Metal Dilution Effects on the Spin-Crossover Properties of the Three

Jul 14, 2005 - Juliusz Wolny , Isabelle Faus , Jennifer Marx , Rudolf Rüffer , Aleksandr Chumakov , Kai Schlage , Hans-Christian Wille , Volker Schü...
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J. Phys. Chem. B 2005, 109, 14859-14867

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Metal Dilution Effects on the Spin-Crossover Properties of the Three-Dimensional Coordination Polymer Fe(pyrazine)[Pt(CN)4] Takeshi Tayagaki,†,‡,# Ana Galet,§ Ga´ bor Molna´ r,† M. Carmen Mun˜ oz,§ Antoine Zwick,| Koichiro Tanaka,‡ Jose´ -Antonio Real,*,⊥ and Azzedine Bousseksou*,† Laboratoire de Chimie de Coordination, CNRS UPR-8241, 205 route de Narbonne, 31077 Toulouse Cedex 4, France, Department of Physics, Kyoto UniVersity, Kyoto 606-8502 Japan, Departament de Fı´sica Aplicada, UniVersitat Polite` cnica de Vale` ncia, Camino de Vera s/n, 46022 Vale` ncia, Spain, Laboratoire de Physique des Solides de Toulouse, CNRS UMR-5477, 118 route de Narbonne, UniVersite Paul Sabatier, 31066 Toulouse, France, and Departament de Quı´mica Inorga´ nica/Institut de Ciencia Molecular, UniVersitat de Vale` ncia, C/Doctor Moliner 50, 46100 Burjassot, Spain ReceiVed: April 26, 2005

The 1A1 / 5T2 spin transition has been investigated in the solid solutions of FexM1-x(pyrazine)[Pt(CN)4] (M ) Ni or Co, 0 e x e 1) having a three-dimensional polynuclear structure. Both Ni and Co dilutions tend to decrease the hysteresis width and smooth the transition curves. The enthalpy (entropy) change associated with the spin transition was found to decrease from 26 kJ mol-1 (84 J K-1 mol-1) for x ) 1 to 12 kJ mol-1 (47 J K-1 mol-1) for 47% Co dilution and to 15 kJ mol-1 (54 J K-1 mol-1) for 59% Ni dilution. Raman spectroscopy revealed a mixed one- and two-mode behavior in the solid solutions. For the first time, a correlation between vibrational frequencies exhibiting one-mode behavior and the entropy change, which drives the spin crossover, is established.

Introduction Spin-crossover complexes have attracted much attention recently from the fundamental point of view and also for their potential applications in molecular display, memory, and switching devices.1,2 Concerning their application for memory devices, it is expected that the complexes exhibit a first-order high-spin (HS) / low-spin (LS) transition accompanied by a large thermal hysteresis loop around room temperature.2a The hysteresis behavior is thought to appear in these materials due mainly to long-range elastic interactions between the spinchanging metal centers.3 To date, numerous highly cooperative spin-crossover materials have been obtained by different chemical synthetic strategies, one of the most successful being the introduction of spin-crossover centers in polymeric networks.4 For designing spin-crossover materials with strong cooperativity, the origin of the interactions should be clarified. In the past, a number of studies have been carried out for understanding the microscopic mechanism of cooperativity1a,5 and several theoretical models have been developed and phenomenologically accounted for the experimental observations.3,6-12 The main thermodynamic models are based on lattice dynamics theory indicating two possible sources of the cooperativity: elastic energy change due to the expansion of the lattice upon spin crossover3 and/or vibrational entropy change due to the anharmonicity of vibrations coupled with the lattice expansion.9,12b A useful way to learn about interactions between spincrossover centers is to move them away from each other by * To whom correspondence should be addressed: J. A. Real ([email protected]) and A. Bousseksou ([email protected]). † Laboratoire de Chimie de Coordination, CNRS UPR-8241. ‡ Department of Physics, Kyoto University. # Present address: Department of Applied Physics, University of Tokyo. § Departament de Fı´sica Aplicada, Universitat Polite ` cnica de Vale`ncia. | Laborataire de Physique des Solides de Toulouse, CNRS UMR-5477. ⊥ Departament de Quı´mica Inorganica/Institut de Cienca Molecular, Universitat de Vale`ncia.

diluting them. This technique gives a control on the strength of the interactions and the number of interacting centers as well. Metal dilution effects on the spin crossover have been studied earlier in some complexes exhibiting thermal spin crossover.13-18 Usually, metal dilution was found to influence the spin equilibrium temperature (Teq, defined as the temperature for which GHS - GLS ) 0) and the completeness of the spin conversion. More importantly, the spin-crossover behavior became more gradual, and for hysteretic spin transitions, the width of the hysteresis loop decreased and finally vanished for increasing dilutions. To date, the effects of metal dilution have been investigated mainly on mononuclear complexes.13-16 A notable exception is the two-dimensional coordination polymer Fe(btr)2(NCS)2‚ H2O (btr ) 4,4′-bis(1,2,4-triazole)). A detailed experimental and theoretical study on this complex revealed that the hysteresis width as well as the enthalpy and entropy changes associated with the spin crossover (∆H and ∆S) decreases almost linearly with increasing dilution for both Fe/Ni and Fe/Co mixed-crystal systems.17 Moreover, in the case of Co dilution, a downward shift of Teq and the appearance of a residual HS fraction at low temperatures have been evidenced. These latter observations, specific to the nature of the diluting metal, were explained by taking into account the size differences of the metal ions. The variation of ∆H and the hysteresis width (i.e., the cooperativity) upon dilution in FexM1-x(btr)2(NCS)2‚H2O was explained by changes in the elastic energy of the lattice.17 In this theory, the energy difference between the HS and LS states depends on the chemical pressure of the substituent ions and therefore ∆H changes with their concentration.3 The cooperativity arises mainly from long-range elastic interactions between the HS and the LS complexes and is therefore determined by the concentration of the spin-crossover ions (Fe(II)) in the mixed crystal.3,12 The dilution dependence of ∆S was associated with entropy changes of vibrational origin.17 It was suggested that this

10.1021/jp0521611 CCC: $30.25 © 2005 American Chemical Society Published on Web 07/14/2005

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Figure 1. Perspective view of the structure of Fe(pyrazine)[Pt(CN)4].

dependence would result from coupling of intramolecular vibrational modes with lattice modes. However, the available experimental data are by no means sufficient to more fully evaluate this hypothesis. The main objective of the present work was therefore to study experimentally metal dilution effects on the vibrational properties of spin-crossover polymers. To accomplish this goal, we decided to investigate Ni(II) and Co(II) metal dilution effects on the three-dimensional coordination polymer Fe(pyrazine)[Pt(CN)4] using magnetic susceptibility measurements, powder X-ray diffraction (PXRD), differential scanning calorimetry (DSC), and Mo¨ssbauer and Raman spectroscopies. This complex belongs to a family of compounds of the formula Fe(pyrazine)[MII(CN)4]‚nH2O (MII ) Ni, Pd or Pt), which are known to exhibit thermal- and pressure-induced spin crossover with strong cooperativity.19 The spin transition from the HS (S ) 2) to the LS state (S ) 0) of Fe(II) ions is accompanied by large hysteresis loops (∼20-30 K) and a pronounced color change in each sample. The HS crystal structure of the Pd and Pt complexes (with n ) 2) has been determined by PXRD.19a This structure is tetragonal (P4/m) and consists of planar polymeric sheets formed from square-planar tetracyano-metalate ions bridged by six-coordinate Fe(II) ions. The iron ions are bridged by bidentate pyrazine ligands leading to a three-dimensional network (Figure 1). Experimental Section Preparation of the Samples. The preparation of the pure compound was described previously in ref 19a. The samples of diluted compounds FexM1-x(pyrazine)[Pt(CN)4] (M ) Ni(II) or Co(II)), noted hereafter as [FexM1-x], were prepared according to the same procedure, replacing the Fe(II) FeCl2‚ 4H2O by a mixture of Fe(II) FeCl2‚4H2O and Ni(II) (or Co(II)) NiCl2‚6H2O (CoCl2‚6H2O) in given ratios (2%, 5%, 10%, 15%, 20%, 25%, 30%, 40%, 50%, 75% of Ni(II) (Co(II))). Iron and nickel (cobalt) fractions were determined from atomic absorption as well as electron microprobe analysis (see Supporting Information). Before the measurements, the samples were heated to 150 °C for 30 min in nitrogen atmosphere. Thermogravimetry analysis proved that this procedure was necessary to remove two molecules of crystal water (see Supporting Information in ref 19a). These dehydrated samples exhibit an “improved” spincrossover behavior in that the transition becomes complete, Teq shifts to room temperature, and the hysteresis loop becomes wider, more abrupt (square-shaped), and reproducible over several cycles.

Tayagaki et al. Powder X-ray Diffraction. Powder diagrams of the pure and diluted compounds were collected at room temperature in the range 2° < 2θ < 60° on a Bruker D500 diffractometer using Cu KR radiation. Magnetic Measurements. The variable-temperature magnetic susceptibility measurements were carried out using a Quantum Design MPMS2 SQUID magnetotometer operating at 1 T magnetic field and at temperatures between 100 and 350 K. The susceptometer was calibrated with (NH4)2Mn(SO4)2‚12H2O. The independence of the susceptibility with regard to the applied magnetic field was checked at room temperature for each compound. Temperature was varied at a rate of 1 K min-1 in the heating and cooling modes. Experimental susceptibilities were corrected for diamagnetism of the constituent atoms by the use of Pascal’s constants. Mo1 ssbauer Spectroscopy. 57Fe Mo¨ssbauer spectra were obtained on a constant-acceleration spectrometer with a 50 mCi 57Co source. The absorber was a sample of ca. 50 mg of polycrystalline powder in a 2 cm diameter sample holder. Spectra were recorded at 300 and 80 K using a liquid nitrogen bath cryostat. A least-squares computer program was used to fit the Mo¨ssbauer parameters.20 Isomer shift is given with respect to metallic iron at room temperature. Differential Scanning Calorimetry. Calorimetric measurements were performed using a differential scanning calorimeter Mettler Toledo DSC821. Low temperatures were obtained with an aluminum block attached to the sample holder, refrigerated with a flow of liquid nitrogen, and stabilized at a temperature of 110 K. The sample holder was kept in a drybox under a flow of dry nitrogen gas to avoid water condensation. The measurements were carried out using around 20 mg of powdered sample sealed in aluminum pans with a mechanical crimp. Temperature and heat flow calibrations were made with standard samples of indium by using its melting transition (429.6 K, 28.45 J g-1). An overall accuracy of (0.2 K in temperature and (2% in the enthalpy is estimated. Molar enthalpy changes associated with the spin crossover of [FexM1-x] complexes (∆Hexp) were directly obtained from the DSC data by integrating the anomalous peak in the baseline subtracted curve. Then, using the relation ∆H ) ∆Hexp/x, we calculated ∆H relative to the spin conversion of 1 mol of Fe(II) ions. The entropy change relative to the spin conversion of 1 mol of Fe(II) ions was finally determined using the relationship ∆S ) ∆H/Teq. Raman Spectroscopy. A He-Ne laser was used for Raman excitation at 632.8 nm. The laser output power was kept at 5 mW. The exciting light was guided through an optical microscope and focused on the sample by a ×40, long working distance objective. Samples were enclosed under nitrogen atmosphere on the coldfinger of a liquid nitrogen cryostat. The scattered light was collected in backscattering configuration using the same objective. The collected light was dispersed by a triple monochromator (Dilor XY). Raman signals were detected by a liquid-nitrogen-cooled, charge-coupled-device detector. Typical integration times for a measurement were around 3-6 min. The polarization of the scattered light was not taken into account because of the polycrystalline nature of the samples. Results Powder X-ray Diffraction. Figure 2 shows selected roomtemperature powder diffractograms in the range from 10° to 60° (in twice the Bragg angle) of the pure and diluted compounds. The presence of well-defined Bragg reflections in

Fe(pyrazine)[Pt(CN)4]

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Figure 3. Mo¨ssbauer spectra of Fe(pyrazine)[Pt(CN)4] obtained at 300 and 80 K. (Lines represent least-squares fit on the experimental data.)

Figure 2. Room-temperature X-ray powder diffraction patterns of FexM1-x(pyrazine)[Pt(CN)4] (M ) Co or Ni) for selected values of x.

the pure Fe(II) and Co(II) diluted samples proves that these samples consist of well-crystallized phases. In the case of Ni(II) substituted samples, the reflections peak-off clearly from the flat background but are somewhat larger indicating a certain degree of structural disorder. The overall diffraction patterns of Ni(II) and Co(II) substituted samples and also of the mixed crystals were found to correspond well to the diffraction pattern of the pure Fe(II) compound. Moreover, it is possible to observe that any one of the (hkl) reflections observed to appear in the powder pattern of mixed crystals is located between the position for the pure Fe(II) compound on the left-hand side and the position for the pure Co(II) (or Ni(II)) compound on the righthand side. These findings show that all of these compounds are isostructural and that the character of solid solution (FexM1-x) can be assigned to the mixed crystals. Mo1 ssbauer Data. Figure 3 shows high- and low-temperature Mo¨ssbauer spectra of the pure Fe(II) complex. At 300 K (in the cooling mode), the Mo¨ssbauer spectrum consists of a single doublet with quadrupole splitting (1.159(5) mm s-1) and isomer shift (1.047(3) mm s-1). These values are typical of Fe(II) ions in the HS state (S ) 2). At 80 K, a new doublet appears with smaller quadrupole splitting (0.306(4) mm s-1) and lower isomer shift (0.439(2) mm s-1) values as expected for a LS state (S ) 0) of Fe(II) ions. Mo¨ssbauer spectra of the diluted complexes revealed only a slight dilution dependence of Mo¨ssbauer parameters as compared to the pure compound. However, the discussion of this point is not in the scope of the present paper. We shall only note that the residual HS fractions at 80 K never exceeded 10% for the mixed crystals and will therefore be neglected in the following analysis.

Figure 4. χT(Fe) vs T curves for some selected x values in the cooling (b, 2, 9, 1) and heating (O, 4, 0, 3) modes. (Lines are included to guide the eye.)

Magnetic Data. The χexpT product, where χexp is the molar magnetic susceptibility, as a function of temperature is determined from magnetic susceptibility measurements. The χexpT product contains Fe and Ni(II) (Co(II)) ions contributions as well. The HS fraction (γHS) is proportional to the iron only contribution (χFeT product), which is easily estimated by using the relationship χexpT ) xχFeT + (1 - x)χNi(Co)T, where χNi(Co) is the measured magnetic susceptibility in the pure Ni(II) (Co(II)) complex. The pure Fe(pyrazine)[Pt(CN)4] sample exhibits a spin transition with a large hysteresis loop around room temperature. When Fe(II) ions are substituted by Ni(II) or by Co(II) ions, the thermal spin-crossover behavior changes drastically. Figure 4 shows the temperature dependence of the HS fraction (γHS) for selected [FexNi1-x] samples. It is well-known that the observation of a hysteresis loop in γHS(T) is the consequence of the presence of a first-order phase transition. In that case, the equilibrium temperature (Teq) is replaced by the critical temperatures T1/2V and T1/2v, defined as the temperature where γHS ) 1/2 in the cooling and heating modes, respectively. The T1/2 values for the [FexNi1-x] and the [FexCo1-x] mixed-crystal series are summarized in parts a and b of Figure 5, respectively. In both cases, the main observation is that with decreasing values of x, the transition becomes more gradual and the width of the hysteresis decreases and finally disappears. We note, however,

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Figure 6. DSC curves of FexNi1-x(pyrazine)[Pt(CN)4] obtained for different x values (heating mode).

Figure 5. Evolution of the spin transition temperatures as a function of x in the cooling (b) and heating (O) modes in (a) FexNi1-x(pyrazine)[Pt(CN)4] and (b) FexCo1-x(pyrazine)[Pt(CN)4]. (Lines represent linear fit on the experimental data.)

that for very small Ni dilutions, the hysteresis width increases somewhat. It is interesting to note also that for the [FexCo1-x] system, the two critical temperatures, T1/2V (cooling mode) and T1/2v (heating mode), decrease by increasing x. If we assume, to a first approximation, that the spin equilibrium temperature can be expressed as Teq = (T1/2V + T1/2v)/2, it appears that the value of Teq decreases also with x. The behavior of the [FexNi1-x] mixed crystals is different in that only T1/2V was found to decrease with decreasing x, whereas the values of T1/2v and Teq show only a slight downshift between 1 > x > 0.5 and remain constant for x < ∼0.5. DSC Data. Figure 6 shows selected DSC curves for the series [FexNi1-x] between 250 and 325 K in the heating mode. When x decreases, the anomalous peak shifts to lower temperatures. Below x ) 0.4, peaks could not be distinguished from the background with any certainty. Parts a and b of Figure 7 show, respectively, the evolution of ∆S and ∆H (both relative to 1 mol of Fe(II) ions) as a function of x for the [FexNi1-x] and the [FexCo1-x] mixed-crystal series, for the nondiluted compound ∆S ) 84 J K-1 mol-1 and ∆H ) 26 kJ mol-1. For Ni(II) and Co(II) dilutions, both ∆H and ∆S show a decreasing tendency in the investigated range, though this tendency appears more clearly in the Co(II) case. For 47% Co(II) dilution, ∆S ) 47 J K-1 mol-1 and ∆H ) 12 kJ mol-1, while for 59% Ni dilution, ∆S ) 54 J K-1 mol-1 and ∆H ) 15 kJ mol-1. It should be noted, however, that some uncertainty arises on ∆H and ∆S values from the measurement of the elemental composition (x) as well as from the subtraction of the unknown baseline, and this latter error increases with the dilution. Temperature Effects on the Raman Spectra. Figure 8a shows typical Raman spectra in the 585-2250 cm-1 frequency

Figure 7. Evolution of the transition entropy (a) and enthalpy (b) (relative to 1 mol of FeII ions) as a function of x in FexNi1-x(pyrazine)[Pt(CN)4] and FexCo1-x(pyrazine)[Pt(CN)4]. (Lines are included to guide the eye.)

range measured at 88, 248, and 328 K. In this frequency range, all Raman lines can be assigned to intramolecular modes of the pyrazine molecule and CN stretching modes around 21002200 cm-1.19b These modes show small frequency shifts upon the spin-state change in agreement with our previous observations.19b,c,e For example, the Raman mode around 650 cm-1, as shown by arrows in Figure 8a, is an excellent marker of the spin transition. We note also that an intensity enhancement of pyrazine modes is observed in the LS state. Figure 8b shows typical Raman spectra in an intermediate frequency range (315-585 cm-1) measured at 88, 248, and 328

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Figure 8. Raman spectra of Fe(pyrazine)[Pt(CN)4]: (a) 585-2250 cm-1, (b) 315-585 cm-1, and (c) 30-315 cm-1.

K. Raman spectra change drastically between 328 and 88 K. According to our earlier assignments on the pure Fe(II) compound, these changes correspond to HS/LS spin crossover.19b The spectra at 248 K are similar to the 88 K spectra, but additional Raman lines, indicated by arrows in Figure 8b, are observed at 248 K. At this temperature, the complex is already in the LS state. From these additional Raman modes, we infer therefore that there might exist two different crystal structures at 248 and 88 K, both containing LS Fe(II) ions. In other words, a structural phase transition, which differs from the spin transition, should take place between 248 and 88 K. Figure 8c shows Raman spectra in the low-frequency range (30-315 cm-1) recorded in the cooling mode. At 328 K, that is, in the HS state, three peaks appear clearly at 50, 175, and 225 cm-1 as indicated by the notation A1, A2, and A3, respectively. The Raman modes A2 and A3 were assigned earlier to HS Fe-ligand stretching modes.19b Since the Raman line A1 disappears around the spin transition, the line A1 is tentatively assigned also to a HS Fe-ligand mode. Between

300 and 250 K, the peaks A1-A3 disappear and Raman modes indicated by B1-B3 appear. When further lowering the temperature (between 200 and 150 K), the modes B1 and B2 disappear and some new modes (C1 and C2) appear. At the same time, the mode B3 shows an intensity enhancement. The Raman mode B3 was earlier described as LS Fe-N(pyrazine) stretching.19b Figure 9 shows the temperature dependence of the integrated Raman intensities of peaks A1, B2, and B3 in the cooling mode. Signal intensities are normalized to the maximum intensity. Peak A1 appears in the HS state. Peak B2 appears in the LS state but only in the intermediate temperature range between 150 and 275 K. Peak B3 is also observed in the low-spin state below 275 K and shows the enhancement of the intensity below 150 K. These spectral changes were found to be completely reproducible over several cooling and heating cycles. The temperature dependence of Raman spectra can be understood as follows: (i) The vibrational structure reflects the spin transition around 275 K. Though the transition appears less

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Figure 9. Intensity of the Raman modes A1, B1, and B3 as a function of the temperature. (Lines are included to guide the eye.)

abrupt than that from the magnetic measurements, we believe this difference is only due to inhomogeneous laser heating effects. (ii) Another structural transition takes place around 175 K in the LS state. The appearance of additional Raman modes suggests that the symmetry of the intermediate LS phase (175275 K) may be lower than that of the low-temperature LS phase. It is interesting to note that in our earlier studies on hydrated samples (Fe(pyrazine)[Pt(CN)4]‚nH2O), we observed only the HS and the low-temperature LS phase but not the intermediate LS phase. Variable-temperature PXRD measurements would be necessary to better describe the structural changes of the hydrated and dehydrated samples. Dilution Effects on the Raman Spectra. Parts a and b of Figure 10 show 298 K (HS) Raman spectra in FexNi1-x(pyrazine)[Pt(CN)4] for different dilutions (x) in the frequency ranges of 585-2250 cm-1 and 30-585 cm-1, respectively. Figure 10a reveals a large decrease in the intensity of pyrazine modes with dilution. Between 585 and 2250 cm-1 we observe only small frequency shifts and some peak broadening. These frequencies, internal pyrazine modes, and CN stretches appear thus not much influenced by either the spin state change or the metal substitution. Between ca. 150 and 585 cm-1, an exchange of the peak intensities can be observed as indicated by the broken lines: The intensity of modes characterizing Fe(pyrazine)[Pt(CN)4] decreases with decreasing x, and simultaneously the Raman modes of Ni(pyrazine)[Pt(CN)4] appear just as if we simply mixed the two compounds. In other words, we observe the well-known “two-mode” behavior of solid solutions.21 Let us note that in these frequency ranges similar dilution effectss not shown hereswere observed for the LS phase of [FexNi1-x] compounds and for the HS and LS phases of the [FexCo1-x] compounds as well. The dilution behavior of Raman modes below 150 cm-1 is more intriguing. Parts a and b of Figure 11 show the Raman spectra of [FexNi1-x] in the low-frequency range (30-150 cm-1) measured at 298 and 88 K, respectively. As indicated by arrows in Figure 11a, the broad peak around 50 cm-1 shifts continuously to higher frequencies with decreasing x. This phenomenon is the so-called one-mode behavior of solid solutions and is typical for vibrational modes implying long-range forces.21 Since this Raman frequency changes drastically upon the spin crossoversas shown in Figure 8csit can be tentatively assigned to Fe-ligand vibrational modes. At 88 K, the weak broad structure appearing around 150 cm-1 in the LS statesindicated by arrows in Figure 11bsalso shifts to lower frequencies with dilution. Parts a and b of Figure 12 depict the dilution dependence of these modes for [FexNi1-x] and [FexCo1-x], respectively.

Figure 10. Raman spectra (288 K) of FexNi1-x(pyrazine)[Pt(CN)4] for different values of x recorded between (a) 585-2250 cm-1 and (b) 30-585 cm-1.

Discussion The main dilution effects observed for the mixed-crystal series [FexNi1-x] and [FexCo1-x] are in agreement with those observed earlier for the compound FexM1-x(btr)2(NCS)2‚H2O (M ) Ni(II), Co(II)).17 The dilution tends to smooth the spin transition curves (Figure 4), and the transition temperatures change also with the dilution (Figure 5). The magnitude of this latter effect depends strongly on the nature of the diluting metal. In the case of Ni(II) (Co(II)), the hysteresis vanishes around x ) 0.5 (0.3). Both the enthalpy and entropy changes associated with the spin conversion expressed per mole of Fe(II) ions show a decreasing tendency with dilution. It seems therefore that in the threedimensional Fe(pyrazine)[Pt(CN)4] compound, similar dilution effects occur than in the two-dimensional Fe(btr)2(NCS)2‚H2O complex. The main novelty of the present work is the investigation of vibrational spectra of the mixed crystals; therefore the discussion will be confined to the vibrational properties. The thermal spin crossover from the LS to the HS state is mainly driven by the entropy difference of two spin states. It is well-established that not only electronic but also vibrational degeneracy changes contribute to this entropy difference.10a,22 To calculate the electronic degeneracies for Fe(II) compounds, in general, only the spin degeneracies (SHS and SLS) are taken into account because of an almost complete quenching of the orbital momentum (L ) 0). It follows that, in the case of Fe(II) ions, ∆S ) R ln(2SHS + 1)/(2SLS + 1) ) 13.4 J K-1 mol-1. Considering the vibrational entropy changes, the contribution

Fe(pyrazine)[Pt(CN)4]

Figure 11. Raman spectra (288 K) of (a) FexNi1-x(pyrazine)[Pt(CN)4] and (b) FexCo1-x(pyrazine)[Pt(CN)4] for different values of x recorded between 30 and 150 cm-1.

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Figure 12. Evolution of low-frequency Raman modes as a function of x, measured at (a) 288 and (b) 88 K. (Lines represent linear fit on the experimental data.)

of an oscillator i of frequency ωi to the total entropy can be written as22

Si(ωi,T) ) pωi/2T tanh(pωi/2kT) - k ln[2 sinh(pωi/2kT)] The decrease in frequencies upon LS f HS crossover results in an entropy increase, expressed by

∆S(T) ) SHS(T) - SLS(T) From the frequency dependence of Si it was shown that only the low-frequency modes give a significant contribution to the total entropy change.22a The vibrational contribution to this latter is typically 25-60 J K-1 mol-1 for iron(II) spin-crossover complexes.22b The correlation between the dilution (x) and ∆S in the spincrossover complexes Fe(btr)2(NCS)2‚H2O and Fe(pyrazine)[Pt(CN)4] is obviously related to the vibrational part of the total entropy change since the electronic part (spin and orbital degeneracies) does not change with the dilution as it can be inferred from the Mo¨ssbauer spectra. It follows that the vibrational frequencies must be sizeably affected by the dilution. This hypothesis is not verified in the Raman spectra above 150 cm-1 where only an exchange of Fe(pyrazine)[Pt(CN)4] and M(pyrazine)[Pt(CN)4] related modes was observed for various values of the dilution factor x. On the other hand, as shown in Figure 12, the low-frequency (