Download electron paramagnetic resonance studies of phase transitions in kcn

ELECTRON PARAMAGNETIC RESONANCE
STUDIES OF PHASE TRANSITIONS IN KCN
J.P. Von Der Weid, L.C. Scavarda Do Carmo, R. Do Santos, B. Koiller, S.
Costa Ribeiro, A. Chaves
To cite this version:
J.P. Von Der Weid, L.C. Scavarda Do Carmo, R. Do Santos, B. Koiller, S. Costa Ribeiro,
et al.. ELECTRON PARAMAGNETIC RESONANCE STUDIES OF PHASE TRANSITIONS IN KCN. Journal de Physique Colloques, 1976, 37 (C7), pp.C7-241-C7-246.
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Submitted on 1 Jan 1976
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JOIJRNAL DE PHYSIQUE
Colloque C7, supplkment au no 12, Tome 37, DCcembre 1976, page C7-241
ELECTRON PARAMAGNETIC RESONANCE STUDIES
OF PHASE TRANSITIONS IN KCN
J. P. VON DER WEID (*), L. C. SCAVARDA DO CARMO,
R. R. DO SANTOS, B. KOILLER and S . COSTA RIBEIRO
Pontificia Universidade Cat6lica do Rio de Janeiro, Rua Marques de S. Vincente,
225 G h e a , Rio de Janeiro, Brasil
and
A. S. CHAVES
Departamento de Fisica Icex, Universidade Federal de Minas Gerais,
C. Postal 1621, 30000 Belo Horizonte, Brasil
R6sum6. - Les proprietes ferroelastiques et ferro6lectriquesdes cristaux de KCN ont ete etudibes
par la RPE des ions molBculaires HCN- et N;. La structure en domaines genBrCe par la transition
de phase cubique -t orthorhombique B 168 K prksente six orientations non equivalentes. L'analyse
du spectre de HCN- entre 83 K et 170 K montre que les ions CN- du rBseau se reorientent entre
les directions [loo] et < 111 > de la cellule orthorhombique. L'Bnergie 6lastique minimale des
directions < 111 > est plus BlevCe que celle de la direction [loo] (AE = 7,4 meV) a partir d'un
Hamiltonien tr6s simple, ou les interactions entre les ions CN- sont de nature electrostatique dipolaire, nous avons montre que la phase ordonnee se pdsente comme un etat antiferroelectrique.
Abstract. - The ferroelastic and ferroelectric properties of KCN crystals were investigated
through the EPR spectra of HCN- and N; molecular ions in the lattice. The domain structure
generated by the cubic + oethorhombic transition at 168 K consist of six non equivalent domain
orientations. The analysis of the HCN- spectra between 83 K and 170 K showed that reorientations of the CN- ions occurs between the [loo] and < 111 > orthorhombic directions, which have
a minimum elastic energy 7.4 meV higher than the [loo]. Based on a simple model Hamiltonian in
which the interactions between the CN- ions are of an electrostatic dipole-dipole nature, we showed
that the ordered phase consist of an antiferroelectricstate.
1. Introduction. - The structure and phase transitions in KCN have been investigated extensively
by several authors [l-51 but the behavior of this
system is not yet well understood. At temperatures
above 168 K, KCN exhibits a cubic NaCl structure,
with the CN- ions behaving as hindered rotators in
the cubic crystalline field. Neutron diffraction measurements on polycrystalline samples [I] or in single
crystals [2] have not decided whether the preferential
orientations of the CN- ions are < 100 >, < 110 >
or < 111 > directions in the fcc cell, but the last
one seems to be kss likely than the other two, which
give equivalent fits to the experimental data [2].
The structure of the orthorhombic phase immediately below 168 K has been determined from the X
ray work, and it is suggested that the CN- ions lie
in a direction closely related to the < 110 > direction
in the cubic phase [3] [4]. A specific heat anomaly
was observed at this critical temperature [6]. The
observation of a second specific heat anomaly at
83 K, with entropy change A S = R In 2 suggested the
following picture for the phase transitions in KCN ;
the first transition is assigned to the orientation of
the elastic dipole moments of the CN- ions, but
allowing still a 1800 flip of the electric dipole moment.
This last degree of freedom should be loss below
83 K in a phase transition associated with the ordering
of the electric dipoles of the CN- ions. However
it is hard to understand how could be possible an
elastic dipole alignment of the CN- ions allowing
still 1800 flips as the electric dipole moment is associated to the order of the molecule with respect to
head and tail.
It is the purpose of this work to investigate this
puzzling
feature of KCN crystals and the domain
(*) Present address : Institut de Physique, Universitk de
Neuchltel, rue A.-L. Breguet 1, CH, 2000 Neuchbtel, Switzer- structure which is formed in the 168 K phase transition.
We used as a probe two paramagnetic molecules
land.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1976759
C7-242
J. P. VON DER WEID er al.
which can be formed in pure or OH- doped KCN,
say, N; and HCN- molecular ions. The simple
electronic structure of N l molecules and the strong
anisotropy of its EPR spectrum allowed us to determine unambiguously the domain structure below
the 168 K phase transition, and compare it to the
one which is previewed from group theory based in
the assumption of < 110 > orientation of the CNions at low temperatures.
On the other hand, the similarity between the HCNmolecuIes and the CN- ions of the host lattice,
together with the strong temperature dependence
of its EPR spectrum allowed us to clarify some aspects
of the puzzling feature associated with the electric
dipole inversion between 83 K and 168 K.
In this paper we are concerned only with symmetry
considerations, so that detailed analysis of EPR
spectra, together with spin Hamiltonian parameters,
will not be discussed here. They will be published
in forthcoming papers. Only the symmetry of the
angular variations of EPR spectra can give us sufficient information for a qualitative picture of the
behavior of KCN crystals.
2. Experimental results. - The formation of the
multidomain structure below 168 K is evident from
the milky aspect that is presented by the crystal
below this temperature. Since we don't know, at
principle, the exact orientation of the orthorhombic
axes of each domain, we will refer the orientation
of the magnetic field in our EPR spectra to the crystalline axes of the cubic crystal at room temperature.
Figure Fa, b and c show the spectra obtained after
room temperature X irradiation of pure KCN samples.
These spectra are very similar to the ones observed
for N r molecules in alkali halides [8, 91 and are
assigned to N z molecules in KCN crystals. They
were obtained with the static magnetic field parallel
to the [I001 and [I101 cubic directions. The spectra
of figure l a and l b were obtained at 63 K and the
spectrum of figure lc was taken at 86 K, where we
can see how the lines become broader with increasing
temperatures due to the reorientation of the molecule
in the lattice. In these spectra we can recognize sets
of pentets with intensity ratio 1 : 2 : 3 : 2 : 1 due to
the hyperfine interaction of the unpaired electron
with the two nitrogen nuclei of the molecule. In
figure 2, we show the angular variation of the speo
trum in a rotation of the magnetic field about the [001]
cubic direction, where 6 is the angle between the static
magnetic field and the [loo] cubic direction. In order
to simplify the drawing, only half of the lines are
shown, the complete angular variation can be obtained
by a reflection of the whole angular variation shown
in figure 2 about 6 = 45O ([I101 cubic direction).
FIG.2. - Angular variation of the EPR lines of the N;
molecular ions. Dots are experimental points. Full line represents
the theoretical fit of the Hamiltonian of 'equation (1) with the
parameters of table I. PI through Pg are six magnetically
inequivalent pentets.
Fro. 1. - EPR spectra of the Nz molecular ions in KCN :
a) Ho/[lOO] cubic direction T = 63 K ; b) Ho/[llO]
cubic
direction T = 63 K ; c) Ho,/[llO]
cubic direction T = 86 K.
Pr through P6 are six magnetically inequivalent pentets.
Figures 3a, b and c show the spectra obtained in
OH' doped KCN after UV irradiation at LNT.
These spectra are very similar to the ones observed
for HCN- molecules in KC1 at 4 K [lo], and are
assigned to HCN- molecules in KCN. The spectra
in figure 3a and 3b were obtained at 60 K with the
magnetic field parallel to the [I001 and [I101 cubic
axes. The spectrum in figure 3c was obtained at
170 K and is isotropic, due to the rapid rotation of
ELECTRON PARAMAGNETIC RESONANCE STUDIES OF PHASE TRANSITIONS IN KCN
T
dt
(a1
i40
-gauss
---.~
4tk
(b)
-
4 0 gauss
,
J+V/\~
(c)
dll+Ah
+-
C7-243
the static magnetic field around the [001] cubic axis
in the (001) plane.
The EPR spectra of HCN- and N l molecules in
KCN are strongly temperature dependent, as can be
seen from figures 1 and 3. This temperature dependence
can be explained by the reorientation of the molecule
in the lattice, with a frequency which increases with
temperatures. For N; molecules we see that the
lines become broader in a continuous way and the
spectrum disappears at about 115 K. No connection
can be made with the phase transition that occurs
at 83 K. On the order hand, we see that the HCNspectrum strongly changes with temperature, presenting the same broadening due to reorientation,
until a different sharp spectrum becomes defined
at 115 K. At this temperature, the molecule is jumping
rapidly enough to average out part of the anisotropies
of the hyperfine interaction. The angular variation
of the EPR signal of HCN- molecules in KCN at
125 K is shown in figure 5. At temperatures higher
than 168 K, the spectrum becomes isotropic, and is
due to a free rotating molecule in the-cubic crystal.
t
FIG. 3. - ESR spectrum of HCN- in KCN for : a) Ho[100]
and b) Ho[llO]direction of the cubic KCN crystal. Spectra (a)
and (b) were made at 65 K and the isotropic spectrum (c) at
170 K. The line indicated by an arrow in spectrum ( c ) is due to
the MgO : Cr+++g-marker.
the molecule in the crystal. In these spectra we recognize a main doublet splitting due to the hyperfine
interaction of the unpaired electron with the hydrogen
nucleus, and a secondary triplet splitting, due to the
hyperfine interaction of the unpaired electron with
the nitrogen nucleus. Figure 4 shows the angular
variation of the EPR spectrum obtained by rotating
FIG. 5. - Inequivalent crystalline domains in a KCN crystal
compared with the cubic direction. The rectangles presented are
faces ab of each domain.
It is important to note that the hyperfine interaction
of the unpaired electron and the nitrogen nucleus is
described by a tensor of axial symmetry with only
one non-zero component. This feature will be very
helpful in analysing the behavior of the molecule
at high temperatures, where the motion of the molecule
averages out part of this anisotropy. The symmetry
axis of this hyperfine tensor is perpendicular to the
CN bond of the molecule [lo].
F I ~ 4.
. - Angular dependence of the ESR spectrum of
HCN- molecules in KCN at 60 K for Ho in the (001) plane of
the cubic crystal. The 1 100 1 direction corresponds to 0 = 0 deg.
3. Discussion. - The symmetry of all angular
variations obtained in KCN crystals clearly shows
that the, overall cubic symmetry of the prototypic
cubic crystal at room temperature is maintained
after the phase transition. The orthorhombic domains
C7-244
J. P. VON DEIR WEID et al.
are not randomly oriented, but disposed in a very
simple way. The number of inequivalent domain
orientations can be predicted from group theory
arguments [l I] as being the order of the cubic group
divided by the order of the orthorhombic group so
that there are six non equivalent domain orientations
in KCN below 168 K. These orientations are shown
in figure 6 where the rectangles represent ab planes
of the orthorhombic crystal. Then, if we know the
orientation of an axis with respect to prototypic
cubic axes, then we also know its orientation with
respect to orthorhombic axes.
FIG. 6. - Angular dependence of the ESR spectrum of
HCN- molecules in KCN at 125 K, for the magnetic field in a
100 ) prototypic plane.
Before discussing in detail the temperature dependence of the EPR spectra of HCN- and N; molecules
in KCN, let us compare them with the similar behavior
of these molecules in KC1 and other alkali halides.
It is known that EPR measurements of these molecules
in alkali halides can only be made at very low temperatures, say, liquid helium temperature. The EPR
spectrum of NZ molecules disappears at higher
temperatures, whereas the changes in EPR spectrum
of HCN- molecules occurs between 4 K and
77 K [12]. It was shown that at 30 K the HCNmolecules jump rapidly between three orientations,
in such a way that the HC bond remains in a < 111 >
direction and the CN bond jumps between the three
< 110 > directions which are obtained by a 1200
rotation of the molecule about the H C bond. The
anysotropic part of the hyperfine interaction of the
unpaired electron with the nitrogen nucleus is comple-
tely averaged out and the hyperfine interaction with
the proton is axially symmetric about a < 111 >
axis. At 77 K the molecule freely rotates, giving an
isotropic spectrum.
The behavior of HCN- and Ny molecules in KCN
is almost the same as described above, but the reorientation phenomena occur at much higher temperatures.
The N, molecule is already stopped in the KCN
lattice at 63 K, and the HCN- molecules start to
jump near 83 K, the free rotation being observed
only after the 168 K orthorhombic to cubic phase
transition. The lower symmetry of the lattice and the
local electric field which must appear in the low
temperature phase seem to play a very important
role in these phenomena.
Up to now very few information can be obtained
from the jumping of N; molecules in KCN crystals.
The gradual disappearance of the spectrum seems to
be completely disconnected from the low temperature
phase transition, and at higher temperatures the EPR
spectrum is so broad that it cannot be seen. On the
other hand, the temperature dependence of the EPR
spectrum of HCN- molecules in KCN showed a
strong connection with both phase transitions, at
83 K and 168 K. Here we will explore the symmetry
changes of the ESR spectrum and the similarity
between the phenomena observed in KCN and KC1
to obtain information about the jumping phenomena
of HCN- molecules in KCN, and furthermore about
the whole KCN lattice since the HCN- molecules
and the CN- ions of the lattice are very similar as
far as mass distribution and electric dipole moment
are concerned.
Two kinds of motion can be recognized in the
HCN- behavior in KCl. The first one, excited at low
temperatures (30 K), is the jumping of the CN bond
of the molecule between three directions which are
the three < 110 > directions mentioned above.
These orientations are obtained from symmetry
operations of the crystal symmetry group, and therefore have the same elastic energy. Hence, the molecule
stays the same fractional time on each orientation,
and since for these three orientations of the molecules,
the symmetry axis of the nitrogen hyperfine splitting
tensor is oriented along the three orthogonal < 100 >
directions, the resulting interaction of the unpaired
electron with the nitrogen nucleus is isotropic. The
averaged interaction of the unpaired electron with
the proton is described by a tensor which is axially
symmetrical with respect to a < 111 > axis. The
second motion is excited at higher temperatures
(77 K) and probably corresponds to the jumping
of the molecules between all possible positions in
the cubic lattice so that all anisotropies of the spectrum are averaged out.
The same general behavior can be recognized in
KCN, although some different aspects must be taken
into account. First of all, the molecule stops at a
ELECTRON PARAMAGNETIC RESONANCE STUDIES OF PHASE TRANSITIONS IN KCN
temperature much higher than in KCI, say 60 K,
and the free rotation is observed only above the phase
transition at 168 K, in the cubic crystal. On the other
hand, the first motion, which is clearly seen above
115 K, presents some different aspects, such as the
remaining anisotropy of the nitrogen hyperfine
splitting tensor. We clearly recognize here the influence
of the lower crystalline symmetry and of the low
temperature phase transition. We can understand the
behavior of the HCN- molecule in KCN through
the following picture : the CN bond of the molecule
jumps between three directions which correspond
nearly to the three < 110 > directions of the distorted
cubic cell. One of these will be the orthorhombic
[loo] direction and will correspond to the direction
of static alignment of the molecule at low temperatures.
The other directions will be close to < 111 > directions of the orthorhombic cell.
The symmetry axis of the nitrogen hyperfine splitting
tensor will jump between the orthorhombic [OOl]
direction and two other directions which are almost
perpendicular to it. Note that the orthorhombic [OOl]
direction is a < 100 > direction of the cubic cell.
Furthermore, we must suppose that the [loo]
orientation of the molecule have a slightly lower
elastic energy than the other two, so that at low
temperature the molecule stops in only one direction.
This supposition accounts also for the symmetry
of the angular variation observed at 125 K. Here the
nitrogen hyperfine splitting is represented by an almost
axially symmetric tensor with major axis aligned in
a < 100 > cubic direction. If the energy associated
to the [loo] orientation of the molecule is lower than
the other two, the symmetry axis of the nitrogen
hyperfine tensor will stay a longer time in one < 100 >
cubic axis than in the plane perpendicular to it, so
that the averaged interaction should be axially symmetric with major axis in a < 100 > direction. The
deviation of this symmetry from the axial one can
be understood if we remember that in the orthorhombic cell we cannot assume that the three directions
between which the symmetry axis of the nitrogen
tensor jumps are perpendicular to each other. The
most important feature is that there must be one
.
:100 > direction for which the interaction should
be much greater than for the plane perpendicular
to it. This can be recognized in the angular dependence
of figure 6, where the major nitrogen splitting is
11.3 gauss along a < 100 > direction of the cubic
crystal, and for the plane perpendicular to it, this
interaction always takes values between 3.6 gauss
and 4.5 gauss.
The effect of the lower symmetry of the KCN
lattice is presented by these two facts : the remaining
anisotropy of the nitrogen splitting tensor and the
fact that the second motion cannot be excited in the
orthorhombic lattice. The free rotation of the molecule
only occurs above the 168 K phase transition from
C7-245
orthorhombic to cubic symmetry. The effect of the
low temperature phase transition appears to be the
freezing of the first motion below the 83 K phase
transition.
We may now extend our discussion to the behavior
of CN- ions in the KCN lattice using the fact that the
elastic dipole moments of HCN- and CN- are very
similar, and that the HC bond of the HCN- molecule
does not play any role in the jumping phenomena
below 168 K. Furthermore, we compared the jumping
frequencies of HCN- molecules with those of CNions in a significant range of temperatures. The first
ones were obtained from our EPR measurements,
whereas the second ones were obtained from dielectric
loss measurements in pure KCN [13]. These jumping
frequencies of HCN- molecules and the CN- ions
in KCN lattice are indeed very similar.
Assuming the same elastic interaction with the
neighbours for both molecules, we may propose the
energy scheme for the CN- molecules reorientation
shown in figure 7, where the continuous line represents
FIG.7. - Energy scheme for the lower energy orientation
of CN- ions in KCN lattice at 60 K. The dashed line represents
the energy pE of the antiferroelectric state.
the elastic interaction with the neighbours and the
dashed line represents the elastic interaction between
the electric dipole of the CN- ions with the local
electric field, which appears below 83 K. Then we
conclude that there will be no static alignment of
elastic dipoles in the [loo] direction of the orthorhombic lattice below the structural phase transition at
168 K, but a dynamic statistical alignment of elastic
dipoles in the [loo] and < 1 1 1 > orthorhombic axes,
with rapid reorientations between them, the probability of [loo] alignment being higher than < 111 >.
This dynamic alignment allows one to understand the
possibility of inversion of the electric dipole moments
at the arion site even in the orthorhombic phase,
where an elastic dipole alignment is observed. This
reorientation is achieved through an intermediate
< 11 1 > orientation, which have an elastic energy
slightly higher than the [loo]. The value of the energy
difference AE between the two orientations can be
obtained from the behavior of the EPR spectrum
C7-246
J. P. VON DER WEID et al.
of HCN- molecules between 115 K and 168 K, since
it must obey Boltzmann statistics. This behaviour
was investigated and it was seen that it indeed obeys
an Arrhenius law and the value for the energy difference AE is 7.4 meV.
Finally we studied the 83 K phase transition based
on a simple model Hamiltonian, in which the interactions between the CN- ions are of an electrostatic
dipole-dipole nature. This leads to the antiferroelectric
state in the ordered phase which is shown in figure 8.
theory approximation, we obtained an expression
for the order parameter (sublattice polarization) of
the transition as a function both of temperature and
electric dipole moment of the CN- ion. The available
experimental value for the electric dipole moment
of CN- ion in KC1 ( p = 0.07 eA) yields a transition
temperature T, = 31.2 K. As this value is not reliable
for KCN crystal, we have used the value that fits
experimental transition temperatures (T, = 83 K) in
order to obtain the order parameter as a function of
temperature, as well as the orientational energy
levels both for the disordered phase and for 0 K.
Detailed analysis of this behavior will be published in a
more complete paper.
4. Conclusions. - In this paper we presented a
simple model for the behavior of the CN- ions in
KCN lattice based essentially in symmetry considerations. Of course these are not the only support for
our conclusions, a much more detailed study of this
system will be presented in a forthcoming paper.
Nevertheless the symmetry arguments presented here
are sufficiently consistent to support the qualitative
picture of the KCN- orthorhombic phase proposed
in this paper. So far we cannot say whether there
are other equilibrium orientations involved in the
jumping of the CN- ions in the lattice, as the HC
bond would not allow the HCN- molecule to occupy
them. However if we take the interatomic distance
between next neighbours along the [loo], < 111 >,
[OlO] and [loo] directions of the orthorhombic cell,
we
see that they are respectively equal to 5.07
FIG. 8. - The antiferroelectric ground state structure of
4.50 A, 4.22 A and 3.07 A, so that it is expected that
KCN.
the < 111 > direction should play the most important
role in the reorientation of the CN- ions.
Finally, we should say that there and still many
Two independent antiferroelectric sublattices can be
seen, one defined by the eight electric dipoles of the features on the behavior of this system that are not
corners and the other defined by the body centered yet well understood. In particular, we must apply
position. One sublattice can be obtained from the this model to calculate the specific heat capacity as
other by an appropriate translation operation. Still a function of temperature to see if it can account
with this model Hamiltonian, but within a mean field correctly for the specific heat measurements 161.
a,
References
[3]
[4]
[5]
[6]
[7]
ATOJI,M., J. Chem. Phys. 54 (1971) 3514.
PRICE,D.L., RoWE, J. M., RUSH,J. J., PRINCE,E., HINKS,
D. G. and SUSMAN,
S., J. Chem. Phys. 56 (1972) 3697.
VERWEEL,
H. J. and BIJVOET,
J. M., 2.Krist. 100 (1938) 201.
BIJVOET,
J. M. and LELY,J. A., Rec. Trav. Chim. 59 (1940)
908.
GONGORA,
A., JULIAN,M. and LUTY,F., 1974 Int. Conf.
on Color Centers in Ionic Crystals, Sendai, Japan
(1974) Abstract G. 126.
SUGA,H., MATSUO,T. and SEKI, S., Bull. Chem. Soc.
Japan 38 (1965) 1115.
VONDER WEID,J. P., Rev. Bras. Fis. 6 (1976) 1.
[8] HAUSMANN,
A., HILSH,R. and SANDER,
W., 2. Phys. 179
(1964) 461.
[9] BRAILSFORD,
J. R., MORTON,J. R. and VANOTTI,L. E.,
J. Chem. Phys. 50 (1969) 1051.
[lo] ADRIAN,F. J., COCHRAN,
E. L., BOWERS,
V. A. and WEATHERLEY,
B. C., Phys. Rev. 177,1(1969) 129.
[ l l ] Arzu, K., Phys. Rev. B 2 , 3 (1970) 754.
[I21 OTHMER,
S. and SILSBEE,
R. H., Bull. Amer. Phys. Soc. 13
(1968) 661.
1131 JULIAN,M. and LUTY, F., International Conference on
Low Lying Lattice Vibrational Modes, Puerto Rico,
1975.