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17O quadrupole resonance study of the ferroelectric phase transition in KH2PO4
Volume 47A, number 2
PHYSICS LETTERS
11 March 1974
170 QUADRUPOLE RESONANCE STUDY OF THE FERROELECTRIC PHASE TRANSITION IN KH2PO4 R. BLINC, J. SELIGER, R. OSREDKAR and M. MALI Institute f. Stefan”, University of Ljublfana, Llubijana, Yugoslavia Received 10 January 1974 The temperature dependence of the 1 ~O NQR spectra in KH2 PD4 has been measured using a proton — double resonance technique in the laboratory frame. The spectra are consistent with a model where the protons rapidly move above T5 between the two equilibrium sites in the O-H--0 bonds, whereas the motion freezes in below T~.
In a continuation of our NMR and NQR studies [e.g. 1] of phase transitions in KH2PO4 type ferroelectric crystals, we have investigated the temperature dependence of the 170 (I = ~)quadrupole coupling in KH2P04. The sample was 10% 170 enriched. The 170 NQR spectra were measured via proton 170 double resonance in the laboratory frame as described previously [2]. The results are shown in fig. 1. The 170 NQR spectra consist in the paraelectric phase of three lines the positions of which do not depend on temperature. At the ferroelectric transition temperature Tc there is an abrupt change in the 170 spectrum. In the ferroelectric phase we have six 17~ lines the positions of i.vhich are again nearly temperature independent. Above Tc all 170 sites in the unit cell are chemically equivalent. The =170 quadrupole coupling 2qQ/h 5.16MHz and the constant equals to e is i~= 0.55. Below Tc we have asymmetry parameter — as described previously [2] —~ two chemically non-
2qQ/h) equivalent 170 sites: (e 1 = 5.96 MHz, ~i = 0.72 2qQ/h) and (e 2 = 4.85 MHz, ~2 = 0.18. The temperature dependence of the I ~0 spectra can be described by the following model: The electric field gradient (EFG) tensor at an 170 site in KH2PO4 is determined by the position of the proton in the PU hydrogen bond linking the 170 site to neighbouring 4 tetrahedra. The hydrogen 70-H--0bond and potential hassotwo ‘ found either thatequilibrium the protonsites, can be in a “far” or in a “close” position. Above T~the proton moves between these two sites. With the help of the normalized 0-H- -0 bond
17
0 NUR IN KOP
vlkhz] 3000
Jo
0_O_0
0
2000
-
0—0—0
_______
1
_________
1000 o—°~ I
I
50
I
100
T
150
I
200 TEK]
Fig. 1. Temperature dependence of the 170 NQR spectra in KH 2PO4.
dipole moment p~(~), we can express the time dependence of the 170 EFG tensor T~(t)as: 1
1
T~(t)= ~ [1 +p~(t)1T(l)+T[l —p~(t)]T(2)
(2)
where T(1) is the EFG tensor for the 170170-H--0 site to which the proton is directly attached whereastheT(2) is theis EFG tensor for bonded, the 170 site to which proton only hydrogen ‘70---H-0. For
=
1, T
1 = T(1), whereas T1 = T(2) form = 1. Since the frequency of the proton motion is much larger than the difference in the quadrupole splitting 131
Volume 47A, number 2
PHYSICS LETTERS
between sites I and 2. the 170 nucleus sees only an effective, tinie averaged field gradient. Since the proton spends for T> T~an equal amount of time in each of these two equilibrium sites. (p(t)~= 0 in the paraelectric phase and (T1(t)) is temperature independent: T> T : KT) = T = ~- [T(l)+T(2fl . (2) c
o
Below T0. on the other hand, (p(t)) is different from zero and equals to the normalized spontaneous polarization p. We find T< Tc :
KT)
=
T 0 +A ~
II March 1974
It should be noted that ifp = I, (T) = T(l) whereas = T(2) for those 17~ sites where p = - 1. The above results thus confirm the existence of a double minimum type 0-H--U potential in KH 2PO4. They further show that the 170 EFG tensor is nearly completely determined by the motion of its closest proton and does not depend on the arrangement of all four protons surrounding a PU4 group as the As EFG tensor [31in KH7AsO4. (T)
(3)
References
(4)
lii R. Blinc, J. Stepitnik, M. Jamlek-Vilfan and S. ~umer,
where
A
=
~ [T(l )--
T(2)] .
The temperature dependence of the l7~ EFG tensor on throughpolarization Tc should beasthus toobserved. that of the going spontaneous it is equal indeed
132
[2] [3]
J. Chem. Phys. 54 (1971) 187. R. Blinc, J. Seliger, R. Osredkar 7umer, and T. Prelesnik, Chem. J. Chem. Phys. Phys. Lett. to be published. R. Blinc, M. Mali, J. Pin and S. 58 (1973) 2262.
PHYSICS LETTERS
11 March 1974
170 QUADRUPOLE RESONANCE STUDY OF THE FERROELECTRIC PHASE TRANSITION IN KH2PO4 R. BLINC, J. SELIGER, R. OSREDKAR and M. MALI Institute f. Stefan”, University of Ljublfana, Llubijana, Yugoslavia Received 10 January 1974 The temperature dependence of the 1 ~O NQR spectra in KH2 PD4 has been measured using a proton — double resonance technique in the laboratory frame. The spectra are consistent with a model where the protons rapidly move above T5 between the two equilibrium sites in the O-H--0 bonds, whereas the motion freezes in below T~.
In a continuation of our NMR and NQR studies [e.g. 1] of phase transitions in KH2PO4 type ferroelectric crystals, we have investigated the temperature dependence of the 170 (I = ~)quadrupole coupling in KH2P04. The sample was 10% 170 enriched. The 170 NQR spectra were measured via proton 170 double resonance in the laboratory frame as described previously [2]. The results are shown in fig. 1. The 170 NQR spectra consist in the paraelectric phase of three lines the positions of which do not depend on temperature. At the ferroelectric transition temperature Tc there is an abrupt change in the 170 spectrum. In the ferroelectric phase we have six 17~ lines the positions of i.vhich are again nearly temperature independent. Above Tc all 170 sites in the unit cell are chemically equivalent. The =170 quadrupole coupling 2qQ/h 5.16MHz and the constant equals to e is i~= 0.55. Below Tc we have asymmetry parameter — as described previously [2] —~ two chemically non-
2qQ/h) equivalent 170 sites: (e 1 = 5.96 MHz, ~i = 0.72 2qQ/h) and (e 2 = 4.85 MHz, ~2 = 0.18. The temperature dependence of the I ~0 spectra can be described by the following model: The electric field gradient (EFG) tensor at an 170 site in KH2PO4 is determined by the position of the proton in the PU hydrogen bond linking the 170 site to neighbouring 4 tetrahedra. The hydrogen 70-H--0bond and potential hassotwo ‘ found either thatequilibrium the protonsites, can be in a “far” or in a “close” position. Above T~the proton moves between these two sites. With the help of the normalized 0-H- -0 bond
17
0 NUR IN KOP
vlkhz] 3000
Jo
0_O_0
0
2000
-
0—0—0
_______
1
_________
1000 o—°~ I
I
50
I
100
T
150
I
200 TEK]
Fig. 1. Temperature dependence of the 170 NQR spectra in KH 2PO4.
dipole moment p~(~), we can express the time dependence of the 170 EFG tensor T~(t)as: 1
1
T~(t)= ~ [1 +p~(t)1T(l)+T[l —p~(t)]T(2)
(2)
where T(1) is the EFG tensor for the 170170-H--0 site to which the proton is directly attached whereastheT(2) is theis EFG tensor for bonded, the 170 site to which proton only hydrogen ‘70---H-0. For
=
1, T
1 = T(1), whereas T1 = T(2) form = 1. Since the frequency of the proton motion is much larger than the difference in the quadrupole splitting 131
Volume 47A, number 2
PHYSICS LETTERS
between sites I and 2. the 170 nucleus sees only an effective, tinie averaged field gradient. Since the proton spends for T> T~an equal amount of time in each of these two equilibrium sites. (p(t)~= 0 in the paraelectric phase and (T1(t)) is temperature independent: T> T : KT) = T = ~- [T(l)+T(2fl . (2) c
o
Below T0. on the other hand, (p(t)) is different from zero and equals to the normalized spontaneous polarization p. We find T< Tc :
KT)
=
T 0 +A ~
II March 1974
It should be noted that ifp = I, (T) = T(l) whereas = T(2) for those 17~ sites where p = - 1. The above results thus confirm the existence of a double minimum type 0-H--U potential in KH 2PO4. They further show that the 170 EFG tensor is nearly completely determined by the motion of its closest proton and does not depend on the arrangement of all four protons surrounding a PU4 group as the As EFG tensor [31in KH7AsO4. (T)
(3)
References
(4)
lii R. Blinc, J. Stepitnik, M. Jamlek-Vilfan and S. ~umer,
where
A
=
~ [T(l )--
T(2)] .
The temperature dependence of the l7~ EFG tensor on throughpolarization Tc should beasthus toobserved. that of the going spontaneous it is equal indeed
132
[2] [3]
J. Chem. Phys. 54 (1971) 187. R. Blinc, J. Seliger, R. Osredkar 7umer, and T. Prelesnik, Chem. J. Chem. Phys. Phys. Lett. to be published. R. Blinc, M. Mali, J. Pin and S. 58 (1973) 2262.