Continuous Change of Second-order Nonlinear Optical Activity in a

Aug 1, 2008 - 0.7, second harmonic generation (SHG) is observed, and the SH light intensity (ISH) gradually increases with increasing x. The crystal ...
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J. Phys. Chem. C 2008, 112, 13095–13098

13095

Continuous Change of Second-order Nonlinear Optical Activity in a Cyano-bridged Coordination Polymer Shin-ichi Ohkoshi,*,† Shintaro Saito,† Tomoyuki Matsuda,† Tomohiro Nuida,† and Hiroko Tokoro†,‡ Department of Chemistry, School of Science, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 Japan and PRESTO, JST, 4-1-8 Honcho Kawaguchi, Saitama, 332-0012, Japan ReceiVed: March 11, 2008; ReVised Manuscript ReceiVed: April 25, 2008

In this work, we continuously control the second-order nonlinear optical activity by tuning the piezoelectric property in a series of rubidium manganese hexacyanoferrates, RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O. Above x ) 0.7, second harmonic generation (SHG) is observed, and the SH light intensity (ISH) gradually increases with increasing x. The crystal structures of this series are analyzed using Rietveld analysis and the maximum entropy method. The crystal structural data shows that the difference between the existing probability of the Rb ion in interstitial site-1 (PRb1) and site-2 (PRb2), PRb1 - PRb2, gradually increases with increasing x. Because the difference between PRb1 and PRb2 produces a 4j rotoinversion, the PRb1 - PRb2 value is considered to be related to the magnitude of piezoelectricity or SH susceptibility (χSH). From the analysis of the χSH tensors elements, the observed x dependence of ISH can be explained by the PRb1 - PRb2 value. Such a tunable system of second-order nonlinear optical activity is very rare in condensed matters. 1. Introduction effect1

A second-order nonlinear optical is observed in piezoelectric crystals, that is, materials with a noncentrosymmetric crystal structure, in the electric dipole transition approximation. As piezoelectric materials, barium titanate (BaTiO3), rochelle salt (KNaC4H4O6), potassium dihydrogen phosphate (KH2PO4), etc. are well-known.2 To control the second-order nonlinear optical activity, tuning of the piezoelectricity is necessary. Our studies have focused on a new way to tune piezoelectricity using a coordination polymer. In our research, we have intensely examined cyanobridged coordination polymers composed of -MA-NC-MB- (MA and MB are transition metal ions), so-called Prussian blue analogs.3–6 A typical Prussian blue analog has a face-centered cubic (fcc) structure of MAII[MBIII(CN)6]2/3 · zH2O. In this structure, one third of [MBIII(CN)6] is vacant, and the MA ion around the vacancy is coordinated by ligand water molecules, whereas the vacancy site of [MBIII(CN)6] is occupied by zeolitic water molecules.4 In contrast, when an alkali (A) ion is present during the synthesis, Prussian blue analogs take the AIMAII[MBIII(CN)6]-type structure. Second harmonic generation (SHG)1 has been observed in compounds with this structure.3o This fact suggests that the centrosymmetric structure of Prussian blue analogs can be broken by the penetration of the A ion. Thus, the following questions come to mind: (i) what is the mechanism of the second-order nonlinear optical activity in an AIMAII[MBIII(CN)6]-type compound? (ii) According to the change in x of AIxMAII[MBIII(CN)6](x+2)/3 · zH2O, does second-order nonlinear optical activity develop suddenly or gradually? In other words, does a material suddenly or gradually become a piezoelectric against changing x? If the piezoelectric property gradually changes, we can control the second-order nonlinear optical activity. In the present work, we prepared a series of RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O and investigated the x depen* To whom correspondence should be addressed. Phone: +81-3-58414331; fax: +81-3-3812-1896; e-mail: [email protected]. † The University of Tokyo. ‡ PRESTO.

dence of the SH light intensity. Moreover, detailed crystal structures were analyzed by Rietveld analysis and the maximum entropy method (MEM), and the results are used to discuss the mechanism of second-order nonlinear optical activity. 2. Experimental Section Materials and Characterization. The samples, RbxMn[Fe(CN)6](x+2)/3 · zH2O, were prepared by reacting an aqueous solution (0.1 mol dm-3) of MnCl2 with a mixed aqueous solution of RbCl (0.1 - 1.6 mol dm-3) and K3[Fe(CN)6] (0.1 mol dm-3) to yield precipitates.5 The formulas of the prepared compounds were confirmed by inductively coupled plasma mass spectrometryandastandardmicroanalyticalmethod;Rb0.58Mn[Fe(CN)6]0.86 · 2.3H2O (x ) 0.58), Rb0.61Mn[Fe(CN)6]0.87 · 2.2H2O (x ) 0.61), Rb0.64Mn[Fe(CN)6]0.88 · 1.9H2O(x ) 0.64),Rb0.67Mn[Fe(CN)6]0.89 · 1.7H2O (x ) 0.67), Rb0.73Mn[Fe(CN)6]0.91 · 1.5H2O (x ) 0.73), Rb0.76Mn[Fe(CN)6]0.92 · 1.2H2O(x ) 0.76),Rb0.79Mn[Fe(CN)6]0.93 · 1.0H2O (x ) 0.79), Rb0.82Mn[Fe(CN)6]0.94 · 1.1H2O (x ) 0.82), Rb0.88Mn[Fe(CN)6]0.96 · 0.6H2O(x ) 0.88),Rb0.91Mn[Fe(CN)6]0.97 · 0.4H2O (x ) 0.91), and Rb0.94Mn[Fe(CN)6]0.98 · 0.2H2O (x ) 0.94). The composition was controlled by the concentration of the RbCl aqueous solution. In the infrared (IR) spectra of these samples, the CN stretching peaks were observed at 2150-2152 cm-1 (strong) and 2071-2079 cm-1 (very weak). The former range was assigned to the CN group of FeIII-CN-MnII, whereas the latter was assigned to the CN group of FeII-CN-MnII. A small amount (∼2%) of RbI2MnII[FeII(CN)6] · 3.5H2O was contained (Supporting Information Table S1). The scanning electron microscope images showed that the prepared samples consisted of cubic microcrystals with particle sizes of ca. 2 µm; 1.8 ( 0.5 µm (x ) 0.58), 2.3 ( 0.9 µm (x ) 0.61), 1.6 ( 0.5 µm (x ) 0.64), 2.9 ( 1.6 µm (x ) 0.67), 2.0 ( 0.7 µm (x ) 0.73), 2.0 ( 0.6 µm (x ) 0.76), 1.9 ( 0.5 µm (x ) 0.79), 1.9 ( 0.6 µm (x ) 0.82), 1.2 ( 0.5 µm (x ) 0.88), 1.4 ( 0.5 µm (x ) 0.91), and 2.1 ( 0.7 µm (x ) 0.94). SHG Measurements. SHG measurements were conducted in the reflection mode using the following equipment. Incident light

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Ohkoshi et al.

Figure 1. (a) The photograph of SH light (532 nm) for x ) 0.58, 0.79, 0.82, and 0.94 (the size of the pictures are 6 mm square). (b) Rb content (x) dependence of SH activity (incident light ) 1064 nm) at room temperature.

was provided by a Q-switched Nd/YAG laser (HOYA Continuum, Minilite II, wavelength of 1064 nm, pulse duration of 10 ns, repetition rate of 5 Hz). SH light (532 nm) was detected by a photomultiplier tube (Hamamatsu, R329-02) through color filters and a bandpass filter. The signal of the photomultiplier was collected by a boxcar integrator (Stanford Research Systems SR250) followed by a computer. The angles of incidence and reflection on the sample were 45°. For the SHG measurement, powder form samples were loaded into a glass cell with a thickness of 0.15 mm. The incident and SH light did not pass through the sample to the backside of the cell. Supporting Information Figure S1 describes a detailed setup for the SHG measurements. The absolute value of the SH light intensity was estimated by comparing to the SH light intensity of potassium dihydrogen phosphate.7 Rietveld Analysis and MEM. The X-ray powder diffraction (XRD) patterns were measured by a Rigaku RINT2100 with Cu KR radiation (λ ) 1.5406 Å) at 293 K. Rietveld analyses were performed by the RIETAN-FP.8a The electron density distributions were calculated with the unit cell divided into 100 × 100 × 100 pixels by MEM using the PRIMA8b program using the structural information obtained from Rietveld refinement. The calculated electron density distributions were visualized by the VESTA program. The isosurface was drawn for an equidensity level of 0.8 eÅ-3, and the contours were drawn from 0 to 8 eÅ-3.

Figure 2. XRD patterns and Rietveld analyses for x ) 0.58 (a), 0.79 (b), and 0.94 (c). Red dots, black line, and blue line are the observed plots, calculated pattern, and their difference, respectively. Green bars represent the calculated positions of the Bragg reflections. Miller indices of black and red are reflections from Fm3jm and F4j3m, respectively. (d) Unit cell used for Rietveld analyses as the initial atomic positions based on ref 5h.

3. Results and Discussion Second Harmonic Generation. Green light (532 nm) radiation was observed with RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O at room temperature as shown in the photographs of Figure 1a when the incident light (1064 nm) was put into the sample. The intensity of the 532 nm light increased with the square of the incident light (Supporting Information Figure S2), indicating that the observed 532 nm light is clearly SH light. Figure 1b shows the SH light intensity (ISH) versus x plots. The samples for x ) 0.58-0.67 did not radiate SH light, but the samples for x g 0.73 radiated SH light, and the ISH value gradually increased with increasing x. Crystal Structure. To understand the gradual increase of ISH against x, the crystal structures of the samples were investigated. As examples, the XRD patterns of the samples for x ) 0.58, 0.79, and 0.94 are shown in Figure 2, panels a-c, respectively. In every sample, XRD spectra composed of a single phase. In x ) 0.58,

the reflections of (200), (220), (222), (400), (420), etc. due to Fm3jm were observed. In contrast, for x ) 0.79, the characteristic reflections from F4j3m, for example, (111), (311), (331), (511), and (333) were observed in addition to the above reflections. In x ) 0.94, the intensity of the characteristic reflection from F4j3m increased with increasing x. The XRD patterns of the other samples are shown in Supporting Information Figure S3. To conduct Rietveld analyses of the XRD patterns, the unit cell in Figure 2d was used as the initial atomic positions, which were based on the data of a single crystal of x ) 0.61.5h Tables 1, S2, and S3 list the occupancy of each atom, result of the Rietveld analyses, and the atomic coordinates, respectively. The distribution of the electron density was determined by MEM. Figure 3 shows the electron density maps obtained by MEM, where the isosurface is drawn for an equidensity level of 0.8 eÅ-3. In x ) 0.58, the interstitial sites of site-1 and site-2 were occupied with a tetrapod-shaped

Optical Activity in a Cyano-bridged Coordination Polymer

J. Phys. Chem. C, Vol. 112, No. 34, 2008 13097

TABLE 1: The Occupancy for Each Atom of RbxMn[Fe(CN)6](x+2)/3 · zH2O x Rb1 Rb2 Fe Mn C N O1a O2a O3a a

0.58

0.61

0.64

0.67

0.73

0.76

0.79

0.82

0.88

0.91

0.94

0.294 0.286 0.86 1 0.86 0.86 0.14 0.18 0.19

0.321 0.289 0.87 1 0.87 0.87 0.13 0.13 0.23

0.376 0.264 0.88 1 0.88 0.88 0.12 0.13 0.16

0.396 0.274 0.89 1 0.89 0.89 0.11 0.14 0.12

0.520 0.210 0.91 1 0.91 0.91 0.09 0.12 0.12

0.588 0.172 0.92 1 0.92 0.92 0.08 0.11 0.07

0.694 0.096 0.93 1 0.93 0.93 0.07 0.07 0.07

0.729 0.091 0.94 1 0.94 0.94 0.06 0.13 0.06

0.829 0.051 0.96 1 0.96 0.96 0.04 0.06 0.03

0.875 0.035 0.97 1 0.97 0.97 0.03 0.05 0.01

0.902 0.038 0.98 1 0.98 0.98 0.02 0.02 0

O1; oxygen atom of ligand water molecule. O2 and O3; oxygen atoms of zeolitic water molecules.

Figure 3. Electron density maps determined by MEM for x ) 0.58, 0.61, 0.64, 0.67, 0.73, 0.76, 0.79, 0.82, 0.88, 0.91, and 0.94. Contours are drawn from 0 to 8 eÅ-3. Isosurface is drawn for an equidensity level of 0.8 eÅ-3, which is drawn by yellow color for clarity.

electron distribution, which were caused by the coexistence of Rb ion and zeolitic waters. In x ) 0.79, the electron density at site-1 took a large sphere-shaped distribution, whereas that at site-2 took a small sphere-shaped distribution. Then, in x ) 0.94, only site-1 was occupied by a Rb ion, and site-2 was empty. Figure 4a plots the existing probabilities of the Rb ion at site-1 (PRb1) and site-2 (PRb2). For x ) 0.58, PRb1 and PRb2 are the same. As x increases, PRb1 gradually increases, but PRb2 decreases. The reason for the penetration of the Rb ion in an alternative fashion is considered to be an electrostatic repulsion between Rb cations. Mechanism of SHG. When the difference between PRb1 and PRb2 is zero, the space group takes a centrosymmetric structure of Fm3jm. In contrast, when the Rb ion penetrates the interstitial site in an alternative fashion, the position of the Rb ion produces a 4j rotoinversion operator, and hence, the crystal structure has the possibility of a piezoelectric fcc structure of F4j3m and generating second-order nonlinear optical activity. That is, with increasing PRb1 - PRb2, the magnitudes of piezoelectricity and SH susceptibility (χSH) increase. It is known that χSH is related to the SH polarization (QSH) as follows: QSH ) χSH i ijk EjEk, where i, j, and k are the

coordinates, χSH ijk is the tensor element of the SH susceptibility, and Ej and Ek are the electric field of the incident wave. The F4j3mSH SH SH type space group has nonzero elements of χxyz , χyzx, and χzxy , but SH SH these three elements have the same value, that is, χxyz ) χyzx ) SH χzxy . Thus, the SH susceptibility is described as follows:

( )( QSH x

0 0 0 χSH xyz 0

QSH ) 0 0 0 0 y QSH z

0 0 0 0

0

χSH xyz 0 0

χSH xyz

)

() E2x

E2y

E2z 2EyEz 2EzEx 2ExEy

(1)

The ISH value for powder-form samples can be described by eq 2

ISH ∝

l2 SH 2 0 2 2 πr (χ ) (I ) sin 2l r xyz

( )

(2)

where r, I0, and l are the particle size of the sample, the intensity of incident light, and the coherent length,9 respectively. The

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Ohkoshi et al. ISH generated from RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O are available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 4. The x dependence of the existing probabilities of the Rb ion at site-1 (PRb1) and site-2 (PRb2). (a) PRb1 and PRb2. (b) (PRb1 PRb2)2.

derivation of this equation is described in the Supporting Information. On the basis of eq 2 and the observed ISH values, the χxyz values were estimated as follows: 0 fm V-1 (x ) 0.58, 0.61, 0.64, and 0.67), 9.9 fm V-1 (x ) 0.73), 14.9 fm V-1 (x ) 0.76), 20.9 fm V-1 (x ) 0.79), 23.9 fm V-1 (x ) 0.82), 28.6 fm V-1 (x ) 0.88), 29.4 fm V-1 (x ) 0.91), and 31.8 fm V-1 (x ) 0.94). Because χSH is related to PRb1 - PRb2, the ISH value should be related to (PRb1 - PRb2)2, based on eq 2. Figure 4b shows the (PRb1 - PRb2)2 versus x plots, which well reproduce the observed ISH versus x plots in Figure 1b, indicating that the fine-tuning of the SHG activity is explained by the continuous change in the PRb1 - PRb2 value. 4. Conclusion In this work, we studied the x dependence of the SH light intensity in RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O. In this series, the penetrated position of Rb ion was tuned and the second-order nonlinear susceptibility continuously changed depending on x. Such a tunable system with second-order nonlinear optical activity is very rare in condensed matters. Acknowledgment. The present research was supported in part by a Grant for the Global COE Program for Chemistry Innovation, a Grant-in-Aid for Scientific Research (B), and a Grant-in-Aid for Exploratory Research from JSPS, JSPS, and RFBR under the Japan-Russia Research Cooperative Program, Iketani Science and Technology Foundation, the Kurata Memorial Hitachi Science and Technology Foundation, The Murata Science Foundation, and CASIO Science Promotion Foundation. Supporting Information Available: The formulas of synthesized RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O, schematic diagram of the SHG setup, SH-light intensity versus incident light intensity for RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O, Rietveld analyses for RbIxMnII[FeIII(CN)6](x+2)/3 · zH2O (x ) 0.61, 0.64, 0.67, 0.73, 0.76, 0.82, 0.88, and 0.91), and derivation of the equation of

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(9) Coherent length of SHG in powder-form samples in the present series is estimated using the equation, l ) λSH/|4(NSH-N0)|, where N0 and NSH are refractive indices at the incident light (1064 nm) and SH light (532 nm), respectively. Here, N0 at 1064 nm and NSH at 532 nm were estimated by the dielectric constants of ′ ) 1.69 and ′′ ) 0.003 at 1064 nm, and ′ ) 1.76 and ′′ ) 0.01 at 532 nm were obtained by spectroscopic ellipsometry.5f Consequently, the estimated l value is 9.9 µm.

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