Inductively Coupled Nonthermal Plasma Synthesis of Size-Controlled γ-Al2O3 Nanocrystals

Gamma alumina (γ-Al2O3) is widely used as a catalyst and catalytic support due to its high specific surface area and porosity. However, synthesis of γ-Al2O3 nanocrystals is often a complicated process requiring high temperatures or additional post-synthetic steps. Here, we report a single-step synthesis of size-controlled and monodisperse, facetted γ-Al2O3 nanocrystals in an inductively coupled nonthermal plasma reactor using trimethylaluminum and oxygen as precursors. Under optimized conditions, we observed phase-pure, cuboctahedral γ-Al2O3 nanocrystals with defined surface facets. Nuclear magnetic resonance studies revealed that nanocrystal surfaces are populated with AlO6, AlO5 and AlO4 units with clusters of hydroxyl groups. Nanocrystal size tuning was achieved by varying the total reactor pressure yielding particles as small as 3.5 nm, below the predicted thermodynamic stability limit for γ-Al2O3.

The detailed structure of γ-Al 2 O 3 still remains unclear owing to the structural complexity and the notorious presence of mixed alumina polymorphs during synthesis [27][28][29]. Many properties and surface characteristics of γ-Al 2 O 3 are still actively debated [29,30]. Nanostructured γ-Al 2 O 3 often results in cube octahedral or octahedral morphology demonstrating distinct surface facets [7,31,32]. These surface facets directly influence the anchoring ability, dispersion, and surface interaction of metal catalyst atoms and their catalytic behaviour [7,31]. Reported synthetic methods that utilize high-temperature conditions often produce polydisperse nanocrystal aggregates with non-reproducible facet orientations, which hamper their catalytic activity.
Here, we report a rapid, single-step, low temperature synthesis of phase-pure facetted γ-Al 2 O 3 nanocrystals using a flow-through nonthermal inductively coupled plasma (ICP) reactor. The nonthermal plasma approach has emerged as a competitive technique in producing a variety of nanoparticles with high-purity and narrow size distributions [33][34][35]. One of the major advantages of nanocrystals synthesis in plasma is the unipolar electrical charging of particles that reduces or eliminates the agglomeration of nanoparticles [33,34]. Exploiting this unique feature, we synthesized γ-Al 2 O 3 nanocrystals with defined surface planes using a low-pressure nonthermal ICP reactor utilizing trimethylaluminum and oxygen as precursors. Cendejas et al., recently studied the crystallization of Al 2 O 3 nanoparticles in a nonthermal capacitively coupled plasma (CCP) reactor and achieved the γ-Al 2 O 3 phase, but their study did not demonstrate control of the nanocrystal size and lacked detailed microstructural characterization [36]. The plasma density of an ICP used in this study is usually more than one order of magnitude higher than that of a CCP [37]. We demonstrate, here, that this causes effective crystallization of the γ-Al 2 O 3 phase [38,39]. We also performed detailed microstructural characterizations of the synthesized γ-Al 2 O 3 nanocrystals, which revealed cuboctahedra morphology with (111) stepped facets. Furthermore, size tuning of γ-Al 2 O 3 nanocrystals was achieved here by varying the total reactor pressure.

γ-Al 2 O 3 Nanocrystal Synthesis
γ-Al 2 O 3 nanocrystals were synthesized using a flow-through, low-pressure, nonthermal ICP reactor, Figure 1, which is similar to a previously published report [40]. A simplified schematic of this system is shown in Figure 1. Briefly, a low-pressure discharge was generated by the application of 120 W radio frequency (13.56 MHz) power to an induction copper coil with three turns, approximately 2.5 cm in length and 2.5 cm in diameter, wrapped around a quartz tube with an outer diameter of 2.5 cm. The RF power was generated by a 13.56 MHz RF power supply (AG 0313, T&C Power Conversion, Rochester, NY, USA) and applied through an impedance matching network (Model HFT1500, Vectronics, Starkville, MS, USA). Trimethylaluminum (TMA, 97%, Sigma Aldrich, St. Louis, MO, USA) vapor, carried by an argon flow, entered through the top inlet mixed with a diluted oxygen/argon flow that entered from the side arm tube before the plasma discharge. In a typical recipe, the TMA volumetric flow rate was about 0.2 standard cubic centimetres per minute (sccm) carried by 6 sccm of argon flowing through the TMA bubbler, in which pressure was stable around 350 Torr. The oxygen volumetric flow rate and the associated argon volumetric flow rate were 2.5 sccm and 60 sccm, respectively. γ-Al 2 O 3 nanocrystals were collected on silicon wafer substrates by inertial impaction [41] using an orifice with a 0.25 × 8 mm rectangular opening. The total reactor pressure was maintained at approximately 3.8 Torr for the typical recipe. The collection rate of γ-Al 2 O 3 nanocrystals was 18 mg/h. Deposited nanocrystals were stored under ambient conditions. Size tuning experiments were carried out by varying the orifice diameter, leading to a change in reactor pressure. While the above-described reaction conditions were kept the same for 0.25 mm and 0.5 mm orifice diameters, 15 sccm of Ar flow with TMA and 5 sccm of O 2 were used for an orifice of 1 mm diameter. The 0.5 mm and 1 mm orifice diameters resulted in total reactor pressures of 2.5 and 1.3 Torr, respectively.

X-ray Diffraction (XRD)
XRD was performed using a Bruker D8 Discover 2D X-ray diffractometer (Bru Billerica, MA, USA) equipped with a Co Kα (λ = 1.79 Å) radiation point source in Br Brentano configuration. The diffraction patterns were collected at 25 °C with a step si 0.01° per step and a retention time of 5 s per increment. Nanocrystals were directly de ited onto Si wafers for XRD analysis. The XRD patterns were converted to Cu source 1.54 Å) for data analysis. Data analysis was performed using the Material Data Inco rated Jade 8.0 software package.

Fourier-Transform Infrared (FT-IR) Spectroscopy
FT-IR spectroscopy was performed on a Bruker Alpha spectrometer (Bruker, B ica, MA, USA) using the attenuated total reflection (ATR) module in a nitrogen fi glovebox. The as synthesized nanocrystals were dissolved in methanol, drop cast ont ATR crystal, and 20 scans were taken for each measurement at 2 cm −1 resolution.

X-ray Photoelectron Spectroscopy (XPS)
XPS was performed with a PHI Versa Probe III XPS and UPS system (Physical tronics, Chanhassen, MN, USA). Samples were directly deposited onto Si wafers for analysis. The binding energy of C 1 s at 284.6 eV was used as a reference. A 55 eV band energy was used to collect high-resolution scans. Peaks were fitted using PHI's Mult software v9. XPS survey scans were taken at a bandpass energy of 280 eV. The at percentages were calculated using Multipak software v9.

Transmission Electron Microscopy (TEM)
High-angle annular dark-field scanning transmission microscopy (HAADF-ST images were collected using an aberration-corrected FEI Titan G2 60-300 (FEI, Hillsb OR, USA) operated at 300 kV with a 25 mrad semi-convergence angle. Transmission tron microscopy (TEM) images were collected using a Thermo Scientific Talos F (Thermo Scientific, Waltham, MA, USA) operated at 200 kV. Samples were directly de

X-ray Diffraction (XRD)
XRD was performed using a Bruker D8 Discover 2D X-ray diffractometer (Bruker, Billerica, MA, USA) equipped with a Co Kα (λ = 1.79 Å) radiation point source in Bragg-Brentano configuration. The diffraction patterns were collected at 25 • C with a step size of 0.01 • per step and a retention time of 5 s per increment. Nanocrystals were directly deposited onto Si wafers for XRD analysis. The XRD patterns were converted to Cu source (λ = 1.54 Å) for data analysis. Data analysis was performed using the Material Data Incorporated Jade 8.0 software package.

Fourier-Transform Infrared (FT-IR) Spectroscopy
FT-IR spectroscopy was performed on a Bruker Alpha spectrometer (Bruker, Billerica, MA, USA) using the attenuated total reflection (ATR) module in a nitrogen filled glovebox. The as synthesized nanocrystals were dissolved in methanol, drop cast onto the ATR crystal, and 20 scans were taken for each measurement at 2 cm −1 resolution.

X-ray Photoelectron Spectroscopy (XPS)
XPS was performed with a PHI Versa Probe III XPS and UPS system (Physical Electronics, Chanhassen, MN, USA). Samples were directly deposited onto Si wafers for XPS analysis. The binding energy of C 1 s at 284.6 eV was used as a reference. A 55 eV bandpass energy was used to collect high-resolution scans. Peaks were fitted using PHI's Multipak software v9. XPS survey scans were taken at a bandpass energy of 280 eV. The atomic percentages were calculated using Multipak software v9.

Transmission Electron Microscopy (TEM)
High-angle annular dark-field scanning transmission microscopy (HAADF-STEM) images were collected using an aberration-corrected FEI Titan G2 60-300 (FEI, Hillsboro, OR, USA) operated at 300 kV with a 25 mrad semi-convergence angle. Transmission electron microscopy (TEM) images were collected using a Thermo Scientific Talos F200X (Thermo Scientific, Waltham, MA, USA) operated at 200 kV. Samples were directly deposited onto lacy/thin double carbon-coated TEM grids. Nanocrystal dimensions were measured using ImageJ. A minimum of 300 particles were counted for every size distribution and the nanoparticle dimensions were reported with geometric standard deviations.

Solid-State Nuclear Magnetic Resonance (NMR) Spectroscopy
Solid-State NMR spectroscopy was performed at the National High Magnetic Field Laboratory in Tallahassee, FL, USA, on a 19.6 T (ν 0 ( 1 H) = 833 MHz) magnet equipped with a Bruker NEO console (Bruker, Billerica, MA, USA) and a 3.2 mm Low-E HX magic-angle spinning (MAS) NMR probe. The magnet field strength was referenced to the 17 27 Al shifts were indirectly referenced to 1% TMS in CDCl3 and aqueous Al(NO 3 ) 3 solution, respectively, using the previously published relative NMR frequencies [42]. The as synthesized γ-Al 2 O 3 nanocrystals were packed into the appropriate sized NMR rotor in a N 2 filled glove-box. All NMR spectra were processed in Bruker Topspin 4.0.7. The 1 H π/2 and π pulse lengths were 5 and 10 µs in duration, respectively, corresponding to a 50 kHz radio frequency. 27 Al centraltransition (CT) selective π/2 and π pulse lengths were 5 and 10 µs in duration, respectively, corresponding to a 16.7 kHz RF field and 50 kHz CT nutation frequency. 1 H and 27 Al longitudinal relaxation constants (T 1 ) were measured using a saturation recovery experiment. A quantitative single-pulse 27 Al NMR spectrum was recorded with a 30 s recycle delay [ca. 10-30 × T 1 ( 27 Al)] and a 10 • tip-angle excitation pulse. A 2D 27 Al → 1 H Dipolarmediated Refocused Insensitive Nuclei Enhanced by a Polarization Transfer (D-RINEPT) 2D correlation NMR spectrum was recorded with previously described NMR pulse sequences [43,44], and the symmetry-based SR4 2 1 heteronuclear dipolar-recoupling sequence [45] was applied to the 1 H spins. A 2D 1 H dipolar double quantum-single quantum (DQ-SQ) homonuclear correlation NMR spectrum was recorded with the previously described back-to-back (BABA) NMR pulse sequence [46,47]. 2D 27 Al dipolar DQ-SQ homonuclear correlation NMR spectra were recorded with BR2 1 2 homonuclear dipolar recoupling and the previously described pulse sequences [48]. A CT (central transition) selective π pulse was applied during the indirect dimension (t 1 ) evolution period to ensure only DQ coherence between two 27 Al spins in the CT spin states were observed [49]. Rotor-assisted population transfer (RAPT) was applied to ±400 kHz off-resonance before all 27 Al → 1 H D-RINEPT and 27 Al DQ-SQ NMR experiments to enhance the 27 Al CT NMR signals [50,51]. Small phase incremental alternation with 64 step (SPINAL-64) [52] heteronuclear decoupling with a 50 kHz 1 H RF field was applied during the detection of 27 Al NMR signals.

Results and Discussion
Freestanding γ-Al 2 O 3 nanocrystals were synthesized using the flow-through nonthermal plasma process discussed above. Even though nucleophilic molecular oxygen is highly reactive towards the electron deficient TMA under ambient conditions, it is found to be rather inert or unreactive with many organometallic precursors including TMA at low-pressure and low-temperature conditions [53,54]. Thus, the pre-mixing of TMA with molecular oxygen before the plasma region did not lead to a reaction of the gas before entering the plasma. The detailed chemistry occurring in the plasma region is poorly understood, but according to the previous reports, oxidation of TMA will proceed through initial decomposition [53], which is followed by the reaction with atomic oxygen. In the plasma region, TMA is expected to rapidly decompose to produce reactive intermediates such as metal atoms (Al) released by electron impact or partially decomposed fragments generated by radical abstraction reactions. These reactive intermediates will react with atomic oxygen to form fully oxidized γ-Al 2 O 3 nanocrystals. Nucleation and growth of these nanocrystals are believed to follow the typical nanoparticle growth in plasmas, where the growth proceeds through the nucleation of clusters that rapidly coagulate to form nanoparticles [55]. Crystallization is induced by the heat generated by energetic surface reactions such as electron-ion recombination and surface chemical reactions [36,39]. Due to the higher plasma density of the ICP, and thus more intensive nanoparticle heating, the Nanomaterials 2023, 13, 1627 5 of 12 nominal power reported here (120 W) is around 2.5 times lower than the required nominal power (300 W) [36] for full crystalline nanoparticles using a CCP.
As synthesized γ-Al 2 O 3 nanocrystals were structurally characterized through the means of XRD, TEM, and FT-IR, XPS, and solid-state NMR spectroscopies. These materials often adopt a defect spinel structure with oxygen atoms forming a face centered cubic structure, and Al cations occupying the interstitial tetrahedral and octahedral sites [12,30,56,57]. FT-IR and XPS were performed to evaluate the surface composition of the plasma synthesized γ-Al2O3 nanocrystals. As shown in Figure 2b, the absorption band ranging from 430-890 cm −1 can be attributed to the characteristic γ-Al2O3 stretching modes of fourfold (AlO4) and six-fold coordinated (AlO6) Al sites [58][59][60]. While peaks at ~890 cm −1 and the shoulder at ~760 cm −1 can be assigned to the Al-O stretching modes of AlO4, the shoulder at ~620 cm −1 relates to the Al-O stretching modes of AlO6. The broad absorption band at ~3570 cm −1 corresponds to the surface-bound and free -OH groups. In Figure 2c, XPS survey of these nanocrystals revealed three main peaks corresponding to the Al 2 p, C 1 s, and O 1s at 74, 285, and 530 eV lines, respectively. The atomic percentage of C was around 12%, which may originate from the methyl groups in TMA or partly due to the contamination in air as samples were briefly exposed to the air during transfer. A marginal C contamination is commonly observed when TMA is used due to the strong Al-C bonds [61,62]. The high-resolution XPS spectrum of Al showed a single peak at 74.2 eV, which corresponds to Al-O bonding in Al2O3 (Figure 2d) [63,64]. The O 1s peak at 530.5 eV can be deconvoluted to two individual peaks, indicating -OH and Al-O surface species (Figure 2e) [63][64][65][66]. The observed XPS features are consistent with the observed absorption peaks in the FT-IR spectrum, as well as the solid-state NMR spectra discussed below.  FT-IR and XPS were performed to evaluate the surface composition of the plasma synthesized γ-Al 2 O 3 nanocrystals. As shown in Figure 2b, the absorption band ranging from 430-890 cm −1 can be attributed to the characteristic γ-Al 2 O 3 stretching modes of four-fold (AlO 4 ) and six-fold coordinated (AlO 6 ) Al sites [58][59][60]. While peaks at 890 cm −1 and the shoulder at~760 cm −1 can be assigned to the Al-O stretching modes of AlO 4 , the shoulder at~620 cm −1 relates to the Al-O stretching modes of AlO 6 . The broad absorption band at~3570 cm −1 corresponds to the surface-bound and free -OH groups. In Figure 2c, XPS survey of these nanocrystals revealed three main peaks corresponding to the Al 2 p, C 1 s, and O 1s at 74, 285, and 530 eV lines, respectively. The atomic percentage of C was around 12%, which may originate from the methyl groups in TMA or partly due to the contamination in air as samples were briefly exposed to the air during transfer. A marginal C contamination is commonly observed when TMA is used due to the strong Al-C bonds [61,62]. The high-resolution XPS spectrum of Al showed a single peak at 74.  [63][64][65][66]. The observed XPS features are consistent with the observed absorption peaks in the FT-IR spectrum, as well as the solid-state NMR spectra discussed below.
We further investigated the local structure of the plasma synthesized γ-Al 2 O 3 nanocrystals via high-field (19.6 T) 1 H and 27 Al magic-angle spinning (MAS) solid-state NMR spectroscopy. A two-dimensional (2D) 27 Al → 1 H dipolar-refocused insensitive nuclei enhanced by the polarization transfer (D-RINEPT) NMR spectrum reveals a broad 1 H NMR signal centered at ca. 3 ppm, correlating to three 27 Al NMR signals centered at ca. 12, 35 and 70 ppm, which are assigned to AlO 6 , AlO 5 and AlO 4 species, respectively (Figure 3a). The short duration of dipolar recoupling (τ rec = 448 µs) ensures that the observed Al sites are likely on the surface of the nanocrystals and capped with hydroxyl groups. A 1 H dipolar double-quantum-single-quantum (DQ-SQ) homonuclear correlation NMR spectrum reveals that the hydroxyl groups are clustered (i.e., spatially proximate to each other) on the surface of the nanocrystal, consistent with the broad stretching band observed in the FT-IR spectrum ( Figure S1). Integration of a quantitative 10 • single-pulse (SP) 27 Al NMR spectrum reveals that the population of AlO 6 , AlO 5 and AlO 4 is ca. 65, 3 and 32%, respectively (Figure 3b). The much larger population of AlO 4 observed in the SP 27 Al NMR spectrum, as compared to the surface-selective D-RINEPT NMR spectrum, suggests that AlO 6 predominantly terminates the surface of the nanocrystal (Figure 3b). Lastly, we recorded 2D 27 Al dipolar DQ-SQ NMR spectra to probe the AlO x -AlO x (x = 4-6) linkages with the nanocrystals ( Figure S2). The 2D 27 Al DQ-SQ NMR spectra reveal intense AlO 6 -AlO 6 and AlO 6 -AlO 4 homonuclear correlations, suggesting that the majority of the nanocrystal contains AlO 6 linked to either another AlO 6 or AlO 4 , consistent with prior NMR experiments on γ-Al 2 O 3 [48]. There were additional weak AlO 4 -AlO 4 correlations, suggesting that this linkage is relatively rare. No correlations involving AlO 5 were observed due to the low population of the AlO 5 site. We note that the observed 27 Al homonuclear correlations of the synthesized γ-Al 2 O 3 nanocrystals are near identical to that of commercially available γ-Al 2 O 3 ( Figure S2). We further investigated the local structure of the plasma synthesized γ-Al2O3 nanocrystals via high-field (19.6 T) 1 H and 27 Al magic-angle spinning (MAS) solid-state NMR spectroscopy. A two-dimensional (2D) 27 Al → 1 H dipolar-refocused insensitive nuclei enhanced by the polarization transfer (D-RINEPT) NMR spectrum reveals a broad 1 H NMR signal centered at ca. 3 ppm, correlating to three 27 Al NMR signals centered at ca. 12, 35 and 70 ppm, which are assigned to AlO6, AlO5 and AlO4 species, respectively (Figure 3a). The short duration of dipolar recoupling (τrec = 448 µs) ensures that the observed Al sites are likely on the surface of the nanocrystals and capped with hydroxyl groups. A 1 H dipolar double-quantum-single-quantum (DQ-SQ) homonuclear correlation NMR spectrum reveals that the hydroxyl groups are clustered (i.e., spatially proximate to each other) on the surface of the nanocrystal, consistent with the broad stretching band observed in the FT-IR spectrum ( Figure S1). Integration of a quantitative 10° single-pulse (SP) 27 Al NMR spectrum reveals that the population of AlO6, AlO5 and AlO4 is ca. 65, 3 and 32 %, respectively (Figure 3b). The much larger population of AlO4 observed in the SP 27 Al NMR spectrum, as compared to the surface-selective D-RINEPT NMR spectrum, suggests that AlO6 predominantly terminates the surface of the nanocrystal (Figure 3b). Lastly, we recorded 2D 27 Al dipolar DQ-SQ NMR spectra to probe the AlOx-AlOx (x = 4-6) linkages with the nanocrystals ( Figure S2). The 2D 27 Al DQ-SQ NMR spectra reveal intense AlO6-AlO6 and AlO6-AlO4 homonuclear correlations, suggesting that the majority of the nanocrystal contains AlO6 linked to either another AlO6 or AlO4, consistent with prior NMR experiments on γ-Al2O3 [48]. There were additional weak AlO4-AlO4 correlations, suggesting that this linkage is relatively rare. No correlations involving AlO5 were observed due to the low population of the AlO5 site. We note that the observed 27 Al homonuclear correlations of the synthesized γ-Al2O3 nanocrystals are near identical to that of commercially available γ-Al2O3 ( Figure S2). HAADF-STEM images were analysed to examine the morphology and the size distribution of plasma synthesized γ-Al2O3 nanocrystals. Figure 4 shows representative HAADF-STEM images and the size histogram of γ-Al2O3 nanocrystals. Overall, the HAADF-STEM images were analysed to examine the morphology and the size distribution of plasma synthesized γ-Al 2 O 3 nanocrystals. Figure 4 shows representative HAADF-STEM images and the size histogram of γ-Al 2 O 3 nanocrystals. Overall, the sample consisted of well-dispersed, facetted nanocrystals with an average crystal diameter of 12.0 nm with a geometric standard deviation of 1.45. The primary morphology of these particles appeared to be cuboctahedral [32], exposing (111), (110), and (001) facets. Highresolution images revealed that the (110) surface was not atomically flat but consisted of stepped facets of alternating (111) surfaces, as shown in Figure 4b. these particles appeared to be cuboctahedral [32], exposing (111), (110), and (001) fac High-resolution images revealed that the (110) surface was not atomically flat but c sisted of stepped facets of alternating (111) surfaces, as shown in Figure 4b.
This observation of surface reconstruction of the (110) surface is consistent with DFT calculations by Pinto et al., suggesting that the (110) facet was thermodynamic favored to reconstruct into (111) facets [67]. Furthermore, enhanced surface contrast w observed in (111) terminating facets (Figures 4a and 5a,b), which corroborates previ literature reports of facetted γ-Al2O3 nanocrystals [7,31,32]. The enhanced surface cont found in cuboctahedral γ-Al2O3 nanocrystals is hypothesized [31] to occur due to the cess Al 3+ cations on (111) surface planes. The presence of excess Al 3+ cations at the na particle's surface is a modification from the bulk structure, which is found to be critica improving the dispersion and the thermal stability of fine metal particle catalysts in Al2O3 catalyst supports [31]. To evaluate the impact of total reactor pressure on the size of γ-Al2O3 nanocryst we varied the reactor pressure by tuning the orifice diameter at constant volumetric fl rates. The orifice width was tuned to 0.25 mm, 0.5 mm, and 1 mm, resulting in 3.8 T 2.5 Torr, and 1.3 Torr total reactor pressures, respectively. The size of γ-Al2O3 nanocrys decreased with decreasing reactor pressure, producing 12.0 nm particles at 3.8 Torr, nm particles at 2.5 Torr, and 4.8 nm particles at 1.3 Torr with geometric standard de tions of 1.45, 1.42 and 1.25, respectively (Figure 5a-d). The morphology of γ-Al2O3 na crystals remained similar under different pressure conditions exhibiting their typical etted nature. In many studies, it has been found that the average nanoparticle This observation of surface reconstruction of the (110) surface is consistent with the DFT calculations by Pinto et al., suggesting that the (110) facet was thermodynamically favored to reconstruct into (111) facets [67]. Furthermore, enhanced surface contrast was observed in (111) terminating facets (Figures 4a and 5a,b), which corroborates previous literature reports of facetted γ-Al 2 O 3 nanocrystals [7,31,32]. The enhanced surface contrast found in cuboctahedral γ-Al 2 O 3 nanocrystals is hypothesized [31] to occur due to the excess Al 3+ cations on (111) surface planes. The presence of excess Al 3+ cations at the nanoparticle's surface is a modification from the bulk structure, which is found to be critical in improving the dispersion and the thermal stability of fine metal particle catalysts in γ-Al 2 O 3 catalyst supports [31].
respectively. Here, the average nanoparticle diameters are found to increase nearly li arly with the estimated gas residence times. Recently, we found the size of the partic leaving a flow-through nonthermal capacitively coupled plasma reactor is mainly de mined by the balance of gas drag forces and electrostatic forces acting on the particles [6 However, it is unclear whether trapping plays a role in the inductively coupled plas reactor. XRD patterns confirmed the crystalline nature of γ-Al2O3 nanoparticles synthesiz under all three pressure conditions (Figure 5e). At the nanoscale, the thermodynamics the growth process drives the crystalline structure of Al2O3 nanocrystals. It was repor that Al2O3 nanoparticles larger than ~20 nm should adopt an α structure, while Al2O3 noparticles smaller than ~6.5 nm will be amorphous [70]. Hence, γ-Al2O3 nanocryst were predicted to be thermodynamically stable in the range ~20-6.5 nm [70]. Our proach demonstrated that the size tuning of γ-Al2O3 is feasible in a range of 12-5 nm w some nanocrystals as small as 3.5 nm, as shown in Figure 5c, which is below the therm dynamically predicted size limit. It will be interesting to explore whether the nontherm plasma environment, where nanoparticles are charged while they grow, more genera allows for the synthesis of material phases outside of thermodynamically predicted s limits. To evaluate the impact of total reactor pressure on the size of γ-Al 2 O 3 nanocrystals, we varied the reactor pressure by tuning the orifice diameter at constant volumetric flow rates. The orifice width was tuned to 0.25 mm, 0.5 mm, and 1 mm, resulting in 3.8 Torr, 2.5 Torr, and 1.3 Torr total reactor pressures, respectively. The size of γ-Al 2 O 3 nanocrystals decreased with decreasing reactor pressure, producing 12.0 nm particles at 3.8 Torr, 8.5 nm particles at 2.5 Torr, and 4.8 nm particles at 1.3 Torr with geometric standard deviations of 1.45, 1.42 and 1.25, respectively (Figure 5a-d). The morphology of γ-Al 2 O 3 nanocrystals remained similar under different pressure conditions exhibiting their typical facetted nature. In many studies, it has been found that the average nanoparticle size correlates nearly linearly with the residence time of particles in the plasma [68]. A slower gas velocity yields longer residence time, thus increasing the size of particles leaving the plasma. Here, for essentially the same total of volumetric flow rate, a wider orifice reduces the pressure in the reactor while increasing the gas velocity. Therefore, an increasing orifice size results in a decreasing residence time and a reduction of the average particle sizes of γ-Al 2 O 3 nanocrystals. Assuming 2 cm for the plasma length, the gas residence times are estimated as 33 ms, 22 ms, and 10 ms with the orifice width of 0.25 mm, 0.5 mm, and 1 mm, respectively. Here, the average nanoparticle diameters are found to increase nearly linearly with the estimated gas residence times. Recently, we found the size of the particles leaving a flowthrough nonthermal capacitively coupled plasma reactor is mainly determined by the balance of gas drag forces and electrostatic forces acting on the particles [69]. However, it is unclear whether trapping plays a role in the inductively coupled plasma reactor.
XRD patterns confirmed the crystalline nature of γ-Al 2 O 3 nanoparticles synthesized under all three pressure conditions (Figure 5e). At the nanoscale, the thermodynamics of the growth process drives the crystalline structure of Al 2 O 3 nanocrystals. It was reported that Al 2 O 3 nanoparticles larger than~20 nm should adopt an α structure, while Al 2 O 3 nanoparticles smaller than~6.5 nm will be amorphous [70]. Hence, γ-Al 2 O 3 nanocrystals were predicted to be thermodynamically stable in the range~20-6.5 nm [70]. Our approach demonstrated that the size tuning of γ-Al 2 O 3 is feasible in a range of 12-5 nm with some nanocrystals as small as 3.5 nm, as shown in Figure 5c, which is below the thermodynamically predicted size limit. It will be interesting to explore whether the nonthermal plasma environment, where nanoparticles are charged while they grow, more generally allows for the synthesis of material phases outside of thermodynamically predicted size limits.

Conclusions
We demonstrated the synthesis of γ-Al 2 O 3 nanocrystals using an inductively coupled nonthermal plasma. While XRD patterns confirmed phase-pure crystalline γ-Al 2 O 3 nanoparticles, TEM images revealed cuboctahedra morphology with (111) stepped facets. The total pressure of the reactor was varied by tuning the orifice diameter at a constant gas flow to yield γ-Al 2 O 3 particles ranging between 5-12 nm. We observed γ-Al 2 O 3 nanocrystals as small as 3.5 nm, which is below the size at which thermodynamics would predict amorphous alumina to be the most stable phase.
Overall, this study demonstrates the single-step synthesis of size-tunable, facetted γ-Al 2 O 3 nanocrystals without additional post-synthetic calcination or annealing steps. These particles, specifically the γ-Al 2 O 3 as small as 3.5 nm , could be used as heterogeneous catalysts and catalytic supports. Their specific surface areas along with catalytic performance need to be probed in future work.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding authors upon reasonable request.