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Journal of Materials ScienceFull Set - Includes `Journal of MaterialsScience Letters' ISSN 0022-2461Volume 51Number 17 J Mater Sci (2016) 51:8156-8167DOI 10.1007/s10853-016-0091-5

Influence of dopants on the thermalproperties and critical behavior of theferroelectric transition in uniaxialferroelectric Sn2P2S6

V. Shvalya, A. Oleaga, A. Salazar,I. Stoika & Yu. M. Vysochanskii

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Influence of dopants on the thermal properties

and critical behavior of the ferroelectric transition

in uniaxial ferroelectric Sn2P2S6

V. Shvalya1,2, A. Oleaga1,*, A. Salazar1, I. Stoika2, and Yu. M. Vysochanskii2

1Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería, Universidad del País Vasco, Alameda Urquijo s/n,

48013 Bilbao, Spain2 Institute for Solid State Physics and Chemistry, Uzhgorod University, Uzhgorod 88000, Ukraine

Received: 11 April 2016

Accepted: 20 May 2016

Published online:

31 May 2016

� Springer Science+Business

Media New York 2016

ABSTRACT

The thermal properties of Sn2P2S6 single crystals doped with Ge, Te, and Sb

have been studied in the neighborhood of the ferroelectric to paraelectric sec-

ond-order phase transition by means of ac photopyroelectric calorimetry, mea-

suring thermal diffusivity. A detailed study of the critical behavior of the

transitions has been undertaken using different theoretical models to study the

influence of the dopants and the physical mechanisms activated. Ge strongly

favors the stereoactivity of the material, which is revealed in the increase of the

critical temperature and the sharpening of the transition; this is due to the

strengthening of the sp2 electronic orbitals hybridization. Sb has a small influ-

ence on the stereoactivity while Te virtually none. In all cases, the ferroelectric

phases are well described using the phenomenological Landau model, while for

the paraelectric ones, a combination of two mechanisms is needed: first-order

fluctuations of the order parameter plus the presence of charged defects, ruling

out other possible mechanisms. The relative importance of the presence of these

defects increases with increasing contents of Ge and Sb, while in the case of Te,

there is only a slight increase with respect to the undoped sample.

Introduction

Sn2P2S6 is a semiconductor ferroelectric with high

electro-optic coefficients which make it promising for

its application as a photorefractive material, whose

properties can be improved by the addition of dif-

ferent dopants [1–3], specially with small percentages

of Te and Sb [4–6]. Besides, from the point of view of

solid state physics, the phase diagram is heavily

altered when S is substituted by Se, or Sn by Pb, to

form the solid state solutions Sn2P2(S1-xSex)6, (PbySn1-y)2P2S6, and (PbySn1-y)2P2Se6, modifying (even

annulling) the second-order ferroelectric transition or

provoking the appearance of incommensurate pha-

ses, first-order phase transitions, a Lifshitz point…[7]. This richness has made these families of uniaxial

Address correspondence to E-mail: alberto.oleaga@ehu.es

DOI 10.1007/s10853-016-0091-5

J Mater Sci (2016) 51:8156–8167Author's personal copy

ferroelectrics specially attractive to study in depth the

physical mechanisms responsible for those varied

phase transitions. One tool suited to that end is the

study of the critical behavior of the transitions. The

evolution of the critical behavior of the second-order

phase transitions with doping in the three afore-

mentioned families has already been studied with

some extension [8–12] but not with any other kind of

dopants yet. Let us bear in mind that Sn2P2S6 has a

monoclinic crystalline structure, which undergoes a

second-order phase transition at about TC = 337 K

from an initial high-temperature paraelectric phase

with a point group symmetry 2/m to the low tem-

perature ferroelectric one with the point group m [1].

In this paper, we are turning our attention to the

evolution of the thermal properties and the critical

behavior of Sn2P2S6 independently doped with three

other species, each of them taking the place of each of

the three original atoms: Ge for Sn, Sb for P, and Te

for S. It is worth recalling that the critical behavior of

the pure Sn2P2S6 has been described by the combi-

nation of two physical mechanisms: first-order fluc-

tuations of the order parameter (polarization) and the

presence of charge defects [8]. Substituting S with Se

in concentrations close to the Lifshitz point turns the

critical behavior to be well described by the Lifshitz

universality class [9], while replacing Sn by Pb pro-

voked a crossover from the described behavior in the

pure sample to a mean-field model [10]. Finally, the

second-order phase transition in Sn2P2Se6 and (PbySn1-y)2P2Se6 with y\ 0.1 belongs to the 3D-XY uni-

versality class [11].

Coming back to doping with Ge, Sb, and Te, in all

cases, the single crystals can only accommodate small

percentages of these ions, it is not possible to form the

full solid solutions as it happens when Pb substitutes

Sn and Se takes the place of S. The interest of Ge lies

on the fact that it takes the place of the Sn2? ions

which play a vital role in the ferroelectricity of the

material: indeed, the mechanism of the tin cations

lone pair formation is related to the appearance of the

spontaneous polarization [13–15]. There is an anti-

bonding mixing of Sn 5s and S 3p orbitals, which in

its turn develops a bonding interaction with the Sn 5p

orbitals, generating lower-energy filled states Sn

5p ? (Sn 5s–S 3p), which are called in brief sp2. This

formation of the Sn2? lone pair electron cloud toge-

ther with the deformation of the nearest polyhedron

formed by the sulfur atoms determines the origin of

the spontaneous polarization. The sp2 hybridization

becomes stronger at the ferroelectric transition,

increasing the spontaneous polarization. Substitution

of Sn by Ge or Pb affects this hybridization,

improving or worsening the stereoactivity of the

cation sublattice. In particular, the smaller energy

distance between Ge 4s and S 3p states would

improve it while the bigger one between Pb 6s and S

3p states would make it weaker. This is revealed in

the phase transition temperature, which is first low-

ered and then frustrated as Pb concentration is

increased [7, 10], while, on the contrary, it is

increased with Ge contents [16]. A strong hybridiza-

tion of Ge states with the tin cation sublattice has

indeed been shown by Grigas et al. [17] using X-ray

photoelectron spectroscopy (XPS). In this same paper,

the influence of doping with Te on the electronic

properties of Sn2P2S6 was also studied with the result

that there is also an effective hybridization of the

tellurium impurity state with the anion (P2S6)-4

sublattice, modifying the energy zones near the top of

the valence band but without involving the Sn2?

states.

The aim of this paper is to study the thermal dif-

fusivity as a function of temperature of Sn2P2S6independently doped with Ge, Te, and Sb in the

neighborhood of the ferroelectric to paraelectric sec-

ond-order phase transition in order to check the

influence of each ion on the thermal properties of the

material and, in particular, on the critical behavior of

the ferroelectric transition compared to that of the

parent compound, already studied in detail [8]. This

will give relevant information about their different

effects on the stereoactivity of the lattice or other

mechanisms.

Experimental procedures

Single Sn2P2S6 crystals doped with Ge, Te, and Sb

ions were obtained by vapor-transport method in a

quartz tube using SnI2 as a transport agent. The

synthesis of the starting material in the polycrys-

talline form was carried out using high-purity ele-

ments Sn (99.99 %), P (99.999 %), S (99.99 %), Ge

(99.999 %), Te (99.99 %), and Sb (99.999 %) in atomic

percentage. The nominal amount of impurities was as

follows: Ge: 3 and 5 %; Te: 1 and 2 %; and Sb: 0.5, 1,

and 2 % (atomic percentages in all cases). The sam-

ples doped with Ge present a light orange color,

while Te- and Sb-doped samples have light brown

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and light red colors, respectively. The samples were

characterized by X-ray diffraction (XRD) technique

performed with DRON—4 diffractometer using Cu

Ka radiation. The diffraction lines broadening anal-

ysis confirms that the XRD pattern of the investigated

doped crystals is similar to the observed one in the

case of the nominally pure (undoped) samples. This

confirmed their good crystal quality as well as dis-

carded the presence of different phases. XRD was

also used to orient the samples before cutting them.

The incorporation of the dopants through this

method had been previously checked by the changes

in ferroelectric and optical properties already pub-

lished [4, 15, 16].

For thermal diffusivity measurements, all samples

have been prepared in the form of thin plane-parallel

slabs with thicknesses in a range of 0.500–0.530 mm

and whose faces were cut in the monoclinic symme-

try plane perpendicular to (001) crystallographic

direction. In order to carry out this kind of study, a

high resolution ac photopyroelectric calorimetry

technique in the standard back detection configura-

tion has been employed. [18, 19] In particular, its

usefulness has been well demonstrated in the thermal

diffusivity study of Sn(Pb)2P2S(Se)6 ferroelectric

mixed compounds [8–11]. In this setup, the front

surface of the sample under study is illuminated by a

modulated low power laser beam, while the rear

surface is in thermal contact with a LiTaO3 pyro-

electric sensor with metallic electrodes on both faces.

Thermal contact between the detector and sample is

guaranteed using a thin (few microns) layer of a heat-

conductive silicon thermal grease. Since the samples

are transparent, their front surfaces have been cov-

ered with a thin layer of graphite to make them

opaque and increase the absorption of the laser beam.

The photopyroelectric signal provided by the sensor

has been processed by a lock-in amplifier in the

current mode.

In order to measure as a function of temperature,

both the detector and the sample have been placed

inside a liquid nitrogen cryostat which can work in

the temperature range 78–450 K. The measurements

have been performed in two steps: first there was a

quick run with a rate of 0.1 K/min to cover a wide

temperature range and then a second one consisted

of high-resolution cooling/heating runs around the

phase transition using variations of temperature as

slow as 25–30 mK/min, with which the stability of

the shape of the phase transition was ensured to

enable the critical behavior study.

According to the experimental conditions, if the

sample is opaque and thermally thick (its thickness l

has to be larger than thermal diffusion length:

l[ l ¼ffiffiffiffiffiffiffiffiffiffiffi

D=pfp

, where f is the frequency of modula-

tion), then the phase and the natural logarithm of the

amplitude of the normalized photopyroelectric cur-

rent at a fixed temperature T have both a linear

dependence on the square root of the frequency with

the same slope m, from which the thermal diffusivity

D can be calculated [19, 20]:

D ¼ l2pm2

ð1Þ

Once the thermal diffusivity has been obtained at

some certain reference temperature Dref the temper-

ature run is performed fixing a frequency of modu-

lation belonging to the linear region explained above.

Defining the phase difference of the electric signal

with temperature as DW(T), the temperature depen-

dence of thermal diffusivity is given as follows [21]:

DðTÞ ¼ 1ffiffiffiffiffiffiffiffi

Dref

p � DW Tð Þl

ffiffiffiffiffi

pfp

" #�2

: ð2Þ

It should be pointed out that measurements have

been carried out under continuous temperature

variation and the experimental data are retrieved

every several seconds, thus obtaining curves with

thousands of experimental points. The experimental

curves shown in all graphs are the ones obtained

experimentally, without any fitting or treatment. In

the continuous runs, the relative resolution of the

points is ±0.0001 mm2/s in D and ±0.001 K in T,

retrieving the precise shape of the thermal diffusivity

as a function of temperature, especially around the

phase transition point. Depending on the thickness of

the particular sample, the modulation frequencies

used for this investigations have been in the range

1–4 Hz, always ensuring that we are working under

the proper theoretical conditions in which Eqs. 1 and

2 are fulfilled.

Experimental results

Thermal diffusivity as a function of temperature has

been measured for all samples in the (001) direction.

The experimental results are presented on Figs. 1, 2,

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and 3. To better compare and see the difference

between each doped sample and the pure one, we

have also included the previously measured thermal

diffusivity for the undoped Sn2P2S6 crystal along the

(001) direction [8]. For all samples, a dip in the tem-

perature evolution of the thermal diffusivity has been

observed, signaling the presence of the second-order

phase transition. It is clearly seen in those figures that

the added impurities have altered the shape of the

thermal diffusivity curve compared to the undoped

crystal.

Introducing Ge2? into the Sn2P2S6 cation sublattice

increases the transition temperature. From the initial

value of 336.2 K for the pure sample, it rises up to

about 349.2 K for the sample doped with 5%Ge,

while the crystal with the nominal concentration of

3%Ge reveals an intermediate value of TC = 346.1 K

(see Fig. 1). An increase in TC had already been

observed by Maior et al. [16] measuring other phys-

ical variables with less resolution. Note that the dip

becomes sharper as Ge contents is increased.

Concerning the effect of Sb, this type of dopant

should substitute P ions in the anion sublattice

(P2S6)4-. As seen from Fig. 2, the transition is slightly

shifted to lower temperatures, but the effect is much

smaller than in Ge, and the anomaly at TC is smeared

when the concentration of Sb increases. For the

samples doped with 2% of Sb, the value of TC is

almost the same as for 1 %, but the general evolution

of the thermal diffusivity curve is altered.

Finally, the impurities of Te added in Sn2P2S6 only

slightly affect the critical temperature (see Fig. 3).

Unfortunately, so far, there is no additional data

related to the influence of Sb and Te on the position of

transition temperature obtained by means of other

techniques.

It is worth noting that there is a common feature in

Figs. 1, 2, and 3. For all samples, the absolute value of

the thermal diffusivity is reduced at ‘‘low’’ dopant

concentrations while a further doping leads to a rise

in thermal diffusivity, though always smaller than in

the undoped sample. In all cases, the absolute values

of D are quite low and fall within the range of poor

thermal conductors, where heat is mainly transferred

by phonons. It is quite common that, in thermal

insulators, small additions of any dopant reduce the

phonon mean free path due to the disorder intro-

duced while from a certain percentage up there is a

relative increment, as it happens here; this has been

observed in ferroelectrics as well as in magnetic

materials. See the case of (PbxSn1-x)2P2S6 [10],

La1-xSrxMnO3 [22], or Nd1-xSrxMnO3 [23].

Critical behavior and fittings

Critical behavior theory assesses that certain physical

quantities present a singularity at the transition

temperature (critical temperature TC) whose partic-

ular mathematical form is related to the physical

mechanisms responsible for the transition; regarding

thermal properties, the most commonly theorized

physical property is specific heat. [24] Thermal dif-

fusivity and specific heat are related by the following

equation:

Figure 1 Thermal diffusivity in the (001) direction as a function

of temperature for Sn2P2S6 doped with Ge: a pure Sn2P2S6 [8];

b Sn2P2S6 ? 3%Ge; c Sn2P2S6 ? 5%Ge.

Figure 2 Thermal diffusivity in the (001) direction as a function

of temperature for Sn2P2S6 doped with Sb: a pure Sn2P2S6 [8];

b Sn2P2S6 ? 0.5%Sb; c Sn2P2S6 ? 1%Sb; d Sn2P2S6 ? 2%Sb.

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cp ¼K

qD; ð3Þ

where K is the thermal conductivity and q the den-

sity, which means that the critical behavior of specific

heat and the inverse of thermal diffusivity is the

same, provided that neither thermal conductivity nor

density have significant changes at the transition,

which is the case in Sn2P2S6 [8, 25].

Different approaches can be undertaken: the first

one is the classical approach using Landau theory

which gives a particular expression for this specific

heat which is used to fit the experimental specific

heat (or the inverse of thermal diffusivity) in the

ferroelectric phase. Taking into account the possible

coupling of polarization to strain in a uniaxial ferro-

electric such as Sn2P2S6, the thermodynamical

potential density reads [8]

F ¼ F0 þat

2P2 þ b

4P4 þ c

6P6 þ 1

2cu2 þ ruP2: ð4Þ

And the specific heat in the ferroelectric phase is

obtained by

cp ¼ �To2F

oT2

� �

P

: ð5Þ

And taking into account Eq. 3, the anomalous part of

the inverse of thermal diffusivity due to the transition

reads, after Ref. [8]

D1

D

� �

¼ p1T

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1� 4p2ðT � TCÞp ; ð6Þ

where p1 ¼ a2

2b0K, p2 ¼ ca

b02, b0 ¼ b� 2r

c2

In order to fit the inverse of thermal diffusivity, the

full fitting equation that will be used is [10]

1

D¼ p3 þ p4ðT � TCÞ þ p1

Tffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1� 4p2ðT � TCÞp ; ð7Þ

where a linear term has been added to account for a

regular contribution to the inverse of the thermal

diffusivity as a function of temperature. This allows

to obtain the values of the phenomenological coeffi-

cients b0 and c, comparing them among the doped

and undoped samples.

But Landau theory does not give a complete pic-

ture of the physics involved as it does not take into

account the fluctuations of the order parameter (po-

larization in this case) while approaching the critical

temperature, which are more and more relevant as

the so called reduced temperature t = (T - TC)/TC

decreases till they dominate the transition. Theoreti-

cal work was developed in literature to extend Lan-

dau’s approach including first-order fluctuations of

the order parameter, with the result that the singu-

larity in specific heat has the following behavior

[7, 26]

Dcp � t�1=2 ð8Þ

which, regarding the fitting of the inverse of thermal

diffusivity, will imply the use of the following

equation

1

D¼ B1 þ C1tþ A1 tj j�a; ð9Þ

with a = 0.5. But this behavior has also failed to be

proved experimentally in most cases in ferroelectrics.

In the case of uniaxial ferroelectrics, the spatially

inhomogeneous distributions of the order parameter

are necessarily associated with the appearance of a

macroscopic electric field, which can have an influ-

ence upon fluctuations. Indeed, the presence of the

dipolar–dipolar interaction attenuates the fluctua-

tions effects and a theoretical development which

takes this interaction into account leads to the fol-

lowing heat capacity anomaly [7, 26]

Dcp � ln t: ð10Þ

This logarithmic correction to the pure Landau

theory has proved extremely successful for many

uniaxial ferroelectric materials. Another possibility is

that the attenuation of fluctuations be small enough

so that Eq. 8 could nearly be of application and that

Figure 3 Thermal diffusivity in the (001) direction as a function

of temperature for Sn2P2S6 doped with Te: a pure Sn2P2S6 [8];

b Sn2P2S6 ? 1%Te; c Sn2P2S6 ? 2%Te.

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only a small logarithmic correction should be intro-

duced; hence, Eq. 8 would turn into

Dcp � t�1=2 ln tj jb ð11Þ

with 0.1\ b\ 0.33 [27, 28]. This equation is equiva-

lent to having in Eq. 8 an exponent slightly closer to

zero than -0.5. Regarding the fitting of the inverse of

thermal diffusivity, the equation to fit is

1

D¼ B2 þ C2tþ A2 tj j�0:5

ln tj jj jb: ð12Þ

Besides, the contribution of defects to the anomaly

in specific heat in ferroelectrics has also been studied.

In general, defects are simply responsible for a

rounding of the anomalies in the phase transitions

but Isaverdiyev et al. [29–31] demonstrated that in the

case of charged defects in ferroelectrics, they can give

rise to stronger anomalies as they can induce long-

range perturbations of the order parameter. The

dependence of the specific heat in this case takes the

form

Dcp � t�3=2: ð13Þ

In the particular case of Sn2P2S6, a combination of

first-order fluctuations and defects, combining Eqs. 8

and 13 was needed to fit the anomalous part of the

specific heat [8] and the resulting fitting equation of

the inverse of thermal diffusivity is [8, 10]

1

D¼ B3 þ C3tþ A3 tj j�0:5þF3 tj j�1:5: ð14Þ

Equations (8)–(14) have been frequently used in

literature to study the critical behavior of ferro-

electrics fitting the paraelectric phase while, as

already mentioned, Eq. 7 is used to fit the ferroelec-

tric phase. In the present study, the fittings of all

Figure 4 Experimental data (circles) for the inverse of thermal

diffusivity as a function of the reduced temperature for Sn2P2S6 ? 3%Ge (a1) and Sn2P2S6 ? 5%Ge (b1). Only a selection of

experimental points is shown, for the sake of clarity. The lines

marked as (1) represent the fits to Eq. 7 for the ferroelectric phases,

while the ones marked as (2) represent the fits to Eq. 14 for the

paraelectric phases. a2, b2 Deviation plots corresponding to the

fits shown above. Open circles are for T\TC and crosses for

T[TC.

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experimental curves of the inverse of the thermal

diffusivity to Eqs. 7, 9, 12, and 14 have been

performed.

Finally, it must be mentioned that if the modern

treatment of critical behavior theory were applied,

fully taking into account the contribution of fluctua-

tions till t ? 0 in its strictest sense, both branches of

the transition (paraelectric as well as ferroelectric)

should comply with the following equation [10, 32]

1

D¼ B4 þ C4tþ A�

4 tj j�a 1þ E� tj j0:5� �

; ð15Þ

where t = (T - TC)/TC is the reduced temperature.

Superscripts ? and - stand for T[TC and T\TC,

respectively. The linear term represents the regular

contribution to the inverse of the thermal diffusivity,

while the last term represents the anomalous

contribution at the second-order phase transition.

The factor under parenthesis is the correction to

scaling that represents a singular contribution to the

leading power as known from experiments and the-

ory [33, 34]. Scaling laws require that there is a

unique critical exponent a for both branches and

rigorous application states that constant B4 needs also

be the same [35]. These conditions have sometimes

been relaxed in literature due to the difficulty of

obtaining good fittings to the experimental data with

those constraints, especially in the case of ferro-

electrics. Different universality classes have been

proposed (for each of them the critical exponent a has

a particular value) taking into account different

physical scenarios in ferroelectrics; a summary can be

found in [36]. But it is worth noting that in the pre-

vious work on Sn2P2S6, it was not possible to find a

Figure 5 Experimental data (circles) for the inverse of thermal

diffusivity as a function of the reduced temperature for Sn2P2S6 ? 0.5%Sb (a1), Sn2P2S6 ? 1%Sb (b1), Sn2P2S6 ? 2%Sb

(c1). Only a selection of experimental points is shown, for the

sake of clarity. The lines marked as (1) represent the fits to Eq. 7

for the ferroelectric phases, while the ones marked as (2) represent

the fits to Eq. 14 for the paraelectric phases. a2, b2, c2 Deviation

plots corresponding to the fits shown above. Open circles are for

T\TC and crosses for T[TC.

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good fitting under these strict conditions [8]. Never-

theless, in this work, the experimental curves have

also been fitted to Eq. 15, using both paraelectric and

ferroelectric branches at the same time.

Figures 4, 5, and 6 present the inverse of the ther-

mal diffusivity in the near vicinity of the critical

temperature for the samples doped with Ge, Sb, and

Te, respectively. These measurements were per-

formed at high resolution in order to obtain the shape

of the transitions with great accuracy. In all cases, it

was not possible to fit the curves to Eq. 15, and the

fittings to Eqs. 9–11 were extremely bad as they could

not follow the experimental curvatures at all. Good

fittings were obtained for the ferroelectric phase to

Eq. 7, from where the phenomenological coefficients

in the Landau expansion were extracted and for the

paraelectric phase to Eq. 14, where the combined

effect of the first-order fluctuations of the order

parameter and the contribution of defects was nec-

essary to obtain a good fitting. The best fittings are

superimposed to the experimental points on Figs. 4,

5, and 6. Tables 1 and 2 contain the particulars of the

fittings (parameters, fitting ranges, and coefficient of

determination R2) as well as the coefficients found in

the fittings, together with the uncertainties. Figures 4,

5, and 6 also contain the deviation plots in which the

difference between the experimental and the fitted

points, normalized, are presented as a percentage, as

another proof of the quality of the fittings. It is worth

noting that, being the experimental uncertainties as

small as mentioned when describing the experimen-

tal techniques, they do not have any significant

influence on the fittings carried out.

Figure 6 Experimental data (circles) for the inverse of thermal

diffusivity as a function of the reduced temperature for Sn2P2S6 ? 1%Te (a1) and Sn2P2S6 ? 2%Te (b1). Only a selection of

experimental points is shown, for the sake of clarity. The lines

marked as (1) represent the fits to Eq. 7 for the ferroelectric phases,

while the ones marked as (2) represent the fits to Eq. 14 for the

paraelectric phases. a2, b2 Deviation plots corresponding to the

fits shown above. Open circles are for T\TC and crosses for

T[TC.

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Discussion

As explained in Experimental results section, Figs. 1,

2, and 3 show the general influence of the different

dopants on the thermal diffusivity of Sn2P2S6. Start-

ing with germanium, an increasing doping percent-

age increases the critical temperature and severely

modifies the shape, making the transition sharper.

The increase in TC is in agreement with a previous

result measuring dielectric permittivity in a 5 %

doped sample (as well as piezoelectric and pyro-

electric coefficients), [16] though our results have a

higher resolution. Both the increase in TC and in the

sharpness of the transitions in the doped samples

illustrate the fact that the ferroelectric transition is

favored with respect to the undoped one, which

suggests that the stereoactivity of the cation sublattice

has been improved with the substitution of Sn2? by

Ge2?. As the spontaneous polarization is attributed in

Sn2P2S6 to the formation of the Sn2? lone pair electron

cloud by means of the sp2 hybridization described in

the introduction [13, 14], the increase in stereoactivity

has to do with the strengthening of this hybridiza-

tion, which has been demonstrated by means of XPS

measurements [17]. Ge plays a role opposite to that of

Pb when it substitutes Sn, the effect of the latter being

a reduction in the stereoactivity of the cation sublat-

tice, lowering the phase transition temperature and

even frustrating it at high concentrations [7, 10]. The

origin of this opposed effect on the stereoactivity lies

in the energy distance between (Ge 4s–Sn 5s–Pb 6s)

and S 3p states; the smaller value in the Ge case

improves it with respect to the higher one in Pb,

favoring or disfavoring the sp2 hybridization. Con-

cerning the critical behavior of Sn2P2S6:Ge, the mod-

els which can describe it are essentially the same ones

as in the undoped Sn2P2S6 [8]: Landau classical

model for the ferroelectric phase and an added con-

tribution of the first fluctuational correction plus the

contribution of defects for the paraelectric one (see

Fig. 4), which means that the presence of Ge does not

alter the physical mechanisms responsible for the

transition but simply enhances its ferroelectric fea-

tures. There is some variation in the fitted critical

parameters obtained, though. Concerning the phe-

nomenological parameters in Landau expansion,

both b0 and c are reduced with respect to the pure

sample (see Table 1). For a second-order phase tran-

sition b0 must be positive (it is negative for a first-

order one), its decrease is due to the fact that the

shape of the transition gets sharper. For the para-

electric phase, the ratio which brings the relative

importance of the contribution of defects with respect

to the first fluctuational correction F3/A3 after Eq. 14

increases from 5.0 9 10-3 in the undoped sample [8]

to 2.3 9 10-2 and 4.6 9 10-2 in the samples doped

with 3 and 5%Ge, showing how the introduction of

Ge increases the importance of the charged defects in

the lattice.

Turning our attention to Sn2P2S6:Sb, we see from

Fig. 2 that 0.5 % gets the transition rounded and

broader but with only a slight reduction in the critical

temperature, which is further reduced up to 3 K with

higher dopings. Both the broadening and the

decrease in TC suggest a slight disfavor of the ferro-

electric transition. The origin of this small reduction

in stereoactivity is not clear, as Sb takes the place of P

in the crystalline network, which is not clearly

involved in the physical mechanism of ferroelectric-

ity. Sb will be introduced in the anion sublattice

(P2S6)4- affecting the energy levels at the top of the

valence band [17]. Unfortunately, there is no infor-

mation on how the introduction of Sb will influence

the electronic states responsible for stereoactivity.

Further studies should be undertaken in this respect.

Concerning critical behavior, again the models which

fit well the experimental curves are the same as in the

case of the pure Sn2P2S6 (see Fig. 5). With the differ-

ence, that the phenomenological coefficient in the

Landau expansion b0 is slightly decreased and c is

heavily reduced when compared to the pure sample

(see Table 1). The reduction in b0 is related to the

broadening of the transition. Regarding the para-

electric phase, the relative contribution of the two

physical mechanisms needed to describe it (first

fluctuational correction and charged defects) also

increases with respect to the undoped sample

(though the effect is less important than in the case of

Ge) as it goes to 1.3 9 10-2 for 0.5 %, 1.6 9 10-2 for

1 %, and finally 1.8 9 10-2 for 2 %.

Finally, in the case of the addition of Te, the critical

temperature is just very slightly increased, with

similar features in the shape of the transition. It could

be said that there is a very slight favoring of the

ferroelectric transition. The effect of Te on the elec-

tronic orbitals has been also studied by XPS [17] with

the conclusion that there is a strong hybridization

with P and S orbitals near the top of the valence band

but with a very slight influence on the Sn2? lone pair,

thus having very little influence on the stereoactivity,

8164 J Mater Sci (2016) 51:8156–8167

Author's personal copy

Tab

le1

Resultsof

thefittingof

theinverseof

thermal

diffusivityusingtheLandaumod

elEq.

7

Sn 2P2S6

3%Ge

5%Ge

0.5%

Sb

1%Sb

2%Sb

1%Te

2%Te

p 1(s/m

m2)

3.3219

10-3±

49

10-6

0.0185

±0.0044

0.0111

±0.0008

0.018±

0.006

0.026±

0.008

0.017±

0.005

3.67

910

-3±

2.19

10-4

2.54

910

-3±

2.59

10-4

p 2(K

-1)

0.0512

±0.0002

10.02±

4.23

4.49

±0.45

0.0037

±0.0008

0.0015

±0.0003

0.0044

±0.0008

0.105±

0.005

0.093±

0.009

Fittedrange

3.29

10-2to

2.09

10-3

3.19

10-2to

1.49

10-3

2.79

10-2to

9.19

10-4

4.29

10-2to

1.99

10-3

6.69

10-2to

3.39

10-3

3.59

10-2to

3.09

10-3

2.89

10-2to

8.69

10-4

3.69

10-2to

1.39

10-3

R2

0.9922

0.9994

0.9994

0.9990

0.9996

0.9996

0.9999

0.9999

b0 (J

m5C-4)

6.19

108

1.69

108

2.59

107

1.69

108

1.19

108

1.79

108

7.89

108

1.19

109

c(J

m9C-6)

2.39

1010

1.69

1010

1.79

109

5.99

107

1.19

108

7.89

107

4.09

1010

7.39

1010

The

columns

show

theadjustable

parametersp 1

andp 2,thefitted

rang

ein

redu

cedtemperature

unitst=

(T-

TC)/TC,thequ

alityof

thefittingthroug

hthecoefficientof

determ

inationR2,as

wellas

thecalculated

phenom

enolog

ical

parametersin

theLandauexpansionb0

andc.

The

values

forSn 2P2S6areextractedfrom

Ref.[8]

Tab

le2

Resultsof

thefittingof

theinverseof

thermal

diffusivityusingEq.

14

Sn 2P2S6

3%Ge

5%Ge

0.5%

Sb

Fittedrang

e2.79

10-2to

6.89

10-4

2.59

10-2to

5.39

10-4

2.99

10-2to

7.29

10-4

3.29

10-2to

1.99

10-3

R2

0.98

10.96

60.98

50.98

8

A3(s/m

m2)

3.25

910

-3±

69

10-4

7.10

910

-4±

2.15

910

-4

6.15

910

-4±

1.65

910

-4

4.06

910

-3±

8.19

10-4

F3(s/m

m2)

1.62

910

-5±

19

10-7

1.60

910

-5±

29

10-7

2.83

910

-5±

29

10-7

5.45

910

-5±

1.09

10-6

F3/A

35.09

10-3

2.39

10-2

4.69

10-2

1.39

10-2

1%Sb

2%Sb

1%Te

2%Te

Fittedrang

e3.69

10-2to

1.29

10-3

3.69

10-2to

2.89

10-3

2.09

10-2to

5.89

10-4

2.39

10-2to

6.99

10-4

R2

0.95

30.98

70.96

70.95

2

A3(s/m

m2)

1.63

910

-3±

2.79

10-4

5.59

910

-3±

8.99

10-4

2.07

910

-3±

2.09

10-4

2.99

910

-3±

6.79

10-4

F3(s/m

m2)

2.52

910

-5±

39

10-7

9.95

910

-5±

1.59

10-6

1.10

910

-5±

19

10-7

1.77

910

-5±

49

10-7

F3/A

31.69

10-2

1.89

10-2

5.39

10-3

5.99

10-3

Ineach

case,therelevant

fittingparametersareshow

ntogether

withthefitted

rang

ein

redu

cedtemperature

unitst=

(T-

TC)/TCas

wellthequ

alityof

thefittingthroug

hthe

coefficientof

determ

inationR2.The

values

forSn 2P2S6areextractedfrom

Ref.[8]

J Mater Sci (2016) 51:8156–8167 8165

Author's personal copy

as our results show. These slight changes imply that

the values of b0 and c are very close to the ones of the

undoped sample. On the other hand, the fitting to the

paraelectric phase corresponds to the combination of

the double mechanism described above with a very

slight increase of the contribution of defects as the

ratio F3/A3 in Eq. 14 takes the value of 5.3 9 10-3 for

1%Te and 5.9 9 10-3 for 2%Te, which means that it is

very close to the one for the undoped sample

(5.0 9 10-3). In all, doping with Te affects the phase

transition very little.

Conclusions

An ac photopyroelectric calorimetry in the back con-

figuration has been used to obtain the thermal diffu-

sivity evolutionwith temperature in the neighborhood

of the second-order ferroelectric phase transition in the

uniaxial ferroelectric Sn2P2S6 dopedwith Ge, Te, or Sb.

Ge strongly favors the stereoactivity of the material,

which has been proved by the increase of the critical

temperature and the sharpening of the transition; this

is due to the strengthening of the sp2 electronic orbitals

hybridization. Sb has a small influence on the

stereoactivity, reducing it a little bit while Te has vir-

tually none. The critical behavior of all samples has

been studied through the inverse of the thermal dif-

fusivity, fitting it to different models and comparing it

with the well-known behavior of the pure sample. In

all cases, the ferroelectric phases are well described

using the phenomenological Landau model. For the

description of the paraelectric ones, the fitted model

takes into account at the same time first-order fluctu-

ations of the order parameter plus the presence of

charged defects, ruling out a mean-field description.

The relative importance of the presence of charged

defects increases with Ge and Sb doping, while in the

case of Te, it remains nearly equal with respect to the

undoped sample.

Acknowledgements

This work has been supported by Gobierno Vasco

(IT619-13), and UPV/EHU (UFI11/55). The authors

thank for technical and human support provided by

SGIker of UPV/EHU. V. Shvalya thanks the Erasmus

Mundus programme ‘‘ACTIVE’’ for his grant.

Compliance with ethical standards

Conflict of interest The authors declare that they

have no conflict of interest.

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