Neutron powder diffraction study of the low-temperature phases of KNO2

Article abstract of DOI:10.1088/0953-8984/10/15/011

We made neutron powder diffraction measurements for phase III (at 4, 120, 180, 220, and 250 K) and phase II (at 280 K) of KNO₂. The structure of phase III was determined by the Rietveld method using the data obtained at 4 K; the initial structu

Full text of DOI:10.1088/0953-8984/10/15/011

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J. Phys.: Condens. Matter 10 (1998) 3341–3351. Printed in the UK
PII: S0953-8984(98)87381-5
Neutron powder diffraction study of the low-temperature
phases of KNO2
∗
N Onoda-Yamamuro†¶, H Honda†+, R Ikeda† , O Yamamuro‡,
T Matsuo‡, K Oikawa§, T Kamiyama§ and F Izumik
† Department of Chemistry, University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305, Japan
‡ Department of Chemistry and Microcalorimetry Research Centre, Graduate School of Science,
Osaka University, Machikaneyama-cho 1-1, Toyonaka, Osaka 560, Japan
§ Institute of Materials Science, University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305, Japan
k National Institute for Research in Inorganic Materials, 1-1 Namiki, Tsukuba, Ibaraki 305,
Japan
Received 8 September 1997, in final form 5 January 1998
Abstract. We made neutron powder diffraction measurements for phase III (at 4, 120, 180,
220, and 250 K) and phase II (at 280 K) of KNO2. The structure of phase III was determined
by the Rietveld method using the data obtained at 4 K; the initial structure parameters were
obtained by a systematic trial-and-error method. Phase III is monoclinic (space group: P21/c)
◦
˚
˚
˚
with a = 4.4010(2) A, b = 9.5967(3) A, c = 6.9817(2) A, β = 108.274(3) , and Z = 4. Both
K+ and NO−2 ions are located at general positions, and the orientations of the NO−2 ions are
completely ordered. The structures of phase III at the higher temperatures were also examined on
the basis of the structure at 4 K. The atomic displacement parameters of the NO−2 ions increased
anomalously with increasing temperature, indicating gradual but remarkable development of the
orientational disorder of NO−2 ions. The structure of phase II was determined to be rhombo-
¯
˚
˚
hedral (space group: R3m) with a = 5.027 90(4) A, c = 10.055 87(8) A, and Z = 3. The
orientations of the NO−2 ions were highly disordered about the 3 axis.
¯
1. Introduction
Potassium nitrite, KNO2, forms three crystalline phases, I, II, and III, depending on the
temperature [1]. The structure of each phase has been studied by means of single-crystal
x-ray diffraction [2]. Phase I (T > 315 K) has a NaCl-type cubic structure in which
the orientations of the NO−2 ions are spherically disordered. Because of the disorder, the
crystal deforms easily under a weak stress, and thus is classified as a plastic crystal. The
¯
structure of phase II (264 K < T < 315 K) is rhombohedral (space group: R3m), and the
orientations of the NO−2 ions are still disordered about a 3 axis. For phase III (T < 264 K),
¯
a monoclinic cell with space group P21/c has been reported [2]. The orientations of the
NO−2 ions have not been determined yet, but they were assumed to be ordered because of
the low symmetry of the crystal structure. No further structural study has been carried out
for phase III.
¶ Present address: Department of Chemical Technology, Kurashiki University of Science and the Arts, 2640
+Nishinoura, Tsurajima-cho, Kurashiki-shi, Okayama 712, Japan.
Present address: Faculty of Science, Yokohama City University, Seto, Kanazawa-ku, Yokohama 236, Japan.
∗
Author to whom any correspondence should be addressed; e-mail: ikeda@staff.chem.tsukuba.ac.jp; fax: +81-
298-53-6503; telephone: +81-298-53-4250.
c
0953-8984/98/153341+11$19.50 ꢀ 1998 IOP Publishing Ltd
3341

3342
N Onoda-Yamamuro et al
Phase III, which is the chief concern of this study, is unusual in that its heat capacity
exceeds the normal vibrational value at temperatures as low as 100 K, and increases further
with increasing temperature toward the III–II transition [1]. The excess entropy due to this
anomaly is larger than the first-order component of the III–II transition entropy as shown
in figure 1. Such an anomaly has never been observed in molecular plastic crystals, and
so could be a characteristic feature of ionic plastic crystals. The heat capacity anomaly
suggests that the orientations of the NO−2 ions become disordered gradually with increasing
temperature over an extremely wide temperature range in phase III. Our 15N and 39K NMR
[3] and dielectric [4] studies also supported the orientational disorder of the NO−2 ions;
i.e., a minimum of the spin–lattice relaxation time T1 appeared at about 160 K in both 15N
and 39K data. Dielectric dispersion occurred in the temperature range 50–120 K for the
frequency range 20–106 Hz. We proposed that these effects arise from the 180◦-flipping
motion of the NO−2 ions in phase III.
Figure 1. The temperature dependence of the excess entropy of KNO2 calculated from heat
capacity data available in the literature [1].
As described above, there is disagreement as to the orientations of the NO−2 ions in
phase III; i.e. structural study [2] suggests orientational ordering of the NO−2 ions while
the calorimetric [1], NMR [3], and dielectric [4] studies favour orientational disorder. The
main purpose of the present study is to examine the orientational order/disorder of the NO2−
ions in phase III by neutron diffraction. We have collected neutron powder diffraction
data on phase III at several temperatures to investigate the temperature dependence of the
structure as well. It is an additional aim of the present work to investigate the orientational
disorder of NO−2 ions in phase II. This phase has been examined by means of single-crystal
x-ray diffraction, and two structural models have been proposed for the orientations of
NO−2 ions [2]. One of them was regarded as more satisfactory on the basis of the bond
lengths. Neutron diffraction is useful for determination of the positions of the disordered
N and O atoms which can hardly be distinguished using x-ray diffraction. The coherent
neutron scattering lengths of N and O atoms are different enough (9.36 fm and 5.803 fm,
respectively) for them to be differentiated by this method.

Neutron powder diffraction study of KNO2
2. Experimental procedure
3343
As a commercial KNO2 sample contained '0.5% of Na+ ions and '3% of NO3− ions,
the sample of KNO2 used in this study was prepared from NaNO2 (Wako Pure Chemical
Industries, Limited) using a cation-exchange method (Diaion SK-1 resin, Mitsubishi Kasei
Corporation). The product was further purified by recrystallization from water. The purity
of the sample was checked by ICP emission spectroscopy (Ash ICAP-757V, Nippon Jarrell)
and ion chromatography (IC 100, Yokogawa) at the Chemical Analysis Centre, University
of Tsukuba. The number fractions of the ions were as follows: K+: 49.95%; Na+: 0.05%;
NO−2 : 50.0%; NO−3 : 0.0%.
The neutron powder diffraction data on KNO2 were collected on the time-of-flight
(TOF) diffractometer VEGA [5] installed at the Neutron Science Laboratory (KENS) of
the High Energy Accelerator Research Organization (KEK). The purified sample ('3.5 g)
was contained in a vacuum-tight cylindrical can made of vanadium (5 mm in diameter and
50 mm in height) under a helium atmosphere. The TOF range of 4.5–42 ms, corresponding
˚
to the d-spacing range of 0.5–4.3 A, was covered in these measurements. The resolution
of the diffraction data (1d/d) was about 0.2%. The diffraction data on phase III were
measured at 4, 120, 180, 220, and 250 K, and those on phase II at 280 K.
Table 1. Refined structural parameters for KNO2 at 4 K. Anisotropic temperature factor:
∗2
∗2
∗2
U
T = exp[−2π2(h2a
U
+ k2b
U
+ l2c
+ 2hka∗b∗U12 + 2hla∗c∗U13 + 2klb∗c∗U23)].
11
22
33
˚
˚
Monoclinic: space group P21/c (No 14). Lattice constants: a = 4.4010(2) A, b = 9.5967(3) A,
◦
˚
c = 6.9817(2) A, b = 108.274(3) , Z = 4. RB = 1.44%, Rwp = 4.34%, Re = 3.83%, and
S = 1.13 for 3348 profile points and 107 variables.
2
˚
x
y
z
B (A )
K
N
0.4105(8) 0.1407(3) 0.2101(5) 0.13(7)
−0.0732(4) 0.4107(2) 0.1839(2)
—
—
—
O(1) 0.2034(5) 0.4127(3) 0.3067(3)
O(2) −0.1615(7) 0.2999(2) 0.0865(3)
2
2
2
2
2
2
2
˚
˚
˚
˚
˚
˚
˚
U11 (A ) U22 (A ) U33 (A ) U12 (A )
U13 (A ) U23 (A )
Beq (A )
N
0.0057(8) 0.0022(7) 0.0060(8) 0.0011(8) −0.0002(7) −0.0012(7)
0.40
O(1) 0.001(1)
O(2) 0.004(1)
0.005(1)
0.006(1)
0.006(1)
0.003(1)
0.0002(14) −0.002(1) −0.0008(11) 0.37
0.0004(11) −0.003(1) −0.0004(10) 0.39
3. Results and discussion
3.1. The structure of phase III
The unit-cell dimensions of phase III were determined by using 48 distinct reflections in
˚
a low-Q region (1.2 < d/A < 4.2). The auto-indexing program DICVOL-91 [6] gave a
◦
˚
˚
˚
monoclinic cell (a = 4.401(2) A, b = 9.596(2) A, c = 6.981(2) A, β = 108.28(4) , and
Z = 4) with figures of merit M(48) = 9.4 [7] and F(48) = 16.0 [8]. From the systematic
absence of reflections (h0l: h + l = 2n; 0k0: k = 2n), the space group was determined to
be P 21/c. This space group was confirmed by Pawley refinement [9] using the program
CAILS [10]. The space group thus determined was the same as suggested by the previous
x-ray diffraction study [2]. In this structure, one molecule forms the asymmetric unit, which
indicates that the NO−2 ions are located at general positions and that all of the NO−2 ions

3344
N Onoda-Yamamuro et al
˚
Table 2. Selected intra- and inter-ionic bond lengths (A) and angles (deg). (The symmetry
codes are: (i) x, 1/2 − y, −1/2 + z; (ii) 1 − x, −1/2 + y, 1/2 − z; (iii) 1 + x, y, z;
and (iv) 1 + x, 1/2 − y, 1/2 + z.)
(a) Intra-ionic distances
N–O(1)
N–O(2)
1.250(2)
1.256(2)
O(1)–N–O(2) 116.9(2)
(b) Shortest inter-ionic
K · · · O distances
K · · · O(1i)
K · · · O(1ii)
K · · · O(1)
K · · · O(2iii)
K · · · O(2iv)
K · · · O(2)
2.723(4)
2.796(4)
2.912(4)
2.766(4)
2.771(4)
2.838(4)
are crystallographically equivalent.
We searched for a starting model for the Rietveld refinement by a trial-and-error method.
The program used was RIETAN-96T [11]. A number of trial models were constructed by
changing the positions and orientations of the K+ and the NO2− ions on the basis of the known
structures of several NO2 and NO3 compounds. For each model, a quick Rietveld refinement
was performed using a limited number of parameters. A slack-constraint technique was
utilized in this stage: the N–O bond length and O–N–O angle were constrained to be within
◦
˚
1.24 ± 0.2 A and 115.0 ± 2.5 , respectively. The expected values of the bond lengths
and the angles were taken from the corresponding data on NaNO2 [12]. A model derived
from the structure of NH2NO2 [13] gave a satisfactorily small S-value (=Rwp/Re) for a
starting structure. The next stage of the refinement was performed without any constraint
on the structural parameters. Anisotropic atomic displacement parameters were assigned to
N and O atoms in this stage. A new technique, called partial profile relaxation [11], was
used in the final stage of the refinement and gave an excellent S-value of 1.13 (compare,
e.g., 1.61 obtained by a previous method). The 107 variable parameters (15 background
parameters, 1 extinction parameter, 1 scale factor, 13 profile parameters, 42 additional
profile parameters for the partial profile relaxation method, 4 lattice constants, 12 atomic
coordinates, 19 isotropic and anisotropic atomic displacement parameters) were refined using
˚
3348 intensity data in the TOF range between 5.5 and 41 ms (d = 0.55–4.1 A). The final
structural parameters are summarized in table 1. Table 2 lists the intra-ionic N–O and inter-
ionic K · · · O bond lengths and the O–N–O bond angle calculated from the refined fractional
coordinates. All of the intra-ionic parameters determined are reasonable compared with the
corresponding values for NaNO2 (see above). The final results of the profile fitting are
illustrated in figure 2.
The structure of KNO2 at 4 K is illustrated in figure 3(a), and its projection along the
c-axis is shown in figure 3(b). The orientations of the NO−2 ions are completely ordered.
As shown by the dashed lines in figure 3(b), each K+ ion is surrounded by six O atoms of
the NO−2 ions, with K · · · O distances of 2.74–2.90 A.
˚
The present structure is different from the structure of the ordered phase (phase II) of
KNO3 [13], though their high-temperature (orientationally disordered) phases are identical,
as detailed later. Phase II of KNO3 has an orthorhombic structure (space group: Pnma),

Neutron powder diffraction study of KNO2
3345
Figure 2. Observed (plus marks) and calculated (solid line) powder diffraction patterns of phase
III at 4 K. The calculated peak positions are given by the short vertical bars, and the differences
between the observed and calculated intensities are shown below them. The Bragg reflections
from the sample environment, which was known from the empty run, were excluded from the
refinement.
Figure 3. (a) A schematic illustration of phase III at 4 K. (b) A schematic view of the structure
of phase III projected along the c-axis. The oxygen coordination around the K+ ion is indicated
by dashed lines (see table 2).
in which the K+ ion, the N atom and one of the O atoms in the NO−3 ion are located on a
mirror plane [14]. The K+ ion in phase II is surrounded by nine O atoms at K–O distances

3346
N Onoda-Yamamuro et al
Figure 4. Observed (plus signs) and calculated (solid line) powder diffraction patterns of phase
III at 120, 180, 220, and 250 K.
˚
between 2.83 and 2.93 A. Such a structural difference between KNO2 and KNO3 may be
associated with the fact that the temperature at which the transition to the rhombohedral
phase of KNO2 (264 K) occurs is much lower than that for KNO3 (401 K) [15].
In a series of monovalent nitrite crystals, the structure of NaNO2 is ordered in the low-
temperature phase and does not form a plastic phase. The structure of NaNO2, which is
orthorhombic, is quite different from the structure of KNO2 phase III. On the other hand,
RbNO2, CsNO2, and TlNO2 form plastic phases as does KNO2 [16–21]. However, the
ordered structures of these nitrites have not been determined yet. It is most probable that

Neutron powder diffraction study of KNO2
3347
CsNO2 and TlNO2 do not form any ordered structures, because NO−2 ions are statically
disordered at low temperatures in immobile glassy states [17]. The successful structure
determination of KNO2 phase III presented here may be significant as a unique case where
the ordered structure into which an ionic plastically crystalline phase eventually transforms
has been solved.
3.2. Orientational disorder of the NO−2 ions in phase III
The diffraction patterns of phase III at the higher temperatures (120, 180, 220, and 250 K)
are shown by plus signs in figure 4. The peak positions and intensities change remarkably
with increasing temperature. The significant decrease in intensities in a lower-d-spacing
region suggests that the orientational disorder of the NO−2 ions develops with increasing
temperature. These data were analysed by the Rietveld method using the structure at 4 K
as the initial model for the refinements. The profile parameters were fixed throughout the
refinement to reduce the number of variable parameters. Isotropic atomic displacement
parameters were used for the final model because no significant improvement of the S-
value was achieved by using anisotropic ones. The diffraction intensities calculated from
the final refinement are shown by the solid line in figure 4. The final S-values for each of
the refinements were as follows: 1.12 (120 K), 1.30 (180 K), 1.81 (220 K), 2.08 (250 K).
Figure 5. The temperature dependence of the lattice parameters (a, b, c, β) and volume (V ) of
the monoclinic cell of phase III.
Figure 5 shows the temperature dependence of the lattice parameters (a, b, c, β) and
volume (V ) of the monoclinic unit cell. It is of interest that b is not sensitive to temperature
while a and c increase remarkably with increasing temperature. The isotropic atomic
displacement parameter, B, is plotted as a function of temperature for each atom in figure 6.
The parameters for phase II, which are determined in the next section, are included to
demonstrate the effect of the III–II transition. B(K+) increases normally as a linear function

3348
N Onoda-Yamamuro et al
Figure 6. The temperature dependence of the atomic displacement parameters, B, for phases II
and III. The data at 280 K are plotted with horizontal shifts of ±5 K to avoid overlapping.
of temperature while the B-values of the N, O1, and O2 atoms in the NO−2 ion increase
steeply as the temperature increases toward the III–II transition temperature. It is noteworthy
that the temperature dependence of the B-values of N, O1, and O2 is similar to that of the
excess entropy shown in figure 1, especially for the temperature at which the anomaly begins
to be significant ('100 K). The present results clearly indicate that the orientations of the
NO−2 ions become disordered gradually with increasing temperature, and the orientational
disordering progresses more rapidly as the III–II transition temperature is approached.
At the III–II phase transition, no discontinuous change of the B-values of the N and
O atoms was observed, in contrast with a discontinuous change of B for the K atom. In
phase II, the NO−2 ions undergo sixfold orientational disordering, as is described in the next
section. Therefore, the present result indicates that the orientational disorder of the NO2−
ions at higher temperatures of phase III is excited as much as in phase II.
At higher temperatures, the refinement results became less satisfactory with larger S-
values, and the bond lengths, l, and angles, θ, for the NO−2 ions deviate more from the ideal
◦
˚
˚
values; e.g., l(N–O1) = 1.14(1) A, l(N–O2) = 1.03(1) A, and θ(O1–N–O2) = 133(1)
at 250 K, compared with the ionic geometry of phase III given in table 2. This must be
caused by the highly disordered orientation of the NO−2 ions, which cannot be represented
by the displacement parameters.
To make a further investigation of the orientational disorder of NO−2 ions, we carried
out a difference Fourier analysis. Figure 7 shows the difference Fourier contour maps of
the section containing N, O1, and O2 atoms. The maximum density position of the N and
two O atoms are connected by the solid straight lines. It is clearly shown that the density
difference develops with increasing temperature. This means that some orientations other
than the stable orientation determined at 4 K are excited at higher temperatures in phase III.
Detailed disorder models, such as those mixing two or more orientations of the NO−2 ions
with different probabilities, should improve the fitting for the data at higher temperatures
if one can find appropriate initial models for the Rietveld refinement. In fact, refinements

Neutron powder diffraction study of KNO2
3349
Figure 7. Difference Fourier contour maps for the section containing N, O1, and O2 atoms.
¯
Table 3. Refined structural parameters for KNO2 at 280 K. Rhombohedral: space group R3m
˚
˚
(No 166). Lattice constants: a = 5.027 90(4) A, c = 10.055 87(8) A, Z = 3. RB = 5.42%,
Rwp = 3.88%, Re = 4.25%, and S = 0.913 for 3805 profile points and 44 variables.
2
˚
x
y
z
B (A )
K
N
O
0
0
−x
1/2
−0.01(6)
5.5(3)
8(5)
0.04(2)
0.164(10) 0.233(5) −0.023(2) 4.7(9)
with several initial models, in which two different NO−2 orientations were mixed with an
equal probability (0.5), were unsuccessful.
3.3. Structure of phase II
According to the single-crystal x-ray diffraction study [2], phase II has a rhombohedral
−
¯
structure (space group: R3m) in which the orientations of the NO2 ions are disordered about
¯
a 3 axis. The following two models given by Solbakk and Strømme [2] were tested in the
Rietveld analysis of the present neutron diffraction data. In model 1, the N atom is located
on the 3 axis (at the 3a position), and the O atoms are located on a mirror plane (at the 18h
¯
position). In model 2, the N atom is placed on the mirror plane (at the 18h position), and the
O atoms are placed at general positions (36i). Solbakk and Strømme favoured model 2 on
the basis of the N–O bond lengths. For both models, Rietveld refinements were performed
with the O–N–O bond angle fixed at 115◦; the refinements did not converge without this
constraint. Isotropic atomic displacement parameters were used for the final model because
no significant improvement of the Rwp-value was achieved by using anisotropic ones. The
Rwp-values obtained for models 1 and 2 were 4.01% and 3.88%, respectively. The N–O
˚
˚
bond length in model 1 (1.00(2) A) was much shorter than the literature value of 1.24 A
˚
[10], while that for model 2 (1.18(4) A) agreed well with it. These results strongly support
model 2, in agreement with the x-ray diffraction study. The results of the Rietveld analysis
with model 2 are illustrated in figure 8, and the refined structural parameters are listed in
table 3. The structure of phase II has no relation to that of phase III. The space group and

3350
N Onoda-Yamamuro et al
Figure 8. Observed (plus signs) and calculated (line) powder diffraction profiles of phase II at
280 K.
relative ionic positions of phase II are the same as those of KNO3 phase I. In KNO3 phase
I, the NO−3 ions have twofold orientational disorder, to satisfy the 3m symmetry.
¯
In this structural model of phase II, NO−2 ions undergo sixfold orientational disordering.
If one takes the large displacement parameters into consideration, the space distribution of
¯
the O atoms is almost continuous around the 3 axis, like a ring doughnut. This situation is
reflected in the weak peak intensities in a lower-d-spacing region as shown in figure 8. The
present result is also consistent with the large total excess entropy of the III–II transition
(25.9 J K−1 mol−1).
4. Conclusions
The neutron powder diffraction data of KNO2 were collected at several temperatures at
which phases III and II are stable, and the structures of these phases were successfully
analysed by the Rietveld method. The structure of phase III is completely ordered at
4 K, and becomes gradually disordered as regards the orientation of the NO−2 ions as the
temperatu−re increases toward the III–II transition temperature. In phase II, the orientations
¯
of the NO2 ions are highly disordered about the rhombohedral 3 axis. The present results are
completely consistent with the previous calorimetric, NMR, and dielectric data, providing
conclusive evidence for the orientational order/disorder of the NO−2 ions in phases III and
II of KNO2.

Neutron powder diffraction study of KNO2
3351
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