Reinvestigation of the stepwise character of the ferroelastic phase transition in lead phosphate-arsenate, Pb3(PO4) 2 -Pb3(AsO4)2

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Reinvestigation of the stepwise character of the

ferroelastic phase transition in lead phosphate-arsenate, Pb3(PO4) 2 -Pb3(AsO4)2

U. Bismayer, E. Salje, C. Joffrin

To cite this version:

U. Bismayer, E. Salje, C. Joffrin. Reinvestigation of the stepwise character of the ferroelastic phase

transition in lead phosphate-arsenate, Pb3(PO4) 2 -Pb3(AsO4)2. Journal de Physique, 1982, 43 (9),

pp.1379-1388. �10.1051/jphys:019820043090137900�. �jpa-00209518�

1379

Reinvestigation ^{of the} stepwise ^{character of the} ferroelastic phase ^transition

in lead phosphate-arsenate, Pb3(PO4)2-Pb3(AsO4)2

U. Bismayer, ^E. Salje

Institut für Kristallographie ^und Petrographie, Universität Hannover, Welfengarten 1, ^D3000 Hannover, Germany

and C. Joffrin

Laboratoire Léon-Brillouin, Université de Paris-Sud, ⁹¹⁴⁰⁵ Orsay, ^France

(Reçu le 20 avril 1982, accepté ^{le 18 mai} 1982)

Résumé.

L’existence d’une déformation statique ^et dynamique ^{dans la} phase intermédiaire entre les phases ^à

haute et à basse température (phases para- ^et ferroélastique) ^{a été} étudiée par la diffusion de ^neutrons à haute

résolution, par diffusion de rayons X ^et par spectroscopie ^{Raman. Le} comportement ^du paramètre ^{d’ordre a été} suivi _par mesure de biréfringence optique ^sous pression uniaxiale. La déformation structurale de la phase ^intermé- diaire, comparée ^{à la structure à haute} température, ^est identique à celle de la phase ferroélastique, ^{mais elle} possède

3 axes binaires de symétrie monoclinique presque équivalents. La réorientation spontanée ^{entre ces trois axes a été} observée en tant qu’effet dynamique (mode flip) pour Pb3(PO4)2. ^{Dans le cas de} Pb3(P1-xAsxO4)2 les déformations

statiques ^{se situent aux} températures ^tout juste au-dessus du point de transition ferroélastique, ^alors qu’aux ^tem- pératures plus ^élevées s’y superpose du mode flip.

Abstract.

The existence of static and dynamic deformation in the intermediate phase between the high ^{and low} temperature phases (para- ^and ferroelastic) ^{has been examined} by high resolution neutron scattering, X-ray ^diffu-

sion and Raman spectroscopy. The behaviour of the order parameter ^was investigated through ^the measurement of optical birefringence under shear stress. It was found that the structural deformation of the intermediate phase, ^as compared ^{with the} high temperature structure, is similar to that of the ferroelastic phase but with three nearly equivalent binary ^{axes of the} monoclinic unit cell. The spontaneous ^thermal switching between these three axes as a dynamical ^effect (flip-mode) is observed in Pb3(PO4)2. ^In Pb3(P1-xAsxO4)2 ^static deformations occur at

temperatures just above the ferroelastic transition point ^{and are} superposed by flipping ^{motion at} higher tempera-

tures.

J. Physique ⁴³ (1982) ^{1379-1388 SEPTEMBRE} 1982,

. Classification Physics ^Abstracts

64.70K

1. Introduction.

Lead phosphate, Pb3(P04)2, ^and

its isomorphs Pb3(As04)2 ^and Pb3(V04)2 ^exhibit ferroelasticity ^{with the} space group C2/c ^{of the} phase

b [1, 2]. ^A paraelastic phase ^a with space group R3m

is approached ^at high temperatures [3, 4] ^{but no direct}

transformation b(C2/c)-a(R3m) ^{was ever observed :} experimental ^studies involving X-ray [5], ^neutron

diffraction [6, 7], ^Raman [8, 9,10], ^infrared spectroscopy [10, 11] ^and electronmicroscopy [12, 13] ^{as well as}

recent calorimetric studies [14] ^indicate clearly ^the

existence of an intermediate pseudo-phase, ab, with local monoclinic symmetry and rhomboedric lattice constants.

First qualitative interpretations ^{of the nature of the}

intermediate phase ^{were based on} the consideration of regions of monoclinic deformations of a trigonal

lattice due to the formation of the ferroelastic domains

in the phase ^a [5]. ^{Later neutron} scattering experi-

ments [ 15, 6] ^{showed a} dominantly dynamic ^character

of the lattice distortion in case of Pb3(P04)2 ^with

relaxation times of the order of 10-11 s. In case of V

doped ^lead phosphate ^the observation of a strong central peak indicated the possibility ^{of much} longer

relaxation times or even static deformation.

As has been shown [16] ^this phase transition is a

typical example ^{for a} three-dimensional order _para- meter behaviour. One component of this order _para- meter describes the structural deformation which. is

mainly ^{due to the} shift of the Pb-atoms from the

pseudoternary ^axis along ^the binary axis. The two other components represent ^the orientation of the

binary ^axis corresponding ^{to the} possible ^domain configurations. ^{The sets of order} parameters (defor-

mation and orientation) ^do not, ⁱⁿ general, ^{vanish at}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019820043090137900

the same transition temperature. ^The following physi-

cal models provide ^the possible mechanisms of the structure in the intermediate phase (ab) :

1) The structural deformations are highly ^corre-

lated and purely ^static. Depending ^{on the} sign ^{of the} exchange energy between the lead-positions ^we expect

one of the following : i) the formation of monoclinic domain patterns, ii) ^a larger ^{unit cell} [17], iii) ^statisti-

cal disorder of the lead atoms about the three possible

lattice sites.

2) The structural deformations are, at least partly, dynamical. ^The corresponding excitation is mainly

the jump of the Pb-atoms between the three sites and this mode was called « flip-mode » by Salje ^{and Deva-} rajan [16]. ^It depends again ^on the correlation length

whether the flip-mode ^{acts as a} local excitation or as a propagating ^{mode with} phase coupled Pb-positions.

In this contribution we present ^new experimental

results on Pb3(PO4)2 ^and Pb3(P1-xAsx04)2 ^which

show that whereas the behaviour of Pb3(P04)2 ^is essentially ^described by ^model 2, ^{the other} quarter-

nary oxides show a superposition of static and dynamic

effects in the ab phase.

2. Raman and neutron scattering.

Early ^Raman spectroscopy studies of Benoit [9] ^{showed a soft}

mode with Ag symmetry ^{in the} ferroelastic phase.

This observation seemed to support ^{the idea of a}

direct transformation C2/c-R3m ^{with one} L-phonon becoming optically active with the symmetry Ag ⁱⁿ

the b phase. ^Raman spectra ^for Pb3(PO4)2 ^and Pb3(PO.97Aso.0304)2 ^{were recorded once again and} they ^are reproduced ⁱⁿ figure ^1. They ^show clearly

Fig. ^1.

Pb-translational mode frequencies (Ag ^and Bg species) ^versus temperature ^for Pbl(POI)2 (full circles) ^and Pb3(Aso.o3P 0.97°4)2 (open circles). ^The Bg ^{frequency values} overlap ^{for both} compounds.

that in Pb3(PO.97Aso.0304)2 ^the Ag ^and Bg ^modes

near 40 cm - 1 shift together ^to give finally ^a single Eg ,

mode. The critical temperature for this line splitting

is that of the _ab-a transformation and is practically independent of the ferroelastic phase transition b-ab.

This observation supports earlier results of [10], [18], showing ^{that the} Ag ^{mode does not act as soft-mode}

for quaternary ^oxides.

The Raman spectrum ^with Ag scattering symmetry is more complex ^{in the case of} Pb3(P04)2 (Fig. 2). ^At temperatures above 150°C we observe at low energies (v - ³⁷ cm-’) ^a scattering signal ^with Ag ^symmetry

which is strongly temperature dependent. ^{This mode}

appears in addition to the Ag-mode ^{at 40 cm -1 which,}

in turn, approaches ^the Bg ^{mode as in case} of the quar- ternary oxides and acts by ^{no means as soft mode} [8].

The additional mode below 37 cm-’ ¹ remains under-

damped ^{even at} temperatures ^{close to the} ferroelastic transition. The temperature dependence of its fre- quency (Fig. 5) ^remains nearly uneffected over this

phase transition; this mode could also be observed in the intermediate phase. ^This proves that even in

Pb3(P04)2 ^the Ag-mode ^{is not the driving soft mode}

of the ferroelastic transformation.

Fig. ^2.

^{Variation of} Ag ^species Pb-translation Raman band with temperature.

A similar behaviour has been theoretically pre- dicted by Yamada et al. [18] who showed that a sof-

tening ^{of a} phonon ^branch may be due to a pseudospin- phonon coupling. ^In Pb3(P04)2 ^the dynamical ^exci-

tation of the pseudospin system ^{is the} flip ^{mode which}

may couple partly with the lowest Ag-mode. ^{It is}

noteworthy that this mode could never be observed in

doped crystals Pb3(PO4)2 : ^{As or} Pb3(P04)z : ^V.

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This interpretation ^{is confirmed} by the results of neutron scattering experiments, ^{where two critical} phonons ^{were found at the L} point ^{of the rhombohe-}

dric Brillouin _zone; one below T c (phase ^{b), the other}

above 300 OC (phase a). ^{In both cases the} square of the observed frequencies depend linearely ^on tempera-

ture [6]. ^{If a soft mode} driving the transition exists at the r point ^its square frequency ^{must also} depend linearely ^on temperature ^{with a} slope easily ^{to be}

calculated from Landau theory [20]. ^In fact the square of the observed soft mode frequencies ^{at the r} point

of the b phase does neither change linearely ^with temperature ^{nor show the} expected slope ^near T c’

The convergence of these results and those obtained

by ^Raman scattering ^{confirm that the} Ag ^{mode is not}

the driving soft mode of the ferroelastic transition.

The previous ^neutron scattering ^studies by

Joffrin et a1. [6] ^{were carried out at} mean reso-

lution (incident wavelength k1 = ^2.662 A-1,

LB V incoherent ^{= 0.2} THz). ^{In these} spectra ^{the over-}

damped ^zone boundary soft mode appears rather

intense, all other components ^are superposed ^and

cannot be extracted from the scattering signal. ^This experimental condition allowed to follow the soft mode at temperatures ^{not too close to} T c ^{where a clear} separation of the central component and the under-

damped optical phonon ^{branch was found.}

The present ^neutron scattering ^{studies were car-}

ried out with high resolution (k1 ^{= 1.55} A-1,

dvincoherent ^{= 0.02} THz). ^The profiles ^{of the} quasi-

elastic neutron scattering signals ^{at the L} point ⁱⁿ

the intermediate phase ^{are shown in} figure ^{3. The} high resolution enables us to recognize ^{the narrow} peaks ^{close to} the central peak. ^The overdamped

Fig. ^3.

Profiles of quasielastic ^neutron scattering ^of Pb3 (PO 4)2 ^at temperatures ^near T c’

critical phonon appears ^as weak side band at the

edges of the central peak. The central component consists of the flip-mode scattering ^and, possibly, ^of

a central peak. ^With increasing temperature ^{its scat-}

tering intensity decreases and simultaneously ^{its line}

width increases. This characteristic allows us to dis-

tinguish ^{between a central} peak (whose ^{width is} independent ^of temperature [21]) ^{and a} flip-mode.

Above 205°C the peak ^{becomes too weak to be} sepa- rated from the background scattering ^{due to the} overdamped optical ^{soft mode.}

If we assume, that the profile ^{of the} flip-mode ^can

be expressed ^as simple relaxation mode of the type [19]

the width indicates roughly ^the flip frequency. ^The

estimated value (1/v & ^{9 x lO-11} s) ^{is in} good agree- ment with the results of microwave absorption expe- riments in the 5 x IO-11 s band.

It is also in good agreement with earlier results of

high r.esolution neutron experiments by ^{Benoit et}

al. [15] provided the central component ^found by ^them

is identified as flip-mode. ^The overdamped phonon

has obviously ^not been measured in this case.

3. X-ray diffusion.

The structural transforma- tion ab-b ^of Pb3(P04)2 ^is always accompanied by ^the

appearance of diffuse superreflexions ^{in the} para- elastic phase [5]. ^{The same effect was} found in the mixed crystals Pb3(PO4)2-Pb3(AS04)2 ^{with much} larger intensities than in Pb3(PO4)2.

Benoit et al. [15] have shown that the origin ^of

the superreflexions ^is purely dynamic ^{in case of} Pb3(P04)2. ^{Here we} will compare the results of

X-ray ^{diffusion of the} ternary ^and quaternary ^oxides.

Figure ^{4 shows the} zero-layer precession photographs perpendicular ^{to a* for} Pb3(PO4)2 ^at Tc ^{+ 1 °C and} Pb3(PO.48Aso.5204)2 ^at Tc ^{+ 5 °C. In} figure ^{5 the} precession-oscillation photographs ^{of some reflexions}

in the plane k ⁼ 3, ^{a* c* are} shown. Both photographs

show that the superreflexions ^{are diffuse with a circular} profile around the pseudoternary axis and extended diffuseness along ^{a*. Similar results were also} reported by Joffrin et al. [5] ^for Pb3(P04)2. ^No analogous

diffuseness could be found around the rhombohedral main reflexions.

At temperatures ^{close to} the ferroelastic transition

point, ^all profiles, those of the main reflexions and the

superreflexions, ^{be come} inhomogeneous. Often focus-

sing ^{due to bent} crystals ^{are observed as in} figure ^6.

All reflexions in the chosen plane ^{a* b*} (1 = 1) ^are

diffuse in the upper part ^{of the} photograph ^and sharp

in the lower part. This indicates that the crystal ^{is bent}

in the cleavage plane ^{bc with an estimated radius of}

20 cm for the bent surface. It was often observed that different parts ^{of the} crystals ^{are bent in} opposite

directions so that the crystal ^{surfaces seem modulated.}

Fig. ^4.

PrecessiQn photographs ^{of the} layer ^{hk3h of} Pb3(PO.52Aso.4804)2 ^at T, ^{+ 5 °C} (a) ^and Pb3(PO4)2 ^at T, ^{+ 1 oc} (b).

This effect is similar to the appearance of ferroelastic twin walls with respect ^{to the} pseudomirrors (113) ^and (113) [ l, 22]. ^The angle between the cleavage plane (100)

and the domain walls is 89.330 in Pb3(P04)2 ^{at room}

temperature leading ^{to an} angle of 178.660 between the (100) ^{faces of} adjacent ^domains. Residual strains in the paraelastic phase ^{bent the} crystals ^{in the same}

manner but without visible domain walls.

Fig. ^5.

Strictly monochromatic precession oscillation

photographs ^{of the} reflections h21 of Pb,(Po,)2 ^at Tc - ^{5 °C} (a), Tc ^{+ 1 oc} (b), ^and T, ^{+ 5 °C} (c). ^These

reflections are symmetry ^{forbidden above} T,, and appear ^as diffuse scattering ^{with a} scattering profile elongated along ^a*.

A comparison ^{of the} profiles ^{of the} superreflexion 021 of Pb3(PO4)2 ^and Pb3(PO.48Aso.5204)2 is given

in figure ^{7. The} important difference between both

profiles is that in Pb3(P04)2 ^{we find} gaussian peaks

in the phase ^{b and} approximately ^Lorenzian profiles

in the phase ab. Just very close to T,, ^{the two} profiles

seem to superpose. On the contrary, ^the profiles ⁱⁿ Pb3(P 0.48Aso.5204)2 ^are always ^a superposition ^of

two peaks : ^a sharp peak ^{with the same} profile ^{as the}

main reflexions and a diffuse peak ^{similar to} Pb3(PO4)2’

If we associate the sharp peak ^{with a static structural}

deformation equivalent ^{to that} of the ferroelastic phase,

a first estimation for the deviations of the Pb2- positions ^{from the} pseudotemary ^{axis can be made.}

The intensity of the central peak ^of 021 ^{has been}

measured relative to the intensity of the main reflexion

1383

Fig. ^6. - Typical precession photograph ^of Pb3(P04)2

in the intermediate phase (hkl) showing focussing effects due to a bent crystal.

Fig. ^7.

^Line profiles of the diffuse scattering ^{near the}

reflex 021 ^of Pb3 (PO 4)2 ^{at different} temperatures ^near T c’

The inset shows the ^same profile ^for Pb3(PO.52Aso.4S04)2

at T c ^{+ 5 °C.}

Fig. 8.

Reflexes with monoclinic symmetry ^near 224 in the plane perpendicular ^{to the} pseudoternary ^{axis. The} crystal ^of Pb,(PO,)2 is monodomainic at 163 °C (a), multidomainic at 178 °C (b) and shows diffuse scattering according ^{to all} possible

domain orientations at 181 °C (c).

040 for Pb3(P04)2 ^{at room} temperature (phase b) ^and

for Pb3(PO.48Aso.5204)2 ^at T,,, ^{+ 35°} (phase ab).

The structure factor of 021 is independent ^{of the} Pbl-positions and its entire intensity is correlated with PbII. Influences of the relatively light P04 tetrahedra, ^{which are} relatively uneffected by ^{the ferro-}

elastic transformation, ^{have been} neglected. ^From

elastic neutron scattering ^{studies on} Pb3(P04)2’,

Guimaraes [33] ^{estimated a} shift of 0.58 (1) ^{A for}

Pbl’ from the ..pseudo-ternary ^{axis at room} tempera-

ture. From (IO217/1040)Pb3(PO4)2 ^and

values and Guimaraes value of 0.58 A for Pb(II)

shift in pure lead phosphate ^{we estimate} Pb(II) ^shift

in the mixed crystal ^{to be 0.037 A. This} corresponds

to the normal thermal atomic displacements. ^This supports ^the idea, that in the quartemary ^{oxides the} Pb-positions ^are shifted from the pseudotrigonal ^axis along ^the binary axis. As the diffuse reflexions show

nearly trigonal symmetry, the shifts occur, presu-

mably statistically, along ^{all three} possible directions.

Nevertheless, the additional part of the diffuse scat-

tering which superpose the sharp superreflexions

indicates a weak dynamical part. The different

behaviour of Pb3(PO4)2 and Pb3(P1-xAsx04)2 ^can

also be seen in the layer ^hk3h representing ^the cleavage plane ^{of the} crystal. ^In figure ^{8 the} precession photos

of this layer, ^{obtained at} 163°C, ^{178 OC and 181} OC,

are shown for Pb3(P04)2. ^{At 163°C we find a} single

domain crystal ^{which becomes} spontaneously ^multi

domain at temperatures ^{close to} T, ^{= 180.4°C.}

Reflexions due to different orientations of the binary

axis _appear at 178°C. Nevertheless, ^the original

domain pattern remains dominant. Just after the phase

transition (Fig. 8) the three orientations become

equivalent with streaks between the superreflexions.

It is important ^{to note that we find in a stress free} crystal the intensities of the superreflexions following strictly ^the trigonal symmetry. ^{This means that the} reorientation of the ferroelastic lattice distortion is

complete ^at the transition point and that the flip-mode

has the same correlation length ^{in this} plane ^{for all}

three orientations of the binary axis. The _average rhombohedral symmetry ^is practically ^{not disturbed}

in the intermediate phase ^of Pb3(P04)z.

This is not the case for Pb3(PO.48Aso.5204)2. ^The diagram ^of its intermediate phase demonstrates clearly

the dominance of the static part ^{of the} superreflexions

and that the diffuse streaks between them are extremely

weak. Furthermore, the average rhombohedral _sym- metry ^{is not} completely ^fulfilled because the inten- sities of the different superreflexions ^are different for the three orientations of the binary axis. This leads to the conclusion that a preferential orientation exists which was often found to be the same as in the cor-

responding ^{domain structure of the} ferroelastic phase.

The observed distortion of the rhombohedric symmetry explains ^also why ^an important ^residual

birefringence is found in the paraelastic phase ^of practically ^all quartemary ^{oxides. It seems} likely ^that

the residual internal strains in the paraphase, ^which

are much stronger ^{in case} of the static distortions of the lattice of the quarternary oxides than in case of the

dynamic modulation of Pb3(P04)2, ^{determine the} preferential orientation of the b axis.

4. Birefringence and critical exponent iB.

^At temperatures ^{not to close to the} Curie-temperature

the order parameters Ql, Q2, Q3 approach ^{the same} temperature dependence ^{and the} spontaneous ^strain follows a simple scaling ^law es - ( Q )2", 1 T - T o 12/1.

A similar behaviour is expected ^{for the} optical ^bire- fringence perpendicular ^{to the} pseudoternary axis, ðnbc, ^which couples linearely ^{with the} spontaneous strain. Wood et a1. [23] ^{found the} coupling ^constants independent ^of temperature. Nevertheless, ^{it must also}

be examined, ^{whether a} reorientation of the optical

indicatrix with increasing temperature gives ^additional change ^{of the} birefringence ^{in the} cleavage plane. ^This

means that we do not know beforehand whether the temperature dependence of the main refractive indices is univocally determined by the ferroelastic strains or

if further temperature ^effects change the orientation of the optical ^axes.

We examined the absolute orientation of the main refractive indices in Pb3(PO4)2 ^and Pb3 (P 0.2Aso.sO 4)2 experimentally. ^{In case of} Pb3(P04)2 the absolute values of the refractive indices at room temperature ^are given by ^{Torres et}

al. [24] ^as

with np ^{in the cleavage plane (b, c) and the angle} between na ^{and a* is 18°. We find} experimentally ^that

this orientation does not change up ^to the transition

point. During ^the first order transition the angle between na and a* vanishes abruptly.

A continuous variation of the orientation of the

optical indicatrix with temperature ^was observed in

Fig. ^9.

Variation of the angle ^between ny ^{and the} pseudo-

ternary axis with temperature.

1385

Pb3(P 0.2Aso.S04)2’ The refractive indices at room

temperature, ^as determined by ^the prism-method, ^{are :}

The angle ^{2 V is 320 ±} 0.5° ; ^the crystal ^is optically positive. ^With increasing temperature, ^the angle between na ^{and a* varies as} given ⁱⁿ figure ^9.

In terms of the order parameter, ^this angle ^follows

from the general form of the index ellipsoid :

with _{x, y,} z parallel c, b and a*. With no and ne ^as

ordinary ^and extraordinary refractive indices of the

paraphase respectively, ^the angle between ny ^{and a*}

becomes

The terms ABik ^{are the} variations of Bik ^with respect ^to their values in the paraphase. It follows from the basic

equations ^{of the} elastooptic effect that [23] :

The value ð-nac ^{= 0.009 and n = 2.1 have been}

measured in the paraphase. ^{The linear} combinations of the elastooptic coefficients a and b were fitted with the experimental ^{data in} figure 9 (a ⁼ 0.0389,

b ⁼ 0.0103). ^In figure ^{9 the} experimental and theore- tical values of 0 are compared. ^At temperatures between 60°C and 158°C we find an excellent agreement between both curves. This _proves that the entire temperature dependence ^{of the} optical ^indicatrix

is determined by the ferroelastic strains and that further temperature ^{effects can} safely ^be neglected.

The critical exponent ^was therefore determined from the temperature dependence ^{of the} optical birefringence ^{in the} cleavage plane. The results are

collected in figure 10; the critical exponents ^{and the} extrapolated Curie-temperatures ^are given in table I.

In case of Pb3(P04)2 ^{our results can be} compared ^with

earlier measurements of Torres et al. [24] ^{and Wood et}

al. [23] ^who found fl ⁼ 1/4 without further curve fit of the exponent. This result is close to the value 0.235 (4) ^{in table} I, ^which is, ^{on the other} hand, ⁱⁿ good agreement with f3 ^{= 0.236 3 as} predicted by

Burkhard et al. [25] for the threedimensional Potts- oscillator.

The dependence of f3 ^on the chemical composition

Fig. 10. - Variation of An with reduced temperature ^t for different values of x in Pb3(P l-xAsx04)2’ (x ⁼ 0.0;

0.23 and 0.3 scale at left ordinate. ^{x =} 0.77 ; 0.85 and 1.0 scale at right ordinate).

Table I.

Orderparameter exponent P for different

chemical compositions ofPb3(P l-xAsx04)2’

is shown graphically ⁱⁿ figure 11 ; figure ¹² gives ^the jump ^{of the} birefringence ^{at the} point ^{of the} phase

transition as a function of the chemical composition.

Both diagrams indicate the first order behaviour for all P-rich compounds ^{and a} nearly ^{second order}

transformation for As-rich compositions. ^{In case of} Pb3(PO.15Aso.8504)2 ^we find the best approach ^to

classical second order transformation with P ^{= 0.50}

and An = 0. The crossover between both regimes

Fig. ^11.

Variation of the critical exponent ^{with x in}

Pb3(P l-xAsx04)2’

Fig. ^12.

Variation of the spontaneous birefringence ^at

the phase transition point ^with the chemical composition.

Fig. ^13.

Experimental ^set up for the measurement of On under shear stress (a) and orientation of the binary ^{axes rela-}

tive to the external stress for small (b) ^and high ^stress (c).

with P;$ 1/4 and fl ⁼ 1/2 ^{near x = 0.65 is cha-}

racterized by ^a nonuniform temperature dependence

of the order parameter. ^At temperatures ^{close to the} Curie-temperature ^the exponent ^{is near to} 1/4 ^whereas

at lower temperatures this value increases to 1/2. ^{In fact}

no tricritical point ^with # ⁼ 1/4 ^{and An = 0 could be}

found in the system Pb3(PO4)2-Pb3(ASO4)2.

5. The optical birefringence ^{under uniaxial stress.}

The order parameters Q, ^and Q2 govern the first order transition in Pb3(P04)2 ^{and indicate the} appreciable order-disorder part ^{of this} transformation.

The ferroelastic phase ^{is the « ordered »} phase ^with respect ^{to the «} disordered )) intermediate phase ^and

residual disorder must be expected ^{in the} ferroelastic

phase ^{close to} the transition point. ^{This disorder is}

due to non coincidence of the local binary ^{axes relative}

to the ferroelastic state. Under the application ^{of an}

external stress parallel ^to the ferroelastic coercitive stress, the ferroelastic state can be switched and the amount of disorder changes under this operation.

Experimentally, ^the set-up depicted ⁱⁿ figure ^{13 was}

used. Crystals under examination were plates ^{with a}

minimum thickness of 0.3 mm and were monodomains from optical observation. After the application ^{of the}

external stress two regimes ^{could be} distinguished (Fig. 14). For pressures below the coercitive pressure of 1.6 bar [26], ^the imposed shear strains are anti-

parallel ^to the ferroelastic strain, ^for higher ^stresses

the ferroelastic domains switch and the imposed

strains are now parallel ^to the ferroelastic strain. The

experimental ^{results are} given ⁱⁿ figure ^{15. In case of} Pb3(P04)2, the ferroelastic transition smooths for

Fig. 14. - Phase diagram ^of Pb3(P04)2 ^{under uniaxial}

stress, bl, b2 ^and b3 represent the directions of the three

binary ^axes.

1387

Fig. ^15.

Variation of An with temperature ^for 1) ^no

shear stress (full circles), 2) ^{for a shear stress} of 0.9 bar

(crosses) ^and 3) ^{for a shear stress of} 1, ^{2 bars} (open circles) (a). ^{Variation of An2 with} temperature ^for 1) ^{no shear stress}

and 2) ^{for a shear stress of 3 bars} (b).

small antiparallel strains with the remaining ^small jumps ^below T c’ The transition temperature ^with An ⁼ 0 increases under stress.

For stresses above 1.6 bar the first order character of the phase transition remains with slightly ^increased

critical exponents f3 (Fig. 15). The transition tempe-

ratures equally increase under stress. When the crys-

tals, ^after being switched, ^are reexamined under normal conditions we find always ^a slightly changed birefringence Anb, ^even in monodomains. This indi- cates clearly ^{that a certain amount of} residual orien- tational disorder persists ⁱⁿ Pb3(P04)2 ^{even at room}

temperature.

A pressure-temperature phase diagram ^{has been}

derived from the observed transition points ^{and is}

shown in figure ^{14. Two} monoclinic phases ^{exist in}

the low temperature range, namely ^the ferroelastic

phase with three stable domain orientation and the

paraelastic, monoclinic form with just ^{one stable}

domain orientation. The transition between both is

always first order. At temperatures ^near T,,, (P ⁼ 0) ^the

transition to the intermediate phase ab takes place.

In Pb3(PO4)2 ^we find this transition to be of second order for imposed ^strains antiparallel ^to the ferro- elastic strain. In the high pressure regime the transition is clearly first order with ^a positive slope dP/dT ^{of the} phase boundary.

In case of Pb3(PO.2Aso.804)2 ^the phase ^transition

at P ⁼ 0 is second order and so is the _pressure induced transformation between the monoclinic phase ^{and the}

intermediate phase (Fig. 16). The transition between the two monoclinic phases is second order. The critical

point ^{T =} Tc, ^{P = 0} is multicritical with the intersec- tion of a first order and second order phase boundary

for each domain orientation, ^{which means that three}

first order and three second order phase ^boundaries

meet at this point.

The observed phase boundary ^{of the} ferroelastic

phase ^of Pb3(P04)2 is, ^within experimental accuracy, identical with those published ^before by Hodenberg

and Salje [2]. ^At temperatures below 160°C they ^find

the same temperature dependence ^{for the} sponta-

neous strain as for the ferroelastic critical stress.

This indicates that the ferroelastic hysteresis [26]

does not change its form with temperature. ^{This is} apparently ^{not true close to} Tc (P ⁼ 0) ^{= 180.4°C.}

Even very weak uniaxial stress smeares out the phase

transformation whereas the ferroelastic strain at

Fig. 16. - Phase diagram ^of Pb,(P,.,Aso.804)2, ^{b1, b2}

and b3 represent the directions of the three binary ^axes.

P ⁼ 0 follows clearly ^the first order transition. A direct comparison between the order-parameter expo- nent, derived from the measured temperature depen-

dence of the spontaneous strain, ^{and the} empirical exponent of the coercitive stress [2], ^as has been done

by Wood et al. [23], ^{is therefore not too} meaningful

because of the nonlinear relation between the two near Tc.

6. Conclusions.

An understanding ^{of the} phase

transitions both in _pure lead phosphate ^{and in} qua-

ternary ^{oxides needs a} precise knowledge ^{of the struc-}

ture of the intermediate’ phase ab. From the results

presented ^{in this} contribution _{the ab} phase ^{of different} compositions ^differs in the relative importance ^of

relaxation processes. In case of quaternary ^{oxides we} found a static lattice deformation in a given tempera-

ture range just ^above Tc. ^{The «} intermediate phase »

must be considered as a real crystallographic phase

and a second transition point appears between the intermediate and the rhombohedric phase. ^{On the}

other hand, ^for pure lead phosphate the structural deformation of the intermediate phase appears ^{as a}

dynamical phenomenon. ^{It seems} likely ^{that even a}

small amount of impurity (5 ^x 10-3) may block the

dynamical behaviour in lead phosphate ^so that static lattice deformations may appear. The point ab-a ^can

hardly be considered as a phase transition point, ^but

is a crossover between an anharmonic to a harmonic

regime [27]. ^{In this case the «} intermediate phase » ab cannot be considered as a phase ^{in the} crystallographic

sense but as an anharmonic regime of the rhombo- hedral phase ^a.

Acknowledgments.

This work has been supported by the Deutsche Forschungsgemeinschaft (Sa 245/7-1).

Part of the X-ray ^{studies were} performed during ^the

visit of E.S. at the Universite de Paris-Sud. He thanks Professor Lambert for her interest and helpful ^dis-

cussions. E.S. and U.B. are also thankful to Dr.

Devarajan ^for many fruitful discussions.

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