The alkyl chain contribution to the specific heat in layer compounds: The ferro-paraelastic phase transition in [C4H9.NH3]2ZnCl4

0038-1098/88 $3.00 + .00 Pergamon Press plc

~ o ~ Solid State Communications, Vol. 68, No. 2, pp. 185-188, 1988. C s ~ P r l n t e d in Great Britain.

THE ALKYL CHAIN CONTRIBUTION TO THE SPECIFIC HEAT IN LAYER COMPOUNDS: THE FERRO-PARAELASTIC PHASE TRANSITION IN

[C4H9.NH3]2ZnCI4 A.L6pez-Echarri, JZubillaga and M.J.Tello Depto. de Fisica de Materia Condensada. Facultad de Ciencias. Universidad del Pals Vasco. Apto 644, Bilbao 48080, Spain. B e c e i v e d 2L; June 1988 by P. B u t l e r

The specific heat of [C4H+NH~]~nCI4 has been measured from 70 K to 310 K, An orthorhombic-mbn'ocli~ic= pha~e transition has been found at 290 K. The values of the most relevant bands of the frequency spectrum and specific heat data in related layer compounds have been used to determine the methylene unit contribution. These results provide a useful information to describe the lattice specific heat of the remaining Zn-crystals.

n-alkanes and in layered compounds. Additional Raman and I.R. spectra have been used to obtain the C4Zn lattice contribution to the specific heat. These results are also valid for the whole Zn-family and, with slight corrections, for other layered crystals with alkyl chains.

I. INTRODUCTION Specific heat measurements on (CnH~.+I.NH3)2MCI4 compounds have been widely used'f0 characterize the variety of phase transitions they exhibit and provide a detailed knowledge of the phase transition thermodynamics. All these compounds show alkyl chains sandwiched by inorganic layers. The characteristics of the substituted metal (M), the different coordination and the tilting of the MCI.4 ions, together with the alkyl chain length, the various interchain interactions and the hydrogen bonding schemes, are considered the main relevant physical mechanisms of the phase transitions present in these crystals. Recent reviews about the subject can be found in references l-~ The tetrahedrally coordinated Zn-compounds (hereafter C.Zn) also show some interesting examples of 'variuos kinds of phase Lransitions. Gyrotropy appears in C~Zn ~ and i>n C~Zn ~, whereas . . . . " ferroelastlclty is .present m CIZn t ) an~d m C~Zn • . In addition, conformational disordered pha"ses are found for n>3 8. In all these cases, calorimetric measurements are highly interesting for the study of the energetics of the alkyl chains in crystalline fields. As far as we are aware, C4Zn is the only short chain Zn-compound for ~vhich experimental information is not yet available. The specific heat measurements presented in this work show a noticeable anomaly at 290 K which corresponds to an orthorhombic-monoclinic (space groups: P n m a and P11211a, respectively) phase transition ~. The phase transition thermodynamic functions have been determined by substraction of a convenient baseline which has been accurately calculated. This has been done by a macroscopic comparison among the specific heats of various Zn-crystals which has permitted a good estimation of the individual CH~ contribution. The obtained results are in agreemenI with the theoretical calculation performed with the known frequencies of the methylene group both in

2. EXPERIMENTAL Single crystals of [C4Hg.NH~]2ZnCI4 were obtained y a slow ~vaporati6r/ method as described bin reference ~. The purity of the synthesized compound was controlled by conventional chemical analysis and X-ray powder diffractometry. A powder sample {35.165 gr,) was used for the adiabatic measurements. These were performed with the automatic experimental set-up described in references I0,II. The calibrated accuracy attains 0.1% of C. between 50 and 330 K. A conventional discontinu6us pulse method as well as continuous heating measurements have been used in the temperature range 70-310 K and the results are presented in figurel. Both experimental procedur.es show a n extremely high specific heat peak at (290.21 + .01 ) K, which attains ten times the baseline value. This C. behaviour is commonly observed in first order 15hase transitions. However, the long tail of the specific heat anomaly below To, which extends down to 180 K, and the absence of thermal hystheresis in the transition temperature, seriously questions the above suggestion. In any case, more experimental information should be necessary in order to establish the order character of this phase transition. 3. RESULTS AND DISCUSSION The constant increment observed on some physical magnitudes when a new CH~ group is added to an alkyl chain is a well know~ fact. The enthalpy of formation of parafines is directly dependent on the number of methylene groups present in the molecule t=,13. Moreover, the specific 185

186

THE ALKYL CHAIN CONTRIBUTION

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Fig. I. Specific Heat of C4Zn between 70 and 310 K.

Fig. 2. CH2 contribution to the specific heat in two

Squared dots represent the conventional adiabatic measurements. The continuous line in the insert shows a heating thermogram (heating rate:l.2 oC/hour). The dashed line is the calculated lattice contribution plus an anharmonic correction.

different crystal environments. Symbols represent the tabulated values obtained by specific heat substraction of various compounds, using equations (I) and (2): A: (C5Zn and C4Zn); V: (CsZn and C2Zn);

heat contribution of each individual CHa .group seems unaffected by the chain length, even m the case of short ones. This is an interesting fact as in these cases the interactions with the extreme methyl groups could not in principle be avoided. A similar result has been observed in the specific heat of other laver compounds with hydrocarbon chains 14. For these reasons, the CH2 contribution to the specific heat can be roughly calculated by simple substraction of the specific heat of the various compounds of the same family. In our case, the u s e o f availble adiabatic data for C~Zn i), C~Zn 4 together with those of C4Zn presen1~ed in this-paper, have permitted to obtain the methylene contribution from the following equation: Cp(CH2) = [Cp(CnZn)-Cp(CmZn)]/ [2(n-m)] ; n > m

(I)

once the phase transition anomalies were excluded. The validity of this calculation is illustrated in figure 2, which also confirms the similar results obtained for the CnCd and families 'o in spite, • . . C_Mn ii of (ts octahedral coordmatlon t4. The physical basts for this good correlation lies on the relatively high frequency modes associated to the CH~ groups, which are .mainly related with the hydrogen vibrations. These hard modes are only slightly dependent on the external interactions with the rest of the organic chain and with the surrounding crystal lattice. These results can also be reinforced from a similar comparison among the specific heats of organic compounds with methylene groups but with a very different molecular structure. Calorimetric data from the [N(C~H2n, t)4]xMCI4 family (n=l,2; x=l,2 and M=Zn,Fe ~Tliave b e e n used for this purpose 16-19. In this case, the methylene contribution has been calculated from: Cp(CH2)=(Cp( [N(CnHan,!),tlxMCl4) - Cp([N(CmH2m+I)4]xMCI4)} / [4(m-n)xl

(2)

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[N(CH3)4]2ZnCI4); D:(N(C2Hs)4FeCI4 and N(CH3)4FeCI4) The solid line represents the CH2 contribution calculated from the frequency spectrum in layer compounds, plus a suitable anharmonic correction (dashed line). after suppression of the various phase transition contributions. The final results are shown in figure 2. Lower values than those attained by the methylene specific heat in the layer compounds are observed throughout the whole temperature range. This effect can be explained by a noticeable shift of the vibrational CH~ frequencies to higher values as a consequence of the very different intermolecular environment. The inflexion point showed by the CH2 specific heat curve around 170 K accounts for the presence of two groups of distinguishable modes. Above this temperature, the specific heat is governed by the high frequency modes associated with the hydrogen vibrations and also with the C-C stretching mode. whereas below tMs temperature the remaining two C-C bending modes are predominant. It should be noted that the addition of a methylene group to an alkyl chain produces a new C-C bond. As an attempt to compare the CH~ contribution obtained by the procedures mentioffed above, with the results one should expect from its vibrational spectrum, the following calculations have beeen performed: we have used the known frequencies of the CH2 vibrations inApArafines and in some related layer compounds 2u-z~. The two C-H stretching modes have been eliminated in our calculations as high frequencies (around 3000 cm -l) do not contribute to the specific heat value below room temperature(< 0.01% of the CHa specific heat), The substraction of the contributions of the four C-H bending modes (1300-1500 cm -I) from the CH~ specific heat, does not eliminate the inflexion poinl mentioned above, which now appear around 280 K.

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This Ca behaviour cannot be explained by the remaining two C-C bending modes as only low frequencies are involved. We should point out that below 300 K, frequency modes below 900 cm -I always lead to negative specific heat curvatures: (dzCp/dTZ)<0, when Einstein functions are used. Therefore, the observed behaviour can only be explained by anharmonic contributions to the specific heat, which can be consequently roughly estimated. On the other hand, the frequencies o f the two C-C bending modes can be calculated from the specific heat behaviour at low temperatures, as in this range the contributions of the high frequency modes as well as the anharmonic effects are negligeable. As found in many solid substances, the anharmonic contribution is supposed to o b e y the Nernst-Lindemann law: C,-Cv = aCpZT, with a-constant. A tentative value for this constant, together with the well known frequencies of the hydrogen vibrations and the obtained estimations for the C-C modes have been used as initial arameters for a least squares fitting procedure. he fina| results show two modes at 114cm -~ and 202 cm -i which agree with the values assigned to the out-of plane and to the chain accordion modes in p.arafines 2°-23 .The C-C stretching _mode at 1012 cm -= a n d the .CH2 rocking (728 cm-' ), wagging (1300 cm -=. ),twisting ( 1360 cm -l ) and scissoring (1466 cm-X), are also in good agreement with the reported values for these vibrations in n-alkanes and in layered crystals. The obtained value for the Nernst-Lmdemann constant was: a = 2.29xi0-5 mol/Joules. Finally, the calculated specific heat for the methylene group has been obtained by using Einstein functions and the results are plotted in figure 2. The preceeding procedures have been also used to calculate the harmonic specific heat of C4Zn, once the methylene contributions are established. We have made use of the frequency assignment on related crystals zq,z) although this information is far from completeness, The main indeterminations lie on the low range of the frequency spectrum, which is associated to the external motions of the molecular groups. These vibrations are highly dependent on the particular crystal field and consequently a comparative assignment is avoided. However, the specific heat contributions of such modes saturate at relatively low temperatures. This means that the behaviour of the specific heat curve throughout the temperature range in which the phase transition takes place is mostly driven by the medium and high frequency modes (above 300 cm-l). For this reason, the calculated curve (see figure I) can be reliably used as a correct baseline to obtain the values of the phase transition thermodynamic functions. Below 120 K, a more precise knowledge of the C~Zn vibrational spectrum from Raman and neutron" scattering data would provide the required information for a better adjustment. The lattice specific heat of the remaining C_Zn compounds are easily determined, once ~he contribution of the methylene group is known. Good fits for C2Zn and C~Zn have been obtained by this method, with only" slight differences in the low frequency modes and in the anharmonic corrections. As cited before, both effects are easily separated as they affect quasi independently the extremes of the measured temperature range.

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THE ALKYL CHAIN CONTRIBUTION

The numerical integration of the C4Zn specific heat curve has shown the following results for the phase transition thermodynamic functions: z~H=930 R and AS= 3.52 R. These values can be compared with the ones presented by CIZn and C~Zn. We should first note that the three crystals IJndergo phase transitions from a common high temperature orthorhombic phase (Pnma) to a monoclinie ferroelastic one, although the fact that CIZn shows a clear first order character, C~Zn a "definitive second order one and that in C4Zfi is ambiguous, remains unexplained. Howevei', the transition temperatures are found to decrease when increasing the number of carbon atoms: T0=426, 310 and 290 K, for n=l,3 and 4, whereas the transition entropy attains higher values: AS= .08, 1.2 and 3.5 R, respectively. These results confirm the influence of disordered processes in the alkyl chain on the phase transition mechanisms, .Ln agreement with X-ray results on CiZn and C~n b,:. On the contrary, the C~Zn and C~Zn crystals undergo an orthorhombic-orth6rhombicJphase transition at almost the same temperature (234 and 249 K respectively) and with similar entropy.values (1.8 and 1,73 R). As suggested in reference ~, this phase transition seems unrelated with the alkyl chain length and could be associated with re-arrangements in the H-bonding schemes. In the case of C,~n the symmetry characterization of both v-,~ses allows for a preliminary phenomenological treatment . As a first approach, the free energy can be expanded in power terms of the order parameter, whose macroscopic form is identified with the complement of the monoclinic angle in the low temperature phase : F = ( I / 2 ) a (T-T0)~12+ (I14)I}~I 4 + (I/6)y~I 8 + . . . (3) Odd power terms are avoided by the centrosymmetric character of the high temperature phase. The behaviour of the order parameter can be estimated from the calorimetric results, as the minimization of eq. 3 relates this magnitude with the transition entropy through equation: -AS=(I/2)ml 2. The behaviour of the transition entropy for T < To is shown in figure 3. A/though the shape of the curve suggests a second order character for this phase transition, a noticeable slope increase near the transition temperature should be noted. In this temperature range, the

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188

THE ALKYL CHAIN CONTRIBUTION

entropy derivative aporoximates the limiting value: (8S/ ST)= - a2/O . "The very high slope of the experimental entropy near Tn suggests a corresponding low value for ~. Thif result could be related with the proximity of a tricritical point for which ~=0. Due to the monoclinic deformation of the low temperature phase, the first order character might be attained by a suitable external stress which would favour a discontinuous jump in the order parameter. The contributions to the specific heat which could arise from critical fluctuations have been also examined by fitting the excess specific heat to the power laws: AC~ - A [ T-To [ -~ for TT0. In tl~e close proximity of To , ( [ T - ~ ] < 0.03 K) a very near to zero value for both critical exponents is obtained. The straight dashed line in the insert of figure 3 show that the order parameter also follows the classical prediction

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in this short temperature range. On the other hand, the tail of the Co curve above the transition temperature can be reasonably fitted for (~'-1.7, in the range 0.03 K < I T-T 0 I < 1 K. This high value, far above the predictions of the renormalization theories, exclude noticeable critical contributions to the specific heat, which could be suppressed by the long ordering imposed by the ferroelastic transition. If this were the ease, the observed specific heat tail could arise from various kinds of sample inhomogenities. This behaviour could also be phenomenologically explained by the presence of internal stresses, as the addition of an elastic term in the free energy expansion describes both the specific heat tail above To as well as the rounding of Co near the transition temperature.

Ackowledgements- This work has been sponsored

by CAICYT,Spain.

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