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Proton-14N double resonance study of the ferroelectric phase transition in (CH3NH3)HgCl3
0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.
Solid State Communications, Vol. 59, No. 12, pp. 877-879, 1986. Printed in Great Britain.
PROTONJ4N DOUBLE RESONANCE STUDY OF THE FERROELECTRIC PHASE TRANSITION IN (CH3NH3)HgC13 J. Seliger, V. Zagar and R. Blinc J. Stefan Institute, E. Kardelj Univeristy of Ljubljana, Ljubljana, Yugoslavia F. Milia and S. Giannacopoulos Nuclear Research Center "Demokritos", Athens, Greece and R. Kind Laboratory of Solid State Physics, Swiss Federal Institute of Technology, H6nggerberg, CH-8093 Ziirich, Switzerland (Received 5 April 1986 by P. Wachter)
The temperature dependence of the 14N electric quadrupole coupling has been determined in the paraelectric and ferroelectric phase of methylammonium mercury chloride. All CH3NH3 groups are chemically equivalent below To. The results are compatible with a model where the CH3NH3 groups move on the surface of a cone the opening of which increases on approaching T e from below. The ferroelectric transition is connected with a disordering of the CH3NH3 groups which are flipping above T e between two equivalent equilibrium sites separated by 90 ° . METHYLAMMONIUM MERCURY CHLORIDE, (CHaNH3)HgC13, undergoes [1-3] a rather peculiar ferroelectric phase transition at Te = 62°C. Instead of decreasing the point group symmetry increases on going from the paraelectric to the ferroelectric phase. In the high temperature paraelectric phase the space group is monoclinic C2 with a = 13.816A, b = 7.880A, c = 9.734A,/3 = 90.49 ° and six formula units per unit cell, z = 6 [1,3]. In the ferroelectric phase below ire the space group is trigonal, P32 with a = b = 7 . 8 1 7 A , c = 9 . 8 2 6 A , /3=90 °, 3 , = 1 2 0 ° and z = 3 [1,3]. Instead of the conventional C-centered unit cell one can also introduce in the high temperature phase a monoclinic primitive unit cell where the number of formula units, z = 3, is the same as in the ferroelectric phase. This fact as well as the increase in the point group symmetry on cooling through Tc have been recently confirmed by a 3sc1 nuclear quadrupole resonance (NQR) study [4] which showed that the number of chemically nonequivalent chlorine sites decreases from five for T > Te to three for T < Te. In order to throw some additiomal light on the role of the CH3NH3 groups in the phase transition mechanism we decided to study the temperature dependence of the ~4N quadrupole coupling via a proton-nitrogen double resonance experiment. The 14N nucleus has a spin one and thus three allowed NQR transitions in zero magnetic field:
v+_ = (3/4)e2qQ/h (1 -+ r//3),
(1)
Vo = v + - v_ = (1/2)r?'e2 qQ/h.
(2)
Here e z qQ/h is the 14N quadrupole coupling constant and 77 the asymmetry parameter. In a smaU magnetic field the ~4N quadrupole energy levels are Zeeman perturbed and the transition frequencies are: 1 7N
v+~1~ = v ÷ + ~
v
1
2
+_+1 V+
V ]
,3'LH ~ v., (3)
1 7N CJ )
=
v _ + -~
1 v
2
1
+--+--
l)_
V+
,
PLH ~
P-,
(4) v
1 7N
Vo + j
v
o)
k
2
1
1
+ -- - -V+ V
l, Vr.n ~ Vo, (5) /
where VLn is the proton Larmor frequency. The 14N NQR spectra of a powdered sample were measured with the proton-nitrogen level crossing technique [5] in the laboratory frame using a pneumatic post to move the sample from the high field to the cross-over field where the transition frequencies of the proton and nitrogen spin systems are matched [5]. To increase the resolution the double frequency irradiation technique [6] was also
877
878 v~ [kHz]'
FERROELECTRIC PHASE TRANSITION IN (CHaNHa)HgCla
Vol. 59, No. 12
CH3 NH3 Hg CI3 I~N NOR
CH3 NH3 HgCI3
700
500
e2qQ h [kHz] 300
"'°--o...O~o
500 %8 o
100
ooo
o
T[°C]
300
Fig. 1. Temperature dependence of the 14N NQR transition frequencies v+ and v_ in (CHaNHa)HgCla. used. Here the system is irradiated in the cross-over field for half a period with vl and for another half with v2 where vl -- vz = Vo. Resonance occurs when Vl ~ v+ and v2 ~ v_. The temperature dependence of the 1aN NQR transition frequencies v+ and v_ is shown in Fig. 1. For T > T c p÷ = p_ and 77 = 0 whereas for T < T e both the difference between u+ and v_ as well as the absolute value of v+ and v_ increase with decreasing temperature. All CHaNHa groups in the paraelectric and ferroelectric unit cells are thus equivalent from an NQR point of view. This is consistent with the proposed crystal structure below Te but not with the one above Tc, where one nitrogen should be in a special and two in general positions. The reason for this discrepancy is unknown. It is of course possible that the difference in the NQR frequencies o f the two sets of chemically non-equivalent nitrogens above Te is smaller than the NQR linewidth which amounts here to about 30kHz. The jump in the transition frequency at Te and the coexistence of paraand ferro-lines demonstrate the first order nature of the transition. The temperature dependences of the 14N quadrupole coupling constant e 2 qQ/h and of the asymmetry parameter 77 are shown in Fig. 2. e2qQ/h continuously decreases from 6 7 0 k H z at -- 150°C to less than 3 0 0 k H z just below T e ~ 62°C. On heating through Tc e2qQ/h discontinuously drops to ~ 120 kHz and does not change on further heating to ~ 95°C. The asymmetry parameter 7, on the other hand, is temperature independent between - 150 and + 25°C and equ~is r~ = 0.325 in this temperature range. Between + 25 and + 62°C it slowly decreases with increasing temperature and then discontinuously drops to zero on heating through To. The above values of e2qQ/h = 670kHz and ~ = 0.325 at T = -- 150°C can be compared with the values e2qQ/h = 913-+ 5kHz and ~7= 0 . 1 0 9 in methylammonium chloride [7] and e2qQ/h = 880kHz, ~7= 0.20 -+ 0.02 in (CHaNH3) 2 CdC14 [5] at T = - - 104°C.
fI°C] ~ o . ~ o
~o--o-.-~--o--o~
0.3 ~ .,q
~x~%
02 0.1 ~-150
- 100
50
0
50
100 T[*C]
Fig. 2. Temperature dependence of the 14N electric quadrupole coupling constant, e2qQ/h, and asymmetry parameter 77 in (CHaNHa)HgC13. The fact that e2qQ/h at - 150°C in (CHaNHa)HgCla is significantly lower than in methyl-ammonium chloride or (CHaNHa)2CdC14 demonstrates that a significant amount of molecular motion and disorder is still present in (CHaNHa)HgCla even at rather low temperatures. Let us now try to understand the fact that far below Te e2 qQ/h is strongly temperature dependent while r/is constant as well as the changes in the 14N quadrupole coupling at T c. In an isolated methyl-ammonium group the charge distribution will have trigonal symmetry (Car) about the C - N bond. The largest principal axis of the electric field gradient (EFG) tensor at the 14N site will be parallel to the C - N bond and the asymmetry parameter will'be zero. The formation of H-bonds of different lengths to the Cl-atoms will destroy the trigonal symmetry and induce a small, but non-zero value of 7?. Let us for the moment neglect this effect and assume that the C - N bond moves with a high enough rate on the surface of a cone with an opening angle t9 around the z-axis among different equilibrium sites with occupation probabilities l+'i. The EFG tensor in the crystal f~lxed x, y, z frame will be now the average of the EFG tensors at the various equilbrium sites Vi:
Vol. 59, No. 12
FERROELECTRIC PHASE TRANSITION IN (CHaNH3)HgCla
¢i
(1"3 = ~ WfV~.
(6)
i=l
The largest principal value (Vzz) in the crystal fixed x, y, z frame will be given by
( g z z ) = Vo(3/2 cos20-- 1/2),
(7)
whereas the other components (V~)-- and r/ - will depend on the various Wi. For Wt = W2 = . . . Wrt in particular, the largest principal axas will point along the rotation axis (z) and (V~x) = ( V ~ > = --
(V,A/2,
(8)
so that z/= 0 independently of O. There are several other specific cases where ~ is non-zero and depends only on the differences of the various Wi -- Wi and not on O. The temperature dependence of eZqQ/h and simultaneous temperature independence of 7/well below T c can be thus very well explained by a model where the C - N groups move the surface of a cone and the opening angle continuously increases with increasing temperatures until it reaches about 35 ° = 0/2 just below Te. The drastic change in the X4N quadrupolar coupling tensor on heating through Te requires the onset of a new type of motion in the paraelectric phase. One possibility which is compatible with the taN data is the onset of flipping of the rotation axis of the "cone" between two equilibrium sites separated by 90 ° . If we choose the flipping axis to be pointed along the x-axis in the crystal FLxed frame we fred for the time averaged value of the EFG tensor with the help of equation (8) (Vxx) = (Vxx),
(9a)
( Vr~) = c l ( V~,y) + c 2( Vzz) ,
(9b)
(Vzz) = cI(Vz,) + c2(Vy~),
(9c)
where ct + c2 = 1. For T > Te we then have ct = c2 = 1/2 so that
(Vxx) = -- (Vzz------)-), 2 (Vzz) 4 '
The largest principal axis of the EFG tensor is now parallel to the flipping (x) axis and perpendicular to the cone rotation axis (z). It should be noticed that this mechanism will yield r~ = 0 for T > Te even though Wi :/: W1 and expression (8) does not hold. If the flipping persists in the ferroelectric phase where cx :~ c2 it will induce a non-zero value of 77 even though Wi = W/= . . . Wn. Close to Te when cl ~ 1/2, c2 ~ 1/2, the largest principal axis of the EFG tensor will be along the flipping (x) axis and n = (cx -- c~ ) [((Z,,) -- ( Z~))/(Vxx)].
n ~
(10c)
resulting in rt = 0 and a drop in e 2 qQ/h for a factor of 1/2.
(v~) + c2()/
for (Vxx) q=(V~v). Whereas for the case of equation (11), r/increases with decreasing temperature it will be temperature independent at lower temperatures and determined by the Wi 4= W/in the case equation (12). The above model thus seems to explain the experimental data for the taN e 2qQ/h and r/in a satisfactory way.
REFERENCES 1. 2. 3.
4. 5.
4 '
[(vx~>-
[(Vxx)-- (V,.,~)]/(Vzz),
and
(11)
The asymmetry parameter here directly measures the difference in the occupation probabilities for the two sites between which the CH~NH3 group is flipping, i.e. it measures the order parameter of the ferroelectric transition. At lower temperatures where ct ~ 1, c2 ~ 0 with decreasing temperature, the largest principal axis will be the z-axis around which the C - N bond is moving on the surface of a cone. In this case we have
(lOa) (lOb)
879
6. 7.
A. Ben Salah, J.W. Bats, R. Kalus, H. Fuess & A. Daoud, Z. Anorg. Allg. Chemic 493, 177 (1982). F. Milia, Solid State Commun. 51,625 (1984). H. Fuess, M. Korfer, H. Arend & R. Kind, Solid State Commun. 56, 137 (1985); A. Ben Salah, A. Daoud, J.L. Miane & J. Ravez, Rev. Chim. Min. 21, 14 (1984). F. Milia & M. Voudouris, Phys. Lett. A (to be published). J. Seliger, R. Blinc, H. Arend & R. Kind, Z. ehysik B25,189 (1976). J. Seliger, unpublished work from this laboratory. D.T. Edmonds, M.J. Hunt & A.L. Mackay, J. Mag. Res. 9, 66 (1973).
Solid State Communications, Vol. 59, No. 12, pp. 877-879, 1986. Printed in Great Britain.
PROTONJ4N DOUBLE RESONANCE STUDY OF THE FERROELECTRIC PHASE TRANSITION IN (CH3NH3)HgC13 J. Seliger, V. Zagar and R. Blinc J. Stefan Institute, E. Kardelj Univeristy of Ljubljana, Ljubljana, Yugoslavia F. Milia and S. Giannacopoulos Nuclear Research Center "Demokritos", Athens, Greece and R. Kind Laboratory of Solid State Physics, Swiss Federal Institute of Technology, H6nggerberg, CH-8093 Ziirich, Switzerland (Received 5 April 1986 by P. Wachter)
The temperature dependence of the 14N electric quadrupole coupling has been determined in the paraelectric and ferroelectric phase of methylammonium mercury chloride. All CH3NH3 groups are chemically equivalent below To. The results are compatible with a model where the CH3NH3 groups move on the surface of a cone the opening of which increases on approaching T e from below. The ferroelectric transition is connected with a disordering of the CH3NH3 groups which are flipping above T e between two equivalent equilibrium sites separated by 90 ° . METHYLAMMONIUM MERCURY CHLORIDE, (CHaNH3)HgC13, undergoes [1-3] a rather peculiar ferroelectric phase transition at Te = 62°C. Instead of decreasing the point group symmetry increases on going from the paraelectric to the ferroelectric phase. In the high temperature paraelectric phase the space group is monoclinic C2 with a = 13.816A, b = 7.880A, c = 9.734A,/3 = 90.49 ° and six formula units per unit cell, z = 6 [1,3]. In the ferroelectric phase below ire the space group is trigonal, P32 with a = b = 7 . 8 1 7 A , c = 9 . 8 2 6 A , /3=90 °, 3 , = 1 2 0 ° and z = 3 [1,3]. Instead of the conventional C-centered unit cell one can also introduce in the high temperature phase a monoclinic primitive unit cell where the number of formula units, z = 3, is the same as in the ferroelectric phase. This fact as well as the increase in the point group symmetry on cooling through Tc have been recently confirmed by a 3sc1 nuclear quadrupole resonance (NQR) study [4] which showed that the number of chemically nonequivalent chlorine sites decreases from five for T > Te to three for T < Te. In order to throw some additiomal light on the role of the CH3NH3 groups in the phase transition mechanism we decided to study the temperature dependence of the ~4N quadrupole coupling via a proton-nitrogen double resonance experiment. The 14N nucleus has a spin one and thus three allowed NQR transitions in zero magnetic field:
v+_ = (3/4)e2qQ/h (1 -+ r//3),
(1)
Vo = v + - v_ = (1/2)r?'e2 qQ/h.
(2)
Here e z qQ/h is the 14N quadrupole coupling constant and 77 the asymmetry parameter. In a smaU magnetic field the ~4N quadrupole energy levels are Zeeman perturbed and the transition frequencies are: 1 7N
v+~1~ = v ÷ + ~
v
1
2
+_+1 V+
V ]
,3'LH ~ v., (3)
1 7N CJ )
=
v _ + -~
1 v
2
1
+--+--
l)_
V+
,
PLH ~
P-,
(4) v
1 7N
Vo + j
v
o)
k
2
1
1
+ -- - -V+ V
l, Vr.n ~ Vo, (5) /
where VLn is the proton Larmor frequency. The 14N NQR spectra of a powdered sample were measured with the proton-nitrogen level crossing technique [5] in the laboratory frame using a pneumatic post to move the sample from the high field to the cross-over field where the transition frequencies of the proton and nitrogen spin systems are matched [5]. To increase the resolution the double frequency irradiation technique [6] was also
877
878 v~ [kHz]'
FERROELECTRIC PHASE TRANSITION IN (CHaNHa)HgCla
Vol. 59, No. 12
CH3 NH3 Hg CI3 I~N NOR
CH3 NH3 HgCI3
700
500
e2qQ h [kHz] 300
"'°--o...O~o
500 %8 o
100
ooo
o
T[°C]
300
Fig. 1. Temperature dependence of the 14N NQR transition frequencies v+ and v_ in (CHaNHa)HgCla. used. Here the system is irradiated in the cross-over field for half a period with vl and for another half with v2 where vl -- vz = Vo. Resonance occurs when Vl ~ v+ and v2 ~ v_. The temperature dependence of the 1aN NQR transition frequencies v+ and v_ is shown in Fig. 1. For T > T c p÷ = p_ and 77 = 0 whereas for T < T e both the difference between u+ and v_ as well as the absolute value of v+ and v_ increase with decreasing temperature. All CHaNHa groups in the paraelectric and ferroelectric unit cells are thus equivalent from an NQR point of view. This is consistent with the proposed crystal structure below Te but not with the one above Tc, where one nitrogen should be in a special and two in general positions. The reason for this discrepancy is unknown. It is of course possible that the difference in the NQR frequencies o f the two sets of chemically non-equivalent nitrogens above Te is smaller than the NQR linewidth which amounts here to about 30kHz. The jump in the transition frequency at Te and the coexistence of paraand ferro-lines demonstrate the first order nature of the transition. The temperature dependences of the 14N quadrupole coupling constant e 2 qQ/h and of the asymmetry parameter 77 are shown in Fig. 2. e2qQ/h continuously decreases from 6 7 0 k H z at -- 150°C to less than 3 0 0 k H z just below T e ~ 62°C. On heating through Tc e2qQ/h discontinuously drops to ~ 120 kHz and does not change on further heating to ~ 95°C. The asymmetry parameter 7, on the other hand, is temperature independent between - 150 and + 25°C and equ~is r~ = 0.325 in this temperature range. Between + 25 and + 62°C it slowly decreases with increasing temperature and then discontinuously drops to zero on heating through To. The above values of e2qQ/h = 670kHz and ~ = 0.325 at T = -- 150°C can be compared with the values e2qQ/h = 913-+ 5kHz and ~7= 0 . 1 0 9 in methylammonium chloride [7] and e2qQ/h = 880kHz, ~7= 0.20 -+ 0.02 in (CHaNH3) 2 CdC14 [5] at T = - - 104°C.
fI°C] ~ o . ~ o
~o--o-.-~--o--o~
0.3 ~ .,q
~x~%
02 0.1 ~-150
- 100
50
0
50
100 T[*C]
Fig. 2. Temperature dependence of the 14N electric quadrupole coupling constant, e2qQ/h, and asymmetry parameter 77 in (CHaNHa)HgC13. The fact that e2qQ/h at - 150°C in (CHaNHa)HgCla is significantly lower than in methyl-ammonium chloride or (CHaNHa)2CdC14 demonstrates that a significant amount of molecular motion and disorder is still present in (CHaNHa)HgCla even at rather low temperatures. Let us now try to understand the fact that far below Te e2 qQ/h is strongly temperature dependent while r/is constant as well as the changes in the 14N quadrupole coupling at T c. In an isolated methyl-ammonium group the charge distribution will have trigonal symmetry (Car) about the C - N bond. The largest principal axis of the electric field gradient (EFG) tensor at the 14N site will be parallel to the C - N bond and the asymmetry parameter will'be zero. The formation of H-bonds of different lengths to the Cl-atoms will destroy the trigonal symmetry and induce a small, but non-zero value of 7?. Let us for the moment neglect this effect and assume that the C - N bond moves with a high enough rate on the surface of a cone with an opening angle t9 around the z-axis among different equilibrium sites with occupation probabilities l+'i. The EFG tensor in the crystal f~lxed x, y, z frame will be now the average of the EFG tensors at the various equilbrium sites Vi:
Vol. 59, No. 12
FERROELECTRIC PHASE TRANSITION IN (CHaNH3)HgCla
¢i
(1"3 = ~ WfV~.
(6)
i=l
The largest principal value (Vzz) in the crystal fixed x, y, z frame will be given by
( g z z ) = Vo(3/2 cos20-- 1/2),
(7)
whereas the other components (V~)-- and r/ - will depend on the various Wi. For Wt = W2 = . . . Wrt in particular, the largest principal axas will point along the rotation axis (z) and (V~x) = ( V ~ > = --
(V,A/2,
(8)
so that z/= 0 independently of O. There are several other specific cases where ~ is non-zero and depends only on the differences of the various Wi -- Wi and not on O. The temperature dependence of eZqQ/h and simultaneous temperature independence of 7/well below T c can be thus very well explained by a model where the C - N groups move the surface of a cone and the opening angle continuously increases with increasing temperatures until it reaches about 35 ° = 0/2 just below Te. The drastic change in the X4N quadrupolar coupling tensor on heating through Te requires the onset of a new type of motion in the paraelectric phase. One possibility which is compatible with the taN data is the onset of flipping of the rotation axis of the "cone" between two equilibrium sites separated by 90 ° . If we choose the flipping axis to be pointed along the x-axis in the crystal FLxed frame we fred for the time averaged value of the EFG tensor with the help of equation (8) (Vxx) = (Vxx),
(9a)
( Vr~) = c l ( V~,y) + c 2( Vzz) ,
(9b)
(Vzz) = cI(Vz,) + c2(Vy~),
(9c)
where ct + c2 = 1. For T > Te we then have ct = c2 = 1/2 so that
(Vxx) = -- (Vzz------)-), 2 (Vzz) 4 '
The largest principal axis of the EFG tensor is now parallel to the flipping (x) axis and perpendicular to the cone rotation axis (z). It should be noticed that this mechanism will yield r~ = 0 for T > Te even though Wi :/: W1 and expression (8) does not hold. If the flipping persists in the ferroelectric phase where cx :~ c2 it will induce a non-zero value of 77 even though Wi = W/= . . . Wn. Close to Te when cl ~ 1/2, c2 ~ 1/2, the largest principal axis of the EFG tensor will be along the flipping (x) axis and n = (cx -- c~ ) [((Z,,) -- ( Z~))/(Vxx)].
n ~
(10c)
resulting in rt = 0 and a drop in e 2 qQ/h for a factor of 1/2.
(v~) + c2(
for (Vxx) q=(V~v). Whereas for the case of equation (11), r/increases with decreasing temperature it will be temperature independent at lower temperatures and determined by the Wi 4= W/in the case equation (12). The above model thus seems to explain the experimental data for the taN e 2qQ/h and r/in a satisfactory way.
REFERENCES 1. 2. 3.
4. 5.
4 '
[(vx~>-
[(Vxx)-- (V,.,~)]/(Vzz),
and
(11)
The asymmetry parameter here directly measures the difference in the occupation probabilities for the two sites between which the CH~NH3 group is flipping, i.e. it measures the order parameter of the ferroelectric transition. At lower temperatures where ct ~ 1, c2 ~ 0 with decreasing temperature, the largest principal axis will be the z-axis around which the C - N bond is moving on the surface of a cone. In this case we have
(lOa) (lOb)
879
6. 7.
A. Ben Salah, J.W. Bats, R. Kalus, H. Fuess & A. Daoud, Z. Anorg. Allg. Chemic 493, 177 (1982). F. Milia, Solid State Commun. 51,625 (1984). H. Fuess, M. Korfer, H. Arend & R. Kind, Solid State Commun. 56, 137 (1985); A. Ben Salah, A. Daoud, J.L. Miane & J. Ravez, Rev. Chim. Min. 21, 14 (1984). F. Milia & M. Voudouris, Phys. Lett. A (to be published). J. Seliger, R. Blinc, H. Arend & R. Kind, Z. ehysik B25,189 (1976). J. Seliger, unpublished work from this laboratory. D.T. Edmonds, M.J. Hunt & A.L. Mackay, J. Mag. Res. 9, 66 (1973).