Introduction

Phases are the fundamental building blocks of material systems [1, 2] and can be used to predict stable phases as a function of temperature and composition [3]. There are several factors that contribute to the cost difference between simulation model-based approaches and traditional experimental methods when predicting the phase properties of materials. One key advantage of simulation-based approaches, such as those found in software, like Thermo-Calc and Fact-Sage, is their ability to accurately predict the behaviour of materials using established thermodynamic models, without the need for expensive and time-consuming experimental trials. These models allow researchers to focus specifically on the area of research interest for the proposed alloy, eliminating the need for extraneous experimentation that may be required with traditional methods. This not only reduces costs and saves time but also enables researchers to make more informed decisions about the properties and behaviour of materials, leading to more accurate and effective results. This will ultimately ensure that the new alloy being designed meets the specific property requirements in terms of composition, processing, and microstructural expectations.

Aluminium-based alloys are complex materials and have been found to possess many advantages, including low density, increased strength (depending on the alloy), good resistance to corrosion, and excellent thermal and electrical conductivity, amongst others [2, 4, 5]. The Al–Ag alloy is a binary system whose phase diagram has been analysed by several researchers using different experimental techniques [6,7,8]. Unfortunately, these works are old with a lot of discrepancies in the results reported. The Al–Ag alloy has been found suitable for grain refining and hardening [9], as electrical conductors [10], and formation of screen printing pastes [11]. The relatively high cost of obtaining silver has also further hindered continued research into this binary alloy system [10]. Optimizing the processing parameters, such as temperature and composition, to prevent defects and achieve desired properties is crucial when preparing alloys. This study addresses this need by utilizing Thermo-Calc software to simulate and predict the phase equilibria of the Al–Ag binary alloy under various conditions, providing researchers with valuable information to improve their experimental approach. By reducing the time and resources required for trial-and-error experiments, this study can significantly improve the preparation method for alloys, specifically for the Al–Ag binary alloy.

Methodology

For this study, Thermo-Calc 2021b software was used to calculate the thermodynamic properties and obtain the phase diagram for the binary Al–Ag system. The CALculation of PHAse Diagrams (CALPHAD) method was used to calculate thermodynamic properties of material systems [1, 12] and the binary calculation template adopted for the equilibrium phase diagram of the Al–Ag binary system. This is consistent with methodologies used by other researchers for previous related works [6,7,8, 13, 14]. The calculation was performed at a temperature range of 250 K to 1300 K and a pressure of 1 bar. The TCBIN: TC Binary Solutions v1.1 database was used to perform the thermodynamic calculation for phase stability of the Al–Ag alloy binary system.

Results and discussion

Figure 1 shows the result of the Thermo-Calc phase equilibria calculation for Al–Ag binary alloy and that obtained from previous research [7, 15,16,17], which demonstrate a satisfactory level of conformity. The Al–Ag phase diagram of Fig. 1a has a total of sixteen fields, including elemental Ag at 0 and elemental Al at 100. Phase properties analysis shows six single phases, namely the liquid phase, fcc_Ag, cub_A13, hcp_A3, bcc_A2, and fcc_Al phases. When compared with Fig. 1b, the phases are labelled as \((Ag),\) μ, \(\delta\), \(\beta\), and \((Al)\), respectively. From the six single phases identified from Fig. 1, three intermediate phases are also observed, namely cub_A13 μ, bcc_A2 \((\beta )\), and hcp_A3 \((\delta )\). Most research studies on Al–Ag alloy have always been on the metastable hcp_AgAl intermediate phase [6, 8, 15, 18]. The ten double-phase reactions obtained are listed in Table 1.

Fig. 1
figure 1

Temperature–composition phase diagram plot of binary Al–Ag alloy system obtained using a Thermo-Calc and b calculated and experimental values [7, 16, 17] under Creative-Common Licence

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Table 1 Calculation result of Al–Ag alloy indicating double phases
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Location of the phase boundaries of the Al–Ag alloy binary system is another aspect where authors’ discrepancies existed for the different results presented which lead McAlister [7] to conclude that there is need to further study these boundary structures. Figure 1a shows a boundary structure for the Ag-rich side extending from 0 to 40.31 at% Al at temperature range of 300.00 K to 1234.96 K. Another boundary structure for the Al-rich side is observed to extend from 40.31 to 99.93 at% Al at a temperature range of 300.00 K to 840.01 K. These results were consistent with the metallographically assessed experimental results of [19,20,21] for both the Al- and Ag-rich sides. Other notable boundaries seen in Fig. 1 include the \(\delta\) boundary present at both the Ag-rich and Al-rich solidus terminals, the μ boundary which is only limited to the Ag-rich terminal, and the \(\beta\) boundary.

Figure 2 shows the intermediate phases, namely the metastable \(\delta\), \(\beta\), and μ intermediate phases. The hcp_A3 intermediate phase from Fig. 2a stabilizes below 734.47 °C compared to 727 °C reported by [7]. This phase extends from 23.02 at% Al at 608.74 °C to 41.27 at% Al at eutectic temperature 566.85 °C. This relatively agrees with 23.0 at% Al at 611 °C to 41.9 at% Al at 567 °C assessed by [7]. The \(bcc\_A2\) intermediate phase (Fig. 2a) stabilizes above 606.94 °C compared to 603 °C reported by [7]. The bcc \(\beta\) intermediate phase extends from 20.90 at% Al at 776.27 °C to 27.86 at% Al at 730.08 °C. This is significantly lower to 20.5 at% Al at 779 °C to 29.8 at% Al at 727 °C assessed by [7]. A cubic μ intermediate phase (Fig. 2b) stabilizes below 457.43 °C and extends from 19.32 at% Al to 27.16 at% Al. This is higher than the single-phase field of 21.2–24.3 at% Al at 300 °C assessed by [7].

Fig. 2
figure 2

Enlarged portion of Fig. 1a showing the a intermediate and b cubic intermediate phases

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The hexagonal phase in Al–Ag alloys (\(\delta\)) has been reported to have a composition near Ag2Al with a probable suggestion that Ag atoms diffuse to stacking faults in the fcc Al-rich alloys [22]. This has thus lead to a debate on the composition and temperature needed to predict the direct transition from the \(\delta\) phase to the \(\beta\) phase with series of discrepancies between experimental and calculated results reported at the intermediate phases [13]. Spencer et al. [23] predicted that the transition to occur between 0.1 and 0.2 at% Al around 1075–1125 K. Hume-Rothery et al. [20] using detailed X-ray and microscopic analysis reported the phase transformation between 24.6 and 25.8 at% Al at a temperature below 604 °C. In this study (Fig. 2), a direct transition from the hcp \((\delta )\) intermediate precipitation phase to high-temperature \(\beta\) phase is predicted to occur at 23.94 at% Al and 606.90 °C which agrees with [20].

Five invariant reactions, namely one eutectic, two peritectic, and two peritectoid regions, are observed in the binary phase diagrams of Fig. 1. The eutectic reaction (Eq. 1) occurred at 566.85 °C at eutectic composition ratio of 65.57 at% Al to 34.43 at% Ag and is consistent with the generally acceptable value of 567 °C [7, 9, 10] but slightly differs at the eutectic composition of 67 at% Al reported by [21, 22] using wet chemical analysis.

$$Liquid \leftrightarrow FCC\_A1 +HCP\_A3.$$
(1)

The \(\beta\) intermediate phase occur at 778.07 °C and 20.79 at% Al from a peritectic reaction (Eq. 2) which agrees with the 778 °C and 20.50 at% Al obtained by [7] albeit to a small degree of uncertainty.

$$Liquid+ FCC\_A1\leftrightarrow BCC\_A2.$$
(2)

A second peritectic reaction (Eq. 3) for \(\delta\) metastable intermediate phase also occurs at 32.76 at% Al and 730.03 °C and is consistent with the value of 726 ± 3 °C at 32.7 at% Al reported [7] to about 4.03 °C uncertainty.

$$Liquid+ BCC\_A2\leftrightarrow HCP\_A3.$$
(3)

A cubic μ structure intermediate phase is formed by a peritectoid reaction (Eq. 4) at 457.43 °C and 22.25 at% Al. A second peritectoid reaction (Eq. 5) is formed at the metastable \(\delta\) intermediate phase at 608.25 °C and 23.05 at% Al. The peritectoid temperatures are both a little higher and lower than that obtained by Ref. [7] at 450 ± 3 °C and 22.9 at% Al and 610 ± 3 °C and 23.5 at% Al, respectively.

$$FCC\_A1 +HCP\_A3\leftrightarrow CUB\_A13,$$
(4)
$$FCC\_A1+BCC\_A2\leftrightarrow HCP\_A3.$$
(5)

The melting point temperature of pure Ag (fcc_A1) shown in Fig. 3a occurs at 961.81 °C and agrees with the widely accepted value of 961.8 °C [7, 24]. Figure 3b also predicts the melting point temperature of pure Al at 660.35 °C and relatively agrees with widely accepted literature value of 660.45 °C [7, 24]. Purity of the materials affects the melting point values of any experimental procedure.

Fig. 3
figure 3

Enlarged portions of Fig. 1 showing a Ag melting point and b Al melting point

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The maximum solid solubility of Al in Ag contained in the Ag-rich terminal (fcc_Ag) obtained is 19.17 at% Al at peritectoid temperature of 457.43 °C as against a higher value of 20.4 at% Al at about 450 °C assessed by [7]. For the Al-rich solid solution (fcc_Al), the maximum solid solubility of Ag in Al obtained is 25.81 at% Ag at eutectic temperature of 566.85 °C which is higher than 23.5 at% Ag at relatively the same eutectic temperature of 567 °C reported by [7].

Conclusion

The temperature–composition phase diagram of the Al–Ag alloy binary system was calculated using the Thermo-Calc (TCBIN database) software. The phase diagram showed in total 16 fields, including the terminal regions at 0 and 100 Al mass percent. Six single phases were equally observed with three intermediate phases, namely μ, \(\beta\), and \(\delta\). Five invariant reactions were equally obtained from the phase diagrams. The melting temperature for pure silver and aluminium inferred from the Thermo-Calc calculation was consistent with widely accepted literature values. The calculation also gave the maximum solubility of Al in Ag and Ag in Al to be 5.60 Al mass percent and 58.17 Ag mass percent, respectively. These results are important for developing novel alloys (particularly suited for thermal applications) from the Al–Ag alloy binary system. The use of the Thermo-Calc simulation model-based software for thermodynamic analysis offers several advantages over traditional methods, including affordability, efficiency, and increased precision. The software can also serve as a guide for experimental work, allowing researchers to focus on specific alloy compositions whilst still obtaining valuable insights.