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Order-disorder phase transition of NH4AlF4 through Raman scattering investigations
M. Couzi, P. Rocquet, J.L. Fourquet
To cite this version:
M. Couzi, P. Rocquet, J.L. Fourquet. Order-disorder phase transition of NH4AlF4 through Raman scattering investigations. Journal de Physique, 1985, 46 (3), pp.435-445.
�10.1051/jphys:01985004603043500�. �jpa-00209982�
Order-disorder phase transition of NH4AlF4 through Raman scattering investigations
M. Couzi, P. Rocquet
Laboratoire de Spectroscopie Infrarouge (LA 124), Université de Bordeaux I, 351, Cours de la Libération, 33405 Talence Cedex, France
and J. L. Fourquet
Laboratoire des Fluorures et Oxyfluorures Ioniques (ERA 689),
Faculté des Sciences, Route de Laval, 72017 Le Mans Cedex, France
(Reçu le 4 juin 1984, révisé le 20 septembre, accepté le 23 octobre 1984 )
Résumé. 2014 Les spectres Raman de basse fréquence (0-600 cm-1) d’un monocristal de NH4AlF4 (composé bidi-
mensionnel de type perovskite) ont été étudiés à différentes températures; la transition de phase D184h ~ D134h ayant
lieu vers 150 K est mise en évidence. Les résultats montrent qu’il s’agit d’une transition de type purement ordre- désordre, associée à la dynamique réorientationnelle des ions NH+4. Un modèle simple de pseudo-spins réorien-
tables dans une matrice rigide constituee de feuillets d’octaèdres AlF6, permet de rendre compte des principales caractéristiques spectrales associées à la transition. L’estimation de l’exposant critique du paramètre d’ordre est
en accord avec un caractère essentiellement tridimensionnel de la transition au voisinage de Tc.
Abstract. 2014 The low-frequency (0-600 cm- 1) Raman spectra of NH4AlF4 single crystals (a perovskite-type layer compound) have been studied at different temperatures, and the D184h ~ D134h phase transition occurring around
150 K is evidenced. The Raman data show that it is purely an order-disorder transformation, connected to the
reorientational dynamics of the NH+4 ions. A simple model of reorientable pseudo-spins in a rigid layered matrix
of corner-sharing AlF6 octahedra describes the main spectral characteristics of the phase transition. The estimate of the critical exponent of the order-parameter is consistent with the essentially three-dimensional character of the transition in the vicinity of Tc.
Classification
Physics Abstracts
63.20 - 64.70K - 78.30
1. Introduction.
Ammonium tetrafluoroaluminate, NH4AlF4, belongs
to the family of perovskite-type layer compounds MAlF4 (M = K, Rb, Tl, NH4) whose structures are
closely related to that of the TlAlF4 aristotype (P 4jmmm-Dlh, with Z = 1) [1-6]. They consist of infinite layers of AlF6 octahedra sharing four atoms,
Feq, in the (001) plane. The unshared fluorine atoms,
Fax, lie along the c axis. The cavities between layers
are occupied by the M + cations (Fig. 1).
In this series of compounds, NH4AlF4 is of special
interest because of the occurrence of an order-disorder
phase transition in the vicinity of 150 K [5, 6]. This
transition was first observed by means of EPR investi- gations, but could not be evidenced by X-ray dif-
Fig. 1. - Schematic representation of the aristotype struc-
ture of NH4AIF 4 : evidence of the layer structure.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004603043500
fraction [5]. It was further confirmed by neutron
diffraction experiments [6]. The space-group deter- mined at room temperature is 14/mcm-D 18 with
Z = 4 in the centred tetragonal unit-cell (note that
the primitive unit-cell contains only two formula units). This structure derives from the parent phase
P 4/mmm by «rotations» (about 90) of the AlF6
octahedra around the c axis, in alternate sense for two consecutive layers; the NH’ groups are statistically
distributed between two energetically equivalent orien- tations, with the H atoms pointing towards the Fax (Fig. 2). Below the phase transition temperature ( ~ 150 K), the AlF6 octahedron layers do not undergo
noticeable distortion, but the NH’ tetrahedra are now ordered, with a « ferro » type ordering for adjacent
tetrahedra in the (001) plane and « anti-ferro » type
ordering for tetrahedra in consecutive layers. The
space-group determined for this ordered phase is
P 42/mbc-D ", with Z = 4 [5, 6]. All these facts tend to indicate that the phase change of NH4AIF, is
Fig. 2. - The two possible orientations of the NH’ group in its Fax cage; Feq atoms have been omitted for clarity.
essentially related to an order-disorder mechanism
arising from the reorientation of the NH’ tetrahedra
in a rigid AlF6 octahedron layered matrix. Hence, from several aspects, the transition of NH4 AIF4
exhibits similarities with the well-known order- disorder phase transitions that occur in the ammonium halides. However, a marked difference lies in the fact that NH+4 -NH+4 interactions are tridimensional in the disordered cubic phase of ammonium halides,
whereas in NH4AlF4 they can be expected to be essentially bidimensional, due to the strong aniso- tropy of the layered structure (Fig. 1).
Raman scattering has been widely used for studying
the order-disorder phase transitions of the ammonium
halides, and the phonon spectrum, influenced by the
disorder of an Ising pseudo-spin variable associated to the NH+ orientation, has been carefully analysed [7-11]. The purpose of the present work is to investigate
the similar transition occurring in NH4AlF4, and to
determine whether or not there is some influence due to the two-dimensional character of this system on
the observed Raman features, or on the transitional characteristics. The first results of this study have
been reported elsewhere [12].
This paper is organized as follows :
A group-theoretical analysis of the order-disorder
D 18 +-+ D13 phase transition of NH4AIF 4 is presented
in section 2. This section also includes a theoretical
study of the fictitious transition leading to the D14h aristotype structure, which is of importance in under- standing the observed Raman spectra, as well as the
group-theoretical analysis of a « sub-cell » model for the external modes of the NH+4 groups. The
experimental procedure is described in section 3.
Our results are presented and discussed in section 4.
§ 4.1 is devoted to the assignment of the Raman spectra of the disordered and of the ordered phase and it
turns out that the spectral characteristics associated to the translational modes of the NH’ are of particular
interest for understanding the transition mechanism.
They are analysed in detail in § 4-2.
2. Group-theoretical analysis.
The D 18 and D 13 space-groups, corresponding to
the two phases of NH4AlF4 stable above and below the transition temperature, respectively, are group-
subgroup related. Note also that D 18 is a subgroup
of the parent structure D14h which is expected to occur
at high temperature, but could not be evidenced with
NH4AlF4 because of the thermal decomposition
that takes place around 620 K [2]. Nevertheless, the fictitious transition D’ -+ D 18 will be considered theoretically, because of the possible existence of premonitory effects due to this transformation in the phases of lower symmetry [13].
The D14h -> D 18 transition involves a doubling of the primitive unit-cell, from which we deduce that the
point A(?:, ?:, ) a a c of the Dih 4h Brillouin zone boundary
becomes a zone-centre (r point) in D 18 - The little
co-group of the wave-vector at the point A is D4h [14],
the one-dimensional representations of which conserve
the crystalline class D4h. Among these one-dimensional
representations of the wave-vector group [14], four
of them lead to the D 18 space-group and in fact, they correspond to the four different solutions asso-
ciated with the different origins of the symmetry
operations for the resulting D 18 space-groups. With the origin taken as being at the site occupied by the Al
atoms (in the following, the origin is always kept on
this site), these four representations are determined
as A+2/A2g, A+3/B1g, A1/A1u and A4 /B2u, while each
one of the At /A1g, A+/B 4 21, A2/A2u and A3/B1u
representations induces a Dl space-group. From the sites that would be occupied by the Al, Feq, Fax and
N atoms in a hypothetical Dl 4h phase [1, 2, 4] and from
those found for these atoms in D 18 [S, 6], the symmetry of the order parameter for this fictitious transition is unambiguously determined. It corresponds to the
Table I. - Compatibility relations of the lattice vibrations in NH4AIF 4 at the fictitious D14h --> D 18 phase tran-
sition.
A2+/A2g representation which becomes the totally symmetric representation at zone centre in the
observed D 18 phase.
The compatibility relations existing between the irreducible representations at the points A and r
of Dih and those at the point r of D 18 are given in
table I, together with the enumeration of the lattice- vibrations at these particular points of the Brillouin
zone. In these enumerations we take into account the vibrational modes that are expected to occur in the low-frequency range (0-600 cm-1) of the Raman
spectra [13], i.e. the modes involving the AlF6 octa-
hedron layers and the external (translational and rotational) vibrations of the NH’ groups. The NH’
internal modes (stretching and bending vibrations) expected in the high frequency range (above
1 000 cm- 1) are not considered here. It is noteworthy
that D 18 corresponds to an orientationally disordered
state of the NH+4 The same holds true for D’ 4h, since
the D4h site symmetry that would have the ammonium ion in this structure can result only from the super-
position of the two possible orientations of the NH’
shown in figure 2. Under these conditions, the enu- meration of the lattice vibrations given in table I is
based on the time and space averaged site symmetry of the NH’ in the Dih and 18 structures. In other words, we have ignored the particular positions statistically occupied by the H atoms. Of course, such
an approximation is not possible for the internal modes of the NH’ groups and their enumeration in the D14h
and D 18 unit-cells cannot be derived by usual group- theoretical methods because of disorder.
Table II gives the composition of lattice-vibrations at the point A of the Dih Brillouin zone. Knowing
that the order parameter for the D14h --> D 18 transition corresponds to A+2/A2g, only one mode involving
motions of the Feq atoms can couple with this order- parameter (Table II). The eigenvector, determined by the projection operator method, corresponds to a
« rotation » of the AIF6 octahedra about the c axis,
Table II. - Composition of the lattice modes of NH4AIF 4 at the point A - - - of the D14h Brillouin-
zone, in terms of displacements of the Al, Fea, Fax atoms
and of translational (T) and rotational (R) vibrations of the NH1 owing to its averaged site symmetry. a is
a pseudo-spin coordinate associated with the orientation
of the NH1.
out of phase from one layer to the next one. This is
the description of the soft-mode which condenses in a static deformation of the lattice in D184h [5, 6], and
which corresponds in this phase to a totally symmetric
vibration (Table I). The order-disorder processes
occurring in NH4AlF4 can be described by a pseudo- spin variable u associated with the orientation of the
NH4+ group. Its character takes on the value + 1 for symmetry operations that leave its orientation
unchanged and - 1 for those that inverse this orien- tation. The pseudo-spin coordinate is related to the
occupation probabilities n and n’ of the NH’ group in its two orientations by :
Hence, a = 0 in the disordered state where n = n’ = 2
and Q = ± 1 in the ordered state where either n = 1,
Table III. - Compatibility relations of the lattice vibrations in NH4AlF4 at the D184h --> D 13 phase transition.
n’ = 0, or n = 0, n’ = 1. At the point A of the D14h
Brillouin zone, Q belongs to the At j A 1 g representation,
and thus cannot couple with the order parameter for the D14h --> D184h transition (Table II). This is in
direct relation with the fact that D 18 remains an orientationally disordered phase. It follows that an
orientationally ordered state of the NH1 is obtained in a unique way from Dlh at the point A. It corres- ponds to the D 17 space-group (which is not observed)
induced by the A’/A representation.
A similar treatment of the D184h --> D4h transition has been made. Here again there is a doubling of the primitive unit-cell, so that the point ZI
of the D184h Brillouin zone boundary becomes a zone-
centre in D4h. Our results are summarized in tables III and IV. The order-parameter for the D184h --> D 13 transi-
tion belongs to the Zj jB1g representation (Table III),
so that two lattice-modes of this representation can couple with the order parameter. They correspond respectively to an internal deformation of the AlF6
octahedra involving the Feq atoms, and to a libration of the NH’ groups (Table IV). Because the D 18 primitive unit-cell contains two NH+4 , the pseudo- spin variable J has two components :
where the subscripts 1 and 2 of n refer to two adjacent NH+4 of the same layer plane. At the point Z, (J 1
transforms according to the Z; jB1g representation,
as does the order parameter, while (J 2 corresponds
to Zl jA1u (Table IV). Hence, there is clearly an order-
(1) Here c’ designates the lattice constant along c of the
conventional crystallographic D 1: unit-cell of multiplicity
two [15] ; a’, b’ and c’ of D1: and D134h are related to a, b
and c of D1h by : a’ = b’ = aJ’i = bJ2, c’ = 2 c.
Table IV. - Composition of the lattice modes of NH4AIF 4 4 4 at the point p Z 0, 0, 2 n cf of the f D184h 4hBrillouin-
zone, in terms of displacements of the Al, Feq, Fax atoms
and of translational (T) and rotational (R) vibrations of
the NH’ owing to their averaged site symmetry. a is a pseudo-spin coordinate associated with the orientations
to the NHZ
disorder mechanism related to the D 18 -+ D13 tran-
sition, and the corresponding coordinate a, leads to a « ferro » type ordering of the NH’ in the layer
planes, and, because of cell doubling involving the point Z, to an « anti-ferro » ordering between planes
as expected in D 13 [5, 6].
Both transitions Dlh -+ D 18 and D184h -> D 13 fulfil
all the Landau and Lifshitz symmetry requirements allowing second-order transformations between com-
mensurate phases.
To summarize, table V gives the composition of the expected K = 0 Raman active phonon modes in the different phases of NH4AlF4. An approximate des- cription of these modes in terms of stretching, bending,
translational and rotational vibrations, is obtained
by the projection operator method. Again, we empha-
Table V. - The Raman active K = 0 vibrational modes of NH4AIF4 in its different structural modifications.
size that D184h is an orientationally disordered phase,
so that the loss of translational invariance of the
crystal due to H atoms results in a breakdown of the K = 0 selection rule. Hence, in addition to the K = 0 modes determined from the averaged structure (Table V), the Raman spectra of NH4AIF4 in the D 18 phase may exhibit features coming from modes
at K :A 0 and resembling a one-phonon density of
states [7-11].
As it will be discussed in section 4. l, the observed translational and rotational vibrations of the NH’
groups can be accounted for by a simplified unit-cell
obtained by ignoring the particular positions of the Feq atoms. Since the only difference between the D14h aristotype structure and the disordered D4h phase
comes from an A+2/A2g displacement of the Feq atoms
(Table II), the simplified « sub-cell » that describes
D 18 is Dlh (Z = 1) with lattice constants a, a, c.
The enumerations of the zone-centre translational and rotational modes of the NH’ group in Dlh are :
The symmetry relations between the D184h unit-cell
and its D ih « sub-cell » are those already given in
table I. The « sub-cell » that describes the ordered
D 13 phase is obtained in a similar way by ignoring the
additional Z’/B,g displacements of the Feq atoms
(Table IV). It corresponds to D104h (Z = 2) with lattice constants a, a, 2 c and is related to D14h by a doubling
of the unit-cell involving the point of the
Brillouin zone boundary. The enumeration of the external modes of the NH+4 and the correlations between the D14h and D104h « sub-cells » are given in
table VI. The pseudo-spin coordinate (7 that describes the reorientation of the NH4+ transforms at the point
Z of D14h according to the Z: jB2g representation,
which becomes the totally symmetric representation
in D104h (Table VI). Hence, an order-disorder mecha- nism can lead from Dlh to the D104h « sub-cell » as
expected. Finally, the D134h unit-cell is related to its
D104h « sub-cell » by a doubling of the cell involving
the point Mj and the corresponding cor-
relations are given in table VII.
Table VI. - Compatibility relations for the NH4+ external modes, between the D14h and D104h « sub-cells ». R and T stand for the rotational and translational vibrations, respectively.
Table VII. - Compatibility relations for the NH’ external modes, between D 13 and its D’o « sub-cell ». R and T
stand for the rotational and translational vibrations, respectively.
3. Experimental details.
The NH4AlF4 single crystal used in this study was prepared by hydrothermal method as described previously [2]. It was cut in the shape of a parallelepiped
of about 2 x 2 x 5 mm3, with faces perpendicular
to the crystallographic c axis (Z direction) and perpen- dicular to directions X’ and Y’ at 450 from the a’ and b’ crystallographic axes in the (a’, b’) plane (Fig. 2).
The Raman spectra were recorded on a CODERG T-800 triple monochromator instrument, coupled
with an argon ion laser Spectra-Physics model 171.
The 5 145 A emission line was used with an incident power of 0.5 to 1 watt. Resolution was about 1 to
2 cm-1.
Low temperature measurements, down to 80 K,
were made with a liquid nitrogen cryostat C3N from
Dilor. Measurements between 80 and 20 K were
performed by using a Cryodine model 20 helium
refrigerator, equipped with the sample holder modi- fication described in [16]. In both cases, the tempera-
ture regulation of the sample was better than + 0.5 K.
In order to be treated numerically, some spectra
were collected and accumulated in the memories of
a PDP 11/03 mini-computer (MINC 11) from Digital.
4. Results and discussion.
The low frequency Raman spectra (0-600 cm-1) of
the NH4AIF4 single crystal were recorded at different temperatures ranging from 20 to 300 K. Different scattering geometries have been used, allowing the
observation of all the Raman tensor elements. With reference to our X’, Y’ and Z laboratory axes defined above, the Raman tensors [17] for crystals with class D4h must be written as :
The A1 g(ax,x, + ay,y,, azz) spectra recorded at room temperature exhibit two strong lines at 525 and 125 cm-1 (Fig. 3a). Lowering the temperature down
to 20 K causes only a slight narrowing of these features
as well as a progressive displacement of the 125 cm-1
line up to - 150 cm-1 (Fig. 3b). The B2g (ax’x’ - ay,y,)
spectrum remains featureless from 300 K down to 20 K and only an extremely weak and broad band is observed at 300 K on the B1g(ax’y’) spectrum at
150 cm -1, which disappears in the low temperature phase at T 150 K (Figs. 3a and 3b). In fact, the
D4h -. D4h phase transition of NH AIF at T = 150 K
is well characterized from the examination of the
Eg(ax,z, ay,z) spectra (Fig. 4), where a broad line at 145 cm-1 of the D184h phase is progressively replaced by a narrow line at 135 cm’ 1, as the crystal is brought
into the D134h phase. A similar spectral evolution is also observed for a broad feature appearing as a shoulder
Fig. 3. - The low frequency Raman spectra of NH4AIF 4
recorded at 300 K (a) and at 20 K (b). The asterisks indicate the orientational spillover of scattering from phonons strongly active with other scattering geometry. The Porto notation is used to denote the scattering geometries [22].
of a strong Eg line at 235 cm-’ and which becomes
progressively a well-defined and narrow line at 250 cm-1 in the D 13 phase (Fig. 4). In figure 5, we have summarized the frequency evolution of the observed features as a function of temperature, through the D184h D134h phase transition. Clearly,
there is no evidence of mode softening associated
with this transformation.
4.1 ASSIGNMENT AND INTERPRETATION OF THE SPEC- TRA. - Two modes with A1g symmetry are expected
in the D 18 phase (Table V). They correspond to a stretching vibration of the AI- Fax bonds and to a
« rotation » of the rigid AIF6 octahedra about the
c axis. We assign the two Alg Raman lines observed at 525 cm-1 and at 125 cm-1 at 300 K to these two modes respectively. This is in accordance with a
previous assignment for the related RbAlF4 crystal [13]. Thus, the 125 cm-1 A1g line corresponds to the
soft-mode for the fictitious D18 -+ D’ transition
(Tables I and II). Indeed, it has a marked tendency
to soften as the temperature is increased (Fig. 5).
This must be imputed to the existence of pretransitional
effects associated with the occurrence of the D4h
aristotype structure at high temperature, but, as
Fig. 4. - The temperature evolution of the Eg(aX,z) Raman
spectrum of NH4AIF 4’
Fig. 5. - The temperature dependence of the phonon frequencies observed on the A1g and Eg spectra ofNH4AIF 4.
already mentioned, the chemical decomposition of
the crystal that occurs around 620 K prevents the observation of such a transition [2]. Now, two addi-
