Results of optical thickness and refractive indices measurements for (NH4)2SbF5 crystal in the temperature range 100-310 K are presented. The measurements were done with interference method using He-Ne laser (λ = 632.8 nm). At To = 292 K and Ta = 168 K two continuous phase transitions with critical indices /3 1 = 0.38 and β2 ≤ 0.57 were observed. Additional anomaly of temperature changes of interference order with maximum at Ta 132 K were found. This anomaly resembles a diffused transition. Temperature-averaged values of derivatives of refractive indices dn g /dT = -3.3 x 10 -5 K and dn m /dT = -2.9 x 10 -5 K -1 evidenced a decrease in optical anisotropy (birefringence) along the b-axis on heating run

B Andriyevsky°

V Stadnyk

Z Czapla

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Vol. 87 (1995) 	 ACTA PHYSICA POLONICA A 	 No. 3
OPTICAL INVESTIGATIONS OF PHASE
TRANSITIONS IN (NH4) 2 SbF5 CRYSTAL
B. ANDRIYEVSKY ° , Z. CZAPLA b AND V. STADNYK a
aLviv State I. Franko University, Kyryla and Mefodiya 8, 290005 Lviv, Ukraine
bInstitute of Experimental Physics, University of Wrocław
Pl. M. Borna 9, 50-204 Wrocław, Poland
(Received March 29, 1994; revised version September 6, 1994)
Results of optical thickness and refractive indices measurements for
(NH4)2SbF5 crystal in the temperature range 100-310 K are presented.
The measurements were done with interference method using He—Ne laser
(λ = 632.8 nm). At To = 292 K and Ta = 168 K two continuous phase
transitions with critical indices /3 1 = 0.38 and β2 ≤ 0.57 were observed. Ad-
ditional anomaly of temperature changes of interference order with maximum
at Ta 132 K were found. This anomaly resembles a diffused transition.
Temperature-averaged values of derivatives of refractive indices dn g /dT =
—3.3 x 10 -5 K and dnm /dT = —2.9 x 10 -5 K -1 evidenced a decrease in
optical anisotropy (birefringence) along the b-axis on heating run.
PACS numbers: 64.70.Kb, 78.20.Fm
1. Introduction
Crystal of (NH4) 2 SbF5 ammonium pentafluoroantimonate (APFA) belongs
to the big family of compounds with chemical formula M2SbF5, where M=Na,
K, Rb, Cs, NH4. Successive phase transitions were reported in (NH4)2SbF5 crys-
tal [1-8]. However, there are discrepancies related to the number of the phase
transitions in this compound. In a paper [6] the proposed phase transitions and
symmetry of particular phases are recollected. In the temperature range 110-330 K
four phase transitions at 138, 165, 257 and 294 K are reported. At 298 K (phase I)
the crystal belongs to orthorhombic system with the space group Cmcm [7]. In
the temperature range 138-294 K monoclinic symmetry (space group C2/c) is
proposed. In the papers [1-3] a transition to superionic phase at 257 K is implied.
however, nuclear quadrupole resonance (NQR) measurements [5] gave evidences
for two phase transitions at 292 K and 169 K only. Additionally the unusual
behaviour of resonance frequency below 169 K is observed. Temperature depen-
dences of lattice parameters [6] confirmed two phase transitions and proved the
(611)
612 B. Andriyevsky, Z. Czapla, V. Stadnyk
change of symmetry from orthorhombic to monoclinic at about 294 K. Optical
observations [8] showed the ferroelastic character of the phase transition at 292 K.
Dielectric measurements showed the change of slope of e' at 169 K and its decrease
in the temperature range 169-120 K. The aim of the presented paper is to obtain
additional information related to the phase transitions sequence and description
of phase transitions character.
2. Experimental
APFA single crystals of good quality were grown from water solution con-
taining stoichiometric quantities of NH 4F and SbF3 with a small excess of HF by
slow evaporation at constant temperature of 301 K. The crystal exhibits a very
distinct cleavage plane (010) perpendicular to the b-axis. In our work the b-cut
samples were used in optical investigations. Optical observations of APFA sam-
ples with polarization microscope at room temperature showed that the crystal is
negative biaxial one. The least n p-halfaxis of optical indicatrix is identical to the
crystallophysical b-axis, the greatest n g — to the a-axis and the middle n n, — to
the c-axis (ng > nm > np ). The parallel surfaces of the samples (necessary in inter-
ference method) were obtained by cleavage of the crystal. The optical interference
method used in measurements is presented schematically in Fig. 1.
The laser beam was focussed by means of lens (2) on the sample (3) which
was placed in cryostat (4). The incident angle of laser beam was a = 3°. There-
fore, an influence of optical anisotropy for the optical thickness of APFA in the
plane of incident beam was negligible. As a result of interference of two beams
reflected from front and back surfaces of the sample one observes two interference
pictures on the screens (7). The direction of linear polarization of laser beam cor-
responded to the bisectrix of right angle between n g- and nm-axes. Two polarizers
(6) oriented along ng- and nm-axes allowed to obtain two interference pictures at
every temperature point. Thus, in this experiment temperature dependences of
two double optical thicknesses changes δ∆g = 2δ(ng • I) and &„m = 2δ(nm • I) of
APFA crystal were measured simultaneously. Here, 1 is the geometric thickness
of a sample. The diameter 0.5-0.6 mm of laser beam did not provide the condi-
tion of monodomain investigation taking into account small width (15-20 pm) of
Optical Investigations of Phase Transitions ... 613
APFA domains [8]. But temperature dependent distinct interference effect in the
whole range 100-310 K evidences small birefringence variation due to ferroelastic
domain structure with respect to acting values of refractive indices. Therefore, one
can say that the domain structure does not influence essentially the temperature
dependence of optical thickness. As well known, as effects of temperature hysteresis
for second order phase transitions are small, the presented investigations of APFA
were performed at continuous increase in temperature with the rate of 1 K/min.
To obtain relative temperature changes of S,6/.6, refractive index n and geometric
thickness of the sample were measured at room temperature with the relative ac-
curacies 10' 4 and 10-2 , respectively. Refractive indices of APFA at room temper-
ature were measured by the immersion and photographic Obreimov's methods [9].
Refractive indices at To = 295 K are equal to: n g = 1.5266, nm = 1.5178 and
np = 1.4703. The temperature changes of double optical thickness SA were esti-
mated with accuracy A/4. Using the values of n Pe. 1.5 and 1 1.5 mm the average
relative error of determination of double optical thickness variations is equal to
7 x 10-5 . Using dependence of δ∆/∆ = f(T) (obtained in this experiment) and
temperature dependences of lattice constant [6] (obtained from Bond's method),
the temperature changes of relative refractive indices δn/n of APFA were obtained
according to the formula
The used method is characterized by high temperature sensitivity. 350-380 inter-
ference extrema (number of points on plots) correspond to 110-310 K temperature
range and 1.5 mm sample thickness. Temperature dependence of interference ex-
trema changes was measured by thermocouple and photodiode with the help of
X-Y recorder.
3. Results and conclusions
Temperature dependences of wavelength-normalized temperature changes of
double optical thickness δ∆λ =2δ(n • l)/λ of APFA for two polarizations of light
E II ng and E II nn, are shown in Fig. 2. The value δ∆λ is equal to the change of
interference maximum: ∆ = kλ  δ∆(T) = δk(T)λ ,δ∆λ ( ) = δ∆(T)/λ = δk(T),
where A is the wavelength of laser light. We shall omit λ-subindex in further
text. These dependences showed similar temperature changes as the b-lattice con-
stant (the b-axis is the direction of light propagation in this experiment). On
heating both the b-lattice constant and δ∆ increase without any discontinuity. At
Tc1 = 292 K and2 =168 K the changes of both quantities are characteristic of
continuous phase transition with a jump-like changes of d(δ∆)/dT (Fig. 2, Fig. 3).
The temperature dependence of d( δ∆ )/dT (curve 1 in Fig. 3) was calculated by
numerical differentiation of the curve 1 in Fig. 2. Assuming that the induced by
spontaneous deformation corresponding δ∆ s,d. value is related to order parameter
with a formula
the critical indices for the phase transitions were obtained. The linear dependence
lg(δ∆) = 2,βlg(Tc — T) is fulfilled satisfactorily in the 71 — (T c — 4 K) temperature
614	 B. Andriyevsky, Z. Czapla, V. Stadnyk
region for both second order phase transitions (Fig. 4, Fig. 5). The calculation
give values of β = 0.38 ± 0.03 and N2 = 0.57 ± 0.04 at Tc1 and Tc2, respectively.
In the range 120-158 K large changes of óa are observed (Fig. 2). This behaviour
is quite similar to that observed for the b-lattice parameter of elementary unit cell
of APFA. Relatively strong temperature change of óA in the range 120-158 K
resulting in pronounced but wide maximum of d(δ∆)/dT value (Fig. 3) resembles
a diffused phase transition at Tc3 P:. 132 K. This behaviour is in qualitative agree-
ment with temperature dependences of Cp [10] and dilatation [6] of APFA. The
similarity of temperature dependences of d(δ∆)/dT and Cp is shown in Fig. 3.
Subtraction of óA contribution resulting from this diffused phase transition-like
Optical Investigations of Phase Transitions ... 	 615
behaviour to the temperature changes of SL" induced by the phase transition at
Tc2 = 168 K gives a decrease in the /32 value to the value much better correspond-
ing to continuous phase transition (β < 0.5) at this temperature 02 < 0.57).
Temperature dependences of double optical thickness changes 6.6, (curves 1 and 2
in Fig. 2) do not allow to estimate temperature dependences of refractive indices of
APFA. Temperature dependences of δn/n were obtained according to the formula
(1) using δ∆/∆ data (this work) and 51/1 data [6]. On the ground of the b-lattice
parameter temperature changes one can state that refractive indices along the s-
and c-axes decrease δng/ng < 0, δnm/nm < 0, and |δng/ngl > |δnm /nm '. These
relations and the values of refractive indices n g > nm > np give decrease in op-
tical anisotropy, i.e. birefringence (n g — nm ) with increase in temperature. It is
616 	 B. Andriyevsky, Z. Czapla, V. Stadnyk
seen in Fig. 6 that the greatest refractive index ng decreases more rapidly than
the middle one n m at increase in temperature. Thus, one can expect the phase
transition appearance to prototype tetragonal phase at higher temperature. Ac-
cording to data presented in Fig. 6 in the temperature range 110-310 K an average
contribution |δn/n1 to the relationship (1) is equal to about 0.2|δ1/l1. The main
contribution (80%) to the temperature changes of double optical thickness for both
polarizations of light results from temperature changes of the b-parameter of the
elementary unit cell according to the formula (1). On the contrary to the mono-
tonical temperature increase in the b-lattice parameter dl/dT > 0 in the range
110-295 K an anomalous increase in δn/n is observed against a background of
monotonically decreasing values of this quantity. Such behaviour corresponds to
the temperature dependences of the a- and c-lattice parameters of APFA [6]. The
subtraction of temperature dependences (1 and 2 in Fig. 2) represents the tem-
perature dependence of multiplication of birefringence (n g — nm ) and the b-lattice
parameter. Anomalous behaviour of this dependence in the temperature range
150-170 K correlates well with a subtraction of the lattice parameters (c — a) [6].
The obtained results show that the anisotropy of the optical indicatrix of APFA
in the plane of n g — nm axes decreases over the temperature range 110-310 K.
To summarize the investigations of (NH4)2SbF5 one can state:
1. using new modification of optical interference method the precise tempera-
ture dependences of double optical thickness were obtained along the b-axis
in the temperature range 110-310 K (a = 632.8 nm);
2. two continuous phase transitions are established at Tc1 = 292 K and Tc2 =
168 K with critical indices ,β1 = 0.38 and N2 < 0.57 respectively;
3. strong temperature changes of double optical thickness in the temperature
range 120-158 K resemble the diffused phase transition at Tc3 .r 132 K.
This work was supported by the research project No. 201289101.
Optical Investigations of Phase Transitions ...	 617
References
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[2] V.V. Urbonavichius, V.E. Shneider, J.P. Grigas, R.L. Davydovitch, Zh. Eksp. Teor.
Fiz. 83, 275 (1982).
[3] L.M. Avkutskij, R.L. Davydovitch, L.A. Zemnukhova, P.S. Gordienko, V.V. Ur-
bonavichius, J.P. Grigas, Phys. Status Solidi B 116, 483 (1983).
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V.I. Sergienko, Zh. Strukt. Khim. 17, 1316 (1972).
[5] N. Nakamura, Z. Nat.forsch A 41, 243 (1986).
[6] A. Waśkowska, Z. Czapla, Cryst. Res. Technol. 24, 1259 (1989).
[7] R.R. Ryan, D.T. Cromer, Inorg. Chem. 11, 2322 (1972).
[8] Z. Czapla, S. Dacko, Ferroelectrics 140, 271 (1993).
[9] I.V. Obreimov, About Applications of Frehnel's Diffraction for the Physical and
Technical Measurements, Acad. Sci. USSR, Moscow 1945, p. 81 (in Russian).
[10] A. Onodera, private communication.


OPTICAL INVESTIGATIONS OF PHASE TRANSITIONS IN (NH4) 2 SbF5 CRYSTAL

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OPTICAL INVESTIGATIONS OF PHASE TRANSITIONS IN (NH4) 2 SbF5 CRYSTAL

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