Co edge. MJS acknowledges the support of CSIRO through the Office of the Chief Executive (OCE) Science Program. CRH gratefully acknowledges the support
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