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Crystal structure and mechanism of proton transport in the hexagonal phase of Cs5H3(SeO4)4·H2O
$otm Sml[! Solid State Ionics69 (1994) 153-161
ELSEVIER
Crystal structure and mechanism of proton transport in the hexagonal phase of Cs5H3 ( S e O 4 ) 4"H20 B.V. M e r i n o v ~, A.I. B a r a n o v , L.A. S h u v a l o v Institute of Crystallography of the Russian Academy of Sciences, Leninsky pr. 59, 117333 Moscow, Russia
J. S c h n e i d e r , H . S c h u l z lnstitut fiir Kristallographie und Mineralogie der Universiti~tMiinchen, Theresienstr. 41, 80333 Mfinchen 2, Germany
Received 10 February 1994;acceptedfor publication 18 February 1994
Abstract An X-ray diffraction single crystal study of the hexagonal high-temperature phase of Cs~H3(SeO4)4"H20 has been performed with the aim of determining the atomic structure and the mechanism of proton transport in this phase. 114,=1257.39, A(Mo Kct)=0.71076 A, hexagonal, P63/mmc, ah= 6.400(3 ), Ch=30.03( 1) A, V= 1065.2 A3, Z=2, Dx= 3.92 g.cm -3,/z= 160.2 cm -~, F(000) = 1104, T=360 K, R(F) =0.042, R(F)w=O.040 for 231 unique reflections. The results show that a dynamically disordered hydrogen bond network (DDHBN), which is responsible for the high protonic conductivity, exists in the hexagonal phase. In addition, some aspects of the high-temperature phase transition II-I were studied.
1. Introduction Alongside the complete and careful study of earlier-known compounds demonstrating properties of protonic conduction (see, e.g., [1-5 ] ), of great importance is the preparation and investigation of new chemical compounds having high protonic conductivity. Recently grown crystals of CssH3(SeO4)4"H20 (CTSeM) and CssH3(SO4)4"H20 (CTSM) and their deuterium analogues [6,7] are compounds belonging to the MsX3(AO4)4"X20 family, where M =NH4, K, Rb, Cs; X = H , D; A=S, Se. Only two representatives (CTSeM and CTSM) of this family have been the object of investigations so far, with intensive study of both of the above compounds in our laboratories. Present address: Hahn-Meitner-InstitutBerlin GmbH, Glienicker straBe 100,D-14109 Berlin,Germany.
The first of these, CTSeM, undergoes an improper ferroelastic first order phase transition at T=345 K [ 6 ]. The transition is accompanied by an increase in crystal symmetry from orthorhombic (space group Pbcn, phase II ) to hexagonal (space group P63/mmc, phase I) and marked changes in the transport properties of the protons (conductivity increases by two orders of magnitude). There are also series of anomflies in the temperature dependence of the dielectric constant at low temperatures [ 6 ]. Additional investigations are needed to reach final conclusions on their nature. With regard to X-ray investigations, data on the orthorhombic CTSeM phase II [ 6 ] and on the hexagonal phases of CTSeM and CTSM [ 8 ] have been obtained. The crystal structure and mechanism of proton transport in the high-temperature hexagonal phase I of CTSeM are discussed in this paper.
0167-2738/94/$07.00 © 1994ElsevierScienceB.V. All rightsreserved SSDI 0167-2738 (94) 00049-X
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B. V. Merinov et al. / Solid State lonics 69 (1994) 153-161
2. Experimental
Colourless translucent single crystals of CTSeM were grown at room temperature in a static regime from a supersaturated solution in the Laboratory of Phase Transition of the Institute of Crystallography (Moscow) by N.M. Schagina. The crystals have a plate-like form. The diffraction data were collected on an Enraf-Nonius CAD-4 automatic 4-circle X-ray diffractometer. The experimental details are listed in Table 1. The lattice constants were refined by leastsquares method from 24 reflections with I 1 < 0< 23. The intensities of reflections with I > 3tr(l) were converted to moduli of structure amplitudes taking into account corrections for the Lorentz and polarisation factors and for absorption. All crystallographic calculations were carried out using the AREN program system [9 ]. Atomic scattering factors were taken from [ 10 ]. All non-hydrogen atoms, except for the oxygen atom of the water molecule, were refined with anisoTable 1 Experimental parameters and details of refinement. Radiation Wavelength (A) Monochromator
Temperature (K) Crystal habit Diameter (mm) Space group ah (A)
ch (A)
r (A3) z D~ (gcm -3) hkl range
Mo Ka 0.71076 •graphite 360 Sphere 0.440 P63/ mmc
6.400(3) 30.03(1 ) 1065.2 2 3.92
0
Scan mode
to
Scan width (*) No. of reflections measured No. of reflections observed (1>3o,) Agreementfactor on IFI No. of unique reflections 20 limits Linear absorption coefficient (cm- t ) Isotropiesecondaryextinction Weight
3.0+0.35tg 0 5125 858
R R,.
0.037 231 1 < 20< 70* 160.2 0.1XI0 -6 1/o2(/7o) 0.042 0.040
tropic thermal parameters. Extinction was taken into account in the isotropic approximation according to Zachariasen's formalism [ 11 ]. Final positional and isotropic thermal parameters are listed in Table 2, the main interatomic distances in Table 3 and the thermal motion ellipsoids in Table 4.
3. Results and discussion 3.1. C r y s t a l s t r u c t u r e
The projection of the atomic structure of the hexagonal phase I of CTSeM is shown in Fig. 1. The Cs atoms completely occupy one 2 (b) and two 4 (D special positions, while the Se atoms occupy two special positions: one of them 4-fold (e) and the other 4-fold (f). Both the crystallographically distinct Se atoms have tetrahedral coordination. However, there are significant differences between the atoms which form the first See4 tetrahedron, and those forming the second. The O atoms that belong to the first tetrahedron completely occupy two special positions [4(e) and 12(k)] while the O atoms belonging to the second tetrahedron partially occupy two special 12 (k) and one general 24(l) position with occupancy coefficients ~ 1/2, 1/3 and 1/4, respectively. As repeatedly described earlier [ 12-16 ], such disordering of oxygen atoms of See4 tetrahedra reflects a dynamic disordering of the hydrogen bond subsystem in phases with high protonic conductivity, and is itself dynamic. Analysis of thermal vibrations (see Table 4) and electron density distribution of the oxygen and selenium atoms in the CTSeM phase I allows us to refer to a relatively static behaviour of the first tetrahedron and quite dynamic behaviour of the second. It should be noted that the picture of the electron density distribution of the second See4 tetrahedron is distinguished by its complexity. That is why, in this case, as in the case of the superprotonic phases of MHAO4 [12,17,18] and M3H(AO4)2 crystals [1315 ], the positions which are assigned to the O atoms of the second (mobile) see4 tetrahedron are, to some degree, average positions and therefore cannot completely reflect the complex picture of the dynamics of this tetrahedron. However, even those positions which have been determined for the O atoms of the "mobile" See4 tetrahedron indicate strong librations
155
B. V. Merinov et al. / Solid State lonics 69 (1994) 153-161
Table 2 Fractional atomic coordinates and isotropic thermal parameters (A z) with e.s.d.'s in parentheses.
Cs(1) Cs(2) Cs(3) Se(1) Se(2) O(I) 0(2) O(3)1 0(3)2 O(4) O(w)
x
y
z
0 1/3 2/3 0 2/3 0.1410(15) 0 0.5381(60) 0.377(15) 0.560(17) 0.272(12)
0 2/3 I/3 0 1/3 0.2820(22) 0 0.0762(85) 0.282(21) 0.280(12) 0.544(17)
1/4 0.13125(9) 0.02835(8) 0.06710(1) 0.1787(1) 0.0534(4) 0.1249(9) 0.2069(15) 0.1842(29) 0.1270(14) 0.2680(28)
0.0762 0.140 0.141
1/4 0.1260 0.1546
#
B,~" 7.65(14) 5.18(8) 3.12(5)
2.76(6)
112
I/4 I13 I/6
6.58(14) 3.94(32) 6.13(87) 7.14(87) 14.7(19) 8.0(17)
8.0 b
H-bonds H(I) H(2) H(3)
0.5381 0.280 0.189
1/3 1/6 1/12
• B~ = (4/3)~sfl0a~aj. b The thermal parameter of this atom was not refined.
(the angle of the libration relative to the central Se atom is approximately 40") and also rotation of the tetrahedron about its axis perpendicular to (001) plane (Fig. 1 ). Significant difficulties were encountered in the localisation of the H20 molecule. DTG data [ 6 ] and Raman spectra [ 19 ] show that the water contents of single crystal specimens does not significantly change up to the melting point, at about 510 K. However, the electron density peak that could be assigned to the H20 molecule is only slightly higher than the errors involved and some non-unique-values for the determination of the H20 position nevertheless remain. Having analysed available data and having attempted several possible sites for the water molecule in the structure of the CTSeM phase I, we arrive at the following conclusion: the oxygen atoms of the two water molecules per unit cell are perhaps disordered over the 12-fold (k) position with occupancy coefficient 1/6. The disordering of the water molecules is not "free", but must be correlated with the disordering of the "mobile" Se(2)O4 tetrahedra so as to avoid anomalously short distances between the water molecules and Se(2)O4 tetrahedra (see Table 3). It should be noted that, in fact, it is impossible to say definitely whether or not there are water molecules in the structure of the hexagonal high-temperature
phase I, if only X-ray diffraction data are being used. Before discussing a hydrogen bond system in CTSeM phase I, we would like to define the term "hydrogen bond position", which will be used subsequently. The term "hydrogen bond position" as used here refers to a crystallographic position which corresponds to the centre of the hydrogen bond, i.e. the middle of the distance between the oxygen atoms which participate in hydrogen bond formatiog. Defining such a notion allows two phenomena to be distinguished: the disordering of the hydrogen bond system as a whole, and the well-known proton disordering within the hydrogen bond, i.e. proton disordering over the two potential minima of a double-well H-bond. Three positions: 6(h), 12(k) and 24(1) of site occupancy about 1/3, 1/6 and 1/ 12, respectively, correspond to the hydrogen bonds formed with participation of the acid protons. In other words, the H-bond network which is ordered in phase II of CTSeM [ 6 ] becomes disordered in phase I. The H-bond lengths that result from the least-squares refinement of the positions of the corresponding oxygen atoms are equal to 2.59 (6), 3.10 (7) and 2.81 (9) A. However, due to dynamic disordering of the hydrogen bond network each oxygen atom of the "mobile" SeO4 tetrahedron alternatively participates in hydrogen bond forma-
Table 3 Main interatomic distances (A). Cs polyhedra
Cs( 1 )-0(3)2 -O(3)~,-~" -O(w) -O(w) i -O(w)* -O(w) t~-~i -O(3)~ -O(3)~-zi -0(2) --0(2) ~t Cs(3)-O(4) - 0 ( 4 ) xii-xiii -O( 1 ) -O( 1 )~ - 0 ( 1 ),,ii - 0 ( 1 ) "a'-m
(Nil)
( N 3) (Nil)
(N2)
(N6)
2.94(9) 2.94(9) 3.06(8) 3.06(8) 3.06(8) 3.06(8) 3.48(4) 3.48(4) 3.76(3) 3.76(3)
Cs(2)-O(3)2 --O(3)~ -O(3)~ -O(3)~ -'~ -O( 1) -O( 1)~ii -O(1 )uii -O(3)i -O(3)~ - 0 ( 3 ) ~ '~ -O(w) ~i -O(w) ~ t -O(w) "~i~ -0(4) -0(4) ~ - 0 ( 4 ) xii - 0 ( 4 ) '~ - 0 ( 4 ) ~" - 0 ( 4 ) n'~ -0(2) --0(2) ~ - 0 ( 2 ) "~
3.02(5) 3.02(5) 3.30( 1) 3.30( 1 ) 3.30( 1 ) 3.30(1)
(N3)
3.06(9) 3.06(9) 3.06(9) 3.06(9) 3.16(13) 3.16(13) 3.16(13) 3.21(5) 3.21 (5) 3.21 (5) 3.30(9) 3.30(9) 3.30(9) 3.44( 11 ) 3.44(6) 3.44(9) 3.44(3) 3.44(7) 3.44(3) 3.700(2) 3.700(2) 3.700(2)
Se tctrahedra
Se( 1)-0(1 ) -O(l)i - 0 ( 1 )~ -0(2)
1.62( 1) 1.62(1 ) 1.62(1 ) 1.73(3)
Se(2)-O(3), --0(3)~ ---0(3)~'~t -0(4) --0(4) ~ii --0(4) ~i --0(3)2 --0(3) i, -0(3)~ - - 0 ' ~3 /~x~tt 2 --0(3)~ '~a~ ---0(3)~~ '
1.66(5) 1.66(5) 1.66(5) 1.66(5) 1.66(5) 1.66(5) 1.72(10) 1.72(6) 1.72(10) 1.72(9) 1.72(9) 1.72(9)
0(2)-0(1 ) 0 ( 2 ) - 0 ( 1 )t 0 ( 2 ) - 0 ( 1 )~ 0 ( 1 ) - 0 ( 1 )~ O(1)-O(1) x O(l)t-O(1) x O(3)rO(3)~ O(3)t-O(3)~ ~'~i 0 ( 4 ) - 0 ( 4 ) x~t 0 ( 4 ) - 0 ( 4 ) xiii 0(4)-0(3)~ 0(4)-0(3)~ 0 ( 4 ) - 0 ( 3 ) ~ "~ 0(3):0(3)~ 0 ( 3 ) : 0 ( 3 ) ~ "~' 0(3)2-0(3)~
2.66(3) 2.66(3) 2.66(3) 2.71(15) 2.71(15) 2.71(15) 2.47(7) 2.47(7) 1.03(14) 1.03(9) 2.70(7) 2.70(7) 3.13(8) 1.29(12) 1.29(12) 1.20(15)
Disordered acid H-bonds O ( 3 h ... 0(3)~a
2.59(6)
0 ( 2 ) ...0(4)
3.10(9)
0 ( 2 ) ...0(3)2
2.81(9)
O(w)-O(3)~ v~ O(w)-O(3)~ O(w)-O(3)~ ii O(w)-O(3)~
(N2)
2.15(10) b 2.53(17) 2.53(9) 2.73(I0)
Disordered water molecule O(w)--O(w) *i O(w)-O(w) ~a O(w)-'O(W) xli
1.08(12) 1.19(14) 1.19(9)
(N2)
• Symmetry codes: (i) x, x - y , z; (ii) y - x , y, z;, (iii) y - x , - x , 1 / 2 - z ; (iv) - y , x - y , l / 2 - z ; (v) - y , - x , 1 / 2 - z ; (vi) - y , x - y , z; (vii) y - x , y, I/2-z;, (viii) y - x , - x , z; (ix) x, x - y , l/2-zq, (x) - y , - x , z; (xi) x, y, 1 / 2 - z ; (xii) 1- y , 1 - x , z; (xiii) 1+ y - x , y, z; (xiv) I - x , I - y , - z ; (xv)y, x, - z ; (xvi) I - x , y - x , - z ; (xvii) l + x , l + x - y , z; (xviii) l + x , y, z; (xix) I - y , - x , z; (xx) I - y , l + x - y , z; (xxi) y - x , I - x , z;, (xxii) x, l + x - y , z; (xxiii) I - y , I - x , 1 / 2 - z ; (xxiv) x, l + x - y , 1 / 2 - z ; (xxv) x, l+y, z; (xxvi) 1 + y - x , 1 +y,z;, (xxvii) 1 - y , x - y , z;, (xxviii) 1+ y - x , 1 - x , z; (xxix) i - y , x - y , z; (xxx) 1+ y - x , y, l / 2 - z . b These distances and probably O (w)-O (3)~,~,a do not really occur in the structure. The water molecule can occupy the corresponding site if the O atoms of the base of the nearest "mobile" Se (2)O4 tetrahedron occupy suitable sites [for instance, O (3)~, O (3)y~' and O(3)~ iii ] of the 24 (1) position.
B. K Merinov et al. / Solid State lonics 69 (1994) 153-161 Table 4 Thermal motionellipsoids
Cs(l)
Cs(2)
Cs(3)
Se(1)
Se(2)
O(1)
0(2)
O(3)1
0(3)2
0(4)
R.m.s. amplitude (A)
~
Pb
~c
0.075 0.108 0.108 0.047 0.075 0.075 0.035 0.035 0.048 0.031 0.037 0.037 0.078 0.086
90 150 60 90 150 60 60 150 90 90 150 60 90 150
90 30 60 90 30 60 60 30 90 90 30 60 90 30
0 90 90 0 90 90 90 90 0 0 90 90 0 90
0.086
60
60
9O
0.040 0.046 0.063 0.069 0.082 0.082 0.042 0.100 0.129 0.029 0.190 0.341 0.058 0.112 0.132
90 180 90 90 150 60 90 90 180 33 123 92 74 120 35
31 60 97 90 30 60 48 56 60 93 38 52 90 0 90
81 90 9 0 90 90 130 40 90 110 127 44 18 90 108
• go, gb and gc are angles between principal axes of thermal motion ellipsoidsand coordinateaxes (o).
tion or not and, in accordance with this, occupies a corresponding position. X-ray data give an average picture and therefore the real lengths of the hydrogen bonds can be shorter than the calculated ones. Moreover, for two last H-bonds [ 3.10 (7) and 2.81 (9) A ], slight tilting of the "static" SeO4 tetrahedron is possible during the formation of the hydrogen bonds. The observed anisotropy of the thermal vibrations of the oxygen atoms belonging to this tetrahedron can be regarded as being caused by these inclinations. As a result of these factors, the true lengths of the hydrogen bonds are then approximately 0.2-0.5 A, less than the calculated O... O distances. From the lengths of all three non-equivalent hydrogen bonds formed with the participation of the acid protons, they are, most
157
probably, of the double-minimum type, and only the hydrogen bond O (3) ~-H ( 1 )...O ( 3 ) ]i that occupy the 6(h) position is symmetric, the others [ 0 ( 2 ) H(2)...O(4) and O(2)-H(3)...O(3)2] are asymmetric even in the high,symmetry phase I. For the sake of completeness of description of the crystal structure of the CTSeM phase I, we return once more to the Cs atoms and, in particular, focus our attention on their coordination polyhedra. As reported above, in the CTSeM crystal structure there are three independent Cs atoms: Cs( 1 ) lies in the 2(b) position; Cs(2) and Cs(3) occupy two 4(f) positions. The Cs(1) polyhedron is the most interesting. Mainly, this polyhedron is formed by the oxygen atoms of the "mobile" SeO4 tetrahedron and of the H20 molecules (except for the two most distant O atoms). Because of the specific behaviour of the "mobile" SeO4 tetrahedron, i.e. the strong librations and rotation, and disordering of the H20 molecules, there are changes not only in the shape of the Cs ( 1 ) polyhedron but also in its coordination number (see Table 3). The maximum number of O atoms coordinating Cs(1) is 17. The corresponding C s ( l ) - O distances lie in the range from 2.94 (8) to 3.76 (3) A. The Cs (2) polyhedron also changes with time, but the coordination number remains constant at 13. Seven vertices of this polyhedron are O atoms of the " m o b i l e " SeO4 tetrahedra and disordered H20 molecules. The remaining six vertices are the O atoms of "static" tetrahedra. The Cs ( 2 )-O distances lie in the range from 3.05( 1 ) to 3.702( 1 ) A. The Cs (3) atoms have an almost ordinary ten-fold coordination. Only one of these oxygen atoms belongs to the "mobile" SeO4 tetrahedron, and it is disordered over three equivalent sites (in Fig. 16 it is the vertex of the "mobile" tetrahedron). The Cs ( 3 ) O distances are equal to 3.02(5)-3.301 (9) A. Such unusual behaviour in the oxygen environment of the first two Cs atoms must influence the Cs( 1 ) and Cs(2) atoms themselves. The thermal parameters (isotropic and anisotropic, i.e. the lengths of the principal axes of the thermal vibration ellipsoids) of Cs( 1 ) are approximately 1.5 times greater than the corresponding values of Cs(2) and twice those of Cs (3). It is possible that the thermal vibrations at least of Cs(l) and Cs(2) atoms are anharmonic.
158
B. V. Merinov et al. / Solid Staw lonics 69 (1994) 153-161
bh ,:,
,,', ,' : ',
;;', ;;" /
; \
/ ~h Fig. 1. Projection of the crystal structure of the hexagonalCTSeM phase I on the (001) plane. Largeopen circles: Cs atoms; tetrahedra: SeO4groups; partly filled circles: H20 molecules.The DDHBN are marked by dashed lines betweentetrahedra and by small open circles which show the H-bondsperpendicularto the (001 ) plane. The smallfilled circlesshowthree equallyprobablesites of a vertex of a SeO4 tetrahedron near a hexad (63) axis and the arrowsbetween them mark librations of the SeO4tetrahedra. Rotations of the tetrahedra are shown by arrows on the largestcircles. The tetrahedra drawn by thin lines showthe other possible orientationsof the SeO4groups.
3.2. Structural m e c h a n i s m o f proton transport
The presence of similar features in the atomic arrangement of crystals of the MaX(AO4)2 and MsXa(AO4)4"X20 families is reflected in the observed physical properties. Protonic conductivity of CTSeM crystals [7], like that of M3X(AO4)2 crystals [ 2,13,20,21 ], is quasi-two-dimensional. In the (001 ) plane of the hexagonal cell the conductivity is 1-2 orders of magnitude higher than in the perpendicular direction. However, there are some important differences in the structural mechanisms of proton conductivity of these two families. In trigonal phases of M3X(AO4)2 the proton pathways in the (001) plane include only symmetrically equivalent sites. As for the hexagonal phase of CTSeM, three non-equivalent acid H-bonds exist in the crystal structure. Moreover, two of the three acid H-bonds are asymmetric, and, therefore, the pathways of proton diffusion in CTSeM include non-equivalent proton sites. From an energetic viewpoint, such motion is less advantageous than motion over symmetrically
equivalent sites. During proton transport in CTSeM different orientations of SeO4 tetrahedra are formed in the crystal structure. If it is assumed that one of a number of orientations of the SeO4 tetrahedra (Fig. 2) can occur in the hexagonal phase of CTSeM at any given moment of time then, as a first approximation, a fragment of the structure of the orthorhombic phase II (Fig. 2a) can be regarded as an example of one of these orientations. At the next moment, SeO4 tetrahedra can mutually change their orientation forming new hydrogen bonds in other possible sites (interbond motion: proton motion between H-bonds, see [ 15,22 ] ), and a new orientation of the tetrahedra is formed (Fig. 2). The projection of the structure, averaged over different orientations of the SeO4 tetrahedra, of the hexagonal phase I of CTSeM along ah is shown in Fig. 3. It is deafly seen that the hydrogen bonds, (marked by dashed lines in Fig. 3) partially occupying the "principal" 6(h), 12(k) and 24(1) positions, join the SeO4tetrahedra into layers perpendicular to the Ch axis. Proton transport mainly occurs within these layers. In the unit cell there are two
B. V. Merinov et al. / Solid State l onics 69 (1994) 153-161
159
ch
t
a
O I
i
t
,"
\
b
'1
."'....
_
..\
i
c
.
i
i
--'',
°'°.
,
t
-O):" '
i "'.
""°.
i",l
o
!"..4 £
F~ 3. Projectionof the crystalstructureof the hexagonalCTSeM d
phase I along ah, averaged over all orientationsof the SeO4tet-
Fig. 2. Examples of different possible orientations of the SeO4 tetrahedra in the hexagonal CTSeM phase I.
circles, H20 molecules;dashed lines: "principal" H-bonds and
such symmetrically equivalent layers which are related by a centre of symmetry. The "static" SeO4 tetrahedra are placed in the outer surfaces of the layers. By slightly changing their orientation, they perform a supporting role in the proton transport process. Only one vertex of these tetrahedra directly participates in the formation of the "principal" hydrogen bonds. The relative inertness of the "static" SeO4 tetrahedra is compensated by the very active behaviour of the "mobile" SeO4 tetrahedra. These tetrahedra play the main role in proton transport and form the cores of the layers. All of the vertices of the "mobile" tetrahedra directly participate in the formation o f a dy-
namically disordered network of "principal" Hbonds. By marked librations and even rotation (see Section 3.3) these tetrahedra perform the function of gear-wheels, which set the mechanism of proton transport in motion. Recall that all of three non-equivalent "principal" hydrogen bonds, formed by the participation of the acid protons, are double-minimum, and that only one of them, which lies in the 6(h) position, is symmetric. Saturation of the "mobile" SeO4 tetrahedra by Hbonds requires a particular proton location in these bonds. A configuration in which the protons are dis-
rahedra. Open circles:Cs atoms;tetrahedra: SeO4groups;dotted dotted lines: "supplementary"H-bonds.
160
B.V. Merinov et al. / Solid State lonics 69 (1994) 153-161
3.3. High-temperature phase transition II-I
subgroup) and multiplication of the cell [ D ~h (Z = 2 ) - D i~ ( Z = 8 ) ], is improper ferroelastic. This is confirmed by the formation of the corresponding domains in phase II. The interrelation of the unit cell parameters of phases I and II can be represented as follows: ah ~ 1/2bo, bh ~ 1/4 (2Co-bo) and Ch~ ao (the subscripts h and o denote hexagonal and orthorhombic phases respectively). The increase of the protonic conductivity by two orders of magnitude in phase I as compared with phase II indicates that changes occur in the nature of the proton subsystem during the II-I transition. In the orthorhombic phase II of CTSeM, the acid protons completely occupy three general 8(d) positions. During the transition to the hexagonal phase these positions are transformed into positions with higher multiplicity (with some approximation three 12(k) and two 24(1) positions which correspond to potential minima of the acid hydrogen bonds (Table 2) can be regarded as these positions), so that the number of sites which the protons can occupy becomes more than the number of protons themselves, i.e. disordering of the hydrogen bond network occurs. Another problem of the II-I phase transition in CTSeM is the problem of reversibility of this transition. Even after pre-heating the crystal, the transition to the hexagonal phase was accompanied by significant deterioration of the quality of the crystal being studied, which was manifested as a marked broadening of the diffraction peaks and a distortion of their shape. It was impossible to use a single crystal X-ray diffraction method for studying the crystal after cooling it from high-temperature hexagonal phase to room temperature. After powder X-ray diffraction investigations 2, it was concluded that, as a rule, the samples return to the initial state (orthorhombic phase) after one or two cycles of heating above the temperature of the II-I phase transition and subsequent cooling to room temperature, although there are some changes in intensities of the reflections. If the number of the heating-cooling cycles is more than two, the diffraction quality of the samples is strongly degraded. These changes correlate with decreasing the
In accordance with the symmetry criteria of Landau's theory of phase transitions [24,25 ], the I-II transition in CTSeM, occurring with a change of symmetry D~h (P63/mmc)-D[ 4 (Pbcn) (group-
2 Structural parameters obtained from the refinement of the atomic structure of the orthorhombic phase II and of the hexagonal phase I from powder diffraction data are in a good agreement with those obtained from single crystal data.
tant enough from each other, i.e. they are in the potential wells which are remote from O atoms of the "mobile" tetrahedra, is the most preferable. For asymmetric hydrogen bonds these potential wells are also deeper. However, during transfer of the protons it is necessary that they be in the potential wells which are nearest to the O atoms of the "mobile" SeO4 tetrahedra (intrabond motion: proton motion within a double-minimum hydrogen bond; see [ 15,22 ] ). Additional energy is required in this case due to the combination of a proton configuration which becomes non-optimal around the "mobile" SeO4 tetrahedra, with proton transfer within the H-bonds from a deeper potential minimum to a relatively shallow one. That is one of the reasons why, in spite of the presence of a dynamically disordered hydrogen bond network (DDHBN), the values of the parameters characterising protonic conductivity in the hexagonal CTSeM phase in the (001) plane (Ha~0.6 eV and tr~ 10 -5 S cm -I ) manifestly do not achieve superionic values (Ha< 0.3 eV and tr> 10 - 3 S c m - l ). Another reason which was discussed in [ 23], is the absence of conduction channels for the protons in the crystal structure of CTSeM. Conductivity along [001 ] is lower (Ha ~ 0.9 eV and 0"~ 10 - 7 S c m - I ) than in the (001)plane because, in order for proton transport to occur in the [001 ] direction, as in the case of the MXAO4 and M 3 X ( A O 4 ) 2 families, there must be formation of "supplementary" H-bonds (shown in Fig. 3 as the dotted lines), the probability of which is markedly lower than that of "principal" H-bonds. It is possible that water molecules also participate in proton transport. The mechanism of proton transfer here is similar to the Grotthuss mechanism, except that the protons are not transferred from one molecule of water to another, but from a n H 2 0 molecule to an O atom (connected to the molecule via a H-bond) of the "mobile" SeO4 tetrahedron, and vice versa.
B. V. Merinov et al. / Solid State Ionics 69 (1994) 153-161
proton conductivity and suppressing its anomaly at the phase transition during heating-cooling cycles. Most probably, it is a consequence of the formation of proton glass state similar to that observed in CTSM crystals [7]. Further investigations are underway which will enable the nature of these phenomena to be determined.
Acknowledgement One of the authors (B.V. Merinov) thanks Alexander von Humboldt Stiftung (Germany) for supporting this work.
References 1 ] A.I. Baranov, LA. Shuvalov and N.M. Schagina, JETP Lett. (USSR) 36 (1982) 459. 2]A.I. Baranov, B.V. Merinov, A.V. Tregubchenko, L.A. Shuvalov and N.M. Schasina, Ferroelectrics 81 (1988) 187. 3]B.V. Merinov, N.B. Bolotina, A.I. Baranov and L.A. Shuvalov, SOy. Phys. Crystallogr. 33 (1988) 824. 4]B.V. Merinov, N.B. Bolotina, A.I. Baranov and L.A. Shuvalov, SOy. Phys. Crystallogr. 36 ( 1991 ) 639. 5] M. Ichikawa, 1". Gustafsson and I. Olovsson, Acta Cryst. B48 (1992) 633. 6]B.V. Merinov, A.I. Baranov, L.A. Shuvalov and N.M. Schagina, SOy. Phys. Crystallogr. 36 (1991) 321. 7]A.I. Baranov, O.A. Kabanov, B.V. Merinov and L.A. Shuvalov, Ferroelectrics 127 (1992) 257. 18] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, J. Schneider and H. Schulz, in preparation.
161
[9] V.I. Andrianov, SOy. Phys. Crystallogr. 32 (1987) 130. [ 10 ] InternationalTables for X-ray Crystallography, Vol. IV (The Kynoch Press, Birmingham, 1974). [ 11 ] W.H. Zachariasen, Acta Cryst. 23 (1967) 558. [12]B.V. Merinov, A.I. Baranov, L.A. Shuvalov and B.A. Maksimov, SOv. Phys. Crystallogr. 32 (1987) 47. [13]A.I. Baranov, I.P. Makarova, L.A. Muradyan, A.V. Tregubchenko, L.A. Shuvalov and V.I. Simonov, SOy.Phys. Crystallogr. 32 (1987) 400. [14]A.I. Baranov, B.V. Merinov, A.V. Tregubchenko, V.P. Khiznichenko, L.A. Shuvalov and N.M. Schagina, Solid State Ionics 36 (1989) 279. [ 15 ] B.V. Merinov, A.I. Baranov, and L.A. Shuvalov, SOy. Phys. Crystallogr. 35 (1990) 200. [16]B.V. Merinov, M.Yu. Antipin, A.I. Baranov, A.V. Tregubchenko, L.A. Shuvalov and Yu.T. Struchkov, SOy. Phys. Crystallogr. 36 ( 1991 ) 488. [17]Z. Jirak, M. Dlouha, S. Vratislav, A.M. Balagurov, A.I. Beskrovnyi, V.I. Gordelii, I.D. Datt and L.A. Shuvalov, Phys. Status Solidi (a) 100 ( 1987 ) KI 17. [18]A.V. Belushkin, W.I.F. David, R.M. Ibberson and L.A. Shuvalov, Acta Cryst. B47 ( 1991 ) 161. [ 19] V.P. Dmitriev, private communication (1992). [20] A.I. Baranov, A.V. Tregubchenko, L.A. Shuvalov and N.M. Schagina, SOy. Phys. Solid State 29 (1987) 1448. [21 ] A. Pawlowski, Cz. Pawlaczyk and B. Hilczer, Solid State Ionics 44 (1990) 17. [22]R. Blinc, J. Dolinsek, G. Lahajnar, I. Zupancic, L.A. Shuvalov and A.I. Baranov, Phys. Status Solidi (b)123 (1984) K83. [ 23 ] B.V. Merinov and L.A. Shuvalov, SOv.Phys. Crystallogr. 37 (1992) 211. [24] L.D. Landau and E.M. Lifshits, Statistical Physics, Vol. 5 ( Nauka, Moscow, 1964). [ 25 ] P. Toledano and J.-CI. Toledano, Ferroelectrics 21 (1978) 587.
ELSEVIER
Crystal structure and mechanism of proton transport in the hexagonal phase of Cs5H3 ( S e O 4 ) 4"H20 B.V. M e r i n o v ~, A.I. B a r a n o v , L.A. S h u v a l o v Institute of Crystallography of the Russian Academy of Sciences, Leninsky pr. 59, 117333 Moscow, Russia
J. S c h n e i d e r , H . S c h u l z lnstitut fiir Kristallographie und Mineralogie der Universiti~tMiinchen, Theresienstr. 41, 80333 Mfinchen 2, Germany
Received 10 February 1994;acceptedfor publication 18 February 1994
Abstract An X-ray diffraction single crystal study of the hexagonal high-temperature phase of Cs~H3(SeO4)4"H20 has been performed with the aim of determining the atomic structure and the mechanism of proton transport in this phase. 114,=1257.39, A(Mo Kct)=0.71076 A, hexagonal, P63/mmc, ah= 6.400(3 ), Ch=30.03( 1) A, V= 1065.2 A3, Z=2, Dx= 3.92 g.cm -3,/z= 160.2 cm -~, F(000) = 1104, T=360 K, R(F) =0.042, R(F)w=O.040 for 231 unique reflections. The results show that a dynamically disordered hydrogen bond network (DDHBN), which is responsible for the high protonic conductivity, exists in the hexagonal phase. In addition, some aspects of the high-temperature phase transition II-I were studied.
1. Introduction Alongside the complete and careful study of earlier-known compounds demonstrating properties of protonic conduction (see, e.g., [1-5 ] ), of great importance is the preparation and investigation of new chemical compounds having high protonic conductivity. Recently grown crystals of CssH3(SeO4)4"H20 (CTSeM) and CssH3(SO4)4"H20 (CTSM) and their deuterium analogues [6,7] are compounds belonging to the MsX3(AO4)4"X20 family, where M =NH4, K, Rb, Cs; X = H , D; A=S, Se. Only two representatives (CTSeM and CTSM) of this family have been the object of investigations so far, with intensive study of both of the above compounds in our laboratories. Present address: Hahn-Meitner-InstitutBerlin GmbH, Glienicker straBe 100,D-14109 Berlin,Germany.
The first of these, CTSeM, undergoes an improper ferroelastic first order phase transition at T=345 K [ 6 ]. The transition is accompanied by an increase in crystal symmetry from orthorhombic (space group Pbcn, phase II ) to hexagonal (space group P63/mmc, phase I) and marked changes in the transport properties of the protons (conductivity increases by two orders of magnitude). There are also series of anomflies in the temperature dependence of the dielectric constant at low temperatures [ 6 ]. Additional investigations are needed to reach final conclusions on their nature. With regard to X-ray investigations, data on the orthorhombic CTSeM phase II [ 6 ] and on the hexagonal phases of CTSeM and CTSM [ 8 ] have been obtained. The crystal structure and mechanism of proton transport in the high-temperature hexagonal phase I of CTSeM are discussed in this paper.
0167-2738/94/$07.00 © 1994ElsevierScienceB.V. All rightsreserved SSDI 0167-2738 (94) 00049-X
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B. V. Merinov et al. / Solid State lonics 69 (1994) 153-161
2. Experimental
Colourless translucent single crystals of CTSeM were grown at room temperature in a static regime from a supersaturated solution in the Laboratory of Phase Transition of the Institute of Crystallography (Moscow) by N.M. Schagina. The crystals have a plate-like form. The diffraction data were collected on an Enraf-Nonius CAD-4 automatic 4-circle X-ray diffractometer. The experimental details are listed in Table 1. The lattice constants were refined by leastsquares method from 24 reflections with I 1 < 0< 23. The intensities of reflections with I > 3tr(l) were converted to moduli of structure amplitudes taking into account corrections for the Lorentz and polarisation factors and for absorption. All crystallographic calculations were carried out using the AREN program system [9 ]. Atomic scattering factors were taken from [ 10 ]. All non-hydrogen atoms, except for the oxygen atom of the water molecule, were refined with anisoTable 1 Experimental parameters and details of refinement. Radiation Wavelength (A) Monochromator
Temperature (K) Crystal habit Diameter (mm) Space group ah (A)
ch (A)
r (A3) z D~ (gcm -3) hkl range
Mo Ka 0.71076 •graphite 360 Sphere 0.440 P63/ mmc
6.400(3) 30.03(1 ) 1065.2 2 3.92
0
Scan mode
to
Scan width (*) No. of reflections measured No. of reflections observed (1>3o,) Agreementfactor on IFI No. of unique reflections 20 limits Linear absorption coefficient (cm- t ) Isotropiesecondaryextinction Weight
3.0+0.35tg 0 5125 858
R R,.
0.037 231 1 < 20< 70* 160.2 0.1XI0 -6 1/o2(/7o) 0.042 0.040
tropic thermal parameters. Extinction was taken into account in the isotropic approximation according to Zachariasen's formalism [ 11 ]. Final positional and isotropic thermal parameters are listed in Table 2, the main interatomic distances in Table 3 and the thermal motion ellipsoids in Table 4.
3. Results and discussion 3.1. C r y s t a l s t r u c t u r e
The projection of the atomic structure of the hexagonal phase I of CTSeM is shown in Fig. 1. The Cs atoms completely occupy one 2 (b) and two 4 (D special positions, while the Se atoms occupy two special positions: one of them 4-fold (e) and the other 4-fold (f). Both the crystallographically distinct Se atoms have tetrahedral coordination. However, there are significant differences between the atoms which form the first See4 tetrahedron, and those forming the second. The O atoms that belong to the first tetrahedron completely occupy two special positions [4(e) and 12(k)] while the O atoms belonging to the second tetrahedron partially occupy two special 12 (k) and one general 24(l) position with occupancy coefficients ~ 1/2, 1/3 and 1/4, respectively. As repeatedly described earlier [ 12-16 ], such disordering of oxygen atoms of See4 tetrahedra reflects a dynamic disordering of the hydrogen bond subsystem in phases with high protonic conductivity, and is itself dynamic. Analysis of thermal vibrations (see Table 4) and electron density distribution of the oxygen and selenium atoms in the CTSeM phase I allows us to refer to a relatively static behaviour of the first tetrahedron and quite dynamic behaviour of the second. It should be noted that the picture of the electron density distribution of the second See4 tetrahedron is distinguished by its complexity. That is why, in this case, as in the case of the superprotonic phases of MHAO4 [12,17,18] and M3H(AO4)2 crystals [1315 ], the positions which are assigned to the O atoms of the second (mobile) see4 tetrahedron are, to some degree, average positions and therefore cannot completely reflect the complex picture of the dynamics of this tetrahedron. However, even those positions which have been determined for the O atoms of the "mobile" See4 tetrahedron indicate strong librations
155
B. V. Merinov et al. / Solid State lonics 69 (1994) 153-161
Table 2 Fractional atomic coordinates and isotropic thermal parameters (A z) with e.s.d.'s in parentheses.
Cs(1) Cs(2) Cs(3) Se(1) Se(2) O(I) 0(2) O(3)1 0(3)2 O(4) O(w)
x
y
z
0 1/3 2/3 0 2/3 0.1410(15) 0 0.5381(60) 0.377(15) 0.560(17) 0.272(12)
0 2/3 I/3 0 1/3 0.2820(22) 0 0.0762(85) 0.282(21) 0.280(12) 0.544(17)
1/4 0.13125(9) 0.02835(8) 0.06710(1) 0.1787(1) 0.0534(4) 0.1249(9) 0.2069(15) 0.1842(29) 0.1270(14) 0.2680(28)
0.0762 0.140 0.141
1/4 0.1260 0.1546
#
B,~" 7.65(14) 5.18(8) 3.12(5)
2.76(6)
112
I/4 I13 I/6
6.58(14) 3.94(32) 6.13(87) 7.14(87) 14.7(19) 8.0(17)
8.0 b
H-bonds H(I) H(2) H(3)
0.5381 0.280 0.189
1/3 1/6 1/12
• B~ = (4/3)~sfl0a~aj. b The thermal parameter of this atom was not refined.
(the angle of the libration relative to the central Se atom is approximately 40") and also rotation of the tetrahedron about its axis perpendicular to (001) plane (Fig. 1 ). Significant difficulties were encountered in the localisation of the H20 molecule. DTG data [ 6 ] and Raman spectra [ 19 ] show that the water contents of single crystal specimens does not significantly change up to the melting point, at about 510 K. However, the electron density peak that could be assigned to the H20 molecule is only slightly higher than the errors involved and some non-unique-values for the determination of the H20 position nevertheless remain. Having analysed available data and having attempted several possible sites for the water molecule in the structure of the CTSeM phase I, we arrive at the following conclusion: the oxygen atoms of the two water molecules per unit cell are perhaps disordered over the 12-fold (k) position with occupancy coefficient 1/6. The disordering of the water molecules is not "free", but must be correlated with the disordering of the "mobile" Se(2)O4 tetrahedra so as to avoid anomalously short distances between the water molecules and Se(2)O4 tetrahedra (see Table 3). It should be noted that, in fact, it is impossible to say definitely whether or not there are water molecules in the structure of the hexagonal high-temperature
phase I, if only X-ray diffraction data are being used. Before discussing a hydrogen bond system in CTSeM phase I, we would like to define the term "hydrogen bond position", which will be used subsequently. The term "hydrogen bond position" as used here refers to a crystallographic position which corresponds to the centre of the hydrogen bond, i.e. the middle of the distance between the oxygen atoms which participate in hydrogen bond formatiog. Defining such a notion allows two phenomena to be distinguished: the disordering of the hydrogen bond system as a whole, and the well-known proton disordering within the hydrogen bond, i.e. proton disordering over the two potential minima of a double-well H-bond. Three positions: 6(h), 12(k) and 24(1) of site occupancy about 1/3, 1/6 and 1/ 12, respectively, correspond to the hydrogen bonds formed with participation of the acid protons. In other words, the H-bond network which is ordered in phase II of CTSeM [ 6 ] becomes disordered in phase I. The H-bond lengths that result from the least-squares refinement of the positions of the corresponding oxygen atoms are equal to 2.59 (6), 3.10 (7) and 2.81 (9) A. However, due to dynamic disordering of the hydrogen bond network each oxygen atom of the "mobile" SeO4 tetrahedron alternatively participates in hydrogen bond forma-
Table 3 Main interatomic distances (A). Cs polyhedra
Cs( 1 )-0(3)2 -O(3)~,-~" -O(w) -O(w) i -O(w)* -O(w) t~-~i -O(3)~ -O(3)~-zi -0(2) --0(2) ~t Cs(3)-O(4) - 0 ( 4 ) xii-xiii -O( 1 ) -O( 1 )~ - 0 ( 1 ),,ii - 0 ( 1 ) "a'-m
(Nil)
( N 3) (Nil)
(N2)
(N6)
2.94(9) 2.94(9) 3.06(8) 3.06(8) 3.06(8) 3.06(8) 3.48(4) 3.48(4) 3.76(3) 3.76(3)
Cs(2)-O(3)2 --O(3)~ -O(3)~ -O(3)~ -'~ -O( 1) -O( 1)~ii -O(1 )uii -O(3)i -O(3)~ - 0 ( 3 ) ~ '~ -O(w) ~i -O(w) ~ t -O(w) "~i~ -0(4) -0(4) ~ - 0 ( 4 ) xii - 0 ( 4 ) '~ - 0 ( 4 ) ~" - 0 ( 4 ) n'~ -0(2) --0(2) ~ - 0 ( 2 ) "~
3.02(5) 3.02(5) 3.30( 1) 3.30( 1 ) 3.30( 1 ) 3.30(1)
(N3)
3.06(9) 3.06(9) 3.06(9) 3.06(9) 3.16(13) 3.16(13) 3.16(13) 3.21(5) 3.21 (5) 3.21 (5) 3.30(9) 3.30(9) 3.30(9) 3.44( 11 ) 3.44(6) 3.44(9) 3.44(3) 3.44(7) 3.44(3) 3.700(2) 3.700(2) 3.700(2)
Se tctrahedra
Se( 1)-0(1 ) -O(l)i - 0 ( 1 )~ -0(2)
1.62( 1) 1.62(1 ) 1.62(1 ) 1.73(3)
Se(2)-O(3), --0(3)~ ---0(3)~'~t -0(4) --0(4) ~ii --0(4) ~i --0(3)2 --0(3) i, -0(3)~ - - 0 ' ~3 /~x~tt 2 --0(3)~ '~a~ ---0(3)~~ '
1.66(5) 1.66(5) 1.66(5) 1.66(5) 1.66(5) 1.66(5) 1.72(10) 1.72(6) 1.72(10) 1.72(9) 1.72(9) 1.72(9)
0(2)-0(1 ) 0 ( 2 ) - 0 ( 1 )t 0 ( 2 ) - 0 ( 1 )~ 0 ( 1 ) - 0 ( 1 )~ O(1)-O(1) x O(l)t-O(1) x O(3)rO(3)~ O(3)t-O(3)~ ~'~i 0 ( 4 ) - 0 ( 4 ) x~t 0 ( 4 ) - 0 ( 4 ) xiii 0(4)-0(3)~ 0(4)-0(3)~ 0 ( 4 ) - 0 ( 3 ) ~ "~ 0(3):0(3)~ 0 ( 3 ) : 0 ( 3 ) ~ "~' 0(3)2-0(3)~
2.66(3) 2.66(3) 2.66(3) 2.71(15) 2.71(15) 2.71(15) 2.47(7) 2.47(7) 1.03(14) 1.03(9) 2.70(7) 2.70(7) 3.13(8) 1.29(12) 1.29(12) 1.20(15)
Disordered acid H-bonds O ( 3 h ... 0(3)~a
2.59(6)
0 ( 2 ) ...0(4)
3.10(9)
0 ( 2 ) ...0(3)2
2.81(9)
O(w)-O(3)~ v~ O(w)-O(3)~ O(w)-O(3)~ ii O(w)-O(3)~
(N2)
2.15(10) b 2.53(17) 2.53(9) 2.73(I0)
Disordered water molecule O(w)--O(w) *i O(w)-O(w) ~a O(w)-'O(W) xli
1.08(12) 1.19(14) 1.19(9)
(N2)
• Symmetry codes: (i) x, x - y , z; (ii) y - x , y, z;, (iii) y - x , - x , 1 / 2 - z ; (iv) - y , x - y , l / 2 - z ; (v) - y , - x , 1 / 2 - z ; (vi) - y , x - y , z; (vii) y - x , y, I/2-z;, (viii) y - x , - x , z; (ix) x, x - y , l/2-zq, (x) - y , - x , z; (xi) x, y, 1 / 2 - z ; (xii) 1- y , 1 - x , z; (xiii) 1+ y - x , y, z; (xiv) I - x , I - y , - z ; (xv)y, x, - z ; (xvi) I - x , y - x , - z ; (xvii) l + x , l + x - y , z; (xviii) l + x , y, z; (xix) I - y , - x , z; (xx) I - y , l + x - y , z; (xxi) y - x , I - x , z;, (xxii) x, l + x - y , z; (xxiii) I - y , I - x , 1 / 2 - z ; (xxiv) x, l + x - y , 1 / 2 - z ; (xxv) x, l+y, z; (xxvi) 1 + y - x , 1 +y,z;, (xxvii) 1 - y , x - y , z;, (xxviii) 1+ y - x , 1 - x , z; (xxix) i - y , x - y , z; (xxx) 1+ y - x , y, l / 2 - z . b These distances and probably O (w)-O (3)~,~,a do not really occur in the structure. The water molecule can occupy the corresponding site if the O atoms of the base of the nearest "mobile" Se (2)O4 tetrahedron occupy suitable sites [for instance, O (3)~, O (3)y~' and O(3)~ iii ] of the 24 (1) position.
B. K Merinov et al. / Solid State lonics 69 (1994) 153-161 Table 4 Thermal motionellipsoids
Cs(l)
Cs(2)
Cs(3)
Se(1)
Se(2)
O(1)
0(2)
O(3)1
0(3)2
0(4)
R.m.s. amplitude (A)
~
Pb
~c
0.075 0.108 0.108 0.047 0.075 0.075 0.035 0.035 0.048 0.031 0.037 0.037 0.078 0.086
90 150 60 90 150 60 60 150 90 90 150 60 90 150
90 30 60 90 30 60 60 30 90 90 30 60 90 30
0 90 90 0 90 90 90 90 0 0 90 90 0 90
0.086
60
60
9O
0.040 0.046 0.063 0.069 0.082 0.082 0.042 0.100 0.129 0.029 0.190 0.341 0.058 0.112 0.132
90 180 90 90 150 60 90 90 180 33 123 92 74 120 35
31 60 97 90 30 60 48 56 60 93 38 52 90 0 90
81 90 9 0 90 90 130 40 90 110 127 44 18 90 108
• go, gb and gc are angles between principal axes of thermal motion ellipsoidsand coordinateaxes (o).
tion or not and, in accordance with this, occupies a corresponding position. X-ray data give an average picture and therefore the real lengths of the hydrogen bonds can be shorter than the calculated ones. Moreover, for two last H-bonds [ 3.10 (7) and 2.81 (9) A ], slight tilting of the "static" SeO4 tetrahedron is possible during the formation of the hydrogen bonds. The observed anisotropy of the thermal vibrations of the oxygen atoms belonging to this tetrahedron can be regarded as being caused by these inclinations. As a result of these factors, the true lengths of the hydrogen bonds are then approximately 0.2-0.5 A, less than the calculated O... O distances. From the lengths of all three non-equivalent hydrogen bonds formed with the participation of the acid protons, they are, most
157
probably, of the double-minimum type, and only the hydrogen bond O (3) ~-H ( 1 )...O ( 3 ) ]i that occupy the 6(h) position is symmetric, the others [ 0 ( 2 ) H(2)...O(4) and O(2)-H(3)...O(3)2] are asymmetric even in the high,symmetry phase I. For the sake of completeness of description of the crystal structure of the CTSeM phase I, we return once more to the Cs atoms and, in particular, focus our attention on their coordination polyhedra. As reported above, in the CTSeM crystal structure there are three independent Cs atoms: Cs( 1 ) lies in the 2(b) position; Cs(2) and Cs(3) occupy two 4(f) positions. The Cs(1) polyhedron is the most interesting. Mainly, this polyhedron is formed by the oxygen atoms of the "mobile" SeO4 tetrahedron and of the H20 molecules (except for the two most distant O atoms). Because of the specific behaviour of the "mobile" SeO4 tetrahedron, i.e. the strong librations and rotation, and disordering of the H20 molecules, there are changes not only in the shape of the Cs ( 1 ) polyhedron but also in its coordination number (see Table 3). The maximum number of O atoms coordinating Cs(1) is 17. The corresponding C s ( l ) - O distances lie in the range from 2.94 (8) to 3.76 (3) A. The Cs (2) polyhedron also changes with time, but the coordination number remains constant at 13. Seven vertices of this polyhedron are O atoms of the " m o b i l e " SeO4 tetrahedra and disordered H20 molecules. The remaining six vertices are the O atoms of "static" tetrahedra. The Cs ( 2 )-O distances lie in the range from 3.05( 1 ) to 3.702( 1 ) A. The Cs (3) atoms have an almost ordinary ten-fold coordination. Only one of these oxygen atoms belongs to the "mobile" SeO4 tetrahedron, and it is disordered over three equivalent sites (in Fig. 16 it is the vertex of the "mobile" tetrahedron). The Cs ( 3 ) O distances are equal to 3.02(5)-3.301 (9) A. Such unusual behaviour in the oxygen environment of the first two Cs atoms must influence the Cs( 1 ) and Cs(2) atoms themselves. The thermal parameters (isotropic and anisotropic, i.e. the lengths of the principal axes of the thermal vibration ellipsoids) of Cs( 1 ) are approximately 1.5 times greater than the corresponding values of Cs(2) and twice those of Cs (3). It is possible that the thermal vibrations at least of Cs(l) and Cs(2) atoms are anharmonic.
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B. V. Merinov et al. / Solid Staw lonics 69 (1994) 153-161
bh ,:,
,,', ,' : ',
;;', ;;" /
; \
/ ~h Fig. 1. Projection of the crystal structure of the hexagonalCTSeM phase I on the (001) plane. Largeopen circles: Cs atoms; tetrahedra: SeO4groups; partly filled circles: H20 molecules.The DDHBN are marked by dashed lines betweentetrahedra and by small open circles which show the H-bondsperpendicularto the (001 ) plane. The smallfilled circlesshowthree equallyprobablesites of a vertex of a SeO4 tetrahedron near a hexad (63) axis and the arrowsbetween them mark librations of the SeO4tetrahedra. Rotations of the tetrahedra are shown by arrows on the largestcircles. The tetrahedra drawn by thin lines showthe other possible orientationsof the SeO4groups.
3.2. Structural m e c h a n i s m o f proton transport
The presence of similar features in the atomic arrangement of crystals of the MaX(AO4)2 and MsXa(AO4)4"X20 families is reflected in the observed physical properties. Protonic conductivity of CTSeM crystals [7], like that of M3X(AO4)2 crystals [ 2,13,20,21 ], is quasi-two-dimensional. In the (001 ) plane of the hexagonal cell the conductivity is 1-2 orders of magnitude higher than in the perpendicular direction. However, there are some important differences in the structural mechanisms of proton conductivity of these two families. In trigonal phases of M3X(AO4)2 the proton pathways in the (001) plane include only symmetrically equivalent sites. As for the hexagonal phase of CTSeM, three non-equivalent acid H-bonds exist in the crystal structure. Moreover, two of the three acid H-bonds are asymmetric, and, therefore, the pathways of proton diffusion in CTSeM include non-equivalent proton sites. From an energetic viewpoint, such motion is less advantageous than motion over symmetrically
equivalent sites. During proton transport in CTSeM different orientations of SeO4 tetrahedra are formed in the crystal structure. If it is assumed that one of a number of orientations of the SeO4 tetrahedra (Fig. 2) can occur in the hexagonal phase of CTSeM at any given moment of time then, as a first approximation, a fragment of the structure of the orthorhombic phase II (Fig. 2a) can be regarded as an example of one of these orientations. At the next moment, SeO4 tetrahedra can mutually change their orientation forming new hydrogen bonds in other possible sites (interbond motion: proton motion between H-bonds, see [ 15,22 ] ), and a new orientation of the tetrahedra is formed (Fig. 2). The projection of the structure, averaged over different orientations of the SeO4 tetrahedra, of the hexagonal phase I of CTSeM along ah is shown in Fig. 3. It is deafly seen that the hydrogen bonds, (marked by dashed lines in Fig. 3) partially occupying the "principal" 6(h), 12(k) and 24(1) positions, join the SeO4tetrahedra into layers perpendicular to the Ch axis. Proton transport mainly occurs within these layers. In the unit cell there are two
B. V. Merinov et al. / Solid State l onics 69 (1994) 153-161
159
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F~ 3. Projectionof the crystalstructureof the hexagonalCTSeM d
phase I along ah, averaged over all orientationsof the SeO4tet-
Fig. 2. Examples of different possible orientations of the SeO4 tetrahedra in the hexagonal CTSeM phase I.
circles, H20 molecules;dashed lines: "principal" H-bonds and
such symmetrically equivalent layers which are related by a centre of symmetry. The "static" SeO4 tetrahedra are placed in the outer surfaces of the layers. By slightly changing their orientation, they perform a supporting role in the proton transport process. Only one vertex of these tetrahedra directly participates in the formation of the "principal" hydrogen bonds. The relative inertness of the "static" SeO4 tetrahedra is compensated by the very active behaviour of the "mobile" SeO4 tetrahedra. These tetrahedra play the main role in proton transport and form the cores of the layers. All of the vertices of the "mobile" tetrahedra directly participate in the formation o f a dy-
namically disordered network of "principal" Hbonds. By marked librations and even rotation (see Section 3.3) these tetrahedra perform the function of gear-wheels, which set the mechanism of proton transport in motion. Recall that all of three non-equivalent "principal" hydrogen bonds, formed by the participation of the acid protons, are double-minimum, and that only one of them, which lies in the 6(h) position, is symmetric. Saturation of the "mobile" SeO4 tetrahedra by Hbonds requires a particular proton location in these bonds. A configuration in which the protons are dis-
rahedra. Open circles:Cs atoms;tetrahedra: SeO4groups;dotted dotted lines: "supplementary"H-bonds.
160
B.V. Merinov et al. / Solid State lonics 69 (1994) 153-161
3.3. High-temperature phase transition II-I
subgroup) and multiplication of the cell [ D ~h (Z = 2 ) - D i~ ( Z = 8 ) ], is improper ferroelastic. This is confirmed by the formation of the corresponding domains in phase II. The interrelation of the unit cell parameters of phases I and II can be represented as follows: ah ~ 1/2bo, bh ~ 1/4 (2Co-bo) and Ch~ ao (the subscripts h and o denote hexagonal and orthorhombic phases respectively). The increase of the protonic conductivity by two orders of magnitude in phase I as compared with phase II indicates that changes occur in the nature of the proton subsystem during the II-I transition. In the orthorhombic phase II of CTSeM, the acid protons completely occupy three general 8(d) positions. During the transition to the hexagonal phase these positions are transformed into positions with higher multiplicity (with some approximation three 12(k) and two 24(1) positions which correspond to potential minima of the acid hydrogen bonds (Table 2) can be regarded as these positions), so that the number of sites which the protons can occupy becomes more than the number of protons themselves, i.e. disordering of the hydrogen bond network occurs. Another problem of the II-I phase transition in CTSeM is the problem of reversibility of this transition. Even after pre-heating the crystal, the transition to the hexagonal phase was accompanied by significant deterioration of the quality of the crystal being studied, which was manifested as a marked broadening of the diffraction peaks and a distortion of their shape. It was impossible to use a single crystal X-ray diffraction method for studying the crystal after cooling it from high-temperature hexagonal phase to room temperature. After powder X-ray diffraction investigations 2, it was concluded that, as a rule, the samples return to the initial state (orthorhombic phase) after one or two cycles of heating above the temperature of the II-I phase transition and subsequent cooling to room temperature, although there are some changes in intensities of the reflections. If the number of the heating-cooling cycles is more than two, the diffraction quality of the samples is strongly degraded. These changes correlate with decreasing the
In accordance with the symmetry criteria of Landau's theory of phase transitions [24,25 ], the I-II transition in CTSeM, occurring with a change of symmetry D~h (P63/mmc)-D[ 4 (Pbcn) (group-
2 Structural parameters obtained from the refinement of the atomic structure of the orthorhombic phase II and of the hexagonal phase I from powder diffraction data are in a good agreement with those obtained from single crystal data.
tant enough from each other, i.e. they are in the potential wells which are remote from O atoms of the "mobile" tetrahedra, is the most preferable. For asymmetric hydrogen bonds these potential wells are also deeper. However, during transfer of the protons it is necessary that they be in the potential wells which are nearest to the O atoms of the "mobile" SeO4 tetrahedra (intrabond motion: proton motion within a double-minimum hydrogen bond; see [ 15,22 ] ). Additional energy is required in this case due to the combination of a proton configuration which becomes non-optimal around the "mobile" SeO4 tetrahedra, with proton transfer within the H-bonds from a deeper potential minimum to a relatively shallow one. That is one of the reasons why, in spite of the presence of a dynamically disordered hydrogen bond network (DDHBN), the values of the parameters characterising protonic conductivity in the hexagonal CTSeM phase in the (001) plane (Ha~0.6 eV and tr~ 10 -5 S cm -I ) manifestly do not achieve superionic values (Ha< 0.3 eV and tr> 10 - 3 S c m - l ). Another reason which was discussed in [ 23], is the absence of conduction channels for the protons in the crystal structure of CTSeM. Conductivity along [001 ] is lower (Ha ~ 0.9 eV and 0"~ 10 - 7 S c m - I ) than in the (001)plane because, in order for proton transport to occur in the [001 ] direction, as in the case of the MXAO4 and M 3 X ( A O 4 ) 2 families, there must be formation of "supplementary" H-bonds (shown in Fig. 3 as the dotted lines), the probability of which is markedly lower than that of "principal" H-bonds. It is possible that water molecules also participate in proton transport. The mechanism of proton transfer here is similar to the Grotthuss mechanism, except that the protons are not transferred from one molecule of water to another, but from a n H 2 0 molecule to an O atom (connected to the molecule via a H-bond) of the "mobile" SeO4 tetrahedron, and vice versa.
B. V. Merinov et al. / Solid State Ionics 69 (1994) 153-161
proton conductivity and suppressing its anomaly at the phase transition during heating-cooling cycles. Most probably, it is a consequence of the formation of proton glass state similar to that observed in CTSM crystals [7]. Further investigations are underway which will enable the nature of these phenomena to be determined.
Acknowledgement One of the authors (B.V. Merinov) thanks Alexander von Humboldt Stiftung (Germany) for supporting this work.
References 1 ] A.I. Baranov, LA. Shuvalov and N.M. Schagina, JETP Lett. (USSR) 36 (1982) 459. 2]A.I. Baranov, B.V. Merinov, A.V. Tregubchenko, L.A. Shuvalov and N.M. Schasina, Ferroelectrics 81 (1988) 187. 3]B.V. Merinov, N.B. Bolotina, A.I. Baranov and L.A. Shuvalov, SOy. Phys. Crystallogr. 33 (1988) 824. 4]B.V. Merinov, N.B. Bolotina, A.I. Baranov and L.A. Shuvalov, SOy. Phys. Crystallogr. 36 ( 1991 ) 639. 5] M. Ichikawa, 1". Gustafsson and I. Olovsson, Acta Cryst. B48 (1992) 633. 6]B.V. Merinov, A.I. Baranov, L.A. Shuvalov and N.M. Schagina, SOy. Phys. Crystallogr. 36 (1991) 321. 7]A.I. Baranov, O.A. Kabanov, B.V. Merinov and L.A. Shuvalov, Ferroelectrics 127 (1992) 257. 18] B.V. Merinov, A.I. Baranov, L.A. Shuvalov, J. Schneider and H. Schulz, in preparation.
161
[9] V.I. Andrianov, SOy. Phys. Crystallogr. 32 (1987) 130. [ 10 ] InternationalTables for X-ray Crystallography, Vol. IV (The Kynoch Press, Birmingham, 1974). [ 11 ] W.H. Zachariasen, Acta Cryst. 23 (1967) 558. [12]B.V. Merinov, A.I. Baranov, L.A. Shuvalov and B.A. Maksimov, SOv. Phys. Crystallogr. 32 (1987) 47. [13]A.I. Baranov, I.P. Makarova, L.A. Muradyan, A.V. Tregubchenko, L.A. Shuvalov and V.I. Simonov, SOy.Phys. Crystallogr. 32 (1987) 400. [14]A.I. Baranov, B.V. Merinov, A.V. Tregubchenko, V.P. Khiznichenko, L.A. Shuvalov and N.M. Schagina, Solid State Ionics 36 (1989) 279. [ 15 ] B.V. Merinov, A.I. Baranov, and L.A. Shuvalov, SOy. Phys. Crystallogr. 35 (1990) 200. [16]B.V. Merinov, M.Yu. Antipin, A.I. Baranov, A.V. Tregubchenko, L.A. Shuvalov and Yu.T. Struchkov, SOy. Phys. Crystallogr. 36 ( 1991 ) 488. [17]Z. Jirak, M. Dlouha, S. Vratislav, A.M. Balagurov, A.I. Beskrovnyi, V.I. Gordelii, I.D. Datt and L.A. Shuvalov, Phys. Status Solidi (a) 100 ( 1987 ) KI 17. [18]A.V. Belushkin, W.I.F. David, R.M. Ibberson and L.A. Shuvalov, Acta Cryst. B47 ( 1991 ) 161. [ 19] V.P. Dmitriev, private communication (1992). [20] A.I. Baranov, A.V. Tregubchenko, L.A. Shuvalov and N.M. Schagina, SOy. Phys. Solid State 29 (1987) 1448. [21 ] A. Pawlowski, Cz. Pawlaczyk and B. Hilczer, Solid State Ionics 44 (1990) 17. [22]R. Blinc, J. Dolinsek, G. Lahajnar, I. Zupancic, L.A. Shuvalov and A.I. Baranov, Phys. Status Solidi (b)123 (1984) K83. [ 23 ] B.V. Merinov and L.A. Shuvalov, SOv.Phys. Crystallogr. 37 (1992) 211. [24] L.D. Landau and E.M. Lifshits, Statistical Physics, Vol. 5 ( Nauka, Moscow, 1964). [ 25 ] P. Toledano and J.-CI. Toledano, Ferroelectrics 21 (1978) 587.