Muon kinetics in heat treated Al (–Mg)(–Si) alloys
Introduction
Muon spin methods are mainly used to probe magnetic properties of materials, but can also be used to study other phenomena as a consequence of their magnetic properties. A common example is solid-state diffusion in non-magnetic materials [1]. The techniques are similar to positron annihilation spectroscopy (PAS) in that unstable elementary particles are implanted in a material and decay, and their decay products are detected outside of the material. The spin precession of muons can be indirectly observed through the positrons they decay into. In a muon spin relaxation (μSR) experiment, muons enter the sample with their spin aligned antiparallel to their direction of motion. With no external field applied, the precession is caused by magnetic fields set up by the atomic nuclei inside the material. In a non-magnetic metal like aluminium, these fields are randomly oriented, and polarized muons become depolarized (“relaxed”) in a matter of microseconds.
Al–Mg–Si alloys constitute most of the worldwide aluminium market as they have good mechanical strength and are easily formable into end products [2]. An optimal heat treatment of alloys containing merely 1% solutes (Mg and Si) typically increases the hardness by a factor of 5 from pure aluminium. After the material is formed, an industrial hardening procedure consists of solution heat treatment (SHT), typically at 550 °C, some (unavoidable) storage at room temperature (RT) and artificial aging (AA), typically at 180 °C. The hardening during heat treatment is caused by precipitation of metastable phases through diffusional phase transitions. Going from low to high aging times/temperatures, the generic precipitation sequence for Al alloys iswhere SSSS is an acronym for supersaturated solid solution. In general, the precipitate phases grow larger and become fewer as we proceed through the sequence.
Al–Mg–Si alloys quenched from SHT are unstable at RT, and atomic clusters (with Mg and Si at Al-face-centred cubic (fcc) positions) form from the SSSS. The clusters in general are too small and coherent with the Al matrix to be observed by transmission electron microscopy (TEM). However, new experimental possibilities have sparked an interest in solute clustering the last decades, with techniques such as PAS [3], [4], atom probe tomography (APT) [5], [6], [7] and differential scanning calorimetry (DSC) [8], [9]. Several independentAPT studies [5], [10] have shown that two kinds of solute clusters can form in Al–Mg–Si alloys. Cluster (1) (the “bad” cluster) forms during RT storage (of alloys with Mg + Si > 1% [10], [11]), has a non-fixed composition and does not grow or develop during further heat treatment. Cluster (2) (the “good” cluster) forms during annealing at 70–150 °C directly after SHT [6] (and during RT storage of alloys with Mg + Si < 1% [10], [11]), has an Mg/Si ratio close to 1 and can develop into hardening β″ precipitates.
The hardening Al–Mg–Si precipitates are all needle shaped, with their main growth/coherency direction along 〈0 0 1〉Al. The most important of these is β″ [12], [13]. At temperatures above 200 °C, Al–Mg–Si alloys over-age, transforming β″ to less coherent precipitates, which causes a drop in hardness. The thermal and mechanical treatments applied to alloys determine their progression through the precipitation sequence. Understanding the early steps, in particular the formation of Mg–Si (–vacancy) clusters, is essential, as the composition, concentration and size of these clusters influence the precipitate microstructure in finished products.
Muons undergo interstitial diffusion inside solids. In aluminium, they have been shown to be trapped by atoms in substitutional lattice positions and by vacancies [14], [15], yielding a lower apparent muon diffusivity. In this work, we exploit this effect and identify the muon trapping behaviour of Mg and Si atoms as well as vacancies in different stages of heat treatment of aluminium alloys. Due to its industrial and scientific interest, we hereby study the ternary Al–Mg–Si system, and we include the binary Al–Mg and Al–Si alloys mainly to help isolate the ternary-specific features in the μSR data. The processes occurring in the binary subsystems are definitely still worth investigating in their own rights, seeing that they are used as alloys for many applications where high strength is not required [2]. No precipitation has been observed in annealed Al–Mg alloys, while diamond Si particles precipitate in the Al–Si system without increasing the hardness significantly [16]. These particles also form in over-aged Si-rich Al–Mg–Si alloys [13]. Very dilute alloys have been probed with μSR before, and small additions of Si, Mg and Cu were found to greatly affect the muon kinetics [17]. Our previous work on the Al–Mg–Si system revealed the presence of a muon trapping peak corresponding to clustering/precipitation [18]. By analysing more conditions and including binary alloys, we aim to improve our understanding of the interactions between muons and precipitates in Al–Mg–Si alloys. The main goal of the current work is to establish a connection between muon trapping rates and the microstructure of materials as found from TEM and APT studies.
We will explore the theory of muons and their interactions with samples in greater detail in the next section. Sections 3 Experimental, 4 Data analysis and simulations explain the procedures of the experiments and the analysis of μSR data. Results from various experiments on Al (–Mg)(–Si) alloys are presented in Section 5. Some mechanisms of muon trapping are proposed in the discussion part (Section 6), and are used to infer the behaviour of vacancies during heat treatment of Al alloys, leading up to the conclusions in Section 7.
Section snippets
Theory
Like electrons, muons are elementary particles in the lepton family. As in most muon spin research [19], we use positively charged muons, since the negatively charged variant has a material-dependent lifetime. The lifetime of a positive muon always has an average value of 2.197 μs. The muon decays into a positron and two neutrinos:
The direction of motion for the positron is asymmetric with respect to the muon spin, a fact which μSR measurements depend on [20]. The exact distribution
Experimental
Samples of pure Al (99.99%) and Al–Mg, Al–Si and Al–Mg–Si alloys were used in the μSR experiments. The material was cast and rolled to 1 mm sheets at the University of Toyama. The sample dimensions were 25 mm × 25 mm × 1 mm. All samples underwent a SHT of 1 h at 575 °C and subsequent quenching in ice water, before one of three heat treatment procedures was performed:
- 1.
μSR measurement directly (approx. 15 min) after quenching, which we call as-quenched (AQ) conditions.
- 2.
Some time, typically days/months of
Data analysis and simulations
Apart from direct visual comparison, our method of choice for interpreting relaxation functions is to compare them to a Monte Carlo simulation. An indeterministic simulation is appropriate, since diffusion, trapping/detrapping by defects, the magnetic field at muon sites and muon decay are all stochastic processes/variables. The magnetic field vectors are Gaussian distributed, with a standard deviation Δ/γμ, where Δ is the dipolar width, proportional to the strength of the magnetic field. An
Reproducibility of measurements
As a check of the consistency of our μSR measurements and of the fitting to simulated data, we have run two equal experiments on the Al–1.6% Mg2Si alloy in an AQ condition. After quenching, the samples were prepared for the measurements, which required keeping them at RT for ≈15 min before cooling down to 20 K. The number of events measured and the number of temperature points were lower in the second run, leading to shorter storage at e.g. 300 K inside the spectrometer. As longer time at higher
Muon trapping in Al (–Mg)(–Si)
We focus here on the bonds formed between muons and various lattice defects in aluminium, which has been shown to greatly influence the measured muon spin relaxation functions.
At low temperatures, Al–Mg has a much higher trapping peak than Al–Si (Fig. 3), leading to a clear conclusion: Mg–μ+ bonds are stronger than Si–μ+ bonds. This is supported by the DFT results for hydrogen–solute bonds in Table 2, and can be qualitatively explained in terms of the lower number of valence electrons in Mg
Conclusion
An extensive study on the muon behaviour in Al–Mg–Si, Al–Mg, Al–Si and pure aluminium has been conducted. Heat treatments were designed for the investigation of diffusion and clustering phenomena in different stages of the precipitation, which is crucial to the properties of commercial Al–Mg–Si alloys. We have shed light on some important findings regarding the muon trapping in the materials and its interpretation in terms of (sub-) nanometer-sized defect content. In particular, muons were
Acknowledgements
This work was financially supported by The Research Council of Norway and Norsk Hydro via project No. 193619, The Norwegian–Japanese Al–Mg–Si Alloy Precipitation Project. The authors kindly acknowledge Dr. Flemming J.H. Ehlers for his contributions to the calculations of hydrogen binding energies.
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