**2. Experimental Methods and Materials**

An AA6082 alloy was used as a base material (1.16% Si, 0.7% Mg, 0.98% Mn, 0.26% Fe, 0.17% Cr, 0.04% Ti) and a 9-mm rod of the same alloy was used for additions. In some experiments, a standard Al5Ti1B rod (LSM, Rotherham, UK) was used (0.2% addition). A total of 10% of AA6082 rod was introduced in each experiment. The choice of the alloy is due to its wide applicability in automotive applications where extrusions are made from direct-chill case billets, so the grain refinement is an important issue. The liquidus of this alloy is 647 ◦C, the equilibrium solidus is 593 ◦C and the nonequilibrium solidus is 533 ◦C, as calculated by Thermocalc software (version 2019a, TCAL 4 database, Thermo-Calc Software AB, Solna, Sweden).

In the experiments with ultrasound, a 5-kW ultrasonic generator and a 5-kW, 17.5-kHz water-cooled transducer (Reltec, Yekaterinburg, Russia) were used at a power of 3 kW (the longitudinal amplitude was ±12 μm). When ultrasound was applied, the rod was inserted tightly into a hole in a steel sonotrode in the half-wavelength position and then fed into the melt while the ultrasonic transducer was on as shown in Figure 1. The sonotrode was not in contact with the melt and was not cooled or heated. As a result of this scheme, the longitudinal oscillations of the sonotrode were transformed into flexural oscillations of the rod with the resultant shorter wavelength and larger amplitudes, up to 25 μm as measured by a contactless vibrometer. Separate experiments in water showed that cavitation conditions were achieved at the tip of the rod as well as in nodes along the rod length. Water is a well-accepted analogue of liquid aluminium with regard to the cavitation behaviour, though the cavitation threshold in liquid Al is about two times higher than in water, 10 μm vs 5 μm peak-to-peak amplitude at 20 kHz [15]. Therefore, the vibration conditions used in these experiments were sufficient to achieve cavitation in liquid Al.

The melt was prepared in clay-graphite crucibles (0.5 kg charge) in an electric resistance furnace (Carbolite, Hope Valley, UK) with melt temperature up to 770 ◦C. Rod introduction was made either without or with ultrasonic vibrations applied into the melt in a temperature range with the final pouring temperature 670 ◦C, i.e., the rod was started to be introduced at a certain given melt temperature and then, while the rod was dissolving, the melt was naturally cooled down to the pouring temperature. Reference samples were prepared by adding the same amount of rod into the melt that was then superheated to 750 ◦C, left in the furnace for 30 min and then cooled in air and cast at 670 ◦C. The rod was not preheated before the introduction. Casting was done in a standard TP-1 mould [16].

**Figure 1.** A schematic of the experiment.

The castings were then sectioned along the vertical centre plane and etched for structure examination. Macroetching was done in a 10% NaOH water solution after grinding. To reveal grain microstructure smaller samples were cut, ground and polished using standard procedures and then anodised in a 5% HFB4 water solution at 20 VDC. The grain structure was subsequently examined in an optical microscope Zeiss Axioscope (Zeiss, Cambridge, UK) in polarised light. For the grain size measurement, the sections in the middle of the sample cross-section were used (see Figure 1a for detail). The grain size was measured using a random linear intercept method with at least 50 grains measured. Statistical analysis of the measured grain size was performed and the average values are reported.
