ELECTRON PARAMAGNETIC RESONANCE STUDIES OF PHASE TRANSITIONS IN KCN

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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:

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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 D O CARMO,

R. R. D O 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 ferro6lectriques des 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 dipo- laire, 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

<

11 1

>

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 antiferroelectric state.

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, K C N 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 < 11 1

>

directions in the fcc cell, but the last one seems t o be kss likely than the other two, which give equivalent fits to the experimental data [2].

The structure of the orthorhombic phase immedia- tely 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

(*) Present address : Institut de Physique, Universitk de Neuchltel, rue A.-L. Breguet 1, CH, 2000 Neuchbtel, Switzer- land.

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 structure which is formed in the 168 K phase transition. We used as a probe two paramagnetic molecules

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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 deter- mine 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 CN-

ions at low temperatures.

On the other hand, the similarity between the HCN-

molecuIes 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 suffi- cient information for a qualitative picture of the behavior of KCN crystals.

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.

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 l c 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.

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

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ELECTRON PARAMAGNETIC RESONANCE STUDIES OF PHASE TRANSITIONS IN KCN C7-243 T

(a

1

dt

i---.~ 4 0 gauss

(b)

-

4tk

4 0 gauss

,

J + V / \ ~

(c)

dll+Ah

+--

t

FIG and and 170

.

3. - ESR spectrum of HCN- in KCN for : a) Ho[100]

b) Ho[llO] direction of the cubic KCN crystal. Spectra (a)

(b) were made at 65 K and the isotropic spectrum ( c ) at 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

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 HCN-

spectrum strongly changes with temperature, pre- senting 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.

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

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C7-244 J. P. VON DE IR 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 a b 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 a t 30 K the HCN- molecules jump rapidly between three orientations, in such a way that the HC bond remains in a

<

11 1

>

direction and the C N 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 t o 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 there- fore 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.

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ELECTRON PARAMAGNETIC RESONANCE STUDIES OF PHASE TRANSITIONS IN KCN C7-245

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

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 CN-

ions 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 orthorhom- bic 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 proba- bility of [loo] alignment being higher than

<

1 1 1 >. 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

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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.

FIG. 8. - The antiferroelectric ground state structure of

KCN.

Two independent antiferroelectric sublattices can be seen, one defined by the eight electric dipoles of the corners and the other defined by the body centered position. One sublattice can be obtained from the other by an appropriate translation operation. Still with this model Hamiltonian, but within a mean field

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

a,

4.50 A, 4.22

A

and 3.07

A,

so that it is expected that the

<

11 1

>

direction should play the most important role in the reorientation of the CN- ions.

Finally, we should say that there and still many features on the behavior of this system that are not yet well understood. In particular, we must apply this model to calculate the specific heat capacity as a function of temperature to see if it can account correctly for the specific heat measurements 161.

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908.

[5] GONGORA, A., JULIAN, M. and LUTY, F., 1974 Int. Conf. on Color Centers in Ionic Crystals, Sendai, Japan

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[ l l ] Arzu, K., Phys. Rev. B 2 , 3 (1970) 754.

[I21 OTHMER, S. and SILSBEE, R. H., Bull. Amer. Phys. Soc. 13

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1131 JULIAN, M. and LUTY, F., International Conference on Low Lying Lattice Vibrational Modes, Puerto Rico,