X-ray Diffraction Study on Restacked Flocculates from Binary Colloidal

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X-ray Diffraction Study on Restacked Flocculates from Binary Colloidal Nanosheet Systems Ti0.91O2MnO2, Ca2Nb3O10Ti0.91O2, and Ca2Nb3O10MnO2 Mitsuko Onoda, Zhaoping Liu,† Yasuo Ebina, Kazunori Takada, and Takayoshi Sasaki* International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1, Namiki, Tsukuba, Ibaraki, 305-0044, Japan ABSTRACT: Two-component colloidal nanosheets were prepared in Ti0.91O2MnO2, Ca2Nb3O10Ti0.91O2, and Ca2Nb3O10MnO2 systems with various compositions, and were flocculated by adding K ions. X-ray powder diffraction patterns of the products showed remarkably broad reflections, and powder pattern simulation was conducted based on the matrix method for diffuse scattering from stacking disorder. An approach similar to that used for analyzing layered composite crystals with onedirectional disorder was adopted for the obtained mixed-layer compounds. The structural characteristics of the restacked nanosheets in the three binary nanosheet systems were found to be dependent on the combined pairs. In the Ti0.91O2MnO2 system, the one-dimensional solid-solution state appeared in the fairly wide composition ranges of x e 0.3 and x g 0.7 for xTi0.91O2(1 x)MnO2, and the one-dimensional two-phase stacking state appeared in the intermediate range of 0.3 < x < 0.7. In the Ca2Nb3O10Ti0.91O2 system, the one-dimensional solid-solution state appeared in the composition ranges x e 0.2 and x g 0.7 for xCa2Nb3O10(1 x)Ti0.91O2, and the one-dimensional two-phase coexistence state appeared in the intermediate range. In the Ca2Nb3O10MnO2 system, flocculation led to phase separation into individually restacked nanosheets, restacked KCa2Nb3O10 and restacked KMnO2, throughout the composition range from 0.9Nb0.1Mn to 0.1Nb0.9Mn. Similarities and differences in flocculation behavior in the three binary systems, Ti0.91O2MnO2, Ca2Nb3O10Ti0.91O2, and Ca2Nb3O10MnO2, were examined.

1. INTRODUCTION Various layered compounds can be exfoliated into their unilamellar crystallites, namely, nanosheets,118 and new types of layered materials such as restacked systems of LiMnO2, KMnO2, KTi0.91O2, and KCa2Nb3O10 have been synthesized from colloidal nanosheets via flocculation with cations.1922 These restacked materials can exhibit attractive properties, such as for photocatalytic water splitting and electrochemical redox reaction with good cycleability, which are dependent on the nanosheets and the organized nanostructures. Thus, it is of considerable importance to obtain structural information on these materials. X-ray powder diffraction patterns of the flocculated products mostly show remarkable broadening of reflections, suggesting that structures of this type are disordered, involving lateral shifts of restacked nanosheets. Such X-ray diffraction (XRD) data are generally difficult to analyze by normal procedures. The matrix method2326 for stacking disorder was used to simulate X-ray powder patterns including diffuse scattering in new types of layered materials. It was revealed that the flocculated LiMnO2 and KMnO2 had a similar disordered structure, in which the probability of a layer sequence with the prevailing shift vector a/3 þ 2b/3 was around 24% and the other stacking modes were random.20,22,27 For the flocculated KTi0.91O2 and KCa2Nb3O10, a satisfactorily good fit was obtained between the simulated and observed patterns assuming a random stacking model.22,28 In addition to these studies, a few r 2011 American Chemical Society

papers focusing on stacking of nanosheets have been recently published, suggesting the evolution of sheet-to-sheet registry under some conditions.21,29 Still, information on structural features of restacked nanosheet systems is limited. This is even much more true for restacked structures composed of two or more different types of nanosheets. The materials made from such binary, or multinary, nanosheet systems may acquire unique, attractive properties through cooperative interaction between the different kinds of nanosheets.18 Therefore, structural characterization of such materials has become essentially important. However, the conventional matrix method cannot be applied singly because of the misfit between the two-dimensional lattices of constituent nanosheets. This technical difficulty may be a main reason why the restacked structures composed of different types of nanosheets has been nearly unexplored. It is true that there have been extensive investigations on structures of mixed-layer compounds, typically interstratified clay minerals such as illitesmectite, illitechlorite, and kaolinitesmectite systems.30 However, the constituent layers in these materials are similar in structural architectures and chemical nature. And one-dimensional diffraction patterns, in general, have only been analyzed. As the first attempt of XRD simulation of the material made from binary nanosheet system, two-component Received: February 15, 2011 Published: April 01, 2011 8555

dx.doi.org/10.1021/jp201477w | J. Phys. Chem. C 2011, 115, 8555–8566

The Journal of Physical Chemistry C colloidal nanosheets in a Ti0.91O2MnO2 system with different compositions were restacked by flocculation with K ions and the products were characterized properly using the matrix method for stacking disorder based on two cell dimensions of constituent nanosheets.22 In this paper, the products of flocculation with K ions of twocomponent colloidal nanosheets in the Ca2Nb3O10Ti0.91O2 and Ca2Nb3O10MnO2 nanosheet systems are analyzed. In addition, the Ti0.91O2MnO2 nanosheet system is re-examined. Then all these three systems are compared with each other in order to elucidate how two different kinds of nanosheets are organized to form a restacked structure. The products must be characterized based on two of the three cell dimensions of constituent nanosheets: for Ti0.91O2 nanosheets (orthorhombic), two-dimensional periods aTi = 0.296 and bTi = 0.377 nm and thickness cTi = 0.932 nm; for MnO2 nanosheets (trigonal), two-dimensional periods aMn = bMn = 0.284 nm and thickness cMn = 0.710 nm; for Ca2Nb3O10 nanosheets (tetragonal), two-dimensional periods aNb = bNb = 0.546 nm and thickness cNb = 1.687 nm. The structural characteristics of the restacked nanosheets in the binary systems are found to be dependent on the combination. We report on the formation of various unique structures via coflocculation from binary colloidal nanosheet systems, which exhibit either mixed stacking of nanosheets or phase separation into individual restacked nanosheets.

2. EXPERIMENTAL SECTION The nanosheets were synthesized according to delamination procedures described in previous papers.6,19 Starting layered precursors of Cs0.35Ti0.91O2, K0.45MnO2, and KCa2Nb3O10 were prepared by normal solid-state calcination of an intimate mixture of alkali metal carbonates and transition metal oxides. The samples were subsequently converted by acid exchange into their respective protonic forms, H0.35Ti0.91O2 3 0.5H2O, H0.13MnO2 3 0.6H2O, and HCa2Nb3O10 3 1.5H2O, and were further delaminated by shaking with tetrabutylammonium hydroxide solution. The resulting colloidal suspensions contained single-layer nanosheets with a lateral size of 3001000 nm. Restacked KTi0.91O2, KMnO2, and KCa2Nb3O10 were synthesized from single-constituent nanosheets, and their respective compositions were determined to be K0.35Ti0.91O2 3 nH2O (n = 0.5), K0.13MnO2 3 nH2O (n = 0.6) and K0.9Ca2Nb3O10 3 nH2O (n = 1.5) based on chemical analysis. The nanosheet suspensions were mixed at various ratios to produce two-component colloidal nanosheets in the Ti0.91O2 MnO2, Ca2Nb3O10Ti0.91O2, and Ca2Nb3O10MnO2 systems. Flocculation was induced by adding a 1 M KCl solution. The composition of the restacked nanosheets was measured by the surfacearea proportion of two kinds of nanosheets in the binary system. Three kinds of flocculated products, Ti0.91O2, MnO2, and Ca2Nb3O10, with the same area S nm2 contain 2S/(0.296 0.377) times the by 0.35K and 0.5H2O, amount of Ti0.91O2 accompanied √ S/(0.284 0.284 3/2) times the amount of MnO2 accompanied by 0.13K and 0.6H2O, and 2S/(0.546 0.546) times the amount of Ca2Nb3O10 accompanied by 0.9K and 1.5H2O, respectively. For example the specimen with a nominal composition of 0.9Ti0.1Mn contains Ti0.91O2 and MnO2 at a ratio √ of 0.9 1.25 to 0.1 using a factor of 2 (0.284 0.284 3/2)/(0.296 0.377) = 1.25, while the specimen with a nominal composition of 0.9Nb0.1Ti contains Ca2Nb3O10 and Ti0.91O2 at a ratio of 0.9 0.38 to 0.1 using a factor of 0.296 0.377/(0.546 0.546) = 0.38, and the specimen with a nominal

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composition of 0.9Nb0.1Mn contains Ca2Nb3O10 and MnO2 at a√ratio of 0.9 0.47 to 0.1 using a factor of 2 (0.284 0.284 3/2)/(0.546 0.546) = 0.47. X-ray powder diffraction data were collected using a Rigaku Rint2000 powder diffractometer with Cu KR radiation and a counterside graphite monochromator.

3. SIMULATION OF DIFFUSE SCATTERING INTENSITY 3.1. Intensity Equation and Simulation Program. The intensity of scattering from a specimen with stacking disorder is generally given in a matrix form2326 by

IðζÞ ¼

N1

∑

ðN jmjÞtr VFQ m

m ¼ ðN 1Þ

where V, F, and Q are matrices with elements (V)st = Vs*Vt, (F)ss = ws, 6 t), (Q)st = Pst exp(iφs), Vs and ws are the layer (F)st = 0 (for s ¼ form factor and existence probability, respectively, Pst is the continuing probability of the tth layer unit after the sth layer unit, and φs = 2πμsζ, where φs is the phase shift due to the sth layer unit, μs is the thickness ratio of the sth layer unit to the standard layer unit, and ζ is the coordinate along c* based on the standard unit. The diffuse intensity distribution of streaks in reciprocal space is calculated as a function of h, k, and ζ using the program FV1,31,32 and its contribution to the powder pattern is calculated using the program PPROFL.33 For the specimen in the binary nanosheet system, part of the procedure for using FV1 and PPROFL was modified by taking into consideration the misfit between two-dimensional lattices of two kinds of nanosheets. Details of the modified procedure are described in sections 3.3, 3.4, and 3.5. The total summation of powder pattern intensity curves is compared with the experimental powder pattern using the leastsquares program LSMIXL22,28 in which the execution modules FV1 and PPROFL are called and used. The profile function is assumed to be Lorentzian in PPROFL with the parameters U, V, and W of Cagliotti et al.34 Preferred-orientation correction using the MarchDollase function35,36 is inserted between FV1 and PPROFL. The MarchDollase preferred orientation factor, (r2 cos2 R þ r1 sin2 R)3/2, in which r is an adjustable parameter and R is the angle in radians between the scattering vector and the preferred orientation direction, can be safely used to treat preferred orientation in the mixtures in quantitative phase analysis.37 In the program LSMIXL, the quantity of Rietveld residual S,38,39 where S is the weighted difference between the observed [y(obs)] and calculated [y(calc)] diffraction patterns, is minimized with the weight, w, equal to the inverse of the counts. The fit of the calculated pattern to the observed one is represented by a profile plot and can also be given numerically using Rp and Rwp S¼ Rp ¼ Rwp ¼

∑i wi ½yi ðobsÞ yi ðcalcÞ2

∑i jyi ðobsÞ yi ðcalcÞj= ∑i yi ðobsÞ

∑i wi ½yi ðobsÞ yi ðcalcÞ = ∑i wi ½yi ðobsÞ 2

1=2

2

3.2. Simulation of Restacked KTi0.91O2, KMnO2, and KCa2Nb3O10. The patterns of restacked KTi0.91O2, KMnO2,

and KCa 2 Nb 3 O 10 are, respectively, orthorhombic with 8556

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The Journal of Physical Chemistry C

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Figure 2. Observed (lower, blue) and calculated (upper, red) X-ray powder diffraction patterns (Cu KR) of (a) restacked KTi0.91O2, (b) restacked KMnO2, and (c) restacked KCa2Nb3O10.

Figure 1. Projection of the fundamental layer unit models of (a) KTi0.91O2 along [0 1 0], (b) KMnO2 along [1 1 0], and (c) KCa2Nb3O10 along [1 1 0]. Red, yellow, and cyan circles represent transition metal, oxygen, and calcium ions, respectively. Green and blue circles represent partially occupied potassium ions and partially occupied H2O, respectively.

aTi = 0.296, bTi = 0.377, cTi = 0.932 nm, trigonal with aMn = bMn = 0.284, cMn = 0.710 nm, and tetragonal with aNb = bNb = 0.546, cNb = 1.687 nm. Some reflections in each pattern are remarkably diffuse, suggesting the existence of a group of streaks parallel to cTi* or cMn* or cNb* in reciprocal space, and they are considered to be due to stacking disorder. Stack operations are defined by placing a new layer unit over the last layer unit after shifting the former by a specific vector in the expression of stacking disorder. The operation is equivalent to the recursive description of stacking in the DIFFaX program40 whose latest version is widely used in many fields such as for clay minerals.41 The lateral shift vectors are selected in a randomized fashion, e.g., nine shift vectors ma/3 þ nb/3 (0 e m e 2, 0 e n e 2), 16 shift vectors ma/4 þ nb/4 (0 e m e 3, 0 e n e 3), and so on. A fundamental layer unit, two-dimensional corrugated layers of TiO6 octahedra containing Ti vacancies accompanied by half the amount of K ions and H2O on each side, is adopted as shown in Figure 1. We use nine shift vectors maTi/3 þ nbTi/3 (0 e m e 2, 0 e n e 2) referring to the data range of X-ray powder diffraction measurement. A random stacking model is adopted, and we calculate the profile based on the probability table P with order r = 9 and the element values Pst = 1/9 and the shift set to 1.0 along cTi. After comparing the calculated and observed powder patterns (Figure 2a) using the program LSMIXL for the number of coherent stacking layers N = 16, the fundamental layer unit with optimum atomic parameters is expressed as 0.91Ti at (1/2, 0, z) and (0, 1/2, 1 z) with z = 0.39, O at (1/2, 1/2, z) and (0, 0, 1 z) with z = 0.45, O at (0, 0, z) and (1/2, 1/2, 1 z) with z = 0.29, 0.14K at (1/2, 0, 0) and (0, 1/2, 1), 0.21K at (0, 1/2, 0) and (1/2, 0, 1), and 0.5H2O at (1/2, 1/2, z) and (0, 0, 1 z) with z = 0.16 based on a cell with aTi, bTi, and cTi.

A fundamental layer unit, composed of a two-dimensional array of edge-shared MnO6 octahedra accompanied by half the amount of K ions and H2O on each side, is adopted. On the basis of a trigonal cell with aMn = bMn and cMn, the fundamental layer unit is expressed by Mn in (0, 0, 1/2), O in (2/3, 1/3, z) and (1/3, 2/3, 1 z) with z = 0.342, 0.0325K in (1/3, 2/3, 0), (2/3, 1/3, 0), (1/3, 2/3, 1), (2/3, 1/3, 1), and 0.3H2O in (0, 0, 0) and (0, 0, 1). Projections of the layer unit are shown in Figure 1. Nine lateral shift vectors maMn/3 þ nbMn/3 (0 e m e 2, 0 e n e 2) are selected. In the experimental pattern, the tail of 10 diffraction bands does not show monotonic decay but has a somewhat wavy profile. The positions of diffuse maxima can lead to a stacking model, in which the probability for the sixth shift vector aMn/3 þ 2bMn/3 prevails over that for the other sequences with order r = 9. We calculate the profile based on the probability table P with Pst = β = 0.24 (1 e s e 9, t = 6) for the lateral shift vector aMn/3 þ 2bMn/3, and Pst = R = (1 β)/(r 1) = 0.095 (1 e s e 9, 1 e t e 5, 7 e t e 9) for the other shift vectors and the shift set to 1.0 along cMn. The calculated pattern for the number of coherent stacking layers N = 16 and the observed pattern are shown in Figure 2b. It can be concluded that the flocculated MnO2 nanosheet with K ions has a disordered structure, in which the probability of a layer sequence with the shift vector aMn/3 þ 2bMn/3, which produces trigonal prismatic sites for guest species, is around 24% and the other stacking modes are random. As a fundamental layer unit of restacked KCa2Nb3O10, a triple-layered perovskite structure accompanied by half the amount of K ions and H2O on each side is adopted. A random stacking model with nine shift vectors maNb/3 þ nbNb/3 (0 e m e 2, 0 e n e 2) is adopted referring to the data range of X-ray powder diffraction measurement. We calculated the profile based on the probability table P with Pst = 1/9 and the shift set to 1.0 along cNb. As described in the previous report,24 broadening of the reflections 00l due to a small finite number of stacking layers N is remarkable, although the shape of scattering for hkζ except 00l is not affected by the value of N. The number of stacking layer units N = 7 as an optimum value of coherent thickness is adopted in the simulation of restacked KCa2Nb3O10. After comparing the calculated and observed powder patterns (Figure 2c) using 8557



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Table 1. Stacking with Shift Vectors and P Table Containing Shift of Origin (a) Possible Intralayer Shift Vectorsa lateral shift lateral shift vector stacking vector stacking

stacking

lateral shift vector

1

0

4

a/3

7

2a/3

2

b/3

5

a/3 þ b/3

8

2a/3 þ b/3

3

2b/3

6

a/3 þ 2b/3

9

2a/3 þ 2b/3

(b) Probability Table P for Misfit Mixed-Layer Compound (order r = 18)b l+1 l

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18

1 D D D D D D D D D

E E E E E E E E E

2

D D D D D D D D D

E E E E E E E E E

3

D D D D D D D D D

E E E E E E E E E

4

D D D D D D D D D

E E E E E E E E E

5 6

D D D D D D D D D D D D D D D D D D

E E E E E E E E E E E E E E E E E E

7

D D D D D D D D D

E E E E E E E E E

8

D D D D D D D D D

E E E E E E E E E

9

D D D D D D D D D

E E E E E E E E E

10 F

F

F

F

F

F

F

F

F

G G G G G H G G G

11 F

F

F

F

F

F

F

F

F

G G G G G H G G G

12 F 13 F

F F

F F

F F

F F

F F

F F

F F

F F

G G G G G H G G G G G G G G H G G G

14 F

F

F

F

F

F

F

F

F

G G G G G H G G G

15 F

F

F

F

F

F

F

F

F

G G G G G H G G G

16 F

F

F

F

F

F

F

F

F

G G G G G H G G G

17 F

F

F

F

F

F

F

F

F

G G G G G H G G G

18 F

F

F

F

F

F

F

F

F

G G G G G H G G G

Nine lateral shift vectors maTi/3 þ nbTi/3 (0 e m e 2, 0 e n e 2), maMn/3 þ nbMn/3 (0 e m e 2, 0 e n e 2), and maNb/3 þ nbNb/3 (0 e m e 2, 0 e n e 2) are selected based on an orthorhombic cell with aTi = 0.296, bTi = 0.377 nm, a trigonal cell with aMn = bMn = 0.284 nm, and a tetragonal cell with aNb = bNb = 0.546 nm, respectively. b The first nine rows and columns and the latter nine rows and columns are assigned to stacking of the first kind of nanosheet and stacking of the second kind of nanosheet with the respective nine shift vectors listed in (a).

of each kind of nanosheet into a co-restacked material is proportional to the respective amount of nanosheet of that kind in the two-component colloidal suspension. This model, in which the distribution of intergrowth is considered to be homogeneous or random, may be referred to as a one-dimensional solid-solution model of the misfit mixed-layer compound by analogy with an ordinary solid solution where the solute is distributed homogeneously, and the symbol SS is used for this model. For misfit mixed-layer compounds, we consider the matrix P for which the elements Pst are continuing probabilities, with order r = 18 as shown in Table 1b. Stack operations are defined by placing a new layer unit with a specific shift vector over the last layer unit in a similar way to that described in section 3.2. In the Ti0.91O2MnO2 binary nanosheet system, the first nine rows and columns are assigned to stacking of KTi0.91O2 sheets with nine shift vectors based on an orthorhombic cell (aTi = 0.296, bTi = 0.377, cTi = 0.932 nm), and the latter nine rows and columns are assigned to stacking of KMnO2 sheets with nine shifts based on a trigonal cell (aMn = bMn = 0.284, cMn = 0.710 nm). Fundamental layer units of KTi0.91O2 and KMnO2 sheets, those used in section 3.2, namely, the respective transition metal oxide nanosheets accompanied by half the respective K ions and H2O on each side, are adopted with z values retained 1 e z e 0 respectively based on cTi and cMn. As the random stacking model is adopted in restacked KTi0.91O2, the element values of P are set to Ps1 = Ps2 = ... = Ps8 = Ps9 = D (1 e s e 9). In restacked KMnO2, the prevailing shift vector aMn/3 þ 2bMn/3 exists. The element values for 10 e s e 18 are Ps10 = Ps11 = ... = Ps14 = Ps16 = Ps17 = Ps18 = G and the ratio of elements Ps15/Psn (=H/G), 10 e n e 14 or 16 e n e 18, is 0.24/0.095, as (1 0.24)/8 = 0.095. We assume a Ti0.91O2 sheet and an MnO2 sheet stacked randomly after another sheet, then Ps10 = Ps11 = ... = Ps17 = Ps18 = E (1 e s e 9) and Ps1 = Ps2 = ... = Ps8 = Ps9 = F (10 e s e 18). The sum total of the probabilities of the sth nanosheet being succeeded by other nanosheets, whatever their kinds, is equal to unity, i.e.

a

the program LSMIXL, the fundamental layer unit with optimum atomic parameters is expressed by Nb in (0, 0, 1/2) and (1/2, 1/2, 1/2), Nb in (0, 0, z), (1/2, 1/2, z), (0, 0, 1 z), (1/2, 1/2, 1 z) with z = 0.749, and Ca in (1/2, 0, z), (0, 1/2, z), (1/2, 0, 1 z), (0, 1/2, 1 z) with z = 0.653, O in (x, x þ 1/2, 1/2), (x, 1/2 x, 1/2), (1/2 x, x, 1/2), and (x þ 1/2, x, 1/2) with x = 0.334, O in (0, 0, z), (1/2, 1/2, z), (0, 0, 1 z), (1/2, 1/2, 1 z) with z = 0.605, O in (x, x þ 1/2, z), (x, 1/2 x, z), (1/2 x, x, z), (x þ 1/2, x, z), (x, x þ 1/2, 1 z), (x, 1/2 x, 1 z), (1/2x, x, 1 z) and (x þ 1/2, x, 1 z) with x = 0.286 and z = 0.737, 0.23K in (0, 0, 0), (1/2, 1/2, 0), (0, 0, 1), and (1/2, 1/2, 1), 0.23K in (1/2, 0, 0), (0, 1/2, 0), (1/2, 0, 1), and (0, 1/2, 1), and 0.8H2O in (0, 1/2, z), (1/2, 0, z), (0, 1/2, 1 z), and (1/2, 0, 1 z) with z = 0.907 based on a cell with aNb, bNb, and cNb. 3.3. One-Dimensional Solid-Solution Model of Misfit Mixed-Layer Compounds in the Binary Nanosheet System. First, we consider a model in which the flocculation probability

18

∑ Pst ¼ 1 t¼1 The element values D, E, F, G, and H, with the conditions 9D þ 9E = 9F þ 8G þ H = 1.0 in the probability table (Table 1b), are used for simulation. The value of F/E expresses the composition of the mixed-layer compound in terms of the surface-area ratio of the nanosheets, as the first and second kinds of nanosheet are obstructed by another kind of nanosheet with the respective probabilities 9E and 9F and then their respective average domain sizes in a co-restacked material are expected to be proportional to 1/(9E) and 1/(9F). To cite a couple of cases, the values D = 0.078, E = 0.033, F = 0.078, G = 0.029, and H = 0.072 are adopted for 0.7Ti0.3Mn with F/E = 0.7/0.3, and the values D = 0.033, E = 0.078, F = 0.033, G = 0.067, and H = 0.168 are adopted for 0.3Ti0.7Mn with F/E = 0.3/0.7. The intensity distribution of streaks or reflections in reciprocal space is calculated using the matrix Q with (Q)st = Pst exp(2πiμsζ), with μs = 1 (1 e s e 9) and μs = cMn/cTi (10 e s e 18), using FV1. For 00ζ reflection calculation, both layer form factors of KTi0.91O2 sheet (1 e s e 9, 1 e t e 9) and KMn oxide sheet (10 e s e 18, 10 e t e 18) are used after normalization of site occupancies and z coordinates. For hTikTiζ reflections except 00ζ based on aTi = 0.296, bTi = 0.377, cTi = 0.932 nm, layer form factors of KTi0.91O2 sheet (1 e s e 9, 1 e t e 9) and zero layer form factors (10 e s e 18, 10 e t e 18) are assigned and used. For hMnkMnζ scattering except 00ζ based on aMn = bMn = 0.284, cMn = 0.710 nm, zero layer 8558


The Journal of Physical Chemistry C form factors (1 e s e 9, 1 e t e 9) and layer form factors of KMnO2 sheet (10 e s e 18, 10 e t e 18) are assigned and used. One scale factor common to 00ζ, hTikTiζ, and hMnkMnζ is used after compensation of the cell difference between the two kinds of nanosheets. The approach is similar to that used for analyzing layered composite crystals with one-directional disorder,4244 although one probability matrix P common to 00ζ, hTikTiζ, and hMnkMnζ is used for the mixed-layer compounds in the present work. The intensity distributions in reciprocal space streaks 00ζ, hTikTiζ, and hMnkMnζ are converted to powder pattern curves and the total summation of powder pattern intensity is compared with the experimental X-ray powder pattern using the program LSMIXL after examining the optimum coherent thickness N of the misfit mixed-layer compound. Values of the lattice constants and atomic coordinates are fixed to those for restacked KTi0.91O2 and KMnO2 described in section 3.2. For the Ca2Nb3O10Ti0.91O2 binary nanosheet system, the first nine rows and columns and the latter nine rows and columns are, respectively, assigned to stacking of KCa2Nb3O10 sheets with nine lateral shifts based on a tetragonal cell (aNb = bNb = 0.546, cNb = 1.687 nm) and stacking of KTi0.91O2 sheets with nine lateral shifts based on an orthorhombic cell (aTi = 0.296, bTi = 0.377, cTi = 0.932 nm). Fundamental layer units of KCa2Nb3O10 and KTi0.91O2 sheets, namely, the respective nanosheets accompanied by half the respective K ions and H2O on each side, are adopted with the z values retained at 1 e z e 0 respectively based on cNb and cTi. As the random stacking model is adopted in both the restacked KCa2Nb3O10 and KTi0.91O2, the element values of P are set to Ps1 = Ps2 = ... = Ps8 = Ps9 = D (1 e s e 9), Ps10 = Ps11 = ... = Ps17 = Ps18 = G = H (10 e s e 18), Ps10 = Ps11 = ... = Ps17 = Ps18 = E (1 e s e 9) and Ps1 = Ps2 = ... = Ps8 = Ps9 = F (10 e s e 18) with the conditions 9D þ 9E = 9F þ 9G = 1.0. To cite a couple of cases, the values D = 0.078, E = 0.033, F = 0.078, and G = H = 0.033 are adopted for 0.7Nb0.3Ti with F/E = 0.7/0.3, and the values D = 0.022, E = 0.089, F = 0.022, and G = H = 0.089 are adopted for 0.2Nb0.8Ti with F/E = 0.2/0.8. The intensity distribution in reciprocal space streaks 00ζ, hNbkNbζ, and hTikTiζ is calculated through similar procedures to those for the Ti0.91O2MnO2 binary nanosheet system, and is converted to powder pattern curves and the total summation of powder pattern intensity is compared with the experimental X-ray powder pattern after selecting the coherent thickness N with each composition. For the Ca2Nb3O10MnO2 binary nanosheet system, the first nine rows and columns and the latter nine rows and columns are, respectively, assigned to stacking of KCa2Nb3O10 sheets with nine lateral shifts based on a tetragonal cell (aNb = bNb = 0.546, cNb = 1.687 nm) and stacking of KMnO2 sheets with nine lateral shifts based on a trigonal cell (aMn = bMn = 0.284, cMn = 0.710 nm). The same element values of P as those for the Ti0.91O2MnO2 binary nanosheet system are adopted. The intensity distribution in reciprocal space streaks 00ζ, hNbkNbζ, and hMnkMnζ and the powder pattern intensity are calculated through similar procedures to those for the Ti0.91O2MnO2 binary nanosheet system, after selecting the coherent thickness N with each composition. 3.4. One-Dimensional Two-Phase Stacking Model of Misfit Mixed-Layer Compounds in the Binary Nanosheet System. For the Ti0.91O2MnO2 binary nanosheet system, 0.7Ti0.3Mn and 0.3Ti0.7Mn were selected as the compositional limit values of homogeneous intergrowth in restacked KTi0.91O2 and KMnO2, respectively, after several preceding

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calculations. In the intermediate range, the continuing probabilities after a Ti0.91O2 sheet in 0.6Ti0.4Mn are assumed to be the same as those in the limit 0.7Ti0.3Mn, and the continuing probabilities after an MnO2 sheet in 0.4Ti0.6Mn are assumed to be the same as those in the limit 0.3Ti0.7Mn. The remaining continuing probabilities are set so as to maintain the composition of each grain at the average composition with the conditions 9D þ 9E = 9F þ 8G þ H = 1.0. Thus, the values D = 0.078, E = 0.033, F = 0.050, G = 0.052, and H = 0.0132 are adopted for 0.6Ti0.4Mn with F/E = 0.6/0.4, and the values D = 0.061, E = 0.050, F = 0.033, G = 0.067, and H = 0.168 are adopted for 0.4Ti0.6Mn with F/E = 0.4/0.6. The same values of D and E as those for 0.7Ti0.3Mn and the same values of F, G, and H as those for 0.3Ti0.7Mn, i.e., D = 0.078, E = 0.033, F = 0.033, G = 0.067, and H = 0.168, are adopted for 0.5Ti0.5Mn, as the composition of 0.5Ti0.5Mn in terms of surface-area ratio of nanosheets is precisely in the middle of that of 0.7Ti0.3Mn and 0.3Ti0.7Mn. The powder pattern curves for 00ζ, hTikTiζ, and hMnkMnζ are calculated similarly to those in section 3.3 and the summation is compared with the experimental X-ray powder pattern using the program LSMIXL after examining the optimum coherent thickness N. Values of the lattice constants and atomic coordinates are fixed to those for restacked KTi0.91O2 and KMnO2 described in section 3.2. In the present model, the values of the continuing probability ratio, D/E and (8G þ H)/F, approach the values in the limits 0.7Ti0.3Mn and 0.3Ti0.7Mn, respectively, as far as the specimen composition permits. We call the present model a one-dimensional two-phase stacking model, using the symbol 2P, of the misfit mixed-layer compound.22,45 For the Ca2Nb3O10Ti0.91O2 binary nanosheet system, the compositional limit of homogeneous intergrowth of Ti0.91O2 sheet in restacked KCa2Nb3O10 and that of Ca2Nb3O10 sheet in restacked KTi0.91O2 were respectively selected to be 0.7Nb0.3Ti and 0.2Nb0.8Ti after several trial calculations. At a composition close to that of 0.7Nb0.3Ti, the continuing probabilities after a Ca2Nb3O10 sheet are assumed to be the same as those in the limit 0.7Nb0.3Ti, and at a composition close to that of 0.2Nb0.8Ti, the continuing probabilities after a Ti0.91O2 sheet are assumed to be the same as those in the limit 0.2Nb0.8Ti. The remaining continuing probabilities are set so as to maintain the composition of each grain at the average composition. To cite a case, the values D = 0.059, E = 0.052, F = 0.022, and G = H = 0.089 are adopted for 0.3Nb0.7Ti with F/E = 0.3/0.7 at a composition close to that of 0.2Nb0.8Ti. The powder pattern curves for 00ζ, hNbkNbζ, and hTikTiζ are calculated, and the summation is compared with the experimental X-ray powder pattern after optimizing the coherent thickness N with each composition. 3.5. Two-Phase Coexistence Model of Misfit Mixed-Layer Compounds in the Binary Nanosheet System. When the specimens in the Ti0.91O2MnO2 binary nanosheet system are assumed to be mixtures of two different solid solutions having the compositions of two limits, 0.7Ti0.3Mn and 0.3Ti 0.7Mn, the specimens with nominal compositions 0.6Ti0.4Mn, 0.5Ti0.5Mn, and 0.4Ti0.6Mn contain 3/4, 1/2, and 1/4 parts of 0.7Ti0.3Mn solid solution to 1/4, 1/2, and 3/4 parts of 0.3Ti0.7Mn solid solution. The simulated X-ray powder diffraction pattern intensity is the weighted mean of the simulated intensity of the solid solutions 0.7Ti0.3Mn and 0.3Ti0.7Mn with respective optimum coherent thickness of N0.7Ti and N0.7Mn. We call this model a one-dimensional two-phase 8559



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Table 2. Results of Pattern Fitting for the Ti0.91O2MnO2 Binary Nanosheet Systema sample name

composition

model

N

0.9Ti0.1Mn

1.125K0.35Ti0.91O2 3 0.1K0.13MnO2 3 nH2O

SS

0.8Ti0.2Mn

1.000K0.35Ti0.91O2 3 0.2K0.13MnO2 3 nH2O

SS

0.7Ti0.3Mn

0.875K0.35Ti0.91O2 3 0.3K0.13MnO2 3 nH2O

0.6Ti0.4Mn

0.750K0.35Ti0.91O2 3 0.4K0.13MnO2 3 nH2O

Rp (%)

Rwp (%)

16

10.4

13.9

16

12.6

15.8

SS

16

13.4

16.9

SS

16

12.5

15.7

2P

16

10.3

13.4

2C 0.5Ti0.5Mn

0.4Ti0.6Mn

0.625K0.35Ti0.91O2 3 0.5K0.13MnO2 3 nH2O

0.500K0.35Ti0.91O2 3 0.6K0.13MnO2 3 nH2O

N0.7Ti

16

N0.7Mn

16

11.0

13.9

14.3

18.4

11.9 12.4

15.2 16.1

SS

16

2P 2C

16

SS

16

14.3

18.2

2P

16

11.8

15.2

16

2C

16

16

16

12.3

15.9

0.3Ti0.7Mn

0.375K0.35Ti0.91O2 3 0.7K0.13MnO2 3 nH2O

SS

16

13.0

16.4

0.2Ti0.8Mn

0.250K0.35Ti0.91O2 3 0.8K0.13MnO2 3 nH2O

SS

16

13.3

17.7

0.1Ti0.9Mn

0.125K0.35Ti0.91O2 3 0.9K0.13MnO2 3 nH2O

SS

16

12.9

17.4

a

Results based on the one-dimensional solid-solution model (SS), one-dimensional two-phase stacking model (2P), and one-dimensional two-phase coexistence model (2C) are listed. Sample name, composition, model symbol, coherent thickness N for the SS or 2P model, coherent thickness N0.7Ti of restacked 0.7Ti0.3Mn and coherent thickness N0.7Mn of 0.3Ti0.7Mn for the 2C model, and Rp and Rwp obtained by the pattern fitting process are listed.

coexistence model, using the symbol 2C, of the misfit mixed-layer compound. In the case of the Ca2Nb3O10Ti0.91O2 binary nanosheet system, the specimens with nominal compositions 0.6Nb0.4Ti, 0.5Nb0.5Ti, 0.4Nb0.6Ti, and 0.3Nb0.7Ti contain 4/5, 3/ 5, 2/5, and 1/5 parts of 0.7Nb0.3Ti to 1/5, 2/5, 3/5, and 4/5 parts of 0.2Nb0.8Ti, as the compositional limits of the solid-solution model in the Ca2Nb3O10Ti0.91O2 system are assumed to be 0.7Nb0.3Ti and 0.2Nb0.8Ti. The simulated X-ray powder diffraction pattern intensity is the weighted mean of the simulated intensity of the solid solutions 0.7Nb0.3Ti and 0.2Nb0.8Ti with respective optimum coherent thickness N0.7Nb and N0.8Ti. 3.6. Mixture Model for the Ca2Nb3O10MnO2 Binary Nanosheet System. For the Ca2Nb3O10MnO2 binary nanosheet system, we examine the model in which the specimen is a mixture of two kinds of restacked nanosheets, KCa2Nb3O10 and KMnO2. The restacked specimen with a nominal composition of xNb (1 x)Mn contains x parts of restacked Ca2Nb3O10 nanosheets to (1 x) parts of restacked MnO2 nanosheets by the surface area proportion of nanosheets. The simulated powder pattern as the weighted mean of that for restacked KCa2Nb3O10 with an optimum coherent thickness NNb and that for restacked KMnO2 with an optimum coherent thickness NMn is compared with the observed powder pattern using LSMIXL.

4. RESULTS 4.1. Ti0.91O2MnO2 Binary Nanosheet System. The X-ray diffraction patterns of the flocculated products from the Ti0.91O2MnO2 nanosheet system were simulated using a coherent thickness N = 16 and the matrix listed in Table 1b based on the onedimensional solid-solution model (SS), section 3.3, one-dimensional two-phase stacking model (2P), section 3.4, and one-dimensional two-phase coexistence model (2C), section 3.5. Table 2 lists the sample name, composition, model symbol, coherent thickness, and Rp and Rwp obtained by the pattern fitting process. With each

Figure 3. Observed (lower, blue) and simulated (upper, red) X-ray powder diffraction patterns (Cu KR): one-dimensional solid-solution model (SS) for specimens of 0.9Ti0.1Mn, 0.8Ti0.2Mn, 0.7Ti0.3Mn, 0.3Ti0.7Mn, 0.2Ti0.8Mn, 0.1Ti0.9Mn and onedimensional two-phase stacking model (2P) for 0.6Ti0.4Mn, 0.5Ti0.5Mn, 0.4Ti0.6Mn.

sample, the values of Rwp for the SS, 2P, and 2C models are compared to each other and the model giving the smallest Rwp is judged to indicate the most stable state. The results listed in Table 2 show that the one-dimensional solid solutions are stable in a fairly wide composition range, 8560



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Figure 4. Schematic representation of restacked two-component nanosheets in the Ti0.91O2MnO2 binary nanosheet system, flocculated with K ions. Intralayer shifts are approximately expressed by lateral shifts. Wide cracks are used to divide the restacked nanosheet image into detached particles with coherent thickness N = 16 for the Ti0.91O2MnO2 binary nanosheet system.

Table 3. Results of Pattern Fitting for the Ca2Nb3O10Ti0.91O2 Binary Nanosheet Systema sample name

composition

model

N

0.9Nb0.1Ti

0.342K0.9Ca2Nb3O10 3 0.1K0.35Ti0.91O2 3 nH2O

SS

4

9.9

12.8

0.8Nb0.2Ti

0.304K0.9Ca2Nb3O10 3 0.2K0.35Ti0.91O2 3 nH2O

SS

4

11.1

14.3

0.7Nb0.3Ti

0.266K0.9Ca2Nb3O10 3 0.3K0.35Ti0.91O2 3 nH2O

SS

4

13.8

17.6

0.6Nb0.4Ti

0.228K0.9Ca2Nb3O10 3 0.4K03.5Ti0.91O2 3 nH2O

SS

4

10.3

13.3

2P

4

10.5

13.6

10.0

12.8

11.0 11.5

14.1 14.9

2C 0.5Nb0.5Ti

0.190K0.9Ca2Nb3O10 3 0.5K0.35Ti0.91O2 3 nH2O

0.4Nb0.6Ti

0.152K0.9Ca2Nb3O10 3 0.6K0.35Ti0.91O2 3 nH2O

3

SS 2P

2

SS

5

2P

5

2C

a

0.114K0.9Ca2Nb3O10 3 0.7K0.35Ti0.91O2 3 nH2O

2

SS

5

2P

5

0.2Nb0.8Ti

0.076K0.9Ca2Nb3O10 3 0.8K0.35Ti0.91O2 3 nH2O

2C SS

0.1Nb0.9Ti

0.038K0.9Ca2Nb3O10 3 0.9K0.35Ti0.91O2 3 nH2O

SS

N0.8Ti

9

4 4

2C

0.3Nb0.7Ti

N0.7Nb

1

9

8

7

Rp (%)

Rwp (%)

9.4

12.2

11.3

14.4

12.2

15.7

9.6

12.3

11.6

14.7

11.7

15.1 13.5 14.4 13.4

7

10.8 11.1

8

10.4

Results based on the one-dimensional solid-solution model (SS), one-dimensional two-phase stacking model (2P), and one-dimensional two-phase coexistence model (2C) are listed. Sample name, composition, model symbol, coherent thickness N for the SS or 2P model, coherent thickness N0.7Nb of restacked 0.7Nb0.3Ti, coherent thickness N0.8Ti of 0.2Nb0.8Ti for the 2C model, and Rp and Rwp obtained by the pattern fitting process are listed.

x e 0.3 and x g 0.7 for xTi0.91O2(1 x)MnO2. In the intermediate range of 0.3 < x < 0.7, the one-dimensional two-phase stacking state is stable. Figure 3 illustrates the X-ray powder diffraction patterns observed and calculated for the one-dimensional solid-solution model of the specimens of x e 0.3 or x g 0.7 and for the one-dimensional two-phase stacking model of 0.3 < x < 0.7. The microscopic images of stacking sequences were simulated using the element values D, E, F, G, and H, random numbers, and the program SQ3.32 The microscopic images obtained for all nine specimens are illustrated in Figure 4. Intralayer shifts are approximately expressed

by lateral displacement. In the range, x e 0.3 and x g 0.7 for xTi0.91O2(1 x)MnO2, the minor nanosheets mostly appear separately or as two or three successive sheets, and this feature corresponds to the one-dimensional solid-solution model. In the range of 0.3 < x < 0.7, the two kinds of nanosheets appear in a rather similar mixed layer state to that of 0.7Ti0.3Mn or 0.3Ti0.7Mn, as shown in Figure 4. 4.2. Ca2Nb3O10Ti0.91O2 Binary Nanosheet System. For the Ca2Nb3O10Ti0.91O2 binary nanosheet system, sample name, composition, optimum coherent lengths of restacked nanosheet, 8561



Figure 5. Observed (lower, blue) and simulated (upper, red) X-ray powder diffraction patterns (Cu KR): one-dimensional solid-solution model (SS) for specimens of 0.9Nb0.1Ti, 0.8Nb0.2Ti, 0.7Nb0.3Ti, 0.2Nb0.8Ti, 0.1Nb0.9Ti and one-dimensional two-phase coexistence model (2C) for 0.6Nb0.4Ti, 0.5Nb0.5Ti, 0.4Nb0.6Ti, 0.3Nb 0.7Ti.

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and Rp and Rwp obtained by the pattern fitting process based on three models, i.e., one-dimensional solid solution (SS), one-dimensional two-phase stacking (2P), and one-dimensional two-phase coexistence (2C), are listed in Table 3. Agreement between the observed and calculated powder diffraction intensity for the onedimensional two-phase stacking model (2P) is worse than that for the one-dimensional solid-solution model throughout the composition range. The results listed in Table 3 show that the onedimensional solid solutions are stable in the composition range, x e 0.2 and x g 0.7 for xCa2Nb3O10(1 x)Ti0.91O2. In the intermediate range of 0.2 < x < 0.7, the one-dimensional two-phase coexistence state is stable. Figure 5 illustrates the X-ray powder diffraction patterns observed and calculated for the one-dimensional solid-solution model of the specimens of x e 0.2 or x g 0.7, and for the one-dimensional two-phase coexistence model of the specimens of 0.2 < x < 0.7. The microscopic images obtained for all nine specimens are illustrated in Figure 6 with approximate expression of two-dimensional intralayer shifts by lateral displacement. In the range x e 0.2 and x g 0.7, the features of the image correspond to the one-dimensional solid-solution model of the mixed-layer compounds although the coherent thickness is rather small compared to the case of the Ti0.91O2MnO2 binary nanosheet system. In the range of 0.2 < x < 0.7, the specimens are mixtures of two different solid solutions having the compositions of two limits, 0.7Nb0.3Ti and 0.2Nb0.8Ti, and with coherent thickness N0.7Nb and N0.8Ti listed in Table 3. 4.3. Ca2Nb3O10MnO2 Binary Nanosheet System. For the Ca2Nb3O10MnO2 binary nanosheet system, agreement between the observed and calculated powder diffraction intensity for the mixture model is better than that for the misfit mixed-layer compound model such as the one-dimensional solid solution throughout the composition range, from 0.9Nb0.1Mn to 0.1Nb0.9Mn. Sample name, composition, optimum coherent length of restacked

Figure 6. Schematic representation of restacked two-component nanosheets in the Ca2Nb3O10Ti0.91O2 binary nanosheet system, flocculated with K ions. Intralayer shifts are approximately expressed by lateral shifts. The values listed in Table 3 for coherent thickness N in the one-dimensional solid-solution model for 0.9Nb0.1Ti, 0.8Nb0.2Ti, 0.7Nb0.3Ti, 0.2Nb0.8Ti, 0.1Nb0.9Ti, and coherent thickness N0.7Nb and N0.8Ti in the two-phase coexistence model for 0.6Nb0.4Ti, 0.5Nb0.5Ti, 0.4Nb0.6Ti, 0.3Nb0.7Ti are used for illustration. 8562



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Table 4. Results of Pattern Fitting for the Ca2Nb3O10MnO2 Binary Nanosheet Sysyema sample name

composition

model

N

0.9Nb0.1Mn

0.423K0.9Ca2Nb3O10 3 0.1K0.13MnO2 3 nH2O

SS

8

MX 0.8Nb0.2Mn

0.376K0.9Ca2Nb3O10 3 0.2K0.13MnO2 3 nH2O

SS

0.329K0.9Ca2Nb3O10 3 0.3K0.13MnO2 3 nH2O

SS

0.282K0.9Ca2Nb3O10 3 0.4K0.13MnO2 3 nH2O

SS

0.5Nb0.5Mn

0.235K0.9Ca2Nb3O10 3 0.5K0.13MnO2 3 nH2O

MX SS

0.4Nb0.6Mn

0.188K0.9Ca2Nb3O10 3 0.6K0.13MnO2 3 nH2O

5

SS

0.1Nb0.9Mn

SS

0.047K0.9Ca2Nb3O10 3 0.9K0.13MnO2 3 nH2O

MX SS

4

4

3

6

12 3

SS

0.094K0.9Ca2Nb3O10 3 0.8K0.13MnO2 3 nH2O

4

10

6

14

MX 0.2Nb0.8Mn

3

10

MX 0.141K0.9Ca2Nb3O10 3 0.7K0.13MnO2 3 nH2O

3

10

MX

0.3Nb0.7Mn

7 6

MX 0.6Nb0.4Mn

NMn

8

MX 0.7Nb0.3Mn

NNb

3

7

14

Rwp (%)

16.2

21.8

10.1

13.1

16.4

20.8

10.4

13.1

19.9

25.6

11.9

15.2

18.8

23.8

10.1 19.1

12.5 24.4

10.4

13.2

19.2

24.2

9.7

12.5

18.5

23.7

10.4

14.2

14.9

18.4

2

7

10.4 14.5

13.2 17.9

1

8

11.0

13.8

14

MX

Rp (%)

Results based on the one-dimensional solid-solution model and the mixture model for the Ca2Nb3O10MnO2 binary nanosheet system are listed. Sample name, composition, SS symbol for the one-dimensional solid-solution model or MX symbol for the mixture model, coherent thickness N of the mixed-layer nanosheets, coherent thickness NNb of restacked Ca2Nb3O10 nanosheets, coherent thickness NMn of restacked MnO2 nanosheets, and Rp and Rwp obtained by the pattern fitting process are listed. a

KCa2Nb3O10 and KMnO2, and Rp and Rwp obtained by the pattern fitting process based on the mixture model are listed in Table 4 compared with those based on the one-dimensional solid-solution model. The results signify that intergrowth of MnO2 nanosheet into restacked KCa2Nb3O10 and intergrowth of Ca2Nb3O10 nanosheet into restacked KMnO2 are not probable in contrast to the misfit mixed-layer compounds in the Ti0.91O2 MnO2 and Ca2Nb3O10Ti0.91O2 nanosheet systems. Figure 7 illustrates the X-ray powder diffraction patterns observed and calculated for the mixture model. A schematic representation of the flocculated state in the Ca2Nb3O10MnO2 nanosheet system is shown in Figure 8. Intralayer shifts are approximately expressed by lateral displacement. Optimum coherent thicknesses NNb and NMn listed in Table 4 are used for illustration.

5. DISCUSSION Experimental patterns with broad reflections, which suggest the presence of irregular stacking, are often observed not only in the restacked nanosheets but also in the materials coflocculated from the binary nanosheet systems. Although high-resolution transmission electron microscope images provide some important information as to stacking disorder, diffuse X-ray scattering is a much more convenient way to identify the average state of stacking disorder. The present work shows that the matrix method is effectively adaptable to calculate the diffuse scattering intensity for a given model throughout reciprocal space and the X-ray powder diffraction pattern in the restacked binary nanosheet systems can be simulated as the sum of the diffuse scattering. Using this method, we demonstrated that the stacking fashion in coflocculated products from the binary colloidal nanosheet systems is dependent on their combination. The products from two-component colloidal nanosheets in the Ti0.91O2MnO2 system suggested the presence of mixedlayer compounds of Ti0.91O2 and MnO2 connected by K ions.

Figure 7. X-ray powder diffraction patterns (Cu KR) observed (lower, blue) and simulated (upper, red) based on the mixture model (MX) for all specimens in the Ca2Nb3O10MnO2 binary nanosheet system.

The one-dimensional solid solutions (SS), i.e., random mixing of two kinds of nanosheets, seem to be stable in a fairly wide 8563



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Figure 8. Schematic representation of restacked two-component nanosheets in the Ca2Nb3O10MnO2 binary nanosheet system flocculated with K ions. Intralayer shifts are approximately expressed by lateral shifts. Optimum coherent thickness NNb and NMn listed in Table 4 for the Ca2Nb3O10MnO2 binary nanosheet system are used for illustration.

composition range, x e 0.3 and x g 0.7 for xTi0.91O2(1 x)MnO2. In the range of 0.3 < x < 0.7, the one-dimensional two-phase stacking state (2P) appears where the values of continuing probability approach the values in 0.7Ti0.3Mn and 0.3Ti0.7Mn as long as the specimen compositions are maintained. In the Ca2Nb3O10Ti0.91O2 system, the one-dimensional solid solutions (SS) seem to be stable in the composition ranges x e 0.2 and x g 0.7 for xCa2Nb3O10(1 x)Ti0.91O2, as shown in Table 3, although the coherent thickness is rather small compared to the case of the Ti0.91O2MnO2 system. The results mean that intergrowth of Ti0.91O2 nanosheet into restacked KCa2Nb3O10 and intergrowth of Ca2Nb3O10 nanosheet into restacked KTi0.91O2 can occur. In the range of 0.2 < x < 0.7, pattern fitting indicates that the specimens are mixtures of two different solid solutions having the compositions of two limits, x = 0.2 and x = 0.7, with the respective small coherent thickness, namely, the onedimensional two-phase coexistence state (2C) with the one-dimensional miscibility gap between 0.7Nb0.3Ti and 0.2Nb0.8Ti. In the Ca2Nb3O10MnO2 system, the simulation did not support the presence of mixing in codeposited nanosheets throughout the composition range, excluding the models for the mixed layers of Ca2Nb3O10 and MnO2, i.e., SS, 2P, and 2C. As shown in Figure 8, nanosheets of Ca2Nb3O10 and MnO2 are flocculated separately by K ions accompanied by H2O. The reasons for the variation in coflocculation behavior are not yet fully clear. The nanosheets are dispersed in aqueous media via rather weak electrostatic interaction, and they are also loosely bound with each other even in the flocculated material. The metastable flocculation structure may be stabilized due to the room-temperature processes for preparation. Diffusion rates of the nanosheets in the dispersion, and flexibility or rigidness of constituent nanosheets may be reflected in the coflocculation

behavior. As several competing effects may be at work, both of the product stability and reaction kinetics need to be considered. The first possible reason for the variation in coflocculation behavior is a thermodynamic relationship between two nanosheets in a costacked material. The thermodynamic relationship may be partially caused by a boundary plane structure related to the atomic architecture of the nanosheets on both sides, and it may also be partially caused by the repulsive interaction energy between two different kinds of nanosheets. Costacked products consist of two kinds of nanosheets with an inherent two-dimensional periodic structure having K ions surrounded by H2O molecules on both sides. The positive charge of the K ions balances the negative charge of the two kinds of nanosheets, achieving total charge neutrality. As the fundamental layer units in the simulation, nanosheets accompanied by half the amount of K ions and H2O on each side, are adopted. The atomic arrangement of a boundary plane at z = 0 in respective layer units are shown in Figure 9. In an actual costacked material, two-dimensional networks of K ions, which are close to superimposition of the atomic positions at z = 1 in the succeeding layer unit with the lateral stacking shift on those at z = 0 in the preceding layer unit, are probably present in the internanosheet galleries. In the Ti0.91O2MnO2 and Ca2Nb3O10Ti0.91O2 nanosheet systems, two atomic arrangements at z = 1 and z = 0 may compromise with each other because of somewhat similar basal surfaces in Figure 9a and Figure 9b or because of the presence of K ions alone in Figure 9a and Figure 9c. The mixed-layer stacking may be driven by fairly low repulsive interaction energy between the two different kinds of nanosheet and by realizable atomic arrangement of boundary planes in the Ti0.91O2MnO2 and Ca2Nb3O10Ti0.91O2 systems. 8564



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the optimum number of stacking nanosheets may be reflected in the coflocculation state. Various restacked nanosheets are reported to exhibit unique and interesting physical properties. Furthermore, the materials made from multiple nanosheets18,4951 or multiple layers5256 using nanosheets as a building block are reported to show an even greater variety of attractive properties. Information about selfassembled multinanosheet structures reported in this work may be useful for understanding and designing various materials including those of multiple layers. As the origin of the characteristics has not yet been fully elucidated, further investigation of the stacking mode in other binary or multinary systems is desired.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Addresses †

Division of Functional Materials and Nano Devices, Ningbo Institute of Materials Technology and Engineering, the Chinese Academy of Sciences, Ningbo 315201, People’s Republic of China.

Figure 9. Atomic arrangement at z = 0 of the fundamental units of (a) KTi0.91O2, (b) KMnO2, and (c) KCa2Nb3O10. Green and blue circles represent partially occupied potassium ions and partially occupied H2O, respectively.

In the case of the Ca2Nb3O10MnO2 nanosheet system, on the other hand, two different atomic arrangements at a boundary plane seem to be difficult to compromise with each other, as H2O molecules in Figure 9b appear to interfere with K ions in Figure 9c. Such substantial differences in structure of two kinds of layer units and/or possible high repulsive interaction energy between two different kinds of nanosheets may result in significant misfit energy in the binary nanosheet system, and the mixed-layer structure may be considerably destabilized. Another possible explanation for the variation in coflocculation behavior may be related to the dispersion state of the nanosheets in colloidal suspensions: spatial separation or homogeneous distribution of two kinds of nanosheets. Recent reports describe anisotropic colloidal particles with a peculiar two-dimensional morphology organizing into lyotropic liquid crystals.46,47 Multicomponent colloids containing plural kinds of particles with different shapes and physical properties can form a variety of liquid structures.48 The colloidal dispersion state in the binary nanosheet system can vary with the individual system. Two kinds of nanosheets in the Ca2Nb3O10MnO2 system may be spatially separated by microphase separation in the dispersion, while more uniform mixing of crystallites may appear in the Ti0.91O2MnO2 and Ca2Nb3O10Ti0.91O2 systems. The difference between the stacking behavior in the intermediate range, the two-phase stacking (2P) in the Ti0.91O2MnO2 system, and the two-phase coexistence (2C) in the Ca2Nb3O10Ti0.91O2 system has not yet been fully clarified. The domain structure in the dispersion, i.e., uniform domains or domains with differences in composition, diffusion rates of the nanosheets in the dispersion, or

’ ACKNOWLEDGMENT We acknowledge Dr. Katsuo Kato for his computer programs. This work was supported partially by the World Premier International Research Center (WPI) Initiative on Materials Nanoarchitectonics, MEXT, Japan, and CREST of the Japan Science and Technology Agency (JST). ’ REFERENCES (1) Sasaki, T.; Watanabe, M.; Hashizume, H.; Yamada, H.; Nakazawa, H. J. Am. Chem. Soc. 1996, 118, 8329. (2) Sasaki, T.; Watanabe, M. J. Am. Chem. Soc. 1998, 120, 4682. (3) Treacy, M. M. J.; Rice, S. B.; Jacobson, A. J.; Lewandowski, J. T. Chem. Mater. 1990, 2, 279. (4) Ebina, Y.; Sasaki, T.; Watanabe, M. Solid State Ionics 2002, 151, 177. (5) Schaak, R. E.; Mallouk, T. E. Chem. Mater. 2002, 14, 1455. (6) Omomo, Y.; Sasaki, T.; Wang, L.; Watanabe, M. J. Am. Chem. Soc. 2003, 125, 3568. (7) Takagaki, A.; Sugisawa, M.; Lu, D.; Kondo, J. N.; Hara, M.; Domen, K.; Hayashi, S. J. Am. Chem. Soc. 2003, 125, 5479. (8) Ida, S.; Ogata, C.; Unal, U.; Izawa, K.; Inoue, T.; Altuntasoglu, O.; Matsumoto, Y. J. Am. Chem. Soc. 2007, 129, 8956. (9) Fukuda, K.; Nakai, I.; Ebina, Y.; Ma, R.; Sasaki, T. Inorg. Chem. 2007, 46, 4787. (10) Ozawa, T. C.; Fukuda, K.; Akatsuka, K.; Ebina, Y.; Sasaki, T. Chem. Mater. 2007, 19, 6575. (11) Fukuda, K.; Akatsuka, K.; Ebina, Y.; Ma, R.; Takada, K.; Nakai, I.; Sasaki, T. ACS Nano 2008, 2, 1689. (12) Akatsuka, K.; Takanashi, G.; Ebina, Y.; Sakai, N.; Haga, M.; Sasaki, T. J. Phys. Chem. Solids 2008, 69, 1288. (13) Ozawa, T. C.; Fukuda, K.; Akatsuka, K.; Ebina, Y.; Sasaki, T.; Kurashima, K.; Kosuda, K. J. Phys. Chem. C 2008, 112, 1312. (14) Ozawa, T. C.; Fukuda, K.; Akatsuka, K.; Ebina, Y.; Sasaki, T.; Kurashima, K.; Kosuda, K. J. Phys. Chem. C 2008, 112, 17115. (15) Ozawa, T. C.; Fukuda, K.; Akatsuka, K.; Ebina, Y.; Kurashima, K.; Sasaki, T. J. Phys. Chem. C 2009, 113, 8735. (16) Dong, X.; Osada, M.; Ueda, H.; Ebina, Y.; Kotani, Y.; Ono, K.; Ueda, S.; Kobayashi, K.; Takada, K.; Sasaki, T. Chem. Mater. 2009, 21, 4366. 8565


The Journal of Physical Chemistry C (17) Jacobson, A. J. Comprehensive Supramolecular Chemistry; Alberti, G., Bein, T., Eds.; Elsevier Science: Oxford, U.K., 1996; Vol. 7, pp 315335. (18) Ma, R.; Sasaki, T. Adv. Mater. 2010, 22, 5082. (19) Ebina, Y.; Sasaki, T.; Harada, M.; Watanabe, M. Chem. Mater. 2002, 14, 4390. (20) Wang, L.; Takada, K.; Kajiyama, A.; Onoda, M.; Michiue, Y.; Zhang, L.; Watanabe, M.; Sasaki, T. Chem. Mater. 2003, 15, 4508. (21) Chen, Y.; Zhao, X.; Ma, H.; Ma, S.; Huang, G.; Makita, Y.; Bai, X.; Yang, X. J. Solid State Chem. 2008, 181, 1684. (22) Onoda, M.; Liu, Z.; Takada, K.; Sasaki, T. J. Appl. Crystallogr. 2009, 42, 22. (23) Hendricks, S.; Teller, E. J. Chem. Phys. 1942, 10, 147. (24) Kakinoki, J.; Komura, Y. J. Phys. Soc. Jpn. 1952, 7, 30. (25) Kakinoki, J.; Komura, Y. Acta Crystallogr. 1965, 19, 137. (26) Kakinoki, J. Acta Crystallogr. 1967, 23, 875. (27) Onoda, M.; Wang, L.; Takada, K.; Sasaki, T. Philos. Mag. 2007, 87, 2767. (28) Onoda, M.; Ebina, Y.; Sasaki, T. J. Appl. Crystallogr. 2009, 42, 1062. (29) Wang, Y.; Sun, C.; Yan, X.; Xiu, F.; Wang, L.; Smith, S. C.; Wang, K. L.; Lu, G. Q.; Zou, J. J. Am. Chem. Soc. 2011, 133, 695. (30) Brindley, G. W. Crystal Structures of Clay Minerals and their X-ray Identification; Brindley, G. W., Brown, G., Eds.; Mineralogical Society: London, 1980; pp 125195. (31) Kato, K.; Kosuda, K.; Koga, T.; Nagasawa, H. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1990, 46, 1587. (32) Kato K. FU1, FV1, SQ1, and SQ3, personal communication, 1991. (33) Kato K. PPROFL, personal communication, 1998. (34) Cagliotti, G.; Paoletti, A.; Ricci, F. P. Nucl. Instrum. Methods 1958, 3, 223. (35) March, A. Z. Kristallogr. 1932, 81, 285. (36) Dollase, W. A. J. Appl. Crystallogr. 1986, 19, 267. (37) Hill, R. J.; Howard, C. J. J. Appl. Crystallogr. 1987, 20, 467. (38) Rietveld, H. M. J. Appl. Crystallogr. 1969, 2, 65. (39) McCusker, L. B.; Von Dreele, R. B.; Cox, D. E.; Lou€er, D.; Scardi, P. J. Appl. Crystallogr. 1999, 32, 36. (40) Treacy, M. M. J.; Newsam, J. M.; Deem, M. W. Proc. R. Soc. London, Ser. A 1991, 433, 499. (41) Kogure, T.; Kameda, J.; Matsui, T.; Miyawaki, R. Am. Mineral. 2006, 91, 1363. (42) Takada, K.; Onoda, M.; Argyriou, D. N.; Choi, Y.-N.; Izumi, F.; Sakurai, H.; Takayama-Muromachi, E.; Sasaki, T. Chem. Mater. 2007, 19, 3519. (43) Takada, K.; Onoda, M.; Choi, Y.-N.; Argyriou, D. N.; Izumi, F.; Sakurai, H.; Takayama-Muromachi, E.; Sasaki, T. Chem. Mater. 2009, 21, 3693. (44) Onoda, M.; Takada, K.; Sasaki, T. J. Appl. Crystallogr. 2010, 43, 677. (45) Although we used the term “one-dimensional two-phase coexistence model” in the previous paper for the same model as that described in section 3.4, we found that this term is well-suited for the model described in section 3.5. We therefore adopted the revised term “one-dimensional two-phase stacking model” for the model described in section 3.4 in the present work. (46) Van der Kooij, F. M.; Lekkerkerker, H. N. W. J. Phys. Chem. B 1998, 102, 7829. (47) Miyamoto, N.; Nakato, T. Adv. Mater. 2002, 14, 1267. (48) Miyamoto, N.; Nakato, T. Langmuir 2003, 19, 8057. (49) Osada, M.; Ebina, Y.; Takada, K.; Sasaki, T. Adv. Mater. 2006, 18, 295. (50) Sakai, N.; Fukuda, K.; Omomo, Y.; Ebina, Y.; Takada, K.; Sasaki, T. J. Phys. Chem. C 2008, 112, 5197. (51) Li, B.-W.; Osada, M.; Ozawa, T. C.; Ebina, Y.; Akatsuka, K.; Ma, R.; Funakubo, H.; Sasaki, T. ACS Nano 2010, 4, 6673. (52) Fang, M.; Kaschak, D. M.; Sutorik, A. C.; Mallouk, T. E. J. Am. Chem. Soc. 1997, 119, 12184.

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(53) Kim, H.-N.; Keller, S. W.; Mallouk, T. E. Chem. Mater. 1997, 9, 1414. (54) Sasaki, T.; Ebina, Y.; Tanaka, T.; Harada, M.; Watanabe, M.; Decher, G. Chem. Mater. 2001, 13, 4661. (55) Wang, L.; Omomo, Y.; Sakai, N.; Fukuda, K.; Nakai, I.; Ebina, Y.; Takada, K.; Watanabe, M.; Sasaki, T. Chem. Mater. 2003, 15, 2873. (56) Akatsuka, K.; Ebina, Y.; Muramatsu, M.; Sato, T.; Hester, H.; Kumaresan, D.; Schmehl, R. H.; Sasaki, T.; Haga, M. Langmuir 2007, 23, 6730.

’ NOTE ADDED AFTER ASAP PUBLICATION This paper was published to the Web on April, 1, 2011, with an error to the heading of Table 1. The corrected version was reposted on April 13, 2011.

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X-ray Diffraction Study on Restacked Flocculates from Binary Colloidal

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