structure of nanocrystalline materials by the atomic … · materials requires detailed knowledge...

STRUCTURE OF NANOCRYSTALLINE MATERIALS BY THE ATOMIC PAIR DISTRIBUTION FUNCTION TECHNIQUE

V. Petkov

Department of Physic, Central Michigan University, Mt. Pleasant, MI 48859

ABSTRACT

The approach of the atomic pair distribution function (PDF) technique to study the structure of nanocrystalline materials is considered and successfully applied to V2O5.nH2O xerogel and Cs intercalated inside the pores of the zeolite ITQ-4. We find that V2O5.nH2O is an assembly of almost perfect bi-layers of VO5 units encapsulating the water molecules. Inside the nanopores of ITQ-4 the cesium ions are found to assemble in short-range ordered zig-zag chains.

INTRODUCTION

Nanocrystalline materials are being extensively studied because they often exhibit interesting and useful properties not occurring in perfect crystals. Examples include nanomagnets, nanocatalysts, nanocomposites with improved optical properties and nanodevices. Understanding and predicting the novel electronic and magnetic properties of all these materials requires detailed knowledge of the atomic ordering. Usually the 3-D structure of materials is obtained from the Bragg peaks in their diffraction patterns. However, materials constructed at the nanoscale often do not possess the translational symmetry and long-range order of conventional crystals. Instead they assume structures of reduced dimensionality and/or accommodate a large number of defects and local disorder. The diffraction patterns of such materials show a pronounced diffuse component and a few Bragg peaks, if any. This poses a real challenge to the traditional techniques for structure determination. The challenge can be met by employing the so-called atomic pair distribution function (PDF) technique. The atomic PDF gives the number of atoms in a spherical shell of unit thickness at a distance r from a reference atom. It peaks at characteristic distances separating pairs of atoms and thus describes the structure of materials. The PDF, G(r)=4πr[ρ(r)-ρo], is the sine Fourier transform of the so-called total scattering structure function, S(Q),

G(r)=(2/π) (1) ∫=

−max

,)sin(]1)([Q

oQ

dQQrQSQ

where ρ(r) and ρo are the local and average atomic number densities, respectively, Q is the magnitude of the wave vector. The structure function S(Q) is related to the coherent part, Icoh.(Q), of the powder diffraction pattern as follows:

S(Q) = 1 + ,)(/)()(22

QfcQfcQI iiiicoh ∑∑

− (2)

where ci and fi are the atomic concentration and x-ray scattering factor, respectively, for the atomic species of type i [1]. As can be seen the atomic PDF is simply another representation of the powder diffraction data; however, exploring the experimental data in real space is

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advantageous and helpful for several reasons, especially in the case of materials with limited structural coherence. First, as eqs. 1 and 2 imply the total powder diffraction pattern, including Bragg peaks as well as diffuse scattering, contributes to the PDF. In this way both the average, long-range atomic structure, manifested in the sharp Bragg peaks, and the local, non-periodic structural imperfections, manifested in the diffuse components of the diffraction pattern, are reflected in the PDF. Note that conventional crystallographic studies take only the Bragg peaks into account. Second, the PDF is obtained with no assumption of periodicity. Thus, materials exhibiting any degree of structural coherence, ranging from perfect crystals to glasses and liquids, can be studied with the same approach. Indeed the PDF technique has been the approach of choice for characterizing liquids and glasses for a long time [1]. However, its application to study intrinsically disordered crystals [2] and nanoparticles [3] has been relatively recent. Third, the PDF is barely influenced by diffraction optics and experimental factors since these are accounted for in the step of normalizing the raw diffraction data and converting it to S(Q) and PDF data [1]. This renders the PDF a structure-dependent quantity giving directly the relative positions of atoms in materials enabling convenient testing and refinement of structural models. Here we demonstrate how the PDF technique works by employing it to determine the structure of two nanocrystalline materials: V2O5.nH2O xerogel and Cs intercalated in the nanopores of the zeolite ITQ-4, Si32O64. The versatile redox, intercalation and electrical properties of V2O5.nH2O xerogel have fascinated researchers for many decades, and inspired an intensive search for potential applications such as chemical sensors, electrochemical and fast switching devices and reversible high energy density batteries. The xerogel has been used as a host material for a large variety of molecular species and even electronically conducting polymers [4]. Despite decades of experimentation with V2O5.nH2O its atomic structure has remained an outstanding issue because the material does not form perfect crystals and exists only as ribbon-like nanoparticles. As such the xerogel exhibits a diffraction pattern poor in Bragg peaks making it impossible to determine the atomic ordering by traditional crystallographic techniques. The structure of the xerogel is an important scientific issue since good knowledge of it is a key prerequisite to the understanding and exploitation of material's properties. Cs-intercalated Si32O64 belongs to the class of novel, and poorly understood, low-dimensional electron systems known as “electrides” [5]. In these materials a low-density gas of correlated electrons is confined in the cavities of an inert nanoporous host coexisting with nanoscale arrays of alkali metal ions that provide charge balance. The confined electron gases exhibit Mott insulating behavior and Heisenberg antiferromagnetism. The first known electrides relied on organic molecules as cation-encapsulating agents, which rendered them unstable at room temperature. Recently, a likely candidate for an inorganic electride that is stable at room temperature has been synthesized by intercalating cesium in the zeolite ITQ-4, Si32O64. Optical and NMR spectra [6] suggest that Cs ionizes to Cs+ cations and trapped electrons inside the nanopores of ITQ-4, but no unequivocal evidence has been advanced so far. Here we use the PDF technique to demonstrate the presence of Cs+ ions and to determine their arrangements inside the nanopores.


0 2 4 6 8 10 12 14 16 18 20 22

0

10

20

30

40

50

60

Q(Å-1)

(b)

In

tens

ity (a

.u.)

Wavevector Q(Å-1)

10

20

30

40

50

60 (a)

Q(Å-1)10 11 12 13

1.5

10 11 12 131.0

1.5

2.0

Figure 1 Powder diffraction patterns of V2O5.nH2O xerogel (a) and crystalline V2O5 (b). A portion of the data is given on an expanded scale in the insets.

0 2 4 6 8 10 12 14 16 18 20 22

-1

0

1

2

(b)

R

educ

ed s

truct

ure

func

tion

Q[S

(Q)-

1]

Wavevector Q(Å-1)

0

1

(a)

Figure 2. Experimental structure functions for V2O5.nH2O xerogel (a) and crystalline V2O5 (b) derived from the XRD patterns of Fig. 1.

EXPERIMENTAL DETAILS Crystalline V2O5 was obtained from Aldrich. The V2O5

.nH2O xerogel was synthesized by melting of crystalline V2O5 at ~800 oC and pouring the melt into deionized water [7]. The resulting gel was allowed to dry at room temperature and ground into fine powder. The powder was sandwiched between Capton foils for the diffraction experiments. Electrides CsxSi32O64 (x=3.6, 4.6) were prepared by mixing dehydrated zeolite ITQ-4 and a weighted amount of cesium metal in sealed borosilicate flasks and heating to 60o C. The amount of absorbed Cs was determined by collection of hydrogen evolved upon reaction with water, and by titration of the CsOH formed [5,8]. As prepared electrides and pristine ITQ-4 were sealed in capillaries and subjected to diffraction experiments. The experiments were carried out at the beam line X7A of the NSLS, Brookhaven National Laboratory using X-rays of energy 30 keV (λ=0.4257 Å). The raw diffraction data were corrected for the decay of the incoming synchrotron radiation beam, for background and Compton scattering, for sample absorption, normalized, i.e. converted into electron units, and then reduced to the corresponding structure functions S(Q). All data processing was done using the program RAD [9]. RESULTS AND DISCUSSION Experimental X-ray powder diffraction (XRD) patterns of crystalline V2O5 and V2O5

.nH2O xerogel are shown in Fig. 1 and the corresponding reduced structure functions, Q[S(Q)-1], in Fig. 2. A comparison between the data in Figs. 1 and 2 exemplifies the different way the same diffraction features show up in the powder XRD patterns and in the structure functions


0 2 4 6 8 10 12 14 16 18 20

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

r (Å)

(b)

Red

uced

PD

F G

(r)

r (Å)

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

r (Å)

(a)

0 10 20 30 40 50-0.5

0.0

0.5

0 10 20 30 40 50

0.0

0.5

Figure 3. Experimental (circles) and calculated (line) PDFs for V2O5.nH2O xerogel (a) and crystalline V2O5 (b). The residual difference is given in the lower part.

Figure 4. Fragment of the 3-D structure of V2O5.nH2O xerogel featuring double layers of VO5 pyramids encapsulating water molecules (circles).

extracted from them. As can be seen in Fig. 1 the XRD patterns are dominated by strong, Bragg peaks at low wave vectors. This renders XRD patterns an experimental quantity that is mainly sensitive to long-range atomic ordering in materials. In total scattering structure functions extracted from the XRD patterns according Eq. (2) all diffraction features, including those at higher values of Q, appear equally strong. This enhances the sensitivity to local atomic ordering and makes the Fourier couple Q[S(Q)-1]/PDF an experimental quantity well suited to study materials with limited structural coherence. That V2O5.nH2O xerogel is such a material is clearly seen in the inset in Fig. 3(a) showing the corresponding PDF decaying to zero already at 50 Å. In contrast, the PDF of a crystal, such as V2O5, persists to much higher real space distances (see the inset in Fig. 3b). The well-known 16-atom unit cell of V2O5 [10] was fit to the experimental PDF observing the symmetry constraints of the Pmmn space group (see Fig. 3b). The fit was done with the program PDFFIT [11]. It yielded the following cell constants for V2O5: a = 11.498(3) Å, b = 3.545(3) Å, c= 4.345(3) Å. They are in good agreement with those obtained by traditional diffraction experiments: a = 11.519 Å, b = 3.564 Å, c= 4.373 Å [10]. The refined atomic positions [7] are also in good agreement with previous results [10]. This agreement well documents the fact that the atomic PDF provides a reliable basis for structure determination. Several structural models were attempted for V2O5.nH2O [7]. Best fit to the PDF date was achieved with a model based on a monoclinic unit cell (Space group C2/m) with parameters a=11.722(3) Å, b= 3.570(3) Å, c=11.520(3) Å, and β=88.65o (see Fig. 3b). Fragment of the 3-D structure is shown in Fig. 4. The refined atomic coordinates are listed in ref. [7]. The PDF based structure determination successfully yields the structure of nanocrystalline V2O5.nH2O in terms of a relatively simple model with only few meaningful parameters such as unit cell and symmetry. This unambiguously shows that the material indeed possesses a significant degree of 3-D atomic ordering, something that is difficult to appreciate by analyzing the XRD pattern (Fig. 1a) alone.


0

20

40

60

80

100S

truct

ure

func

tions

Q[S

(Q)-

1](a)

Q(Å-1)

Wave vector Q(Å-1)

Cs4.6Si32O64

Cs3.6Si32O64

Inte

nsity

, a.u

.

Si32O64

1 2 3 4 5 60

5

10

15

Cs4.6Si32O64

Si32O64

0 2 4 6 8 10 12 14 16 18 20-2

0

2

4

6

8

10

Cs4.6Si32O64

Cs3.6Si32O64

Si32O64(b)

Figure 5. Powder diffraction patterns (a) and the corresponding structure functions (b) of pristine Si32O64 and electrides CsxSi32O64. A portion of the diffraction patterns is given on an expanded scale in the inset.

0 2 4 6 8 10 12 14 16 18 20-1

0

1

2

3

4

5

Cs4.6Si32O64

Cs3.6Si32O64

Si32O64

r (Å)

Red

uced

PD

F G

(r)

Figure 6. Experimental (circles) and model (line) PDFs for CsxSi32O64 (x=0,3.6, 4.6).

Sharp Bragg peaks are present in the diffraction pattern of pristine Si32O64

(Fig. 5a). The corresponding G(r) (Fig. 6) also features sharp peaks reflecting the presence of a long-range ordered network of SiO4 units in this crystalline material. A model PDF calculated on the basis of the well-known 96-atom unit cell (Space group I2/m) of Si32O64 [12] is also shown in Fig. 6. As expected the model and experimental data agree quite well. Bragg peaks in the diffraction patterns of the samples loaded with Cs are significantly attenuated (see the inset in Fig. 5a) and already at ~ 2 Å-1 merge into a slowly oscillating diffuse component. This reflects the tendency of the zeolite host to become structurally disordered upon absorbing alkali metals. The significant diffuse scattering present in the CsxSi32O64 diffraction patterns contains important information about the structure of the intercalants that is lost in a usual crystallographic analysis relying on the Bragg scattering only. In the total structure functions extracted from the diffraction patterns (see Fig. 5b) all components of the diffraction data, including the weak but equally important features at higher wave vectors Q, are taken into account and the corresponding PDFs, shown in Fig. 6, appear rich in distinct, structure-related features. Evidently, although the silicate framework in CsxSi32O64 electrides is distorted, its topology is preserved, and locally they remain well-ordered materials. In particular, the building SiO4 units, seen as a sharp peak at 1.61 Å in all three PDFs, remain intact. To identify the atomic ordering in the assembly of intercalated Cs atoms/ions we considered several structural models and tested them against the experimental PDFs. The models were constructed by placing cesium atoms and/or ions inside the nanopores in Si32O64. Best agreement with the experimental PDF data (see Fig. 6) was achieved with Cs+ ions occupying positions 4h (1/2, 0.870(5), 0) and 4g (0,0.370(5),0) of the Space group I2/m. According to the model, Cs+ ions sit close to the walls of the nanopores in ITQ-4 forming an assembly of short-range ordered zig-zag chains (see Fig. 4 in ref. [8]).


CONCLUSIONS The PDF technique yields the structure of materials in terms of quantitative parameters such as unit cell and atomic coordinates even when the atomic ordering is limited to the nanometer length-scale and the diffraction data are poor in Bragg peaks. The approach requires that the diffraction data is carefully collected over a wide range of wave vectors and converted into the corresponding atomic PDF. Then, like all powder diffraction techniques, the 3-D structure is inferred through modeling. The PDF technique is an essential complement to the traditional crystallographic approaches for structure determination that are mostly sensitive to the long-range atomic ordering in materials. ACKNOWLEDGEMENTS Most of the results reported here were obtained while the author was with Michigan State University. The work was partially supported by DOE Grant DE-FG02-97ER45651. NSLS is supported by DOE under Contract No. DE-AC02-98CH10886. The author thanks S.J.L. Billinge, M.G. Kanatzidis, J. Dye, P.N. Trikalitis and T. Vogt for the fruitful cooperation. REFERENCES [1] H.P. Klug and L.E. Alexander, X-ray diffraction procedures for polycrystalline and amorphous materials, (Wiley, New York, 1974); B.E. Warren, X-ray diffraction, (Dover, New York, 1990). [2] T. Egami, Mater. Trans. 31 (1990) 163; S.J.L. Billinge, R. G. DiFrancesco, G. H. Kwei, J. J. Neumeier and J.D. Thompson, Phys. Rev. Lett. 77 (1996) 715; V. Petkov and S.J.L. Billinge, Physica B 305 (2001) 83. [3] V. Petkov, S.J.L. Billinge, J. Heising and M.G.Kanatzidis, J. Am Chem. Soc. 122 (2000) 11571; V. Petkov, S.J.L. Billinge, P. Larson, S.D. Mahanti, T. Vogt, K. K. Rangan, and M.G. Kanatzidis, Phys. Rev. B 65 (2002) 92105. [4] J. Livage, O. Pelletier, P. Davidson J. Sol-Gel Sci. Techn. 19 (2000) 275; A. Raju, C.N.R. Rao, J. Chem. Soc. Chem. Comm. 18 (1991) 1260; C. Imawan, H. Steffes, F. Solzbacher, F. Obermeier, Sensors and Actuators B 77 (2001) 346. A 76 (1983) 661. (f) E. Shoji, D.A. Butty, Electrochim Acta 45 (2000) 3757. [5] J.L. Dye, Science 247 (1990) 663; J.L. Dye, Nature 365 (1993) 10; J.L. Dye, Inorg. Chem. 36, (1997) 3816. [6] A.S. Ichimura, J.L. Dye, M.A. Camblor and L.A. Villaescusa, J. Am. Chem. Soc. 124 1170 (2002). [7] V. Petkov, P.N. Trikalis E.S. Bozin, S.J.L. Billinge, T. Vogt and M.G. Kanatzidis, J. Am. Chem. Soc. 124 (2002) 10157. [8] V. Petkov, S.J.L. Billinge, T. Vogt, A.S. Ichimura and J.L. Dye, Phys. Rev. Lett. 89 (2002) 075502. [9] V. Petkov, J. Appl. Cryst. 22 (1989) 387. [10] R. Wyckoff in Crystal Structures (Wiley, New York) 1964. [11] Th. Proffen and S.J.L. Billinge, J. Appl. Cryst. 32 (1999) 572. [12] P.A. Barrett, M.A. Camblor, A. Corma, R.H. Jones and L.A. Villaescusa, Chem. Mater. 9 (1997) 1713.


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