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Heat capacities of the electron acceptor 7,7,8,8-tetracyano- quinodimethane (TCNQ) and its radical-ion salt NH4+(TCNQ)− showing spin-Peierls transition
ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 70 (2009) 1066–1073
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Heat capacities of the electron acceptor 7,7,8,8-tetracyano- quinodimethane (TCNQ) and its radical-ion salt NH+4(TCNQ) showing spin-Peierls transition$ Toshihiro Kotani a,b, Michio Sorai a,, Hiroshi Suga a a b
Research Center for Molecular Thermodynamics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Intellectual Property Department, Sumitomo Electric Industries, Ltd., Koyakita, Itami, Hyogo 664-0016, Japan
a r t i c l e in f o
a b s t r a c t
Article history: Received 3 March 2009 Received in revised form 23 May 2009 Accepted 25 May 2009
Heat capacities of the electron acceptor 7,7,8,8-tetracyanoquinodimethane (TCNQ) and its radical-ion salt NH4-TCNQ have been measured at temperatures in the 12–350 K range by adiabatic calorimetry. A l-type heat capacity anomaly arising from a spin-Peierls (SP) transition was found at 301.3 K in NH4TCNQ. The enthalpy and entropy of transition are DtrsH ¼ (66777) J mol1 and DtrsS ¼ (2.1970.02) J K1 mol1, respectively. The SP transition is characterized by a cooperative coupling between the spin and the phonon systems. By assuming a uniform one-dimensional antiferromagnetic (AF) Heisenberg chains consisting of quantum spin (S ¼ 1/2) in the high-temperature phase and an alternating AF nonuniform chains in the low-temperature phase, we estimated the magnetic contribution to the entropy as DtrsSmag ¼ 0.61 J K1 mol1 and the lattice contribution as DtrsSlat ¼ 1.58 J K1 mol1. Although the total magnetic entropy expected for the present compound is R ln 2 ( ¼ 5.76 J K1 mol1), a majority of the magnetic entropy (4.6 J K1 mol1) persists in the high-temperature phase as a shortrange-order effect. The present thermodynamic investigation quantitatively revealed the roles played by the spin and the phonon at the SP transition. Standard thermodynamic functions of both compounds have also been determined. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Magnetic materials D. Magnetic properties D. Phase transitions D. Specific heat D. Thermodynamic properties
1. Introduction Owing to strong quantum fluctuations, interesting phenomena are expected to occur in low-dimensional quantum spin systems [1]. Spin-Peierls transitions [2–8] take place in a system consisting of quantum spin (S ¼ 1/2) antiferromagnetic Heisenberg chains through the interchain spin-phonon coupling. In 1974 Pytte [2] revealed that at the spin-Peierls transition temperature (TSP) lattice instability takes place and a system of uniform antiferromagnetic Heisenberg chains in the high-temperature phase is transformed to a system of dimerized or alternating antiferromagnetic chains in the low-temperature phase. The spin-Peierls transition is thus the magnetic analog of the electronic Peierls transition [9,10]. The first experimental evidence was reported in 1975 by Bray et al. [11,12] for organic compounds TTF-CuBDT (TSP ¼ 12.4 K) and TTF-AuBDT (TSP ¼ 2.06 K) [TTF ¼ tetrathiafulvalene, BDT ¼ S4C4(CF3)4] and then in 1979 by Huizinga et al. [13] for MEM-(TCNQ)2 (TSP ¼ 18 K) (MEM ¼ N-methyl-N-ethyl-morpholinium; TCNQ ¼ 7,7,8,8-tetracyanoquinodimethane). More
$ Contribution No. 125 from the Research Center for Molecular Thermodynamics. Corresponding author. Fax: +81727530922. E-mail address: [email protected] (M. Sorai).
0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.05.023
examples have been found thereafter. In addition to those organic compounds, the spin-Peierls transition was found to occur even in pure inorganic compounds: CuGeO3 (TSP ¼ 14 K) by Hase et al. [14,15] in 1993 and a0 -NaV2O5 (TSP ¼ 34 K) by Isobe and Ueda [16] in 1996. The essential concept of the spin-Peierls transition is the instability of one-dimensional spin systems leading to dimerization in the chains and the formation of a singlet ground state with a magnetic energy gap, which are caused by the coupling between spin and lattice. Direct evidence for the dimerization is obtained by X-ray diffraction [17,18]. Since the spin-Peierls transition is related to a spin-gap system, as in the case of the Haldane gap [19,20], magnetic susceptibility is rapidly reduced below TSP [11–14,16,21,22] and also magnetic heat capacity manifests a characteristic temperature dependence at low temperature [13,23–28]. In advance of recognition of the spin-Peierls transition, however, Vegter et al. [29,30] and Andre´ et al. [31] had reported that radical-ion salts M-TCNQ (M ¼ alkali metal ion or NH+4) belonging to low conducting one-dimensional antiferromagnetic systems exhibit structural phase transitions accompanied by dimerization of TCNQ radical-ions in the temperature range of 200–400 K. Although the transition temperatures are much higher than those of traditional spin-Peierls compounds, temperature dependence of their magnetic susceptibilities [29–32] and X-ray diffraction [33–37] showed similar behavior to the usual
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spin-Peierls transition. Takaoka and Motizuki [38] theoretically treated the phase transitions occurring in M-TCNQ salts as the spin-Peierls transition. Based on X-ray diffraction analysis, Kobayashi [33] found two crystal modifications in NH4-TCNQ: Form I shows a dimerization transition at (30175) K, while form II at around 215 K. Both phase transitions were interpreted in terms of a spin-Peierls transition. As a part of calorimetric studies on charge transfer complexes, we measured heat capacity of form I of NH4-TCNQ crystal in the 12–340 K range three decades ago and briefly reported the results as an oral presentation [39]. Although the experimental results [29,30,33] support the spin-Peierls nature of this salt, we wondered whether the phase transition observed at high temperature (301.3 K) is a genuine spin-Peierls transition because the spin energy is usually considered to be weak. Therefore, our conclusion at that time was ‘‘a spin-Peierls-like transition’’. However, since the circumstantial evidences are now favorable for the spin-Peierls transition, we decided to revisit our archive calorimetric data and to explore the nature of the phase transition along this line. Although many papers concerning heat capacity measurements have been reported [13,23–28], they are mainly concerned with comparison of the experimental heat capacity jump at TSP with the mean-field theory or temperature dependence of heat capacity at low temperature to verify the existence of a spin-gap. However, since one of the most characteristic aspects of the spinPeierls transition is the coupling between spin and lattice (or phonon), it is crucially important to evaluate each contribution to the phase transition. The most suitable tool for this purpose is the entropy diagnoses [40–43]. The objective of the present paper is, therefore, to throw light on the roles played by spin and phonon from the viewpoint of entropy. Another purpose of the present paper is to provide thermodynamic quantities of the most representative electron acceptor TCNQ. In spite of fundamentally important material, no heat capacity measurements have been hitherto reported.
2. Experimental
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dried in vacuum at 95–100 1C for 42 h, and then dissolved in methanol dried with molecular sieves. NH4-TCNQ crystals were prepared by mixing both solutions at 70–75 1C under a stream of nitrogen gas. The obtained NH4-TCNQ was dried in a vacuum at ambient temperature for 91 h. The elemental analysis for the sample was as follows: Calculated for C12H8N5: C, 64.86; H, 3.63; N, 31.51%. Found: C, 64.94; H, 3.57; N, 31.43%. 2.2. Physical methods Prior to heat capacity measurements, thermal behavior of TCNQ and NH4-TCNQ crystals was preliminarily examined by use of home-built differential thermal analysis (DTA) apparatus in the 90–350 K temperature range. The mass of sample used for DTA run was about 200 mg and average heating/cooling rate was 3 K min1. Heat capacity measurements were performed by use of an adiabatic calorimeter [45] in the 12–340 K temperature range. Mass of the specimen loaded in the calorimeter cell was 9.7893 g (0.044050 mol) and 14.2335 g (0.069707 mol), and the density of crystal assumed for buoyancy correction was 1.25 and 1.4 g cm3 for NH4-TCNQ and TCNQ, respectively. To aid the heat transfer inside the cell, a small amount of helium gas at 0.02 MPa was sealed in the cell. The temperature scale of the calorimeter is based on the IPTS-68. Infrared (IR) spectra in the 4000–400 cm1 wave number region were recorded for Nujol mulls with an Infrared Spectrophotometer (Model DS-402G, Japan Spectroscopic Co., Ltd.) at 103, 297, and 340 K, and in the 400–30 cm1 range with a far IR Spectrophotometer (Model FIS-3, Hitachi, Ltd.) at 99, 260, 297, and 330 K.
3. Results DTA heating curves for different samples of TCNQ are shown in Fig. 1. Sample 1 prepared by drying the recrystallized crystals in a vacuum at room temperature for 5 d exhibited a small peak at
2.1. Preparation of samples
sample 1
Endothermic
The TCNQ sample for heat capacity measurements was prepared as follows: Commercially available TCNQ (extra-pure grade; Tokyo Kasei Kogyo Co., Ltd.) was recrystallized from acetonitrile and dried in a vacuum at ambient temperature for 5 d (sample 1). In order to remove the solvent which may be occluded in the recrystallized sample, the crystals were ground to powder, then dried in vacuum at 50–90 1C for 3 d (sample 2), and finally at 110–125 1C for 6 h (sample 3). The acetonitrile used for recrystallization was purified in advance by calcium hydride and diphosphorus pentaoxide in a usual way. Elemental analysis yielded the following mass percentages. Calculated for C12H4N4: C, 70.59; H, 1.97; N, 27.44%. Found: C, 70.70; H, 1.92; N, 27.49%. NH4-TCNQ was first reported by Melby et al. [44], who prepared it by mixing an acetonitrile solution of TCNQ and a methanol solution of NH4I. Kobayashi [33] reported later that there exist two crystal forms (I and II): One is purple form I prepared from a tetrahydrofuran solution of TCNQ and a methanol solution of NH4I, while the other is bluish-purple form II obtained from acetonitrile solutions of TCNQ and NH4I. Although we tried to prepare two crystal forms, only form I was obtained as explained below. Therefore, sample of NH4-TCNQ for heat capacity measurements was prepared by the method of Melby et al. [44] as follows: TCNQ was dissolved in acetonitrile. On the other hand, NH4I crystals (suprapure grade; E. Merck) were ground to powder,
sample 2
sample 3
200
250
300
T/K Fig. 1. DTA heating curve of TCNQ crystal. Commercially available TCNQ was recrystallized from acetonitrile and dried in a vacuum at room temperature for 5 d (sample 1). Sample 1 was ground to powder and dried in vacuum at 50–90 1C for 3 d (sample 2), and then dried at 110–125 1C for 6 h (sample 3).
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229 K. The peak area was reduced by grinding sample 1 to powder and drying in vacuum at 50–90 1C for 3 d (sample 2). Sample 3 corresponds to the specimen obtained by further drying sample 2 at 110–125 1C for 6 h but it still gave rise to the anomaly, though small. Judging from these facts, it is very likely that this anomaly may originate in the melting of acetonitrile (Tfus ¼ 229.3 K) entrapped in TCNQ crystals during recrystallization from an acetonitrile solution. It is often the case that the solvent occluded in the crystallites is very difficult to remove. In the case of NH4-TCNQ, a sharp endothermic peak without detectable thermal hysteresis was observed around 300 K, independently of the method of sample preparation. This temperature is very close to those previously reported for the crystal form I by differential scanning calorimetry (DSC) and magnetic susceptibility measurements [29,30], IR spectroscopy [46], and X-ray diffraction [33]. In addition to the peak around 300 K, another small anomaly with thermal hysteresis of 20–30 K was recorded around 229 K on heating for all the samples. The peak area of this anomaly became smaller by grinding and drying treatment of the crystals. Since this anomaly bears a close resemblance to that found in TCNQ, the cause of this anomaly is also the fusion of acetonitrile trapped in the sample. Heat capacity measurements for NH4-TCNQ were performed in six series in the 12–340 K temperature range. The results were evaluated in terms of Cp, the molar heat capacity under constant pressure, and listed in Table A1 (Electronic Annex of this paper) and plotted in Fig. 2. A l-type heat capacity anomaly was observed at 301.3 K. This anomaly just corresponds to the phase transition observed at 300 K by magnetic susceptibility measurement [29,30], 305 K by IR spectroscopy [46], and (30175) K for the crystal form I by X-ray diffraction [33]. As can be seen from Fig. 3, the heat capacity peak due to the phase
400
series 1 series 6
350
Cp / J K−1 mol−1
1068
300
250 260
240
280
300
320
340
T/K Fig. 3. Molar heat capacities of NH4-TCNQ (crystal form I) in the phase transition region. Broken line implies the estimated normal heat capacity.
400 220
⇓ 250
NH4-TCNQ
TCNQ
200
Cp / J K−1 mol−1
Cp / J K−1 mol−1
300
NH4-TCNQ series 1 series 3 series 4 series 5
210
⇓ 240
TCNQ
100
series 1 200
0 0
100
200
300
T/K Fig. 2. Observed molar heat capacities of TCNQ and NH4-TCNQ (crystal form I) in the 13–350 K temperature range.
230 220
230 T/K
Fig. 4. Molar heat capacities of NH4-TCNQ and TCNQ around 225 K. Vertical arrows indicate the temperatures at which a small heat capacity peak appears.
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transition was reproducible. Aside from the phase transition peak, a tiny anomaly was observed at 226 K. This anomaly exhibited a supercooling effect characteristic of a first-order phase transition (series 5 measurement in Fig. 4). As revealed by DTA, it is very likely that this small anomaly is caused by the fusion of acetonitrile solvent (Tfus ¼ 229.3 K, DfusH ¼ 8.17 kJ mol1) accidentally occluded in the crystal lattice. If this is the case, the fraction of the occluded acetonitrile is 0.0015 mol because the excess enthalpy due to the anomaly is DH ¼ 12 J. Heat capacities of TCNQ were measured in the 13–352 K range. Observed molar heat capacities are given in Table A2 (Electronic Annex of this paper) and plotted in Fig. 2. It is of interest that the molar heat capacities of TCNQ are larger in a low temperature region below 55 K than those of NH4-TCNQ, in spite of less molecular degrees of freedom. As in the case of NH4-TCNQ, a very small heat capacity anomaly was observed at 229 K also for TCNQ (Fig. 4). As discussed above, this anomaly may be caused by fusion of acetonitrile occluded in TCNQ crystals. In order to estimate the excess heat capacity due to the phase transition at 301.3 K, the so-called normal heat capacity was determined as follows: Below the transition temperature, the normal heat capacity was calculated on the basis of an effective frequency distribution method [47], using Cp values in the temperature ranges of 12–200 K, 200–230 K (supercooled region), and 230–240 K, and the normal mode frequencies of the intramolecular vibrations above 800 cm1 assigned from the present IR spectra and literature values. Above the transition temperature the normal heat capacity was determined by linear extrapolation of the Cp data in the 320–340 K range down to the transition temperature. The normal heat capacities thus determined are drawn by the broken line in Fig. 3. The present data analysis gave rise to a heat capacity jump of DCp(normal) ¼ 9.3 J K1 mol1 at the phase transition temperature, suggesting a remarkable change in the molecular packing scheme between the low- and high-temperature phases. The enthalpy and entropy gains due to the phase transition were determined to be DtrsH ¼ (66777) J mol1 and DtrsS ¼ (2.1970.02) J K1 mol1 (R ln 1.3: R being the gas constant), respectively. Standard thermodynamic functions of NH+4(TCNQ) and TCNQ are listed in Tables A3 and A4 as a function of temperature in the 20–350 K range (Electronic Annex of this paper). Intensity of many IR absorption bands of NH4-TCNQ crystal showed remarkable change on passing through the phase transition temperature: Strong in the low-temperature phase while weak in the high-temperature phase. Quite interestingly, totally symmetric molecular vibrations (Ag) of the TCNQ anion, which are normally IR-inactive, are activated by the electronvibration mechanism [48,49] encountered in charge transfer complexes. By referring to the band-assignments for IR spectra of (1:1) alkaline salts of TCNQ [46,50–52], temperature-sensitive IR bands recorded for the present NH4-TCNQ crystal at 2200, 1578, 1340, 1183, 714, and 617 cm1 can be assigned as n2, n3, n4, n5, n7, and n8, modes of the totally symmetric molecular vibrations, respectively.
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capacity of TCNQ within 72% above 200 K. Heat capacity data of electron acceptors and donors serve as a useful tool to estimate a baseline for phase transition, especially when the heat capacity anomaly is sluggish and spreads over a wide temperature region. In that sense, the thermodynamic quantities of TCNQ determined by the present study contribute to a valuable database. 4.2. Nature of the phase transition in NH4-TCNQ As reported in the X-ray structural study by Kobayashi [33], the phase transition at 301.3 K observed by the present heat capacity measurement is caused by a monomer-dimer transition, in which a uniform chain of the TCNQ ions in the high-temperature phase is transformed to a nonuniform chain due to bimolecular association of TCNQ in the low-temperature phase. This structural change is evidenced also by IR spectroscopy. As an example, temperature dependence of the n2 mode corresponding to the CN stretching vibration of TCNQ anion is shown in Fig. 5 in the 24002100 cm1 wave number region. As in the case of K-TCNQ and Rb-TCNQ [46,50–52], the drastic reduction of the peak intensity, above the transition temperature, of the central of the three bands observed in the C–N stretching region can be attributed to a decreased number of crystal field components expected as a consequence of the reduction of the unit cell dimensions in going through the phase transition [33,46,51]. On the other hand, temperature dependence of the magnetic susceptibility of NH4-TCNQ reported by Vegter and Kommmandeur [30] (see Fig. 6) bears close resemblance to that of a charge transfer complex TTF-CuS4C4(CF3)4 [11,12], the first example showing the spin-Peierls transition and those of analogous
4. Discussion 4.1. Heat capacity of the electron acceptor TCNQ TCNQ is a typical electron acceptor but there have been no reports concerning its heat capacity measurements. Apparent addition rule of heat capacity holds well in many cases. For example, the molar heat capacity of TTF-TCNQ [53] showing the Peierls transition, where TTF is tetrathiafulvalene, coincides with the sum of the heat capacity of TTF [54] and the present heat
Fig. 5. IR absorption spectra due to the C–N stretching modes of NH4-TCNQ crystal in the 2400–2100 cm1 wave number region.
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700
χ / 10−4 emu
| J/k| / K
2
600
= 0.8
1
500
= 0.7 300
320
340
= 0.5
300 T/K
400
Fig. 6. Temperature dependence of the magnetic susceptibilities of NH4-TCNQ. Solid curve: Experimental values reported by Vegter and Kommandeur [30]. Broken lines: Theoretical curves with different values of the parameter g ( ¼ J2/J1) defined as the ratio of two alternating exchange interaction parameters in the TCNQ antiferromagnetic linear chain with J1,2 ¼ J0[17d(T)], where d(T) is an alternating parameter [57].
complexes M-TCNQ (M ¼ Na, K, Rb, Cs) [30]. The characteristic behavior of the magnetic susceptibility of these complexes has been theoretically interpreted by Takaoka and Motizuki [38] on the basis of the one-dimensional antiferromagnetic Heisenberg model involving the spin-lattice interaction leading to the spinPeierls transition. Based on these evidences, the phase transition observed in NH4-TCNQ crystal can be attributed to the spinPeierls transition. Prior to thermodynamic investigation of the phase transition in NH4-TCNQ crystal, characterization of the low- and hightemperature phases are briefly discussed in the following two sections on the basis of the magnetic data previously reported.
400
where k is the Boltzmann constant. The broken curve drawn in Fig. 7 corresponds to the values estimated by the least squares fitting (a ¼ 0.01542 K1, b ¼ 13.35, c ¼ 3358 K). The J value at the phase transition temperature Ttrs ¼ 301.3 K is J(Ttrs)/k ¼ 735 K. 4.4. Magnetic properties of the low-temperature phase Beni [56] and Pytte [2] treated the following Hamiltonian describing spins (S ¼ 1/2) with one-dimensional Heisenberg interaction, coupled to a three-dimensional lattice: H¼
X j
1 2Jðj; j þ 1ÞðSj Sjþ1 Þ 4
(2)
The exchange interaction parameter J(j, j+1) is a function not only of the spin-spin interaction but also of the lattice displacement. This Hamiltonian leads to the same form as a conventional Peierls transitions [9,10] and brings about a second-order phase transition at the spin-Peierls transition temperature (TSP). The exchange interaction parameters of such a nonuniform chain (J1 and J2) are given by the following equation [3]: J1;2 ¼ J 0 expð2bxÞ ¼ J 0 expðdÞ
4.3. Magnetic properties of the high-temperature phase Magnetic properties of the high-temperature phase characterized by a uniform stack of the TCNQ (spin S ¼ 1/2) ions are well described by the one-dimensional antiferromagnetic Heisenberg model by Bonner and Fisher [55]. By comparing the observed magnetic data [30] with the theoretical magnetic susceptibility of one-dimensional system, one can determine values of exchange interaction parameter J(T) as a function of temperature. The resultant J(T) values are plotted in Fig. 7. A noticeable feature is that J(T) is remarkably decreased as the temperature is increased. This is caused by the thermal expansion along the TCNQ stacking axis. This type of behavior is also reported for K-TCNQ [32]. When the intermolecular distance between adjacent TCNQ ions may be assumed to be proportional to temperature, the exchange interaction parameter is approximated as jJðTÞ=kj ¼ aT 2 þ bT þ c
380
Fig. 7. Temperature dependence of the spin exchange interaction parameter J in the high-temperature phase of NH4-TCNQ above the phase transition at 301.3 K. Broken curve corresponds to the least squares fit with quadratic temperature.
0 200
360 T/K
(1)
(3)
where b is a parameter characterizing the extension of the wave function, x is the distance in unit of the lattice parameter, and J0 is the value of exchange parameter without distortion. In the case of NH4-TCNQ, it corresponds to J0/k ¼ J(Ttrs)/k ¼ 735 K. In the limit of small d, the dimerization of the spin sites leads to an alternating exchange: J1;2 ðTÞ ¼ J 0 ½1 dðTÞ
(4)
Below the phase transition temperature TSP, a gap 2D(T) appears in the excitation spectrum, which separates the singlet ground state from spin-wave excitations [13]. This D(T) follows a BCS-type temperature dependence and is related to d(T) as follows:
dðTÞ ¼
DðTÞ 2pJ 0
with
pffi1þ
2
p
(5)
In the Hartree-Fock approximation, Bulaevskii [57] derived the equation of magnetic susceptibility for an alternating antiferro-
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1.0
(T) /max
0.8
0.6
0.4 Ttrs 0.2
0.0 220
240
260 T/K
280
300
320
Fig. 8. Temperature dependence of the parameter d(T) characterizing the alternating Heisenberg chain with J1,2(T) ¼ J0[17d(T)]. The values are reduced by dmax ¼ 0.33, a convergent value at low temperature. Solid circles imply the values estimated from the experimental data [30]. The broken curve is an eye guide.
magnetic Heisenberg chain: N g 2 m2B aðTÞ 2J0 ½1 þ dðTÞbðTÞ vðTÞ ¼ A exp kT T
(6)
where a(T) and b(T) are constants depending on the value g(T) ¼ J2/J1. Magnetic susceptibility curves estimated from this equation are shown in Fig. 6 by broken line for three representative values of g ¼ 0.8 (d ¼ 0.111), g ¼ 0.7 (d ¼ 0.176), and g ¼ 0.5 (d ¼ 0.333), in which g and d are related as d ¼ (1g)/(1+g). The alternating parameter d can be determined, as a function of temperature, by equalizing the observed magnetic susceptibility [30] to Eq. (6). The parameter d(T) thus estimated is shown in Fig. 8. As the temperature is lowered, the value of d(T) is increased and eventually approaches a convergent value dmax ¼ 0.33 below ca. 240 K. This fact implies that the dimerization of TCNQ anions is enhanced with decreasing temperature till about 240 K. In what follows, this temperature will be designated as T0. The ratio d(T)/ dmax shown in Fig. 8 serves as an order parameter in the lowtemperature phase. By substituting d ¼ 0.333 and J0/k ¼ 735 K for Eq. (5), one obtains the ratio of the energy gap at 0 K [2D(0)] and the phase transition temperature (Ttrs ¼ 301.3 K) as 2D(0)/Ttrs ¼ 5.32. It is of interest that this value is rather close to 3.53 derived for the BCS theory, although the spin-Peierls and the superconductive transitions are different phenomena. 4.5. Thermodynamic investigation of the phase transition Fundamental concept of the spin-Peierls transition is to describe the quantum spin system of antiferromagnetic linear chain in terms of the pseudo-fermion and to take into account its interaction with phonon. For such a system, a lattice distortion arising from dimerization is expected to appear at low-temperature side. We thus consider both the spin and the lattice systems to interpret thermodynamically the nature of the spin-Peierls phase transition. The observed entropy of transition DtrsS may be assumed to consist of the magnetic and the lattice contributions:
Dtrs S ¼ Dtrs Smag þ Dtrs Slat
(7)
Fig. 9. Schematic drawing of the magnetic heat capacity (top) and the entropy gain due to the magnetic origin in NH4-TCNQ crystal (down). T0 is the temperature, below which the progressive dimerization substantially ceases. DSm and DSd are the magnetic entropy of the uniform (monomer) and nonuniform (dimer) antiferromagnetic Heisenberg chain models at Ttrs and T0, respectively. In the actual situation, the value DSd(T0) is buried in the estimated normal heat capacity. DSsro is the entropy due to the short-range-order effect in the monomer chain above Ttrs.
As to the magnetic system, we assume that the monomer-dimer transition occurs at Ttrs in the one-dimensional S ¼ 1/2 antiferromagnetic Heisenberg chains. As schematically shown in Fig. 9, the total magnetic entropy, Smag(T ¼ N), consists of the following components: Smag ðT ¼ 1Þ ¼ DSd ðT 0 Þ þ Dtrs Smag þ DSsro ðT trs oTo1Þ ¼ R ln 2 (8) where DSd(T0) is the magnetic entropy of the nonuniform (dimer) antiferromagnetic Heisenberg chain at T0E240 K, below which the progressive dimerization substantially ceases, and DSsro (TtrsoToN) is the entropy due to the short-range-order effect in the uniform (monomer) chain above Ttrs. In the actual situation, the value DSd(T0) is buried in the estimated normal heat capacity. On the other hand, the magnetic entropy of the uniform chain (monomer) at Ttrs [DSm(Ttrs)] is the sum of two contributions:
DSm ðT trs Þ ¼ DSd ðT 0 Þ þ Dtrs Smag
(9)
DSm(Ttrs) and DSd(T0) can be theoretically estimated on the basis of the following one-dimensional antiferromagnetic Heisenberg
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model: H¼
X
2J 0 ðS2j S2j1 þ gS2j S2jþ1 Þ
(10)
j
where g is the alternation (or dimerization) parameter. For the uniform chain (g ¼ 1) one can use the model calculation by Bonner and Fisher [55] and by Blo¨te [58], while for the nonuniform chain (ga1) by Duffy and Barr [59]. Since the parameters J0 and g for NH4-TCNQ have been determined as J0/ k ¼ 735 K and g ¼ 0.5, one can calculate as follows: DSd(T0) ¼ 0.58 J K1 mol1 and DSm(Ttrs) ¼ 1.19 J K1 mol1, and hence DtrsSmag ¼ 0.61 J K1 mol1. The transition entropy for the lattice system is thus determined as DtrsSlat ¼ 1.58 J K1 mol1 from Eq. (7). It was revealed that the contribution from the magnetic origin to the entropy of transition is as small as 28% and the remaining 72% arises from the phonon system. Moreover, the entropy due to the short-range-order effect in the uniform (monomer) chain above Ttrs is estimated as DSsro(TtrsoToN) ¼ 4.57 J K1 mol1 from Eq. (8), which is 80% of the total magnetic entropy (R ln 2). The fact that the majority of the magnetic entropy remains above Ttrs as the short-range-order effect is characteristic of the low-dimensional magnets. As to the energy (or enthalpy), we can discuss as follows: Fig. 10 shows temperature dependence of the enthalpy gain DH(T) reduced by the observed enthalpy of transition DtrsH ¼ (66777) J mol1. As in the case of entropy, the enthalpy due to the phase transition consists of contributions from both the spin and the lattice systems. Pytte [2] showed that in the limit of small distortion (d) in the alternating antiferromagnetic Heisenberg chain of Bulaevskii [57] the gain in spin energy (DtrsHmag) on distorting below Ttrs is proportional to (d ln d)2. On the other hand, the cost in lattice energy (DtrsHlat) due to dimerization of the radical anions is proportional to d2. Under these assumptions, the net enthalpy DH(d) due to the spin and the lattice system is written as
nHðdÞ ¼ aðd ln dÞ2 þ ð1=2Þbd2
(11)
where a and b are constants. As shown in Fig. 8, the d value increases with decreasing temperature and reaches to a constant
1.0
Experimental Calculated
ΔH (T) /ΔtrsH
0.8
value dmax ¼ 0.33 around 240 K. By a least squares fit of d vs. T in the range 240 KrTr301 K, d can be expressed as a function of temperature. By scaling the absolute value jDH(dmax)j with DtrsH, the two parameters were determined to be a ¼ 5130 J mol1 and b ¼ 604 J mol1. For comparison, thus determined quantities [DH(dmax)DH(d)]/DH(dmax) are also plotted in Fig. 10 by solid circles. Calorimetrically observed quantities DH(T)/DtrsH are well reproduced by the quantities [DH(dmax)DH(d)]/DH(dmax) derived from the magnetic susceptibility data [30]. From Eq. (11) and dmax ¼ 0.333, the energy gain due to the spin is estimated to be DtrsHmag ¼ 688 J mol1 and the cost in lattice energy is DtrsHlat ¼ 33 J mol1. On the other hand, according to the theory of alternating antiferromagnetic Heisenberg chain by Duffy and Barr [59], the energy gain of the spin system by the dimerization becomes 660 J mol1, for d ¼ 0.33 (g ¼ 0.5) and J0/k ¼ 735 K. In spite of different models, this value agrees well with DtrsHmag ( ¼ 688 J mol1) estimated from a(d ln d)2.
4. Conclusions Heat capacity measurements for the organic radical-ion salt NH4-TCNQ and the electron acceptor TCNQ crystals were carried out by adiabatic calorimetry at the temperatures in the range 12–350 K. The radical-ion salt exhibited a l-type phase transition at 301.3 K. By assuming a uniform antiferromagnetic S ¼ 1/2 Heisenberg linear chains in the high-temperature phase and an alternating linear chains in the low-temperature phase, the observed entropy of transition DtrsS ¼ (2.1970.02) J K1 mol1 was reasonably accounted for in terms of a magnetic contribution DtrsSmag ¼ 0.61 J K1 mol1 and a lattice contribution DtrsSlat ¼ 1.58 J K1 mol1. Although the total magnetic entropy expected for the present compound is R ln 2 ( ¼ 5.76 J K1 mol1), a majority of the magnetic entropy (4.6 J K1 mol1) was found to persist in the high-temperature phase as a short-range-order effect. On the other hand, the observed enthalpy of transition DtrsH ¼ (66777) J mol1 was interpreted as the sum of the gain in spin energy (DtrsHmag ¼ 688 J mol1) and the cost in lattice energy (DtrsHlat ¼ 33 J mol1) due to dimerization of the TCNQ anions in the low-temperature phase. The present thermodynamic investigation quantitatively revealed that the l-type phase transition at 301.3 K takes place as a result of cooperative coupling between the spin and the phonon (lattice) systems. Together with previously reported magnetic susceptibility [29,30] and X-ray diffraction [33], the present calorimetry evidenced that the phase transition occurring in the radical-ion salt NH4-TCNQ is caused by the spin-Peierls transition.
0.6 Appendix A. Supporting Information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jpcs.2009.05.023.
0.4
0.2 References
0.0 240
260
280 T/K
300
320
Fig. 10. Temperature dependence of the enthalpy gain due to the phase transition in NH4-TCNQ crystal reduced by the observed enthalpy of transition DtrsH ¼ (66777) J mol1. Open circles: Observed values DH(T)/DtrsH. Solid circles: Values estimated from the magnetic susceptibility data [DH(dmax)DH(d)]/ DH(dmax).
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Heat capacities of the electron acceptor 7,7,8,8-tetracyano- quinodimethane (TCNQ) and its radical-ion salt NH+4(TCNQ) showing spin-Peierls transition$ Toshihiro Kotani a,b, Michio Sorai a,, Hiroshi Suga a a b
Research Center for Molecular Thermodynamics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Intellectual Property Department, Sumitomo Electric Industries, Ltd., Koyakita, Itami, Hyogo 664-0016, Japan
a r t i c l e in f o
a b s t r a c t
Article history: Received 3 March 2009 Received in revised form 23 May 2009 Accepted 25 May 2009
Heat capacities of the electron acceptor 7,7,8,8-tetracyanoquinodimethane (TCNQ) and its radical-ion salt NH4-TCNQ have been measured at temperatures in the 12–350 K range by adiabatic calorimetry. A l-type heat capacity anomaly arising from a spin-Peierls (SP) transition was found at 301.3 K in NH4TCNQ. The enthalpy and entropy of transition are DtrsH ¼ (66777) J mol1 and DtrsS ¼ (2.1970.02) J K1 mol1, respectively. The SP transition is characterized by a cooperative coupling between the spin and the phonon systems. By assuming a uniform one-dimensional antiferromagnetic (AF) Heisenberg chains consisting of quantum spin (S ¼ 1/2) in the high-temperature phase and an alternating AF nonuniform chains in the low-temperature phase, we estimated the magnetic contribution to the entropy as DtrsSmag ¼ 0.61 J K1 mol1 and the lattice contribution as DtrsSlat ¼ 1.58 J K1 mol1. Although the total magnetic entropy expected for the present compound is R ln 2 ( ¼ 5.76 J K1 mol1), a majority of the magnetic entropy (4.6 J K1 mol1) persists in the high-temperature phase as a shortrange-order effect. The present thermodynamic investigation quantitatively revealed the roles played by the spin and the phonon at the SP transition. Standard thermodynamic functions of both compounds have also been determined. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Magnetic materials D. Magnetic properties D. Phase transitions D. Specific heat D. Thermodynamic properties
1. Introduction Owing to strong quantum fluctuations, interesting phenomena are expected to occur in low-dimensional quantum spin systems [1]. Spin-Peierls transitions [2–8] take place in a system consisting of quantum spin (S ¼ 1/2) antiferromagnetic Heisenberg chains through the interchain spin-phonon coupling. In 1974 Pytte [2] revealed that at the spin-Peierls transition temperature (TSP) lattice instability takes place and a system of uniform antiferromagnetic Heisenberg chains in the high-temperature phase is transformed to a system of dimerized or alternating antiferromagnetic chains in the low-temperature phase. The spin-Peierls transition is thus the magnetic analog of the electronic Peierls transition [9,10]. The first experimental evidence was reported in 1975 by Bray et al. [11,12] for organic compounds TTF-CuBDT (TSP ¼ 12.4 K) and TTF-AuBDT (TSP ¼ 2.06 K) [TTF ¼ tetrathiafulvalene, BDT ¼ S4C4(CF3)4] and then in 1979 by Huizinga et al. [13] for MEM-(TCNQ)2 (TSP ¼ 18 K) (MEM ¼ N-methyl-N-ethyl-morpholinium; TCNQ ¼ 7,7,8,8-tetracyanoquinodimethane). More
$ Contribution No. 125 from the Research Center for Molecular Thermodynamics. Corresponding author. Fax: +81727530922. E-mail address: [email protected] (M. Sorai).
0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.05.023
examples have been found thereafter. In addition to those organic compounds, the spin-Peierls transition was found to occur even in pure inorganic compounds: CuGeO3 (TSP ¼ 14 K) by Hase et al. [14,15] in 1993 and a0 -NaV2O5 (TSP ¼ 34 K) by Isobe and Ueda [16] in 1996. The essential concept of the spin-Peierls transition is the instability of one-dimensional spin systems leading to dimerization in the chains and the formation of a singlet ground state with a magnetic energy gap, which are caused by the coupling between spin and lattice. Direct evidence for the dimerization is obtained by X-ray diffraction [17,18]. Since the spin-Peierls transition is related to a spin-gap system, as in the case of the Haldane gap [19,20], magnetic susceptibility is rapidly reduced below TSP [11–14,16,21,22] and also magnetic heat capacity manifests a characteristic temperature dependence at low temperature [13,23–28]. In advance of recognition of the spin-Peierls transition, however, Vegter et al. [29,30] and Andre´ et al. [31] had reported that radical-ion salts M-TCNQ (M ¼ alkali metal ion or NH+4) belonging to low conducting one-dimensional antiferromagnetic systems exhibit structural phase transitions accompanied by dimerization of TCNQ radical-ions in the temperature range of 200–400 K. Although the transition temperatures are much higher than those of traditional spin-Peierls compounds, temperature dependence of their magnetic susceptibilities [29–32] and X-ray diffraction [33–37] showed similar behavior to the usual
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spin-Peierls transition. Takaoka and Motizuki [38] theoretically treated the phase transitions occurring in M-TCNQ salts as the spin-Peierls transition. Based on X-ray diffraction analysis, Kobayashi [33] found two crystal modifications in NH4-TCNQ: Form I shows a dimerization transition at (30175) K, while form II at around 215 K. Both phase transitions were interpreted in terms of a spin-Peierls transition. As a part of calorimetric studies on charge transfer complexes, we measured heat capacity of form I of NH4-TCNQ crystal in the 12–340 K range three decades ago and briefly reported the results as an oral presentation [39]. Although the experimental results [29,30,33] support the spin-Peierls nature of this salt, we wondered whether the phase transition observed at high temperature (301.3 K) is a genuine spin-Peierls transition because the spin energy is usually considered to be weak. Therefore, our conclusion at that time was ‘‘a spin-Peierls-like transition’’. However, since the circumstantial evidences are now favorable for the spin-Peierls transition, we decided to revisit our archive calorimetric data and to explore the nature of the phase transition along this line. Although many papers concerning heat capacity measurements have been reported [13,23–28], they are mainly concerned with comparison of the experimental heat capacity jump at TSP with the mean-field theory or temperature dependence of heat capacity at low temperature to verify the existence of a spin-gap. However, since one of the most characteristic aspects of the spinPeierls transition is the coupling between spin and lattice (or phonon), it is crucially important to evaluate each contribution to the phase transition. The most suitable tool for this purpose is the entropy diagnoses [40–43]. The objective of the present paper is, therefore, to throw light on the roles played by spin and phonon from the viewpoint of entropy. Another purpose of the present paper is to provide thermodynamic quantities of the most representative electron acceptor TCNQ. In spite of fundamentally important material, no heat capacity measurements have been hitherto reported.
2. Experimental
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dried in vacuum at 95–100 1C for 42 h, and then dissolved in methanol dried with molecular sieves. NH4-TCNQ crystals were prepared by mixing both solutions at 70–75 1C under a stream of nitrogen gas. The obtained NH4-TCNQ was dried in a vacuum at ambient temperature for 91 h. The elemental analysis for the sample was as follows: Calculated for C12H8N5: C, 64.86; H, 3.63; N, 31.51%. Found: C, 64.94; H, 3.57; N, 31.43%. 2.2. Physical methods Prior to heat capacity measurements, thermal behavior of TCNQ and NH4-TCNQ crystals was preliminarily examined by use of home-built differential thermal analysis (DTA) apparatus in the 90–350 K temperature range. The mass of sample used for DTA run was about 200 mg and average heating/cooling rate was 3 K min1. Heat capacity measurements were performed by use of an adiabatic calorimeter [45] in the 12–340 K temperature range. Mass of the specimen loaded in the calorimeter cell was 9.7893 g (0.044050 mol) and 14.2335 g (0.069707 mol), and the density of crystal assumed for buoyancy correction was 1.25 and 1.4 g cm3 for NH4-TCNQ and TCNQ, respectively. To aid the heat transfer inside the cell, a small amount of helium gas at 0.02 MPa was sealed in the cell. The temperature scale of the calorimeter is based on the IPTS-68. Infrared (IR) spectra in the 4000–400 cm1 wave number region were recorded for Nujol mulls with an Infrared Spectrophotometer (Model DS-402G, Japan Spectroscopic Co., Ltd.) at 103, 297, and 340 K, and in the 400–30 cm1 range with a far IR Spectrophotometer (Model FIS-3, Hitachi, Ltd.) at 99, 260, 297, and 330 K.
3. Results DTA heating curves for different samples of TCNQ are shown in Fig. 1. Sample 1 prepared by drying the recrystallized crystals in a vacuum at room temperature for 5 d exhibited a small peak at
2.1. Preparation of samples
sample 1
Endothermic
The TCNQ sample for heat capacity measurements was prepared as follows: Commercially available TCNQ (extra-pure grade; Tokyo Kasei Kogyo Co., Ltd.) was recrystallized from acetonitrile and dried in a vacuum at ambient temperature for 5 d (sample 1). In order to remove the solvent which may be occluded in the recrystallized sample, the crystals were ground to powder, then dried in vacuum at 50–90 1C for 3 d (sample 2), and finally at 110–125 1C for 6 h (sample 3). The acetonitrile used for recrystallization was purified in advance by calcium hydride and diphosphorus pentaoxide in a usual way. Elemental analysis yielded the following mass percentages. Calculated for C12H4N4: C, 70.59; H, 1.97; N, 27.44%. Found: C, 70.70; H, 1.92; N, 27.49%. NH4-TCNQ was first reported by Melby et al. [44], who prepared it by mixing an acetonitrile solution of TCNQ and a methanol solution of NH4I. Kobayashi [33] reported later that there exist two crystal forms (I and II): One is purple form I prepared from a tetrahydrofuran solution of TCNQ and a methanol solution of NH4I, while the other is bluish-purple form II obtained from acetonitrile solutions of TCNQ and NH4I. Although we tried to prepare two crystal forms, only form I was obtained as explained below. Therefore, sample of NH4-TCNQ for heat capacity measurements was prepared by the method of Melby et al. [44] as follows: TCNQ was dissolved in acetonitrile. On the other hand, NH4I crystals (suprapure grade; E. Merck) were ground to powder,
sample 2
sample 3
200
250
300
T/K Fig. 1. DTA heating curve of TCNQ crystal. Commercially available TCNQ was recrystallized from acetonitrile and dried in a vacuum at room temperature for 5 d (sample 1). Sample 1 was ground to powder and dried in vacuum at 50–90 1C for 3 d (sample 2), and then dried at 110–125 1C for 6 h (sample 3).
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229 K. The peak area was reduced by grinding sample 1 to powder and drying in vacuum at 50–90 1C for 3 d (sample 2). Sample 3 corresponds to the specimen obtained by further drying sample 2 at 110–125 1C for 6 h but it still gave rise to the anomaly, though small. Judging from these facts, it is very likely that this anomaly may originate in the melting of acetonitrile (Tfus ¼ 229.3 K) entrapped in TCNQ crystals during recrystallization from an acetonitrile solution. It is often the case that the solvent occluded in the crystallites is very difficult to remove. In the case of NH4-TCNQ, a sharp endothermic peak without detectable thermal hysteresis was observed around 300 K, independently of the method of sample preparation. This temperature is very close to those previously reported for the crystal form I by differential scanning calorimetry (DSC) and magnetic susceptibility measurements [29,30], IR spectroscopy [46], and X-ray diffraction [33]. In addition to the peak around 300 K, another small anomaly with thermal hysteresis of 20–30 K was recorded around 229 K on heating for all the samples. The peak area of this anomaly became smaller by grinding and drying treatment of the crystals. Since this anomaly bears a close resemblance to that found in TCNQ, the cause of this anomaly is also the fusion of acetonitrile trapped in the sample. Heat capacity measurements for NH4-TCNQ were performed in six series in the 12–340 K temperature range. The results were evaluated in terms of Cp, the molar heat capacity under constant pressure, and listed in Table A1 (Electronic Annex of this paper) and plotted in Fig. 2. A l-type heat capacity anomaly was observed at 301.3 K. This anomaly just corresponds to the phase transition observed at 300 K by magnetic susceptibility measurement [29,30], 305 K by IR spectroscopy [46], and (30175) K for the crystal form I by X-ray diffraction [33]. As can be seen from Fig. 3, the heat capacity peak due to the phase
400
series 1 series 6
350
Cp / J K−1 mol−1
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300
250 260
240
280
300
320
340
T/K Fig. 3. Molar heat capacities of NH4-TCNQ (crystal form I) in the phase transition region. Broken line implies the estimated normal heat capacity.
400 220
⇓ 250
NH4-TCNQ
TCNQ
200
Cp / J K−1 mol−1
Cp / J K−1 mol−1
300
NH4-TCNQ series 1 series 3 series 4 series 5
210
⇓ 240
TCNQ
100
series 1 200
0 0
100
200
300
T/K Fig. 2. Observed molar heat capacities of TCNQ and NH4-TCNQ (crystal form I) in the 13–350 K temperature range.
230 220
230 T/K
Fig. 4. Molar heat capacities of NH4-TCNQ and TCNQ around 225 K. Vertical arrows indicate the temperatures at which a small heat capacity peak appears.
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transition was reproducible. Aside from the phase transition peak, a tiny anomaly was observed at 226 K. This anomaly exhibited a supercooling effect characteristic of a first-order phase transition (series 5 measurement in Fig. 4). As revealed by DTA, it is very likely that this small anomaly is caused by the fusion of acetonitrile solvent (Tfus ¼ 229.3 K, DfusH ¼ 8.17 kJ mol1) accidentally occluded in the crystal lattice. If this is the case, the fraction of the occluded acetonitrile is 0.0015 mol because the excess enthalpy due to the anomaly is DH ¼ 12 J. Heat capacities of TCNQ were measured in the 13–352 K range. Observed molar heat capacities are given in Table A2 (Electronic Annex of this paper) and plotted in Fig. 2. It is of interest that the molar heat capacities of TCNQ are larger in a low temperature region below 55 K than those of NH4-TCNQ, in spite of less molecular degrees of freedom. As in the case of NH4-TCNQ, a very small heat capacity anomaly was observed at 229 K also for TCNQ (Fig. 4). As discussed above, this anomaly may be caused by fusion of acetonitrile occluded in TCNQ crystals. In order to estimate the excess heat capacity due to the phase transition at 301.3 K, the so-called normal heat capacity was determined as follows: Below the transition temperature, the normal heat capacity was calculated on the basis of an effective frequency distribution method [47], using Cp values in the temperature ranges of 12–200 K, 200–230 K (supercooled region), and 230–240 K, and the normal mode frequencies of the intramolecular vibrations above 800 cm1 assigned from the present IR spectra and literature values. Above the transition temperature the normal heat capacity was determined by linear extrapolation of the Cp data in the 320–340 K range down to the transition temperature. The normal heat capacities thus determined are drawn by the broken line in Fig. 3. The present data analysis gave rise to a heat capacity jump of DCp(normal) ¼ 9.3 J K1 mol1 at the phase transition temperature, suggesting a remarkable change in the molecular packing scheme between the low- and high-temperature phases. The enthalpy and entropy gains due to the phase transition were determined to be DtrsH ¼ (66777) J mol1 and DtrsS ¼ (2.1970.02) J K1 mol1 (R ln 1.3: R being the gas constant), respectively. Standard thermodynamic functions of NH+4(TCNQ) and TCNQ are listed in Tables A3 and A4 as a function of temperature in the 20–350 K range (Electronic Annex of this paper). Intensity of many IR absorption bands of NH4-TCNQ crystal showed remarkable change on passing through the phase transition temperature: Strong in the low-temperature phase while weak in the high-temperature phase. Quite interestingly, totally symmetric molecular vibrations (Ag) of the TCNQ anion, which are normally IR-inactive, are activated by the electronvibration mechanism [48,49] encountered in charge transfer complexes. By referring to the band-assignments for IR spectra of (1:1) alkaline salts of TCNQ [46,50–52], temperature-sensitive IR bands recorded for the present NH4-TCNQ crystal at 2200, 1578, 1340, 1183, 714, and 617 cm1 can be assigned as n2, n3, n4, n5, n7, and n8, modes of the totally symmetric molecular vibrations, respectively.
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capacity of TCNQ within 72% above 200 K. Heat capacity data of electron acceptors and donors serve as a useful tool to estimate a baseline for phase transition, especially when the heat capacity anomaly is sluggish and spreads over a wide temperature region. In that sense, the thermodynamic quantities of TCNQ determined by the present study contribute to a valuable database. 4.2. Nature of the phase transition in NH4-TCNQ As reported in the X-ray structural study by Kobayashi [33], the phase transition at 301.3 K observed by the present heat capacity measurement is caused by a monomer-dimer transition, in which a uniform chain of the TCNQ ions in the high-temperature phase is transformed to a nonuniform chain due to bimolecular association of TCNQ in the low-temperature phase. This structural change is evidenced also by IR spectroscopy. As an example, temperature dependence of the n2 mode corresponding to the CN stretching vibration of TCNQ anion is shown in Fig. 5 in the 24002100 cm1 wave number region. As in the case of K-TCNQ and Rb-TCNQ [46,50–52], the drastic reduction of the peak intensity, above the transition temperature, of the central of the three bands observed in the C–N stretching region can be attributed to a decreased number of crystal field components expected as a consequence of the reduction of the unit cell dimensions in going through the phase transition [33,46,51]. On the other hand, temperature dependence of the magnetic susceptibility of NH4-TCNQ reported by Vegter and Kommmandeur [30] (see Fig. 6) bears close resemblance to that of a charge transfer complex TTF-CuS4C4(CF3)4 [11,12], the first example showing the spin-Peierls transition and those of analogous
4. Discussion 4.1. Heat capacity of the electron acceptor TCNQ TCNQ is a typical electron acceptor but there have been no reports concerning its heat capacity measurements. Apparent addition rule of heat capacity holds well in many cases. For example, the molar heat capacity of TTF-TCNQ [53] showing the Peierls transition, where TTF is tetrathiafulvalene, coincides with the sum of the heat capacity of TTF [54] and the present heat
Fig. 5. IR absorption spectra due to the C–N stretching modes of NH4-TCNQ crystal in the 2400–2100 cm1 wave number region.
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700
χ / 10−4 emu
| J/k| / K
2
600
= 0.8
1
500
= 0.7 300
320
340
= 0.5
300 T/K
400
Fig. 6. Temperature dependence of the magnetic susceptibilities of NH4-TCNQ. Solid curve: Experimental values reported by Vegter and Kommandeur [30]. Broken lines: Theoretical curves with different values of the parameter g ( ¼ J2/J1) defined as the ratio of two alternating exchange interaction parameters in the TCNQ antiferromagnetic linear chain with J1,2 ¼ J0[17d(T)], where d(T) is an alternating parameter [57].
complexes M-TCNQ (M ¼ Na, K, Rb, Cs) [30]. The characteristic behavior of the magnetic susceptibility of these complexes has been theoretically interpreted by Takaoka and Motizuki [38] on the basis of the one-dimensional antiferromagnetic Heisenberg model involving the spin-lattice interaction leading to the spinPeierls transition. Based on these evidences, the phase transition observed in NH4-TCNQ crystal can be attributed to the spinPeierls transition. Prior to thermodynamic investigation of the phase transition in NH4-TCNQ crystal, characterization of the low- and hightemperature phases are briefly discussed in the following two sections on the basis of the magnetic data previously reported.
400
where k is the Boltzmann constant. The broken curve drawn in Fig. 7 corresponds to the values estimated by the least squares fitting (a ¼ 0.01542 K1, b ¼ 13.35, c ¼ 3358 K). The J value at the phase transition temperature Ttrs ¼ 301.3 K is J(Ttrs)/k ¼ 735 K. 4.4. Magnetic properties of the low-temperature phase Beni [56] and Pytte [2] treated the following Hamiltonian describing spins (S ¼ 1/2) with one-dimensional Heisenberg interaction, coupled to a three-dimensional lattice: H¼
X j
1 2Jðj; j þ 1ÞðSj Sjþ1 Þ 4
(2)
The exchange interaction parameter J(j, j+1) is a function not only of the spin-spin interaction but also of the lattice displacement. This Hamiltonian leads to the same form as a conventional Peierls transitions [9,10] and brings about a second-order phase transition at the spin-Peierls transition temperature (TSP). The exchange interaction parameters of such a nonuniform chain (J1 and J2) are given by the following equation [3]: J1;2 ¼ J 0 expð2bxÞ ¼ J 0 expðdÞ
4.3. Magnetic properties of the high-temperature phase Magnetic properties of the high-temperature phase characterized by a uniform stack of the TCNQ (spin S ¼ 1/2) ions are well described by the one-dimensional antiferromagnetic Heisenberg model by Bonner and Fisher [55]. By comparing the observed magnetic data [30] with the theoretical magnetic susceptibility of one-dimensional system, one can determine values of exchange interaction parameter J(T) as a function of temperature. The resultant J(T) values are plotted in Fig. 7. A noticeable feature is that J(T) is remarkably decreased as the temperature is increased. This is caused by the thermal expansion along the TCNQ stacking axis. This type of behavior is also reported for K-TCNQ [32]. When the intermolecular distance between adjacent TCNQ ions may be assumed to be proportional to temperature, the exchange interaction parameter is approximated as jJðTÞ=kj ¼ aT 2 þ bT þ c
380
Fig. 7. Temperature dependence of the spin exchange interaction parameter J in the high-temperature phase of NH4-TCNQ above the phase transition at 301.3 K. Broken curve corresponds to the least squares fit with quadratic temperature.
0 200
360 T/K
(1)
(3)
where b is a parameter characterizing the extension of the wave function, x is the distance in unit of the lattice parameter, and J0 is the value of exchange parameter without distortion. In the case of NH4-TCNQ, it corresponds to J0/k ¼ J(Ttrs)/k ¼ 735 K. In the limit of small d, the dimerization of the spin sites leads to an alternating exchange: J1;2 ðTÞ ¼ J 0 ½1 dðTÞ
(4)
Below the phase transition temperature TSP, a gap 2D(T) appears in the excitation spectrum, which separates the singlet ground state from spin-wave excitations [13]. This D(T) follows a BCS-type temperature dependence and is related to d(T) as follows:
dðTÞ ¼
DðTÞ 2pJ 0
with
pffi1þ
2
p
(5)
In the Hartree-Fock approximation, Bulaevskii [57] derived the equation of magnetic susceptibility for an alternating antiferro-
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1.0
(T) /max
0.8
0.6
0.4 Ttrs 0.2
0.0 220
240
260 T/K
280
300
320
Fig. 8. Temperature dependence of the parameter d(T) characterizing the alternating Heisenberg chain with J1,2(T) ¼ J0[17d(T)]. The values are reduced by dmax ¼ 0.33, a convergent value at low temperature. Solid circles imply the values estimated from the experimental data [30]. The broken curve is an eye guide.
magnetic Heisenberg chain: N g 2 m2B aðTÞ 2J0 ½1 þ dðTÞbðTÞ vðTÞ ¼ A exp kT T
(6)
where a(T) and b(T) are constants depending on the value g(T) ¼ J2/J1. Magnetic susceptibility curves estimated from this equation are shown in Fig. 6 by broken line for three representative values of g ¼ 0.8 (d ¼ 0.111), g ¼ 0.7 (d ¼ 0.176), and g ¼ 0.5 (d ¼ 0.333), in which g and d are related as d ¼ (1g)/(1+g). The alternating parameter d can be determined, as a function of temperature, by equalizing the observed magnetic susceptibility [30] to Eq. (6). The parameter d(T) thus estimated is shown in Fig. 8. As the temperature is lowered, the value of d(T) is increased and eventually approaches a convergent value dmax ¼ 0.33 below ca. 240 K. This fact implies that the dimerization of TCNQ anions is enhanced with decreasing temperature till about 240 K. In what follows, this temperature will be designated as T0. The ratio d(T)/ dmax shown in Fig. 8 serves as an order parameter in the lowtemperature phase. By substituting d ¼ 0.333 and J0/k ¼ 735 K for Eq. (5), one obtains the ratio of the energy gap at 0 K [2D(0)] and the phase transition temperature (Ttrs ¼ 301.3 K) as 2D(0)/Ttrs ¼ 5.32. It is of interest that this value is rather close to 3.53 derived for the BCS theory, although the spin-Peierls and the superconductive transitions are different phenomena. 4.5. Thermodynamic investigation of the phase transition Fundamental concept of the spin-Peierls transition is to describe the quantum spin system of antiferromagnetic linear chain in terms of the pseudo-fermion and to take into account its interaction with phonon. For such a system, a lattice distortion arising from dimerization is expected to appear at low-temperature side. We thus consider both the spin and the lattice systems to interpret thermodynamically the nature of the spin-Peierls phase transition. The observed entropy of transition DtrsS may be assumed to consist of the magnetic and the lattice contributions:
Dtrs S ¼ Dtrs Smag þ Dtrs Slat
(7)
Fig. 9. Schematic drawing of the magnetic heat capacity (top) and the entropy gain due to the magnetic origin in NH4-TCNQ crystal (down). T0 is the temperature, below which the progressive dimerization substantially ceases. DSm and DSd are the magnetic entropy of the uniform (monomer) and nonuniform (dimer) antiferromagnetic Heisenberg chain models at Ttrs and T0, respectively. In the actual situation, the value DSd(T0) is buried in the estimated normal heat capacity. DSsro is the entropy due to the short-range-order effect in the monomer chain above Ttrs.
As to the magnetic system, we assume that the monomer-dimer transition occurs at Ttrs in the one-dimensional S ¼ 1/2 antiferromagnetic Heisenberg chains. As schematically shown in Fig. 9, the total magnetic entropy, Smag(T ¼ N), consists of the following components: Smag ðT ¼ 1Þ ¼ DSd ðT 0 Þ þ Dtrs Smag þ DSsro ðT trs oTo1Þ ¼ R ln 2 (8) where DSd(T0) is the magnetic entropy of the nonuniform (dimer) antiferromagnetic Heisenberg chain at T0E240 K, below which the progressive dimerization substantially ceases, and DSsro (TtrsoToN) is the entropy due to the short-range-order effect in the uniform (monomer) chain above Ttrs. In the actual situation, the value DSd(T0) is buried in the estimated normal heat capacity. On the other hand, the magnetic entropy of the uniform chain (monomer) at Ttrs [DSm(Ttrs)] is the sum of two contributions:
DSm ðT trs Þ ¼ DSd ðT 0 Þ þ Dtrs Smag
(9)
DSm(Ttrs) and DSd(T0) can be theoretically estimated on the basis of the following one-dimensional antiferromagnetic Heisenberg
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model: H¼
X
2J 0 ðS2j S2j1 þ gS2j S2jþ1 Þ
(10)
j
where g is the alternation (or dimerization) parameter. For the uniform chain (g ¼ 1) one can use the model calculation by Bonner and Fisher [55] and by Blo¨te [58], while for the nonuniform chain (ga1) by Duffy and Barr [59]. Since the parameters J0 and g for NH4-TCNQ have been determined as J0/ k ¼ 735 K and g ¼ 0.5, one can calculate as follows: DSd(T0) ¼ 0.58 J K1 mol1 and DSm(Ttrs) ¼ 1.19 J K1 mol1, and hence DtrsSmag ¼ 0.61 J K1 mol1. The transition entropy for the lattice system is thus determined as DtrsSlat ¼ 1.58 J K1 mol1 from Eq. (7). It was revealed that the contribution from the magnetic origin to the entropy of transition is as small as 28% and the remaining 72% arises from the phonon system. Moreover, the entropy due to the short-range-order effect in the uniform (monomer) chain above Ttrs is estimated as DSsro(TtrsoToN) ¼ 4.57 J K1 mol1 from Eq. (8), which is 80% of the total magnetic entropy (R ln 2). The fact that the majority of the magnetic entropy remains above Ttrs as the short-range-order effect is characteristic of the low-dimensional magnets. As to the energy (or enthalpy), we can discuss as follows: Fig. 10 shows temperature dependence of the enthalpy gain DH(T) reduced by the observed enthalpy of transition DtrsH ¼ (66777) J mol1. As in the case of entropy, the enthalpy due to the phase transition consists of contributions from both the spin and the lattice systems. Pytte [2] showed that in the limit of small distortion (d) in the alternating antiferromagnetic Heisenberg chain of Bulaevskii [57] the gain in spin energy (DtrsHmag) on distorting below Ttrs is proportional to (d ln d)2. On the other hand, the cost in lattice energy (DtrsHlat) due to dimerization of the radical anions is proportional to d2. Under these assumptions, the net enthalpy DH(d) due to the spin and the lattice system is written as
nHðdÞ ¼ aðd ln dÞ2 þ ð1=2Þbd2
(11)
where a and b are constants. As shown in Fig. 8, the d value increases with decreasing temperature and reaches to a constant
1.0
Experimental Calculated
ΔH (T) /ΔtrsH
0.8
value dmax ¼ 0.33 around 240 K. By a least squares fit of d vs. T in the range 240 KrTr301 K, d can be expressed as a function of temperature. By scaling the absolute value jDH(dmax)j with DtrsH, the two parameters were determined to be a ¼ 5130 J mol1 and b ¼ 604 J mol1. For comparison, thus determined quantities [DH(dmax)DH(d)]/DH(dmax) are also plotted in Fig. 10 by solid circles. Calorimetrically observed quantities DH(T)/DtrsH are well reproduced by the quantities [DH(dmax)DH(d)]/DH(dmax) derived from the magnetic susceptibility data [30]. From Eq. (11) and dmax ¼ 0.333, the energy gain due to the spin is estimated to be DtrsHmag ¼ 688 J mol1 and the cost in lattice energy is DtrsHlat ¼ 33 J mol1. On the other hand, according to the theory of alternating antiferromagnetic Heisenberg chain by Duffy and Barr [59], the energy gain of the spin system by the dimerization becomes 660 J mol1, for d ¼ 0.33 (g ¼ 0.5) and J0/k ¼ 735 K. In spite of different models, this value agrees well with DtrsHmag ( ¼ 688 J mol1) estimated from a(d ln d)2.
4. Conclusions Heat capacity measurements for the organic radical-ion salt NH4-TCNQ and the electron acceptor TCNQ crystals were carried out by adiabatic calorimetry at the temperatures in the range 12–350 K. The radical-ion salt exhibited a l-type phase transition at 301.3 K. By assuming a uniform antiferromagnetic S ¼ 1/2 Heisenberg linear chains in the high-temperature phase and an alternating linear chains in the low-temperature phase, the observed entropy of transition DtrsS ¼ (2.1970.02) J K1 mol1 was reasonably accounted for in terms of a magnetic contribution DtrsSmag ¼ 0.61 J K1 mol1 and a lattice contribution DtrsSlat ¼ 1.58 J K1 mol1. Although the total magnetic entropy expected for the present compound is R ln 2 ( ¼ 5.76 J K1 mol1), a majority of the magnetic entropy (4.6 J K1 mol1) was found to persist in the high-temperature phase as a short-range-order effect. On the other hand, the observed enthalpy of transition DtrsH ¼ (66777) J mol1 was interpreted as the sum of the gain in spin energy (DtrsHmag ¼ 688 J mol1) and the cost in lattice energy (DtrsHlat ¼ 33 J mol1) due to dimerization of the TCNQ anions in the low-temperature phase. The present thermodynamic investigation quantitatively revealed that the l-type phase transition at 301.3 K takes place as a result of cooperative coupling between the spin and the phonon (lattice) systems. Together with previously reported magnetic susceptibility [29,30] and X-ray diffraction [33], the present calorimetry evidenced that the phase transition occurring in the radical-ion salt NH4-TCNQ is caused by the spin-Peierls transition.
0.6 Appendix A. Supporting Information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jpcs.2009.05.023.
0.4
0.2 References
0.0 240
260
280 T/K
300
320
Fig. 10. Temperature dependence of the enthalpy gain due to the phase transition in NH4-TCNQ crystal reduced by the observed enthalpy of transition DtrsH ¼ (66777) J mol1. Open circles: Observed values DH(T)/DtrsH. Solid circles: Values estimated from the magnetic susceptibility data [DH(dmax)DH(d)]/ DH(dmax).
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