- Email: [email protected]
Two-step freezing process in the mixed crystal RADP
76
Journal of Non-Crystalline Solids 131-133 (1991) 76-79 North-Holland
Two-step freezing process in the mixed crystal RADP H. Grimm lnstitut far Festkb'rperforschung, Forschungszentrum Jiilich GrabH, W-5170 Jiilich, Germany
E. C o u r t e n s IBM Research Division, Ziirich Research Laboratory, CH-8803 Riischlikon, Switzerland
K. Parlinski Institute of Nuclear Physics, 31-342 Cracow, Poland
Two, significantly different, temperatures are found to be related to the freezing process in the mixed crystal Rb0.3s(ND4)0.62D2PO4. This observation - based on neutron, Brillouin, and dielectric methods - indicates a temperature region of enhanced spatial heterogeneity in the relaxational dynamics of the system. A molecular dynamics simulation supports this interpretation.
1. Introduction Mixed crystals with competing order parameters are interesting model systems for studying the mechanism by which the bandwidth of interaction leads to a randomly frozen state. For the system under consideration Rbl_x(NH4)xH2PO4 (RADP) and its deuterated isomorph, the order parameters are associated with those configurations of the bistable hydrogen bonds ( O - H - . . O) which are favoured by the cations Rb ÷ and NH~-. The hydrogen bond configurations couple linearly to polarization and strain. The configurations are incompatible, since Rb ÷ favours a long-wavelength (F-point), ferroelectric configuration, whereas NH~- favours a short-wavelength (Zpoint), antiferroelectric configuration. The corresponding phase transition temperatures are nearly equal. The frustration induced by the mixture of both cations leads to a broad range of concentration (0.22 < x < 0.74) without change of space group [1]. Two properties may characterize this range: (i) the dielectric relaxational behaviour deviates distinctly from an Arrhenius type of description [2] and (ii) incommensurate short-range
order developes for wavevectors q0 = (0.25-0.35) a * on the ~-line which connects the F- and the Z-point [3,4].
2. Experimental procedure This report summarizes neutron- and lightscattering data obtained for a large, optically transparent crystal with c o m p o s i t i o n Rb0.38 (ND4)0.62D2PO4, weight of 1.78 g, and degree of deuteration better than 99% as determined by N M R . Its lattice parameters at ambient temperature, a = (7.441 + 0.001) ,A and c -- (8.560 + 0.001) •A are in agreement with the composition. The dielectric data have been obtained for crystal platelets from the same batch. The susceptibility was measured in the frequency ranges 300 Hz to 3 M H z by dielectric response, 3 to 23 G H z by light scattering, and 2 to 250 G H z by neutron scattering. The broad peak for the incommensurate short-range order is found at q0 = 0.35 a * . The neutron spectra were obtained from a comparison of the scattering at this position with that ob-
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
77
H. Grimm et al. / Two-step freezing process in the mixed crystal RADP I
tained for in the neighourhood of the diffuse peak. Details on the experimental methods have been reported previously for the dielectric measurements [2], the neutron [5,6] and the Brillouin scattering experiments [7,8]. A molecular dynamics simulation has been performed on a simplified two-dimensional model of RADP. Its construction was based on the competition between the ferro- and antiferro-modes. A detailed description of the potential has been reported earlier [9].
I
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i
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z
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~
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,o
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0.5
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./
I~ °
Z r"t
The temperature dependence of the relaxational properties is compared to the evolution of the incommensurate short-range order peaks in fig. 1. Two steps of the freezing process are recognizable, as indicated by the vertical arrows. Figure l(b) shows the temperature dependence of the widths and the peak value of the short-range order peak. Both quantities saturate around Tso = 90 K. The discontinuity of the spatial width or inverse correlation length is certainly not influenced by the much smaller instrumental resolution. However, one would expect a resolution dependence for the peak value because of the varying degree of integration of the spectral response in frequency. Within statistical errors and systematic errors due to subtraction of the incoherent background, we do not observe such a resolution dependence for the three sets of data obtained with different resolution. Therefore, we conclude that the scattering at the elastic setting of the instrument is dominated by a narrow central component. On the other hand, the existence of a slowing down quasi-elastic component at the wavevector q0 had been clearly identified in frequency scans with the 35 G H z resolution [6]. The description in terms of one Lorentzian results in the relaxation times, ~, which are compared with the information about the distribution of relaxation times (peak and width of Gaussian in log(z)) obtained from the dielectric and Brillouin data in fig. l(a). Somewhat larger relaxation times result for the neutron data if allowance is made for a distribution having a width similar to that obtained from the Brillouin data [8]. A rather continuous slowing of relaxation
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8
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100 200 TEHPERATURE (K)
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Fig. 1. (a) Temperature dependence of the spectrum of relaxation times as determined by the indicated methods. A Ganssian in log(z) was assumed for the analysis of the dielectric and Brillouin scattering data. Its full width at half maximum is
indicated by the solid lines. The neutron scattering data result from an analysis of the quasi-elastic scattering at qo by a single Lorentzian. The dot-dashed curve corresponds to the VogelFulcher type description with the parameters obtained previously from the dielectric data [2]. The vertical arrow indicates TvF. (b) Temperature dependence of widths and peak value of the incommensurate short-range order peaks. The widths were measured perpendicular to the Z-line along ( * ) and perpendicular (O) to the tetragonal axis. The peak value was measured with frequency resolutions of 250 GHz (o), 35 GHz (n), and 2 GHz (zx).The vertical arrow indicates Tso.
times over ten decades in time is observed which extrapolates to macroscopic times at Tvv -----30 K.
4. Discussion The observations indicate a large temperature range with coexistence of already 'frozen' regions with still fluctuating regions. Within the limits of space and time for a molecular dynamics study,
H. Grimm et al. / Two-step freezing process in the mixed crystal RADP
78
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[ g:--.""-'o*'g'~*'l"..":. . ; ".,": ..; "..":"..': .. I .. t** "~$.~1 [~-I.~'I'N.,.,.: "..,',,i...',,;g',,.;...';'.;:',;'1;,'1"~1~'11 1. ~.lk~.l....: ....:-...I ~.'I ;..I-.,.*-..': i,¢1~-1;~', ~ ' I ~ ! ! ......~.1;.. : ....: ....I .~.|...T...: ..;: -.."f:..I-.;" _.....:.,,'_| !
l . i" " I '*¢: " "-" " " ; "~'l'&; I " " :" " : ' ~ ' 1 " ~ I ~ " ,"" ": ' " :~~*~! i..~I" ,'I', .'I'* ." ,~', . ' l ' ~ ' l ' & ; |'. ": ". -","~768~'1 ~ ' : ". -" : " , ¢ : ! 1I'*.',"7"I'.." '.." : ". ,'1"~; l "~" :'..' : '. ' l ~ l ' ~ i ' , " ' : : " ; : ; 4 ~ . i-'"*', ; " : " ' : " " : ' ~ ; I "~ I " " ; "~' I ';i'l'&" - " ; ; : "" " ' : ; ' : : l
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[.-.~1"~': "..":",i"I ",~I :&.T~I';¢I ; ,' I :N.'I,, .'~.;~I:(~:l:~:l|
Fig. 2. Map of squared fluctuations (proportional to the seize of symbols) in the hydrogen b o n d network of the two-dimensional R A D P model. The time average corresponds to 104 iteration steps of the molecular dynamics simulation. (a) refers to the pure system (x = 0) close to the ferroelectric phase transition ( T - - 0.97 Tc). (b) refers to the mixed systern(x = 0.62) at T = 1.1 Tso ).
such a spatial heterogeneity is also indicated in the two-dimensional short-range model of the hydrogen bond network of RADP [9]. Characteristic patterns of the mean squared displacements are compared in fig. 2 for the pure system (a) and the frustrated mixture (b). For the pure, translationally invariant case, the spatial heterogeneity reflects the finite time average of the slow critical fluctuations. They move freely and degenerate displacement patterns (domains) merge. This type of pattern is restricted to a narrow region around the phase transition temperature Tc. On cooling the frustrated system, one observes a similar development of critical fluctuations which, however, become increasingly pinned to regions of 'advantageous' cation distributions. Local freezing occurs with much sharper boundaries of the regions of strongly fluctuating particles, as compared with the pure case. The local freezing enhances the effect of the intrinsic random fields due to the cation distribution [10]. In the configurational average, the displacement patterns of these already frozen regions are initially governed by the effective medium, i.e. by its minimum at the wavevector q0 on the Z-line [11]. This influence of the effective medium becomes negligibly small when compared with the random fields at the temperature Tso where the short-range order saturates. Isolated, fluctuating clusters which are pinned to frustrated regions are still visible at temperatures much below Tso [9].
5. Conclusions The rubidium-ammonium mixture in R A D P induces anomalies both in the frequency- and wavevector dependence of the susceptibility. Phenomena, typical for an incommensurate soft mode and for a broad distribution of random fields and interactions, are reflected in TVF = 30 K, Tso = 90 K, and the appearence of a central peak in the spectra at q0 already at ambient temperature. The consideration of both the self- and distinct correlations seems necessary for a modelling of this mixed crystal. The authors thank Professor H. Arend from ETH Ziirich for kindly supplying the crystals and Dr M. Mali from the University of Ziirich for the N M R titration. This study has benefitted from fruitful collaborations with Drs W. Schweika, J. Martinez, and P. Xhonneux.
References
[1] F o r a recent review see: E. Courtens, Ferroelectrics 72 (1987) 229. [2] E. Courtens, Phys. Rev. B33 (1986) 2975. [3] E. Courtens, T.F. R o s e n b a n m , S.E. Nagler and P.M. Horn, Phys. Rev. B29 (1984) 515. [4] R.A. Cowley, T. R y a n and E. Courtens, J. Phys. C18 (1985) 2793. [5] H. G r i m m , K. Parlinski, W. Schweika, E. Courtens a n d H. Arend, Phys. Rev. B33 (1986) 4969.
H. Grimm et al. / Two-step freezing process in the mixed crystal RADP [6] H. Grimm and J. Martinez, Z. Phys. B64 (1986) 13. [7] E. Courtens, R. Vacher and Y. Dagorn, Phys. Rev. B36 (1987) 318. [8] P. Xhonneux, E. Courtens and H. Grimm, Phys. Rev. B38 (1988) 9331. [9] K. Parhnski and H. Grimm, Phys. Rev. B33 (1986) 4868; B37 (1988) 1925.
79
[10] R. Blinc, J. Dolinsek, V.H. Schmidt and D.C. Ailion, Europhys. Lett. 6 (1988) 55. [11] R.A. Cowley, T.W. Ryan and E. Courtens, Z. Phys. B65 (1986) 181.
Journal of Non-Crystalline Solids 131-133 (1991) 76-79 North-Holland
Two-step freezing process in the mixed crystal RADP H. Grimm lnstitut far Festkb'rperforschung, Forschungszentrum Jiilich GrabH, W-5170 Jiilich, Germany
E. C o u r t e n s IBM Research Division, Ziirich Research Laboratory, CH-8803 Riischlikon, Switzerland
K. Parlinski Institute of Nuclear Physics, 31-342 Cracow, Poland
Two, significantly different, temperatures are found to be related to the freezing process in the mixed crystal Rb0.3s(ND4)0.62D2PO4. This observation - based on neutron, Brillouin, and dielectric methods - indicates a temperature region of enhanced spatial heterogeneity in the relaxational dynamics of the system. A molecular dynamics simulation supports this interpretation.
1. Introduction Mixed crystals with competing order parameters are interesting model systems for studying the mechanism by which the bandwidth of interaction leads to a randomly frozen state. For the system under consideration Rbl_x(NH4)xH2PO4 (RADP) and its deuterated isomorph, the order parameters are associated with those configurations of the bistable hydrogen bonds ( O - H - . . O) which are favoured by the cations Rb ÷ and NH~-. The hydrogen bond configurations couple linearly to polarization and strain. The configurations are incompatible, since Rb ÷ favours a long-wavelength (F-point), ferroelectric configuration, whereas NH~- favours a short-wavelength (Zpoint), antiferroelectric configuration. The corresponding phase transition temperatures are nearly equal. The frustration induced by the mixture of both cations leads to a broad range of concentration (0.22 < x < 0.74) without change of space group [1]. Two properties may characterize this range: (i) the dielectric relaxational behaviour deviates distinctly from an Arrhenius type of description [2] and (ii) incommensurate short-range
order developes for wavevectors q0 = (0.25-0.35) a * on the ~-line which connects the F- and the Z-point [3,4].
2. Experimental procedure This report summarizes neutron- and lightscattering data obtained for a large, optically transparent crystal with c o m p o s i t i o n Rb0.38 (ND4)0.62D2PO4, weight of 1.78 g, and degree of deuteration better than 99% as determined by N M R . Its lattice parameters at ambient temperature, a = (7.441 + 0.001) ,A and c -- (8.560 + 0.001) •A are in agreement with the composition. The dielectric data have been obtained for crystal platelets from the same batch. The susceptibility was measured in the frequency ranges 300 Hz to 3 M H z by dielectric response, 3 to 23 G H z by light scattering, and 2 to 250 G H z by neutron scattering. The broad peak for the incommensurate short-range order is found at q0 = 0.35 a * . The neutron spectra were obtained from a comparison of the scattering at this position with that ob-
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
77
H. Grimm et al. / Two-step freezing process in the mixed crystal RADP I
tained for in the neighourhood of the diffuse peak. Details on the experimental methods have been reported previously for the dielectric measurements [2], the neutron [5,6] and the Brillouin scattering experiments [7,8]. A molecular dynamics simulation has been performed on a simplified two-dimensional model of RADP. Its construction was based on the competition between the ferro- and antiferro-modes. A detailed description of the potential has been reported earlier [9].
I
"
i
tu 10-s2E I--
,
1Cl)
dielectric
\I~,\
i
1 0 - ~a "o
1,/3
z
Brit/ouin
t,
~
I
I
i
, ,"
,o
,z
i
~ ......
0.5
010.~
./
I~ °
Z r"t
The temperature dependence of the relaxational properties is compared to the evolution of the incommensurate short-range order peaks in fig. 1. Two steps of the freezing process are recognizable, as indicated by the vertical arrows. Figure l(b) shows the temperature dependence of the widths and the peak value of the short-range order peak. Both quantities saturate around Tso = 90 K. The discontinuity of the spatial width or inverse correlation length is certainly not influenced by the much smaller instrumental resolution. However, one would expect a resolution dependence for the peak value because of the varying degree of integration of the spectral response in frequency. Within statistical errors and systematic errors due to subtraction of the incoherent background, we do not observe such a resolution dependence for the three sets of data obtained with different resolution. Therefore, we conclude that the scattering at the elastic setting of the instrument is dominated by a narrow central component. On the other hand, the existence of a slowing down quasi-elastic component at the wavevector q0 had been clearly identified in frequency scans with the 35 G H z resolution [6]. The description in terms of one Lorentzian results in the relaxation times, ~, which are compared with the information about the distribution of relaxation times (peak and width of Gaussian in log(z)) obtained from the dielectric and Brillouin data in fig. l(a). Somewhat larger relaxation times result for the neutron data if allowance is made for a distribution having a width similar to that obtained from the Brillouin data [8]. A rather continuous slowing of relaxation
I
~< 10 "10 <~
>-
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,
~'-i'"
a
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(b)
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~
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/
I
0
8
o.o
an~
t 0
"005
I
100 200 TEHPERATURE (K)
LI'
no
0
Z
300
Fig. 1. (a) Temperature dependence of the spectrum of relaxation times as determined by the indicated methods. A Ganssian in log(z) was assumed for the analysis of the dielectric and Brillouin scattering data. Its full width at half maximum is
indicated by the solid lines. The neutron scattering data result from an analysis of the quasi-elastic scattering at qo by a single Lorentzian. The dot-dashed curve corresponds to the VogelFulcher type description with the parameters obtained previously from the dielectric data [2]. The vertical arrow indicates TvF. (b) Temperature dependence of widths and peak value of the incommensurate short-range order peaks. The widths were measured perpendicular to the Z-line along ( * ) and perpendicular (O) to the tetragonal axis. The peak value was measured with frequency resolutions of 250 GHz (o), 35 GHz (n), and 2 GHz (zx).The vertical arrow indicates Tso.
times over ten decades in time is observed which extrapolates to macroscopic times at Tvv -----30 K.
4. Discussion The observations indicate a large temperature range with coexistence of already 'frozen' regions with still fluctuating regions. Within the limits of space and time for a molecular dynamics study,
H. Grimm et al. / Two-step freezing process in the mixed crystal RADP
78
•
"
I:: ~01 :?:t:~:¢...:....:..;z::.z.-..s.-..s~i!~s....:::l ':': •
''"
'"'
l-.".'.:: '..:l:~l:--~ . . . . . . . . ".:l'.~I . * ..~o. . . . ::-'3 * * * :'~:~:"::': * * * . .:..:13 ° . ° ..::.. . * ":'-i
II f '.. . ':I ' . . ' I ' , . ' l ' * i ' l ' * .
I * I .. r .* . * - I , , l * * I - , 1 ~ 8 ~ N I [..*'g ' " I ~'1"*;"1"/": ' ; : "*': : " "": '*": " ': *~"( l : ? : l 3 'l[_~.'ll
[ g:--.""-'o*'g'~*'l"..":. . ; ".,": ..; "..":"..': .. I .. t** "~$.~1 [~-I.~'I'N.,.,.: "..,',,i...',,;g',,.;...';'.;:',;'1;,'1"~1~'11 1. ~.lk~.l....: ....:-...I ~.'I ;..I-.,.*-..': i,¢1~-1;~', ~ ' I ~ ! ! ......~.1;.. : ....: ....I .~.|...T...: ..;: -.."f:..I-.;" _.....:.,,'_| !
l . i" " I '*¢: " "-" " " ; "~'l'&; I " " :" " : ' ~ ' 1 " ~ I ~ " ,"" ": ' " :~~*~! i..~I" ,'I', .'I'* ." ,~', . ' l ' ~ ' l ' & ; |'. ": ". -","~768~'1 ~ ' : ". -" : " , ¢ : ! 1I'*.',"7"I'.." '.." : ". ,'1"~; l "~" :'..' : '. ' l ~ l ' ~ i ' , " ' : : " ; : ; 4 ~ . i-'"*', ; " : " ' : " " : ' ~ ; I "~ I " " ; "~' I ';i'l'&" - " ; ; : "" " ' : ; ' : : l
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f."
...-.'.'.
[.-.~1"~': "..":",i"I ",~I :&.T~I';¢I ; ,' I :N.'I,, .'~.;~I:(~:l:~:l|
Fig. 2. Map of squared fluctuations (proportional to the seize of symbols) in the hydrogen b o n d network of the two-dimensional R A D P model. The time average corresponds to 104 iteration steps of the molecular dynamics simulation. (a) refers to the pure system (x = 0) close to the ferroelectric phase transition ( T - - 0.97 Tc). (b) refers to the mixed systern(x = 0.62) at T = 1.1 Tso ).
such a spatial heterogeneity is also indicated in the two-dimensional short-range model of the hydrogen bond network of RADP [9]. Characteristic patterns of the mean squared displacements are compared in fig. 2 for the pure system (a) and the frustrated mixture (b). For the pure, translationally invariant case, the spatial heterogeneity reflects the finite time average of the slow critical fluctuations. They move freely and degenerate displacement patterns (domains) merge. This type of pattern is restricted to a narrow region around the phase transition temperature Tc. On cooling the frustrated system, one observes a similar development of critical fluctuations which, however, become increasingly pinned to regions of 'advantageous' cation distributions. Local freezing occurs with much sharper boundaries of the regions of strongly fluctuating particles, as compared with the pure case. The local freezing enhances the effect of the intrinsic random fields due to the cation distribution [10]. In the configurational average, the displacement patterns of these already frozen regions are initially governed by the effective medium, i.e. by its minimum at the wavevector q0 on the Z-line [11]. This influence of the effective medium becomes negligibly small when compared with the random fields at the temperature Tso where the short-range order saturates. Isolated, fluctuating clusters which are pinned to frustrated regions are still visible at temperatures much below Tso [9].
5. Conclusions The rubidium-ammonium mixture in R A D P induces anomalies both in the frequency- and wavevector dependence of the susceptibility. Phenomena, typical for an incommensurate soft mode and for a broad distribution of random fields and interactions, are reflected in TVF = 30 K, Tso = 90 K, and the appearence of a central peak in the spectra at q0 already at ambient temperature. The consideration of both the self- and distinct correlations seems necessary for a modelling of this mixed crystal. The authors thank Professor H. Arend from ETH Ziirich for kindly supplying the crystals and Dr M. Mali from the University of Ziirich for the N M R titration. This study has benefitted from fruitful collaborations with Drs W. Schweika, J. Martinez, and P. Xhonneux.
References
[1] F o r a recent review see: E. Courtens, Ferroelectrics 72 (1987) 229. [2] E. Courtens, Phys. Rev. B33 (1986) 2975. [3] E. Courtens, T.F. R o s e n b a n m , S.E. Nagler and P.M. Horn, Phys. Rev. B29 (1984) 515. [4] R.A. Cowley, T. R y a n and E. Courtens, J. Phys. C18 (1985) 2793. [5] H. G r i m m , K. Parlinski, W. Schweika, E. Courtens a n d H. Arend, Phys. Rev. B33 (1986) 4969.
H. Grimm et al. / Two-step freezing process in the mixed crystal RADP [6] H. Grimm and J. Martinez, Z. Phys. B64 (1986) 13. [7] E. Courtens, R. Vacher and Y. Dagorn, Phys. Rev. B36 (1987) 318. [8] P. Xhonneux, E. Courtens and H. Grimm, Phys. Rev. B38 (1988) 9331. [9] K. Parhnski and H. Grimm, Phys. Rev. B33 (1986) 4868; B37 (1988) 1925.
79
[10] R. Blinc, J. Dolinsek, V.H. Schmidt and D.C. Ailion, Europhys. Lett. 6 (1988) 55. [11] R.A. Cowley, T.W. Ryan and E. Courtens, Z. Phys. B65 (1986) 181.