Specific heat of nickel hexammine nitrate

ELSEVIER

Physica B 217 (1996) 57-62

Specific heat of nickel hexammine nitrate Lidia Piekara-Sady Institute of Molecular Physics, Polish Academy of Sciences, Poznah, Poland

Received 18 May 1994;revised 20 July 1994 and 26 June 1995

Abstract

Specific heat calculations for hexammines with halogen anions agreed well with experiment [1]. cSwas calculated as a sum of individual contributions from various types of thermal excitation of a crystal. This was done by making use of the spectroscopic data available for these crystals. Larger values of the specific heat, experimentally measured, for hexammines with complex anions (NO3, CIO 3, BF~, C10£) are expected to come from an additional number of degrees of freedom of the complex anion. An attempt has been made to calculate specific heat versus temperature for nickel hexammine nitrate. The upper limit of v = 140 cm- 1, the frequency of the NO~ local mode active exclusively in the high-temperature phase I above T¢1 = 243 K, was concluded.

1. Introduction

Specific heat has been measured for many compounds of the [Me(NHa)6]X 2 family (hereafter referred to in an abbreviated form as MeAX). The observation of specific heat systematics in hexammine compounds has been made [1]. In order to correct for the phase transition contributions to the observed curve, we decompose the experimental heat capacity additively into the "normal" (baseline) and transition parts. The estimation of the baseline is the usual procedure required to separate the anomalous part of specific heat related to phase transitions from the remaining contributions of the crystal lattice. The baseline is usually determined by interpolation of the "normal" heat capacity into the transition region. Once the phase transition anomalies are excluded, the experimental specific heat versus temperature dependencies are practically coincident for a given geometry of the anion X - , i.e. for spherical halogen, tetrahedral BF£ and CIO~, triangular N O 3 . An analysis of the smoothed experimental data (i.e. normal heat capacity) was undertaken for hexammines with halogen

anions using a combination of Debye and Einstein functions and the available spectroscopic data [1]. We will briefly outline some of the aspects of the analysis and present a further one for NiANO3. [Ni(NH3)6](NO3)2,the most extensively studied among hexammines as well as the most interesting crystal, was chosen as representative of the complex anion compounds. Hexammines are isomorphic in the high-temperature phase; at room temperature they crystallize in the regular form with the space group Fm3m [6]. A primitive cell contains one molecule (one complex cation [Me(NH3)6] 2+ and two anions X-). The structure and binding energy present in hexammines permits a distinction between lattice modes of cations [Me(NH3)6] 2 + and anions X - and those related to internal vibrations of the complex cation. The lattice modes are associated with translational vibrations of the centers of mass of cations and anions as well as with torsional motions of the complex ions. It was assumed that each of the three acoustic modes can be represented by a Debye spectrum while the optical modes can be associated with the Einstein spectra. This assumption has previously been made in some ionic

0921-4526/96/$15.00 © 1996 ElsevierScienceB.V. All rights reserved SSDI 0921-4526(95)00535-8

58

L. Piekara-Sady/Physica B 217 (1996) 57-62

crystals (e.g. R2MX 6 class [19]). Additionally, Einstein representation of the complex cation internal vibrations was taken into account in the analysis of specific heat for hexammines with halogen (simple) anions [1]. A Debye function with a characteristic temperature of 57 K (calculated for NiANO3 [1]) accounted for acoustic modes contribution. The other contributions, from optical lattice modes including librations of the complex cations, internal vibrations of cations, torsions, rocking modes and internal vibrations of NH 3 groups, were found from the Einstein formula. Thus, the specific heat of hexammines with simple (halogen) anions. CsimpJo, was represented by the sum of Debye and Einstein functions [1]. To determine the "normal" specific heat, i.e. outside the transition regions, for NiANO3, the assumption that the measured heat capacity excluding the transition regions may be written as the sum can still be employed, viz. Cs = Clat -~- Cinl,

(1)

where c~,t and ci., are the respective contributions from the lattice (acoustic and optical) vibrations including the librations or torsional oscillations of the ions, and the internal vibrations of the complex ions. Following the successful analysis of hexammines with simple anions (CI-, Br-, J-) it seems feasible to treat hexammines with complex anions (NO3, CIO3, BF,~, C10,~) in the same way. Greater Cs values can be assigned to an additional number of degrees of freedom of a complex anion. The aim of this study was to calculate Cs for NiANO3 as the sum C(NiANO3) = Csimple -~- CN03,

(2)

where C~impleis Cs calculated in Ref. [1] c~ for hexammines with halogen anions and CNO3is the contribution from the NO3 anion, i.e. additional contributions of complex anion will be taken into account.

2. Results and discussion 2.1. An analysis o f the specific heat data

The first step in the analysis is to calculate CNo3 from spectroscopic information, including

NO3 internal vibrations and the torsional mode of the NO3. The CNO3contribution to the specific heat is decomposed as follows: CNo3 = ci°, + c, . . . .

(3)

where ci,, is the contribution from the internal vibrations of NO3 and ctors is from the NO3 torsions. The vibrational frequencies of internal modes, 1340, 1040, 830 and 700 cm -1, were determined from the Raman [11, 12] and infrared spectra [13]. The temperature dependence of the vibrational frequencies was neglected since the corresponding modes were virtually unchanged in this temperature range [11-13]. The torsional nitrate mode at 65 cm- 1 was identified in the Raman spectra [12]. Vibrational heat capacities of each mode were calculated by the Einstein function, including a factor for degeneracy n for a particular mode: c,, = n N kB(x 2 eX)/(e x -- 1)2 ,

(4)

where x = h o / k B T . This completes the accounting for the internal and torsional modes of NO3 (Eq. (3)).

2.2. An analysis o f the (cp - cv) term

Although the quantity actually measured calorimetricatly is the heat capacity of the solid in equilibrium with its saturated vapor, it effectively equals cp. However, the correction of c~, to cp should be considered since Debye and Einstein models refer to conditions of constant volume. Lack of data forced us to neglect the (Cp - cv) term in calculations for hexammines with halogen anions [1]. In the case of NiANO3 we could calculate this term and found this contribution very significant. The following procedure was adopted. The calculation was based on the thermodynamic equation c, - cv = [32 V T / X T ,

(5)

where [3, V and X T represent cubic expansion coefficient, molar volume and isothermal compressibility, respectively. Hexammine nickel nitrate occurs in three solid modifications. Temperature-dependent structures

59

L. Piekara-Sady/ Physica B 217 (1996) 57-62

I

c [J/mot. K ]

350 ~-

Cexp A

+

5C

+

+

•

•

+

•

•

o

o

•

o

o

+ + •

•

•

o

o

•

o

o

+ -4:

250

150 _

+ +

/;

.~ +

o

o

~- C s i m p t e ÷Cint N03 Ctors ÷

+(~p-~vl

L

I

I

I

50

100

150

200

I

250 T [ K ] 300

Fig. 1. The experimentaldata of specificheat for NiANO3 smoothedthrough the transitions: solid line;dashed line stands for the phase transition at Tc~anomalousregion. Points denote calculatedvalues. Above250 K, the residual,(cexp- cca~c),givesce~tr~No~contribution. C~impl~points are from Ref. [1].

are as follows [6, 14, 15, 17]: cubic I

, cubic II

Tel = 2 4 3 K

Fm3m

Pa3

Tcz=90K

, orthorhombic Pmmm.

Below T~2, NiANO3 undergoes a phase transition of the glass type [16, 18]. Values of thermal expansion/~ [3--5] and compressibility XT [5] were available for NiANO3 in phase I and in phase II as well. The molar volumes at 292 K (phase I) and 153 K (phase II) were also reported [6]. Eq. (5) was first applied at T = 292 K (for phase I) and then at T=153K (for phase II) giving a ( c p - c ~ ) of 34.7 J/mol K at 292 K and 39.9 J/mol K at 153 K, which amount to 8.6% and 13.6% of the actual experimental values, respectively. To obtain (cp - cv) in the whole temperature range we must resort to estimation using a well-known semiempirical expression: c p - c~ = Ac 2 T.

(6)

To establish the value of A, Eq. (6) was used for T = 2 9 2 K and T = 1 5 3 K with ( c p - c , , ) already calculated from Eq. (5). It gives A~ = 7.23x 10-7 mol/J for phase I (i.e. for T > 243 K) and An = 2.995 x 10-6 mol/J for phase

II (i.e. for T <243 K). The values of Ai and A, were then used to extrapolate (cp - cv) over the temperature range 243-300 K and below 243 K, respectively (Eq. (6)). The resulting Cp - c j T ) dependence is presented in Fig. 1 together with other contributions. In (cp - cv) correction the effect of the thermal expansion is dominant. Dilatometric studies [3] showed the increase in the thermal expansion coefficient with increasing temperature in the pretransition region. Thus, we shall proceed on the assumption that Eq. (2) should be modified with (c~ - c~,)correction. Hence, the specific heat for NiANO3 is written as the sum of the following terms: CNiANO3 =

Csimple -~

(Cp --

Cv) -~- CNO 3 .

(7)

The results consecutively added according to Eqs. (7) and (3) are shown in Fig. 1. In the figure calculated points are presented together with the smoothed through the transitions experimental data (solid plus dashed line). Below the large specific heat anomaly associated with the phase transition at Tel = 243 K (from phase II to phase I) the experimental curve of the specific heat is well described by the sum of the following contributions: [ C s i m p l e -t- CintNO3 -~ CtorsNO 3 -~- (Cp -- Cv) ]. The analysis seems to be satisfactory below Tc~, taking

L, Piekara-Sady / Physica B 217 (1996) 57-62

60

I Cs[ J/rnot.K ]

NiANO3 MgANO3 /

500

)', )1

400 3OO 200

1OO' O

I

I

I

I

I

I

60

1OO

140

180

220

260

T [ K]

Fig. 2. Experimental temperature dependences of specific heat for hexammines with NO3 anions [7-9]. Circles represent calculated specific heat, including the cc=,aNo3 term for NiANOs. The experimental curve for MgANO3 [10] is also shown. The large c= anomalies are presented schematically and the small anomalies are omitted for clarity of the picture.

into account the rough approximation of the phonon spectrum of NiANO3. However, for T >Tel, this sum gives smaller values than the experimental ones (see Fig. 1 above 250 K). Above Tel, for temperatures T > 243 K, the residual specific heat was obtained by subtracting [Csimple Jr CintNO3 "Jr CtorsNO 3 "]'- (Cp -- Co)] from the e x perimental values; this deviation of the calculated from the experimental values averages 15 J/tool K. This residual is considered as Cex,,NO3- Fitting the residue to the Einstein formula, taking tentatively one degree of freedom for each NO3 group gave only the frequency upper limit of 140 cm-1 since the contributions from all the modes of v < 140 cm-1 have already attained the maximum value of nR (where n is the degeneracy of the mode) in this temperature range. Next, this maximum value, i.e. 2R, as additional contribution has been added for T > 250 K to the calculated values (presented in Fig. 1 as triangles); the final result is given in Fig. 2. This figure shows both the smoothed experimental data [7-9] and the calculated points for NiANO3, including an extra contribution besides those specified by Eq. (7) and (3). The experimental curve for MgANO3 [10] is also shown in Fig. 2 to demonstrate that the "normal" heat capacities, once transition anomalies are excluded, are very close to each other for both nitrate hexa-

mmines. In the figure the large anomalies are presented schematically and the small ones are omitted for clarity of the picture. This completes the calculation of the specific heat of nickel hexammine nitrate.

3. Some speculations on the high-temperature extra term CcxtraNOs

We assumed that CextraNO3contains contributions from NO3 because the calculation of the effect of NH 3 deuteration on the specific heat of NiANO3 [20] suggested that all NH3-related contributions have been properly accounted for. The internal nitrate vibrations and NO3 torsions (around the axis perpendicular to the NO3 plane) have been considered so far. For temperatures above Tel = 243 K another NO3 mode may be considered. The cubic phase I with the space group Fm3m, stable above 243 K, accommodates the octahedral cations [Me(NH3)6] 2 + at the sites of the respective symmetry of the cation, while the site point symmetry of the triangular anions is that of a tetrahedron. Thus, NO3 groups having C3v symmetry must be orientationally disordered to be compatible with the tetrahedral symmetry of the anion site in the

L. Piekara-Sady/Physica B 217 (1996) 57 62

../....""

"'""',...

®o

v,/f/jj~

Fig. 3. NO~- reorientation in the cubic high-temperature phase I (T >243 K) between two possible sites around the A A' axis. Large circles symbolize oxygen atoms, small circles the nitrogen atom.

lattice [6, 14]. The X-ray studies [6] revealed four equivalent diffused maxima of the electron density distribution in the vicinity of the anion position. These four maxima are produced by orientational disorder of the NO3 among four equally probable positions specified by four faces of the tetrahedron. Additionally, dielectric and spectroscopic studies suggested nitrate reorientation in phase I [2, 15]. The X-ray data showed that each triangular NO3 group possibly executes oscillations between two equivalent configurations in the high-temperature phase I (Fig. 3) [14, 15]. As these reorientations cannot account for a contribution to the specific heat, we assume that in the room temperature modification the nitrate group undergoes torsional oscillations around the A-A' axis (specified in Fig. 3) in each of the possible positions. The NO3 reorientation is supposed to stop below Tel = 243 K in phase II [2, 15], nitrate triangles take one of the two alternative configurations; the symmetry site of nitrate anion is then reduced from Td to C3v [15,6]. Accordingly, only for T >243 K additional contribution to the specific heat from NO3 oscillations might be expected. In summary, the vibrational spectrum of a crystal was separated into lattice and groups (complex ions) modes. The corresponding frequencies were known from spectroscopic studies and their specific heat contribution was calculated by means of a combination of Debye (accounting for acoustic modes [1]) and Einstein functions. (cp - c~) correc-

61

tion could also be determined. To complete high temperature contribution, the disorder and local osdilations of NO3 groups were assumed and introduced above the phase transition temperature Tel = 243 K. The thermal effect was then an increase in heat capacity beyond that expected from the crystal vibrations. This extra heat capacity is a clear indication for an additional degree of freedom, not yet accounted for in the analysis. If this degree of freedom in the form of some NO3 local mode may be treated as an Einstein oscillator, the upper limit of the frequency of this oscillator could be estimated. The effect of deuteration of NH 3 groups on the specific heat of nickel hexamine nitrate has already been analyzed [20]. The agreement between the experimental specific heat of the deuterated crystal and that calculated within this model confirms validity of the analysis. This result shows that all degrees of freedom as well as ( % - c~) correction have been satisfactorily accounted for.

Acknowledgements The author expresses thanks to Prof. J. Stankowski for stimulating discussions.

References [1] L. Piekara-Sady and J. Stankowski, Physica B 152 (1988) 347. [2] B.O. Fimland, T. How and I. Svare, Physica Scripta 33 (1986) 456. [3] L. Piekara-Sady, M. Krupski, J. Stankowski and D. Gajda, Physica B 132 (1986) 118. [4] S.R. Hughes, PhD Thesis, University College, Cardiff

0980). [5] J. Stankowski and M. Krupski, Bull. Acad. Polon. Sci. XXVI/8 (1978) 755. [6] A. Hoser, PhD Thesis, A. Mickiewicz University, Poznafi (1982). [7] E.A. Long and F.C. Toettcher, J. Am. Chem. Soc. 64 (1942) 629. [8] J. Bousquet, M. Prost and M. Diot, J. Chim. Physique 6 (1972) 1004. [9] A. Migdat-Mikuli, E. Mikuli, M. Rachwalska, T. Stanek, J.M. Janik and J.A. Janik, Physica B 104 (1981) 331. [10] J.A. Janik, J.M. Janik, A. MigdaI-Mikuli, M. Rachwalska, T. Stanek, K. Otnes, B.O. Fimland and 1. Svare, Physica B 122 (1983) 315.

62

L. Piekara-Sady / Physica B 217 (1996) 57-62

[11] J.A. Janik, J.M. Janik, A. Migdat-Mikuli, E. Mikuli and T. Stanek, J. Mol. Struct. 115 (1984) 5. [12] T.E. Jenkins, L.T.H. Ferris, A.R. Bates and R.D. Gillard, J. Phys. C 11 (1978) L77. [13] S. Isotani, W. Sano and J.A. Ochi, J. Phys. Chem. Solids 36 (1975) 95. [14] S.H. Yu, Nature 114 (1938) 158. [15] S.H. Yu, Nature 150 (1942) 347.

[16] Z. Trybula and J. Stankowski, Physica B 154 (1988) 87. [17] S. Hodorowicz, J. Czerwonka, J.M. Janik and J.A. Janik, Physica B 111 (1981) 155. [ 18] J. Czaplicki, N. Weiden and A. Weiss, Physica B 154 (1988) 93. [19] V. Novotny, C.A. Martin, R.L. Armstrong and P.M. Meincke, Phys. Rev. B (15) (1977) 382. [20] L. Piekara-Sady, J. Phys.: Condens. Matter 7 (1995) 4207.