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Neutron powder diffraction studies of some superprotonic and mixed crystals with disordered hydrogen bonds
Journal of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 374 (1996) 161-169
Neutron powder diffraction studies of some superprotonic mixed crystals with disordered hydrogen bonds
and
A.V. Belushkin”>*, R.M. Ibbersonb, L.A. Shuvalovc aFrank Laboratory of Neutron Physics, JINR 141980 Dubna, Russia ‘ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 OQX, UK ‘Institute of Crystallography RAS, 117333 Moscow, Russia
Received 3 February 1995; accepted in final form 16 May 1995
Abstract Neutron diffraction is well known as an effective tool for studying proton location in a crystal lattice. During the last decade, the development of high-resolution powder diffractometers has provided an alternative method to single-crystal neutron diffraction in order to obtain this detailed structural information. The powder technique is rapid and appropriate, particularly in cases where obtaining single crystals is technically difficult. In this paper, several examples of the study of crystals with disordered hydrogen bonds are presented using the High-Resolution Powder Diffractometer, at the ISIS pulsed neutron source. These include a detailed description of the hydrogen bonding and phase transition behaviour in CsHS04 and in Cs,D(SeO,), and recent structural investigations on the mixed crystal K1_x(ND4)xD2P04.
1. Introduction Neutron diffraction has a particular advantage over X-ray diffraction in the determination of lightatom positions in the presence of heavy atoms in both organic and inorganic crystal structures. An
especially important case is that of hydrogen and its isotope deuterium for which techniques other than neutron diffraction are somewhat insensitive. In general, single-crystal diffraction provides the most accurate and precise measurements about the structural parameters of the system. However, in a number of cases it is technically very difficult to obtain single crystals that are large enough for neutron experiments, or such crystals are destroyed
* Corresponding author.
undergoing reconstructive phase transitions. The alternative is to use powder diffraction and a fullprofile (Rietveld) refinement procedure. Highresolution powder data minimises the Bragg peak overlap intrinsic to a l-dimensional powder diffraction profile and enables both accurate and precise structural studies to be carried out. In addition, the use of pulsed neutron sources and the time-of-flight technique gives advantages by the exploitation of the polychromatic neutron spectrum produced by the source. Moreover, a rich epithermal (short wavelength) flux provides the researcher with access to the very small interplane-distance region of a diffraction pattern. These characteristics are especially useful in the study of high-symmetry crystals (which produce a limited number of reflections at large d-spacings), some types of disorder and crystals with impurities where a large number
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of resolved reflections are required in order to perform a successful multiphase refinement. In this paper we present results of time-of-flight high-resolution neutron powder diffraction investigations of hydrogen-bonded compounds that exhibit different types of proton order-disorder transitions.
2. The high-resolution
powder diffractometer
(HRPD)
The HRPD at the ISIS pulsed neutron source (see for example Ref. [l]) is the highest resolution neutron diffractometer in the world and is designed to achieve an optimal balance between the maximum practical resolution attainable and reasonable counting times. The instrument is situated 100 m from a 100 K liquid-methane gadoliniumpoisoned moderator and incorporates a specially designed neutron guide in order to maintain a useful neutron flux over the long flightpath. The guide and moderator provide HRPD with an incident neutron flux of 0.5 I X 5 12 A, witoh a peak flux intensity at wavelengths around 2 A. The 100 m flightpath of HRPD minimises the timing uncertainty in the resolution function, and geometric contributions are minimised by utilising backscattering geometry. For the typically used (higher flux) 1 m position of the sample from the detector, the average scattering angle is 168.33” and the resolution is Ad/d M 8 x 10e4. Importantly, the resolution function is essentially independent of neutron wavelength. This factor, together with the availability of a significant epiJherma1 neutron flux, which gives access to sub-Angstrom Bragg reflections, is crucial to obtaining a high degree of accuracy in structural parameters. Diffractometers such as HRPD can yield extremely impressive powder-diffraction patterns containing a large number of reflections and hence a large amount of information. This enables HRPD to tackle areas more traditionally associated with single-crystal work, such as the study of “molecular” crystals. Structural studies in this area were pioneered with accurate and precise work on the structure of benzene [2], from which highquality data allow a full refinement including
anisotropic displacement parameters. The results were in good agreement with the best single-crystal measurements. Given the convenience of powderdiffraction data collection, for example in the case of low melting point compounds, and the short data collection times required, this is an extremely impressive result with considerable implications in organic crystal chemistry. The most obvious implication of the ability to study organic structures from powder samples is that it provides an opportunity to examine phase transitions. Not only is a rather rapid data collection time required to study, for example, the temperature dependence of a structure adequately, but also frequently the occurrence of a phase transition will destroy a single-crystal sample. Powder diffraction overcomes both these problems and work at ISIS on structural changes for example in the prototypic fullerene ChO, have shown that extremely subtle structural changes in this material can be characterised by using high-resolution neutron powder diffraction [3,4], helping, in this case, to resolve a problem in one of the hottest topics in structural science in recent years. Such an ability to study phase transitions in organics has large potential interest for both fundamental and practical reasons. For example, such experiments will yield information on the fundamental mechanisms governing transitions in organic systems. In addition, however, there are extremely practical benefits in terms of studying molecular energetics, with implications for reactivity, conformation and polymorphism. The limits of this technique in terms of unit-cell size (and indirectly the size and complexity of the structure) are continually being expanded, with one of the largest unit cell volumes successfully studied on HRPD to date being well over 1000 A3 in the case of toluene [5]. The potential of the technique in this area is outstanding.
3. The superprotonic phase transition in CsHS04 Caesium hydrogen sulphate and its deuterated analogue provide a classical example of a hydrogen-bonded superprotonic crystal [6]. At 414 K (412 K for the deuterated crystal), the
A.V. Belushkin et al./Journal of Molecular Structure 374 (1996) 161-169
structure undergoes a first-order phase transition characterised by a sharp increase in conductivity, reaching a value of lo-* R-i cm-‘. This superprotonic transition is of the improper ferroelastic type with a large spontaneous shear strain, lo-*. The latter leads to the destruction of single crystals just above the phase-transition temperature and therefore complicates any structural study. Attempts to solve the structure of the hightemperature phase and to explain the observed high protonic conductivity were made using X-ray diffraction on minute single crystals that could survive the transition [7] and by neutron powder diffraction using a medium-resolution diffractometer at a steady-state reactor [8]. Although the atomic coordinates for the heavy atoms (Cs and S) were in very good agreement in both studies, two different and conflicting models are proposed for the structure of the superprotonic phase with regard to the positions of oxygen atoms and protons. Furthermore, both models predict different mechanisms of protonic transport with neither in agreement with all other reported properties of the superprotonic phase. The structure obtained from the X-ray study assumed that oxygen occupies 16h positions in an 14,/amd lattice with a site occupancy of 0.5. This led to the conclusion that the protons are most probably stochastically distributed over the 8e sites; however, the possibility of 16h sites for the protons was also mentioned. Such a model implies unreasonably large distortions of the SO4 groups for proton migration through the lattice to occur. In addition, this model does not explain the experimentally observed proton conductivity which is essentially isotropic. Because the 8e sites form planes perpendicular to the tetragonal axis and are separated by a rather large distance, the proton conductivity is expected to be larger in the basal plane than along the tetragonal axis. Furthermore, the orientational disorder of HSO; groups observed by optical spectroscopy [9] and the entropy change at the transition, equal to 1.32R [lo], were not consistent with the structural model and there is no experimental data to support a hydrogendeuterium isotope effect on the phase-transition temperature. The second model, proposed on the basis of the
163
experiment using a conventional medium-resolution neutron diffractometer [8], assumed that, in the superprotonic phase, oxygen atoms occupy 32i positions with a probability of 0.5 and that the protons are stochastically distributed over the 16f positions with a site occupation factor of 0.25. The proton transport in this model is connected with the librational motion of HSO; groups and proton transfer between neighbouring 16h sites is achieved without distortion of the HSOT groups. This model successfully explains the observed entropy of the transition. The theoeretical value, R ln4, is in good agreement with the experimentally determined value, and the orientational disorder of HSOT groups is also explained. However, this model does not predict the observed lower conductivity along the tetragonal axis in comparison with that in the basal plane. Furthermore, the absence of an isotope effect on the transition temperature is not explained. In order to solve this structural problem, an experiment on HRPD using a deuterated (CsDSOJ sample was performed [ 111.Time-of-flight data were recorded over a d-spacing range of 0.6-5.4 A to yield a high-quality diffraction pattern. The data reveal only a limited number of high-intensity reflections occurring at large d-spacings. Thus, the majority of the structural information was contained in the data below d = 1.3 A. This fact highlights the limitations of the previous X-ray and medium-resolution neutron-diffraction studies. Data analysis was carried out using the in-house suite of time-of-flight profile refinement programs in order to obtain a definitive structure of the hightemperature phase. Although both models discussed above were initially tried in the profile refinement procedure, neither gave satisfactory results. The X-ray model yielded unrealistic distortions of SO4 tetrahedra and, using the model from the initial neutron study, a stable convergent refinement could not be achieved. In fact, a structural model proposed previously which combines elements of both models was found to best fit the data and readily explain all features of the superprotonic phase transition. It was found that, in the superprotonic phase, the oxygen site becomes split not into two, as predicted previously, but into four 32i sites in the crystal lattice. This permits the SO4
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A. V. Belushkin et a/./Journal of Molecular Structure 374 (1996) 161-169
group in the superprotonic phase to have four different orientations between which it can stochastically reorient, in contrast to the one, fully ordered, orientation of this group below the transition. Hydrogen bonding is thus possible both via 16h and 8e crystallographic sites, forming a highly disordered network with many vacant proton sites. This facilitates proton migration through the lattice in all crystallographic directions, explaining the isotropic nature of the protonic conductivity. The model assumes that the superprotonic phase transition in CsHS04 is governed by SO4 tetrahedra disordering over four orientations instead of just one possible orientation below the transition. This readily explains the observed transition entropy and, because the proton disorder in this model is only a secondary effect caused by SO4 dynamic orientational disorder, the virtual absence of the isotope effect on the phase-transition temperature also becomes clear. The orientational disorder of SO4 tetrahedra in this structural model is in full agreement with the results of optical spectroscopy mentioned above. Subsequently these structural results have been confirmed independently by quasi-elastic neutronscattering experiments [ 121 which prove the dynamic disorder of HSOT groups and longrange proton diffusion through the lattice.
4. The low-temperature phase transition in Cs@@eO& Tri-caesium deuterium biselenate undergoes a phase transition at 168 K which was first detected by dielectric measurements [13]. In the hydrogenated analogue, the transition temperature is much lower, by some 50 K. The large isotope effect on phase-transition temperature is indicative of the important role played by hydrogen bonds in the phase-transition mechanism. In order to study this phase transition, a single-crystal X-ray experiment was performed [14] and, independently, a high-resolution powder diffraction study using HRPD was carried out [15]. Both experiments gave consistent results for the atomic coordinates and temperature factors of the heavy atoms. Above the phase transition, CssD(Se04)2 is
monoclinic with space group C2/m and Z = 2 [ 141.The hydrogen bonds link selenium tetrahedra to form dimers with the deuteron situated either on a two-fold axis or disordered between two positions close to the two-fold axis. The lowtemperature phase transition in this compound involves the loss of the C-base centring observed at temperatures above the transition. As a result, the symmetry of the crystal below the transition becomes P2t/m. The phase transition does not lead to any significant changes in the atomic coordinates of any atoms except the deuterons. Below the transition, deuterium atoms no longer lie on a two-fold axis and thus are not constrained by symmetry to be equidistant from the tetrahedral selenate groups in the hydrogen-bonding scheme. The neutron powder diffraction experiment allowed a detailed description of the deuterium atom ordering in the low-temperature structure to be obtained which was not described by the single-crystal X-ray study. Since full details of the structure analysis are presented in the papers cited above, only the characteristic hydrogen-bond dimensions will be discussed here. Fig. 1 shows a schematic illustration of the hydrogen bond in Cs3D(Se04)2. It is evident that the deuteron is not equidistant from the neighbouring Se04 groups. The observed orientation of the thermal ellipsoid for the deuteron is perpendicular to the hydrogen bond. Furthermore, attempts to refine the structure assuming there to be two positions for deuterium along the bond have shown that only one of these two positions is fully occupied. These two findings exclude the possibility of deuterium atom disorder along the bond. The characteristic distances of the hydrogen bond are the following: ro_o =02.550(8) A, ro_o = 1.017(8) A, To-o’ = 1.533(8) A, (02,-D-022 = 178.4(7)“. Using the approach proposed in Ref. [16], one can calculate the distance, 6, between two deuteron sites in the hydrogen bond, above the phasetransition temperature, on the basis of structural data obtained below the transition. In the case of tri-caesium biselenate, this value is 0.52 A. To our knowledge, Cs3D(Se04)2 and NasH(S04)2 [17] are the only examples among the family of Me3H(X04)2 (Me=Na, K, Rb, Cs; X=S, Se) for which the value of S is precisely known. It is
A.V. Belushkin et al./Journal of Molecular Structure 374 (1996) 161-169
Fig. 1. Schematic illustration of the hydrogen-bond
therefore impossible at this stage to investigate whether there are any correlations between this parameter and the phase-transition temperature, as has been done for other hydrogen-bonded crystals [l&19]. However, a linear relation is observed between the transition temperature and oxygenoxygen hydrogen-bond distance at the transition temperature for this family of compounds [20]. We found that it is also possible to establish a relation between the hydrogen-bond length at room temperature (at which most of the experiments are performed) and the phase-transition temperature. I 2.55 -
2.51 1 0
I 50
I 100
I 150
I 200
Temperature, K Fig. 2. The relation between the phase-transition temperature associated with proton ordering in the hydrogen bond and the hydrogen-bond length ro_o defined at room temperature (according to Refs. [20-231).
165
structure in the low-temperature phase of Cs3(D(Se04)2
Fig. 2 shows a plot of the transition temperatures for different Me3H(A04)2 crystals versus ro_o distances obtained at room temperature. Two straight lines drawn through the experimental points (one line describes the hydrogeneous compounds and the other the deuterated analogues) on extrapolation intersect at absolute zero temperature at approximately the same ro-o value 2.517 A (note that the discrepancies, f0.002 A from this mean value are less than the experimental errors for the ro_o values). This value can therefore be considered as being the critical ro_o value for the phase transition. Thus, all crystals of the MesH(Se04)2 family which at room temperature have a hydrogen-bond length less than 2.517 A should not have a phase transition at lower temperatures associated with proton ordering in their hydrogen bonds. Clearly this conclusion is made on the basis of a limited set of data and more experiments are required in order to verify it. Nevertheless, our conclusion is suppotted by the fact that Na3H(S04)* bra-o = 2.432 A [17]), K3H(S04)z (ro-o = 2.493 A [24]), Rb3H(S04)2 (Y~_~~=2.485 A [25]) and Rb3H(Se04)2 (ro-o = 2.514 A [26]) do not undergo such a phase transition. We suggest, therefore, that, from knowledge of the roomtemperature structures of this type of compound, one can reliably predict the existence or absence of phase transitions connected with proton ordering to the hydrogen bond and the temperature of transition (without the need to measure the
166
A.V. Belushkin et al./Journal of Molecular
temperature dependence of the crystal structure and without any assumptions about this dependence [201).
5. The mixed crystal K1_JND4),DzP04 Mixtures of certain ferroelectric and antiferroelectric crystals, over a particular composition range, transform into a proton dipolar glass at low temperature (see Ref. [27] for a review). Proton dipolar glasses may be regarded as having properties comparable to those exhibited by magnetic spin glasses. Pure parent compounds of these mixed crystals undergo a phase transition, associated with proton .ordering in the hydrogen bonds, which, in turn, leads to the appearance of dipolar moments that may be ordered either ferroelectrically or antiferroelectrically. When the parent compounds are mixed in appropriate proportions, the ferroelectric and antiferroelectric interactions compete, leading to frustration effects in the dipolar moment subsystem. The long-range electric order is thus suppressed and a proton dipolar glassy state results. However, and in contrast with magnetic spin glasses, the freezing into a proton glass state occurs over a large temperature range and has direct structural and dynamic consequences that can be studied experimentally. The mixed crystal Kt _x(ND4xD2P04 (DKADP) belongs to this class of compound. Its parent compounds KD2P04 [28] and ND4D2P04 (DADP) [29] are isostructural at room temperature and belong to the tetragonal space group 142d. On cooling, KADP undergoes a first-order phase transition from a paraelectric into a ferroelectric (FE) state (orthorhombic, space group Fdd2) and DADP undergoes a first-order transition into an antiferroelectric (AFE) state (orthorhombic, space group P2t2t2t). On mixing, the transition temperature decreases with increasing concentration of DADP and, over a specific composition range, 0.2 5 x _<0.8, neither an FE nor an AFE transition is realised [30]. Competition between FE and AFE interactions leads to the formation of a frustrated system which is believed to retain the tetragonal structure characteristic of the paraelectric state. This conclusion has been drawn on
Structure 374 (1996) 161-169
the basis of structural studies of a related system, Rb, _JND&D2P04 (RADP). The RADP system was extensively studied by different methods because these crystals are easily obtained across the whole composition range, due to the very similar unit-cell parameters of the crystal lattices of the parent compounds and the similar ionic radii of Rb and NH+ In particular, studies of the temperature variation of structure in the glass composition RADP [31,32] have shown that the tetragonal structure, characteristic of the paraelectric phase of the sample, is preserved down to liquid-helium temperature. Diffuse scattering was observed along the (100) direction, which peaks at a wave vector that corresponds to neither the FE nor the AFT phases of parent compounds. This diffuse scattering is quasi-elastic in character at temperatures above about 100 K; below this point, spatial correlations become static and saturate at about 30 K. In addition, anomalous thermal expansion of the crystal lattice is observed at low temperatures, due to proton glass formation as a result of the competing interactions between the different types of proton ordering [31,33]. Our aim was to investigate the temperature variation of the structure of DKADP and compare the results with those already observed in RADP. DKADP has not been previously studied because of the difficulties in obtaining samples of a homogeneous glass composition. The problem is caused by a large mismatch of the c-lattice parameters of the parent compounds. The powder DKADP sample was measured on HRPD and a section of the powder diffraction profile is shown in Fig. 3. All the lines may be indexed using the tetragonal space group 142d, characteristic of the paraelectric phase of the parent compounds. The lattice parameters obtained, a = b = 7.51079(3) A and c = 7.32968(7) A, are indicative of an ammonium concentration in the sample of x = 0.64 [34]. The most striking feature of the diffraction pattern obtained is that the width of most of the lines is considerably in excess of instrumental resolution and, moreover, neighbouring lines can have very different widths. Closer inspection reveals that the broadest peaks correspond to lines with larger 1 Miller indices. For example, a Gaussian fit to the group of diffraction
167
A.V. Belushkin et aLlJournal of Molecular Structure 374 (1996) 161-169
II
200 -
I !
1 /I
Diffraction
n
pattern
obtained 150 -
F r :: s
sample
from at
DKADP
room
temperature 100 -
/
h g t r-
:
50-
r”
1
6
m
1
‘0-I
,
I
1.8
1.7
1.9
I
2.0
D-spacing
/
2.1
(Angstrom)
/
2.2
I
I
2.3
Fig. 3. A section of the diffraction pattern obtained from &,36(NH4)0.64D2P04 at room temperature. The anisotropic peak-width variation of the diffraction lines is clearly seen.
lines around 2 A (see Fig. 3) shows that the (321) peak at d = 2.0037 A has a width of 0.0044 A, the (312) peak at 1.9933A has a width of 0.0075 A, and the (213) peak at d = 1.9763 A has a width of 0.016 A. This effect is attributedto large intrinsic
g 2.652 -
~.3S(ND4b4D2P04
??
cl (22O)posilion
1. 0
8, 50
0
1
100
”
’
.
150
“1.
200
’
250
300
1
TempetaUe (10
Fig. 4. The temperature dependence of the (220) diffraction line position for both crystal sublattices.
strains caused by the mismatch of the c-lattice parameters of the parent compounds. On cooling, the sample shows normal unit-cell contraction down to about 150 K. However, below this temperature splitting of some diffraction lines is observed; a shoulder appears, which increases in intensity with decreasing temperature. The magnitude of the splitting is essentially independent of temperature. For example, Fig. 4 shows the temperature dependence of the (220) diffraction peak position and its “shoulder”. The change in the diffraction pattern cannot be explained as being due to the precipitation of AFE and FE phases of the parent compounds. However, it is possible to index the observed diffraction profile assuming that there are two phases in the sample at low temperatures. One phase is orthorhombi$, with lattice parameters a = 7.4888 A, b = 7.5251 A, c = 7.2627 A, and the other phase is tetragonal, with0 lattice parameters 0 a = b = 7.4868 A, c = 7.2257 A. Fig. 5 illustrates the temperature changes of the
A. V. Belushkin et al./Journal of Molecular Structure 374 (1996) 161-169
168
,
.j.
‘i
Ko.,(NH4)o,~D2P04 i
;L_i 2.55
2.60
2.65
T=mK
1
2.70
d-swing, Angstrom
Fig. 5. A section of the diffraction pattern from the K,,36(NH4)0.MD2P04 sample at 290 K and 5 K. The inset shows the temperature dependence of the integrated intensity of the (220) reflection of one of the sublattices, together with the fit based on the empirical formula (see text).
diffraction pattern; the temperature dependence of the integrated intensity of the (220) reflection of the orthorhombic lattice is shown inset. The intensity of the corresponding line of the tetragonal lattice decreases coherently. Other lines show similar behaviour with temperature. It is possible to fit the observed temperature dependence using an empirical formula: Z = const x [{1 + tanha}(TO - T)] the result of the fit is shown in the inset in Fig. 5 by a solid line. Fitted parameters averaged over several different reflections are cx = (0.041 f 0.004) K-’ and To = (114 f 1) K. Qualitatively, this behaviour of the intensity can be explained within the multifractal formalism for the process of growth of the new phase [35]. However, a more comprehensive analysis of the data is still in progress. It is
interesting to note that To is very close to the estimated value of the temperature at which the reorientational motion of all ammonium groups in the protonated KADP sample become frozen [36]. In addition, this temperature is very close to the value at which the dynamic spatial correlations in RADP transform into static correlations [32]. Thus, the observed splitting may be attributed to the formation of a mixed state characterised by two sublattices, one of which retains tetragonal symmetry, characteristic of the paraelectric phase, the other of which is orthorhombic. We believe that this effect is a consequence of the frustration imposed by competing FE and AFE interactions. In RADP, this frustration leads to the appearance of diffuse streaks and, in our case, we believe the effect is more pronounced and leads to the formation of two sublattices because of stronger internal strains in DKADP. Finally, we note that the observed splitting disappears when the sample is heated above 150 K and that at room temperature the diffraction pattern of the thermally cycled sample is exactly the same as for the starting material. A full structural analysis of these data is presently under way and will be published elsewhere.
Acknowledgements The authors wish to express their thanks to Mrs. N.M. Shchagina, Mrs. R.M. Fedosyuk and Mrs. V.V. Dolbininoy for sample preparation, and the Daresbury and Rutherford Appleton Laboratory for access to the ISIS facilities.
References [l] J.L. Finney and C.C. Wilson, in J.B. Garbarczyk and D.W. Jones (Eds.), Organic Crystal Chemistry, Oxford University Press, Oxford, 1991, pp. 143-162. [2] W.I.F. David, R.M. Ibberson, G.A. Jeffreyand J.R. Ruble, Physica B, 180/181 (1992) 597-600. [3] W.I.F. David, R.M. Ibberson and T. Matsuo, Proc. R. Sot. London, Ser. A, 442 (1993) 129-146. [4] B.T.M. Willis, in D.W. Jones and A. Katrusiak (Eds.), Correlations, Transformations and Interactions in Organic Crystal Chemistry, Oxford University Press, Oxford, 1994, pp. 11-19.
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[5] R.M. Ibberson, W.I.F. David and M. Prager, J. Chem. Sot., Chem. Commun., (1992) 143881439. [6] AI. Baranov, L.A. Shuvalov and N.M. Shchagina, JETP Len., 36 (1982) 459. [7] B.V. Merinov, AI. Baranov, L.A. Shuvalov and B.A. Maksimov, Sov. Phys. Crystallogr., 31 (1987) 47. [S] Z. Jirak, M. Dlouha, S. Vratislav et al., Phys. Status Solidi A, 100 (1987) K117. [9] V.P. Dmitriev, V.V. Loshkarev, L.M. Rabkin, L.A. Shuvalov and Yu.1. Yuzyuk, Sov. Phys. Crystallogr., 31 (1986) 673. [lo] M. Komukae, T. Osaka, Y. Makita, T. Ozaki, K. Itoh and E. Nakamura, J. Phys. Sot. Jpn., 50 (1981) 3187. [ll] A.V. Belushkin, W.I.F. David, R.M. Ibberson and L.A. Shuvalov, Acta Crystallogr., Sect. B, 47 (1991) 161. [12] A.V. Belushkin, C.J. Carlile and L.A. Shuvalov, J. Phys. Condens. Matter, 4 (1992) 389. [13] M. Komukae, T. Osaka, T. Kaneko and Y. Makita, J. Phys. Sot. Jpn., 54 (1985) 3401. [14] M. Ichikawa, T. Gustafsson and I. Olovsson, Acta Crystallogr., Sect. B, 48 (1992) 633. [15] A.V. Belushkin, R.M. Ibberson and L.A. Shuvalov, Kristallografiya, 38 (1993) 63. (161 A. Katrusiak, Phys. Rev. B, 48 (1993) 2992. [17] W. Joswig, H. Fuess and G. Ferraris, Acta Crystallogr., Sect. B, 38 (1982) 2798. [18] M.I. McMahon, R.J. Nelmes, W.F. Kuhs, R. Dorwarth, R.O. Piltz and Z. Tun, Nature 348 (1990) 317. [19] A. Katrusiak, Phys. Rev. B, 51 (1995), in press. [20] M. Ichikawa, T. Gustafsson and I. Olovsson, Solid State Commun., 87 (1993) 349. [21] M. Ichikawa, S. Sato, M. Komukae and T. Osaka, Acta Crystallogr., Sect. C, 48 (1992) 1569.
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[22] M. Ichikawa, T. Gustafsson and I. Olovsson, Acta Crystallogr., Sect. C, 48 (1992) 603. [23] B.V. Merinov, N.B. Bolotina, A.I. Baranov and L.A. Shuvalov, Kristallografiya, 33 (1988) 1387. [24] Y. Noda, S. Uchiyama, K. Kafuku, H. Kasatani and H. Terauchi, J. Phys. Sot. Jpn., 59 (1990) 2804. [25] S. Fortier, M.E. Fraser and D. Heyding, Acta Crystallogr., Sect. C, 41 (1985) 1139. [26] I.P. Makarova, I.A. Verin and N.M. Schchagina, Sov. Phys. Crystallogr., 31 (1986) 105. [27] U.T. H(ichli, K. Knorr and A. Loidl, Adv. Phys., 39 (1990) 538. [28] R.J. Nelmes, Z. Tun and W.F. Kuhs, Ferroelectrics, 71 (1987) 125. [29] A.W. Hewat, Nature, 246 (1973) 90. [30] Y. Ono, T. Hikita and T. Ikeda, J. Phys. Sot. Jpn., 56 (1987) 577. S.A. Gridnev, L.N. Korotkov, S.P. Rogova, L.A. Shuvalov and R.M. Fedosyuk, Ferroelectrics, 126 (1992) 167. [31] E. Courtens, T.F. Rosenbaum, S.E. Nagler and P.M. Horn, Phys. Rev. B, 29 (1984) 515. [32] H. Grimm, K. Parlinski, W. Schweika, E. Courtens and H. Arend, Phys. Rev. B, 33 (1986) 4969. [33] S. Hayase, K. Kannon, H. Sakashita and H. Terauchi, J. Phys. Sot. Jpn., 55 (1986) 2695. [34] Y. Ono, T. Hikita and T. Ikeda, J. Phys. Sot. Jpn., 56 (1987) 577. (351 A.I. Olemskoi and A. Ya. Flat, Phys.-Usp., 36 (1993) 1087. [36] A.V. Belushkin, C.J. Carlile and L.A. Shuvalov, J. Phys. Condens. Matter, 6 (1994) 9929.
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 374 (1996) 161-169
Neutron powder diffraction studies of some superprotonic mixed crystals with disordered hydrogen bonds
and
A.V. Belushkin”>*, R.M. Ibbersonb, L.A. Shuvalovc aFrank Laboratory of Neutron Physics, JINR 141980 Dubna, Russia ‘ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 OQX, UK ‘Institute of Crystallography RAS, 117333 Moscow, Russia
Received 3 February 1995; accepted in final form 16 May 1995
Abstract Neutron diffraction is well known as an effective tool for studying proton location in a crystal lattice. During the last decade, the development of high-resolution powder diffractometers has provided an alternative method to single-crystal neutron diffraction in order to obtain this detailed structural information. The powder technique is rapid and appropriate, particularly in cases where obtaining single crystals is technically difficult. In this paper, several examples of the study of crystals with disordered hydrogen bonds are presented using the High-Resolution Powder Diffractometer, at the ISIS pulsed neutron source. These include a detailed description of the hydrogen bonding and phase transition behaviour in CsHS04 and in Cs,D(SeO,), and recent structural investigations on the mixed crystal K1_x(ND4)xD2P04.
1. Introduction Neutron diffraction has a particular advantage over X-ray diffraction in the determination of lightatom positions in the presence of heavy atoms in both organic and inorganic crystal structures. An
especially important case is that of hydrogen and its isotope deuterium for which techniques other than neutron diffraction are somewhat insensitive. In general, single-crystal diffraction provides the most accurate and precise measurements about the structural parameters of the system. However, in a number of cases it is technically very difficult to obtain single crystals that are large enough for neutron experiments, or such crystals are destroyed
* Corresponding author.
undergoing reconstructive phase transitions. The alternative is to use powder diffraction and a fullprofile (Rietveld) refinement procedure. Highresolution powder data minimises the Bragg peak overlap intrinsic to a l-dimensional powder diffraction profile and enables both accurate and precise structural studies to be carried out. In addition, the use of pulsed neutron sources and the time-of-flight technique gives advantages by the exploitation of the polychromatic neutron spectrum produced by the source. Moreover, a rich epithermal (short wavelength) flux provides the researcher with access to the very small interplane-distance region of a diffraction pattern. These characteristics are especially useful in the study of high-symmetry crystals (which produce a limited number of reflections at large d-spacings), some types of disorder and crystals with impurities where a large number
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of resolved reflections are required in order to perform a successful multiphase refinement. In this paper we present results of time-of-flight high-resolution neutron powder diffraction investigations of hydrogen-bonded compounds that exhibit different types of proton order-disorder transitions.
2. The high-resolution
powder diffractometer
(HRPD)
The HRPD at the ISIS pulsed neutron source (see for example Ref. [l]) is the highest resolution neutron diffractometer in the world and is designed to achieve an optimal balance between the maximum practical resolution attainable and reasonable counting times. The instrument is situated 100 m from a 100 K liquid-methane gadoliniumpoisoned moderator and incorporates a specially designed neutron guide in order to maintain a useful neutron flux over the long flightpath. The guide and moderator provide HRPD with an incident neutron flux of 0.5 I X 5 12 A, witoh a peak flux intensity at wavelengths around 2 A. The 100 m flightpath of HRPD minimises the timing uncertainty in the resolution function, and geometric contributions are minimised by utilising backscattering geometry. For the typically used (higher flux) 1 m position of the sample from the detector, the average scattering angle is 168.33” and the resolution is Ad/d M 8 x 10e4. Importantly, the resolution function is essentially independent of neutron wavelength. This factor, together with the availability of a significant epiJherma1 neutron flux, which gives access to sub-Angstrom Bragg reflections, is crucial to obtaining a high degree of accuracy in structural parameters. Diffractometers such as HRPD can yield extremely impressive powder-diffraction patterns containing a large number of reflections and hence a large amount of information. This enables HRPD to tackle areas more traditionally associated with single-crystal work, such as the study of “molecular” crystals. Structural studies in this area were pioneered with accurate and precise work on the structure of benzene [2], from which highquality data allow a full refinement including
anisotropic displacement parameters. The results were in good agreement with the best single-crystal measurements. Given the convenience of powderdiffraction data collection, for example in the case of low melting point compounds, and the short data collection times required, this is an extremely impressive result with considerable implications in organic crystal chemistry. The most obvious implication of the ability to study organic structures from powder samples is that it provides an opportunity to examine phase transitions. Not only is a rather rapid data collection time required to study, for example, the temperature dependence of a structure adequately, but also frequently the occurrence of a phase transition will destroy a single-crystal sample. Powder diffraction overcomes both these problems and work at ISIS on structural changes for example in the prototypic fullerene ChO, have shown that extremely subtle structural changes in this material can be characterised by using high-resolution neutron powder diffraction [3,4], helping, in this case, to resolve a problem in one of the hottest topics in structural science in recent years. Such an ability to study phase transitions in organics has large potential interest for both fundamental and practical reasons. For example, such experiments will yield information on the fundamental mechanisms governing transitions in organic systems. In addition, however, there are extremely practical benefits in terms of studying molecular energetics, with implications for reactivity, conformation and polymorphism. The limits of this technique in terms of unit-cell size (and indirectly the size and complexity of the structure) are continually being expanded, with one of the largest unit cell volumes successfully studied on HRPD to date being well over 1000 A3 in the case of toluene [5]. The potential of the technique in this area is outstanding.
3. The superprotonic phase transition in CsHS04 Caesium hydrogen sulphate and its deuterated analogue provide a classical example of a hydrogen-bonded superprotonic crystal [6]. At 414 K (412 K for the deuterated crystal), the
A.V. Belushkin et al./Journal of Molecular Structure 374 (1996) 161-169
structure undergoes a first-order phase transition characterised by a sharp increase in conductivity, reaching a value of lo-* R-i cm-‘. This superprotonic transition is of the improper ferroelastic type with a large spontaneous shear strain, lo-*. The latter leads to the destruction of single crystals just above the phase-transition temperature and therefore complicates any structural study. Attempts to solve the structure of the hightemperature phase and to explain the observed high protonic conductivity were made using X-ray diffraction on minute single crystals that could survive the transition [7] and by neutron powder diffraction using a medium-resolution diffractometer at a steady-state reactor [8]. Although the atomic coordinates for the heavy atoms (Cs and S) were in very good agreement in both studies, two different and conflicting models are proposed for the structure of the superprotonic phase with regard to the positions of oxygen atoms and protons. Furthermore, both models predict different mechanisms of protonic transport with neither in agreement with all other reported properties of the superprotonic phase. The structure obtained from the X-ray study assumed that oxygen occupies 16h positions in an 14,/amd lattice with a site occupancy of 0.5. This led to the conclusion that the protons are most probably stochastically distributed over the 8e sites; however, the possibility of 16h sites for the protons was also mentioned. Such a model implies unreasonably large distortions of the SO4 groups for proton migration through the lattice to occur. In addition, this model does not explain the experimentally observed proton conductivity which is essentially isotropic. Because the 8e sites form planes perpendicular to the tetragonal axis and are separated by a rather large distance, the proton conductivity is expected to be larger in the basal plane than along the tetragonal axis. Furthermore, the orientational disorder of HSO; groups observed by optical spectroscopy [9] and the entropy change at the transition, equal to 1.32R [lo], were not consistent with the structural model and there is no experimental data to support a hydrogendeuterium isotope effect on the phase-transition temperature. The second model, proposed on the basis of the
163
experiment using a conventional medium-resolution neutron diffractometer [8], assumed that, in the superprotonic phase, oxygen atoms occupy 32i positions with a probability of 0.5 and that the protons are stochastically distributed over the 16f positions with a site occupation factor of 0.25. The proton transport in this model is connected with the librational motion of HSO; groups and proton transfer between neighbouring 16h sites is achieved without distortion of the HSOT groups. This model successfully explains the observed entropy of the transition. The theoeretical value, R ln4, is in good agreement with the experimentally determined value, and the orientational disorder of HSOT groups is also explained. However, this model does not predict the observed lower conductivity along the tetragonal axis in comparison with that in the basal plane. Furthermore, the absence of an isotope effect on the transition temperature is not explained. In order to solve this structural problem, an experiment on HRPD using a deuterated (CsDSOJ sample was performed [ 111.Time-of-flight data were recorded over a d-spacing range of 0.6-5.4 A to yield a high-quality diffraction pattern. The data reveal only a limited number of high-intensity reflections occurring at large d-spacings. Thus, the majority of the structural information was contained in the data below d = 1.3 A. This fact highlights the limitations of the previous X-ray and medium-resolution neutron-diffraction studies. Data analysis was carried out using the in-house suite of time-of-flight profile refinement programs in order to obtain a definitive structure of the hightemperature phase. Although both models discussed above were initially tried in the profile refinement procedure, neither gave satisfactory results. The X-ray model yielded unrealistic distortions of SO4 tetrahedra and, using the model from the initial neutron study, a stable convergent refinement could not be achieved. In fact, a structural model proposed previously which combines elements of both models was found to best fit the data and readily explain all features of the superprotonic phase transition. It was found that, in the superprotonic phase, the oxygen site becomes split not into two, as predicted previously, but into four 32i sites in the crystal lattice. This permits the SO4
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group in the superprotonic phase to have four different orientations between which it can stochastically reorient, in contrast to the one, fully ordered, orientation of this group below the transition. Hydrogen bonding is thus possible both via 16h and 8e crystallographic sites, forming a highly disordered network with many vacant proton sites. This facilitates proton migration through the lattice in all crystallographic directions, explaining the isotropic nature of the protonic conductivity. The model assumes that the superprotonic phase transition in CsHS04 is governed by SO4 tetrahedra disordering over four orientations instead of just one possible orientation below the transition. This readily explains the observed transition entropy and, because the proton disorder in this model is only a secondary effect caused by SO4 dynamic orientational disorder, the virtual absence of the isotope effect on the phase-transition temperature also becomes clear. The orientational disorder of SO4 tetrahedra in this structural model is in full agreement with the results of optical spectroscopy mentioned above. Subsequently these structural results have been confirmed independently by quasi-elastic neutronscattering experiments [ 121 which prove the dynamic disorder of HSOT groups and longrange proton diffusion through the lattice.
4. The low-temperature phase transition in Cs@@eO& Tri-caesium deuterium biselenate undergoes a phase transition at 168 K which was first detected by dielectric measurements [13]. In the hydrogenated analogue, the transition temperature is much lower, by some 50 K. The large isotope effect on phase-transition temperature is indicative of the important role played by hydrogen bonds in the phase-transition mechanism. In order to study this phase transition, a single-crystal X-ray experiment was performed [14] and, independently, a high-resolution powder diffraction study using HRPD was carried out [15]. Both experiments gave consistent results for the atomic coordinates and temperature factors of the heavy atoms. Above the phase transition, CssD(Se04)2 is
monoclinic with space group C2/m and Z = 2 [ 141.The hydrogen bonds link selenium tetrahedra to form dimers with the deuteron situated either on a two-fold axis or disordered between two positions close to the two-fold axis. The lowtemperature phase transition in this compound involves the loss of the C-base centring observed at temperatures above the transition. As a result, the symmetry of the crystal below the transition becomes P2t/m. The phase transition does not lead to any significant changes in the atomic coordinates of any atoms except the deuterons. Below the transition, deuterium atoms no longer lie on a two-fold axis and thus are not constrained by symmetry to be equidistant from the tetrahedral selenate groups in the hydrogen-bonding scheme. The neutron powder diffraction experiment allowed a detailed description of the deuterium atom ordering in the low-temperature structure to be obtained which was not described by the single-crystal X-ray study. Since full details of the structure analysis are presented in the papers cited above, only the characteristic hydrogen-bond dimensions will be discussed here. Fig. 1 shows a schematic illustration of the hydrogen bond in Cs3D(Se04)2. It is evident that the deuteron is not equidistant from the neighbouring Se04 groups. The observed orientation of the thermal ellipsoid for the deuteron is perpendicular to the hydrogen bond. Furthermore, attempts to refine the structure assuming there to be two positions for deuterium along the bond have shown that only one of these two positions is fully occupied. These two findings exclude the possibility of deuterium atom disorder along the bond. The characteristic distances of the hydrogen bond are the following: ro_o =02.550(8) A, ro_o = 1.017(8) A, To-o’ = 1.533(8) A, (02,-D-022 = 178.4(7)“. Using the approach proposed in Ref. [16], one can calculate the distance, 6, between two deuteron sites in the hydrogen bond, above the phasetransition temperature, on the basis of structural data obtained below the transition. In the case of tri-caesium biselenate, this value is 0.52 A. To our knowledge, Cs3D(Se04)2 and NasH(S04)2 [17] are the only examples among the family of Me3H(X04)2 (Me=Na, K, Rb, Cs; X=S, Se) for which the value of S is precisely known. It is
A.V. Belushkin et al./Journal of Molecular Structure 374 (1996) 161-169
Fig. 1. Schematic illustration of the hydrogen-bond
therefore impossible at this stage to investigate whether there are any correlations between this parameter and the phase-transition temperature, as has been done for other hydrogen-bonded crystals [l&19]. However, a linear relation is observed between the transition temperature and oxygenoxygen hydrogen-bond distance at the transition temperature for this family of compounds [20]. We found that it is also possible to establish a relation between the hydrogen-bond length at room temperature (at which most of the experiments are performed) and the phase-transition temperature. I 2.55 -
2.51 1 0
I 50
I 100
I 150
I 200
Temperature, K Fig. 2. The relation between the phase-transition temperature associated with proton ordering in the hydrogen bond and the hydrogen-bond length ro_o defined at room temperature (according to Refs. [20-231).
165
structure in the low-temperature phase of Cs3(D(Se04)2
Fig. 2 shows a plot of the transition temperatures for different Me3H(A04)2 crystals versus ro_o distances obtained at room temperature. Two straight lines drawn through the experimental points (one line describes the hydrogeneous compounds and the other the deuterated analogues) on extrapolation intersect at absolute zero temperature at approximately the same ro-o value 2.517 A (note that the discrepancies, f0.002 A from this mean value are less than the experimental errors for the ro_o values). This value can therefore be considered as being the critical ro_o value for the phase transition. Thus, all crystals of the MesH(Se04)2 family which at room temperature have a hydrogen-bond length less than 2.517 A should not have a phase transition at lower temperatures associated with proton ordering in their hydrogen bonds. Clearly this conclusion is made on the basis of a limited set of data and more experiments are required in order to verify it. Nevertheless, our conclusion is suppotted by the fact that Na3H(S04)* bra-o = 2.432 A [17]), K3H(S04)z (ro-o = 2.493 A [24]), Rb3H(S04)2 (Y~_~~=2.485 A [25]) and Rb3H(Se04)2 (ro-o = 2.514 A [26]) do not undergo such a phase transition. We suggest, therefore, that, from knowledge of the roomtemperature structures of this type of compound, one can reliably predict the existence or absence of phase transitions connected with proton ordering to the hydrogen bond and the temperature of transition (without the need to measure the
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A.V. Belushkin et al./Journal of Molecular
temperature dependence of the crystal structure and without any assumptions about this dependence [201).
5. The mixed crystal K1_JND4),DzP04 Mixtures of certain ferroelectric and antiferroelectric crystals, over a particular composition range, transform into a proton dipolar glass at low temperature (see Ref. [27] for a review). Proton dipolar glasses may be regarded as having properties comparable to those exhibited by magnetic spin glasses. Pure parent compounds of these mixed crystals undergo a phase transition, associated with proton .ordering in the hydrogen bonds, which, in turn, leads to the appearance of dipolar moments that may be ordered either ferroelectrically or antiferroelectrically. When the parent compounds are mixed in appropriate proportions, the ferroelectric and antiferroelectric interactions compete, leading to frustration effects in the dipolar moment subsystem. The long-range electric order is thus suppressed and a proton dipolar glassy state results. However, and in contrast with magnetic spin glasses, the freezing into a proton glass state occurs over a large temperature range and has direct structural and dynamic consequences that can be studied experimentally. The mixed crystal Kt _x(ND4xD2P04 (DKADP) belongs to this class of compound. Its parent compounds KD2P04 [28] and ND4D2P04 (DADP) [29] are isostructural at room temperature and belong to the tetragonal space group 142d. On cooling, KADP undergoes a first-order phase transition from a paraelectric into a ferroelectric (FE) state (orthorhombic, space group Fdd2) and DADP undergoes a first-order transition into an antiferroelectric (AFE) state (orthorhombic, space group P2t2t2t). On mixing, the transition temperature decreases with increasing concentration of DADP and, over a specific composition range, 0.2 5 x _<0.8, neither an FE nor an AFE transition is realised [30]. Competition between FE and AFE interactions leads to the formation of a frustrated system which is believed to retain the tetragonal structure characteristic of the paraelectric state. This conclusion has been drawn on
Structure 374 (1996) 161-169
the basis of structural studies of a related system, Rb, _JND&D2P04 (RADP). The RADP system was extensively studied by different methods because these crystals are easily obtained across the whole composition range, due to the very similar unit-cell parameters of the crystal lattices of the parent compounds and the similar ionic radii of Rb and NH+ In particular, studies of the temperature variation of structure in the glass composition RADP [31,32] have shown that the tetragonal structure, characteristic of the paraelectric phase of the sample, is preserved down to liquid-helium temperature. Diffuse scattering was observed along the (100) direction, which peaks at a wave vector that corresponds to neither the FE nor the AFT phases of parent compounds. This diffuse scattering is quasi-elastic in character at temperatures above about 100 K; below this point, spatial correlations become static and saturate at about 30 K. In addition, anomalous thermal expansion of the crystal lattice is observed at low temperatures, due to proton glass formation as a result of the competing interactions between the different types of proton ordering [31,33]. Our aim was to investigate the temperature variation of the structure of DKADP and compare the results with those already observed in RADP. DKADP has not been previously studied because of the difficulties in obtaining samples of a homogeneous glass composition. The problem is caused by a large mismatch of the c-lattice parameters of the parent compounds. The powder DKADP sample was measured on HRPD and a section of the powder diffraction profile is shown in Fig. 3. All the lines may be indexed using the tetragonal space group 142d, characteristic of the paraelectric phase of the parent compounds. The lattice parameters obtained, a = b = 7.51079(3) A and c = 7.32968(7) A, are indicative of an ammonium concentration in the sample of x = 0.64 [34]. The most striking feature of the diffraction pattern obtained is that the width of most of the lines is considerably in excess of instrumental resolution and, moreover, neighbouring lines can have very different widths. Closer inspection reveals that the broadest peaks correspond to lines with larger 1 Miller indices. For example, a Gaussian fit to the group of diffraction
167
A.V. Belushkin et aLlJournal of Molecular Structure 374 (1996) 161-169
II
200 -
I !
1 /I
Diffraction
n
pattern
obtained 150 -
F r :: s
sample
from at
DKADP
room
temperature 100 -
/
h g t r-
:
50-
r”
1
6
m
1
‘0-I
,
I
1.8
1.7
1.9
I
2.0
D-spacing
/
2.1
(Angstrom)
/
2.2
I
I
2.3
Fig. 3. A section of the diffraction pattern obtained from &,36(NH4)0.64D2P04 at room temperature. The anisotropic peak-width variation of the diffraction lines is clearly seen.
lines around 2 A (see Fig. 3) shows that the (321) peak at d = 2.0037 A has a width of 0.0044 A, the (312) peak at 1.9933A has a width of 0.0075 A, and the (213) peak at d = 1.9763 A has a width of 0.016 A. This effect is attributedto large intrinsic
g 2.652 -
~.3S(ND4b4D2P04
??
cl (22O)posilion
1. 0
8, 50
0
1
100
”
’
.
150
“1.
200
’
250
300
1
TempetaUe (10
Fig. 4. The temperature dependence of the (220) diffraction line position for both crystal sublattices.
strains caused by the mismatch of the c-lattice parameters of the parent compounds. On cooling, the sample shows normal unit-cell contraction down to about 150 K. However, below this temperature splitting of some diffraction lines is observed; a shoulder appears, which increases in intensity with decreasing temperature. The magnitude of the splitting is essentially independent of temperature. For example, Fig. 4 shows the temperature dependence of the (220) diffraction peak position and its “shoulder”. The change in the diffraction pattern cannot be explained as being due to the precipitation of AFE and FE phases of the parent compounds. However, it is possible to index the observed diffraction profile assuming that there are two phases in the sample at low temperatures. One phase is orthorhombi$, with lattice parameters a = 7.4888 A, b = 7.5251 A, c = 7.2627 A, and the other phase is tetragonal, with0 lattice parameters 0 a = b = 7.4868 A, c = 7.2257 A. Fig. 5 illustrates the temperature changes of the
A. V. Belushkin et al./Journal of Molecular Structure 374 (1996) 161-169
168
,
.j.
‘i
Ko.,(NH4)o,~D2P04 i
;L_i 2.55
2.60
2.65
T=mK
1
2.70
d-swing, Angstrom
Fig. 5. A section of the diffraction pattern from the K,,36(NH4)0.MD2P04 sample at 290 K and 5 K. The inset shows the temperature dependence of the integrated intensity of the (220) reflection of one of the sublattices, together with the fit based on the empirical formula (see text).
diffraction pattern; the temperature dependence of the integrated intensity of the (220) reflection of the orthorhombic lattice is shown inset. The intensity of the corresponding line of the tetragonal lattice decreases coherently. Other lines show similar behaviour with temperature. It is possible to fit the observed temperature dependence using an empirical formula: Z = const x [{1 + tanha}(TO - T)] the result of the fit is shown in the inset in Fig. 5 by a solid line. Fitted parameters averaged over several different reflections are cx = (0.041 f 0.004) K-’ and To = (114 f 1) K. Qualitatively, this behaviour of the intensity can be explained within the multifractal formalism for the process of growth of the new phase [35]. However, a more comprehensive analysis of the data is still in progress. It is
interesting to note that To is very close to the estimated value of the temperature at which the reorientational motion of all ammonium groups in the protonated KADP sample become frozen [36]. In addition, this temperature is very close to the value at which the dynamic spatial correlations in RADP transform into static correlations [32]. Thus, the observed splitting may be attributed to the formation of a mixed state characterised by two sublattices, one of which retains tetragonal symmetry, characteristic of the paraelectric phase, the other of which is orthorhombic. We believe that this effect is a consequence of the frustration imposed by competing FE and AFE interactions. In RADP, this frustration leads to the appearance of diffuse streaks and, in our case, we believe the effect is more pronounced and leads to the formation of two sublattices because of stronger internal strains in DKADP. Finally, we note that the observed splitting disappears when the sample is heated above 150 K and that at room temperature the diffraction pattern of the thermally cycled sample is exactly the same as for the starting material. A full structural analysis of these data is presently under way and will be published elsewhere.
Acknowledgements The authors wish to express their thanks to Mrs. N.M. Shchagina, Mrs. R.M. Fedosyuk and Mrs. V.V. Dolbininoy for sample preparation, and the Daresbury and Rutherford Appleton Laboratory for access to the ISIS facilities.
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