Nuclear Quadrupole Resonance and Nuclear Magnetic Resonance Studies of K,PtCl Type Mixed Crystals BY COSTASDIMITROPOULOS J. VAN DER KLINK AND JACQUES Experimental Physics Laboratory Ecole Polytechnique Fedkale de Lausanne 33 Av. de Cour CH- 1007 Lausanne Switzerland AND J. PELZLAND M. REGELSBERGER Experimental Physics Institute VI Ruhr University Bochum W. Germany AND K. ROSSLER Inorganic Chemistry Institute K.F.A.-Julich W. Germany Received 19th January 1979 Phase transitions from cubic to lower symmetry phases in antifluorite (K,PtCI,) structures have been ascribed to lattice mode-softening. We study the effect of impurities on lattice vibrations and transition temperatures in such structures. For mixed rhenates we find a lowering of the frequency of the lattice vibrations with increasing impurity content and a corresponding increase in transition temperature.For mixed stannates the n.q.r. signal disappears at high temperature perhaps due to reorientational motion of the stannate anion. Many compounds of the K2PtC16 (R2MX6) type exhibit the cubic antifluorite structure at room temperature. Upon lowering the temperature some of them (but not e.g. K2PtCl itself) undergo one or several structural phase transitions to lower symmetry forms.' We will be concerned only with the high-temperature purely dis- placive transitions that destroy the cubic symmetry. These transitions can be described in terms of a reorientation of the MXg-octahedra combined with a distor-tion of the cubic R+-array. Theoretical descriptions2 of the lattice dynamics at the transition involve a de- crease in frequency (" softening ") of the optical phonon which describes the rotational oscillation of the rigid octahedra within the cation environment.The distortion of the lattice below the transition is then a consequence of the freezing-out of the eigen- vector of the same soft-mode phonon. In the low-temperature phases these phonons may be observed by Raman and infrared spectroscopy it has been shown by O'Leary and Wheeler2 that in the cubic phase the n.q.r. frequency of the halogens in the anion octahedra reflects the soft-mode behaviour. There exist other factors affecting the n.q.r. frequency however and we will attempt in the following a systematic decomposition of the experimental results into the various contributions.In suitably chosen systems such a decomposition may be facilitated by the study of mixed crystals. If one of the components is present in only low concentration it may be considered a random point defect in the matrix of c. DIMITROPOULOS et al. the other c~mponent.~ If the point defect distorts the lattice by its size the effect may be described by an elastic variation assuming an electric field gradient that varies linearly with the stress. If the point defect fits neatly in the host lattice its different mass may shift the frequency of the lattice vibrations and thus change the temperature dependence of the n.q.r. frequency. The results we have obtained4 on K2(ReC1,),-,(ReBr,) can be satisfactorily described by a combination of these effects.In those mixed crystals the phase transi- tion seems to be of the same type as in the pure hexa~hlororhenate,~ i.e. driven by softening of the zone-centre rotary-lattice mode frequency. The data on [K,-,(NH,),] SnCI indicate a phase transition in the pure potassium compound driven by softening of a rotary mode6 that has not been unambiguously assigned due to a lack of crystallographic data in the low-temperature phase. Our first data on the mixed crystal however indicate that a blocking of SnCli- octahedra nearest to the ammonium ions seems to influence the occurrence of the transition. Both in the pure and mixed crystals we observe that the n.q.r. signals disappear at ~350K; a tentative hypothesis connects this phenomenon to a possible anomaly in the NHZ proton relaxation in the pure ammonium compound.’ MECHANISMS THAT CONTRIBUTE TO THE N.Q.R.FREQUENCY The field gradients that determine the n.q.r. frequency arise partly from the (mainly) covalent bonds within the MXi-octahedron and partly from the ionic lattice of all other ions. Calculations show the former to be the more important.’ Far above the transition the resonance frequency usually decreases when the temperature is raised. Bayer’ has attributed this decrease to increasing amplitudes of torsional motions internal to the molecules effectively averaging the field gradient. Later author^^^'^ have refined this description and have pointed out that Bayer’s effect really was (av/W), whereas the usual experimental results give (2v/o’T),.The thermodynamical relation between these quantities has been derived by Kushida Benedek and Bloembergen’ as where C( is the thermal expansion coefficient and IC the compressibility of the crystal. In most cases (av/ 2P)Tis small and positive and the last term may be safely neglected. In some instances however of which K,ReCl is an example (av/JP),is large and negative.” This has been explained by Haas and MarramI2 using the Townes and Dailey theory13 to include the effect of the destruction of x-bonding with increasing temperature. In K,PtCI type crystals approaching the transition temperature from the high-temperature side one usually finds a drop in the observed frequency below the value extrapolated from high temperatures.This behaviour has been identified by O’Leary and Wheeler2 as representative of the occurrence of mode-softening. If the impurity atom has a mass different from the original one the resulting change in vibrational frequencies will change the slope (av/aT) of Bayer’s theory but the value extrapolated to zero temperature should remain unaltered. Addi-tionally in mixed-crystal systems the strain field resulting from the inclusion of point defects gives rise to a temperature-independent shift of the n.q.r. frequency that is also proportional to the increase in the lattice parameter Aa.3*4 N.Q.R. + N.M.R. OF KzPtCI6 TYPE MIXED CRYSTALS 35C1 N .Q .R . I N K2(ReC16),- ,.(ReBr,) The 35Cl n.q.r. frequencies measured in the cubic phase of these mixed crystals4 are shown again in fig.1. To separate the different contributions the data have been analysed as follows. f f + ** -i+ 13.8901 + ,.1 * it 5? + 0 st Of I N + it 57 t I + it 0 I 13.8801 n +F. \ t-+ 0 x c n 3 + sc '9 I sc 0 13.870 * In m 13.860 1 tL9 I Ill1 111 I1 I1 I I1 I1 I1 1 111 I11 I Ill I I/ /I ,I It II 1 1 150 200 250 200 temperature l/K FIG.1.-Ti n.q.r. frequency in the cubic phase of K,(ReC16),-,(ReBr6)x mixed crystals as a func-x tion of temperature for different impurity fractions x * x = 0.000; 0,= 0.023; +t x = 0.076; + x = 0.279. The region above room temperature has been extrapolated down to zero temperature.Differences in the extrapolated values for different x have been attributed to the temperature-independent effect of the strain field. Three samples with x = 0.019 x = 0.023 and x = 0.076 yielded an average value of 90x kHz for this shift. The calculated value4 is 120x kHz and in view of the uncertainty in the values of the parameters entering this calculation we consider the agreement satisfactory. The fourth sample with x = 0.279 gave approximately 45x kHz for this shift. We suppose that at this concentration the linear elasticity theory is no longer valid. Next a correction was applied' to obtain (dv/W) according to eqn (1). Finally c. DIMITROPOULOSet al. in fig (2) we show the normalized n.q.r. frequency,f obtained from ~(x,T)in fig.1 as where (3) 1-20 1-0 = 2.16 - 1 a". Aa (4) The meaning of the symbols is the same as bef~re,~ and vo = 13.868 MHz is the extrapolated frequency at zero temperature and zero impurity c~ncentration.~ For x = 0.279 we halved the value of [ in view of the extrapolation discussed above. --_ ---_ 0.998 -**-***@@ -_-_ -__-..---_ 0.gg6t /a/ ;:;;; --_ 0.996 *@ a-* lel -_;-*-a-.-. 150 200 250 300 temperature 7/K FIG.2.-Normalized 35CIn.q.r. frequency f in mixed rhenates. The data from fig. 1 have been corrected for specific volume effects and impurity strain field effects according to eqn (2). The value Jr = 1 in (a)corresponds to 13.868 MHz. The slope of the dashed line changes with x showing that the average lattice vibration frequencies diminish with increasing substitution.The levelling-off of f towards the transition temperature indicates mode-softening. (a) x = 0 (6)x = 0.0190 (c) x = 0.0234 (d) x = 0.0760 (e) x = 0.2790. N.Q.R. + N.M.R. OF K,PtCI TYPE MIXED CRYSTALS The dashed lines in fig. 2 represent the fit to the highest-temperature points and indi- cate the Bayer behaviour. The systematic change in the slope (from 165 Hz K-' for x = 0 to 177 Hz K-l for x = 0.076) reflects the lowering in the frequency of the lattice vibrations due to the difference in mass between the impurity and the original ion. A similar decrease in frequency has been observed for the internal vibrations of (ReC1,)'-in the cubic phase.4 At a given temperature far above the transition we expect therefore that the fre- quency of the rotary lattice mode responsible for the transition will also be lower in the mixed crystal than in the pure compound.It seems probable then that the rotary lattice mode frequency as the temperature decreases will approach zero at a higher temperature when the impurity fraction x is increased so that the transition will occur at a higher temperature. This corresponds to what is actually observed the transition temperature increases z 7 K when changing x from 0.0 to 0.076 and the experimental frequencies near the transition show the deviation characteristic2 for a soft-mode process. 35Cl N .Q. R . IN [(NH4)xK1-x]2 SnCI Experiments on these systems are still in progress so some of our conclusions will be incomplete and tentative.Fig. 3 shows the observed n.q.r. frequencies in mixed 15.30C 15.250 2 T x 15.200 0-2 Y-Li z G 15.150 In m b 15.100 260 280 300 320 340 temperature TIK FIG.3.-35Cl n.q.r. frequency in [(NH4)0.01K0.99]2 SnCI as a function of temperature. Above 260 K the crystal structure is cubic but additional lines are found around 15.14 MHz. These are supposed to arise from NH4+-nearest neighbours. All signals disappear around 350 K. c. DIMITROPOULOS et al. crystals of lowest impurity concentration above and just below the high-temperature transition. The behaviour is similar to that of the pure omp pound'^*'^ except that additional lines occur in the cubic phase of the mixed crystal.We attribute these to those chlorine atoms that are nearest-neighbours to the (NH,)+. In contrast to the case of the rhenates the lattice distortion upon substitution is extremely small in the stannates l6 so that the signals of nearest-neighbours are not necessarily wiped out but only shifted towards higher frequency. Our observation that the intensity of these additional lines relative to the normal low-frequency line increases with increasing (NH,)+ concentration lends further support to this assumption. The well-resolved doublet observed immediztely above the transition might correspond to two possible orientations of the NH4+. In the pure ammonium compound one orientation" is energetically favoured; but perhaps the slightly different geometry in the mixed crystal diminishes this energy difference to a sufficient extent.At higher temperatures the splitting disappears and a single broad line is observed. This then might indicate rapid changes from one orientation to the other. We expect the corrections that had to be applied to the observed frequencies in the rhenates in order to bring out the Bayer-type of behaviour to be less important in the stannates since here at least the observed (av/aT),is of normal sign. No measure-ments of (av/aP) are available however to corroborate this supposition. The shift due to the strain field can probably be neglected since Aa/a is an order of magnitude smaller16 than in the rhenates. Any data reduction is made virtually impossible however by the fact that the n.q.r.signals both in the pure potassium compound and in the mixed crystal disappear at z 350 K. The highest temperature attained in previous investigation^'^ of 35Cln.q.r. in KzSnC16was 320 K and this signal loss has not been observed. As is clear from the reduced plots in fig. 2 a temperature range of a few times T is necessary for a reliable extrapolation to byo. Thus although the temperature-dependence of the low-frequency line in the cubic phase is consistent with soft-mode behaviour as observed from Raman spectra6 and 35Cl n.q.r. relaxation timesI5 in KzSnC16 no cIear presentation as in the case of the rhenates (cf. fig. 2) is possible. The effect of substitution on the transition temperature shown in fig. 4 however seems too important to be explained by a change in phonon frequencies alone.The points show transition temperatures as measured by n.q.r.; the line has been derived from d.s.c. (differential scanning calorimetry) measurements.16 The latter results have been interpreted as an indication that the regions near the (NH,)+ ion do not undergo a structural transformation consistent with our interpretation of the additional doublet in the mixed crystals. An empirical rule has been established by BrownI8 relating the occurrence of a structural phase transition to the relative sizes of cations and anions. If this ratio is unfavourable the anion reorientation that accompanies the transition cannot take place and the compound remains undistorted. Since the pure (NH4)2 SnCI does not show a tran~ition,'~ we suppose that the ammonium ion in the K&C& matrix blocks the rotation of the SnC162- octahedra.Since the structural transformation involves a small rotation of the octahedra the mean transition temperature is depressed by the restoring torque exerted by the ammoniuni ions. PROTON N.M.R. IN [(NH,) K1J2 SnCI The proton spin-lattice relaxation times T1in (NH4)2 SnBr,' and (NH4)Z PtBr6l9 have been shown to exhibit discontinuities at the temperature where the phase transi- tion occurs. The results of our investigation of Tl in a mixed crystal are shown in N.Q.R. + N.M.R. OF KZPtCI TYPE MIXED CRYSTALS FIG.4.-Phase transition temperature from cubic to lower symmetry T in mixed stannates [(NH,) K1-J2 SnC16 as a function of impurity fraction x.The points have been determined by n.q.r.; the line represents results obtained by differential scanning calorimetry. The fairly large slope of -516 K suggests geometric hindering of the anion reorientation by the ammonium ion as the main cause for the change of T with x. 102 --8---5- -3-m / / 1 -/ h" 2-/ / ,/. *. .-E 10' -A . --.s 8 -a 4' 0- -/. L L a 5 ;d4 -C 0 w 2 3-Q 2-I I I I I 5 4 3 2 FIG.5.-Ammonium proton spin-lattice relaxation time in [(NH4)0.01 SnCI as a function of temperature at a Larmor frequency of 92 MHz. The phase transition occurs around lo3 T-' = 3.9 K-'. The onset around T = 300 K of a new relaxation mechanism tentatively ascribed to anion reorientation may mask the change in slope expected at the phase transition.The slope of the dashed line corresponds to an activation energy of 590 K as determined by quasielastic neutron scattering in the pure ammonium compound. c. DIMITROPOULOS et al. fig. 5. The phase transition occurs around lo3 T-' = 3.9 K-'. The slope of the dashed line indicates the activation energy E = 590 K for rotational motion of the (NH,) + ion in (NH4)2SnC16 derived from quasielastic neutron ~cattering.'~A significant deviation from this slope implying a maximum in T, occurs at tempera- tures higher than the transition temperature. We tentatively correlate this to the Tl and Tlpbehaviour in (NH4)2SnCl found by Strange and Teren~i.~ They observe a maximum in Tlpand suggest that it might be due to (SnCl,)2- reorientation analogous to an effect they find in (NH,),SiF,.In the same temperature region a change of 15.070 1 temperature TlK FIG.6.-The frequency of the 35CI n.q.r. low-frequency line in the cubic phase for the pure potassium stannate (filled circles) and for [(NH4)0.035 SnC& (open circles). The change of slope with x at high temperatures (and final disappearance of the signal) are considered anomalous and may be related to the proton relaxation results of fig. 5. (av/aT') for the 35Cln.q.r. frequency has been 0b~erved.l~ Their Tl data suggest a maximum at higher temperature as well although they do not comment on this. Such an onset of (SnC16)2- reorientation might be also the cause of the rapid decrease in the 35Cln.q.r.frequency for [(NH,) K1-,l2 SnCI and the final disappearance of the n.q.r. signal around 350 K shown in fig. 6. This question will need further experi- mental and theoretical work to be settled however. R. L. Armstrong and H. M. van Driel Ado. Nuclear Quadrupole Resonance 1975 2 179. G. P. O'Leary and R. G. Wheeler Phys. Rev. B 1970,1,4409. J. Pelzl H. Vargas D. Dautreppe and H. Schulz J. Phys. Chem. Solids 1975,36 791. C. Dimitropoulos J. Pelzl H. Lerchner M. Regelsberger K. Rossler and A. Weiss J. Mag-netic Resonance 1978 30 415. N.Q.R. + N.M.R. OF K,PtCI TYPE MIXED CRYSTALS H. M. van Driel R. L. Armstrong and M. M. McEnnan Phys. Rev. B 1975,12,488. J. Pelzl P. Engels and R. Florian Phys. Stat.Sol. b 1977 82 145. J. H. Strange and M. Terenzi J. Phys. Chem. Solids 1972 33 923. H. Bayer 2.Phys. 1951 130 227. T. Kushida G. B. Benedek and N. Bloembergen Phys. Rev. 1956 104 1364. 'O.H. 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