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X-ray diffraction study of the structural phase transitions in RbCN under high pressure
Pergamon
PII: SOO22-3697(97)00151-O
J. Phys. Chem Solids Vol58. No. 12. pp. 2lOI-2106.1997 0 1997 Elsevier Science Ltd. All rights reserved in Greaf Britain 002%3697/97 517.00 + 0.00
Printed
X-RAY DIFFRACTION STUDY OF THE STRUCTURAL PHASE TRANSITIONS IN RbCN UNDER HIGH PRESSURE S. SHINOHARAS, Department
H. IWASAKIt
of Physics, Faculty of Science and Engineering,
and Y. YOSHIMURA
Ritsumeikan
University,
Kusatsu, Shiga 525-77, Japan
(Received 15 April 1997; accepted 30 May 1997) Abstract-Pressure-induced structural changes in RbCN were studied by X-ray diffraction. A single crystal sample was loaded in a miniature diamond-anvil cell and diffraction patterns were recorded at room temperature by the precession method on a laboratory radiation source. It was confirmed that a two-step structural transition takes place up to a pressure of 2 GPa: from the NaCI-type to the CsCI-type structure and further to the monoclinic structure. The CsCl-type structure forms with its (111) plane parallel to the three equivalent ( 100)planes of the NaCI-type structure. The monoclinic structure with the space group Cm forms as a result of preferential alignment of the CN molecules in the direction of one of the body-diagonals of the CsCl lattice with its (010) plane parallel to the ( 110) plane of the lattice. No definite conclusion was obtained regarding the head-and-tail ordering of the CN molecules. 0 1997 Elsevier Science Ltd. All rights reserved Keywords: A. alkali cyanide, C. high pressure, C. X-ray diffraction,
1. INTRODUCTION One of the alkali cyanides,
RbCN, crystallizes
under
atmospheric pressure in the NaCl-type structure, which is hereafter called the Bl structure. In this structure the dumbbell shaped CN molecules are in an orientationally disordered state, i.e. their axes are distributed statistically in the four equivalent
(111) directions
D. phase transition
We carried out an X-ray diffraction study on the phase transitions in RbCN using single crystal samples to obtain more precise information
regarding the crystal structure
and the orientation relationship between the structures involved. The results are described in the following sections.
of the
cubic lattice. The B 1 structure is stable only in a limited
2. EXPERIMENTAL PROCEDURES
range of pressure and a phase transition takes place at 0.56 GPa at room temperature X-ray diffraction
[ 1, 21. It was shown by at higher
[3], hereafter called the B2
cleaved to obtain pieces of rectangular prism, approximately 0.15 X 0.15 X 0.10 mm3 in size.
that the structure
pressure is of the CsCl-type
Single crystals of RbCN were purchased from the crystalgrowth laboratory of the University of Utah. They were
forming
structure, in accordance with the prediction based on the phase transition sequence observed in the alkali halides.
The high pressure apparatus employed was a miniature
The CN molecules in the B2 structure of RbCN are still
diamond-anvil
in an orientationally disordered state, the axes being distributed in the four body-diagonal directions of the
In order to generate pressure in the cell, it was inserted
B2 structure. Upon further compression, transition
a second phase
takes place at a pressure of 1.8 GPa and the
structure formed has been claimed to be isostructural to the high pressure phase of KCN [3]. It has a monoclinic symmetry
with the CN molecules
direction. The orientationally as RbCNIV, structures
ordered phase is designated
while the phases
are designated
aligned in a specific with the Bl
as RbCNI
and B2
and RbCNIII$,
respectively [3]. These results were, however, obtained using powdered samples.
tTo whom all correspondence should be addressed. $Present address: Cartridge Center, CANON INC., Toride, Chiba 302, Japan. gRbCNI1 refers to the phase forming at low temperatures.
cell designed by Iwasaki and Okazaki [4].
in a piston-cylinder pressing device and force was applied to the anvils by rotating the loading screw. The pressure thus generated
could be clamped.
A piece of
single crystal was put in a hole, 0.3 mm in diameter, of the Inconel gasket with the (100) plane of the B 1 structure nearly parallel to the anvil face, whose diameter was 0.6 mm. A mixture of ethanol and methanol used as the pressure transmitting pressure
was
estimated
by
was
medium. The sample measuring
the
lattice
parameter of the sample itself and referring to the pressure-volume relation of RbCN given by Striissner et al. [3]. The diamond-anvil cell containing the compressed sample was mounted on a goniometer head on the Enraf-Nonius X-ray precession camera. Diffraction patterns were taken using Zr-filtered
MoK cr-radiation
S. SHINOHARA et al.
2102
from a rotating-anode type X-ray generator (RIGAKURU200) with operating conditions of 50 kV and 150 mA. It took, on average, 40 h to take one pattern with a precession angle of ~1= 25’.
3. PHASE TRANSITIONS AND STRUCTURR OF THE HIGH PRESSURE PHASES
3.1. Transition from RbCNI to RbCNIII In the zero-layer precession pattern taken on a lightly compressed sample, the diffraction spots of the Bl structure with the indices 020, 002, 022, 040, 004, 042, 024 etc. are seen to form a square network. The pattern is schematically shown, omitting strong diffraction spots from the anvil diamonds and diffuse halos from pressure transmitting medium, in Fig. 1. With an increase in pressure new diffraction spots appeared, but those of the Bl structure still remained, indicating the coexistence of the two phases. After several compression steps a diffraction pattern representative of the high pressure phase was obtained, shown in Fig. 2. As a result of the introduction of strains accompanied by the structural transition, the diffraction spots have been elongated so that they appear as arcs. Their 28 values measured on the pattern show that they can be indexed in terms of the B2 structure: 12 diffraction arcs arranged on the innermost circle are the 1IO-type reflections, the next four arcs are the 11 l-type reflections and those arranged on the outer two circles are the 21 land 220-type reflections, respectively. The lattice parameter is a = 0.401 t 0.001 nm, suggesting that the sample pressure is 1.5 GPa. Comparison with the lattice parameter of the B 1 structure shows that there is a volume contraction of more than 10% on the Bl-B2 transition. In the reciprocal lattice of the B2 structure, there is no plane section on which the reflections of the above four
Fig. 2. Arrangement of the diffraction spots, elongated to appear as arcs, of RbCNIII having the B2 structure at a pressure of 1.5 GPa. The arcs with black and white markings represent the reflections from the two orientation variants belonging to the A-group orientation and the arcs with shaded marking represent the reflections from the variants belonging to the B-group orientation.
types lie and therefore the high pressure phase RbCNIII cannot be in a single crystal state. However, the regular arrangement of the diffraction arcs in Fig. 2 shows that the B2 structure forms with a definite orientation relationship to the B 1 structure. 3.2. Orientation relationship between the BI and B2 structures If the Ill-type reflections in Fig. 2 are ignored, the arrangement of the 1lo-, 21 l- and 220-type reflections can be explained by the superposition of the two sets of reflections for the (111) section of the reciprocal lattice of the B2 structure, one being rotated by 90” to the other around the [ 11l] direction. The orientation of the B2 structure with respect to the Bl structure is then expressed as (11 l)nZ//(lOO)nI with
[iio],,//[oi ilB,eqno
and [ 110]n2N[01l]a,.
(1)
Indices assigned to the diffraction arcs in Fig. 2 are based on these orientations. They are called the A-group orientation. _________,_____,______f____~_____~_________.The 1ll-type reflections in Fig. 2 arise from the 020 040 domains with an orientation other than that expressed by eqn (1). It is highly likely that the B2 structure also 0 0 d 0 0 forms with its (111) plane parallel to the other cube faces, (010) and (001) planes, of the Bl structure. In order to confirm this, a precession pattern was taken with the sample crystal rotated by 15” around the axis through the horizontal pair of the 11 l-type reflections in Fig. 2. The pattern characteristic of the superposition of the Fig. 1. Arrangement of the diffraction spots of RbCNI having the (llO)- and (21 I)-sections of the reciprocal lattice of Bl structure constructed from the zero-layer X-ray precession pattern. The (100) section of the reciprocal lattice is shown. the B2 structure was obtained, just as expected. The
Structural phase transitions
in RbCN
2103
b
Fig. 4. The structure of monoclinic RbCNIV depicted to show the relation to the cubic CsCl lattice (shown by broken lines). The center of the CN molecules is on the face-center of the (100) and (010) planes with the dumbbell axis in the [IO11 direction. Fig. 3. Arrangement of the diffraction spots, elongated to appear as arcs, of RbCNIV having the monoclinic structure at a pressure of 2 GPa. The arcs with black, white and shaded markings represent the reflections arising from splitting the corresponding reflections of the B2 structure (the inset shows the correspondence). The reflection 00 I- 110 arises from the 100 reflection of the B2 structure and appears in the pattern as a result of the intersection of its extended intensity region with the zero-layer
section of the reciprocal lattice. orientation with the (111) plane parallel (001)
planes
of the Bl
to the (010) and
structure is called the B-group
ratio of the A-group
approximately
to the B-group
relationship
found
observed in the pressure-induced Bl-B2 potassium and rubidium halides [5-71. 3.3.
is
1:2.
The orientation
(001) planes displaced in the [ 1 lo] direction (or the (010) planes in the [loll direction or the (100) planes in the [Ol l] direction). The resulting structure is that of the high pressure phase KCNIV proposed by Decker et al. [8]. The
orientation. Judging from the intensity of the reflections, the volume
cubic lattice. If this direction is [ll 11, the alignment induces a shearing deformation of the lattice with the
in RbCN
was
transition
in
relationship between that structure and the B2 structure is shown in Fig. 4. It is base-centered monoclinic, space group Cm. The lattice parameters are expressed in terms of that of the B2 structure as follows: U=2
x Qaz, 6~2
x agz, c=anz
and P<90”.
Two molecular units are contained in the unit cell. Since there are four equivalent body-diagonal
directions, there
must be corresponding sets of monoclinic orientations with respect to the B2 structure. If all possible orientations of the monoclinic
Transition from RbCNIll to RbCNIV
With a further increase in pressure, a second structural
(2)
structure structure
exist with the lattice parameters given by eqn (2). each of
change took place and the arrangement of the diffraction
the 1 lo-type reflections of the B2 structure must split into
arcs changed into that shown in Fig. 3. The elongation of the arcs becomes more appreciable, but their arrangement
four and the 11 l-type reflections into three, whereas the observed number of splittings is two for the two types of
is still regular, indicating
reflections.
that RbCNIV forms with a
definite orientation relationship. Inspection of the diffraction pattern in Fig. 3 has shown that some of the diffraction arcs arise from splitting of the reflections
of RbCNIII. As shown in the inset, the arcs
The expected
number of splittings
of the
21 l-type reflections is seven, contrary to the observation. In the original diffraction pattern of RbCNIV, two additional weak diffraction arcs are seen with the lowest 20 value, as shown in Fig. 3. They correspond
to the
arranged on the inner two circles are the splitting pairs of
lOO-type reflections
the 1 IO-type reflections of the B2 structure and the next arcs on the horizontal line are the splitting pair of the
tions, belonging to the B-group orientation, are, however,
11l-type reflection. The arcs arranged on the outermost
slightly above and below. Appreciable elongation of the diffraction arcs with increasing pressure has caused the
circle correspond, as their 28 value suggests, to one of the splitting components of the 2 11 -type reflections. The splitting suggests the distortion of the cubic lattice
of the B2 structure. These reflec-
not on the explored section of the reciprocal
edge of their intensity
lattice but
region to reach the plane of
and it must be associated with the orientational ordering of the CN molecules. A possible direction of the prefer-
the section. Each of the lOO-type reflections must appear asadoublet, whereasitappearsasasinglearcinthepattem. All the discrepancies in the number of splittings can be
ential alignment is along one of the body-diagonals
explained by assuming that the lattice parameters of the
of the
S. SHINOHARA et al.
2104
Table 1. Observed and calculated d-values of the reflections of RbCNIV at 2 GPa. a = 0.5759 nm, b = 0.5440 nm, c = 0.3964 nm and fi = 85.49”. F(M) is the structure factor calculated for the structure without the head-and-tail ordering of the CN dumbbells. F(M) of the structure with that ordering is nearly the same. m is the multiplicity factor caused by the presence of the orientation variants Reflections arising from the A-group orientation of the B2 structure hkl d,,, (nm) h&z dab Mm) 111
0.2872 0.287
200 lloB2
lobs
strong
0.287 1 0.2721
iii
0.272
020 202
strong
0.2720
In
496
4
496
2
599
4
599
2
0.1691
-
0.1690
311
288
0.1599 0.160
i 022 131
211B2
IF(hk0i*
weak
0.1598
288
i 0.1598
31i
288
{ 202 13i { 400 222
0.1436
-
169
-
169
0.1435 220B2
222
0.1361
-
040
289
Reflections arising from the B-group orientation of the B2 structure hkl dobr (nm) d,,l Mm) hkls2 001 10082
I ohs
IFW)12
201
226
2
0.3949
226
4
324
2
182
4
182
2
0.2415
0.241
021
m
0.3952 0.397
{ 110
medium
0.2241 0.223
lllBZ
289
-
0.1360
medium
{ 2oi
0.2240
The indices assigned in terms of the monoclinic lattice,
monoclinic structure are not as given by eqn (2), but deviate slightly from them, as will be shown below.
listed in the second column in Table 1, are compatible
3.4. Structure of RbCNIV
reflections
with the extinction rule of the space group Cm, i.e. the hkE Adjustment
of the lattice parameters
was made using
with h + k odd are absent. The volume per
atom calculated
from eqn (3) is V = 0.0206 nm3. The
the observed d-values of all the diffraction arcs, yielding
P-V relation given by Striissner et al. [3] suggests that the
the results
pressure at which the diffraction pattern of RbCNIV was taken is 2 GPa. The volume contraction on the
a = 0.5759 nm, b = 0.5440 nm, c = 0.3964 nm and /3 = 85.49”.
(3)
The estimated accuracy is ? 0.001 nm for a, b and c and + 0. lo for /I. Comparison of the observed and calculated d-values is shown in Table 1. It is seen that the adjusted lattice parameters
give d-values
which explain
BZmonoclinic
transition is 4%.
The monoclinic
structure of RbCNIV shown in Fig. 4
is described in terms of the atomic positions of the space group Cm as follows: Rb on 2a (xab, 0, ~a,,) + (0, 0,O) and (l/2,1/2,0)
satisfactorily
the observed number of splittings for the 1 lOa*-, lOOa*and 1 11a2-type reflections. For the 211a2-type reflections, the results of the calculation suggest that they appear as a triplet, still in disagreement with the observation. Intensity calculation of the triplet components will account for the observed number of splittings.
C on 2a (xc, 0, zc) + (0, 0,O)and (l/2, l/2,0)
N on 2a (XN,0, zN) + (O,O, 0) and (l/2,1/2,0). The rubidium atoms are put on the comers of the lattice
Structuralphase transitions in RbCN with xab = zab = 0. If the CN dumbbells are exactly on the face-diagonals of the (010) plane, xc = zc and xN = zn. There are two possibilities to be considered: if the headand-tail ordering of the dumbbells is present, xc and xn each have a definite value, while, if not, the statistical average is to be taken into account. Firstly, the first possibility is considered. According to the results of two independent neutron diffraction studies [9, lo], the distance between the carbon and nitrogen atoms in RbCN is 0.118 nm. The covalent bond distance is, in general, the same irrespective of the orientation of the molecules and xc and XNare set to be 0.4 19 and 0.58 1, respectively, in RbCNIV so that they yield the observed distance by neutron diffraction. For the second possibility, the probability for the carbon atoms to have xc = 0.419 is the same as that for xc = 0.58 1 and the same is true for the nitrogen atoms. The structure factor F(W) of the reflections was calculated for the two possibilities. It is shown that the difference in ]F(hkl)l’ is very small, of the order of 0.1%. This is due to the relatively small X-ray scattering power of the carbon and nitrogen atoms. The IF(hkl)l’ values listed in the sixth column in Table I are those calculated for the second possibility, no account having been taken of thermal vibration of atoms. In the seventh column, the multiplicity factor m of the reflections is shown, for which the presence of all possible orientations of the monoclinic structure with respect to the B2 structure is assumed. An approximate measure of the intensity is given as a sum of the product oi ]F(M)(* and m over the reflections with nearly the same d-values. Visually estimated intensity of the original diffraction pattern is shown in the fifth column. It is seen in Table 1 that the calculated intensity is compatible with the visually estimated intensity for the respective groups of reflections arising from the different orientations. It is not possible to detect the existence of the head-and-tail ordering of the CN dumbbells, even if the intensity of the reflections were measured quantitatively, for the difference in intensity between the structures with and without ordering is very small, as described above, far beyond the accuracy attainable in the present type of measurement. The results of the structure factor calculation suggest that the intensity is not the same for the triplet components of the 2 11s2-type reflections: the central one, the superposition of 022, 13 1 and 3 1i reflections, is the strongest, while the other two, the superposition of the 202 and 3 11 and that of the 202 and 131 reflections, are weaker. They are therefore not observable owing to the absorption effect, in agreement with the observation. The results of the structure factor calculation also suggest that the doublet arising from the 1lOs*-type reflections is asymmetric in intensity, whereas it appears symmetric in the original diffraction pattern. The dis-
2105
crepancy is explained by assuming the difference in the volume fraction of the orientation variants: the reflections arise from the B2 structure with the A-group orientation, whose [1 1l] direction is parallel to the axis of the diamond-anvil cell, i.e. parallel to the direction of compression, while the [ 1ii], [i 1i] and [ii I] directions are inclined to the axis. Since the cubic lattice is sheared in the alignment direction of the CN molecules on the transition from the B2 to monoclinic, as shown in Fig. 4, the uniaxial component of pressure may prevent them from aligning in the [ll l] direction, resulting in a decrease in the volume fraction of such orientation variants of the monoclinic structure. This is reflected in an apparent decrease in m for the 11i and 020 reflections, the high angle component of the doublet. A similar case is that with the doublet arising from the 111s2-type reflections. It is to be noted that although the sample cell was filled with a liquid pressure transmitting medium, there was a uniaxial component of pressure. 4. DISCUSSION
The present authors carried out an X-ray diffraction study at ambient pressure on the structural change in RbCN with declining temperature using single crystal samples [ 111. The Bl structure is transformed into a hybrid structure consisting of monoclinic and triclinic structures. The transformation is associated with orientational ordering of the CN molecules, but it was found that the direction of preferential alignment of the molecules is not along one of the body-diagonals of the cubic lattice. Volume contraction upon ordering is 2%, smaller than that observed for pressure-induced ordering. It is notable that in orientational ordering at low temperatures an atomic plane exists whose orientation and d-value remain unchanged even when the crystal lattice is distorted into the monoclinic or tricilinic. No definite conclusion was obtained on the head-and-tail ordering of the CN molecules, in agreement with the indication from the dielectric constant measurements [ 121. The effect of pressure, on the other hand, is first to change the structure from Bl to B2 accompanied by a large volume contraction. Orientational ordering of the CN molecules then occurs in the B2 structure with the direction of preferential alignment along one of the body-diagonals. It seems that the structural change in RbCN at low temperatures is governed mainly by the electrostatic and core-repulsive interaction energy between the CNand Rb+ ions [ 131 and that the structure formed is that which gives the lowest energy. Under high pressure, on the other hand, the volume principle is dominant and the structure formed first is that which gives the higher packing density, i.e. the B2 structure, in which there is no orientational ordering of the CN molecules. RbCN
2106
S. SHINOHARA et al.
then yields the pressure by choosing one of the bodydiagonals of the cubic lattice as the direction of preferential alignment of the CN molecules. This direction is not the direction for which the electrostatic and core-repulsive interaction energy is lowest, but the direction for which a larger volume contraction is possible. No definite conclusion was obtained regarding the presence of the head-and-tail ordering of the CN dumbbells in RbCNIV. The present authors are not aware of measurements hitherto made under pressure using methods other than diffraction to detect the ordering. Neutron diffraction may be suitable for that purpose. The results of the structure factor calculation mentioned above suggest that the reflections of RbCNIV sensitive to ordering are 001, 112 etc. Care should be taken regarding the overlapping of the reflections with different indices arising from other orientation variants.
BEFBBBNCES
1. Clark, J. B. and Pistorius,C. W. F. T., SolidSrare Common.,
1969,7,187. 2. Dultz, W. and Rehaber, E., Phys. Rev., 1983, B28,2114. 3. Stissner, K., Hochheimer, H. D., Honle, W. and Werner, A., J. Chem. Phys., 1985.83.2435. 4. Iwasaki, H. and Okazaki, Y., to be published. 5. Okai, B., J. Phys. Sot. Jpn, 1980,48,5 14. 6. Okai, B.,J. Phys. Sot. Jpn, 1981,50,3189. 7. Fujiwara, H., Nakagiri, N. and Nomura, N., J. Phys. Sot. Jpn, 1983.52, 1665. 8. Decker. D. L., Beyerlein, R. A., Roult. G. and Worlton, T. G., Phys. Rev., 1974, BlO, 3584. 9. Ehrhardt, K. D., Press, W. and Heger, G.. Acra Ctysr., 1983, B39, 171. 10. Rowe, J. M., Rush, J. J. and Luty, F., Phys. Rev., 1984,829, 2168. 11. Yoshimura, Y., Shinohara, S., Tsuda, N. and Iwasaki, H., J. Phys. Sot. Jpn, 1996,65,2099. 12. Kondo, Y., Schoemaker, D. and Luty, F., Phys. Rev., 1979, B19,4210. 13. Matsubara, T. and Nagamiya, T., Sci. Papers Osaka Univ. 1949, No. 14.
PII: SOO22-3697(97)00151-O
J. Phys. Chem Solids Vol58. No. 12. pp. 2lOI-2106.1997 0 1997 Elsevier Science Ltd. All rights reserved in Greaf Britain 002%3697/97 517.00 + 0.00
Printed
X-RAY DIFFRACTION STUDY OF THE STRUCTURAL PHASE TRANSITIONS IN RbCN UNDER HIGH PRESSURE S. SHINOHARAS, Department
H. IWASAKIt
of Physics, Faculty of Science and Engineering,
and Y. YOSHIMURA
Ritsumeikan
University,
Kusatsu, Shiga 525-77, Japan
(Received 15 April 1997; accepted 30 May 1997) Abstract-Pressure-induced structural changes in RbCN were studied by X-ray diffraction. A single crystal sample was loaded in a miniature diamond-anvil cell and diffraction patterns were recorded at room temperature by the precession method on a laboratory radiation source. It was confirmed that a two-step structural transition takes place up to a pressure of 2 GPa: from the NaCI-type to the CsCI-type structure and further to the monoclinic structure. The CsCl-type structure forms with its (111) plane parallel to the three equivalent ( 100)planes of the NaCI-type structure. The monoclinic structure with the space group Cm forms as a result of preferential alignment of the CN molecules in the direction of one of the body-diagonals of the CsCl lattice with its (010) plane parallel to the ( 110) plane of the lattice. No definite conclusion was obtained regarding the head-and-tail ordering of the CN molecules. 0 1997 Elsevier Science Ltd. All rights reserved Keywords: A. alkali cyanide, C. high pressure, C. X-ray diffraction,
1. INTRODUCTION One of the alkali cyanides,
RbCN, crystallizes
under
atmospheric pressure in the NaCl-type structure, which is hereafter called the Bl structure. In this structure the dumbbell shaped CN molecules are in an orientationally disordered state, i.e. their axes are distributed statistically in the four equivalent
(111) directions
D. phase transition
We carried out an X-ray diffraction study on the phase transitions in RbCN using single crystal samples to obtain more precise information
regarding the crystal structure
and the orientation relationship between the structures involved. The results are described in the following sections.
of the
cubic lattice. The B 1 structure is stable only in a limited
2. EXPERIMENTAL PROCEDURES
range of pressure and a phase transition takes place at 0.56 GPa at room temperature X-ray diffraction
[ 1, 21. It was shown by at higher
[3], hereafter called the B2
cleaved to obtain pieces of rectangular prism, approximately 0.15 X 0.15 X 0.10 mm3 in size.
that the structure
pressure is of the CsCl-type
Single crystals of RbCN were purchased from the crystalgrowth laboratory of the University of Utah. They were
forming
structure, in accordance with the prediction based on the phase transition sequence observed in the alkali halides.
The high pressure apparatus employed was a miniature
The CN molecules in the B2 structure of RbCN are still
diamond-anvil
in an orientationally disordered state, the axes being distributed in the four body-diagonal directions of the
In order to generate pressure in the cell, it was inserted
B2 structure. Upon further compression, transition
a second phase
takes place at a pressure of 1.8 GPa and the
structure formed has been claimed to be isostructural to the high pressure phase of KCN [3]. It has a monoclinic symmetry
with the CN molecules
direction. The orientationally as RbCNIV, structures
ordered phase is designated
while the phases
are designated
aligned in a specific with the Bl
as RbCNI
and B2
and RbCNIII$,
respectively [3]. These results were, however, obtained using powdered samples.
tTo whom all correspondence should be addressed. $Present address: Cartridge Center, CANON INC., Toride, Chiba 302, Japan. gRbCNI1 refers to the phase forming at low temperatures.
cell designed by Iwasaki and Okazaki [4].
in a piston-cylinder pressing device and force was applied to the anvils by rotating the loading screw. The pressure thus generated
could be clamped.
A piece of
single crystal was put in a hole, 0.3 mm in diameter, of the Inconel gasket with the (100) plane of the B 1 structure nearly parallel to the anvil face, whose diameter was 0.6 mm. A mixture of ethanol and methanol used as the pressure transmitting pressure
was
estimated
by
was
medium. The sample measuring
the
lattice
parameter of the sample itself and referring to the pressure-volume relation of RbCN given by Striissner et al. [3]. The diamond-anvil cell containing the compressed sample was mounted on a goniometer head on the Enraf-Nonius X-ray precession camera. Diffraction patterns were taken using Zr-filtered
MoK cr-radiation
S. SHINOHARA et al.
2102
from a rotating-anode type X-ray generator (RIGAKURU200) with operating conditions of 50 kV and 150 mA. It took, on average, 40 h to take one pattern with a precession angle of ~1= 25’.
3. PHASE TRANSITIONS AND STRUCTURR OF THE HIGH PRESSURE PHASES
3.1. Transition from RbCNI to RbCNIII In the zero-layer precession pattern taken on a lightly compressed sample, the diffraction spots of the Bl structure with the indices 020, 002, 022, 040, 004, 042, 024 etc. are seen to form a square network. The pattern is schematically shown, omitting strong diffraction spots from the anvil diamonds and diffuse halos from pressure transmitting medium, in Fig. 1. With an increase in pressure new diffraction spots appeared, but those of the Bl structure still remained, indicating the coexistence of the two phases. After several compression steps a diffraction pattern representative of the high pressure phase was obtained, shown in Fig. 2. As a result of the introduction of strains accompanied by the structural transition, the diffraction spots have been elongated so that they appear as arcs. Their 28 values measured on the pattern show that they can be indexed in terms of the B2 structure: 12 diffraction arcs arranged on the innermost circle are the 1IO-type reflections, the next four arcs are the 11 l-type reflections and those arranged on the outer two circles are the 21 land 220-type reflections, respectively. The lattice parameter is a = 0.401 t 0.001 nm, suggesting that the sample pressure is 1.5 GPa. Comparison with the lattice parameter of the B 1 structure shows that there is a volume contraction of more than 10% on the Bl-B2 transition. In the reciprocal lattice of the B2 structure, there is no plane section on which the reflections of the above four
Fig. 2. Arrangement of the diffraction spots, elongated to appear as arcs, of RbCNIII having the B2 structure at a pressure of 1.5 GPa. The arcs with black and white markings represent the reflections from the two orientation variants belonging to the A-group orientation and the arcs with shaded marking represent the reflections from the variants belonging to the B-group orientation.
types lie and therefore the high pressure phase RbCNIII cannot be in a single crystal state. However, the regular arrangement of the diffraction arcs in Fig. 2 shows that the B2 structure forms with a definite orientation relationship to the B 1 structure. 3.2. Orientation relationship between the BI and B2 structures If the Ill-type reflections in Fig. 2 are ignored, the arrangement of the 1lo-, 21 l- and 220-type reflections can be explained by the superposition of the two sets of reflections for the (111) section of the reciprocal lattice of the B2 structure, one being rotated by 90” to the other around the [ 11l] direction. The orientation of the B2 structure with respect to the Bl structure is then expressed as (11 l)nZ//(lOO)nI with
[iio],,//[oi ilB,eqno
and [ 110]n2N[01l]a,.
(1)
Indices assigned to the diffraction arcs in Fig. 2 are based on these orientations. They are called the A-group orientation. _________,_____,______f____~_____~_________.The 1ll-type reflections in Fig. 2 arise from the 020 040 domains with an orientation other than that expressed by eqn (1). It is highly likely that the B2 structure also 0 0 d 0 0 forms with its (111) plane parallel to the other cube faces, (010) and (001) planes, of the Bl structure. In order to confirm this, a precession pattern was taken with the sample crystal rotated by 15” around the axis through the horizontal pair of the 11 l-type reflections in Fig. 2. The pattern characteristic of the superposition of the Fig. 1. Arrangement of the diffraction spots of RbCNI having the (llO)- and (21 I)-sections of the reciprocal lattice of Bl structure constructed from the zero-layer X-ray precession pattern. The (100) section of the reciprocal lattice is shown. the B2 structure was obtained, just as expected. The
Structural phase transitions
in RbCN
2103
b
Fig. 4. The structure of monoclinic RbCNIV depicted to show the relation to the cubic CsCl lattice (shown by broken lines). The center of the CN molecules is on the face-center of the (100) and (010) planes with the dumbbell axis in the [IO11 direction. Fig. 3. Arrangement of the diffraction spots, elongated to appear as arcs, of RbCNIV having the monoclinic structure at a pressure of 2 GPa. The arcs with black, white and shaded markings represent the reflections arising from splitting the corresponding reflections of the B2 structure (the inset shows the correspondence). The reflection 00 I- 110 arises from the 100 reflection of the B2 structure and appears in the pattern as a result of the intersection of its extended intensity region with the zero-layer
section of the reciprocal lattice. orientation with the (111) plane parallel (001)
planes
of the Bl
to the (010) and
structure is called the B-group
ratio of the A-group
approximately
to the B-group
relationship
found
observed in the pressure-induced Bl-B2 potassium and rubidium halides [5-71. 3.3.
is
1:2.
The orientation
(001) planes displaced in the [ 1 lo] direction (or the (010) planes in the [loll direction or the (100) planes in the [Ol l] direction). The resulting structure is that of the high pressure phase KCNIV proposed by Decker et al. [8]. The
orientation. Judging from the intensity of the reflections, the volume
cubic lattice. If this direction is [ll 11, the alignment induces a shearing deformation of the lattice with the
in RbCN
was
transition
in
relationship between that structure and the B2 structure is shown in Fig. 4. It is base-centered monoclinic, space group Cm. The lattice parameters are expressed in terms of that of the B2 structure as follows: U=2
x Qaz, 6~2
x agz, c=anz
and P<90”.
Two molecular units are contained in the unit cell. Since there are four equivalent body-diagonal
directions, there
must be corresponding sets of monoclinic orientations with respect to the B2 structure. If all possible orientations of the monoclinic
Transition from RbCNIll to RbCNIV
With a further increase in pressure, a second structural
(2)
structure structure
exist with the lattice parameters given by eqn (2). each of
change took place and the arrangement of the diffraction
the 1 lo-type reflections of the B2 structure must split into
arcs changed into that shown in Fig. 3. The elongation of the arcs becomes more appreciable, but their arrangement
four and the 11 l-type reflections into three, whereas the observed number of splittings is two for the two types of
is still regular, indicating
reflections.
that RbCNIV forms with a
definite orientation relationship. Inspection of the diffraction pattern in Fig. 3 has shown that some of the diffraction arcs arise from splitting of the reflections
of RbCNIII. As shown in the inset, the arcs
The expected
number of splittings
of the
21 l-type reflections is seven, contrary to the observation. In the original diffraction pattern of RbCNIV, two additional weak diffraction arcs are seen with the lowest 20 value, as shown in Fig. 3. They correspond
to the
arranged on the inner two circles are the splitting pairs of
lOO-type reflections
the 1 IO-type reflections of the B2 structure and the next arcs on the horizontal line are the splitting pair of the
tions, belonging to the B-group orientation, are, however,
11l-type reflection. The arcs arranged on the outermost
slightly above and below. Appreciable elongation of the diffraction arcs with increasing pressure has caused the
circle correspond, as their 28 value suggests, to one of the splitting components of the 2 11 -type reflections. The splitting suggests the distortion of the cubic lattice
of the B2 structure. These reflec-
not on the explored section of the reciprocal
edge of their intensity
lattice but
region to reach the plane of
and it must be associated with the orientational ordering of the CN molecules. A possible direction of the prefer-
the section. Each of the lOO-type reflections must appear asadoublet, whereasitappearsasasinglearcinthepattem. All the discrepancies in the number of splittings can be
ential alignment is along one of the body-diagonals
explained by assuming that the lattice parameters of the
of the
S. SHINOHARA et al.
2104
Table 1. Observed and calculated d-values of the reflections of RbCNIV at 2 GPa. a = 0.5759 nm, b = 0.5440 nm, c = 0.3964 nm and fi = 85.49”. F(M) is the structure factor calculated for the structure without the head-and-tail ordering of the CN dumbbells. F(M) of the structure with that ordering is nearly the same. m is the multiplicity factor caused by the presence of the orientation variants Reflections arising from the A-group orientation of the B2 structure hkl d,,, (nm) h&z dab Mm) 111
0.2872 0.287
200 lloB2
lobs
strong
0.287 1 0.2721
iii
0.272
020 202
strong
0.2720
In
496
4
496
2
599
4
599
2
0.1691
-
0.1690
311
288
0.1599 0.160
i 022 131
211B2
IF(hk0i*
weak
0.1598
288
i 0.1598
31i
288
{ 202 13i { 400 222
0.1436
-
169
-
169
0.1435 220B2
222
0.1361
-
040
289
Reflections arising from the B-group orientation of the B2 structure hkl dobr (nm) d,,l Mm) hkls2 001 10082
I ohs
IFW)12
201
226
2
0.3949
226
4
324
2
182
4
182
2
0.2415
0.241
021
m
0.3952 0.397
{ 110
medium
0.2241 0.223
lllBZ
289
-
0.1360
medium
{ 2oi
0.2240
The indices assigned in terms of the monoclinic lattice,
monoclinic structure are not as given by eqn (2), but deviate slightly from them, as will be shown below.
listed in the second column in Table 1, are compatible
3.4. Structure of RbCNIV
reflections
with the extinction rule of the space group Cm, i.e. the hkE Adjustment
of the lattice parameters
was made using
with h + k odd are absent. The volume per
atom calculated
from eqn (3) is V = 0.0206 nm3. The
the observed d-values of all the diffraction arcs, yielding
P-V relation given by Striissner et al. [3] suggests that the
the results
pressure at which the diffraction pattern of RbCNIV was taken is 2 GPa. The volume contraction on the
a = 0.5759 nm, b = 0.5440 nm, c = 0.3964 nm and /3 = 85.49”.
(3)
The estimated accuracy is ? 0.001 nm for a, b and c and + 0. lo for /I. Comparison of the observed and calculated d-values is shown in Table 1. It is seen that the adjusted lattice parameters
give d-values
which explain
BZmonoclinic
transition is 4%.
The monoclinic
structure of RbCNIV shown in Fig. 4
is described in terms of the atomic positions of the space group Cm as follows: Rb on 2a (xab, 0, ~a,,) + (0, 0,O) and (l/2,1/2,0)
satisfactorily
the observed number of splittings for the 1 lOa*-, lOOa*and 1 11a2-type reflections. For the 211a2-type reflections, the results of the calculation suggest that they appear as a triplet, still in disagreement with the observation. Intensity calculation of the triplet components will account for the observed number of splittings.
C on 2a (xc, 0, zc) + (0, 0,O)and (l/2, l/2,0)
N on 2a (XN,0, zN) + (O,O, 0) and (l/2,1/2,0). The rubidium atoms are put on the comers of the lattice
Structuralphase transitions in RbCN with xab = zab = 0. If the CN dumbbells are exactly on the face-diagonals of the (010) plane, xc = zc and xN = zn. There are two possibilities to be considered: if the headand-tail ordering of the dumbbells is present, xc and xn each have a definite value, while, if not, the statistical average is to be taken into account. Firstly, the first possibility is considered. According to the results of two independent neutron diffraction studies [9, lo], the distance between the carbon and nitrogen atoms in RbCN is 0.118 nm. The covalent bond distance is, in general, the same irrespective of the orientation of the molecules and xc and XNare set to be 0.4 19 and 0.58 1, respectively, in RbCNIV so that they yield the observed distance by neutron diffraction. For the second possibility, the probability for the carbon atoms to have xc = 0.419 is the same as that for xc = 0.58 1 and the same is true for the nitrogen atoms. The structure factor F(W) of the reflections was calculated for the two possibilities. It is shown that the difference in ]F(hkl)l’ is very small, of the order of 0.1%. This is due to the relatively small X-ray scattering power of the carbon and nitrogen atoms. The IF(hkl)l’ values listed in the sixth column in Table I are those calculated for the second possibility, no account having been taken of thermal vibration of atoms. In the seventh column, the multiplicity factor m of the reflections is shown, for which the presence of all possible orientations of the monoclinic structure with respect to the B2 structure is assumed. An approximate measure of the intensity is given as a sum of the product oi ]F(M)(* and m over the reflections with nearly the same d-values. Visually estimated intensity of the original diffraction pattern is shown in the fifth column. It is seen in Table 1 that the calculated intensity is compatible with the visually estimated intensity for the respective groups of reflections arising from the different orientations. It is not possible to detect the existence of the head-and-tail ordering of the CN dumbbells, even if the intensity of the reflections were measured quantitatively, for the difference in intensity between the structures with and without ordering is very small, as described above, far beyond the accuracy attainable in the present type of measurement. The results of the structure factor calculation suggest that the intensity is not the same for the triplet components of the 2 11s2-type reflections: the central one, the superposition of 022, 13 1 and 3 1i reflections, is the strongest, while the other two, the superposition of the 202 and 3 11 and that of the 202 and 131 reflections, are weaker. They are therefore not observable owing to the absorption effect, in agreement with the observation. The results of the structure factor calculation also suggest that the doublet arising from the 1lOs*-type reflections is asymmetric in intensity, whereas it appears symmetric in the original diffraction pattern. The dis-
2105
crepancy is explained by assuming the difference in the volume fraction of the orientation variants: the reflections arise from the B2 structure with the A-group orientation, whose [1 1l] direction is parallel to the axis of the diamond-anvil cell, i.e. parallel to the direction of compression, while the [ 1ii], [i 1i] and [ii I] directions are inclined to the axis. Since the cubic lattice is sheared in the alignment direction of the CN molecules on the transition from the B2 to monoclinic, as shown in Fig. 4, the uniaxial component of pressure may prevent them from aligning in the [ll l] direction, resulting in a decrease in the volume fraction of such orientation variants of the monoclinic structure. This is reflected in an apparent decrease in m for the 11i and 020 reflections, the high angle component of the doublet. A similar case is that with the doublet arising from the 111s2-type reflections. It is to be noted that although the sample cell was filled with a liquid pressure transmitting medium, there was a uniaxial component of pressure. 4. DISCUSSION
The present authors carried out an X-ray diffraction study at ambient pressure on the structural change in RbCN with declining temperature using single crystal samples [ 111. The Bl structure is transformed into a hybrid structure consisting of monoclinic and triclinic structures. The transformation is associated with orientational ordering of the CN molecules, but it was found that the direction of preferential alignment of the molecules is not along one of the body-diagonals of the cubic lattice. Volume contraction upon ordering is 2%, smaller than that observed for pressure-induced ordering. It is notable that in orientational ordering at low temperatures an atomic plane exists whose orientation and d-value remain unchanged even when the crystal lattice is distorted into the monoclinic or tricilinic. No definite conclusion was obtained on the head-and-tail ordering of the CN molecules, in agreement with the indication from the dielectric constant measurements [ 121. The effect of pressure, on the other hand, is first to change the structure from Bl to B2 accompanied by a large volume contraction. Orientational ordering of the CN molecules then occurs in the B2 structure with the direction of preferential alignment along one of the body-diagonals. It seems that the structural change in RbCN at low temperatures is governed mainly by the electrostatic and core-repulsive interaction energy between the CNand Rb+ ions [ 131 and that the structure formed is that which gives the lowest energy. Under high pressure, on the other hand, the volume principle is dominant and the structure formed first is that which gives the higher packing density, i.e. the B2 structure, in which there is no orientational ordering of the CN molecules. RbCN
2106
S. SHINOHARA et al.
then yields the pressure by choosing one of the bodydiagonals of the cubic lattice as the direction of preferential alignment of the CN molecules. This direction is not the direction for which the electrostatic and core-repulsive interaction energy is lowest, but the direction for which a larger volume contraction is possible. No definite conclusion was obtained regarding the presence of the head-and-tail ordering of the CN dumbbells in RbCNIV. The present authors are not aware of measurements hitherto made under pressure using methods other than diffraction to detect the ordering. Neutron diffraction may be suitable for that purpose. The results of the structure factor calculation mentioned above suggest that the reflections of RbCNIV sensitive to ordering are 001, 112 etc. Care should be taken regarding the overlapping of the reflections with different indices arising from other orientation variants.
BEFBBBNCES
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