PARTICULATE MORPHOLOGY OF NANOSTRUCTURED MATERIALS

The aim of this study was to develop a technique to analyze the crystalline and particulate morphology of highly disperse complex metal and metalloid oxides, which include both crystalline and amorphous phases, using X-ray diffraction (XRD) data to compute crystallite size distributions (CSD) compared to the particles size distribution functions estimated from high-resolution transmission electron microscopy (TEM) images treated with specific software. Two versions of the XRD treatment methods were used: (i) full profile analysis (FPA) of whole XRD patterns with a self-consistent regularization (SCR) procedure using models for spherical and lamellar crystallites that allows us to estimate relative contributions of crystallites of different shapes; and (ii) analysis of main pure XRD lines with consideration of corrections on an instrumental line profile and background using a regularization procedure with models of spherical or lamellar crystallites. The XRD and TEM based approaches were tested to analyze the crystalline and particulate morphology of various disperse materials: complex (binary and ternary) fumed oxides with silica/alumina, silica/titania, and alumina/silica/titania including crystalline alumina and titania and amorphous silica; nanocomposites CeO2–ZrO2/SiO2 (10 : 10 : 80 wt.%) and TiO2–ZrO2/SiO2 (10 : 10 : 80 wt.%) including crystalline and amorphous phases and synthesized using a liquid-phase method and fumed silica A–300 as a substrate; and natural clays of complex composition including several crystalline phases. Obtained results show that the developed approaches to analyze the XRD patterns could be effectively used to compute the CSD in parallel with TEM image treatments, using specific software, for a deeper insight into crystalline and particulate morphology of various disperse materials.


INTRODUCTION
The particulate morphology (PM) plays an important role on applications of disperse materials such as adsorbents, fillers, catalysts, thickeners, carriers, etc. [1][2][3][4][5]. There are such direct methods to analyze the PM as transmission (TEM) and scanning (SEM) electron microscopies and atom force microscopy [6,7]. Accurate treatment of the corresponding images with specific software gives the particle size distribution (PaSD) functions. Additionally, there are various methods giving indirect information on the PM such as small angle X-ray (or neutron) scattering (SAXS) [8][9][10], X-ray diffraction (XRD) [11][12][13], dynamic and static light scattering [14,15], adsorption (for nonporous nanoparticles of fumed oxides) [16,17] and other methods. Some of these methods give information on amorphous and crystalline particles, but others describe only crystalline phases. In the case of complex particles including several crystalline and amorphous phases, to obtain more accurate information, several methods from two mentioned groups (direct vs. indirect ones) should be used. The XRD data could be used for simple estimation of average sizes of crystallites (d cr ) using Scherrer or Debye-Scherrer equations [12,18]. Additionally, the XRD data could be used to estimate the crystallite size distribution (CSD) functions using full profile analysis of selected lines or total XRD patterns [19,20]. To calculate the broadened line (pure) profile related to the crystallite size/faulting effects of materials studied, as well a size distribution function, one could use two integral equations [19,20]: where I ex.obs. () is the experimentally observed X-ray diffraction profile, C is a constant, h i.p. is the instrumental profile, i(s) is the pure crystallite size/faulting profile, D is the crystallite size, g(D) is the CSD function, 2 is the scattering angle, 2 hkl is the scattering angle corresponding to a peak [19] 2 2sin 2sin hkl hkl s s r The variable ε in eq. (1) corresponds to the angular deviation of a point from the true Bragg angle 2 0 ; and ε and the auxiliary variable t have the dimension of 2.
The CSD function g(D) could be computed by solving integral eq. (1) and then eq. (2) (note that eq. (2) corresponds to spherical crystallites) with a regularization procedure, e.g. CONTIN [21]. This approach could be applied to a selected line or to the full profile of total XRD patterns analyzed after background subtraction and normalization. The aim of this study is to analyze the XRD data for various metal or metalloid oxides (MO) such as fumed MO (FMO) (Figs. 1-4, Table), oxides deposited onto fumed silica (Figs. 5 and 6), and natural clays (Figs. [7][8][9], to obtain the CSD functions compared to the PaSD functions computed using TEM images treated with ImageJ (granulometry plugin) [22].

X-RAY POWDER ANALYSIS
X-ray diffraction patterns for some samples were recorded at room temperature using a Russia) with CuK  ( = 0.15418 nm) radiation and a Ni filter in the 2 range from 10 to 70°.
XRD patterns of FMO and clay samples were recorded over 2θ = 4-80° range using a DRON-4-07 (Burevestnik, St. Petersburg) diffractometer with CuK  radiation and a Ni filter. Analysis of the crystalline structures was carried out using the JCPDS Database (International Center for Diffraction Data, PA, 2001) [30]. To estimate the instrumental line profile (h i.p. in eq. (1)), XRD pattern of large crystallites (> 100 nm) of silicon was used.

HIGH-RESOLUTION TRANSMISSION ELECTRON MICROSCOPY (HRTEM)
The particulate morphology of CeO 2 -ZrO 2 /SiO 2 and TiO 2 -ZrO 2 /SiO 2 samples preheated at 550 °C was analyzed using Transmission Electron Microscope (TEM) employing a Tecnai G2 T20 X-TWIN (FEI Co., USA) apparatus operating at voltage of 200 kV with LaB 6 electron source. The presence of metals and their elemental composition were recorded by using energy dispersive X-ray (EDX). The samples were supported on holey carbon copper grids by dropping ethanol suspensions containing uniformly dispersed oxide powders.
HRTEM (JEM-2100F, Japan) images of FMO were recorded for powder samples added to acetone (for chromatography) and sonicated. Then a drop of the suspension was deposited onto a copper grid with a thin carbon film. After acetone evaporation, sample particles remained on the film were studied with HRTEM.

RESULTS AND DISCUSSION
Complex binary (SA, ST) and ternary (AST) fumed oxides (Table) include crystalline alumina and titania, but silica is always amorphous (Fig. 1) [23,24,31]. For ST samples, titania (both anatase and rutile phases) crystallites are typically embedded into silica shells (Fig. 2 b, c). For SA (Fig. 2 a), both large polycrystalline and small particles (crystallites) are observed as well for AST [31]. During pyrogenic synthesis, AlCl 3 used as a precursor should be sublimated, and its reactivity differs from that of SiCl 4 and TiCl 4 that results in enhanced nonuniformity of complex binary and ternary FMO (Fig. 2) [24,31]. In the case of fumed ST20 and TiO 2 (20 wt. %) deposited onto A-300 as well AST1, amorphous silica significantly contributes the XRD patterns ( Fig. 1). For other FMO samples, contribution of amorphous phases is much smaller that allows us to use eqs. (1) and (2) to compute the CSD functions with a regularization procedure for total XRD patterns. In the case of full profile analysis (FPA) of the total XRD patterns, the regularization procedure was modified to selfconsistent regularization (SCR) previously used to treat nitrogen adsorption (models of slitshaped and cylindrical pores and voids between spherical nanoparticles) and SAXS (models of spherical, cylindrical and lamellar particles) data [16,17,31,32]. An additional advantage of the SCR procedure is the possibility to estimate weight contributions of pores or particles (or crystallites) of different shapes.
The FPA applied with the SCR procedure (using spherical and lamellar models of crystallites) without corrections on the instrumental line profile due to equipment effects provides appropriate fitting of total XRD pattern ( Fig. 3 a). However, in this approach, the CSD could give smaller sizes of crystallites than those observed in HRTEM images since the broader the line, the smaller is the corresponding crystallite. Therefore, the CSD functions (Fig. 4) were also computed using the main lines of crystalline titania: anatase (2  25.3°) and rutile (27.4°), and crystalline alumina (67.1°) with consideration of the instrumental line profile due to equipment effects. An increase in titania amounts in ST and AST results in an increase in sizes of titania crystallites (Fig. 4) (the corresponding XRD lines become narrower) because growing of titania particles (cores in core-shell particles) is faster in the flame than silica particles (shells). In the case of fumed ST20 and titania (20 wt. %) deposited onto A-300, the CSD functions are similar due to the same amounts of titania and the same second (silica) phase. Minimal sizes of crystallites are observed for alumina alone or SA and AST samples (Fig. 4) that is in agreement with TEM images (Fig. 2 d, f).

Table.
Composition, specific surface area (S BET ) and pore volume (V p ) of fumed oxides     Direct comparison of the CSD (XRD) and PaSD (HRTEM) (Figs. 5 and 6) shows that the latter can include both crystalline and amorphous phases. This is well seen for ZrTiO x /SiO 2 sample (Fig. 6). As a whole, the sizes of crystallites estimated using corrected (pure) XRD lines correspond to the crystallite sizes (preheating at 1100°C) observed in HRTEM images (preheating at 550 °C, crystallites are observed in TEM images, but XRD does not sense them in contrast to samples preheated at 1100 o C [26][27][28]) with maximal magnification for ZrTiO x /SiO 2 and ZrCeO x /SiO 2 (Figs. 5 and 6).

Vp (cm 3 /g)
More complex XRD patterns are observed for natural oxides, e.g. clays (Fig. 7) due to presence of several oxide phases of various shapes including nearly spherical (quartz) and larger lamellar (kaolinite and other clays) structures (Fig. 8) [29]. Therefore, the SCR/FPA procedure was used with two models for spherical and lamellar crystallites. Note that the SCR procedure gives a strongly major contribution of lamellar crystallites for clays studied. In the case of corrected XRD data on the instrumental line profile, the analysis was carried out for the main lines in the XRD patterns. The SCR/FPA without any experimental correction gives smaller crystallite sizes similar to those observed for other materials studied (Fig. 9). Comparison of the CSD (Fig. 9) and PaSD (Fig. 8) shows that relatively large lamellar clay particles have much smaller thickness because the CSD function for the lamellar model corresponds to the lamellar thickness.

CONCLUSION
In this work, a method based on X-ray diffraction data and TEM images was developed to analyze the particulate and crystalline morphology of various metal and metalloid oxides comparing the CSD (XRD) and PaSD (TEM) functions. Two versions of the XRD treatment method were used: (i) full profile analysis of whole XRD patterns with a selfconsistent regularization procedure using models of spherical and lamellar crystallites; and (ii) analysis of main XRD lines with consideration of corrections on the instrumental line profile caused by the equipment effects. These approaches were used for the characterization of the particulate (TEM) and crystalline (XRD) morphology of various materials: complex fumed oxides with silica/alumina, silica/titania and alumina/silica/titania; nanocomposites