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Unusual heat capacity of the ferric spin-crossover complex, [Fe(acpa)2]PF6, showing a gradual but complete spin-state interconversion at the fast spin-flipping rate†
J. Ph.w. Chem. Solids Vol. 51. No. 8. pp. 941-951. 1990
c4322-3697190 13.00 + 0.00
Printed in Great Britain.
8
1990 Pcrgamon Press plc
UNUSUAL HEAT CAPACITY OF THE FERRIC SPIN-CROSSOVER COMPLEX, [Fe(acpa),]PF,, SHOWING A GRADUAL BUT COMPLETE SPIN-STATE INTERCONVERSION AT THE FAST SPIN-FLIPPING RATE? MICHIO SORAI,~ YONEZO MAEDA~ and HIROKI OSHIO~ SMicrocalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan $Department
of Chemistry, Faculty of Science, Kyushu University, Higashiku, Fukuoka 812, Japan TInstitute for Molecular Science, Okazaki, Aichi 444, Japan (Received 5 October 1989; accepted 24 January 1990)
Abstract-The heat capacity of the iron(II1) spin-crossover complex [Fe(acpa),]PF, [Hacpa = N-(l-acetyl2-propylidene)(2-pyridylmethyl)amine], which shows fast electronic relaxation between S = l/2 (2Tti) and S = 5/2 (6A,,) in comparison with the s’Fe Mdssbauer lifetime (lo-’ s), was measured with an adiabatic calorimeter in the IS-320 K range. Variable temperature IR and Raman spectra were recorded between 84 and 300 K. An unusually broad heat-capacity peak starting from * 120 K, culminating at _ 190 K, and terminating at -280 K was observed. A normal heat capacity curve which separates the excess heat capacity from the observed values was determined. The enthalpy and entropy arising from the spin-crossover phenomenon were 7025 J mol-’ and 36.19 J K-’ mol-‘, respectively. The entropy gain was well accounted for in terms of the sum (37.69 J K-’ mol-‘) of the contribution from a change in the spin-manifold R ln(6/2) (= 9.13 J K-’ mol-‘) and from a change in the skeletal normal modes of vibration detected by IR and Raman spectra (28.56 J K-‘mol-‘). To elucidate the question, Why does the spin-crossover occur so gradually for the complexes of the fast electronic relaxation type?, the Frenkel theory of heterophase fluctuation in liquids was applied. As a result, the number of molecules in a domain was proved to be as small as five. This makes a large fluctuation possible between the low and high spin states, eventually leading to the spin-equilibrium type transition taking place over a wide temperature range. Keywords: Spin-crossover, spin-state interconversion, heat capacity, iron(II1) complex, Frenkel model, heat capacity anomaly, infrared spectra, Raman spectra.
1. INTRODUCTION Studies of spin-crossover phenomena occurring between low- and high-spin states have been extensively developed for octahedral iron(H) and iron(III) complexes [l-3]. This is due to the fact that 57Fe serves as a good probe of the Miissbauer spectroscopy by which both the low- and high-spin states can be directly observed. In particular, temperature dependence of the Miissbauer spectra can provide detailed information about the degree and the rate of the spinstate interconversion and thereby give a useful clue to the mechanisms of the spin-crossover phenomena. As widely recognized, the spin-crossover phenomena are phenomenologically classified into two groups: one is the so-called “spin-transition type” in which the spin-state interconversion between the lowand high-spin states takes place abruptly within a narrow temperature range, say, several kelvins and the other is the “spin-equilibrium type” in which the spin-state interconversion occurs gradually over a wider temperature range than 100 K. These two types
tcontribution search Center.
No. 24 from the Microcalorimetry
Re-
are encountered in both the iron(I1) and iron(II1) complexes,‘though there are very few iron(II1) complexes that show the spin-transition type behavior. Typical examples of the spin-transition type are [Fe(phen),(NCS),] [4, 51 for the iron(I1) complexes and [Fe(3-OMe-SalEen),]PF, [6,7] for the iron(II1) complexes, while representatives of the spin-equilibrium type are [Fe(Z-pic),]Cl,-EtOH [8,9] and [Fe(S,CNR,),] [lo, 111 for the iron(I1) and iron(II1) complexes, respectively. The choice as to which type of the spin-crossover a given complex follows, is made according to the strengths of the Jahn-Teller coupling between the d-electrons and local distortions [12] and of the intermolecular coupling between the intramolecular distortions and/or a lattice strain [13, 141. On the other hand, an alternative classification of the spin-crossover complexes has been made according to the rate of the spin-state interconversion: one is the “fast electronic relaxation type” in which the spin-flip rate is faster than the “Fe Miissbauer lifetime (IO-‘s) and the other is the “slow electronic relaxation type”. Since each spectroscopy has its own time-scale and the 57Fe Mossbauer lifetime is not a standard of the time-scale, a classification of this type
941
942
MI~HIO.Sorur et al.
may be criticized. From an experimental viewpoint, however, this is a convenient classification for two reasons. First, an increasing number of iron complexes in which spins flip at a rate greater than or equal to the inverse of the “Fe Mijssbauer lifetime have recently been reported [15-291 and those Miissbauer spectra show relaxation phenomena in the spin-transition region. Second, those complexes showing the fast electronic relaxation between the low- and high-spin states are at present encountered only in the iron(III) complexes and exhibit a smooth increase of the magnetic moments with increasing temperature, i.e. the spin-equilibrium type. It should be remarked here that no iron complexes of the fast electronic relaxation type which belong to the spintransition type have been known. The present iron(II1) complex [Fe(acpa),]PF, [Hacpa = N-( 1-acetyl-2-propylidene) (2-pyridylmethyl)amine] (see Fig. 1) shows a spin-crossover phenomenon between S = l/2 (2r2,) and S = 5/2 (6AIg) with a fast spin-interconversion rate of about (0.5 - 3) x lo6 s-i over the - 110 to -280 K range. This complex, therefore, belongs to the spinequilibrium type with fast electronic relaxation time [29]. In the case of the iron complexes of the spintransition type, the spin-state interconversion takes place through a phase transition which has been clearly demonstrated by heat capacity measurements [5,7,30]. The main purpose of the present paper is to elucidate the thermal properties of the iron complex of the spin-equilibrium type with fast electronic relaxation time and to compare the results with those of the spin-transition type. Calorimetric measurements so far made for the iron complexes of the spin-equilibrium type involve (i) [Fe(II) (2-pic),]Cl,. EtOH [9], (ii) [Fe(III)(3OEt-SalAPA),]CIO,.CgHg [31] and (iii) (Fe(III)(3OEt-SalAPA),]ClO,~C,H,Cl [32]. The complex (i) belongs to the slow electronic relaxation type whereas (ii) and (iii) are of the fast electronic relaxation type. Regardless of the spin-interconversion rate, these three complexes exhibited a well-resolved heat capacity peak(s) arising from the phase transition(s) as well as a broad heat capacity hump extending over a wide temperature range. In these complexes, reorientational motions of the solvate molecules such as ethanol, benzene and chlorobenzene are strongly coupled with the spin-state interconversion. There-
Fig. 1. Schematic drawing of the tridentate ligand (acpa).
fore, the phase transitions observed for these three complexes seem to be a consequence of the cooperative coupling between the orientational disordering and the spin-state interconversion. In contrast to this, PF; anions in the present complex [Fe(acpa),]PF, are known to be in an ordered state without any reorientational motions even in the high-spin phase (at 293 K) [29]. In this sense, [Fe(acpa),]PF, is a suitable material for the elucidation of the intrinsic thermal properties of the spin-crossover complexes classified as the spin-equilibrium type.
2. EXPERIMENTAL 2.1. Sample preparation The complex [Fe(acpa)z]PF, was prepared and carefully purified by recrystallization from dichloromethane according to the method previously described [29]. Analysis: calculated for FeCuH2,N,02PF,: C, 45.62; H, 4.52; N, 9.67%. Found: C, 45.65; H, 4.50; N, 9.70%. 2.2. Heat capacity measurements Heat capacities were measured with an adiabatic calorimeter [33] from 15 to 320 K. A calorimeter cell [34] made of gold-plated copper was loaded with 16.7887 g (or 0.0289818 mol) of polycrystalline [Fe(acpa),]PF, with buoyancy correction using the density of 1.472 g cmv3 [29]. A small amount of helium gas was sealed in the cell to aid the heat transfer. 2.3. Vibrational spectroscopies Variable temperature IR spectra were recorded for Nujol mulls between 88 and 300 K with an infrared spectrophotometer Model DS-402G (Japan Spectoscopic Co.) in the 4000_400cm-’ range and with a far-infrared spectrophotometer Model FIS-3 (Hitachi) in the 400-30cm-’ range. Multitemperature spectra in the Raman lOOO-80cm-i range were recorded for a KBr disk between 84 and 294 K with a laser Raman spectrophotometer Model R-800 (Japan Spectroscopic Co.) using the 514.5 nm line from an Ar source for excitation.
3. RESULTS Calorimetric measurements were made in five series, the results of which were evaluated in terms of C,, the molar heat capacity at constant pressure. The experimental data are listed in Table 1 and plotted in Fig. 2. A heat capacity anomaly forming a broad hump was observed over a range from - 120 to -280 K. Since this temperature range just corresponds to the anomalous region where the magnetic moment is altered from the low- to high-spin values [29], the present heat capacity anomaly obviously arises from the spin-state interconversion.
943
Unusual heat capacity of [Fe(acpa),]PF, Table 1. Molar heat capacity of [Fe(acpa),]PF, T
CD
CD
T
X
JX-lmol-1
K
JX-'mol-'
88.294
90.721 93.094 95.417 97.695 99.931 102.129 104.291 106.420 108.618 110.588 112.629 114.646 116.638 118.607 120.554 122.480 124.667 135.234 137.552 139.846 142.115
226.77 232.16 237.33 242.02 246.70 251.36 256.02 260.86 265.47 269.91 274.25 278.40 282.34 286.36 290.49 294.60 298.85 303.96 328.38 334.13 339.93 345.78
144.360 146.582 148.780 150.955 153.107 165.237 157.344 159.428 161.488 163.526 165.796 168.307 170.792 173.240 175.651 178.027 180.371 182.687 186.006 187.331 189.641 191.939
352.01 358.54 365.15 372.12 379.30 388.87 396.04 403.53 412.52 422.10 433.57 447.14 461.24 475.72 490.21 604.19 517.06 628.10 637.56 544.89 649.83 552.96
18.406 19.268 20.150 21.047 22.130 23.387 24.649 25.882 27.074 28.241
43.47 46.09 48.91 52.04 55.94 60.34 64.75 69.01 72.88 76.71
29.554 31.001 32.565 34.240 35.998 39.864 41.070 42.649 44.306 46.033
121.549 123.601 125.915 128.347 130.749 133.045 134.693 136.399 138.705 140.986 143.243 145.477 147.687 149.873 152.037 154.178 156.297
296.84 301.41 306.54 311.91 317.45 322.84 326.66 331.03 336.73 342.55 348.65 354.86 361.35 368.16 375.38 382.74 390.56
16.118 16.977 17.846 18.726 19.633 20.568 21.530 22.683 24.007 25.321 26.628 28.050 29.658 31.014 32.570 34.209 35.892 37.697 278.954 281.887 284.810 287.718
(relative molecular mass 579.285)
T
CD
CD
T
X
JX-lmol-1
X
JX-'rol-'
1 194.226 196.506 198.777 201.041 203.297 205.546 207.790 210.030 212.266 214.499 216.817 219.221 221.626 224.033 226.448 228.862 231.275 233.686 236.094 238.498 240.898 243.294
655.42 667.82 660.02 562.44 564.39 566.42 567.31 567.47 566.90 566.28 566.23 563.32 660.63 658.11 556.95 655.70 554.67 563.82 553.19 553.87 554.86 556.20
246.684 248.068 260.i47 252.820 265.186 257.645 259.897 262.570 265.668 268.655 271.526 274.488 277.438 280.376 283.302 286.216 289.116 291.999 294.870 297.733 300.585
567.56 558.95 560.78 562.91 666.11 567.58 570.36 573.39 577.20 680.97 686.17 689.81 593.50 597.65 801.79 606.74 610.48 614.75 618.80 622.68 627.95
Series 80.87 85.47 90.10 95.22 100.78 111.54 114.69 118.86 123.37 128.12
2 47.819 49.667 51.599 53.667 55.580 57.638 59.753 61.970 64.233
132.86 138.04 143.66 149.20 154.62 160.01 165.03 169.63 174.61
66.651 69.215 71.908 74.636 77.262 79.803 82.267 84.663 86.999
179.31 184.51 190.48 196.62 202.57 208.07 213.36 218.77 223.97
158.392 160.465 182.514 184.667 167.065 169.573 172.042 174.475 176.872 179.235 181.568 163.886 186.203 188.614 190.812 193.099 195.377
Ssriee 398.90 407.60 416.92 427.10 439.78 463.49 468.01 482.80 496.94 610.55 523.06 633.38 641.57 647.39 651.53 554.51 556.81
3 197.646 199.907 202.161 204.407 206.647 208.882 211.113 213.342 215.569 217.883 220.295 222.716 225.139 227.561 229.962 232.401
559.0s 561.35 663.65 566.66 566.80 567.54 667.32 566.85 666.71 563.64 561.64 559.61 657.60 656.89 554.81 554.02
237.235 234.646 242.061 244.452 246.848 249.238 251.621 254.000 256.372 258.737 261.423 264.428 267.421 270.402 273.369 276.324
653.28 654.61 556.33 556.53 568.07 559.50 561.86 563.97 566.49 668.86 571.68 575.48 579.29 583.31 588.26 591.95
36.01 39.84 42.66 46.04 47.50 50.63 54.06 57.93 62.63 67.08 71.26 75.82 60.68 85.28 90.04 95.00 100.02 104.97
39.182 40.670 42.334 44.212 48.026 47.737 49.361 60.910 62.393 63.820 55.197 56.629 67.819 59.073 60.294 61.704 63.293 64.836
Series 109.57 113.72 118.16 123.44 128.36 132.97 137.41 141.82 148.27 150.03 153.73 167.39 160.73 163.73 166.46 169.34 172.74 175.97
4 66.339 67.914 69.686 71.651 73.742 75.841 77.882 81.028 83.458 85.823 88.861 91.915 94.260 96.567 98.810 101.024 103.201
178.85 181.85 186.60 189.97 194.77 199.43 203.99 210.98 216.18 221.44 228.09 234.78 239.67 244.41 249.09 253.66 259.46
105.343 107.454 109.535 111.687 113.614 115.615 117.693 119.548 121.483 123.396 125.291 127.168 129.024 130.864 132.688 134.496 138.288
263.18 267.72 272.17 276.45 280.28 284.27 288.20 292.43 296.66 301.06 305.23 309.38 313.85 317.89 322.18 326.62 330.90
695.76 600.08 604.69 608.32
290.610 293.488 296.366 299.217
Series 613.09 616.30 620.90 626.53
5 302.066 304.628 306.612 308.692
630.05 633.22 636.60 639.72
310.764 312.829 316.257 318.046
642.68 645.58 649.51 663.81
Seriee
944
MICHIOSORAIer ai.
645
436 I
600
300
K
273 K 230K 210K 190 K 170 K 150K 130K
F
0’
I
100
0
I
I
200
300
P--
103 K t 662
T/K 4k2
Fig. 2. Molar heat capacity of [Fe(acpa),]PF,. Broken curve indicates the normal (or lattice) heat capacity curve. Although the crystal system and space group of [Fe(acpa)z]PF, in the low-spin state at - 120 K are identical with those in the high-spin state at -290 K (monoclinic and P2/a), the average bond distances of Fe-N and Fe-O are shortened by 0.106 and 0.050 A, respectively, and thereby the effective molecular volume is reduced by 23 A3 [29]. When such a drastic change occurs in a molecule, one can expect significant changes in the IR and Raman spectra. In fact, as shown in Figs 3-5, the IR and Raman spectra
300
700
600
500
LOO
5
/cm-l Fig. 4. Variable temperature IR spectra of [Fe(acpa),]PF, in the 70&400cm-’ range.
contain characteristic bands whose intensities vary strongly with temperature. Although we have not assigned these bands theoretically, it is very likely that they are the skeletal modes of the [FeN,O,] core. Those bands whose intensities are decreased with increasing temperature would be the skeletal modes of the complex in the low-spin state while those bands
K
23OK 299K
2lOK
190 K
ISOK
170 K 86 K
3’71 400
64K
2’67 I
I
I
300
200
100
P
30
/cm-l
temperature far-IR spectra of Fig. 3. Variable [Fe(acpa)JPF, in the 400-30cm-’ range. In this and in Figs 4 and 5, shaded bands are sensitive to temperature and tentatively assigned to the skeletal modes of the [FeN,O,] core.
I
10
500
I
I
400
300
3
I 200
L
10
/cm-l
Fig. 5. Variable temperature laser Raman spectra of [Fe(acpa)JPF, in the 600-80 cm-’ range, recorded by using an Ar source.
Unusual heat capacity of [Fe(acpa)*]PF, whose intensities are increased with increasing temperature would be the modes characteristic of the high-spin state. The effect of changes in the skeletal modes by the spin states upon the heat capacities will be described in Section 5.
600 -
4. SEPARATION OF HEAT CAPACITY ANOMALY For determination of the excess heat capacities due to the spin-crossover phenomenon, it is necessary to estimate a “normal” heat capacity curve or a lattice heat capacity, C,,, . To this end, an effective frequency distribution method [35] was employed. The normal heat capacity of a solid reflects both a continuous acoustic phonon distribution and many discrete optical branches corresponding to intramolecular vibrational modes. From IR and Raman spectra, one can know the fundamental frequencies of these vibrational modes, though not all. The principle of the effective frequency distribution method [35] is to include the normal modes that cannot be assigned, into a continuous phonon distribution and to determine an effective frequency distribution spectrum by least-squares fitting to the observed heat capacities. Since the present compound consists of 62 atoms, the number of degrees of freedom for a formula unit is 186. Among them, 41 modes of intramolecular vibration (129 degrees of freedom) were reasonably assigned on the basis of the IR and Raman spectra with the aid of the literature [3-O]. As can be seen from Fig. 1, the ligand consists of an acetylacetonelike moiety, for which the assignments have been made theoretically [36], a methylene group and a pyridine moiety [37-391, while the counter anion is hexafluorophosphate [40]. The remaining 57 degrees of freedom and the (C, - C,.) correction were effectively included in a continuous spectrum spanning the 0-700cm-’ range, which consists of two Debye distributions and three constant distributions. Contribution of the 129 optical modes to the normal heat capacity was calculated according to the Einstein model. We determined independently the normal or lattice heat capacity curves for the low-spin state, C,,,(LS), and for the high-spin state, C,,(HS), as follows. For the C,,,(LS), we used 35 C, values in the 15-40 K range and 40 C, values in the 75-120 K range. The reason why we skipped the C, data in the 40-75 K range is that in this temperature region the observed heat capacity curve showed a tiny hump, whose origin has not been interpreted. On the other hand, we used 16 C, values in the 290-320 K range for the C,,(HS). In order to avoid trivial results (i.e. negative frequency distributions), we added 24 C, data in the 15-30 K range as if they belonged to the values of the high-spin state. As shown in Fig, 6, the “best” fit frequency distribution spectra reproduced the 75 C, values for the low-spin state within kO.241 J K-i mol-’ of the r.m.s. deviation and the 40 C’, values for the “high-spin” state within
01
I
0
1
-I
300
200
100 l-/K
Fig. 6. Normal or lattice heat capacities of [Fe(acpa),]PF,. C,,(LS) and C,,(HS) are the lattice heat-capacity curves for the pure low- and high-spin states, respectively, while C,, corresponds to the real lattice heat capacity. Closed circles indicate the observed heat capacities. kO.322 J K-i mol-‘. Extrapolation of the best fit C, curve for the low-spin state below 15 K enables us to evaluate the standard thermodynamic functions of [Fe(acpa),]PF,. Table 2 lists the heat capacity C;, molar entropy So, enthalpy function (H” - Hg)/T, and the Gibbs function -(Go - Hz)/T at rounded temperature. The next step is to estimate the real normal heatcapacity curve, C,,, on the basis of C,,,(LS) and C,,(HS), according to the following relationship
C,,, =fHs&(HS)
+ (1 -fHs)Cbc(LS),
(1)
where fHs means the high-spin fraction. The temperature dependence of fHscan be evaluated from the observed magnetic moment [29] by the equation, /& =f&~a(HS)*
+ (1 -fus)~ee(LS)*,
(2)
where pcRstands for the observed value while p&LS) and perr(HS) are the magnetic moments for the low- and high-spin states, respectively. Based on experiment [29], we adopted p,&LS) = 2.05~~ for the low-spin S = l/2 state and p,e(HS) = 5.97~~ for the high-spin S = 5/2 state, where pa is the Bohr magneton. The high-spin fraction thus obtained is plotted in Fig. 7 by open circles. The S-shaped curve suggests a gradual spin-state interconversion for a system in which there exists a Gibbs free energy difference, AC, between the high- and low-spin states:
fHs= l/i1+ w@GIW},
(3)
where R is the gas constant. Equation (3) is rewritten as follows: AC/R = T In{(llf,,)
- I}.
(4)
Mm-no SORAIet al.
946 Table
2.
Standard thermodynamic functions for [Fe(acpa),]PF, J K-t mol-I); the values in parentheses are extrapolated
co P
T/K
So
(HO- H;)/T
-(GO-
(in
po)/T
i8 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310
(3.943) (17.713) (32.788) 48.501 82.150 111.911 139.049 165.678 186.297 208.536 230.572 251.496 273.088 293.404 315.889 340.279 368.622 405.777 456.209 514.935 550.349 561.440 567.468 562.097 554.807 654.683 560.308 570.450 582.797 597.072 612.015 626.918 641.588
(1.367) (8.111) (18.115) 29.822 66.012 83.781 111.677 139.510 166.613 192.952 218.797 244.191 269.179 293.803 318.174 342.464 366.882 391.819 417.879 445.655 414.614 503.142 530.720 557.042 581.853 605.424 628.165 650.330 672.072 693.536 714.752 736.737 756.532
(1.021) (5.774) (12.242) 19.457 34.890 60.468 65.483 80.081 93.806 106.796 119.328 131.490 143.394 155.037 166.539 118.075 189.802 202.105 215.519 230.561 246.624 262.097 276.540 289.686 301.355 311.880 321.685 331.047 340.132 349.060 357.876 366.581 375.210
(0.346) (2.337) (5.873) 10.365 21.122 33.313 46.195 69.428 72.808 86.157 99.469 112.701 125.785 138.766 151.636 164.388 177.080 189.714 202.360 215.095 227.989 241.045 254.179 267.357 280.499 293.546 306.480 319.283 331.940 344.476 356.876 369.157 381.322
298.15
623.479
731.869
364.975
366.894
5 :x 20 30 40 50 60 70
As plotted in Fig. 8, the AC/R derived from eqns (2) and (4) (open circles) were well reproduced by the following quadratic equation in the temperature (solid curve),
Now that the high-spin fraction, fHs, has been determined as a function of temperature, we can estimate the lattice heat capacity, C,,, according to eqn (I). The C,,, thus estimated is shown in Fig. 2 by the broken curve and in Fig. 6 by a dotted curve. AC/R = -0.03426T2+1.7436T + 1067.1.(5) At low temperatures the C,,, curve asymptotically approaches to C,,,(LS) while at high temperatures it The high-spin fraction shown by the solid curve in is approximated by C,,,(HS). Fig. 7 corresponds to the calculated values based on The difference between the observed and normal eqns (3) and (5). heat capacities shown in Fig. 2 or Fig. 6 corresponds
1000
l.OOE 5 0.75. 2 IA ,s 0.50-
0 e .
:: 6
I:
0.25-
i
-1000
0.00 -
-2om
T/K Fig. 7. Temperature dependence of the high-spin fraction of [Fe(acpa),]PF,. Open circles indicate the values derived from eqn (2) and the observed magnetic moments [29], while the solid curve is calculated on the basis of eqns (3) and (5).
0
100
200
300
T/K
Fig. 8. The Gibbs free energy difference, AG/R, between the high- and low-spin states of [Fe(acpa),]PF,. Open circles are derived from eqns (2) and (4). while the solid curve is calculated from eqn (5).
Unusual heat capacity of [Fe(acpa),]PF,
1 00
30
T
i
z E
80
i r c) .
60 LO
34
20
947
ij
E
5
r
-9 .
w Q
20 t
I
1lY
A,,.S=3&19JK-'rival-' 0 0-tI
I
100
T/K
200
300
T/K
Fig. 9. The excess heat capacity, AC,,, of [Fe(acpa),]PF, arising from the spin-crossover phenomenon. The broken curve indicates the theoretical values calculated by eqn (15).
Fig. I I. Temperature dependence of the excess entropy of [Fe(acpa),]PF, arising from the spin-crossover phenomenon. The ultimate value at high temperatures corresponds to the total entropy change, AmS.
to the excess heat capacity,
The high-spin fraction thus obtained calorimetrically is compared in Fig. 12 with the values determined from the magnetic moment [29] and eqn (2). Since the two sets off,, agree well, the separation of the heat capacity anomaly from the observed values seems to have been done reasonably.
crossover
phenomenon.
AC,, due to the spinIn Fig. 9, AC, is plotted as a
function of temperature. Deviation from the normal heat capacity curve occurred at _ 120 K, peaked _ 190K, and came back to the normal curve at -280 K. Interestingly, this broad AC, peak exhibits a shoulder at its high temperature side as if the heat capacity anomaly would consist of two broad peaks. The enthalpy, Atn H, and entropy, A,, S, arising from the spin-crossover phenomenon were determined by integration of AC, with respect to T and In T, respectively. Temperature dependences of the excess enthalpy and entropy are shown in Figs 10 and 11, respectively. The ultimate values at high temperatures correspond to A,=H and A,,S, respectively, and they amounted to A,,H = 7025J mol-’ and A,,,S = 36.19 J K-t mol-I. From a thermodynamic viewpoint, the high-spin fraction at a given temperature can be related to the enthalpy gain, AH(T), at T K by the following equation,
f~s=AHVY4,
(6)
H.
5. ENTHALPY AND ENTROPY SPIN-STATE
OF THE INTERCONVERSION
Although the heat capacity anomaly observed for the present spin-crossover complex [Fe(acpa), JPF, belongs to neither a first-order nor a second-order phase transition, one can still claim that this unusual heat capacity anomaly would originate in a kind of phase transition characterized by weak cooperativity, i.e. a higher-order phase transition. In what follows, therefore, we shall regard this anomaly as a “phase transition”. The enthalpy and entropy gained at a phase transition are described as follows, A,, H = H;(HT)
- HO,(LT)
= {H;(HT) - H:(HT)) ml0
1
- {H;&T)
- H;(LT)} + {H,O(HT) - H,O(LT)j
(7)
6000
and AmS = SO,(HT) - S;(LT),
1 loo
I
I
200
300
T/K
I
Fig. 10. Temperature dependence of the excess enthalpy of
[Fe(acpa),]PF, arising from the spin-crossover phenomenon. The ultimate value at high temperatures corresponds to the total enthalpy change, A,,H.
(8)
where “HT” and “LT” stand for the high and low temperature phases, respectively. Even if the mechanisms are identical among phase transitions (i.e. equal A,,S), the magnitude of A,_ H depends on the temperature at which a phase transition occurs: the higher the transition temperature, the higher the transition enthalpy, and vice versa. Such variations are caused by the fact that the enthalpy difference at 0 K, {Hi(HT)- H,O(LT)), depends strongly on a given system. This quantity is usually hard to
MICHIO S~RAI er al.
938
I ;
I
I
I
I
Table 3. Skeletal vibrational modes tentatively assigned
l.OO-
for the pseudo octahedral core [FeN,OJ (in units of cm-‘)
0.75-
Mode Degeneracy
? IA 0.50.5
Low-spin state High-spin state Difference
5: s 0.25.P r 0.00 -
I
0
I
I
I
loo
200
300
T/
I
K
Fig. 12. Temperature dependence of the high-spin fraction of [Fe(acpa),]PF,. The solid curve is derived from calorimetric measurements [eqn (6)], while the open circles are derived from the magnetic moments 1291[eqn (2)].
but is inevitably included in an observed transition enthalpy, A,,,H. In contrast, there exists no entropy difference at 0 K unless a given system is in a non-equilibrium state. Consequently, the transition entropy is easy to consider theoretically. The transition entropy (A,,,S = 36.19 J K-’ mol-‘) determined for the present complex [Fe(acpa),]PF, is comparable with those for other iron(III) spin-crossover complexes such as [Fe(3-OMe-SalEen),]PF, (A’,,S = 36.74 J K-’ mol-‘) [7], [Fe(3-OEtSalAPA)2]C10,*C,H, (38.4) (311 and [Fe(3-OEtSalAPA),]CIO,.C,H,Cl (37.2) [32], while it is much smaller than those for the iron(I1) complexes such as estimate
FeWen)2WShl
(48.78) PI, Fe(phen)2WCSe)21
(51.22) [5] and [Fe(Zpic),]Cl,.EtOH (50.59) [9]. The transition entropy consists mainly of three contributions: (i) a change in the spin-manifold between the low- and high-spin states; (ii) a change in the phonon system, in particular drastic changes in the bond lengths between the central iron ion and the ligands; and (iii) an order-disorder phenomenon of the solvate molecules and/or the counter-anion, if any. Since a change of the spin states for the iron(II1) complexes occurs between the spin quantum number S = 5/2 (6A,I) of the high-spin state and S = l/2 (‘r,,) of the low-spin state, the contribution from the spin-manifold to the transition entropy [item (i)] is R ln(6/2) = 9.13 J K-‘mol-‘. On the other hand, the spin-crossover for the iron(H) complexes occurs between S = 2 (sr,,) and S = 0 (‘A,,) and hence the spin entropy is R ln(5/1) = 13.38 J K-’ mol-‘. In the case of the present complex, as it does not contain any solvate molecules and the counter-anion, PF;, is in an ordered state without any reorientational motion even in the high-spin phase (at 293 K) [29], we need not take into account the contribution of item (iii) to the transition entropy. The remaining contribution is, therefore, the so-called phonon entropy [item (ii)]. As can be seen from Figs 3-5, variable temperature IR and Raman spectra have demonstrated characteristic bands whose intensities
of [Fe(acpa),]PF,
VI ,
‘2’
‘;
‘;
‘;
;
662 645 17
462 348 114
473 438 35
412 305 107
371 208 163
267 160 107
varied strongly with temperature. Although we have not theoretically assigned these bands, it is very likely that they might be the skeletal modes of the [FeN,O,] core. An octahedral MX, molecule has six normal modes of vibration designated as v,(A,,), vz(Eg), v,(F,,), v,(F’,), v,(F&) and v,(F,,). Since the present complex has lower symmetry than the octahedral MX6, it is expected that the degeneracy of some of the normal modes would be lifted and that inactive modes in 0, symmetry would become active in a lower symmetry. For simplicity, however, we shall treat the present complex as if it belonged to 0, symmetry, and tentatively assign the temperature sensitive bands. For example, the band at 412 cm-’ whose intensity is increased with decreasing temperature (see Fig. 4) was assigned to the v, mode of the low-spin state while it would be shifted to the band at 305 cm-’ in the high-spin state whose intensity is increased with increasing temperature (Fig. 3). All the assignments tentatively made are listed in Table 3. The heat capacities arising from these six normal modes (15 degrees of freedom) were calculated for both spin states on the basis of the Einstein model and shown in Fig. 13, in which they are designated as C phonon(LS)and Cphonon(HS), respectively. By virtue of the high-spin fraction,&,, derived from eqn (2), the heat capacity of the complex in a spin-equilibrium stateV Cphonon(Equil), was determined as follows, c phonon (EqW
=fi
Cphonon(HS) + (1
-fHS
)c,h,,,,(Ls)~
tg)
The phonon entropy, A.,,S(phonon), is obtainable by integration of the hatched part surrounded by Cphonon0-W and Cphonon(Equil) curves in Fig. 13 with respect to In T to give 28.56 J K-’ mol-‘. As a result, the observed entropy gain, AtRS = 36.19 J K-’ mol-‘, arising from the spin-state interconversion was found to be reasonably accounted for in terms of the sum (37.69 J K-’ mol-‘) of the contribution from a change in the spinmanifold (9.13 J K-’ mol-‘) and the contribution from a change in the skeletal normal modes (28.56 J K-’ mol-‘). On the other hand, the hatched area itself corresponds to a part of the phonon enthalpy given by the following quantity: A’,,H(phonon)
- {H&honon.
HS)
- H,,(phonon, LS)} = 3260 J mol-‘.
(10)
949
Unusual heat capacity of [Fe(acpa),]PF,
T/K
Fig. 13. Heat capacities arising from six skeletal normal modes (15 degrees of freedom) of [Fe(acpa)zJPF,. c rt,,,&-S) and C,,,,, (HS) correspond to the heat capacities of pure low- and high-spin states, respectively, while c phonon(Equil) corresponds to the spin-equilibrium state. Explanation of the hatched area is given in the text.
As described above, it is usually hard to estimate the contents of A,H because of the lack of the experimental value at 0 K, (H&IS) - H,(LS)). Fortunately, however, as will be discussed in Section 6, we were able to determine this value to be 2220 J mol-’ for the present complex [Fe(acpa),]PF, [see eqn (IS)]. By subtracting this value and the quantity given by eqn (IO) from the observed A,,H = 7025 J moi-‘, we obtain the following quantity: A,,,H(spin) - (H,,(spin, HS) - H&pin,
LS)]
=1545Jmol-‘. Thus, we can summarize the transition follows:
(11)
enthalpy as
Am H = A,, H(spin) + A,,, H(phonon) = [{H&pin,
HS) - H,(spin, HS))
- (Hr(spin, LS) - H,(spin, LS)}] + [(H,(phonon,
HS) - H,,(phonon, HS))
- ~H~~phonon, LS) - H*(phonon, LS))] + [(HO(spin, HS) + H,(phonon,
HS)j
- (H,,(spin, LS) f H,(phonon,
LS))]
=(1545+3260+2220)Jmol-’ = 7025 J moI_‘.
(12)
6. MECHANISM OF THE SPIN-STATE INTERCONVERSION
Since the present spin-crossover is associated with the transfer of two electrons between ea and fZg
orbitals, it brings about more or less changes in the molecular geometry. In fact, IR and Raman spectra (Figs 3-5) showed a significant shift of the skeletal modes of vibration between the lowand high-spin states. At first glance, the magnitude of the shift covering a range of 17-163 cm-’ (see Table 3) seems very large. However, in the case of [Fe(‘phen),(NCS),], which belongs to the spin-transition type, some of the six skeletal modes are known to shift by 150-250 cm-’ between the low- and highspin states [5,41]. Therefore, it is very likely that the present assignment, though tentative, is reasonable. Regardless of the spin-crossover types (either the spin-transition or the spin-equilibrium types), one can conclude that the spin-state interconversion is accompanied by a drastic change in the molecular geometry around the central iron ion. Moreover, as in the case of the spin-transition type [S], we can arrive at the conclusion that, unlike previous predictions [42,43], the energy separation between the *7’%ground state and the higher 6A,, state is nearly independent of temperature. If the energyseparation varies with temperature, a continuous shift of the skeletal modes would be expected; but this is not the case. At extremely low temperatures, the electronic ground state is really 'T,. On the other hand, at high enough temperatures, the 6Au state becomes the ground state by virtue of the dominant entropy term in the Gibbs free energy due to the spin-manifold and the softening of the skeletal modes of vibration. Although the present study revealed that the spinstate interconversion in the spin-equilibrium type proceeds similarly to that in the spin-transition type, one may ask why does the spin-crossover occur so gradually for the complexes of the fast electronic relaxation type? In order to elucidate this question, we shall apply here the Frenkel theory of heterophase fluctuation in liquids [44]. This model assumes that one phase contains “embryos” of a second phase in the transition region and that each embryo consists of a uniform size. The assumption of such embryos with a critical size does not conflict with the present IR and Raman spectra which give evidence for coexistence of the high- and low-spin states over the temperature region in which the spin-t~nsition occurs. Let us consider a system consisting of N cells each of which contains n molecules. The product of N and n is equated to the Avogadro constant NA. By assuming a simple linear interpolation with the high temperature mole fraction x between the Gibbs energy G, of the low temperature phase and the corresponding quantity G, of the high temperature phase, we obtain the Gibbs energy at TK, G =xGH+(l
-x)GL
+ NkTffxlnx +(I -x)in(l
-x)),
(13)
MICHIOSORAIet al.
950
where k is the Boltzmann constant. The equilibrium mole fraction is determined by the requirement that (dG/dx), = 0; x = I/{ 1 + exp(AG/NkT)},
(14)
where AC = G, - CL. The molar heat capacity at constant pressure C, is obtained by the following relation,
C,=&MT)+(l
-x)&.(7-))
= XC,.” + (1 - X)C,.‘ +
{b(T) - HL.(T)}* exp(AGINkT) NkT*{ 1 + exp(AG/NkT)}*
’
(13
where H means molar enthalpy, and C,,, and C,,, the “normal” heat capacities of the high and low temperature phases, respectively. At the transition temperature T,, the Gibbs free energies of both phases must be equal. By substituting the condition AC = 0 at T = T, into eqn (15), we obtain a maximum value of C,: C,(Tc) = i&,,~(Tc)
The value of n is extremely small in comparison with 95 and 77 found for [Fe(phen)z(NCS)2] and [Fe(phen),(NCSe),] of the spin-transition type [5]. This fact obviously indicates that the cooperativity of the spin-state interconversion is much weaker for the spin-equilibrium type than for the spin-transition type. In other words, excitation of the high-spin embryo in the low-spin phase can take place in a small unit when the complexes belong to the spinequilibrium type. When the number of molecules in a cell or domain is small, the effect of the spin-state interconversion happening in a given domain upon the adjacent cells would be weak, eventually leading to a large fluctuation between the low- and high-spin states. This is the reason why the spin-crossover of the spin-equilibrium type takes place over a wide temperature range.
REFERENCES 1. 2. 3. 4. 5. 6.
+ C,.,(Tc)J
7.
+{H,(Tc) The number foIlows:
- Hr(Tc))*/4NkTc2.
of ceils is, therefore,
determined
(16) as
8. 9. 10.
N=
4kTc2[C,&)
I&V-c) - H,U’c)12 - {&.tVc) + C,.,(Tc)}Pl
Il.
(17) For the present complex [Fe(acpa),]PF,, we adopted the values of Tc= 189.641 K, C,(T,)= 549.83 J K-’ mol-‘, and {CpeH(TC) + C,,(Tc)}/2 = {C,,,(HS, Tc)+ C,,,(LS, Tc)}/2 =431.93 J K-’ mol-‘. On the other hand, integration of C,,(HS) and C,,,(LS) shown in Fig. 6 with respect to T gives {H"(T)-H"(O)} and {H,(T)- H,(O)},respectively. In order to adjust AC = 0 at T,, we added 2220 J mol-’ which corresponds to the enthalpy difference between the high- and low-spin states at 0 K, that is, H"(O)- H,(O)= 2220Jmol-‘.
(18)
As a result, the number of cells was determined to be N = 1.21 x lo”. Consequently, the number of molecules in a cell or a domain was estimated to be n = 5. The broken curve in Fig. 9 shows the excess heat capacity calculated on the basis of eqn (15). The gross aspect of AC, is well accounted for in terms of the Frenkel model.
12. 13.
Giitlich P., Strucr. Bonding 44, 83 (1981). Rao C. N. R., Int. Rev. phys. Chem. 4, 19 (1985). Kiinig E., Ritter G. and Kulshreshtha S. K., Chem. Rev. 85, 219 (1985). KSnig E. and Madeja K., Inorg. Chem. 6, 48 (1967). Sorai M. and Seki S., J. phys. Sot. Japan 33,575 (1972); J. Phys. Chem. Solids 35, 555 (1974). Haddad M. S., Lynch M. W., Federer W. D. and Hendrickson D. N., Inorg. Chem. 20, 123 (1981). Sorai M. and Hendrickson D. N., Heat Capacity Measurements of [Fe(III)(3-OMe-SalEen)1]PF, (unpublished results). Sorai M., Ensling J. and Giitlich P., Chem. Phys. 18, 199 (1976). Kaji K. and Sorai M., Thermochim. Acra 88, 185 (1985). Ewald A. H.. Martin R. L.. Ross I. G. and White A. H.. Proc. R. So;. AZSO, 235 (i964). Ewald A. H., Martin R. L., Sinn E. and White A. H., Inorg. Chem. 8, 1837 (1969). Kambara T., J. them. Phys. 70, 4199 (1979). Sasaki T. and Kambara T., J. them. Phys. 74, 3472
(1981). 14. Kambara T., J. them. Phys. 74, 4557 (1981). 15. Frank E. and Abeledo C. R., Inorg. Chem. 5, 1453
(1966). 16. Golding R. M. and Whitfield H. J., Trans. Faraday Sot. 62, 1713 (1966). 17. Rickards R.. Johnson C. E. and Hill H. A. 0.. J. them. Phys. 48, 5231 (1968). 18. Merrithew P. B. and Rasmussen P. G., Inorg. Chem. 11, 325 (1972). 19. Hall G. R. and Hendrickson D. N., Inorg. Chem. 15, 607 (1976). 20. Kunze K. R.. Perry D. L. and Wilson L. J., Inorn.
Chem. 16, 594 (197;). 21. Oshio H.. Maeda Y. and Takashima Y.. Inorz. Chem. 22, 2684 i1983). 22. Maeda Y., Tsutsumi N. and Takashima Y., Inorg. Chem. 23, 2440 (1984). 23. Federer W. D. and Hendrickson D. N., Inorg. Chem. 23,
3861, 3870 (1984). 24. Timken M. D., Hendrickson D. N. and Sinn E., Inorg. Chem. 24, 3947 (1985). 25. Matsumoto N., Ohta S., Yoshimura C., Ohyoshi A., Kohata S., Okawa H. and Maeda Y., J. them. Sot. Dalton Trans. 2575 (1985). 26. Timken M. D., Abdel-Mawgoud A. M. and Hendrickson D. N., Inorg. Chem. 25, 160 (1986).
Unusual heat capacity of [Fe(acpa),]PF, 27. Timken M. D., Strouse C. E., Soltis S. M., Daverio S. A., Hendrickson D. N.. Abdel-Mawgoud A. M. and Wilson S. R., /. Am. them. Sot. 108, 395 (1986). 28. Maeda Y., Takashima Y., Matsumoto N. and Ohyoshi A., 1. &em. Sot. Dalton Trans. 11I5 (1986). 29. Maeda Y.. Oshio H.. Takashima Y.. Mikuriva M. and Hidaka M., Inorg. &em. 25, 2958 (1986). 30. Shipilov V. I., Zelentsov V. V., Zhdanov V. M. and Turdakin V. A., JETP Lerr. 19, 294 (1974). 31. Kaji K., Sorai M. and Hendrickson D. N., Heat Capacity Measurements of [Fe(III)(3-OEtSalAPA),]CIO,.C,H, (unpublished results). 32. Nagano Y., Sorai M. and Hendrickson D. N.. Heat Capacity Measurements of [Fe(III)(3-OEtSalAPA),]CIO,.C,H,CI (unpublished results). 33. Sorai M. and Kaji K., Construction of an Adiabatic Calorimeter Capable of Measuring Heat Capacities Between 13 and 520 K (unpublished). 34. Ogasahara K., Sorai M. and Suga H., Molec. Cryst. !iq. Cryst. 71, 189 (1981).
951
35. Sorai M. and Seki S.. J. phys. Sot. Japan 32, 382 (1972). 36. Mikami M., Nakagawa I. and Shimanouchi T., Spectrochirn. Acra 23A, 1037 (1967). 37. Kline C. H., Jr and Turkevich J., J. them. Phys. 12,300
(1944). 38. Corrsin L., Fax B. J. and Lord R. C., 1. them. Phys. 21, 1170 (1953). 39. McCullough J. P., Douslin D. R.. Maserly J. F.,
Hossenlopp I. A., Kincheloe T. C. and Waddington G.. J. Am. them. Sot. 79, 4289 (1957). 40. Mayfield H. G. and Bull W. E.. J. them. Sot. A. 2279 (1971). 41. Takemoto J. H. and Hutchinson B., fnorg. nucl. Chem. Lett. 8, 769 (1972); Inorg. Chem. 12, 705 (1973). 42. KBnig E. and Kremer S., Theoret. chim. Acla 20, 143
(1971). 43. Kiinig E., Ber. Bunsenges. phys. Chem. 76, 975 (1972). 44. Frenkel J., in Kinetic Theory of Liquids, Chap. VII.
Oxford University Press. London (1947).
c4322-3697190 13.00 + 0.00
Printed in Great Britain.
8
1990 Pcrgamon Press plc
UNUSUAL HEAT CAPACITY OF THE FERRIC SPIN-CROSSOVER COMPLEX, [Fe(acpa),]PF,, SHOWING A GRADUAL BUT COMPLETE SPIN-STATE INTERCONVERSION AT THE FAST SPIN-FLIPPING RATE? MICHIO SORAI,~ YONEZO MAEDA~ and HIROKI OSHIO~ SMicrocalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan $Department
of Chemistry, Faculty of Science, Kyushu University, Higashiku, Fukuoka 812, Japan TInstitute for Molecular Science, Okazaki, Aichi 444, Japan (Received 5 October 1989; accepted 24 January 1990)
Abstract-The heat capacity of the iron(II1) spin-crossover complex [Fe(acpa),]PF, [Hacpa = N-(l-acetyl2-propylidene)(2-pyridylmethyl)amine], which shows fast electronic relaxation between S = l/2 (2Tti) and S = 5/2 (6A,,) in comparison with the s’Fe Mdssbauer lifetime (lo-’ s), was measured with an adiabatic calorimeter in the IS-320 K range. Variable temperature IR and Raman spectra were recorded between 84 and 300 K. An unusually broad heat-capacity peak starting from * 120 K, culminating at _ 190 K, and terminating at -280 K was observed. A normal heat capacity curve which separates the excess heat capacity from the observed values was determined. The enthalpy and entropy arising from the spin-crossover phenomenon were 7025 J mol-’ and 36.19 J K-’ mol-‘, respectively. The entropy gain was well accounted for in terms of the sum (37.69 J K-’ mol-‘) of the contribution from a change in the spin-manifold R ln(6/2) (= 9.13 J K-’ mol-‘) and from a change in the skeletal normal modes of vibration detected by IR and Raman spectra (28.56 J K-‘mol-‘). To elucidate the question, Why does the spin-crossover occur so gradually for the complexes of the fast electronic relaxation type?, the Frenkel theory of heterophase fluctuation in liquids was applied. As a result, the number of molecules in a domain was proved to be as small as five. This makes a large fluctuation possible between the low and high spin states, eventually leading to the spin-equilibrium type transition taking place over a wide temperature range. Keywords: Spin-crossover, spin-state interconversion, heat capacity, iron(II1) complex, Frenkel model, heat capacity anomaly, infrared spectra, Raman spectra.
1. INTRODUCTION Studies of spin-crossover phenomena occurring between low- and high-spin states have been extensively developed for octahedral iron(H) and iron(III) complexes [l-3]. This is due to the fact that 57Fe serves as a good probe of the Miissbauer spectroscopy by which both the low- and high-spin states can be directly observed. In particular, temperature dependence of the Miissbauer spectra can provide detailed information about the degree and the rate of the spinstate interconversion and thereby give a useful clue to the mechanisms of the spin-crossover phenomena. As widely recognized, the spin-crossover phenomena are phenomenologically classified into two groups: one is the so-called “spin-transition type” in which the spin-state interconversion between the lowand high-spin states takes place abruptly within a narrow temperature range, say, several kelvins and the other is the “spin-equilibrium type” in which the spin-state interconversion occurs gradually over a wider temperature range than 100 K. These two types
tcontribution search Center.
No. 24 from the Microcalorimetry
Re-
are encountered in both the iron(I1) and iron(II1) complexes,‘though there are very few iron(II1) complexes that show the spin-transition type behavior. Typical examples of the spin-transition type are [Fe(phen),(NCS),] [4, 51 for the iron(I1) complexes and [Fe(3-OMe-SalEen),]PF, [6,7] for the iron(II1) complexes, while representatives of the spin-equilibrium type are [Fe(Z-pic),]Cl,-EtOH [8,9] and [Fe(S,CNR,),] [lo, 111 for the iron(I1) and iron(II1) complexes, respectively. The choice as to which type of the spin-crossover a given complex follows, is made according to the strengths of the Jahn-Teller coupling between the d-electrons and local distortions [12] and of the intermolecular coupling between the intramolecular distortions and/or a lattice strain [13, 141. On the other hand, an alternative classification of the spin-crossover complexes has been made according to the rate of the spin-state interconversion: one is the “fast electronic relaxation type” in which the spin-flip rate is faster than the “Fe Miissbauer lifetime (IO-‘s) and the other is the “slow electronic relaxation type”. Since each spectroscopy has its own time-scale and the 57Fe Mossbauer lifetime is not a standard of the time-scale, a classification of this type
941
942
MI~HIO.Sorur et al.
may be criticized. From an experimental viewpoint, however, this is a convenient classification for two reasons. First, an increasing number of iron complexes in which spins flip at a rate greater than or equal to the inverse of the “Fe Mijssbauer lifetime have recently been reported [15-291 and those Miissbauer spectra show relaxation phenomena in the spin-transition region. Second, those complexes showing the fast electronic relaxation between the low- and high-spin states are at present encountered only in the iron(III) complexes and exhibit a smooth increase of the magnetic moments with increasing temperature, i.e. the spin-equilibrium type. It should be remarked here that no iron complexes of the fast electronic relaxation type which belong to the spintransition type have been known. The present iron(II1) complex [Fe(acpa),]PF, [Hacpa = N-( 1-acetyl-2-propylidene) (2-pyridylmethyl)amine] (see Fig. 1) shows a spin-crossover phenomenon between S = l/2 (2r2,) and S = 5/2 (6AIg) with a fast spin-interconversion rate of about (0.5 - 3) x lo6 s-i over the - 110 to -280 K range. This complex, therefore, belongs to the spinequilibrium type with fast electronic relaxation time [29]. In the case of the iron complexes of the spintransition type, the spin-state interconversion takes place through a phase transition which has been clearly demonstrated by heat capacity measurements [5,7,30]. The main purpose of the present paper is to elucidate the thermal properties of the iron complex of the spin-equilibrium type with fast electronic relaxation time and to compare the results with those of the spin-transition type. Calorimetric measurements so far made for the iron complexes of the spin-equilibrium type involve (i) [Fe(II) (2-pic),]Cl,. EtOH [9], (ii) [Fe(III)(3OEt-SalAPA),]CIO,.CgHg [31] and (iii) (Fe(III)(3OEt-SalAPA),]ClO,~C,H,Cl [32]. The complex (i) belongs to the slow electronic relaxation type whereas (ii) and (iii) are of the fast electronic relaxation type. Regardless of the spin-interconversion rate, these three complexes exhibited a well-resolved heat capacity peak(s) arising from the phase transition(s) as well as a broad heat capacity hump extending over a wide temperature range. In these complexes, reorientational motions of the solvate molecules such as ethanol, benzene and chlorobenzene are strongly coupled with the spin-state interconversion. There-
Fig. 1. Schematic drawing of the tridentate ligand (acpa).
fore, the phase transitions observed for these three complexes seem to be a consequence of the cooperative coupling between the orientational disordering and the spin-state interconversion. In contrast to this, PF; anions in the present complex [Fe(acpa),]PF, are known to be in an ordered state without any reorientational motions even in the high-spin phase (at 293 K) [29]. In this sense, [Fe(acpa),]PF, is a suitable material for the elucidation of the intrinsic thermal properties of the spin-crossover complexes classified as the spin-equilibrium type.
2. EXPERIMENTAL 2.1. Sample preparation The complex [Fe(acpa)z]PF, was prepared and carefully purified by recrystallization from dichloromethane according to the method previously described [29]. Analysis: calculated for FeCuH2,N,02PF,: C, 45.62; H, 4.52; N, 9.67%. Found: C, 45.65; H, 4.50; N, 9.70%. 2.2. Heat capacity measurements Heat capacities were measured with an adiabatic calorimeter [33] from 15 to 320 K. A calorimeter cell [34] made of gold-plated copper was loaded with 16.7887 g (or 0.0289818 mol) of polycrystalline [Fe(acpa),]PF, with buoyancy correction using the density of 1.472 g cmv3 [29]. A small amount of helium gas was sealed in the cell to aid the heat transfer. 2.3. Vibrational spectroscopies Variable temperature IR spectra were recorded for Nujol mulls between 88 and 300 K with an infrared spectrophotometer Model DS-402G (Japan Spectoscopic Co.) in the 4000_400cm-’ range and with a far-infrared spectrophotometer Model FIS-3 (Hitachi) in the 400-30cm-’ range. Multitemperature spectra in the Raman lOOO-80cm-i range were recorded for a KBr disk between 84 and 294 K with a laser Raman spectrophotometer Model R-800 (Japan Spectroscopic Co.) using the 514.5 nm line from an Ar source for excitation.
3. RESULTS Calorimetric measurements were made in five series, the results of which were evaluated in terms of C,, the molar heat capacity at constant pressure. The experimental data are listed in Table 1 and plotted in Fig. 2. A heat capacity anomaly forming a broad hump was observed over a range from - 120 to -280 K. Since this temperature range just corresponds to the anomalous region where the magnetic moment is altered from the low- to high-spin values [29], the present heat capacity anomaly obviously arises from the spin-state interconversion.
943
Unusual heat capacity of [Fe(acpa),]PF, Table 1. Molar heat capacity of [Fe(acpa),]PF, T
CD
CD
T
X
JX-lmol-1
K
JX-'mol-'
88.294
90.721 93.094 95.417 97.695 99.931 102.129 104.291 106.420 108.618 110.588 112.629 114.646 116.638 118.607 120.554 122.480 124.667 135.234 137.552 139.846 142.115
226.77 232.16 237.33 242.02 246.70 251.36 256.02 260.86 265.47 269.91 274.25 278.40 282.34 286.36 290.49 294.60 298.85 303.96 328.38 334.13 339.93 345.78
144.360 146.582 148.780 150.955 153.107 165.237 157.344 159.428 161.488 163.526 165.796 168.307 170.792 173.240 175.651 178.027 180.371 182.687 186.006 187.331 189.641 191.939
352.01 358.54 365.15 372.12 379.30 388.87 396.04 403.53 412.52 422.10 433.57 447.14 461.24 475.72 490.21 604.19 517.06 628.10 637.56 544.89 649.83 552.96
18.406 19.268 20.150 21.047 22.130 23.387 24.649 25.882 27.074 28.241
43.47 46.09 48.91 52.04 55.94 60.34 64.75 69.01 72.88 76.71
29.554 31.001 32.565 34.240 35.998 39.864 41.070 42.649 44.306 46.033
121.549 123.601 125.915 128.347 130.749 133.045 134.693 136.399 138.705 140.986 143.243 145.477 147.687 149.873 152.037 154.178 156.297
296.84 301.41 306.54 311.91 317.45 322.84 326.66 331.03 336.73 342.55 348.65 354.86 361.35 368.16 375.38 382.74 390.56
16.118 16.977 17.846 18.726 19.633 20.568 21.530 22.683 24.007 25.321 26.628 28.050 29.658 31.014 32.570 34.209 35.892 37.697 278.954 281.887 284.810 287.718
(relative molecular mass 579.285)
T
CD
CD
T
X
JX-lmol-1
X
JX-'rol-'
1 194.226 196.506 198.777 201.041 203.297 205.546 207.790 210.030 212.266 214.499 216.817 219.221 221.626 224.033 226.448 228.862 231.275 233.686 236.094 238.498 240.898 243.294
655.42 667.82 660.02 562.44 564.39 566.42 567.31 567.47 566.90 566.28 566.23 563.32 660.63 658.11 556.95 655.70 554.67 563.82 553.19 553.87 554.86 556.20
246.684 248.068 260.i47 252.820 265.186 257.645 259.897 262.570 265.668 268.655 271.526 274.488 277.438 280.376 283.302 286.216 289.116 291.999 294.870 297.733 300.585
567.56 558.95 560.78 562.91 666.11 567.58 570.36 573.39 577.20 680.97 686.17 689.81 593.50 597.65 801.79 606.74 610.48 614.75 618.80 622.68 627.95
Series 80.87 85.47 90.10 95.22 100.78 111.54 114.69 118.86 123.37 128.12
2 47.819 49.667 51.599 53.667 55.580 57.638 59.753 61.970 64.233
132.86 138.04 143.66 149.20 154.62 160.01 165.03 169.63 174.61
66.651 69.215 71.908 74.636 77.262 79.803 82.267 84.663 86.999
179.31 184.51 190.48 196.62 202.57 208.07 213.36 218.77 223.97
158.392 160.465 182.514 184.667 167.065 169.573 172.042 174.475 176.872 179.235 181.568 163.886 186.203 188.614 190.812 193.099 195.377
Ssriee 398.90 407.60 416.92 427.10 439.78 463.49 468.01 482.80 496.94 610.55 523.06 633.38 641.57 647.39 651.53 554.51 556.81
3 197.646 199.907 202.161 204.407 206.647 208.882 211.113 213.342 215.569 217.883 220.295 222.716 225.139 227.561 229.962 232.401
559.0s 561.35 663.65 566.66 566.80 567.54 667.32 566.85 666.71 563.64 561.64 559.61 657.60 656.89 554.81 554.02
237.235 234.646 242.061 244.452 246.848 249.238 251.621 254.000 256.372 258.737 261.423 264.428 267.421 270.402 273.369 276.324
653.28 654.61 556.33 556.53 568.07 559.50 561.86 563.97 566.49 668.86 571.68 575.48 579.29 583.31 588.26 591.95
36.01 39.84 42.66 46.04 47.50 50.63 54.06 57.93 62.63 67.08 71.26 75.82 60.68 85.28 90.04 95.00 100.02 104.97
39.182 40.670 42.334 44.212 48.026 47.737 49.361 60.910 62.393 63.820 55.197 56.629 67.819 59.073 60.294 61.704 63.293 64.836
Series 109.57 113.72 118.16 123.44 128.36 132.97 137.41 141.82 148.27 150.03 153.73 167.39 160.73 163.73 166.46 169.34 172.74 175.97
4 66.339 67.914 69.686 71.651 73.742 75.841 77.882 81.028 83.458 85.823 88.861 91.915 94.260 96.567 98.810 101.024 103.201
178.85 181.85 186.60 189.97 194.77 199.43 203.99 210.98 216.18 221.44 228.09 234.78 239.67 244.41 249.09 253.66 259.46
105.343 107.454 109.535 111.687 113.614 115.615 117.693 119.548 121.483 123.396 125.291 127.168 129.024 130.864 132.688 134.496 138.288
263.18 267.72 272.17 276.45 280.28 284.27 288.20 292.43 296.66 301.06 305.23 309.38 313.85 317.89 322.18 326.62 330.90
695.76 600.08 604.69 608.32
290.610 293.488 296.366 299.217
Series 613.09 616.30 620.90 626.53
5 302.066 304.628 306.612 308.692
630.05 633.22 636.60 639.72
310.764 312.829 316.257 318.046
642.68 645.58 649.51 663.81
Seriee
944
MICHIOSORAIer ai.
645
436 I
600
300
K
273 K 230K 210K 190 K 170 K 150K 130K
F
0’
I
100
0
I
I
200
300
P--
103 K t 662
T/K 4k2
Fig. 2. Molar heat capacity of [Fe(acpa),]PF,. Broken curve indicates the normal (or lattice) heat capacity curve. Although the crystal system and space group of [Fe(acpa)z]PF, in the low-spin state at - 120 K are identical with those in the high-spin state at -290 K (monoclinic and P2/a), the average bond distances of Fe-N and Fe-O are shortened by 0.106 and 0.050 A, respectively, and thereby the effective molecular volume is reduced by 23 A3 [29]. When such a drastic change occurs in a molecule, one can expect significant changes in the IR and Raman spectra. In fact, as shown in Figs 3-5, the IR and Raman spectra
300
700
600
500
LOO
5
/cm-l Fig. 4. Variable temperature IR spectra of [Fe(acpa),]PF, in the 70&400cm-’ range.
contain characteristic bands whose intensities vary strongly with temperature. Although we have not assigned these bands theoretically, it is very likely that they are the skeletal modes of the [FeN,O,] core. Those bands whose intensities are decreased with increasing temperature would be the skeletal modes of the complex in the low-spin state while those bands
K
23OK 299K
2lOK
190 K
ISOK
170 K 86 K
3’71 400
64K
2’67 I
I
I
300
200
100
P
30
/cm-l
temperature far-IR spectra of Fig. 3. Variable [Fe(acpa)JPF, in the 400-30cm-’ range. In this and in Figs 4 and 5, shaded bands are sensitive to temperature and tentatively assigned to the skeletal modes of the [FeN,O,] core.
I
10
500
I
I
400
300
3
I 200
L
10
/cm-l
Fig. 5. Variable temperature laser Raman spectra of [Fe(acpa)JPF, in the 600-80 cm-’ range, recorded by using an Ar source.
Unusual heat capacity of [Fe(acpa)*]PF, whose intensities are increased with increasing temperature would be the modes characteristic of the high-spin state. The effect of changes in the skeletal modes by the spin states upon the heat capacities will be described in Section 5.
600 -
4. SEPARATION OF HEAT CAPACITY ANOMALY For determination of the excess heat capacities due to the spin-crossover phenomenon, it is necessary to estimate a “normal” heat capacity curve or a lattice heat capacity, C,,, . To this end, an effective frequency distribution method [35] was employed. The normal heat capacity of a solid reflects both a continuous acoustic phonon distribution and many discrete optical branches corresponding to intramolecular vibrational modes. From IR and Raman spectra, one can know the fundamental frequencies of these vibrational modes, though not all. The principle of the effective frequency distribution method [35] is to include the normal modes that cannot be assigned, into a continuous phonon distribution and to determine an effective frequency distribution spectrum by least-squares fitting to the observed heat capacities. Since the present compound consists of 62 atoms, the number of degrees of freedom for a formula unit is 186. Among them, 41 modes of intramolecular vibration (129 degrees of freedom) were reasonably assigned on the basis of the IR and Raman spectra with the aid of the literature [3-O]. As can be seen from Fig. 1, the ligand consists of an acetylacetonelike moiety, for which the assignments have been made theoretically [36], a methylene group and a pyridine moiety [37-391, while the counter anion is hexafluorophosphate [40]. The remaining 57 degrees of freedom and the (C, - C,.) correction were effectively included in a continuous spectrum spanning the 0-700cm-’ range, which consists of two Debye distributions and three constant distributions. Contribution of the 129 optical modes to the normal heat capacity was calculated according to the Einstein model. We determined independently the normal or lattice heat capacity curves for the low-spin state, C,,,(LS), and for the high-spin state, C,,(HS), as follows. For the C,,,(LS), we used 35 C, values in the 15-40 K range and 40 C, values in the 75-120 K range. The reason why we skipped the C, data in the 40-75 K range is that in this temperature region the observed heat capacity curve showed a tiny hump, whose origin has not been interpreted. On the other hand, we used 16 C, values in the 290-320 K range for the C,,(HS). In order to avoid trivial results (i.e. negative frequency distributions), we added 24 C, data in the 15-30 K range as if they belonged to the values of the high-spin state. As shown in Fig, 6, the “best” fit frequency distribution spectra reproduced the 75 C, values for the low-spin state within kO.241 J K-i mol-’ of the r.m.s. deviation and the 40 C’, values for the “high-spin” state within
01
I
0
1
-I
300
200
100 l-/K
Fig. 6. Normal or lattice heat capacities of [Fe(acpa),]PF,. C,,(LS) and C,,(HS) are the lattice heat-capacity curves for the pure low- and high-spin states, respectively, while C,, corresponds to the real lattice heat capacity. Closed circles indicate the observed heat capacities. kO.322 J K-i mol-‘. Extrapolation of the best fit C, curve for the low-spin state below 15 K enables us to evaluate the standard thermodynamic functions of [Fe(acpa),]PF,. Table 2 lists the heat capacity C;, molar entropy So, enthalpy function (H” - Hg)/T, and the Gibbs function -(Go - Hz)/T at rounded temperature. The next step is to estimate the real normal heatcapacity curve, C,,, on the basis of C,,,(LS) and C,,(HS), according to the following relationship
C,,, =fHs&(HS)
+ (1 -fHs)Cbc(LS),
(1)
where fHs means the high-spin fraction. The temperature dependence of fHscan be evaluated from the observed magnetic moment [29] by the equation, /& =f&~a(HS)*
+ (1 -fus)~ee(LS)*,
(2)
where pcRstands for the observed value while p&LS) and perr(HS) are the magnetic moments for the low- and high-spin states, respectively. Based on experiment [29], we adopted p,&LS) = 2.05~~ for the low-spin S = l/2 state and p,e(HS) = 5.97~~ for the high-spin S = 5/2 state, where pa is the Bohr magneton. The high-spin fraction thus obtained is plotted in Fig. 7 by open circles. The S-shaped curve suggests a gradual spin-state interconversion for a system in which there exists a Gibbs free energy difference, AC, between the high- and low-spin states:
fHs= l/i1+ w@GIW},
(3)
where R is the gas constant. Equation (3) is rewritten as follows: AC/R = T In{(llf,,)
- I}.
(4)
Mm-no SORAIet al.
946 Table
2.
Standard thermodynamic functions for [Fe(acpa),]PF, J K-t mol-I); the values in parentheses are extrapolated
co P
T/K
So
(HO- H;)/T
-(GO-
(in
po)/T
i8 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310
(3.943) (17.713) (32.788) 48.501 82.150 111.911 139.049 165.678 186.297 208.536 230.572 251.496 273.088 293.404 315.889 340.279 368.622 405.777 456.209 514.935 550.349 561.440 567.468 562.097 554.807 654.683 560.308 570.450 582.797 597.072 612.015 626.918 641.588
(1.367) (8.111) (18.115) 29.822 66.012 83.781 111.677 139.510 166.613 192.952 218.797 244.191 269.179 293.803 318.174 342.464 366.882 391.819 417.879 445.655 414.614 503.142 530.720 557.042 581.853 605.424 628.165 650.330 672.072 693.536 714.752 736.737 756.532
(1.021) (5.774) (12.242) 19.457 34.890 60.468 65.483 80.081 93.806 106.796 119.328 131.490 143.394 155.037 166.539 118.075 189.802 202.105 215.519 230.561 246.624 262.097 276.540 289.686 301.355 311.880 321.685 331.047 340.132 349.060 357.876 366.581 375.210
(0.346) (2.337) (5.873) 10.365 21.122 33.313 46.195 69.428 72.808 86.157 99.469 112.701 125.785 138.766 151.636 164.388 177.080 189.714 202.360 215.095 227.989 241.045 254.179 267.357 280.499 293.546 306.480 319.283 331.940 344.476 356.876 369.157 381.322
298.15
623.479
731.869
364.975
366.894
5 :x 20 30 40 50 60 70
As plotted in Fig. 8, the AC/R derived from eqns (2) and (4) (open circles) were well reproduced by the following quadratic equation in the temperature (solid curve),
Now that the high-spin fraction, fHs, has been determined as a function of temperature, we can estimate the lattice heat capacity, C,,, according to eqn (I). The C,,, thus estimated is shown in Fig. 2 by the broken curve and in Fig. 6 by a dotted curve. AC/R = -0.03426T2+1.7436T + 1067.1.(5) At low temperatures the C,,, curve asymptotically approaches to C,,,(LS) while at high temperatures it The high-spin fraction shown by the solid curve in is approximated by C,,,(HS). Fig. 7 corresponds to the calculated values based on The difference between the observed and normal eqns (3) and (5). heat capacities shown in Fig. 2 or Fig. 6 corresponds
1000
l.OOE 5 0.75. 2 IA ,s 0.50-
0 e .
:: 6
I:
0.25-
i
-1000
0.00 -
-2om
T/K Fig. 7. Temperature dependence of the high-spin fraction of [Fe(acpa),]PF,. Open circles indicate the values derived from eqn (2) and the observed magnetic moments [29], while the solid curve is calculated on the basis of eqns (3) and (5).
0
100
200
300
T/K
Fig. 8. The Gibbs free energy difference, AG/R, between the high- and low-spin states of [Fe(acpa),]PF,. Open circles are derived from eqns (2) and (4). while the solid curve is calculated from eqn (5).
Unusual heat capacity of [Fe(acpa),]PF,
1 00
30
T
i
z E
80
i r c) .
60 LO
34
20
947
ij
E
5
r
-9 .
w Q
20 t
I
1lY
A,,.S=3&19JK-'rival-' 0 0-tI
I
100
T/K
200
300
T/K
Fig. 9. The excess heat capacity, AC,,, of [Fe(acpa),]PF, arising from the spin-crossover phenomenon. The broken curve indicates the theoretical values calculated by eqn (15).
Fig. I I. Temperature dependence of the excess entropy of [Fe(acpa),]PF, arising from the spin-crossover phenomenon. The ultimate value at high temperatures corresponds to the total entropy change, AmS.
to the excess heat capacity,
The high-spin fraction thus obtained calorimetrically is compared in Fig. 12 with the values determined from the magnetic moment [29] and eqn (2). Since the two sets off,, agree well, the separation of the heat capacity anomaly from the observed values seems to have been done reasonably.
crossover
phenomenon.
AC,, due to the spinIn Fig. 9, AC, is plotted as a
function of temperature. Deviation from the normal heat capacity curve occurred at _ 120 K, peaked _ 190K, and came back to the normal curve at -280 K. Interestingly, this broad AC, peak exhibits a shoulder at its high temperature side as if the heat capacity anomaly would consist of two broad peaks. The enthalpy, Atn H, and entropy, A,, S, arising from the spin-crossover phenomenon were determined by integration of AC, with respect to T and In T, respectively. Temperature dependences of the excess enthalpy and entropy are shown in Figs 10 and 11, respectively. The ultimate values at high temperatures correspond to A,=H and A,,S, respectively, and they amounted to A,,H = 7025J mol-’ and A,,,S = 36.19 J K-t mol-I. From a thermodynamic viewpoint, the high-spin fraction at a given temperature can be related to the enthalpy gain, AH(T), at T K by the following equation,
f~s=AHVY4,
(6)
H.
5. ENTHALPY AND ENTROPY SPIN-STATE
OF THE INTERCONVERSION
Although the heat capacity anomaly observed for the present spin-crossover complex [Fe(acpa), JPF, belongs to neither a first-order nor a second-order phase transition, one can still claim that this unusual heat capacity anomaly would originate in a kind of phase transition characterized by weak cooperativity, i.e. a higher-order phase transition. In what follows, therefore, we shall regard this anomaly as a “phase transition”. The enthalpy and entropy gained at a phase transition are described as follows, A,, H = H;(HT)
- HO,(LT)
= {H;(HT) - H:(HT)) ml0
1
- {H;&T)
- H;(LT)} + {H,O(HT) - H,O(LT)j
(7)
6000
and AmS = SO,(HT) - S;(LT),
1 loo
I
I
200
300
T/K
I
Fig. 10. Temperature dependence of the excess enthalpy of
[Fe(acpa),]PF, arising from the spin-crossover phenomenon. The ultimate value at high temperatures corresponds to the total enthalpy change, A,,H.
(8)
where “HT” and “LT” stand for the high and low temperature phases, respectively. Even if the mechanisms are identical among phase transitions (i.e. equal A,,S), the magnitude of A,_ H depends on the temperature at which a phase transition occurs: the higher the transition temperature, the higher the transition enthalpy, and vice versa. Such variations are caused by the fact that the enthalpy difference at 0 K, {Hi(HT)- H,O(LT)), depends strongly on a given system. This quantity is usually hard to
MICHIO S~RAI er al.
938
I ;
I
I
I
I
Table 3. Skeletal vibrational modes tentatively assigned
l.OO-
for the pseudo octahedral core [FeN,OJ (in units of cm-‘)
0.75-
Mode Degeneracy
? IA 0.50.5
Low-spin state High-spin state Difference
5: s 0.25.P r 0.00 -
I
0
I
I
I
loo
200
300
T/
I
K
Fig. 12. Temperature dependence of the high-spin fraction of [Fe(acpa),]PF,. The solid curve is derived from calorimetric measurements [eqn (6)], while the open circles are derived from the magnetic moments 1291[eqn (2)].
but is inevitably included in an observed transition enthalpy, A,,,H. In contrast, there exists no entropy difference at 0 K unless a given system is in a non-equilibrium state. Consequently, the transition entropy is easy to consider theoretically. The transition entropy (A,,,S = 36.19 J K-’ mol-‘) determined for the present complex [Fe(acpa),]PF, is comparable with those for other iron(III) spin-crossover complexes such as [Fe(3-OMe-SalEen),]PF, (A’,,S = 36.74 J K-’ mol-‘) [7], [Fe(3-OEtSalAPA)2]C10,*C,H, (38.4) (311 and [Fe(3-OEtSalAPA),]CIO,.C,H,Cl (37.2) [32], while it is much smaller than those for the iron(I1) complexes such as estimate
FeWen)2WShl
(48.78) PI, Fe(phen)2WCSe)21
(51.22) [5] and [Fe(Zpic),]Cl,.EtOH (50.59) [9]. The transition entropy consists mainly of three contributions: (i) a change in the spin-manifold between the low- and high-spin states; (ii) a change in the phonon system, in particular drastic changes in the bond lengths between the central iron ion and the ligands; and (iii) an order-disorder phenomenon of the solvate molecules and/or the counter-anion, if any. Since a change of the spin states for the iron(II1) complexes occurs between the spin quantum number S = 5/2 (6A,I) of the high-spin state and S = l/2 (‘r,,) of the low-spin state, the contribution from the spin-manifold to the transition entropy [item (i)] is R ln(6/2) = 9.13 J K-‘mol-‘. On the other hand, the spin-crossover for the iron(H) complexes occurs between S = 2 (sr,,) and S = 0 (‘A,,) and hence the spin entropy is R ln(5/1) = 13.38 J K-’ mol-‘. In the case of the present complex, as it does not contain any solvate molecules and the counter-anion, PF;, is in an ordered state without any reorientational motion even in the high-spin phase (at 293 K) [29], we need not take into account the contribution of item (iii) to the transition entropy. The remaining contribution is, therefore, the so-called phonon entropy [item (ii)]. As can be seen from Figs 3-5, variable temperature IR and Raman spectra have demonstrated characteristic bands whose intensities
of [Fe(acpa),]PF,
VI ,
‘2’
‘;
‘;
‘;
;
662 645 17
462 348 114
473 438 35
412 305 107
371 208 163
267 160 107
varied strongly with temperature. Although we have not theoretically assigned these bands, it is very likely that they might be the skeletal modes of the [FeN,O,] core. An octahedral MX, molecule has six normal modes of vibration designated as v,(A,,), vz(Eg), v,(F,,), v,(F’,), v,(F&) and v,(F,,). Since the present complex has lower symmetry than the octahedral MX6, it is expected that the degeneracy of some of the normal modes would be lifted and that inactive modes in 0, symmetry would become active in a lower symmetry. For simplicity, however, we shall treat the present complex as if it belonged to 0, symmetry, and tentatively assign the temperature sensitive bands. For example, the band at 412 cm-’ whose intensity is increased with decreasing temperature (see Fig. 4) was assigned to the v, mode of the low-spin state while it would be shifted to the band at 305 cm-’ in the high-spin state whose intensity is increased with increasing temperature (Fig. 3). All the assignments tentatively made are listed in Table 3. The heat capacities arising from these six normal modes (15 degrees of freedom) were calculated for both spin states on the basis of the Einstein model and shown in Fig. 13, in which they are designated as C phonon(LS)and Cphonon(HS), respectively. By virtue of the high-spin fraction,&,, derived from eqn (2), the heat capacity of the complex in a spin-equilibrium stateV Cphonon(Equil), was determined as follows, c phonon (EqW
=fi
Cphonon(HS) + (1
-fHS
)c,h,,,,(Ls)~
tg)
The phonon entropy, A.,,S(phonon), is obtainable by integration of the hatched part surrounded by Cphonon0-W and Cphonon(Equil) curves in Fig. 13 with respect to In T to give 28.56 J K-’ mol-‘. As a result, the observed entropy gain, AtRS = 36.19 J K-’ mol-‘, arising from the spin-state interconversion was found to be reasonably accounted for in terms of the sum (37.69 J K-’ mol-‘) of the contribution from a change in the spinmanifold (9.13 J K-’ mol-‘) and the contribution from a change in the skeletal normal modes (28.56 J K-’ mol-‘). On the other hand, the hatched area itself corresponds to a part of the phonon enthalpy given by the following quantity: A’,,H(phonon)
- {H&honon.
HS)
- H,,(phonon, LS)} = 3260 J mol-‘.
(10)
949
Unusual heat capacity of [Fe(acpa),]PF,
T/K
Fig. 13. Heat capacities arising from six skeletal normal modes (15 degrees of freedom) of [Fe(acpa)zJPF,. c rt,,,&-S) and C,,,,, (HS) correspond to the heat capacities of pure low- and high-spin states, respectively, while c phonon(Equil) corresponds to the spin-equilibrium state. Explanation of the hatched area is given in the text.
As described above, it is usually hard to estimate the contents of A,H because of the lack of the experimental value at 0 K, (H&IS) - H,(LS)). Fortunately, however, as will be discussed in Section 6, we were able to determine this value to be 2220 J mol-’ for the present complex [Fe(acpa),]PF, [see eqn (IS)]. By subtracting this value and the quantity given by eqn (IO) from the observed A,,H = 7025 J moi-‘, we obtain the following quantity: A,,,H(spin) - (H,,(spin, HS) - H&pin,
LS)]
=1545Jmol-‘. Thus, we can summarize the transition follows:
(11)
enthalpy as
Am H = A,, H(spin) + A,,, H(phonon) = [{H&pin,
HS) - H,(spin, HS))
- (Hr(spin, LS) - H,(spin, LS)}] + [(H,(phonon,
HS) - H,,(phonon, HS))
- ~H~~phonon, LS) - H*(phonon, LS))] + [(HO(spin, HS) + H,(phonon,
HS)j
- (H,,(spin, LS) f H,(phonon,
LS))]
=(1545+3260+2220)Jmol-’ = 7025 J moI_‘.
(12)
6. MECHANISM OF THE SPIN-STATE INTERCONVERSION
Since the present spin-crossover is associated with the transfer of two electrons between ea and fZg
orbitals, it brings about more or less changes in the molecular geometry. In fact, IR and Raman spectra (Figs 3-5) showed a significant shift of the skeletal modes of vibration between the lowand high-spin states. At first glance, the magnitude of the shift covering a range of 17-163 cm-’ (see Table 3) seems very large. However, in the case of [Fe(‘phen),(NCS),], which belongs to the spin-transition type, some of the six skeletal modes are known to shift by 150-250 cm-’ between the low- and highspin states [5,41]. Therefore, it is very likely that the present assignment, though tentative, is reasonable. Regardless of the spin-crossover types (either the spin-transition or the spin-equilibrium types), one can conclude that the spin-state interconversion is accompanied by a drastic change in the molecular geometry around the central iron ion. Moreover, as in the case of the spin-transition type [S], we can arrive at the conclusion that, unlike previous predictions [42,43], the energy separation between the *7’%ground state and the higher 6A,, state is nearly independent of temperature. If the energyseparation varies with temperature, a continuous shift of the skeletal modes would be expected; but this is not the case. At extremely low temperatures, the electronic ground state is really 'T,. On the other hand, at high enough temperatures, the 6Au state becomes the ground state by virtue of the dominant entropy term in the Gibbs free energy due to the spin-manifold and the softening of the skeletal modes of vibration. Although the present study revealed that the spinstate interconversion in the spin-equilibrium type proceeds similarly to that in the spin-transition type, one may ask why does the spin-crossover occur so gradually for the complexes of the fast electronic relaxation type? In order to elucidate this question, we shall apply here the Frenkel theory of heterophase fluctuation in liquids [44]. This model assumes that one phase contains “embryos” of a second phase in the transition region and that each embryo consists of a uniform size. The assumption of such embryos with a critical size does not conflict with the present IR and Raman spectra which give evidence for coexistence of the high- and low-spin states over the temperature region in which the spin-t~nsition occurs. Let us consider a system consisting of N cells each of which contains n molecules. The product of N and n is equated to the Avogadro constant NA. By assuming a simple linear interpolation with the high temperature mole fraction x between the Gibbs energy G, of the low temperature phase and the corresponding quantity G, of the high temperature phase, we obtain the Gibbs energy at TK, G =xGH+(l
-x)GL
+ NkTffxlnx +(I -x)in(l
-x)),
(13)
MICHIOSORAIet al.
950
where k is the Boltzmann constant. The equilibrium mole fraction is determined by the requirement that (dG/dx), = 0; x = I/{ 1 + exp(AG/NkT)},
(14)
where AC = G, - CL. The molar heat capacity at constant pressure C, is obtained by the following relation,
C,=&MT)+(l
-x)&.(7-))
= XC,.” + (1 - X)C,.‘ +
{b(T) - HL.(T)}* exp(AGINkT) NkT*{ 1 + exp(AG/NkT)}*
’
(13
where H means molar enthalpy, and C,,, and C,,, the “normal” heat capacities of the high and low temperature phases, respectively. At the transition temperature T,, the Gibbs free energies of both phases must be equal. By substituting the condition AC = 0 at T = T, into eqn (15), we obtain a maximum value of C,: C,(Tc) = i&,,~(Tc)
The value of n is extremely small in comparison with 95 and 77 found for [Fe(phen)z(NCS)2] and [Fe(phen),(NCSe),] of the spin-transition type [5]. This fact obviously indicates that the cooperativity of the spin-state interconversion is much weaker for the spin-equilibrium type than for the spin-transition type. In other words, excitation of the high-spin embryo in the low-spin phase can take place in a small unit when the complexes belong to the spinequilibrium type. When the number of molecules in a cell or domain is small, the effect of the spin-state interconversion happening in a given domain upon the adjacent cells would be weak, eventually leading to a large fluctuation between the low- and high-spin states. This is the reason why the spin-crossover of the spin-equilibrium type takes place over a wide temperature range.
REFERENCES 1. 2. 3. 4. 5. 6.
+ C,.,(Tc)J
7.
+{H,(Tc) The number foIlows:
- Hr(Tc))*/4NkTc2.
of ceils is, therefore,
determined
(16) as
8. 9. 10.
N=
4kTc2[C,&)
I&V-c) - H,U’c)12 - {&.tVc) + C,.,(Tc)}Pl
Il.
(17) For the present complex [Fe(acpa),]PF,, we adopted the values of Tc= 189.641 K, C,(T,)= 549.83 J K-’ mol-‘, and {CpeH(TC) + C,,(Tc)}/2 = {C,,,(HS, Tc)+ C,,,(LS, Tc)}/2 =431.93 J K-’ mol-‘. On the other hand, integration of C,,(HS) and C,,,(LS) shown in Fig. 6 with respect to T gives {H"(T)-H"(O)} and {H,(T)- H,(O)},respectively. In order to adjust AC = 0 at T,, we added 2220 J mol-’ which corresponds to the enthalpy difference between the high- and low-spin states at 0 K, that is, H"(O)- H,(O)= 2220Jmol-‘.
(18)
As a result, the number of cells was determined to be N = 1.21 x lo”. Consequently, the number of molecules in a cell or a domain was estimated to be n = 5. The broken curve in Fig. 9 shows the excess heat capacity calculated on the basis of eqn (15). The gross aspect of AC, is well accounted for in terms of the Frenkel model.
12. 13.
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