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Shear transformation in the layered compound KAlF4 : low temperature phase structure and transformation
mechanism
J.M. Launay, A. Bulou, A.W. Hewat
To cite this version:
J.M. Launay, A. Bulou, A.W. Hewat. Shear transformation in the layered compound KAlF4 : low temperature phase structure and transformation mechanism. Journal de Physique, 1985, 46 (5), pp.771-782. �10.1051/jphys:01985004605077100�. �jpa-00210019�
Shear transformation in the layered compound KAIF4 :
low temperature phase structure and transformation mechanism
J. M. Launay (*,~), A. Bulou (*), A. W. Hewat (+),
A. Gibaud (*), J. Y. Laval (~) and J. Nouet (*)
(*) Laboratoire de Physique de l’Etat Condensé, E.R.A. n° 682, C.N.R.S., Faculté des Sciences, 72017 Le Mans Cedex, France
(~) Laboratoire d’Etude et de Synthèse des Microstructures, E.R.A. n° 912, C.N.R.S., ESPCI, 10, rue Vauquelin,
75231 Paris Cedex 05, France
(+) Institut Laue Langevin, 156 X Centre de Tri, 38042 Grenoble Cedex, France (Reçu le ler octobre 1984, révisé le 23 novembre 1984, accepté le 8 janvier 1985)
Résumé. 2014 Le composé lamellaire KAIF4 subit une transition de phase structurale au voisinage de 250 K. Les deux phases ont été étudiées par diffraction de rayons X, d’électrons et par affinement du profil des raies de diffrac- tion de neutrons. La phase ambiante (groupe d’espace quadratique D54h 2014 P 4/mbm 2014 Z = 2; a = b = 5,045 A,
c = 6,159 A) dérivée du type T1A1F4 a été confirmée. Nous avons déterminé la structure basse température (mono- clinique, P 21/m, Z = 4; am = 7,340 Å, bm = 7,237 Å, cm = 6,407 Å, 03B2 = 106,8° à 4 K) qui est très voisine de la structure de KFeF4. Nous montrons par des arguments structuraux que cette transition de phase du premier ordre
est principalement caractérisée par un glissement dans la direction [100] des feuillets successifs ce qui permet d’expliquer après transition la désorientation de 16° entre les microcristaux mâclés mise en évidence par diffraction de rayons X et par microscopie électronique.
Abstract. 2014 The layered compound KA1F4 undergoes a structural phase transition in the vicinity of 250 K.
Both phases have been studied by X-ray and electron diffraction and by profile refinement of the neutron powder diffraction patterns. The room temperature structure (tetragonal space group D54h 2014 P 4/mbm 2014 Z = 2 ;
a = b = 5.045 Å, c = 6.159 A) derived from the T1A1F4 type is confirmed. We have determined the low tempera-
ture structure (monoclinic, P 21/m, Z = 4; am = 7.340 A, bm = 7.237 A, cm = 6.407 Å, 03B2 = 106.8° at 4 K) closely
related to the KFeF4 structure. From structural argument it is shown that this first order transition is mainly
characterized by a gliding of the successive sheets in the [100] direction. This can explain the 16° misorientation of twinned microcrystals resulting from the transition as shown by X-ray diffraction and by electron microscopy.
Classification Physics Abstracts 64.70K - 61.60
1. Introduction.
The structures of the tetrafluoroaluminates AAlF4 (A = K, Rb, Tl, NH4) are closely related to the ideal tetragonal TlAlF4 structure described by Brosset
(P 4/mmm- Dih; Z = 1 ; a=3.616(3)Å, c=6.366 (3) A}
[1, 2]. These compounds consist of infinite layers of AIF6 octahedra sharing four Feq atoms in the (001)
plane; unshared fluorine atoms are denoted FaX and
lie along the c axis. Each octahedron is centred in a
square based parallelepiped of cations A (Fig. 1).
The ideal structure (denoted phase I) is encountered in TlAlF4 and RbAlF4 at high temperature [3, 4]. On
the other hand, this ideal structure is not observed for
KAIF4, even at high temperature. In this case, the
structure is derived from the ideal one by correlated
rotations of the AlF6 octahedra around the fourfold axis and the space group is P 4/mbm - Dlh, Z = 2
Fig. 1. - Ideal structure of the tetrafluoroaluminates
AAIF 4 (A = Tl, Rb, K, NH4).
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004605077100
(phase II) [2, 5]. All these compounds undergo struc-
tural phase transitions (SPT). In RbAlF4 and TlAlF4
the transitions can be explained by octahedron rota- tions [3, 4]. In KAIF 4’ a discontinuous SPT is observed in the vicinity of 250 K [5-7] with a large heat of tran-
sition (3.15 cal/g) as determined from DSC. The attempts to describe the transition by octahedron
rotations alone have always failed. Moreover the
crystal breaks up at the transition. The symmetry determination of the new phase (III) by X-ray diffrac-
tion on crystal is thus very difficult. The determination of the lattice symmetry of phase III has been performed
on powder by long wavelength neutron diffraction and by electron diffraction which allows the selection of small single domains. The structure parameters have been determined by neutron powder profile
refinement at 4 K. It must be pointed out that the
thermal hysteresis is very large (- 100 K) so that the
low temperature structure is still present and can be studied at room temperature.
2. Experimental.
Single crystals are prepared by the horizontal Bridgman method from a non-stoichiometric mixture
(0.51 KF + 0.49 AlF 3) chosen in reference to the KF-AlF3 phase diagram [6]. The powder used for the neutron scattering experiments is obtained by pulve- rizing crystals in order to get high purity samples.
However, this powder gives enlarged diffraction lines and it must be annealed at 350 OC before being studied by the neutron powder profile refinement method.
The neutron diffraction patterns were collected at
4 K and at room temperature on the DIA neutron powder diffractometer at the LL.L. (Grenoble-France).
The angular range was 2 0 = 180 to 1600 in steps 0.050 with an incident wavelength of 1.909 A. The
refinements were carried out with the Rietveld pro- gram [8] modified for thermal anisotropy [9]. Preli- minary neutron diffraction powder patterns were collected at 2.990 A in order to determine the lattice symmetry.
X-ray investigations have been performed in the
two phases (II and III) both on powders and on crystals which are always largely misorientated after transition.
For electron diffraction experiments the samples
have been thinned by cleavage parallel to the basal plane and quenched to liquid nitrogen temperature.
Electron diffraction diagrams have been recorded at 100 keV on a Siemens Elmiskop IA and on a Jeol
100 CX equipped with a cooling and temperature regulating device.
3. Neutron diffraction study.
3.1 ROOM TEMPERATURE PHASE. - The room tem-
perature structure (phase II) determined by Nouet
et al. [5] is confirmed by neutron powder profile refine-
ment. The results are given in table I. The large R factor
Table I. - Atomic coordinates j’or KAlF4 in the
space group P 4/mbm at room temperature obtained
from neutron powder profile refinement at a 1.909 A wavelength. R factors are defined by : RNUC =
100 Z ) I (obs.) - SI (ca/.) /Z 1 (obs.) ; R pROF =
100 E Y (obs.) - S Y (ca/.) liE Y (obs.) with 1 (obs.),
1 (caL) the integrated intensity of reflections, Y (obs.),
Y (caL) the intensity data point and S the scale factor.
The Bij are defined by Bij = 8 a’ ui Uj > and are
given in Å 2. Standard deviations are given in paren- theses.
is imputed to the presence in the diffraction powder pattern of several lines still larger than the instrumental width which perturbs the classical Rietveld method.
Analysis of both X-ray and neutron diffraction lines width is in progress.
3.2 Low TEMPERATURE PHASE. - In order to deter- mine the lattice type of the low temperature phase,
we have recorded a neutron powder diffraction pattern of KAlF 4 at 4 K with a A = 2.99 A wave- length so that the maximum splitting between the diffraction lines is obtained. The diffraction angle is
measured with a great accuracy owing to the presence of diffraction lines due to A/3. We have used a general
program for the search of the lattice parameters [10].
The most reliable solution is obtained for an ortho- rhombic unit cell with parameters ao = 3.670 A, bo = 7.237 A, co = 12.267 A and from the conditions
limiting reflections, a B centred space group can be
Table II. - Atomic coordinates for KAlF4 in the
space group Bmmb at 4 K obtained from neutron powder profile refinement at a 1.909 A wavelength.
The R factors are defined in table L
proposed. This suggests a structure similar to KFeF4 [11]. Refinements performed in the corresponding
space group Bmmb (D2h, no 63, Z = 4) give the
results of table II. The reliability is quite satisfactory
if compared to the corresponding one obtained at
room temperature for phase II where the structure is unambiguously known [5]. However some very weak
intensity lines are observed in addition to the expected
lines. Such lines are also mentioned in KFeF4 [11].
This is in particular the case of the intensity diffracted
between 024 and 032 lines denoted by full arrows
in figure 2a. This figure represents the pattern prepared
for the refinement i.e. the experimental pattern in which the intensity has been set zero outside the region
where diffraction lines are expected (the diffraction lines are Gaussian peaks truncated to 1.5 times the
full width at half height on either side of the peak centre). Clearly, some parts of the diffraction pattern
are not expected in the framework of this orthorhombic cell (dotted arrows) and particularly between the two lines mentioned above (dashed arrows). This intensity
arises from at least two lines as evidenced on the diffraction powder pattern recorded at 2.99 A (Fig. 3).
As can be seen in table III, any orthorhombic cell with the lattice parameters of Bmmb space group,
even though primitive, cannot account for the exis- tence of these two lines. The smallest cell which can
explain the presence of such diffraction lines is the monoclinic cell am = 2 ao, bm = bo, cm = ( - ao + co)/2 (Table III, Fig. 4a). The monoclinic subgroups of
Bmmb with this cell are either P 2,/m (C2 2h) or P 21/a (C’2h). Refinements have been performed in both
space groups and a better agreement between calcu- lated and observed powder patterns is obtained with P 21/m. The results of the refinement are summarized in table IV and the observed and calculated patterns
Fig. 2. - Part of the neutron powder diffraction pattern of KAlF 4 at 4 K with a 1.909 A wavelength : (a) experimental pattern prepared for the refinement in the Bmmb space group. The full arrows indicate the 024 and 032 orthorhombic diffraction lines mentioned in the text. The dashed and dotted arrows indicate parts of the pattern where the inten- sity is not predicted in the Bmmb space group; (b) experi-
mental pattern prepared for the refinement in the P 21/m
space group; (c) calculated pattern in the P 21/m space group.
Fig. 3. - Part of the neutron powder diffraction pattern of KAIF 4 at 4 K with a 2.99 A wavelength. The full arrows
indicate the 024 and 032 orthorhombic lines as in figure 2a.
The dashed arrows indicate the diffraction lines characte- ristic of the monoclinic symmetry.
Table III. - Indexation of the diffracted intensity lying between the 024 and 032 orthorhombic diffraction
lines. The relationship between the orthorhombic and the monoclinic cells is shown in figure 4.
are shown in figures 2b and 2c. The number of diffrac- tion lines used for the refinement is 414 instead of 128 in the Bmmb space group. In order not to greatly
increase the number of refined parameters the following assumptions have been made about the mean-square
displacement matrix :
i) the directions of the semi-major axes are set parallel to the axes of the pseudo-orthorhombic cell.
We note by Bi° the corresponding components of the mean-square displacement matrix expressed in this pseudo-orthorhombic cell.
ii) the mean-square displacements for atoms having
the similar surrounding have been set equal :
Fig. 4. - (a) Relationship between the orthorhombic B centred cell (parameters ao, bo, co) and the monoclinic pri-
mitive cell (parameters am, bm, cm). (b) Relationship between
the room temperature cell (parameters at, ht, ct-tetragonal
space group P 4/mbm) and the monoclinic cell (parameters
am, bm, cm-monoclinic space group P 21/m).
where the subscripts are defined in table IV.
The mean-square displacements expressed in the
orthorhombic cell are given in table V. The absorption
correction on the Bij which is much smaller than the standard deviation, has not been taken into account
[12]. The results are discussed in chapter 6.
4. Electron diffraction and electron microscopy study.
As was shown in chapter 3, the low temperature phase
of KAlF4 is monoclinic but closely related to an
Table IV. - Atomic coordinates for KAlF4 in the space group P 21 /m at 4 K obtained from neutron powder profiles refinement at a 1.909 A wavelength. The R factors are defined in table I.
Table V. - Mean-square displacements (8 n2 ui uj ») expressed in the pseudo-orthorhombic coordinates and
deduced from the refinement in the P 21/m space group.
orthorhombic B-centred cell. According to the low
distortion of the orthorhombic cell and to the weak-
ness of the spots arising from the monoclinic symme- try, it is convenient to analyse the electron diffraction
diagrams in the framework of the orthorhombic cell whenever possible. The relationships between the
Miller indices in both cells are :
4.1 SCANNING ELECTRON MICROSCOPY (S.E.M.). -
In order to examine the samples after the transition,
S.E.M. experiments have been carried out. The study
Fig. 5. - Photographs of KAlF 4 in phase III obtained by Scanning Electron Microscopy. The scale given on each photo- graph is expressed in um : (a) Crystal surface after the transition. The breaks are evidenced owing to the edge contrast (clea-
vage plane normal to the electron beam). (b) Detail of the surface in the vicinity of a break. (c) Evidence of twinned domains
(cleavage plane tilted by about 52° with respect to the electron beam). (d) Evidence of sheets and twinned domains observed
on the sample edge when the crystal has partially transited.
has shown the existence of breaks (Figs. 5a, 5b) on the
surface of the sample about 5 pm long, generally parallel to [110] and [110] axes of phase II. Figure 5c
shows the crystal surface near a break, when the sample is rotated by 520 for visualization. On figure 5b
the measured angles of the surface related to the flat surface prior to the transition reach the value of 250.
On figure 5c the orientation contrast shows the pre-
sence of twinned domains which were orthogonal
before the transition.
When the sample is examined parallel to the sheets
in phase III, it is shown that micronic twin domains
are tilted from the well-stacked configuration they had
before the transition (see Fig. 5d). The measured angle
of this tilt, whose [010] axis is perpendicular to the sample edge, is about 1 5°.
4.2 TRANSMISSION ELECTRON MICROSCOPY (T.E.M.).
- Phase II of KAIF4 has been studied by T.E.M.
experiments and compared to RbAlF4. The results are reported in [7].
The low temperature phase is studied at room tem-
perature on quenched sample by a selected area
electron diffraction technique. (001)*, (101)*, (103)*, (01T)* and (311)* planes are observed in the pseudo-
orthorhombic reciprocal lattice.
When the electron beam is set perpendicular to the cleavage plane (tilt = 00), (101)* plane is commonly
observed (see Fig. 6a). This frequent observation of the
(101)* plane can be explained by the tilting of twin
domains revealed on the sample edge b1 S.E.M.
(see Fig. 5d). The (001)* plane and the (103)* plane
are simultaneously observed (Fig. 6b). Note that the former corresponds to a 16.80 tilting around the
[010]* direction of the (101)* plane which is the most frequently observed. Table VI shows the agree-
Table VI. - Experimental and calculated ( from neu-
tron results) interplanar spacings ratio in the (101)*,
(001)* and (103)* planes.
ment between experimental and calculated data for several interplanar spacings. From these data, the experimental values of ao and bo pseudo-orthorhombic parameters are deduced : ao = 3.7 (2) A and bo = 7.3 (4) A. Moreover the doubling of the co parameter in relation to phase II may be inferred from these results.
Furthermore, the existence rule h + I = 2 n corres-
ponding to the pseudo-orthorhombic B centred group
is confirmed. The (hko : k = 2 n) existence rule can be verified in spite of the frequent occurrence of double diffraction. In figure 6a, weak extra spots arrowed in the (101)* plane correspond to the doubling of the
ao parameter and can be indexed in the monoclinic cell (am, bm, cm, P) proposed from the neutron diffrac-
tion analysis. From neutron diffraction results, it can
be shown that the calculated intensities of these spots, indexed 130 and 310 in the monoclinic cell are not
negligible.
When the sample is tilted by 300 around [100]*, the (011)* plane is observed (Fig. 6c). The existence rules h + 1 = 2 n and hko : k = 2 n are again well confirmed,
but extraspots are evidenced on the diagram (see arrows). These extraspots belong to the (112)* plane
from phase II tetragonal cell. Table VII shows a very
good agreement between measured and calculated
interplanar spacings for phase II and phase III. This hypothesis of the simultaneous presence of phases II
and III is compatible with the evolution of the diffrac- tion diagram during observation. The transformation into phase II is probably induced by the heating
caused by the electron beam. A more complicated reciprocal plane is shown in figure 6d which corres- ponds to (311)*. The experimental and calculated interplanar spacings are shown in table VIII. This
diagram confirms the pseudo-orthorhombic B-centred
lattice. Extra spots caused by the doubling of the ao
parameter are not evidenced in this plane owing to
their very small intensities.
Other tilts have been used for studying the reciprocal
lattice : the diagrams are often difficult to index owing to the occurrence of simultaneous reflections from different reciprocal planes and several mis- orientated twin domains. However, the four planes
shown are sufficient to corroborate the cell deduced from the neutron scattering study.
Table VII. - Experimental and calculated interplanar spacings (dhkl) : (a) in the (011)* plane (phase III : ortho- rhombic cell); (b) in the (112)* plane (phase II : tetragonal cell):
©O*
7
u
u e cC 0 2
S
00 ..d ’-’
oJS
.
. =’ 0
Table VIII. - Experimental and calculated interplanar spacings (dhki) and angle in the (31T)* plane (phase III :
orthorhombic cell).
5. X-ray diffraction study.
As was confirmed by S.E.M., KAlF4 crystals undergo important breaks at the transition and the phase III
domains are mutually misorientated. Owing to the
small domains size the X-ray diffraction diagram
arises from several crystallites and the analysis is
difficult. Figure 7 represents a typical diffraction dia-
Fig. 7. - Transmission X-ray diffraction diagram of KAlF 4-phase III at room temperature. The X-ray beam is
normal to the cleavage plane with a 1.54 A wavelength (monochromatized CuKal X-ray radiation) focalized on a cylindrical film.
gram obtained on a fixed sample with copper Ka
monochromatic wavelength on cylindrical film. The important number of spots and their spreading come
from a distribution of misorientated microcrystals.
Programmes have been developed in order to get
quantitative information from these diagrams. This analysis showed that the misorientation angles are mainly centred at ± 15° in agreement with the results of chapter 4. More detailed results will be published
later.
6. Discussion.
6.1 LOW TEMPERATURE STRUCTURE OF KAlF4. -
As shown in chapter 3, the structure of KAlF4 at low temperature is monoclinic but very close to an ortho- rhombic B face centred cell. The fl angle of the pseudo-
orthorhombic cell is 90.180. So it is convenient to
represent the structure in this pseudo-orthorhombic
cell by the different projections shown in figures 8a, b, c. These projections clearly evidence that the octa- hedron distortion is small, as is also shown in figure 9.
So we can describe this structure according to an
ideal orthorhombic one represented in figure 10 and corresponding to the Bmmb space group (parameters ao, bo, co) (Note that due to the K+ ion positions it is
not possible to describe this ideal structure in the cell ao, bo/2, co as did Hidaka et al. [13] in the study of KFeF4). Phase III of KAIF4 is derived from this ideal structure by :
i) octahedron tilts around [100] (about 10 degrees)
and K+ displacements along [001] both consistent with the Bmmb space group;
ii) octahedron tilts around [001] (about 4 degrees)
which are responsible for the doubling of ao parameter and the subsequent monoclinic symmetry.
Note that the absolute values of the B°ij (table V)
probably are not quite exact due to large uncertainty
on the background for diffraction angles greater than 800. However their relative values are in agree- ment with those expected i.e. the mean-square displa-
cements are less important along the AIF bond than
in the plane perpendicular to this bond. The relative value of the B°ij for axial fluorine and equatorial fluo-
rine is also consistent with those expected (except for B 22 (Fax) which would be greater). Then we can predict that the thermal vibration mainly arises from libration of quite rigid octahedra. A last point to note is
the important decreasing of potassium fluoride inter- atomic distance (dKF = 2.85 A in phase II ; dKF =
2.63 A in phase III). This is related to the change of
coordinence of potassium ions since the theoretical value [14] is d N 2.82 Å in phase II where the coordi-
nence is 8 and d = 2.62 A in phase III where the coor-
dinence is about 6.
6.2 MECHANISM OF THE TRANSITION. - Comparison
of the structures of phase II and phase III of KAIF4 (1 )
shows that the AlF6 sheets have undergone a ( - ao/2) displacement along the [100] pseudo-orthorhombic
axis. Moreover we note that in phase II the successive
octahedra along the [001] axis are tilted around this axis in the same sense. In phase III this tilt angle is
(1) The space group P 21/m (phase III) is a subgroup of
P 4/mbm (phase II) with a 450 rotation of the unit cell around the tetragonal axis (Fig. 4b).
Fig. 8. - Projection of the ionic positions represented in
the pseudo-orthorhombic cell : (a) (100) plane; (b) (010) plane; (c) (001) plane.
Fig. 9. - Bond lengths and angles in the AIF6 octahedra (phase III P 21/m).
Fig. 10. - Ideal structure from which the low temperature phase of KAlF4 is derived by AIF 6 tilts and K displacements
as indicated by arrows.
