The financial support for this work was provided by the Ministry of Education, Science and Technological Development of Republic of Serbia (Projects Nos. 45020 and 172056).
The sonochemical approach is widely used for the synthesis of a great variety of advanced inorganic materials, including metal oxides and hydroxides, from solutions and suspensions [1–4], in hydrothermal media  and in solid phase [6,7]. The advantages of the ultrasound-assisted sol–gel technique over conventional routes of nanomaterials synthesis include shortening the synthesis duration due to faster hydrolysis, leading to more uniform particle size distribution, higher surface area, better thermal stability, and improved phase purity . Examples of successful ultrasound-assisted sol–gel synthesis of metal oxide nanostructures include TiO2[8–10], ZnO [11–13], MoO3, In2O3, ZrO2, SiO2[17–19], etc. It was shown that in a number of cases, sonochemically prepared materials demonstrate better characteristics than those synthesized by conventional methods. For example, nickel hydroxides obtained by ultrasonic-assisted techniques [20–23] possessed higher electrochemical performance. Similarly, layered double hydroxides obtained by an ultrasound-enhanced technique showed larger adsorption capacity for humic substances . Recently, formation of high specific surface area porous adsorbents with the use of ultrasound was also reported [25,26].
When power ultrasound is introduced in the liquid-based media, absorbed acoustic channel modulator gives rise to a number of physical effects, resulting in turbulent fluid movement in the vicinity of cavitational bubbles [27–29]. Near the phase boundary (e.g. solid–liquid interface), high speed microjets and shockwaves are formed . Thus, acoustic treatment of suspensions consisting of relatively large particles, of which the size is comparable to the size of a collapsing cavitation bubble (d>0.5–1μm), can lead to several specific effects, including de-agglomeration, decrease of mean particle size, increase of the surface area, amorphization etc. [31–33]. Interestingly, cavitation bubble nucleation and collapse near the solid–liquid boundary is strongly dependent on a number of factors, including the wettability of the surface .
Zirconia and zirconia-based materials are of great importance because of the wide variety of their industrial applications (catalysts, oxygen-conducting materials etc.) [35–37]. The most convenient approach to synthesize these materials is based on the precipitation of amorphous hydrous zirconia gels in aqueous media using zirconium-containing precursors (e.g., zirconyl nitrate, zirconium alkoxides) and subsequent thermal or hydrothermal treatment of the resulting ZrO2·xH2O gel [38,39]. The morphology and phase composition of such synthesized zirconia is, to a large extent, governed by the structure of the precursor gel, which in turn depends on the conditions of precipitation (e.g. composition, temperature, acidity of starting solution, etc.) [39–41]. For example, variation of precipitation pH changes the relative rates of the hydrolysis and condensation of zirconium-based clusters. The excess of alkali in the reaction media results in rapid hydrolysis and condensation, forming a branched metal oxy-hydroxide network. In particular, hydrous zirconia precipitated above the point of zero charge possesses a higher specific surface area and surface fractal dimension than when it is synthesized at low pH . Similar behavior was shown for gels synthesized from zirconium isopropylate . High surface fractal dimensions of amorphous hydrous zirconia obtained by the sol–gel route may, in some cases, remain unchanged, even after crystallization .
Recently, the application of ultrasound to the synthesis of zirconia-based materials has attracted certain interest. For example, it was established that ultrasonic cavitation disaggregates the agglomerates of zirconia colloidal particles, reduces the amount of physically and chemically bound water (as well as the amount of adsorbed ions), and leads to a notable increase in the specific surface area of zirconia amorphous samples [16,43]. Ultrasonically treated zirconia was shown to transform faster from the monoclinic to the tetragonal phase . Obviously, these changes in the properties of zirconia are closely related to the effects of ultrasonication on the structure of amorphous hydrous zirconia formed during sonochemical-assisted precipitation, but these important structural aspects still remain virtually unstudied. Moreover, the corresponding experimental reports are contradictory. For instance, it was shown  that sonication increases the rate of linear polymeric clusters formation and notably decreases the gyration radius of ZrO2 particles. Contrariwise, our later experiments [46,47] revealed the increase in the surface fractal dimension and in the size of individual particles in sonochemically prepared amorphous zirconia gels . Up to now, studies on the fractal structure of gels forming under the action of ultrasound were conducted primarily for hydrous silica [48,49]. For example, Vollet et al.  have shown that ultrasound-stimulated wet silica gels possessed a lower fractal dimension than conventional ones. However, upon drying the former has shown a higher pore volume and specific surface area.