Effect of electrolyte temperature on the formation of self-organized anodic niobium oxide microcones in hot phosphate-glycerol electrolyte

Nanoporous niobium oxide films with microcone-type surface morphology were formed by anodizing at 10 V in glycerol electrolyte containing 0.6 mol dm⁻³ K₂HPO₄ and 0.2 mol dm⁻³ K₃PO₄ in a temperature range of 428-453 K. The microcones appeared after prolonged anodizing, but the required time was largely reduced by increasing electrolyte temperature. The anodic oxide was initially amorphous at all temperatures, but crystalline oxide nucleated during anodizing. The anodic oxide microcones, which were crystalline, appeared on surface as a consequence of preferential chemical dissolution of initially formed amorphous oxide. The chemical dissolution of an initially formed amorphous layer was accelerated by increasing the electrolyte temperature, with negligible influence of the temperature on the morphology of microcones up to 448 K.     

Synthesis of [Ru3(μ3-NPh)(Br)(CO)9] on self-assembled monolayers of di(3-aminopropyl)viologen/ITO surfaces and its application to photoelectrochemical cells

Triruthenium carbonyl clusters {[Ru₃(Br)(CO)₁₁]⁻ (denoted as Ru-1), [Ru₃(μ₂-Br)(CO)₁₀]⁻ (denoted as Ru-2), and [Ru₃(μ₃-NPh)(Br)(CO)₉]⁻ (denoted as Ru-3)} were synthesized on di(3-aminopropyl)viologen (DAPV)/indium tin oxide (ITO) using a surface reaction in a ruthenium (III) carbonyl [Ru₃(CO)₁₂] solution, and were applied to photoelectrochemical cells (PECs) at the molecular level. The formation of DAPV on ITO was realized in the form of self-assembled monolayers. Ru₃(CO)₁₂ then easily reacted with the Br⁻ of DAPV, and a mixture of Ru-1 and Ru-2 was formed on DAPV/ITO. Furthermore, Ru-3 was successfully anchored on DAPV/ITO by adding nitrosobenzene in order to react with Ru-2 on DAPV/ITO. The photocurrents of (Ru-1 and Ru-2)/DAPV/ITO and Ru-3/DAPV/ITO in PECs at the molecular level were 6.3 nA cm⁻² and 8.6 nA cm⁻², respectively. The quantum yield of Ru-3/DAPV/ITO was ∼0.8%. Time-resolved photoluminescence spectroscopy and emission spectroscopy were recorded to bring out the photoinduced charge transfer process from ruthenium clusters to DAPV.     

Behavior of Ru surfaces after ozonated water treatment

In order for the development of cleaning technology of extreme ultra violet lithography photomask, the behavior of Ru surfaces after treatment with ozonated deionized water (DIO₃) solution was studied using Ru and ruthenium oxide particles and 2 nm-thick Ru capping layers. No significant changes in crystalline structures or chemical states of the Ru surfaces, nor any similarities with the structures or states of ruthenium oxide, were observed after DIO₃ treatment. Oxidation of ruthenium to form RuO₂ or RuO₃ was not observed. Adsorption of H₂O molecules on the Ru layer increased the surface roughness, but the desorption of H₂O molecules recovered it. Local chemisorption of H₂O molecules on the Ru surface may be the reason why rougher Ru surfaces were observed after DIO₃ cleaning.     

In situ XPS study of Pd(1 1 1) oxidation. Part 1: 2D oxide formation in 10 mbar O2

The oxidation of the Pd(1 1 1) surface was studied by in situ XPS during heating and cooling in 3 × 10⁻³ mbar O₂. A number of adsorbed/dissolved oxygen species were identified by in situ XPS, such as the two dimensional surface oxide (Pd₅O₄), the supersaturated O_ads layer, dissolved oxygen and the R 12.2° surface structure.Exposure of the Pd(1 1 1) single crystal to 3 × 10⁻³ mbar O₂ at 425 K led to formation of the 2D oxide phase, which was in equilibrium with a supersaturated O_ads layer. The supersaturated O_ads layer was characterized by the O 1s core level peak at 530.37 eV. The 2D oxide, Pd₅O₄, was characterized by two O 1s components at 528.92 eV and 529.52 eV and by two oxygen-induced Pd 3d_5/2 components at 335.5 eV and 336.24 eV. During heating in 3 × 10⁻³ mbar O₂ the supersaturated O_ads layer disappeared whereas the fraction of the surface covered with the 2D oxide grew. The surface was completely covered with the 2D oxide between 600 K and 655 K. Depth profiling by photon energy variation confirmed the surface nature of the 2D oxide. The 2D oxide decomposed completely above 717 K. Diffusion of oxygen in the palladium bulk occurred at these temperatures. A substantial oxygen signal assigned to the dissolved species was detected even at 923 K. The dissolved oxygen was characterised by the O 1s core level peak at 528.98 eV. The “bulk” nature of the dissolved oxygen species was verified by depth profiling.During cooling in 3 × 10⁻³ mbar O₂, the oxidised Pd²⁺ species appeared at 788 K whereas the 2D oxide decomposed at 717 K during heating. The surface oxidised states exhibited an inverse hysteresis. The oxidised palladium state observed during cooling was assigned to a new oxide phase, probably the R 12.2° structure.     

Growth and decay of the Pd(1 1 1)-Pd5O4 surface oxide: Pressure-dependent kinetics and structural aspects

Growth and decomposition of the Pd₅O₄ surface oxide on Pd(1 1 1) were studied at sample temperatures between 573 and 683 K and O₂ gas pressures between 10⁻⁷ and 6 × 10⁻⁵ mbar, by means of an effusive O₂ beam from a capillary array doser, scanning tunnelling microscopy (STM) and thermal desorption spectrometry (TDS). Exposures beyond the p(2 × 2)O adlayer (saturation coverage 0.25) at 683 K (near thermodynamic equilibrium with respect to Pd₅O₄ surface oxide formation) lead to incorporation of additional oxygen into the surface. To initiate the incorporation, a critical pressure beyond the thermodynamic stability limit of the surface oxide is required. This thermodynamic stability limit is near 8.9 × 10⁻⁶ mbar at 683 K, in good agreement with calculations by density functional theory. A controlled kinetic study was feasible by generating nuclei by only a short O₂ pressure pulse and then following further growth kinetics in the lower (10⁻⁶ mbar) pressure range.Growth of the surface oxide layer at a lower temperature (573 K) studied by STM is characterized by a high degree of heterogeneity. Among various metastable local structures, a seam of disordered oxide formed at the step edges is a common structural feature characteristic of initial oxide growth. Further oxide nucleation appears to be favoured along the interface between the p(2 × 2)O structure and these disordered seams. Among the intermediate phases one specifically stable phase was detected both during growth and decomposition of the Pd₅O₄ layer. It is hexagonal with a distance of about 0.62 nm between the protrusions. Its well-ordered form is a superstructure.Isothermal decay of the Pd₅O₄ oxide layer at 693 K involves at first a rearrangement into the structure, indicating its high-temperature stability. This structure can break up into small clusters of uniform size and leaves a free metal surface area covered by a p(2 × 2)O adlayer. The rate of desorption increases autocatalytically with increasing phase boundary metal-oxide. We propose that at close-to-equilibrium conditions (693 K) surface oxide growth and decay occur via this intermediate structure.     

Hydroxylation-induced modifications of the Al2O3/NiAl(0 0 1) surface at low water vapour pressure

STM, STS, LEED and XPS data for crystalline θ-Al₂O₃ and non-crystalline Al₂O₃ ultra-thin films grown on NiAl(0 0 1) at 1025 K and exposed to water vapour at low pressure (1 × 10⁻⁷-1 × 10⁻⁵ mbar) and room temperature are reported. Water dissociation is observed at low pressure. This reactivity is assigned to the presence of a high density of coordinatively unsaturated cationic sites at the surface of the oxide film. The hydroxyl/hydroxide groups cannot be directly identify by their XPS binding energy, which is interpreted as resulting from the high BE positions of the oxide anions (O_1s signal at 532.5-532.8 eV). However the XPS intensities give evidence of an uptake of oxygen accompanied by an increase of the surface coverage by Al³⁺ cations, and a decrease of the concentration in metallic Al at the alloy interface. A value of ∼2 for the oxygen to aluminium ions surface concentration ratio indicates the formation of an oxy-hydroxide (AlO_xOH_y with x + y ∼ 2) hydroxylation product. STM and LEED show the amorphisation and roughening of the oxide film. At P(H₂O) = 1 × 10⁻⁷ mbar, only the surface of the oxide film is modified, with formation of nodules of ∼2 nm lateral size covering homogeneously the surface. STS shows that essentially the valence band is modified with an increase of the density of states at the band edge. With increasing pressure, hydroxylation is amplified, leading to an increased coverage of the alloy by oxy-hydroxide products and to the formation of larger nodules (∼7 nm) of amorphous oxy-hydroxide. Roughening and loss of the nanostructure indicate a propagation of the reaction that modifies the bulk structure of the oxide film. Amorphisation can be reverted to crystallization by annealing under UHV at 1025 K when the surface of the oxide film has been modified, but not when the bulk structure has been modified.     

Selective MOCVD of titanium oxide and zirconium oxide thin films using single molecular precursors on Si(1 0 0) substrates

Titanium oxide (TiO₂) and zirconium oxide (ZrO₂) thin films have been deposited on modified Si(1 0 0) substrates selectively by metal-organic chemical vapor deposition (MOCVD) method using new single molecular precursor of [M(OⁱPr)₂(tbaoac)₂] (M=Ti, Zr; tbaoac=tertiarybutyl-acetoacetate). For changing the characteristic of the Si(1 0 0) surface, micro-contact printing (μCP) method was adapted to make self-assembled monolayers (SAMs) using an octadecyltrichlorosilane (OTS) organic molecule which has -CH₃ terminal group. The single molecular precursors were prepared using metal (Ti, Zr) isopropoxide and tert-butylacetoacetate (tbaoacH) by modifying standard synthetic procedures. Selective depositions of TiO₂ and ZrO₂ were achieved in a home-built horizontal MOCVD reactor in the temperature range of 300-500 °C and deposition pressure of 1×10⁻³-3×10⁻² Torr. N₂ gas (5 sccm) was used as a carrier gas during film depositions. TiO₂ and ZrO₂ thin films were able to deposit on the hydrophilic area selectively. The difference in surface characteristics (hydrophobic/hydrophilic) between the OTS SAMs area and the SiO₂ or Si-OH layer on the Si(1 0 0) substrate led to the site-selectivity of oxide thin film growth.     

Impact of O2 exposure on surface crystallinity of clean and Ba terminated Ge(1 0 0) surfaces

In analogy with the case of Sr on Si [Y. Liang, S. Gan, M. Engelhard, Appl. Phys. Lett. 79 (2001) 3591], we studied surface crystallinity and oxidation behaviour of clean and Ba terminated Ge(1 0 0) surfaces as a function of oxygen pressure and temperature. The structural and chemical changes in the Ge surface layer were monitored by LEED, XPS and real-time RHEED. In contrast to the oxidation retarding effect, observed for 1/2 monolayer of Sr on Si, the presence of a Ba termination layer leads to a pronounced increase in Ge oxidation rate with respect to clean Ge. In fact, while the Ge(1 0 0) surface terminated with 1/2 ML Ba amorphizes for a pO₂ of 10⁻² Torr, LEED indicates that clean Ge forms a thin (4.5 Å), 1 × 1 ordered oxide upon aggressive O₂ exposure (150 Torr, 200 °C, 30 min). We briefly discuss the origins for the difference in behaviour between Ba on Ge and Sr on Si.     

Driving force for the WO3(0 0 1) surface relaxation

The optimized structure of the WO₃(0 0 1) surface with various types of termination ((1 × 1)O, (1 × 1)WO₂, and c(2 × 2)O) has been simulated using density functional theory with the Perdew-Wang 91 gradient corrected exchange-correlation functional. While the energy of bulk WO₃ depends weakly on the distortions and tilting of the WO₆ octahedra, relaxation of the (0 0 1) surface results in a significant decrease of surface energy (from 10.2 × 10⁻² eV/Ų for the cubic ReO₃-like, c(2 × 2)O-terminated surface to 2.2 × 10⁻² eV/Ų for the relaxed surface). This feature illustrates a potential role of surface relaxation in formation of crystalline nano-size clusters of WO₃. The surface relaxation is accompanied by a dramatic redistribution of the density of states near the Fermi level, in particular a transformation of surface electronic states. This redistribution is responsible for the decrease of electronic energy and therefore is suggested to be the driving force for surface relaxation of the WO₃(0 0 1) surface and, presumably, similar surfaces of other transition metal oxides.     

Ruthenium adsorption and diffusion on the GaN(0 0 0 1) surface

We report first principles calculations to analyze the ruthenium adsorption and diffusion on GaN(0 0 0 1) surface in a 2×2geometry. The calculations were performed using the generalized gradient approximation (GGA) with ultrasoft pseudopotential within the density functional theory (DFT). The surface is modeled using the repeated slabs approach. To study the most favorable ruthenium adsorption model we considered T₁, T₄ and H₃ special sites. We find that the most energetically favorable structure corresponds to the Ru- T₄ model or the ruthenium adatom located at the T₄ site, while the ruthenium adsorption on top of a gallium atom (T₁ position) is totally unfavorable. The ruthenium diffusion on surface shows an energy barrier of 0.612 eV. The resultant reconstruction of the ruthenium adsorption on GaN(0 0 0 1)- 2×2 surface presents a lateral relaxation of some hundredth of Å in the most stable site. The comparison of the density of states and band structure of the GaN(0 0 0 1) surface without ruthenium adatom and with ruthenium adatom is analyzed in detail.     

A nanogravimmetric investigation of the charging processes on ruthenium oxide thin films and their effect on methanol oxidation

The charging processes and methanol oxidation that occur during the oxidation-reduction cycles in a ruthenium oxide thin film electrode (deposited by the sol-gel method on Pt covered quartz crystals) were investigated by using cyclic voltammetry, chronoamperometry and electrochemical quartz crystal nanobalance techniques. The ruthenium oxide rutile phase structure was determined by X-ray diffraction analysis. The results obtained during the charging of rutile ruthenium oxide films indicate that in the anodic sweep the transition from Ru(II) to Ru(VI) occurs followed by proton de-intercalation. In the cathodic sweep, electron injection occurs followed by proton intercalation, leading to Ru(II). The proton intercalation/de-intercalation processes can be inferred from the mass/charge relationship which gives a slope close to 1 g mol⁻¹ (multiplied by the Faraday constant) corresponding to the molar mass of hydrogen. From the chronoamperometric measurements, charge and mass saturation of the RuO₂ thin films was observed (440 ng cm⁻²) during the charging processes, which is related to the total number of active sites in these films. Using the electrochemical quartz crystal nanobalance technique to study the methanol oxidation reaction at these films was possible to demonstrate that bulk oxidation occurs without the formation of strongly adsorbed intermediates such as CO_ads, demonstrating that Pt electrodes modified by ruthenium oxide particles can be promising catalysts for the methanol oxidation as already shown in the literature.     

On the preparation and electronic properties of clean W(1 1 0) surfaces

We have studied the influence of oxygen pressure during the cyclic annealing used for the cleaning of W(1 1 0) surfaces. For this purpose the surface morphology and electronic properties are measured by means of scanning tunneling microscopy (STM) and spectroscopy (STS), respectively. It is found that the surfaces with impurity atom densities as low as 2 × 10⁻³ can be obtained by gradually reducing the oxygen pressure between subsequent annealing cycles down to about 2 × 10⁻⁸ mbar in the final cycle. Only on the clean surface a bias-dependent spatial modulation of the local density of states (LDOS) is observed at step edges and around impurity sites by STS. In addition, we find a pronounced peak in the occupied states. In combination with density functional theory calculations these features can be traced back to a dispersive p_z-d_xz-type surface resonance band and the lower band edge of a surface state, respectively.     

The effect of deposition temperature on the surface coverage and morphology of iron-phosphate coatings on low carbon steel

The influence of deposition temperature and concentration of NaNO₂ in the phosphating bath on the surface morphology and coverage of iron-phosphate coatings on low carbon steel was investigated. The phosphate coatings were chemically deposited on steel from phosphate bath at different temperatures (30-70 °C) and with the addition of different amounts of accelerator, NaNO₂ (0.1, 0.5 and 1.0 g dm⁻³). The morphology of phosphate coatings was investigated using scanning electron microscopy (SEM) and atomic force microscopy (AFM). The composition of iron-phosphate coatings was determined using energy dispersive X-ray spectroscopy (EDS) and X-ray diffraction (XRD). Surface coverage was evaluated by the voltammetric anodic dissolution (VAD) technique.It was shown that the increase in temperature of the NaNO₂-free phosphating bath up to 70 °C caused an increase in surface coverage. The addition of NaNO₂ in the phosphating bath significantly increased the surface coverage of phosphate coatings deposited at temperatures lower than 50 °C. The phosphate crystals were of laminated and needle-like structures for deposits obtained at temperatures lower than 50 °C, while at higher temperatures needle-like structure was transformed to laminated structure. The increase in NaNO₂ concentration in the phosphating bath from 0.1 to 1.0 g dm⁻³ did not significantly increase the surface coverage, but decreased the crystals size, consequently favouring the phosphate nucleation and better packing of the crystals.     

A combined ab initio and atomistic simulation study of the surface and interfacial structures and energies of hydrated scheelite: introducing a CaWO4 potential model

Density functional theory (DFT) calculations of the calcium tungstate material scheelite CaWO₄ have shown that water introduced into the bulk material remains undissociated and leads to swelling and layering of the structure, a behaviour which may resemble silicate clays more than three-dimensional poly-anionic materials, but which results in a structure that is even more similar to a rare hydrous calcium carbonate phase--a finding which suggests the existence of semi-crystalline hydrous pre-cursor phases to the dehydrated scheelite material. An interatomic potential model was derived for CaWO₄ which adequately reproduces structural and physical properties of the material and is in good agreement with the DFT calculations in respect of the structure and energy of hydration (DFT: 85 kJ mol⁻¹, atomistic: 105 kJ mol⁻¹). Atomistic simulations of a range of scheelite surfaces confirm the dominance of the experimental {1 0 1} and {0 0 1} cleavage planes in the morphology of the dry crystal and the presence of the experimentally found {1 0 3} and {1 0 1} surfaces in the hydrated morphology. Hydration of the surfaces shows non-Langmuir behaviour, where the interactions between surface calciums and oxygen atoms of the water molecules outweigh hydrogen-bonding to the surface oxygen atoms or intermolecularly within the water layer. The hydration energies indicate physisorption of water, ranging from 22 kJ mol⁻¹ on the {0 0 1} surface to 78 kJ mol⁻¹ on the more reactive {1 0 3} surface.     

Formation mechanism of Si(1 0 0) surface morphology in alkaline fluoride solutions

Formation mechanism of Si(1 0 0) surface morphology in alkaline fluoride solutions was investigated both theoretically and experimentally. By analysis of Raman spectra of silicon wafer surfaces and three kinds of etching solutions (NaOH, NaOH/NH₄F, and NaOH/NH₄F/Na₂CO₃) with and without addition of Na₂SiO₃·9H₂O, no Si-F bond is formed, F⁻ and CO₃²⁻ ions accelerate the condensation of Si-OH groups. Based on experimental results, it is proposed that bare silicon and silicon oxide coexist at the wafer surface during etching process and silicon oxide of different structure, size, and site at the surface manufacture different surface morphology in alkaline fluoride solution.     

Property improvement of pulsed laser deposited boron carbide films by pulse shortening

Growth characteristics and surface morphology of boron carbide films fabricated by ablating a B₄C target in high vacuum with a traditional KrF excimer laser and a high brightness hybrid dye/excimer laser system emitting at the same wavelength while delivering 700 fs pulses are compared. The ultrashort pulse processing is highly effective. Energy densities between 0.25 and 2 J cm⁻² result in apparent growth rates ranging from 0.017 to 0.085 nm/pulse. Ablation with nanosecond pulses of one order of magnitude higher energy densities yields smaller growth rates, the figures increase from 0.002 to 0.016 nm/pulse within the 2-14.3 J cm⁻² fluence window. 2D thickness maps derived from variable angle spectroscopic ellipsometry reveal that, when ablating with sub-ps pulses, the spot size rather than the energy density determines both the deposition rate and the angular distribution of film material. Pulse shortening leads to significant improvement in surface morphology, as well. While droplets with number densities ranging from 1 × 10⁴ to 7 × 10⁴ mm⁻² deteriorate the surface of the films deposited by the KrF excimer laser, sub-ps pulses produce practically droplet-free films. The absence of droplets has also a beneficial effect on the stoichiometry and homogeneity of the films fabricated by ultrashort pulses.     

Bulk and surface properties of spinel Co3O4 by density functional calculations

DFT calculations are employed to bulk and surface properties of spinel oxide Co₃O₄. The bulk magnetic structure is calculated to be antiferromagnetic, with a Co²⁺ moment of 2.631 μ_B in the antiferromagnetic state. There are three predicted electron transitions O(2p) → Co²⁺(t_2g) of 2.2 eV, O(2p) → Co³⁺(e_g) of 2.9 eV and Co³⁺(t_2g) → Co²⁺(t_2g) of 3.3 eV, and the former two transitions are close to the corresponding experimental values 2.8 and 2.4 eV. The naturally occurring Co₃O₄ (1 1 0) and (1 1 1) surfaces were considered for surface calculations. For ideal Co₃O₄ (1 1 0) surfaces, the surface relaxations are not significant, while for ideal Co₃O₄ (1 1 1) surfaces the relaxation of Co²⁺ cations in the tetrahedral sites is drastic, which agrees with the experiment observation. The stability over different oxygen environments for possible ideal and defect surface terminations were explored.     

DFT study on dissociative adsorption of SiH4 and GeH4 on SiGe(1 0 0)-2 × 1 surface

SiH₄ and GeH₄ dissociative adsorptions on a buckled SiGe(1 0 0)-2 × 1 surface have been analyzed using density functional theory (DFT) at the B3LYP level. The Ge alloying in the Si(1 0 0)-2 × 1 surface affects the dimer buckling and its surface reactivity. Systematic Ge influences on the reaction energetics are found in SiH₄ and GeH₄ reactions with four dimers of Si^∗-Si, Ge^∗-Si, Ge^∗-Ge, and Si^∗-Ge (∗ denotes the protruded atom). On a half H-covered surface, the energy barriers for silane and germane adsorption are higher than those on the pristine surface. The energy barrier for silane adsorption is higher than the corresponding barrier for germane adsorption. Rate constants are also calculated using the transition-state theory. We conclude that the SiGe surface reactivity in adsorption reaction depends on the Ge presence in dimer form. If the surface Ge is present in form of Ge^∗-Ge, the surface reactivity decreases as the Ge^∗-Ge content increases. If the surface Ge prefers to be in form of Ge^∗-Si at low Ge contents, the surface reactivity increases first, then decreases at high Ge surface contents when Ge^∗-Ge prevails. The calculated rate constant ratio of GeH₄ adsorption on Si^∗-Si over Ge^∗-Ge at 650 °C is 2.1, which agrees with the experimental ratio of GeH₄ adsorption probability on Si(1 0 0) over Si(1 0 0) covered by one monolayer Ge. The experimental ratio is 1.7 measured through supersonic molecular beam techniques. This consistency between calculation and experimental results supports that one monolayer of Ge on Si(1 0 0) exists in form of Ge^∗-Ge dimer.     

Analyzing in-plane magnetic anisotropy from surface morphology for amorphous films

A method is developed to analyze the in-plane magnetic anisotropy from surface morphology for amorphous films. The lateral sizes along radial direction (R_RD) and tangent direction (R_TD) of rotational substrate, which are extracted from the surface morphology of Co_66.3Zr_33.7 amorphous films, are used to calculate stress anisotropy energy E_σ. It is found that E_σ is consistent with the magnetic anisotropy energy K_μ for the samples deposited on Si (1 0 0) substrate and then a relationship K_μ ∝ 1/R_RD − 1/R_TD can be obtained. This method is sensitive to the initial state of substrate so its application range is discussed.     

Surface reaction characteristics at low temperature synthesis BaTiO3 particles by barium hydroxide aqueous solution and titanium tetraisopropoxide

Well-crystallized cubic phase BaTiO₃ particles were prepared by heating the mixture of barium hydroxide aqueous solution and titania derived from the hydrolysis of titanium isopropoxide (TTIP) at 328 K, 348 K or 368 K for 24 h. The morphology and size of obtained particles depended on the reaction temperature and the Ba(OH)₂/TTIP molar ratio. By the direct hydrolytic reaction of titanium tetraisopropoxide, the high surface area titania (TiO₂) was obtained. The surface adsorption characteristics of the titania particles had been studied with different electric charges OH⁻ ions or H⁺ ions. The formation mechanism and kinetics of BaTiO₃ were examined by measuring the concentration of [Ba²⁺] ions in the solution during the heating process. The experimental results showed that the heterogeneous nucleation of BaTiO₃ occurred on the titania surface, according to the Avrami's equation.