Exafs Crossover

22 September 2000

Chemical Physics Letters 328 Ž2000. 188–196 www.elsevier.nlrlocatercplett

Spin crossover in iron žII / tris ž2-ž 2-pyridyl /benzimidazole/ complex monitored by the variable temperature EXAFS Roman Boca Werner b, Wolfgang Haase b ˇ a,) , Martina Vrbova´ a, Rudiger ¨ a

b

Department of Inorganic Chemistry, SloÕak Technical UniÕersity, SK-812 37 BratislaÕa, SloÕakia Institute of Physical Chemistry, Darmstadt UniÕersity of Technology, D-64287 Darmstadt, Germany Received 1 June 2000; in final form 2 August 2000

Abstract Standard EXAFS equipment has been utilized in conducting the variable temperature experiments using the wFeŽpybzim. 3 xŽClO4 . 2 P H 2 O sample, pybzim being a bidentate 2-Ž2-pyridyl.benzimidazole ligand. There is a jump in the metal–ligand ŽFe–N. distance comparable with the step in the effective magnetic moment. The distance increases from 1.95 ˚ In the transition region, the error bars are much broader than before and after this region. The transition to 2.11 A. temperature taken from the fittings is 132 K, which is about 9 K lower than that from magnetic susceptibility measurements. q 2000 Published by Elsevier Science B.V.

1. Introduction Monitoring of the spin crossover Žlow-spin to high-spin transition. may be done by several experimental techniques w1–5x. Most frequently the variable temperature magnetic susceptibility measurements are applied showing a jump of the effective magnetic moment at the transition temperature. Analogous information, however, can be drawn from the Mossbauer spectra, variable temperature infrared ¨ ŽIR. spectra, electron spectra, calorimetric measurements, etc. The X-ray structure data on single crystals show that the metal–ligand bond lengths increase by ca. 15% during the spin crossover. Similar information may be drawn from EXAFS data on

) Corresponding author. Fax: q421-52431-98; e-mail: [email protected]

powder samples. Such an investigation is the subject of the present study. In contrast to the X-ray data, which were collected only at two temperatures Žbelow and above the transition temperature., the EXAFS data were scanned continuously, at 32 different temperatures. This allows a dense mapping of the structural changes during the spin crossover, which may help in developing more complete theoretical models of the spin crossover phenomenon. In parallel to the theories that embody the macroscopic parameters Žthe elastic bulk modulus, the Poisson ratio w6x. an alternative theory could be based upon the microscopic parameters Žharmonic potential characterized by the equilibrium distances and the force constants.; for that reasoning the detailed information about the structural changes within the chromophore are ultimate. The spin crossover in the complex under study – wFeŽpybzim. 3 xŽClO4 . 2 P nH 2 O has been reported sev-

0009-2614r00r$ - see front matter q 2000 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 9 0 2 - 7

R. Boca ˇ et al.r Chemical Physics Letters 328 (2000) 188–196

Fig. 1. Sketch of the structure of the bidentate ligand pybzim Žleft. and the tridentate ligand bzimpy Žright..

eral times w7–12x so that the system is well characterized. Both the magnetic susceptibility data and the Mossbauer spectra show the spin transition at ¨ Tc s 141 K for the monohydrate. However, the sample shows a variable content of crystal water and a different amount of an underlying paramagnetism due to the presence of the paramagnetic impurity that grows with the sample aging. The structure of the bidentate ligand Žpybzim. is shown in Fig. 1 along with an analogous tridentate ligand Žbzimpy. whose complex was used during the data analysis.

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package w14x. The amplitude and phase functions which are needed for fitting the x Ž k . data were obtained from simulations of the EXAFS function of th e lo w -s p in Ž a t 2 9 8 K . c o m p o u n d wFeŽbzimpy. 2 xŽClO4 . 2 P 0.25H 2 O for which the structure data have been presented elsewhere w15x and showing R 1ŽFe–Npy . s 1.87 and R 2 ŽFe–N bzim . s 1.99 = 10y1 0 m. In principle there are six different Fe–N distances with six different Debye–Waller factors. Together with the E0 shift, the reduction factor and the coordination numbers of each shell, we have 20 variables, which is too much for fitting. Therefore some simplifications have been introduced: Ži. the E0-shift was determined Žfitted. ones at lowest temperature, for all other temperatures this fitted value was taken as a fixed parameter; Žii. six Fe–N distances were distributed into two shells for which different Debye– Waller factors were considered. Consequently only five variables to be optimized survive: the distances R 1ŽFe–Npy . and R 2 ŽFe–N bzim ., the corresponding Debye–Waller factors s 1 and s 2 , and the amplitude reduction factor.

2. Experimental 2.1. Sample preparation The ligand pybzim Žs 2-Ž2-pyridyl.benzimidazole. and its FeŽII. complex was prepared according to the literature w11,13x. Anal. Calc. for C 36 H 27 Cl 2 FeN9 O 8 P H 2 O, hereafter 1, Žfound.: C, 50.4 Ž51.1.; H, 3.4 Ž3.5.; N, 14.7 Ž14.7.%.

2.3. Magnetic susceptibility measurements Temperature dependence of the magnetic susceptibility has been measured using the Faraday-type balance at the applied field of B s 1.4 T. A correction for the underlying diamagnetism has been calculated using the set of Pascal constants.

2.2. EXAFS measurements and analysis 3. Results and discussion The sample for the EXAFS measurements was prepared in the form of a pellet in which the grounded complex Žca. 50 mg. with the double amount of special polyethylene powder were pressed into a pill Ždiameter, 13 mm; height, ca. 1 mm.. The sample was exposed to standard equipment in the HASYLAB at DESY ŽHamburg, beamline E4, resolution 1 eV.. The EXAFS spectra were measured on the iron K-edge at 32 different temperatures between 50 and 300 K with smaller steps in the region of the spin crossover. The raw data were manipulated with the programs AUTOBK and FEFFIT from the UWXAFS

The results of the EXAFS analysis for a single temperature are exemplified in Fig. 2. It can be seen that the fitting the EXAFS function is quite satisfactory. The temperature dependence of the metal–ligand distances R 1 and R 2 is shown in Fig. 3 Žleft.. An assignment whether R 1 belongs to Fe–Npy or Fe– N bzim is impossible on the basis of the EXAFS data alone. However, relying to the analogy with the low-spin complex wFeŽbzimpy. 2 xŽClO4 . 2 P 0.25H 2 O we assume that the low-temperature data on 1 could be assigned as R 1ŽFe–Npy . - R 2 ŽFe–N bzim .. The

R. Boca ˇ et al.r Chemical Physics Letters 328 (2000) 188–196

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Fig. 2. Experimental Žsolid. and calculated Ždashed. Fourier transform of the EXAFS function for 1 at 90 K.

temperature dependence of the Debye-Waller factors s 1 and s 2 is shown in Fig. 3 Žright.. The discrepancy factor of the fit presented at the same place shows the reliability of the extracted data. The temperature dependence of the averaged metal–ligand distance RŽFe–N. is shown in Fig. 4 ˚ Žleft.. The distance increases from 1.95 to 2.11 A with a jump centered at 132 K. In the transition ˚. region, the error bars are much greater Ž"0.07 A ˚ Ž . than before and after this region "0.015 A . Lower Ž R LS . and upper Ž R HS . limits of the interatomic distances were used in calculating the conversion curve – the high-spin mole fraction Ž x HS . versus temperature according to the formula x HS s

R T y R LS R HS y R LS

.

Ž 1.

Such a function is presented in Fig. 4 Žcenter.. The transition temperature read off at x HS s 0.5 is Tc s 132 K. Finally an Arrhenius plot was generated, i.e. ln K versus 1rT function where the low-spin to high-spin equilibrium constant was calculated as follows: x HS Ks . Ž 2. 1 y x HS In these calculations an eventual contamination of the sample by FeŽIII. impurities has been ignored.

The corresponding plot is displayed in Fig. 4 Žright.. The evident non-linearity around ln K s 0 shows that a simple Boltzmann equilibrium is violated so that the spin transition in the present case is influenced by some degree of cooperativity. Among a variety of spin crossover model the Ising-like model has been utilized in the numerical analysis. It is based on the Hamiltonian Hˆ s Ž D0r2 . sˆ y J² s :sˆ

Ž 3.

that accounts for the site formation energy D0 , and the spin–spin interaction taken in the mean-field approximation. Here the fictitious spin sˆ adopts values of y1 for low-spin and q1 for the high-spin state, respectively. Its thermal average, ² s :, is directly related to the high-spin mole fraction: x HS s Ž1 q ² s :.r2. The essential features of such a model are well described elsewhere w16–20x. Consequently an implicit equation is to be iterated ²s :s

y1 q f Ž ² s : . 1 q f Ž ² s :.

.

Ž 4.

In the simplest version the function f Ž² s :. is expressed in the form f s reff exp y Ž D0 y 2 J² s : . rkT

Ž 5.

R. Boca ˇ et al.r Chemical Physics Letters 328 (2000) 188–196 Fig. 3. Temperature dependence of the fitted EXAFS data: Žleft. metal–ligand distances R1 Žcircles., R 2 Žsquares., R Žtriangles.; Župper right part. Debye–Waller factors; Žlower right part. discrepancy factor of the fit.

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192 R. Boca ˇ et al.r Chemical Physics Letters 328 (2000) 188–196

Fig. 4. EXAFS data: temperature dependence of the averaged Fe–N distances for 1 with error bars Žleft.; high-spin mole fraction Žcenter.; an Arrhenius plot Žright.. Open symbols, experimental data; full points, calculated data based on the fit of the high-spin mole fraction.

R. Boca ˇ et al.r Chemical Physics Letters 328 (2000) 188–196

where the effective degeneracy ratio, reff s rel r vib ) 5, accounts for the electronic as well as vibrational contribution Ž rel s 5.. In a more advanced treatment the vibrational contribution is averaged over m-active modes Ž m s 15 for a hexacoordinate complex. and thus w18x

½

f s rel

1 y exp Ž hn LS rkT . 1 y exp Ž hn HS rkT .

= exp  y m Ž hn HS y hn LS . r2 qD0 y 2 J² s : rkT 4 .

Ž 6.

ŽThe temperature variation of the vibrational contribution dominates at low temperatures and modifies the linearity of the Arrhenius plot.. During the fitting procedure Eq. Ž4. needs to be iterated for each temperature and a trial set of parameters D0 , J, reff andror hn HS and hn LS . As a result of the fitting Žthe discrepancy factor RŽ x HS . s 0.051 for all 32 data points. the final set of the spin-crossover parameters resulted: D0rk s 1847 K, Jrk s 127 K, hn HS rk s 400 K, and hn LS rk s 609 K. Of main interest is the cooperativity parameter J which adopts a considerable value. Its positive sign means that the given center prefers neighbours of the like spin. Just this parameter is responsible for the non-linearity of the Arrhenius plot around ln K s 0. Being, however, below the critical limit, Jrk - Tc , no thermal hysteresis effect occurs. The magnetic susceptibility recorded on the same sample has been converted to the effective magnetic moment, calculated as X meffrm B s 798 Ž xmol T.

1r2

.

The amount of PI has been determined by fitting the low-temperature ŽLT. magnetic data to the Curie–Weiss function,

xmol Ž LT . s x PI x PI 2 s x PI C0 g PI SPI Ž SPI q 1 . r3 r Ž T y Q PI . . Ž 8.

m

5

Ž 7.

Its temperature dependence is shown in Fig. 5 Žleft.. The value of meffrm B f 1.0 below 70 K indicates the presence of a paramagnetic impurity ŽPI.. This is the only source of the paramagnetism at low temperature and in no case it could be ignored as far as the magnetic data are concerned.

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Ž C0 s NA m 0 m 2B rk comprises the fundamental physical constants in their usual meaning. by assuming that for an FeŽIII. center the values of S PI s 5r2 and g PI s 2.0 can be safely fixed. Then Q PI s y4.53 K and x PI s 0.0269 resulted. The subsequent analysis relies on the balance

x T s x LS x LS q x HS x HS q x PI x PI

Ž 9.

and the normalization of the mole fractions 1 s x LS q x HS q x PI .

Ž 10 .

Under these assumptions, the following equations are fulfilled x HS s

Ž x T T . y Ž x LS T . Ž 1 y x PI . y Ž x PI T . x PI , Ž x HS T . y Ž x LS T . Ž 11 .

and Ks

x HS x LS

s

x HS 1 y x HS y x PI

.

Ž 12 .

Having x PI already determined, and assuming that x LS s 0 for the diamagnetic S s 0 state, the evaluation of x HS s f ŽT . and ln K s f Ž1rT . functions is an easy task provided that the Ž x HS T . product is read-off as the maximum of the experimental values ŽFig. 5 Žcenter and right... Based on these plots, one can conclude that the magnetic data show similar, although not identical, behaviour of the spin crossover when compared to EXAFS data. The transition temperature is about 9 K higher, Tc s 141 K, which nicely matches with earlier magnetic susceptibility and Mossbauer spectra investiga¨ tions w11,12x. Again a cooperativity effect is well evident around ln K s 0. The fitting procedure based on magnetic data has been applied to the magnetic susceptibility function

2 2 w SHS Ž S HS q1. r3 x r T q x PI C0 g PI w SPI Ž SPI q1. r3x r Ž T y Q PI . x T s x HS x HS q x PI x PI s w Ž 1q² s : . r2x C0 g HS

Ž 13 .

194 R. Boca ˇ et al.r Chemical Physics Letters 328 (2000) 188–196

Fig. 5. Magnetic susceptibility data: temperature dependence of the effective magnetic moment for 1 Žleft, inset: magnetic susceptibility in 10 9 m3 moly1 .; high-spin mole fraction Žcenter.; an Arrhenius plot Žright.. Open circles, experimental data; full points, calculated data based on the fit of the magnetic susceptibility.

R. Boca ˇ et al.r Chemical Physics Letters 328 (2000) 188–196

with SHS s 2; g HS is taken as a free parameter. Here Eq. Ž4. again is iterated for each temperature and a trial set of the spin crossover parameters. Since the low-temperature data interfere with the strong signal of the paramagnetic susceptibility, a reliable determination of hn HS and hn LS is disabled. As a result of the fitting Žthe discrepancy factor RŽ x . s 0.015 for 53 data points. the magnetic-set of the spin-crossover parameters resulted: D0rk s 397 K, Jrk s 122 K, reff s 16.4; the magnetogyric factor of the high-spin state becomes g HS s 2.301. It can be concluded that these values are not too far from those based upon the EXAFS data. Since in this model the molar transition entropy is D S s Rln reff s 23.2 J Ky1 moly1 and the molar transition enthalpy is D H s R D0 s 3.30 kJ moly1 , a simple relationship for the transition temperature should be obeyed: Tc s D HrDS s 142 K. This value matches with the experimental readings on the basis of magnetic data. The difference in Tc as predicted from the EXAFS ŽTc s 132 K. and magnetic susceptibility data ŽTc s 141 K. may have several origins: Ži. applied pressure of several tons under the pelletization of the sample; Žii. lowered thermal conductivity of the sample owing to the presence of the polyethylene in the pellet; Žiii. oversimplified analysis of the EXAFS function assuming an averaged Fe–N shell Žin fact, two stereoisomers, mer- and fac-, may be present and two different Fe–NŽpyridine. and Fe–NŽbenzimidazole. distances.; Živ. Eq. Ž1. is fulfilled only approximately; Žv. there is a different response of the bulk magnetism and the geometry of the chromophore on temperature increase. In conclusion, this is the case when the spin crossover is fully monitored by the EXAFS data. Previous EXAFS investigations have been limited to two or a few temperature points only w21–28x. The EXAFS data show similar, although not identical, profile of the spin crossover when compared to magnetic susceptibility and Mossbauer spectra data: ¨ the transition temperature is about 9 K lower, Tc s 132 K, relative to magnetic susceptibility data. A considerable cooperativity effect is evident at the transition region Žca. x HS f 0.5 or ln K f 0.; its magnitude evaluated in terms of the Ising-like Hamiltonian is Jrk s 127 K.

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Acknowledgements DFG is acknowledged for financial support and the HASYLAB for the beam-time. R.W. acknowledges TU Darmstadt for support during Ph.D. study.

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