Correlation between crystallite sizes and microstrains in TiO2 nanopowders

Journal of Crystal Growth 198/199 (1999) 516—520

Correlation between crystallite sizes and microstrains in TiO  nanopowders L.E. Depero*, L. Sangaletti, B. Allieri, E. Bontempi, A. Marino, M. Zocchi Istituto Nazionale per la Fisica della Materia and Dipartimento di Chimica e Fisica per l+Ingegneria e per i Materiali, Universita% di Brescia, Via Valotti 9, 25133 Brescia, Italy

Abstract Nanopowders of TiO doped with by V, Nb, Ta were obtained by laser-induced pyrolysis. The profiles of the  diffraction peaks were Fourier analysed with a single-peak method and the microstructural parameters 1M2 (average crystallite size) and 1e2 (mean-square root microstrain) were estimated. A linear correlation between 1e21M2 and 1/1M2 was observed in both anatase and rutile phases. For a given crystallite size, the microstrains as well as the dispersion of data were larger in anatase then in rutile. Indeed, one of the factors inducing the anatase-to-rutile transformation may be the presence of larger microstrains in anatase. In rutile, the high correlation found between 1e21M2 and 1/1M2 suggests that in this phase the microstrains present in the structure are due only to the geometrical constraints of the surface. Indeed, for infinite crystallite size no microstrains are expected. In anatase, microstrains depend also on the specific cation present in the crystallite.  1999 Elsevier Science B.V. All rights reserved. PACS: 64.70; 61.46; 61.10 Keywords: TiO ; Anatase; Rutile; Microstrains; Nanopowders 

1. Introduction The recent interest in the properties of ceramics having grain sizes less than 100 nm [1—3] has created a need for developing processing routes for the manufacturing of these materials [4] and for the investigation of the physical properties [5—7]. A laser-induced process has been studied and

* Corresponding author. E-mail: [email protected].

developed for the synthesis either of pure TiO  powders, to use as a catalyst support [8], or of mixed oxides to be used directly in the selective catalytic reduction of nitrogen oxides with ammonia [9]. Moreover, the nanocrystalline materials based on TiO can be used as precursor powders in  thick film preparation for sensor applications [10] and other semiconductor devices [11]. Great interest is devoted to the kinetics of grain growth [12—16] and to the potential identification of the inhibitors of grain growth in nanocrystallite TiO 

0022-0248/99/$ — see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 1 0 8 6 - 0

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nanophases. The phase of the TiO powders grown  by laser induced process is anatase and intense effort has been recently devoted to study the effects of different cations on the anatase—rutile transformation. In particular, powders of pure TiO and  powders of TiO mixed with V, Nb, Ta [12—16], Al,  and Ga [17] oxides have been prepared and analysed. The microstructural parameters 1M2 (average crystallite size) and 1e2 (mean-square root microstrain) have been evaluated by Fourier analysis of the diffraction profile. Vanadium-titanium oxides were also analysed by small angle X-ray and neutron scattering [18, 19]. In these studies, the presence of different metals in the TiO powders  has been correlated to the temperature of the anatase—rutile transformation and to the microstructural parameters of the mixed oxide powders before the thermal treatments. Unlike V which inhibits the growth only of anatase [12,13], the other metals (Nb,Ta, Al, and Ga) inhibit the growth of both anatase and rutile, which show a similar particle growth kinetics [14—17]. This behaviour makes the use of these TiO nanopowders of par ticular technological relevance, in view of the fact that the reduced size of the nanopowders is maintained both in the low (anatase crystallites) and in

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the high (rutile crystallites) temperature range. On this basis, an interesting correlation between the microstrains and the crystallite average size has been evidenced. In this paper, we compare and discuss the microstructural evolution of all the powders previously investigated [12—17].

2. Experimental procedure The detailed description of the operational principle and the experimental apparatus used for the laser induced synthesis were reported elsewhere [9]. The last step of the powder production was a one-day long annealing treatment in air at 400°C. All the diffraction experiments were performed on a Philips MPD1830 automated powder diffractometer. The thermal treatments were carried out in air. The duration of the treatments is indicated in Table 1. The profiles of the diffraction peaks were Fourier analysed by means of a program developed by Luterotti and Scardi [20] and based on algorithms derived by Nandi et al. [21]. In particular, the reflections 1 0 1 and 1 1 0 were considered for the anatase and the rutile phases respectively. The

Table 1 Temperatures of the annealing treatments, temperature range (*¹ ) corresponding to the coexistence of the anatase and rutile phases, U0 and annealing time for all the samples considered in the present study. Each annealing treatment was performed in air. The complete transformation of anatase into rutile was achieved for temperatures above the upper limit of *¹ U0 Sample

Ref.

Annealing temperature (°C)

Annealing time (h)

*¹ (°C) U0

Pure TiO 

[12—14]

18

700—800

TiO —V 18%  TiO —V 23%  TiO —V 30%  TiO —Nb 3% 

[13] [13] [13] [15]

4 4 4 18

400—530 400—530 400—530 550—800

TiO —Nb 20% 

[15]

18

550—850

TiO —Ta 2% 

[16]

18

400—800

TiO —Ta 10% 

[16]

18

400—800

TiO —Al 9% 

[17]

18

400—800

TiO —Ga 10% 

[17]

400,450,500,550,600,650,700, 750,800,850,900,950,1000 400,420,450,500,510,520,530 400,420,450,500,510,520,530 400,420,450,500,510,520,530 400,450,500,550,600,650,700, 750,800,850,900,950,1000 400,450,500,550,600,650,700, 750,800,850,900,950,1000 400,450,500,550,600,650,700, 750,800,850,900,950,1000 400,450,500,550,600,650,700, 750,800,850,900,950,1000 400,450,500,550,600,650,700, 750,800,1000,1400 400,450,500,550,600,650, 700,750,800, 1000,1400

18

400—800

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instrumental function to be deconvoluted from the observed profile was determined by measuring the diffraction pattern of a standard KCl. All the samples and the treatments considered in this paper are reported in Table 1.

3. Results and discussion Pure TiO powders and TiO powders mixed   with other metal oxides were obtained by laserinduced synthesis. These compounds were thermally treated for studying the effect of the metal on the anatase—rutile transformation and the microstructural evolution of both anatase and rutile. Asgrown samples were mostly pure anatase and after their thermal treatment they transformed into rutile. A temperature range (*¹ ) was identified U0 in which the anatase and rutile phases were observed to coexist. The upper and lower limits of *¹ are reported in Table 1. The complete transU0 formation of anatase into rutile was achieved for temperatures above the upper limit of *¹ . The U0 study of the microstructural evolution of rutile was not possible in pure TiO and in samples contain ing V, since very large crystallite immediately formed when the anatase—rutile transformation appeared, as indicated by the width of the XRD profiles which was comparable to that of the standard. On the contrary, in powders containing Al, Nb, Ta, or Ga, the kinetics of growth for the rutile crystallites was slow, as indicated by the large width of the rutile reflections in the X-ray diffraction pattern. Consequently, microstructural parameters of these materials could be determined. The linear correlation between 1e21M2 and 1/1M2 for the rutile phase is shown in Fig. 1. Since this correlation is independent of the cations, it is likely due only to the effect of the surface constraint on the crystal structure. Indeed, the surface tension can induce surface stresses that, in small crystals or thin whiskers, may result in an increase of the lattice spacing [22]. However, for the rutile crystallites no significant change in the reflection positions has been detected indicating that the surface stress may be balanced in the bulk by the microstrains identified in our analyses. Interestingly, a straight line passing through the origin is able to perfectly

Fig. 1. Correlation between 1e21M2 and 1/1M2 for the rutile phase.

fit the experimental data (Fig. 1). This supports the hypothesis that microstrains depend only on the surface, since a crystallite free of microstrain is expected in the case of an infinite size. Before investigating the significance of the correlation between microstrains and crystallite size, a few definitions should be recalled. If the periodicity of the structure corresponding to the analysed reflection is a, the undistorted size of the crystallite is M"na, where n is the number of unit cells of the crystallite in the a direction. Because of the distortion, M is changed by *M"Z a (with 1Z 2"0) L L [23]. The ratio *M/M"e is the component of the microstrain along the a direction in the structure, averaged over M, therefore e"Z /n. The single line L Fourier analysis assumes a gaussian distribution for Z : L p(Z )"q/p exp(!qZ). L L In terms of such distribution 1Z2"1/q. Since L 1M2"na, then 1e21M2"1Z2a. L In view of the linear correlation found in Fig. 1, 1Z2 is proportional to 1/1M2, i.e., the full L

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size, a straight line, parallel to that found for rutile, can be identified (dashed line in Fig. 2). As a consequence, a finite and constant value of the microstrain can be predicted for anatase crystallites at infinite size. This observation may at least partially explain the high stability of the large single crystal of rutile compared to that of anatase.

4. Conclusion

Fig. 2. Correlation between 1e21M2 and 1/1M2 for the anatase phase. The linear fitting of the rutile data is also reported (full line). By considering only the lowest strain values observed at a given crystalline size, a straight line, parallel to that found for rutile, can be identified (dashed line).

width at the half maximum of the Gaussian distribution of Z (1/q) is proportional to the inverse of L the average number of cells (1/n). The correlation between the 1e21M2 and 1/1M2 of pure and doped TiO powders for  anatase is shown in Fig. 2. For a given crystallite size, the microstrains present in anatase are always larger than those found in rutile, as indicated by the linear fitting of the rutile data shown in the same figure. Empty squares, circles and rhombuses represent the data collected for Ti—V oxides at different V content. Generally, the microstrains present in Ti—V compounds are larger than those found in powders containing Nb, Ta, Al, or Ga. This suggests that anatase microstrains depend on the crystallite size and on the specific cation in the structure. Indeed, a recent study shows that the surface structure of the naturally grown TiO  anatase is very sensitive to physical influences [24]. In anatase, a quite large dispersion of data can be observed (Fig. 2). However, considering only the lower values of strain observed at a given crystallite

These results show a correlation between crystallite sizes and microstrains in both anatase and rutile TiO nanopowders. Similar behaviour has  been observed also in commercial catalysts based on TiO [14] and similar kinetics of growth have  been reported in the case of anatase powders obtained by sol—gel procedure based on TEM experiments [25]. However, since it was reported that nanocrystals of TiO synthesised by aerogel were  practically free of microstrains [26], we cannot exclude that the discussed relationship between microstrains and size may be limited to the laserinduced synthesis. The strong surface effects indicated by our results are in agreement with a recent X-ray absorption fine structure (XAFS) study of TiO nanoparticles,  where a shorter Ti—O distance for surface atoms as compared with that found in the bulk are reported [27]. This effect was attributed to Ti—OH bonding on the surface. The XAFS spectra revealed also the existence of an increasing disorder of the lattice for decreasing sizes of the nanoparticles. This disorder was attributed to a decrease in the coordination number for the third shell of O atoms, while the coordination of the Ti remained octahedral. In other investigations, measurements of the excess of enthalpy in ultrafine grained titanium dioxide have been explained on the basis of a size-dependent nonstoichiometry of TiO [28].  These observations may contribute to explain the different behaviour of anatase and rutile found in the present study. Indeed, the importance of oxygen vacancies in the anatase stabilisation has been already observed and discussed [14,29,30]. The presence of intrinsic defects in anatase may justify the microstrains expected in this phase even at infinite particle sizes.

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The effect of the surface on phase stability has been considered also to explain the formation of cubic ZrO nanopowders [31] that, at room tem perature, should have a monoclinic structure. Indeed, in this compound the metastable cubic phase can be stabilised by small crystallite sizes or by the presence of doping metals. In this perspective, also the facility to obtain anatase nanopowders with respect to single crystals could be explained by surface effects. References [1] [2] [3] [4]

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