Heat Capacities and Phase Transitions of Protonated and Deuterated

Noriko Onoda-Yamamuro‡. Institute for Molecular Science, Myodaiji-cho, Okazaki, Aichi 444, Japan. Osamu Yamamuro, Takasuke Matsuo,* and Hiroshi Suga...
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J. Phys. Chem. 1996, 100, 19647-19652

19647

Heat Capacities and Phase Transitions of Protonated and Deuterated Methylammonium Tetrafluoroborates† Noriko Onoda-Yamamuro‡ Institute for Molecular Science, Myodaiji-cho, Okazaki, Aichi 444, Japan

Osamu Yamamuro, Takasuke Matsuo,* and Hiroshi Suga§ Department of Chemistry and Microcalorimetry Research Center, Faculty of Science, Osaka UniVersity, Toyonaka, Osaka 560, Japan ReceiVed: June 4, 1996; In Final Form: September 25, 1996X

Heat capacities of CH3NH3BF4 and CD3ND3BF4 were measured in the temperature ranges 5-300 and 13300 K, respectively. A large heat capacity peak due to a first-order transition appeared at (251.3 ( 0.1) K for CH3NH3BF4 and (251.6 ( 0.1) K for CD3ND3BF4. The transition entropies of CH3NH3BF4 and CD3ND3BF4 were 20.47 ( 0.02 and 20.47 ( 0.02 J K-1 mol-1, respectively. A broad hump of the heat capacity was found at around 40 K in both samples. The excess entropy due to this anomaly was 2.90 J K-1 mol-1 for CH3NH3BF4 and 2.77 J K-1 mol-1 for CD3ND3BF4. These data indicate that the effects of deuterium substitution on both anomalies are minor in this compound. It was concluded from the analysis of entropy that both anomalies of CH3NH3BF4 and CD3ND3BF4 are due to ordering of the highly disordered orientations of methylammonium and tetrafluoroboric ions suggested by the previous X-ray and neutron diffraction study. Raman and IR spectra of CH3NH3BF4 and CD3ND3BF4 were measured and used in the estimation of the normal (vibrational) parts of the heat capacity.

1. Introduction +

Methylammonium (MA) ion CH3NH3 forms NaCl, CsCl, anti-fluorite, and perovskite type crystals with various counteranions: X- (X ) Cl, Br, I), MX62- (M ) Sn, Pt, Te), SO42-, NO3-, SCN-, and BF4-.1,2 In terms of the molecular interaction, these substances can be regarded as a hybrid between ionic and molecular crystals, since both van der Waals interaction of -CH3 and Coulomb energy due to -NH3+ are important. This allows them to possess a certain degree of freedom of molecular motion that characterizes molecular crystals while retaining the stability of the ionic lattices. Another notable aspect of interest is the anisotropy of the rotational motion of the MA ion arising from its C3V symmetry; two types of rotational modes are possible, one around the C-N axis and the other the angular displacement of the C-N axis itself. These properties lie at the basis of various phase transitions that occur in many of the MA compounds. We have studied these transitions from thermodynamic,3-13 structural,14-18 and dielectric19,20 points of view. Tetrafluoroboric ion BF4- is a stable anion with tetrahedral symmetry. Rotational states of BF4- ions and their collective disordering transitions have been studied in several ionic compounds with alkali metal,21-23 ammonium,21,24 and tetramethylammonium ions.25,26 For MABF4, however, only our studies by differential scanning calorimetry (DSC)5 and X-ray and neutron diffractions18 have been reported so far. We have found a first-order transition at around 250 K. Both CH3NH3+ and BF4- groups are highly disordered in their orientation in * To whom correspondence should be sent. Phone: +81-6-850-5396. Fax: +81-6-850-5397. E-mail: [email protected]. † Contribution No. 124 from the Microcalorimetry Research Center. ‡ Present Address: Department of Chemistry, University of Tsukuba, Tsukuba, Ibaraki 305, Japan. § Present Address: Research Institute for Science and Technology, Kinki University, Kowakae, Higashi-Osaka 577, Japan. X Abstract published in AdVance ACS Abstracts, November 1, 1996.

S0022-3654(96)01616-4 CCC: $12.00

the room temperature phase. It was pointed out that the transition involved orientational ordering of both CH3NH3+ and BF4- ions. In this study, the mechanism of the phase transitions in CH3NH3BF4 and CD3ND3BF4 is investigated from the thermodynamic point of view by low-temperature calorimetry. The effect of deuterium substitution can be important if the transition is related to the rotational motion of CH3NH3+ ions as in the case of (NH4)2MX6 (M ) Se, Te, Pb, Pt, Pd, X ) Cl, Br).27-33 IR and Raman spectra were also measured for both samples to estimate the heat capacity contribution from the intraionic vibrations of CH3NH3+ and BF4- ions. 2. Experimental Section A. Adiabatic Calorimetry. For both CH3NH3BF4 and CD3ND3BF4, we used the same batch of the samples as those used in the X-ray and neutron diffraction studies.18 The amounts of CH3NH3BF4 and CD3ND3BF4 loaded in the sample cells were 3.8944 g (0.032 762 mol) and 3.1267 g (0.025 032 mol), respectively. The dead space of the sample cell (about 3 cm3 for both samples) was filled with helium gas at atmospheric pressure at room temperature to enhance thermal equilibration at low temperature. The adiabatic calorimeters and sample cells used in this study have been reported elsewhere.34,35 The temperature was measured using Rh-Fe resistance thermometers (27 Ω at 273 K, purchased from Oxford Instruments Company) calibrated on the temperature scale EPT76 (T < 30 K) and IPTS68 (T > 30 K). The heat capacity difference caused by the conversion to the new temperature scale ITS9036 was estimated to be smaller than 0.05% over the 5-300 K temperature range. The accuracy of the heat capacity measurement was better than 1% at T < 20 K, 0.3% at 20 < T < 30 K, and 0.1% at T > 30 K. The heat capacity measurement was carried out by the standard intermittent heating method, i.e., repetition of equili© 1996 American Chemical Society

19648 J. Phys. Chem., Vol. 100, No. 50, 1996

Onoda-Yamamuro et al.

TABLE 1: Experimental Molar Heat Capacities of CH3NH3BF4 (M ) 118.87 g mol-1) T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

5.74 6.18 6.66 7.18 7.74 8.32 8.92 9.51 10.09 10.64 11.18 11.75 12.43 13.13 13.83 14.52 15.22 15.93 16.65 17.37 18.11 18.87 19.66 20.47 21.29 22.11 22.94 23.80 24.70 25.62 26.55 27.49 28.42

0.36761 0.46065 0.54860 0.69188 0.87194 1.0999 1.3728 1.6843 2.0194 2.3806 2.7538 3.1836 3.7367 4.3611 5.0373 5.7478 6.5119 7.3429 8.2347 9.1877 10.185 11.251 12.366 13.588 14.895 16.230 17.588 19.043 20.564 22.157 23.774 25.500 27.238

29.36 30.32 31.31 32.28 33.24 34.20 35.16 36.13 37.09 38.07 39.06 40.04 41.02 42.00 42.98 43.97 44.98 45.98 47.00 48.02 49.05 50.08 51.10 52.11 53.14 54.18 55.24 56.31 57.39 58.48 59.58 60.69 61.80

29.098 30.871 32.670 34.615 36.473 38.096 39.973 41.648 43.187 44.663 46.123 47.458 48.668 49.827 50.850 51.787 52.809 53.688 54.607 55.560 56.540 57.403 58.438 59.289 60.137 61.097 61.953 62.886 63.737 64.577 65.527 66.393 67.282

62.93 64.07 65.21 66.37 67.53 68.70 69.87 71.06 72.25 73.45 74.66 75.88 77.10 78.33 79.57 80.81 82.06 83.32 84.40 85.84 87.29 88.76 90.23 91.71 93.21 94.71 96.23 97.76 99.30 100.85 102.41 103.97 105.55

68.106 68.961 69.832 70.614 71.372 72.271 73.124 73.872 74.772 75.676 76.379 77.261 78.152 79.003 79.788 80.454 81.367 82.139 82.705 83.592 84.479 85.379 86.134 86.984 87.797 88.569 89.483 90.292 91.024 91.755 92.601 93.467 94.253

107.14 108.75 110.38 112.01 113.67 115.34 117.01 118.69 120.38 122.08 123.78 125.50 127.22 128.95 130.69 132.44 134.20 135.97 137.74 139.53 141.33 143.13 144.94 146.77 148.60 150.45 152.31 154.18 156.06 157.96 159.87 161.79 163.72

95.021 95.767 96.500 97.260 98.016 98.684 99.475 100.33 101.15 101.90 102.63 103.36 104.08 104.82 105.60 106.32 106.96 107.68 108.39 109.16 109.91 110.57 111.29 111.94 112.69 113.54 114.21 114.84 115.51 116.28 117.01 117.71 118.44

165.66 167.62 169.59 171.57 173.56 175.56 177.58 179.61 181.66 183.73 185.81 187.91 190.02 192.14 194.28 196.43 198.56 200.78 202.98 205.18 207.41 209.64 211.90 214.16 216.44 218.71 220.99 223.29 225.60 227.93 230.95 233.27 235.61

119.12 119.81 120.57 121.32 122.01 122.69 123.42 124.15 124.95 125.64 126.39 127.14 127.90 128.59 129.36 130.13 130.86 131.60 132.35 133.09 133.91 134.74 135.51 136.23 136.99 137.77 138.64 139.43 140.24 141.04 142.07 142.94 143.90

237.96 240.32 242.70 245.06 247.39 249.57 250.82 251.17 251.40 251.78 252.89 254.88 257.16 259.48 261.80 264.15 266.51 268.88 270.04 272.40 274.78 277.18 279.60 282.02 284.47 286.93 289.40 291.88 294.38 296.91 299.44

144.79 145.99 147.23 151.61 157.06 230.09 2361.1 6051.1 4873.5 2159.1 347.40 170.12 156.08 151.35 151.19 151.63 152.09 152.63 152.82 153.37 153.97 154.40 154.93 155.55 156.20 156.56 157.23 157.76 157.85 158.76 158.92

TABLE 2: Experimental Molar Heat Capacities of CD3ND3BF4 (M ) 124.91 g mol-1) T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

T (K)

Cp (J K-1 mol-1)

14.07 14.51 15.12 15.78 16.46 17.13 17.80 18.49 19.21 19.98 20.79 21.62 22.47 23.35 24.25 25.14 26.02 26.89 27.74 28.58 29.41 30.29 31.24 32.22 33.18 34.12 35.05 35.96 36.85 37.75 38.64 39.54

5.6061 6.1448 6.9065 7.6823 8.5829 9.5275 10.440 11.481 12.599 13.805 15.140 16.487 17.937 19.514 21.143 22.750 24.364 25.948 27.593 29.280 31.067 32.588 34.502 36.557 38.518 40.527 42.504 44.385 46.215 48.070 49.872 51.595

40.43 41.33 42.23 43.14 44.05 44.96 45.88 46.80 47.72 48.65 49.58 50.51 51.45 52.40 53.36 54.34 55.32 56.31 57.30 58.31 59.32 60.35 61.37 62.41 63.45 64.50 65.56 66.62 67.69 68.77 69.86 70.95

53.200 54.674 56.116 57.336 58.560 59.646 60.697 61.564 62.374 63.198 63.998 64.725 65.383 66.095 66.829 67.572 68.359 69.067 69.755 70.503 71.241 71.969 72.757 73.465 74.180 74.975 75.675 76.406 77.207 77.931 78.630 79.383

72.04 73.15 74.26 75.37 76.49 77.62 78.76 79.90 81.05 82.22 83.41 84.61 85.83 87.05 88.29 89.54 90.79 92.06 93.34 94.63 95.93 97.23 98.53 99.84 101.16 102.49 103.84 105.19 106.55 107.93 109.31 110.71

80.047 80.856 81.546 82.211 83.004 83.664 84.399 85.166 85.739 86.403 87.109 87.818 88.568 89.211 89.907 90.573 91.259 92.019 92.641 93.366 94.035 94.609 95.319 95.942 96.562 97.267 97.869 98.530 99.206 99.733 100.47 101.10

112.12 114.29 115.96 117.65 119.35 121.06 122.78 124.51 126.26 128.02 129.79 131.57 133.35 135.16 136.98 138.82 140.68 142.55 144.44 146.35 148.27 150.21 152.17 154.14 156.13 158.14 160.16 162.20 164.25 166.33 168.41 170.52

101.65 102.52 103.18 104.01 104.68 105.45 106.23 106.86 107.68 108.38 109.12 109.87 110.52 111.32 112.10 112.76 113.59 114.33 115.02 115.91 116.62 117.33 118.19 118.95 119.66 120.55 121.26 122.01 122.88 123.69 124.40 125.33

172.64 174.77 176.92 179.07 181.25 183.44 185.66 187.89 190.13 192.38 194.65 196.92 199.20 201.49 203.80 206.11 208.43 210.76 213.11 215.46 217.82 220.19 222.57 224.96 227.36 229.77 232.18 234.60 236.98 239.35 241.73 244.06

126.25 126.87 127.78 128.70 129.45 130.28 131.22 132.08 132.83 133.81 134.81 135.60 136.43 137.43 138.42 139.19 140.16 141.08 142.14 142.89 143.88 144.93 146.05 147.07 148.09 149.37 150.94 152.76 154.34 156.72 160.42 168.79

246.30 248.25 249.76 250.80 251.35 251.62 251.94 252.90 254.79 257.16 259.60 262.08 264.55 267.04 269.53 272.04 274.57 277.10 279.65 282.22 284.79 287.38 289.98 292.60 295.22 297.86 300.51

195.83 322.00 552.58 1118.2 3135.1 4673.0 2368.0 437.90 195.28 165.46 161.17 160.80 161.38 162.17 162.95 163.76 164.21 165.01 165.99 167.03 168.01 168.71 169.32 170.42 171.49 172.31 172.74

bration and energizing intervals. The temperature ranges of the measurement were 5-300 K for CH3NH3BF4 and 13-300 K for CD3ND3BF4. The temperature step for each measurement was 1-2.5 K in the normal region and was reduced to 0.1 K around the peak of the transition. Single-step heating experiments were performed separately to determine the transition enthalpy precisely.

B. IR and Raman Spectroscopy. The IR spectra of CH3NH3BF4 and CD3ND3BF4 were measured at room temperature in the wavenumber range 400-4000 cm-1 with a JASCO spectrometer Model DS-402G. CH3NH3BF4 crystal was ground and suspended in a Nujol mull. CD3ND3BF4 crystal was ground with dried KBr powder and shaped into a thin disk by applying pressure. We avoided Nujol because D atoms of the ND3 group

Methylammonium Tetrafluoroborates

J. Phys. Chem., Vol. 100, No. 50, 1996 19649 TABLE 3: Temperatures, Enthalpies, and Entropies of the Phase Transitions of CH3NH3BF4 and CD3ND3

CH3NH3BF4 CD3ND3BF4

Ttrs (K)

∆H (kJ mol-1)

∆S (J K-1 mol-1)

251.3 251.6

5.144 5.138

20.47 20.47

TABLE 4: Vibrational Assignments for the MA+ Ion and BF4- Ion in CH3NH3BF4 and CD3ND3BF4 νobs/cm-1 ions

mode

symmetry

CH3NH3BF4

CD3ND3BF4

MA+

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12 ν1 ν2 ν3 ν4

A1 A1 A1 A1 A1 A2 E E E E E E A1 E F2 F2

3028 2920 1501 1408 1003

2180a 2102a 1179 1066 895

3099 2969 1578 1469 1255 924 771 363 1070 525

2293a 2242a 1113 1041 1003 673 771 363 1070 525

Figure 1. Heat capacities of CH3NH3BF4 (open circles) and CD3ND3BF4 (closed circles) crystals.

BF4-

a These values are calculated from the data of CH NH BF . See 3 3 4 text for the details.

Figure 2. Excess entropies due to the transitions of CH3NH3BF4 (open circles) and CD3ND3BF4 (closed circles) crystals.

are readily substituted by H atoms of water occluded in the Nujol mull. The Raman spectra were recorded at room temperature in the range 50-2000 cm-1 with a JASCO spectrometer Model R750 using nonpolarized argon laser light with a wavelength of 5145 Å. The samples were loaded in sealed Pyrex-glass capillary tubes. For CD3ND3BF4, the sampling was performed in dry nitrogen atmosphere to avoid contamination by atmospheric water. 3. Results and Discussion A. Heat Capacities. The molar heat capacities of CH3NH3BF4 and CD3ND3BF4 crystals are collected in Tables 1 and 2 and also plotted in Figures 1 and 2, respectively. A phase transition appeared at around 250 K for both samples. In addition to this transition, a broad hump of the heat capacity was observed around 40 K for both samples. Any unusual relaxation effect, such as sometimes observed in tunneling effects with slow nuclear spin conversion, was not observed. This also precludes the possibility of glass transitions as the cause of these humps. The heat capacity of CD3ND3BF4 is larger than that of CH3NH3BF4 in the whole temperature range. This is due to the mass effect on the frequencies of the vibrational modes related to the MA ions. B. Phase Transitions. To extract the excess heat capacity ∆Cp due to the phase transition, the vibrational heat capacity (base line) was determined by least-squares fitting. The thirdorder polynomial function reproduced the experimental data well at temperatures of 210-235 and 265-290 K for CH3NH3BF4

and 200-220 and 280-300 K for CD3ND3BF4. The excess entropy due to the transition ∆S was calculated by integrating ∆Cp/T and is plotted as a function of temperature in Figure 2. This figure shows that the transition is typical first order for both samples. The thermodynamic quantities (temperature, enthalpy, and entropy) related to the transition are summarized in Table 3. Evidently, the isotope effect is small for the transition temperature and entropy. The relation between the large transition entropy and the orientational disorder of the CH3NH3+ and BF4- ions will be discussed later together with the excess entropy due to the broad heat capacity anomaly around 40 K. C. IR and Raman Spectra. The wavenumbers of the 12 intraionic vibrational modes of MA+ ion and 4 of the BF4- ion were determined by the IR and Raman spectra at room temperature. They are summarized in Table 4 for CH3NH3BF4 and CD3ND3BF4. The wavenumbers of the modes ν1, ν2, ν7, and ν8 of CD3ND3+, which are expected to be 2100-2300 cm-1, could not be determined because of peak broadness and overlap. They were therefore determined from the data of CH3NH3+ by multiplying the wavenumber ratio ν(D)/ν(H) found in CH3NH3Cl and CD3ND3Cl.37,38 The torsional mode ν6 is nonactive for both IR and Raman. D. Thermal Anomaly in the Low-Temperature Phase. The anomaly around 40 K is very broad and not evidently distinct from the background Cp. To demonstrate that this anomaly contains some contribution other than the vibrational heat capacity and to separate it from the vibrational part, a model function

Cp ) C(ac-lat,3) + C(op-lat,3) + C(MA-intvib,17) + C(MA-introt,1) + C(MA-extrot,1) + C(MA-lib,2) + C(BF-intvib,9) + C(BF-lib,3) + ∆Ccorr (1) was fitted to the experimental heat capacities over various temperature ranges around 40 K. The idea was that the fitting would be poor if the experimental data contained a nonvibra-

19650 J. Phys. Chem., Vol. 100, No. 50, 1996

Onoda-Yamamuro et al.

tional part. If this was the case, we should be able to extract the excess part by fitting the vibrational function to a data set that excluded the systematically deviating region. In eq 1, C(aclat,3), C(op-lat,3), C(MA-intvib,17), C(MA-introt,1), C(MAextrot,1), C(MA-lib,2), C(BF-intvib,9), and C(BF-lib,3) are the heat capacities due to the acoustic lattice vibration, translational optical lattice vibration, MA intraionic vibration, MA intraionic rotation about the C-N axis (torsion ν6), MA overall (external) rotation about the C-N axis, rotational vibration of the MA C-N axis itself (libration), BF4- intraionic vibration, and BF4libration, respectively. The number in parentheses denotes the degrees of freedom included in each term. The last term in eq 2 gives the correction for the difference between Cp and CV, which is given by

∆Ccorr ) ACp2T

(2)

where A is a constant and T the temperature. C(ac-lat,3) was approximated by a Debye function and C(op-lat,3) by an Einstein function. C(MA-intvib,17), C(MA-introt,1), C(MAextrot,1), C(MA-lib,2), C(BF-intvib,9), and C(BF-lib,3) were represented by the combination of 33 Einstein functions. The use of this model function based on the additivity of each contribution of the heat capacity has provided satisfactory results in the fitting of the heat capacities of other salts containing methylammonium ions.6-12 All the frequencies (Einstein temperatures) of the intraionic vibrations of MA and BF4- ions except ν6 were determined from the IR and Raman spectra as described above. The frequency of ν6 was estimated to be 255 cm-1 for CH3NH3BF4 and 187 cm-1 for CD3ND3BF4 from the activation energy (8.0 kJ mol-1) of the intraionic rotation about the C-N axis determined by NMR study.39 The Debye temperature θD(aclat,3), four Einstein temperatures θE(op-lat,3), θE(MA-extrot,1), θE(MA-lib,2), θE(BF-lib,3), and the correction coefficient A were determined by a least-squares fitting method to the experimental heat capacities. The entire data in the range covering the anomalous region (5-200 K) was fitted first. The result was very poor with the calculated Cp curve significantly lower than the observed values around 40 K. Therefore, the data points around 40 K were excluded from the data set for the fitting step by step until a satisfactory fitting was obtained. The temperature regions used for the final fitting were 5-20 and 80-200 K for CH3NH3BF4 and 14-22 and 100-180 K for CD3ND3BF4. The calculated heat capacities were shown by solid curves in Figure 3. The parameters determined by the final fitting were θD(ac-lat,3) ) 99.7 K, θE(op-lat,3) ) 194.1 K, θE(MA-extrot,1) ) 194.6 K, θE(MA-lib,2) ) 190.5 K, θE(BF-lib,3) ) 108.8 K, and A ) 2.08 × 10-6 mol J-1 for CH3NH3BF4 and θD(ac-lat,3) ) 100.4 K, θE(op-lat,3) ) 197.5 K, θE(MA-extrot,1) ) 190.4 K, θE(MA-lib,2) ) 113.4 K, θE(BFlib,3) ) 113.4 K, and A ) 1.87 × 10-6 mol J-1 for CD3ND3BF4. Figures 4 and 5 show the excess heat capacities and excess entropies due to the anomalies. The temperature of the maximum of ∆Cp was 39 K for CH3NH3BF4 and 43 K for CD3ND3BF4. The total entropy due to the anomaly was 2.90 J K-1 mol-1 for CH3NH3BF4 and 2.77 J K-1 mol-1 for CD3ND3BF4. The anomaly depends on the hydrogen isotopes, as Figures 4 and 5 show. The isotope effect is larger than in the first-order transition at 250 K. However, the actual shape of the heat capacity hump depends to a considerable extent on the estimated vibrational base line because of its small magnitude. In the following, we discuss the isotope-independent aspects of the hump in view of the small isotope dependence.

Figure 3. Heat capacity anomalies of CH3NH3BF4 (upper) and CD3ND3BF4 (lower) crystals in the low-temperature region. The solid curves represent the normal (vibrational) heat capacities determined by the least-squares fitting (see text for the details).

Figure 4. Excess heat capacities due to the anomalies of CH3NH3BF4 (open circles) and CD3ND3BF4 (closed circles) crystals in the lowtemperature region.

Such humps are often associated with a set of a few isolated states involving nuclear spin and electronic degrees of freedom and even disorder of atomic positions in a molecular system.40 Therefore, an attempt was made to fit a two-state Schottky function to the excess heat capacity. The number (per chemical unit) of the entities responsible for the anomaly and the energy splitting were varied as adjustable parameters for the fitting. The result was unsatisfactory; the calculated heat capacity always decreased considerably more slowly than the experimental curves at higher temperatures. It is concluded that the anomaly around 40 K is neither due to a vibrational effect nor

Methylammonium Tetrafluoroborates

J. Phys. Chem., Vol. 100, No. 50, 1996 19651

Figure 6. Model of orientational disorder of CD3ND3+ and BF4- ions. The C3 axis of CD3ND3+ ion and the C2 or C3 axis of the BF4- ion coincide with the crystallographic C4 axis.

TABLE 6: Molar Thermodynamic Functions of CD3ND3BF4 0 (M ) 124.91 g mol-1, R ) 8.314 51 J K-1 mol-1, Φm ) T 0 T 0 ∆0 Sm - ∆0 Hm/T) Figure 5. Excess entropies due to the heat capacity anomalies of CH3NH3BF4 (open circles) and CD3ND3BF4 (closed circles) crystals in the low-temperature region.

TABLE 5: Molar Thermodynamic Functions of CH3NH3BF4 0 (M ) 118.87 g mol-1, R ) 8.314 51 J K-1 mol-1, Φm ) T 0 T 0 ∆0 Sm - ∆0 Hm/T) T/K

o Cp,m /R

0 ∆T0 Hm /RT

0 ∆T0 Sm /R

0 Φm /R

5 10 15 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 260 270 273.15 280 290 298.15 300

0.02967 0.2361 0.7578 1.536 3.637 5.701 6.904 7.916 8.810 9.619 10.35 11.00 11.59 12.14 12.66 13.15 13.62 14.08 14.52 14.95 15.38 15.80 16.21 16.63 17.05 17.53 18.19 18.39 18.46 18.65 18.91 19.10 19.12

0.007375 0.05902 0.1959 0.4301 1.138 2.037 2.897 3.651 4.325 4.937 5.499 6.017 6.496 6.944 7.363 7.759 8.135 8.492 8.834 9.161 9.477 9.783 10.08 10.37 10.65 10.93 13.83 13.99 14.04 14.15 14.31 14.44 14.47

0.009837 0.07870 0.2620 0.5825 1.590 2.937 4.346 5.697 6.985 8.215 9.391 10.52 11.59 12.62 13.62 14.57 15.50 16.39 17.26 18.10 18.92 19.72 20.50 21.26 22.01 22.75 26.63 27.31 27.53 27.99 28.65 29.17 29.29

0.002462 0.01968 0.06614 0.1524 0.4516 0.9000 1.449 2.045 2.660 3.278 3.892 4.499 5.095 5.680 6.252 6.813 7.361 7.897 8.423 8.937 9.441 9.935 10.42 10.89 11.36 11.82 12.80 13.32 13.49 13.83 14.33 14.73 14.82

a simple Schottky anomaly. It may be some type of a weak cooperative effect (a higher order transition?). Similar broad heat capacity anomalies appear in NH4BF4,24 NH4ReO4,41 NH4ClO4,42 and NH4IO4,43 though their excess entropies are larger than that of CH3NH3BF4. The minor deuterium substitution effects of these compounds44,45 are also similar to the present result. Interestingly, no heat capacity anomaly was observed in KBF4.24 There may be a common disordering mechanism that requires participation by both the tetrahedral anion and ammonium or methylammonium ion. A possibility arises from the low-symmetry environment formed by the tetrahedral anions around the cation. Because of the low symmetry, it may have secondary potential minima as a

T/K

0 Cp,m /R

0 ∆T0 Hm /RT

0 ∆T0 Sm /R

0 Φm /R

5 10 15 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 260 270 273.15 280 290 298.15 300

0.02894 0.2326 0.7843 1.665 3.857 6.304 7.736 8.627 9.471 10.24 10.93 11.55 12.11 12.63 13.13 13.63 14.11 14.58 15.04 15.51 15.98 16.46 16.93 17.43 17.99 18.93 19.37 19.60 19.72 19.98 20.40 20.72 20.77

0.007224 0.05791 0.1969 0.4504 1.208 2.179 3.168 4.004 4.726 5.368 5.948 6.477 6.965 7.415 7.836 8.232 8.607 8.966 9.310 9.641 9.963 10.28 10.58 10.88 11.18 11.48 14.40 14.58 14.64 14.77 14.96 15.11 15.14

0.009638 0.07719 0.2623 0.6045 1.678 3.126 4.710 6.200 7.594 8.910 10.16 11.34 12.47 13.54 14.58 15.57 16.52 17.45 18.35 19.22 20.07 20.90 21.72 22.52 23.30 24.09 28.03 28.76 28.99 29.48 30.19 30.76 30.89

0.002413 0.01928 0.06538 0.1541 0.4706 0.9473 1.542 2.196 2.868 3.542 4.208 4.863 5.503 6.129 6.739 7.335 7.915 8.483 9.036 9.578 10.11 10.63 11.14 11.64 12.13 12.61 13.63 14.18 14.35 14.71 15.23 15.65 15.74

function of the orientation of the ammonium or methylammonium ion. Thermal excitation into such subminima, modified with a bit of cooperativity, would give rise to an excess heat capacity that accounts for the experimental results. E. Origin of the Excess Entropy. To investigate the origin of the excess entropy due to the first-order transition and the broad anomaly, we have calculated the orientational entropy of methylammonium and tetrafluoroboric ions based on the structure determined by the X-ray and neutron diffraction study.18 The contribution due to the volume change, which is approximated by ∆S ) R∆V/κ,46 was neglected because of the lack of the thermal expansivity (R) and isothermal compressibility (κ) data. In most of the other methylammonium compounds,6-13 the orientational entropy is dominant for the order-disorder transitions. However, it is obviously desirable to consider the volume effect in a full microscopic analysis of the entropy. The space group of the high-temperature phase is P4/nmm. A model of orientational disorder of CD3ND3+ and BF4- ions, which was determined by our X-ray and neutron diffraction study, is shown in Figure 6. There are two types of orientational

19652 J. Phys. Chem., Vol. 100, No. 50, 1996 disorder of the BF4- ion: one (66%) with its C2 axis coinciding with the crystallographic C4 axis and the other (34%) with its C3 axis coinciding with the same crystallographic axis. The major and minor orientations are accompanied by 2-fold and 4-fold orientational disorder around the C4 axis, respectively. The total entropy due to the orientational disorder of BF4- ion is calculated to be R ln 4.8 (13.1 J K-1 mol-1) by the equation of mixing entropy

∆S ) -R[2(0.66/2) ln(0.66/2) + 4(0.34/4) ln(0.34/4)] (3) The number of disordered orientations of CH3NH3+ ion with its C3 axis coinciding with the crystallographic C4 axis was not determined even by the neutron diffraction experiments; the nuclear density distribution of the D atoms is too broad for them to be assigned distinct positions. With this lack of knowledge, the orientational disorder of the CH3NH3+ ion is assumed to be 4-fold, the minimum number of orientations required by the symmetry consideration, giving the orientational entropy of R ln 4 (11.5 J K-1 mol-1). The 4-fold disorder of CH3NH3+ ion was experimentally confirmed for CH3NH3Cl.16 The total orientational entropy is calculated to be 24.6 J K-1 mol-1, which should agree with the total excess entropy if the crystal is orientationally ordered at 0 K. This value actually agrees with the observed total excess entropy (23.37 J K-1 mol-1) within an error of 5%. Thus, we conclude, from both structural and thermodynamic points of view, that the first-order transition and the broad anomaly of CH3NH3BF4 and CD3ND3BF4 are due to ordering of the highly disordered orientations of methylammonium and tetrafluoroboric ions; the ordering occurs mostly (88%) at the first-order transition. Structural studies in the low-temperature region are obviously desirable for a clearer description of the ordering process. Acknowledgment. The authors thank Mr. Shin-ichi Ishikawa and Mr. Mitsuo Ohama of Faculty of Science, Osaka University for their help in IR and Raman spectroscopic experiments. Appendix Standard Thermodynamic Functions. The molar heat capacities, enthalpies, entropies, and Giauque functions of CH3NH3BF4 and CD3ND3BF4 were calculated from the smoothed heat capacity data and summarized in Tables 5 and 6, respectively. Extrapolation of the heat capacity down to 0 K was performed by using the model functions described in the main text. References and Notes (1) Parsonage, N. G.; Staveley, L. A. K. Disorder in Crystals; Clarendon Press: Oxford, 1978. (2) Yamamuro, O.; Onoda-Yamamuro, N.; Matsuo, T.; Suga, H.; Kamiyama, T.; Asano, H.; Ibberson, R. M.; David, W. I. F. Proc. Int. Symp. AdV. Nucl. Energy Res., 5th 1993, 2, 604. (3) Matsuo, T.; Ueda, M.; Suga, H. Chem. Phys. Lett. 1981, 82, 577. (4) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. Thermochim. Acta 1986, 98, 327. (5) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. Thermochim. Acta 1986, 99, 67.

Onoda-Yamamuro et al. (6) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. J. Chem. Thermodyn., 1986, 18, 939. (7) Onoda, N.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1986, 47, 211. (8) Onoda, N.; Matsuo, T.; Suga, H. Philos. Mag. 1988, A57, 245. (9) Matsuo, T.; Yan, H.; Suga, H. J. Phys. Chem. Solids 1988, 49, 85. (10) Onoda-Yamamuro, N.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1990, 51, 1383. (11) Onoda-Yamamuro, N.; Matsuo, T.; Suga, H. J. Chem. Thermodyn. 1991, 23, 987. (12) Kume, Y.; Matsuo, T.; Suga, H. Thermochim. Acta 1991, 183, 245. (13) Onoda-Yamamuro, N.; Yamamuro, O.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1992, 53, 277. (14) David, W. I. F.; Harrison, W. T. A.; Ward, R. L.; Leadbetter, A. J.; Matsuo, T.; Suga, H. Physica B 1989, 156-157, 96. (15) Yamamuro, O.; Matsuo, T.; Suga, H.; David, W. I. F.; Ibberson, R. M.; Leadbetter, A. J. Acta Crystallogr. B 1992, 48, 329. (16) Yamamuro, O.; Onoda-Yamamuro, N.; Matsuo, T.; Suga, H.; Kamiyama, T.; Ishigaki, T.; Asano, H. J. Phys. Chem. Solids 1994, 55, 383. (17) Onoda-Yamamuro, N.; Yamamuro, O.; Matsuo, T.; Suga, H.; Oikawa, K.; Tsuchiya, N.; Kamiyama, T.; Asano, H. Physica B 1995, 213214, 411. (18) Yamamuro, O.; Onoda-Yamamuro, N.; Matsuo, T.; Suga, H.; Kamiyama, T.; Ishigaki, T.; Asano, H. J. Phys. Chem. Solids 1995, 56, 183. (19) Yamamuro, O.; Oguni, M.; Suga, H. Bull. Chem. Soc. Jpn. 1987, 60, 779. (20) Onoda-Yamamuro, N.; Yamamuro, O.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1992, 53, 935. (21) Clark, M. J. R.; Lynton, H. Can. J. Chem. 1969, 47, 2579. (22) Caron, A. P.; Huettner, D. J.; Ragle, J. L.; Sherk, L.; Stengle, T. R. J. Chem. Phys. 1967, 47, 2577. (23) Huettner, D. J.; Ragle, J. L.; Sherk, L.; Stengle, T. R.; Yeh, H. J. C. J. Chem. Phys. 1968, 48, 1739. (24) White, M. A.; Green, N. H.; Staveley, L. A. K. J. Chem. Thermodyn. 1981, 13, 283. (25) Giuseppetti, G.; Mazzi, F.; Tadini, C.; Ferloni, P.; Torre, S. Z. Kristallogr. 1992, 202, 81. (26) Zabinska, G.; Ferloni, P.; Sansei, M. Thermochim. Acta 1987, 122, 87. (27) Kume, Y.; Miyazaki, Y.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1992, 53, 1297. (28) Kume, Y.; Muraoka, H.; Matsuo, T.; Suga, H. J. Chem. Thermodyn. 1994, 26, 211. (29) Weir, R. D.; Westrum, E. F., Jr. J. Chem. Thermodyn. 1990, 22, 1097. (30) Weir, R. D.; Westrum, E. F., Jr. J. Chem. Thermodyn. 1990, 23, 653. (31) Callanan, J. E.; Weir, R. D.; Westrum, E. F., Jr. J. Chem. Thermodyn. 1992, 24, 1001. (32) Callanan, J. E.; Weir, R. D.; Westrum, E. F., Jr. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 1585. (33) Muraoka, H.; Matsuo, T.; Kume, Y. Solid State Commun. 1995, 93, 529. (34) Moriya, K.; Matsuo T.; Suga, H. J. Chem. Thermodyn. 1982, 14, 1143. (35) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. Bull. Chem. Soc. Jpn. 1987, 60, 1269. (36) Goldberg, R. N.; Weir, R. D. Pure Appl. Chem. 1992, 64, 1545. (37) Cabana, A.; Sandorfy, C. Spectrochim. Acta 1962, 18, 843. (38) The´areˆt, A.; Sandorfy, C. Spectrochim. Acta 1967, 23A, 519. (39) Ikeda, R.; Kume, Y.; Nakamura, D. J. Magn. Reson. 1976, 24, 9. (40) Matsuo, T.; Suga, H. Thermochim. Acta 1986, 109, 63. (41) Wire, R. D.; Staveley, L. A. K. J. Chem. Phys. 1980, 73, 1386. (42) Westrum, E. F.; Justice, B. H. J. Chem. Phys. 1969, 50, 5083. (43) Brown, R. J. C.; Callanan, J. E.; Weir, R. D.; Westrum, E. F. J. Chem. Thermodyn. 1987, 19, 1173. (44) Brown, R. J. C.; Callanan, J. E.; Weir, R. D.; Westrum, E. F. J. Chem. Thermodyn. 1986, 18, 787. (45) Stephenson, C. C.; Orcehotsky, R. S.; Smith, D. Thermodynamics Symposium; Scha¨fer, K., Ed.; Heidelberg, 1967; Vol. C.IV 2, p 1. (46) Sandrock, R.; Schneider, G. M. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 197.

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