Calorimetric and IR spectroscopic studies of phase transitions in methylammonium trihalogenoplumbates (II)†

J. ffip Printed

Chew. Solids Vol. 51. No. 12. pp. 1383-1395. in Great Britam.

1990

002%3697/w s3.M) + 0.00 0 1990 Pergamon Pm5 pk

CALORIMETRIC AND IR SPECTROSCOPIC STUDIES PHASE TRANSITIONS IN METHYLAMMONIUM TRIHALOGENOPLUMBATES (II)7

OF

NORIKO ONODA-YAMAMURO,TAKASUKE MATSUOand HIROSHISUGA Department of Chemistry and Microcalorimetry Research Center, Faculty of Science, Osaka University,

Toyonaka, Osaka 560, Japan (Received

10

May

1990;

17 July

accepted

1990)

Abstract-Heat capacitiesof CH,NH,PbX, (X = Cl, Br, I) were measured between 13 and 300 K (365 K for the iodide). Two anomalies were found in the chloride and the iodide, and three in the bromide. All the phase transitions were of the first order, although the highest temperature transitions in the bromide and the iodide were close to second order. Their temperatures and entropies are as follows: CH,NH,PbCl,:

171.5 K (14.6 J K-‘mol-I),

CH,NH,PbBr,:

148.8 K (11.2 J K-‘mol-I),

177.2 K (10.0 J K-‘mol-I); 154.0 K(4.1 J K-‘mol-I),

236.3 K (8.2 J K-‘mol-‘); CH,NH,PbI,:

161.4 K (19.0 J K-‘mol-I),

330.4 K (9.7 J K-‘mol-I).

The transition entropies indicated that the phase transitions are of the order-disorder type. They are interpreted with three possible models involving the methylammonium ions disordered with respect to the orientation of the C-N axis itself and around the C-N axis. The infrared line width of the v,~ vibration of the methylammonium ion depended markedly on the temperature and was interpreted as caused by the hindered rotational motion in the cubic and tetragonal phases. Keywords: Phase transition, heat capacity, transition entropy, methylammonium trihalogenoplumbate (II), infrared line broadening, orientation disorder

1. INTRODUCIION In recent years, extensive investigations have been made on structural phase transitions in crystals containing the methylammonium ion CH,NHJ (abbreviated as MA hereafter). One notices that a number of them have cubic symmetry in the highest temperature phases in spite of the polarity of an MA ion (the symmetry C,). To satisfy the site symmetry in the cubic phases, the cation has to be orientationally disordered. The corresponding entropy is expected to disappear on cooling through one or more phase transitions at low temperatures. The MA ion can have two types of orientational disorder; one is the orientation of the C-N axis relative to the crystal axes and the other related to the rotation around the C-N axis. Phase transitions involving the former are found MAPbCI, orthorhombic

in MAX (X = Br, I) [l, 21, MACIO., [3,4], MANO [51, WAhW [61 and WV2[TeX61(X = Cl, Br, I) [7,8]. Those involving the latter type of disorder are found in MAX (X = Cl, Br, I) [9, IO] and (MA),(TeX,] (X = Cl, Br, I) [7,8]. Recently, the ordering around the C-N axes was confirmed by neutron diffraction in MAI [l 1] and (MA)2[SnCI,]

WI. Methylammonium

MAPbX, (X = Cl, Br, I) have the cubic perovskite structure [13]. All three compounds undergo phase transitions [14, 151. Temperature-dependent structures determined by Poglitsch and Weber are as follows [14]:

I-

tetragonal

II -

172.9 K

MAPbBr, orthorhombic

II

l;5;

trihalogenoplumbates(I1)

tetragonal

cubic 178.8 K

II I~~J.LK tetragonal I -

cubic 236.9 K

MAPbI, orthorhombic

II -

tetragonal 162.2 K

t Contribution Research Center.

No.

21 from

the

Microcalorimetry

I-

cubic. 327.4 K

It is to be noted that the bromide has two tetragonal phases. 1383

One of them corresponds

to the tetragonal

N. OSODA-YAMAMURO et al.

1384

phase of the chloride and the other to that of the iodide. According to Poglitsch and Weber, the space groups are as follows (141: cubic: Pm3m, tetragonal tetragonal orthorhombic orthorhombic

I: 14/mcm, II: P4/mmm, I: P222,, II: Pna2,.

The authors noticed that there are eight equivalent orientations for an MA ion lying along the body diagonals in the cubic phase. They carried out dielectric measurement between 100 and 300 K and found a picosecond relaxation due to the dynamic disorder of the reorientating MA ion in the high temperature phase of each compound. A discontinuity in the dielectric constant was found at the orthorhombic II-tetragonal transition for the bromide and the iodide. However, no significant change was found at the tetragonal I-cubic transition in the bromide. For the chloride, it was not clear whether the discontinuity occurred at the orthorhombic I-tetragonal II transition or at the tetragonal II-cubic transition, because the temperatures of these transitions are very close to each other. The tetragonal I-cubic transition of the iodide was not studied dielectrically (141 because of the higher transition temperature. Taking account of these experimental results, Poglitsch and Weber suggested that MA ions are disordered in the tetragonal phase as well as in the cubic phase and become ordered at the tetragonal-orthorhombic transition. Moreover, they deduced by an argument based on site symmetry that the C-N axis of the MA ion in the orthorhombic phase has head-to-tail disorder in the chloride whereas it is ordered in the bromide and the iodide. Molecular motion of the MA ion was also reported in NMR study [15]. The long spin-lattice relaxation times r, of *H and 14H nuclei and the absence of quadrupole splitting indicated extremely rapid overall reorientation of the C-N axis in the cubic phase. A small 2H quadrupole splitting was observed in the tetragonal I phases of the bromide and the iodide. However, the relatively long T, suggested rapid motion of the MA ion also taking place in the orthorhombic phase. The motion may probably be restricted to rotation around the C-N axis in view of the quadrupole splitting found in the *H resonance. The purpose of the present work was to clarify the nature and the mechanism of the phase transitions in MAPbX, from the calorimetric point of view and to compare the results with those on (MA),[TeX,] [7,8]. Infrared spectroscopy turned out to be informative in providing additional evidence which supports the picture of rapid ionic motion in MAPbX, crystals.

2. EXPERIMENTAL MAPbX, (X = Cl, Br, I) crystals were prepared by drop-by-drop addition of aqueous solution of Pb(CH,COJr to an excess quantity of hot aqueous solution of MAX (X = Cl, Br, I) and slow cooling to about 5 “C. For MAPbI,, the temperature was kept above 40 “C because otherwise yellow crystals of composition (MA),PbL, - 2HrO formed [16]. Cubeshaped crystals of l-2 mm on the edge were obtained. They were colorless for the chloride, orange for the bromide and black for the iodide. Elemental analysis gave the following results: MAPbCI,:

C 3.58% (talc. 3.48%), H 1.82% (1.75%), N 4.09% (4.05%), Pb 59.56% (59.95%), Cl 30.87% (30.77%);

MAPbBr,:

C 2.50% (2.51%), H 1.35% (1.26%), N 2.92% (2.92%), Pb 43.20% (43.26%) Br 50.08% (50.05%);

MAPbI,:

c 1.90% (1.94%), H 0.98% (0.98%) N 2.29% (2.26%) Pb 33.37% (33.42%) I not analysed for.

The heat capacities were measured with a computerized adiabatic calorimeter described elsewhere [ 17, 181.The temperature ranges of the measurement were between 13 and 300 K, 13 and 300 K and 13 and 365 K, respectively, for MAPbCl,, MAPbBr, and MAPbI,. The mass of the calorimetric sample was 6.0483 g for MAPbCl,, 8.8810 g for MAPbBr, and 9.3384 g for MAPbI,. The IR absorption was measured with a Nihonbunko spectrometer Model DS-402G. The spectral slit width was 1 cm-’ at 1000 cm-‘. The low temperature spectra were obtained with a variable temperature cell using cold nitrogen gas flow. The sample temperature was detected with a chromel-constantan thermocouple embedded in the KBr (KC1 for MAPbCl,) plate and was kept within f0.2 K of the intended temperatures.

3. RESULTS AND DISCUSSION 3.1. Infrared absorption Internal vibrations of an MA ion are classified into A,, A2 and E species according to the C,, symmetry of the molecular ion. Fundamental vibrations were assigned by comparison with the well-documented spectra of the MA ion in other compounds [19]. The assignments are given in Table 1. These frequencies were used in the calculation of the vibrational heat capacity described below.

Phase transitions in methylammonium Table I. Vibrational frquencies

Mode

Symmetry

“I “1 “I “4 “3

A, A, A, A, A,

“6

4

“7 “8

2993 2917 1500 1420 978

E E

3080 2963 1588 1485 1250 922

“IO

“8,

E

E E

(II)

1385

ion (MA ion) in MAPbX, (X = Cl. Br. I)

CH,NH,PbCJ

“9 “II

of the CH,NH:

trihalogenoplumbates

CH,NH,PbBr,

CH, NH, WI,

3035 2926 1500 1408 966 Internal rotation, see text 3085 2967 1584 1449 1252 918

3012 2924 1486 1406 961

Some of the spectra were strongly dependent on the temperature. Figure 1 shows the temperature variation of the Ye (C-N stretching, -98Ocm-‘) and the v,* spectra (rocking, -910 cm-‘) of the MA ion in MAPbCI,, MAPbBr, and MAPbI,. The arrows in the figures indicate their respective transition temperatures. For the three compounds, the v,~ spectra were very broad at room temperature and narrowed as the temperature was reduced. For MAPbCl,, no obvious change of the viz line shape occurred as the 178.8 K transition temperature was traversed. On further cooling, the spectrum split into two components, which is seen as a shoulder at 130 K and as well-separated peaks at 88 K. For MAPbBr,, the splitting occurred below the

3098 2963 1578 1460 1240 907

148.8 K phase transition as a weak shoulder. Except for the narrowing, no drastic change was observed at the phase transition at 236.3 K or 154.0 K. The splitting of the v,? spectra in MAPbI, occurred at the 161.4K phase transition. The spectrum in the highest temperature phase (~330.4 K) was not recorded. In all of the compounds, the splitting occurred below the tetragonal-orthorhombic transition rather than the cubic-tetragonal or the tetragonal-tetragonal transition. In the tetragonal phases, the viz spectra were singlets in these compounds. Apparently the threefold symmetry about the C-N axis of the MA ion is preserved not only in the cubic phase but also in the tetragonal phases.

g/cm-I 1000

950 ,

900 I

850

1000

950 I

900 I

Fig. 1. Temperature variation of the infrared spectra in the vJ (C-N stretching, -98Ocm-‘) and v,? (rocking, -9lOcrn-‘) region of the MA ion in MAPbX, (X = Cl. Br, I). Arrows indicate the phase transition temperatures.

850

1386

N. ONODA-YAMAMURO er

al.

3.2. Broadening of the infrared spectral lines The line width of the E modes of the MA ion was explained by the rapid reorientation about the C-N axis in (MA),[SnCI,], (MA)2[TeBr,] and (MA),reI,] [7, 20,211. The correlation time and the activation energy derived from the line width agreed with those from NMR for these compounds. We analyzed the vIZ line width in the same way. The v,r line shape was assumed to be Lorentzian: In [f,(J)/l(?)]

= a/[($ - to)* + b*],

(1)

where I(i) is the observed IR intensity at G, I,(c) the incident intensity, G0the frequency of the band center, and b the half-width at half-maximum. In fitting the function to the experimental data, the base intensity f,(t) was assumed to be linear in i. A non-linear least-squares program written in BASIC was used to determine the best-fit parameter values. Some of the typical results are shown in Fig. 2 for MAPbBr,. The line shapes were reproduced well at all temperatures in the cubic and two tetragonal phases. The line width parameter b is related to the correlation time T, by T, = l/(27&),

(2)

where c is the velocity of light [22]. The instrumental width was corrected by the method of Ramsay [23]. A small constant width remaining at the lowest temperature was determined by extrapolation based on the Arrhenius law for the temperature dependence of 5,. For MAPbBr3, the extrapolation was separately carried out for the cubic phase and the tetragonal I phase. The Arrhenius plot of rr is given in Fig. 3. They were straight lines to a good approximation. The activation energies obtained from the slopes were 2.4 kJ mol-i for the cubic phase of MAPbCI, and 2.6 kJ mol -I for the tetragonal I phase of MAPbI,. For MAPbBr,, activation energies of 2.4

Fig. 2. Comparison of the experimental and the best-fit Lorentxian curves of the vu mode of the MA ion in MAPbBr,.

Fig. 3. Arrhenius plots of the correlation time T, of the reorientation of the MA ion in MAPbX, (X = Cl, Br, I); (0) MAPbCI,, (A) MAPbBr,, (0) MAPbI,. Arrows indicate the phase transition temperatures.

and 2.0 kJmol-’ were obtained for the cubic and tetragonal I phase, respectively. These are the activation energies for the hindered rotational motion of the MA ion about the C-N axis (external rotation). For the sake of comparison the activation energies obtained in the same way for other compounds are 3.2, 4.0, 3.9 and 3.1 kJ mol-’ for (MA),[SnCI,] [20], (MA)2]SnBr,l, (MA),jTeBr,l and WA),[TeI,l 171. respectively. Wasylishen ef af. obtained - 1.2 kJ mol-’ for both MAPbCI, and MAPbBr, at 303 K in NMR study [15]. Xu obtained 5.1, 3.9 and 5.8 kJ mol-’ for the orthorhombic phase of MAPbCI,, MAPbBr, and MAPbI,, respectively, by the same method [24]. The larger values reported by Xu compared with those determined here indicate that this motion is more hindered in the orthorhombic phase than in the cubic and tetragonal phases. 3.3. Heat capacity The numerical values of the molar heat capacity are summarized in Appendices A-C, and shown in Figs 4, 5 and 6 for MAPbCI,, MAPbBr, and MAPbI,, respectively. The dotted curves in the figures represent the normal heat capacities determined as described below. The thermodynamic functions derived from the calorimetric data are given in

Fig. 4. Molar heat capacity of MAPbCl,.

1387

Phase transitions in methylammonium trihalogenoplumbates (II) Appendices D, E and F for MAPbCI,, MAPbBr, and MAPbI,, respectively. For T < 10 K where the heat capacities were not measured, they are calculated by using known vibrational frequencies, barriers of hindered rotations and optimized Debye and Einstein parameters (see below). Two anomalies were found at 171.5 and 177.2 K in MAPbCI, and 161.4 and 330.4 K in MAPbI,, respectively. Three anomalies occurred at 148.8, 154.0 and 236.3 K in MAPbBr,. Their temperatures agree satisfactorily with those which have been reported (Ref. IO, see Introduction). The phase transitons in MAPbCI, and two lower temperature phase transitions in MAPbBr, occur at close temperatures and their pre- and post-transition effects overlap with each other. The highest temperature transitions in MAPbBr, and MAPbI, have a strong precursory effect on the heat capacities. It is interesting that the heat capacities of the highest temperature phases are almost constant for all of these compounds. 3.4. Determination of the base lines of the heat capacities We decompose the experimental heat capacity additively into the normal and transitional parts. The normal part consists of the vibrational heat capacity and a small correction for the dilation. There are 36 degrees of vibrational freedom in MAPbX,. Out of the 18 internal degrees of freedom for an MA ion, 17 fundamental vibrations were determined by IR absorption spectroscopy, as shown in Table 1. The heat capacities of these vibrations were calculated by using the Einstein function. The remaining one is the internal rotation for which the barrier height has been estimated to be 8.0 kJ mol-’ [25]. For the external rotation, we adopted the barriers obtained by Xu by NMR measurement. We could have used the barrier height derived from the IR line width but we employed the NMR values because the theoretical background is better established for the NMR T, than the IR line width. (However, there was no significant difference between the resulting base lines calculated from the different barrier heights. For MAPbCI,, the entropy change of the 171.5 K transition was

Fig. 5. Molar heat capacity of MAPbBr,.

3001

x

200-

$ 4

-

\ J

IOO-

CH,NH,Pbl,

100

200

300

350

T/K

Fig. 6. Molar heat capacity of MAPbI,.

14.6 J K-‘mol-’ from the NMR barrier height and 15.2 J K-‘mol-’ from IR.) Energy levels of the hindered rotations were calculated using the tabulated eigenvalues of the Mathieu equation. There remain 17 vibrational modes to be taken into account; 14 optical modes (two librational modes of the MA ion and 12 translational modes) and three acoustic modes. Contributions from these modes to the heat capacities were approximated by the Debye and Einstein functions. The normal heat capacity CnO_, was thus decomposed as follows: CnOrmll = C(internal

vib., 17, E)

+ C(hindered + C(libration, + i

rot., 2, M) 2, E) + C(acoustic,

C(optical, 3, Ei) + AC,‘T.

3, D) (3)

i-1

In this expression, each term except the last is labelled by the respective mode, the corresponding number of degrees of freedom, and the model function used for the calculation (E = Einstein Approximation, D = Debye approximation and M = the sum over states of the Mathieu levels). In the actual calculation, a better fitting was obtained when one of the Einstein functions of weight 3 was replaced with a Debye function. Two Einstein parameters each with the degeneracy of 3 converged to approximately equal values. They were combined to one Einstein temperature with the degeneracy of 6. Thus, the model heat capacity function contained two Debye temperatures 0,,, three Einstein temperatures 19~.and the C,, - C, correction coefficient A as the parameters to be determined by the least-squares method. In the actual application of the interpolation function (3) one is often left with an arbitrariness as to the temperature intervals of the experimental data which are to be included in the least-squares fitting. This is particularly true below the transition temperature where the gradual increase of the heat capacity is appreciable. This situation can be coped with by adding to the interpolation function a term representing the gradual increase of the heat capacity below

N.

1388

ONODA-YAMAMURO et al.

Table 2. Temperature regions of the heat capacity data used in the fitting and optimized parameters of CH,NH,PbX, (X = Cl, Br. I) Temperature region used in the fitting Parameters optimized @o(3)(KI 6,(31 (Kl @a(2)(K) t%(3) (K) e,(6) (Kl A x IO-‘/(mol J-‘) T,, (K)

CH, NH, PbCI,

CH, NH, PbBr,

CH,NH,PbI,

13-115 K 295-300 K

13-100 K 295-300 K

13-105 K 36@-365K

81.7 224.6 318.9 86.2 165.7 8.86 231.4

107.0 194.1 41.3 67.3 163.2 8.20 229.7

121.9 90.0 25.0 63.4 168.4 6.48 243.2

T,. For this purpose, we used the heat capacity of the spin l/2 Ising model solved by the mean field approximation. The heat capacity of the Ising system cannot be given in closed form even in the simplest approximation, therefore we solved numerically the self-consistency relation for the order parameter. The heat capacity is given by the temperature derivative of the squared order parameter, which also evaluated numerically. The resulting heat capacity was expressed as a universal function of the temperature as follows: C(Ising) 7

3 1 “a;l;.;;5;‘“‘”

where r, is the transition temperature in the mean field approximation. The numerical factors in eqn (4) were determined by the least-squares method to best reproduce the computed mean field heat capacity. The heat capacity function (4) was added to the model function, eqn (3), for T < T, of the lowesttemperature transition. For T > T, eqn (3) was used as it stands. By this modification, experimental data closer to T, could be included in the leastsquares calculation of the base line than was previously possible. The parameter values thus determined are given in Table 2 together with the temperature regions of the heat capacity data used in the fitting.

I so

I 200

100

T/K

Fig. 7. Excess heat capacity of MAPbCl,.

300

3.5. Enthalpy and entropy of transition The differences between the experimental and normal heat capacities are shown in Figs 7, 8 and 9 for MAPbCI,, MAPbBr, and MAPbI,, respectively. Integration of the excess heat capacity and the addition of the discontinuous part at the phase transition gave the transition enthalpy and entropy. They are given in Table 3. Since the phase transitions were overlapped, as shown in Figs 7,8 and 9, they were divided at the temperatures where the excess heat capacities took the minimum values. The entropy values indicate that all the phase transitions in these compounds are of the order-disorder type because they are of the order of Rlnn with n in the range 2-10. They are shown graphically in Fig. 10 from which one sees that the high temperature limiting values of the transition entropies in these compounds are close to one another. We conclude that these compounds have the same extent of disorder in the cubic phase. Figures 11, 12 and 13 show the temperature dependence of the entropy of transition in MAPbCI,, MAPbBr, and MAPbI,, respectively. It should be noted that the discontinuous parts of the transition entropies of the highest temperature transitions in MAPbBr, and MAPbI, are much smaller than those of the other transitions. For MAPbBr,, it is 0.3 J K-‘mol-’ which is only 3.7% of the transition entropy (8.2 J K-‘mol-‘), compared with the discontinuities 9.0 J K-‘mol-’ (80%) and 2.6 J K-‘mol-’ (62%) of the two lower temperature transitions. For MAPbI,,

s

100

2do

T/K

Fig. 8. Excess heat capacity of MAPbBr,.

1

Phase transitions in methylammonium

trihalogcnoplumbates

(II)

1389

30-

-

-i z

-

E TX 20-

24.6 -

Rbl3.3

23.6

1

26.7

Rk3.2

Rh2.7

_

4 . v) L?

;

Rkl.7 IO-

Rh9.9 Rh5.9

I

50

200

100

300

I

0

350

Rh3.9

X=CI

T/K

Br

I

CH3NH3PbX3

Fig. 9. Excess heat capacity of MAPbI,.

Fig. 10. Transition entropy of MAPbX, (x = Cl, Br, I).

the corresponding entropy 0.5 J K-‘mol-’ (5.5%) is again a very small value compared with 14.8 J K-‘mol-’ (78%) of the lower temperature transition. As shown in Figs 11 and 12, the excess heat capacities of the tetragonal I-cubic transitions extend over a wide temperature range below the transition temperature. These results indicate that the tetragonal I-cubic transitions have a character of higher order transitions, even though they are first order transitions by the thermodynamic definition. 3.6. Mechanism of the phase transitions In the cubic phase, the MA ion lies at the center of the regular cube formed by eight Pb?+ ions. This requires the MA ion to be disordered in a certain way. Several different sets of orientations are possible for an MA ion, each of which satisfies the cubic site symmetry. They are shown schematically in Fig. 14. Arrows in the cube indicate the orientations of the C-N axis of the MA ion. The MA ion points to the face centers (along the fourfold axes) in (A), the middle of the cube edge (along the twofold axes) in (B) and the cube comer (along the threefold axes) in (C). There are three fourfold axes, six twofold axes and four threefold axes in the cube. If the MA ion is disordered with respect to head and tail, the number of equivalent orientations of the MA ion is (A) 6, (B) 12 and (C) 8, respectively. Since the MA ion possessing threefold symmetry lies (A) on the fourfold axes and (B) on the twofold axes, it must be disordered around the C-N axis as well. Therefore the MA ion has (A) four and (B) two equivalent orientations Table 3. Temperatures,

enthalpies and entropies of the phase transitions of CH,NH,PbX, (X = Cl. Br. I)

Ad (kJ mol-‘)

4,s

(J K-‘mol-‘)

CH,NH, PbCI,

171.5 177.2

2.40 I .92

14.6 (RlnS.8) 10.0 (Rhi3.3)

CH,NH,PbBr,

148.8 154.0 236.3 161.4 330.4

1.59 0.62 1.71 2.98 2.58

1I.2 (Rln3.8)

CH,NH,PbI,

4.1 (Rlnl.7) 8.2 (Rln2.7) 19.0 (Rln9.8j 9.7 (Rln3.2)

around the C-N axis. The number of equivalent orientations of the MA ion is (A) 6 x 4 = 24 and (B) 12 x 2 = 24, respectively. Assuming that the MA ion is completely ordered in the orthorhombic phase, the entropy change associated with these ordering processes is Rln24 = 26.4 J K-‘mol-’ in both cases. It is close to the experimental values 24-29 J K-‘mol-‘. In the case of(C) which was suggested by Poglitsch and Weber, it is not required from the symmetry that the MA ion be. disordered around the C-N axis because the symmetries of the site and the MA ion coincide. However the entropy of this orientational disorder (Rln8) is much smaller than the experimental value. Therefore one must assume that the MA ion is disordered around the axis also in this model, even though this is not forced by the symmetry. In the following, we discuss the mechanisms of the phase transitions of the three compounds based on the above three types (A, B and C) of the orientational disorder. MAPbBr,. The experimental values of the transition entropies Rln2.7, Rln1.7 and Rln3.8 for the three phase transitions in decreasing order of temperature are very close to Rln3, Rln2 and Rln4, respectively. In model (A), the MA ion has six equivalent orientations along the cube edges. If we assume that the orientation of the MA ion is restricted to two of 30 I

f

20 P

4 \ w t d

10

. .._..

0

1 50

. .._.

.

_..

... ..

2do

100

T/K

Fig. Il. Transition entropy of MAPbCI,.

I

300

1390

N.OSODA-YAMAMURO

et al.

30-

5 E ; kzoi \

I 97 1 _____.___...._._

VI r a

I

30

i 19.0

I

200

100

IOI

300

T/K

T/K

Fig. 12. Transition entropy of MAPbBr,.

Fig. 13. Transition entropy of MAPbI,.

them along the fourfold axis in the tetragonal I phase and that the head-to-tail disorder of the MA ion is further removed in the tetragonal II phase, then the entropy change associated with each ordering is Rln3 and Rln2, respectively. If the remaining disorder of the MA ion around the C-N axis is removed in the orthorhombic II phase, the entropy change associated with it should be Rln4. In model (B), the MA ion has 12 equivalent orientations of the C-N axis. Assuming that four orientations in which the C-N axis lies normal to the fourfold axis of the tetragonal cell are allowed in the tetragonal I phase, the entropy _ associated with the cubic-tetragonal I transition will be Rln3. However

(A)

,:_ _...._ m

tetragonal

cubic

R In 3

there is no further ordered pattern of the tetragonal symmetry which can be derived from this partially ordered model and which one may identify with the tetragonal II phase. If the MA ion chooses another orientation along the fourfold axis of the tetragonal crystal in the tetragonal II phase, which is the same as (A), the tetragonal symmetry is of course satisfied. Considering that the equivalent orientations around the C-N axis change from two to four, the entropy change associated with it is Rln(4 x 2) - Rln(1 x 4) = Rln2. The tetragonal I-tetragonal II transition is of the first order in this model whereas it can be of a higher order in model(A).

I

tetragonal II

orthorhombic I,11

,’

.’

.’

6 ~4

2 x4

\

R In 2

m

0) R In 3

.’

8x3

8x1

:I---

.. -.

4x1

Fig. 14. Possible orientations and ordering processes of a CH,NH: ion. Arrows indicate the orientations of a C-N axis. + disordered around the C-N axis. r: ordered around the C-N axis.

Phase transitions in methylamrnonium trihalogenoplumbates (II)

In mode! (C), the MA ion has eight equivalent orientations along the body diagonals of the cube. If one assumes that the MA ion has three quivafent orientations around the C-N axis in the cubic phase and that the corresponding disorder is removed in the tetragona! I phase, the expected entropy change of this orientational ordering, Rln3, agrees with the experimental value. The orientational disorder of the MA ion is preserved through the cubic-tetragonal I transition in this model in accord with the suggestion by Poglitsch and Weber. If the head-to-tail disorder of the MA ion is removed in the tetragona! II phase and the fourfold disorder of the orientation of the C-N axis is removed in the orthorhombic II phase, the entropy changes associated with this sequence of ordering are Rln2 and Rln4. It should be pointed out that the site symmetry of the MA ion in the tetragona! II phase of the above models is 4mm rather than 4/mmm of the space group P4/mmm. The latter requires the head-to-tail disorder of the C-N axis. However, the entropies of transition support the 4mm models. MAPM,. The highest temperature phase of this crystal has the same symmetry as MAPbBr,and the symmetry of the tetragona! phase is the same as that of the high temperature tetragonal phase of MAPbBr,. The experimental entropy of the tetragona! I-cubic transition is 9.7 J K-‘mol-’ (R!n3.2), which agrees well with the model entropy of the tetragona! I-cubic transition of MAPbBr,. The structure of the orthorhombic phase is also the same as MAPbBr,. Since MAPbBr, has one more phase in the temperature range between the orthorhombic II and the tetragonal I phases, the entropy of orthorhombic II-tetragona! I transition in MAPM, should be compared with the sum of the entropies of the orthorhombic II-tetragona! II transition and tetragona! II-tetragona! I transition in MAPbBr,. The sum of the mode! entropies of these transitions is Rln8 = 17.3 J K-‘mol-t. The experimental value is 19.0 J K-‘mot-’ (Rln9.8) in good agreement with the model entropy. MAPbCl,. The tetragonal phase of MAPbC!, has the same symmetry as the low temperature tetragonal phase of MAPbBr,. Therefore the experimental entropy of the tetragona! II-cubic transition of MAPbC13 is expected to be close to the sum of the entropies of the tetragona! II-tetragona! I and tetragonal I-cubic transitions of MAPbBr,. The sum of these mode! entropies is Rln6. The experimental entropy is 10.0 J K-‘mol-’ (R!n3.3), which is rather closer to that of the tetragona! I-cubic transition than to the sum of the two entropies. Poglitsch and Weber suggested the persistence of the head-to-tail disorder of the MA ion in the orthorhombic phai [14]. However, no transitions have been observed between 13 K (the lowest temperature of the measurement) and 171.5 K (the temperature of the orthorhombic I-tetragona! II transition) in MAPbCI,. This fact indicates strongly that the head-to-tail disorder has

1391

already been removed. The entropy of the orthorhombic I-tetragona! II transition is 14.6 J K-i mol-‘. One expects the same entropy change for this transition as for the orthorhombic II-tetragona! II transition of the MAPbBr, crystal. However, this is not the case; the latter amounts to 11.2 J K-‘mol-*. The sum of the transition entropies of MAPbCl> is very close to that of MAPbBr,, even thou& there is no obvious correspondence between the steps by which the disordering proceeds in the two crystals. In contrast to ABO,-type oxides and ABF,-type fluorides, only a few ABX,-type halides are known to crystallize in the perovskite structures. CsPbC!, takes the cubic perovskite structure at high temperature and undergoes three successive phase transitions at 310, 315 and 320 K 126-291. The phase transitions have been accounted for by the soft mode concept [30]. The small entropies, 1.0 J K-lmol-’ for the transition at 320 K and 1.5 J K-‘mol-’ for the sum of the entropies of the transitions at 310 and 315 K [3!] are characteristic of displacive transitions. A similar amount of vibrational entropy may be involved in the transition entropies discussed here. However, it is a tiny correction to the entropy arising from the orientationa! disroder in MAPbX,. The entropies of the tetragonal-cubic transition in the perovskite crystals RbCaF) and TICdF, [32] are also of the same order of magnitude as those of CsPbC!,. At present, we cannot distinguish the three disordered models concerning the orientation of the MA ion in the cubic phases of MAPbX, crystals from the entropy consideration alone. There is little distinction among them in the preference of packing, because MA ions and halogen ions form cubic closest packing in the cubic phase. Calculation of the intermolecular interactions is desirable to determine the energetically favored orientation of the MA ion. Ac&nowiedgements-We thank Mr S. Ishikawa for taking the IR spectra and Mr Q. Xu for communicating to us his unpublished results of the NMR measurements. We also

thank Mr H. Minari and Mt M. Okumiya for the chemical analysis of the sample.

REFERENCES I. Tansho M., Nakamura D. and Ikeda R., Z. rVarur/. 44a, 738 (1989). 2. Ishida H., Ikeda R. and Nakamura D., /Yrys. Stow Solidi (a) 70, Kl51 (1982). 3. Stammler M., Bruener R.. Schmidt W. and Orcutt D.. Adv. X-ray Anal. 9, 170 (1968). 4. Zanarxi P. F., Acta crystaliogr.B24, 499 (1968). 5. Ishida H., Ikeda R. and Nakamura D., Chem. Lert. 1943 (1982). 6. ishida H.. Matsuhashi N., Ikeda R. and Nakamura D., Chem. Lett. 1859 (1985). 7. Onoda N.. Matsuo T. and Suaa H.. J. Phss. Chem. Solidr 47, 211 (1986). . 8. Onoda N.. Matsuo T. and Suga H., Phil. Mug. ASI, 245, (1988). 9. Aston J. Cl. and Ziemer C. W., J. Am. chern. Sot. 68, 1405, (1946).

1392

N. ONODA-YAMAMUCO~~

10. Yamamuro

O., Oguni M., Matsuo T. and Suga H., J. &em. Thermodynam. 18, 939 (1986). II. Yamamuro O., Matsuo T., Suga H.. David W. I. F., Ibberson R. M. and Leadbetter A. J., to be published. 12. David W. I. F., Harrison W. T. A., Ward R. L., Leadbetter A. J.. Matsuo T. and Suga H., Physica B 156, 157, 96 (1989). 13. Weber D., 2. Natur/. 33b, 1443 (1978). 14. Poglitsch A. and Weber D., J. them. Phys. 87, 6373

al.

20. Matsuo T., Ueda M. and Suga H.. Chem. Phys. Lett. 82, 577 (1981).

21. Cho Y. H., Kobayashi M. and Tadokoro H., J. them. Phys. 84, 4643 (1986).

22. Rothschild W. G., Dynamics of Molecular Liquids, Chaps I and 2. John Wiley, New York (1984). 23. Ramsay D. A., J. Am. them. Sot. 74, 72 (1952). 24. Private communication from Xu Q. 25. Ikeda R., Kume Y. and Nakamura D. J. magn. Reson.

(1987).

24, 9 (1976).

15. Wasylishen

R. E.. Knop 0. and MacDonald J. B., Solid

26. Moller C. K., Mat. Fys. Medd. Danske Vindensk Selsk.

St. Commun. 56, 581 (1985).

32, No. 2 (1959).

16. Vincent

B. R., Robertson K. N., Cameron T. S. and Knop O., Can. J. Chem. 65, 1042 (1987). 17. Tatsumi M., Matsuo T., Suga H. and Seki S., Bull. them. Sot. Jap. 48, 3060 (1975). 18. Matsuo T. and Suga H., Thermochim. Acta 88, 149 (1985). 19. Sandius T. and Meinander N., J. molec. Struct 76, 227 (1981) and Oxton I. A., Knop 0. and Duncan J. L., J. molec. Struct. 38, 25 (1977).

27. Sakudo T., Unoki H., Fujii Y., Kobayashi J. and Yamada M., Phys. Lett. A28, 542 (1969). 28. Hirotsu S. and Sawada S., Phys. Lett. AZ& 762 (1969). Jensen N. T., J. them. Phys. SO, 559 (1969). ::: Fujii Y., Hoshino S., Yamada Y. and Shirane G., Phys. Rev. B9, 4549 (1974). 31. Hirotsu S., J. phys. Sot. Jap. 31, 552 (1971). 32. Ho J. C. and Unruh W. P., Phys Rev. B13, 447 (1976).

APPENDIX

A

Table Al. Molar heat capacity of CH,NH,PbCI, Ta”

K 13.09 13.17 14.43 15.09 15.71 16.56 11.45 18.37 19.30 20.18 21.08 21.99 22.87 23.76 24.65 25.43 26.13 26.86 27.61 28.29 29.02 29.88 30.73 31.51 32.41 33.43 34.42 35.49 36.70 31.94 39.14 40.43 41.90 43.43 44.93

J

CP -1 K-?-ml

Ta”

8.114 9.185 10.26 11.42 12.61 14.09 15.83 17.71 19.67 21.56 23.43 25.37 27.20 29.18 31.04 32.72 34.22 35.17 31.37 38.90 40.41 42.28 44.11 45.90 47.81 49.81 51.82 53.97 56.32 58.71 60.96 63.36 66.05 68.76 71.40

46.38 47.86 49.37 50.82 52.29 53.82 55.43 57.06 58.66 60.29 61.96 63.66 65.46 67.32 69.15 71.00 12.91 74.89 76.89 78.87 80.82 82.80 84.79

K

iE go:49 92.69 94.87 97.02 99.15 101.26 103.42 105.64 107.83 110.01

5 J

T

a”

K-lmol-1

K

73.88 76.34 78.77 81.13 83.44 85.72 88.04 90.32 92.44 94.54 96.51 98.55 100.6 102.1 104.6 106.5 108.4 110.2 112.0 113.7 115.4 117.0 118.6 119.8 121.3 122.8 124.5

112.18 114.34 116.54 118.80 121.05 123.29 125.51 127.73 .130.00 132.33 134.64 136.95 139.25 141.54 143.89 146.29 148.68 151.06 153.45 155.82 158.25 160.73 163.20 164.70 166.76 168.37 169.54 170.28 170.83 171.23 171.62 172.04 172.60 173.15 173.70

:::*: t2a:7 130.0 131.4 132.6 134.0 135.1

Ta”

C? -1

J K-lmol

Ta”

JK-?wl-'

174.34 175.05 115.76 176.47 177.00 177.20 177.35 177.61 177.99 178.37 178.75 179.14 179.52 179.91 180.87 182.41 183.95 185.49 187.28 189.33 191.37 193.59 195.88 198.30 200.80 203.27 205.73 208.18 210.63 213.07 215.50 216.80 219.23 221.66 224.08

136.4 137.4 138.6 139.1 140.8 141.8 142.8 143.7 144.1 145.6 146.6 147.4 148.4 149.2 150.1 150.9 151.7 152.6 153.4 154.2 154.9 155.9 156.7 157.3 158.2 159.4 161.5 169.3 202.0 1388 2229 177.0 175.5 175.5 175.8

APPENDIX

K

GP 176.3 177.0 177.7 180.0 223.3 3633 853.4 196.6 119.1 174.8 172.9 172.3 171.7 w: 169:9 169.6 169.3 169.1 168.9 168.8 168.6 168.4 168.5 168.3 168.3 168.2 168.1 168.0 168.0 168.3 168.4 168.3 168.3 168.2

CP

K

JK-+ncl -1

226.50 228.91 231.32 233.72 237.16 238.50 240.a9 243.28 245.66 248.03 250.41 252.71 255.14 257.11 259.47 261.82 264.17 266.52 268.86 271.20 273.53 275.86 278.19 280.51 282.83 285.15 287.46 289.77 291.03 293.33 295.63 297.93 300.23

166.2 168.3 168.3 168.3 168.7 168.5 168.3 168.4 168.2 168.3 168.3 168.3 168.4 168.5 168.4 168.4 168.6 168.6 168.7 168.7 168.9 169.0 169.0 169.1 169.3 169.3 169.7 170.4 170.8 170.1 169.8 170.0 170.2

B

Table BI. Molar heat capacity of CH,NH,PbBr, T

a”

C?

T

-2%

K

JK-?i~ol-~

K

12.78 13.44 14.17 14.91 15.66 ;;::;

14.54 16.37 la.19 20.07 22.06 26.08 24.20

48.72 :x': 52:99 54.42 57.28 55.86

CP J K-lmol=l 95.86 98.18 100.3 102.4 104.4 108.1 106.3

Tav K 115.42 117.42 119.45 121.47 123.48 1:::::

r a”

CT J K-h 146.6 147.3 14a.o 148.8 149.4 150.8 150.2

-1

K 164.58 167.41 170.22 ;;;.8"; 17a:sa Jai.35

CP JK-lml-l 168.8 168.9 169.2 169.6 170.1 170.8 170.5

I

av

CP

K

JX-lmcl-l

236.31 236.43 236.60 236.78 236.95 238.40 237.49

132.7 241.5 181.2 178.5 176.2 173.7 174.9

Phase transitions in methylammonium

trihalogenoplumbates

1393

(II)

Table Bl (confind) 17.91 18.62 19.33 20.00 20.66 21.38 22.12 22.85 23.59 24.35 25.11 25.86 26.61 27.42 28.28 29.12 29.96 30.89 31.95

28.21 30.14 31.96 34.01 35.79 37.70 39.57 41.46 43.41 45.36 47.30 ::*A; 53:os ::*:; 59:20 61.37 63.91 66.38 68.75 71.00 73.51 76.17 78.93 81.58 84.07 86.53 88.92 91.20 93.59

::% 35:16 36.31 37.62 39.04 40.44 41.78 43.14 44.51 45.84 47.25

58.81 60.47 62.09 63.72 65.41 67.12 68.86 70.67 72.50 74.30 76.08 77.89 79.71 81.52 83.31

109.9 111.9 113.8 115.5 117.2 11a.s 120.5 122.0 123.5 124.9 126.3 127.6 128.7 ::z 132:2 133.5 134.4 135.7 136.3 137.5 138.1 139.1 140.0 140.9 141.7 142.8 143.5 144.3

~65~;: 88179 90.60 92.44 94.30 96.16 98.00 99.87 101.76 103.65 105.53 107.46 109.46 111.46 113.44

__.

145.1

145.8

129.59 131.64 133.66 135.65 137.63 139.60 141.55 143.30 144.96 145.91 146.75 147.48 148.09 148.57 148.94 149.40 149.94 150.44 151.06 151.68 152.17 152.62 153.07 153.61 154.41 155.23 155.87 156.50 1:X 161.74

151.7 x 153:s 151.5 155.3 156.0 157.2 158.5 159.3 161.1 164.2 175.4 468.0 3331 228.5 186.4 186.2 186.9 188.1 191.7 195.1 197.2 203.4 479.6 171.7 169.7 169.1 168.7 168.6 168.5

APPENDIX

184.10 186.84 189.56 191.14 193.30 195.45 197.60 199.75 201.88 204.02 206.14 208.26 210.37 212.47 214.57 216.66 218.75 220.83 222.90 224.96 227.02 228.80 230.31 231.56 232.57 233.58 234.55 235.15 235.67 235.85 236.02

171.3 171.8 172.4 172.6 173.1 173.4 173.7 174.3 174.8 175.0 175.7 176.1 176.6 177.1 177.7 178.1 178.5 179.4 180.1 180.8 181.7 182.7 183.7 185.0 186.5 187.4 190.1 191.7 196.4 199.1 201.0

173.5 172.8 173.0 172.7 172.9 172.4 171.9 171.9 171.5 171.5 171.1 171.1 170.9 170.9 170.7 171.0 170.4 170.5 170.2 170.3 170.5 170.3 170.1 170.0 170.4 171.1 170.6 170.1 170.3 170.7

264.14 266.59 269.03 271.47 273.90 276.33 278.75 261.17 283.59 286.01 288.42 290.83 293.23 295.64 298.04 300.44

C

Table Cl. Molar heat capacity of CH,NH,PbI, T

av

R

12.67 13.46 14.32 15.21 16.04 16.84 17.64 18.50 19.39 20.25 21.08 21.94 22.63 23.58 24.33 25.18 26.07 27.00 27.91 ::*1J: 31:30 32.41 33.50 34.72 36.08 37.37 38.59 39.79 40.99 ::% 44168 45.96 47.47 49.07 50.51 51.91 53.29 54.67 56.06 57.49 58.96 60.47 62.02

J

5 K-lml -1 22.91 25.28 27.93 30.45 32.91 35.17 37.46 40.01 42.54 44.98 47.22 49.43 51.76 53.71 55.55 57.66 59.80 61.99 64.16 66.59 69.29 71.85 74.33 76.59 79.08 81.73 84.12 86.35 88.43 90.45 92.39 94.39 96.32 98.27 100.5 102.6 104.6 106.4 108.2 109.8 111.4 113.0 114.5 116.0 117.4

Ta” -

x

63.61 65.26 66.99 68.75 70.55 72.39 74.26 76.17 78.11 80.08 82.08 83.07 85.20 87.30 89.37 91.42 ;:*:: 97144 99.47 101.55 103.61 105.65 107.68 109.70 ix 115:as 117.94 120.01 122.08 124.13 126.18 128.22 130.30 132.43 134.56 136.67 138.78 140.88 142.98 145.12 147.31 149.50 151.00

J

CP

Ta”

It-lmol-l

K

118.8 120.3 121.8 123.1 124.4 125.7 127.0 128.2 129.4 130.7 131.9 132.5 ;::*t 136:0 137.1 138.1 139.1 140.1 141.1 142.0 143.0 143.9 144.9 145.7 146.7 147.5 148.4 149.3 150.2 151.0 151.9 152.8 153.7 154.6 155.5 156.5 157.4 158.4 159.4 160.5 161.6 162.8 164.3 165.3

152.94 154.36 155.25 156.13 157.01 157.89 158.76 159.43 159.79 160.05 160.31 160.54 160.72 160.90 161.05 161.19 161.38 161.65 161.95 162.27 162.59 163.11 163.84 164.66 165.64 166.76 168.02 169.42 171.26 173.46 175.66 177.91 180.21 182.50 184.80 18-7.09 189.44 191.83 194.22 196.57 198.88 201.12 203.30 205.47 207.64

CP J X-'m01-~ 166.8 168.2 168.9 170.0 171.2 172.7 175.6 178.8 180.8 185.1 190.0 197.6 206.8 227.4 266.6 407.5 8410 481.2 164.9 162.8 162.0 161.7 161.6 161.4 161.6 161.8 161.9 162.1 162.4 162.8 163.2 163.6 164.0 164.4 164.9 165.3 165.8 166.2 166.6 167.0 167.6 168.1 168.4 168.9 169.4

T

a”

it 209.81 211.99 214.15 216.32 218.49 220.66 222.95 225.24 227.52 229.81 232.13 234.50 236.66 239.19 241.50 243.86 246.26 248.01 250.35 252.75 255.15 257.55 259.94 262.34 264.73 267.13 269.52 271.91 274.30 276.69 279.14 281.64 284.14 286.65 289.15 291.64 294.14 296.64 299.14 301.45 303.57 305.69 307.81 309.92 311.03

J

C? R-?ml-1 169.8 170.3 170.8 171.3 171.6 172.1 172.6 173.1 173.6 174.2 174.6 175.1 175.5 176.1 176.7 177.1 177.5 178.0 178.6 179.0 179.4 179.6 180.4 181.1 181.6 182.0 182.6 183.0 183.6 184.1 184.7 185.3 185.9 186.6 187.8 188.9 188.2 188.7 189.6 190.4 190.8 191.4 192.1 192.7 193.1

T

CP

a”

I; 312.94 314.84 316.73 318.62 320.13 322.52 323.52 324.89 325.53 326.45 327.61 328.55 329.04 329.41 329.66 329.91 330.15 330.36 330.56 330.74 330.87 331.08 331.52 332.18 332.96 333.80 334.70 336.69 339.03 ::E: 344162 346.73 348.63 350.89 353.16 ::z: 360:17 362.58 365.00

J

K-lmol-l 193.7 194.5 195.4 196.4 197.2 199.1 200.0 201.8 202.7 204.4 207.5 211.2 213.5 217.1 218.9 222.0 245.8 856.9 321.7 203.2 195.5 191.0 185.5 183.3 182.3 181.8 181.5 181.3 180.6 180.5 180.4 180.4 180.4 180.3 180.1 160.0 180.0 179.8 179.9 180.0 180.1

1394

N.ONODA-YAMAMURO

APPENDIX

Table DI. Thermodynamic -T K

cp /R

:i

‘x:4’ 5:113

30

40

65: ii 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300

7.537 9.610 11.31 12.68 13.81 ix: 16:25 16.87 17.41 17.88 18.30 18.72 20.01 20.59 20.31 20.24 20.23 20.24 20.25 20.25 20.25 20.26 20.29 20.31 20.34 20.39 20.45 20.47

(H-H~)/RT

2

30 40 65: ii 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300

R

-(C-Ho)/RT (0.03772) 0.2827 0.7764 1.444 2.219 3.055 3.921 4.797 5.670 6.532 7.379 8.208 9.017 9.807 10.58 11.33 12.05 12.84 13.64 14.41 15.16 15.88 16.58 17.26 17.92 18.56 19.18 19.37 19.78 20.36 20.83 20.93

‘?;::2’

21557 4.367 6.279 8.186 10.04 11.81 13.49 15.08 16.60 18.04 19.41 20.72 21.97 23.16 24.31 27.45 28.56 29.60 30.58 31.52 32.42 33.29 34.11 34.91 35.67 35.91 36.41 37.12 37.69 37.82

E

functions of CH,NH,PbBr,

(H-H~)/

‘9.;;8”’

‘p. g;

71142 9.713 11.78 13.40 14.61 15.52 16.26 16.85 17.38 17.84 18.24 18.71 22.41 20.28 20.35 20.52

21777 4.201 5.518 6.702 7.749 8.666 9.470 10.18 10.81 11.38 11.89 12.36 13.87 14.58 14.92 15.23 15.51 15.78 16.03 16.27 16.51 16.78 16.93 17.08 17.20 17.24 17.32 17.43 17.51 17.53

:z: 21:22 21.54 22.07 20.83 20.66 20.55 20.51 20.5020.48 20.44 20.49 20.52

S/R

(0.1135) 0.7596 1.781 2.923 4.059 5.131 6.115 7.009 7.817 8.551 9.219 9.831 10.39 10.91 11.39 11.84 12.26 14.61 14.91 15.18 15.42 15.64 15.84 16.03 16.19 16.35 16.50 16.54 16.63 16.76 16.86 16.88

Table El. Thermodynamic cp /

D

functions of CH,NH,PbC&

APPENDIX

-T K

et al.

RT

S/R

1)

‘1. g91

$.05;;;7)

4:107 6.527 8.925 11.22 13.38 15.40 17.27 19.01 20.64 22.17 23.62 24.99 21.38 29.01

1:330 2.326 3.407 4.520 5.633 6.729 7.797 8.832 9.833 10.80 11.73 12.63 13.50 14.42 15.32 16.18 17.01 17.81 18.59 19.34 20.07 20.78 21.47 22.13 22.78 22.98 23.41 24.02 24.50 24.61

::*

:z

34:62 35.61 36.58 37.55 38.40 39.21 39.98 40.22 40.73 41.45 42.01 42.14

-(C-H~)/RT

Phase transitions in methylammonium APPENDIX

Table Fl. Thermodynamic -T

K

:: :8 i8

El 1:: 110

120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 320 330 340 350 360

cp / R

a.299 10.68 12.51 13.89 14.92 15.72 16.39 17.00 17.55 18.06 la.58 19.12 19.80 22.15 19.51 19.72 19.95 20.18 20.43

20.69 20.94

21.20 21.46 21.71 21.97 22.05 22.23 22.52 22.17 22.83 23.18 23.71 27.82 21.71 21.67 21.63

trihalogenoplumbates

1395

(II)

F

functions of CH,NH,Pb&

(H-HO)/

3.682 5.146 6.443 7.575 a.553 9.401 10.14 lo.80 11.39 11.92 12.41 12.87 13.31 13.76 15.81 16.03 16.23 16.42 16.60 16.78 16.96 17.13 17.30 17.46 17.62 17.68 17.78 17.94 18.07 la.10 18.26 la.42 18.60 18.76 la.85 la.92

RT

S/R (0.8044) 3.159 5.900 8.626 11.21 13.62 15.84 17.89 19.78 21.54 23.19 24.74 26.20 27.60 28.94 30.26 33.25 34.37 35.45 36.48 31.41 38.42 39.35 40.24 41.12 41.96 42.79 43.04 43.59 44.37 45.00 45.14 45.90 46.64 47.40 48.11 48.74 49.35

-(G-H,)/

‘KS’ 2:217 3.481 4.771 x

a:490 9.641 10.74 ii.80 12.82 13.79 14.73 15.63 16.50 17.44 la.35 19.22 20.06 20.86 21.64 22.39 23.11 23.82 24.50 25.16 25.37 25.81 26.43 26.93 27.04 27.64 28.22 28.79 29.35 29.89 30.43

RT