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Symmetric hydrogen bonds in ice X
Volume 101A, number 3
PHYSICS LETTERS
19 March 1984
SYMMETRIC HYDROGEN BONDS IN ICE X K.R. HIRSCH and W.B. HOLZAPFEL Physik, Universitiit-GH-Paderborn,Postfach 16 21, D-4790 Paderborn, Fed. Rep. Germany Received 8 November 1983
Raman measurements on Ice VIII under pressures up to 50 GPa reveal strong line shifts, changes in isotope frequency ratio, intensity decreases, and the appearance of one new line around 38 GPa. These observations are consistent with the formation of symmetric hydrogen bonds and a new phase, Ice X, with euprit structure.
Due to the asymmetry of the hydrogen bonds in all the phases of ice that were known up to now [ 1] a rich variety of order-disorder transitions has been observed for ice under pressure. The ordered low temperature phase Ice VIII and the disordered high temperature phase Ice VII were considered to be the "ultimate" high pressure phases of ice [2]. Only an "average" structure with space group O4(Pn3m) with two oxygens on the 2a sites and the four protons disordered with equal probability over the 8e sites can be assigned to Ice VII [2]. The ordering of the protons in Ice VIII results in a slight tetragonal distortion of this structure and leads to the space group D19(I41/ amd) with oxygen on 8e and protons on 16h sites [2]. Earlier X-ray studies and theoretical considerations for Ice VII and VIII under pressure lead to the conclusion that the hydrogen bonds may become symmetric in these phases somewhere between 35 and 80 GPa [3]. An analysis of the related structural changes reveals that both structures should transform into a new ordered structure, Ice X, with space group O4(Pn3m), with the two oxygens on the 2a sites, and with the four hydrogens on the 4b sites. This structure is well known also as the cuprit structure, which is observed in Cu20, Ag20 and Pb20 at normal pressure [4]. A detailed analysis of the Raman and infrared activities for both Ice VIII and this Ice X reveals [5] that all the Raman active modes of Ice VIII should disappear at the VIII ~ X phase transition and only 142
one new lattice mode should become Raman active in Ice X. This VTT2g mode corresponds to a motion of the oxygen lattice only, totaly decoupled from the proton motions at the P point, and therefore, no isotope effect is expected for this mode in D20 with respect to H20-Ice X. Raman data for H20 and D20 under pressures up to 50 GPa at a temperature of 100 K show [5] (A) a strong decrease in the stretching frequencies o 1 Alg , v 1BIg and o3Eg in Ice VIII (fig. 1), (B)a strong decrease in the intensities of all the Raman-active stretching modes from ten times the intensity of the VT(Blg + Eg) lattice modes at 3 GPa to below their intensity at 30 GPA, (C) the disappearance of these last lattice modes of Ice VIII around 50 GPa and the appearance of a new lattice made around 38 GPa, and (D) an isotope frequency ratio of 1.05 for these lattice modes in Ice VIII and of 1.0 for the new lattice mode attributed to Ice X. Since the pressure is not hydrostatic in these experiments, the local pressure may deviate by +10% from the average pressure measured by a ruby manometer. Therefore, the presence of Raman lines for both Ice VIII and the new phase lee X in a finite range of the nominal pressure (fig. 1) could result just from inhomogeneous stresses. Finally, (E) it can be noticed, that the decrease in the mode frequencies by 26% from the VT(BI~ + Eg) modes of Ice VIII to the OTT2g modes o~ Ice X (fig. 1) corresponds at least qualitatively to what one expects from the dispersion of the phonon branches in Ice I [6], which indicates that these Raman active OT(Blg + Eg) modes of Ice 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 101A, number 3
PHYSICS LETTERS =
2500 -
.
!
|
|
v
Vl Big
6~_
X~x---X_ x _ "X"--X ~x~x.__ "~ ~X"x"X~X X
ZOOO" r~
!
19 March 1984
~"-"---"
x~
-~.~.~.,~
1500'
-xx-x-_._~xV3 Eg ~---~-~--. Vl Alg
D20 of 100 K
N ¢-
VR2 B2g
<3
~,~ttc=~_Tr~. . . . . . ,
"r
..... V-----TB,g + VT Eg ...
10
:__?R
E g VT T2g
,
20
30
Pressure (GPo) Fig'. 1. Variation of Raman-active mode frequencies of D2 O-Ice VIII (crosses) and Ice X (circles) under pressure.
VIII correspond to zone boundary modes of this OTT2g branch of Ice X as a result of the increase in the unit cell at the transition from Ice X to Ice VIII. The pressure dependence of the IR-active modes of Ice VII was determined up to 12 GPa also just recently [7]. A linear extrapolation of the VRE13u- and the o2Alu-mode frequencies with pressure suggests that these modes become degenerate in both H20 and D20 Ices at around 22 GPa as required in the transition to the high symmetry phase Ice X. However, there is no reason to trust in such a linear extrapolation to twice the pressure of the experimental data. Furthermore, the Ice V I I - X transition may occur at room temperature also at some lower pressure than the Ice V I I I - X transition at 100 K, and nothing is known yet about the triple point between the phases V I I VIII-X. A model for the hydrogen bonds in Ice VIII can be based on one a priori symmetric double well potential [3] for the correlated motions of all the protons in any of the stretching modes (o I Alg , o 1 Blg and u3Eg ) at the F point if one takes the slight differences between these mode frequencies into account by additional small proton-proton coupling parameters. In a first approximation, each side of this symmetric double well potential can be represented by an effective Morse potential Z(x) = A(eZ~x
_ 2e~x) ,
where A represents the barriere height between the two wells. This very crude approximation has the essential advantage that it gives closed quantum mechanical solutions [8] for the energy levels
En
= -A
[1 - (hoo/A)(n + -~)] ,
with the "harmonic" frequency
%
=
(~121r)V'-'~lm.
For the first Raman frequency, one obtaines u 1 = o0(1 - hoo/2A), where A is considered now to depend on the oxygen-oxygen distance d. For o0, one can take the "harmonic" value from the free water molecule since the experimentally observed value for the isotope ratio of the pressure dependences [2]
dvi(H20)/dP dui(D20)/dP
=
1.8
ensures that u0 depends only very weakly on d. In fact, the value of 2 for this ratio would require a constant value of u0 within this model. If one assumes a decrease of A(d) which corresponds to a Landau-type expansion of the free energy [9], one finds a variation of the type A ( d ) = A**(d - de)/(d - do) whereA** = 9.6 X 10-19 Nm represents the value of A for the OlAlg mode of the free molecule [10]. d e and d o are free parameters which are determined by a fit to the experimental data, fig. 2. The best fit for the o 1 Alg mode gives a critical oxy143
Volume 101A, number 3 o
!
PHYSICS LETTERS t
|
i
i
2500!
"'~°'eo-o.~... °o..~ V3Eg -%b. " ~ Vl A1g °~'oo ~
2250 E
0
2000 E > 1750
.£3 D
1500
219
I
28
t
27
216
O-0 Bindingdistonce{A)
215
Fig. 2. Variation of stretching frequencies of D2 O-Ice VIII with respect to the bond length. The continuous lines represent two-parameter fits to the experimental data. gen--oxygen distance d e = 2.32 A where A ( d c ) = 0, whereas the best fit for the o3Eg mode corresponds to the slightly smaller value o f 2.26 A with d o = 0.35 A in b o t h cases. We are aware o f the fact, that this model must be regarded as a crude approximation, however, it represents reasonably the steep decrease in the barrier for the proton in the hydrogen bonds o f Ice VIII as the bondlength d approaches a critical value o f d e ~- 2.3 A. The deviations o f the fitted curves in fig. 2 from the experimental data at low pressures (d > 2.9 A) are attributed to b o n d bending [5] which appears to be significant only in the low pressure region and has been neglected also in the present considerations.
144
19 March 1984
It can be noticed, further more, that a stiffening in the equation o f state of Ice VII and VIII at d e had been predicted theoretically [3] and this stiffening has been observed in fact in recent Brillouin scattering experiments [11] on Ice VII at a pressure o f about 42 GPa which corresponds to a d e ~ 2.5 A in reasonable agreement with the present results. Finally, one should be aware o f the possibility that gradual disorder o f the protons in Ice X could cause at elevated temperatures a strong protonic conduction prior to melting and possibly could lead also to one more cubic phase of Ice with complete proton disorder and the "average" space group O2h(Pn3n).
References [ 1 ] B. Kamb, Crystallography of ice, in: Physics and chemistry of ice, eds. E. Whalley, S.I. Jones and L.W. Gold (Royal Soc. of Canada, Ottawa, 1973). [2] B. Kamb and B.L. Davis, Proc. Nat. Acad. Sci. USA 52 (1964) 1433. [3] W.B. Holzapfel, J. Chem. Phys. 56 (1976) 712. [4] R.W.G. Wyckoff, Crystal structures col. 1 (Wiley, New York, 1963). [5 ] K.R. Hirsch, Dissertation, University of Paderborn (1983); K.R. Hirsch and W.B. Holzapfel, to be published. [6] H. Bilz and W. Kress, Phonon dispersion relations in insulators, in: Solid state science, Vol. 10 (Springer, Berlin, 1979) p. 187. [7] W.B. Holzapfel, B. Seiler and M.F. Nicol, Lunar Planet. Sci. XIV (1983) 321. [8] L.D. Landau and E.M. Lffschitz, Lehrbuch dot theor. Phys, Vol. 3 (Akademie-Verlag, Berlin, 1974). [9] W. Dultz and E. Rehaber, Phys. Rev. B28 (1983) 2114. [10] R. Chidambaram, J. Chem. Phys. 36 (1962) 2361. [11 ] A. Pollan, private communication (1983).
PHYSICS LETTERS
19 March 1984
SYMMETRIC HYDROGEN BONDS IN ICE X K.R. HIRSCH and W.B. HOLZAPFEL Physik, Universitiit-GH-Paderborn,Postfach 16 21, D-4790 Paderborn, Fed. Rep. Germany Received 8 November 1983
Raman measurements on Ice VIII under pressures up to 50 GPa reveal strong line shifts, changes in isotope frequency ratio, intensity decreases, and the appearance of one new line around 38 GPa. These observations are consistent with the formation of symmetric hydrogen bonds and a new phase, Ice X, with euprit structure.
Due to the asymmetry of the hydrogen bonds in all the phases of ice that were known up to now [ 1] a rich variety of order-disorder transitions has been observed for ice under pressure. The ordered low temperature phase Ice VIII and the disordered high temperature phase Ice VII were considered to be the "ultimate" high pressure phases of ice [2]. Only an "average" structure with space group O4(Pn3m) with two oxygens on the 2a sites and the four protons disordered with equal probability over the 8e sites can be assigned to Ice VII [2]. The ordering of the protons in Ice VIII results in a slight tetragonal distortion of this structure and leads to the space group D19(I41/ amd) with oxygen on 8e and protons on 16h sites [2]. Earlier X-ray studies and theoretical considerations for Ice VII and VIII under pressure lead to the conclusion that the hydrogen bonds may become symmetric in these phases somewhere between 35 and 80 GPa [3]. An analysis of the related structural changes reveals that both structures should transform into a new ordered structure, Ice X, with space group O4(Pn3m), with the two oxygens on the 2a sites, and with the four hydrogens on the 4b sites. This structure is well known also as the cuprit structure, which is observed in Cu20, Ag20 and Pb20 at normal pressure [4]. A detailed analysis of the Raman and infrared activities for both Ice VIII and this Ice X reveals [5] that all the Raman active modes of Ice VIII should disappear at the VIII ~ X phase transition and only 142
one new lattice mode should become Raman active in Ice X. This VTT2g mode corresponds to a motion of the oxygen lattice only, totaly decoupled from the proton motions at the P point, and therefore, no isotope effect is expected for this mode in D20 with respect to H20-Ice X. Raman data for H20 and D20 under pressures up to 50 GPa at a temperature of 100 K show [5] (A) a strong decrease in the stretching frequencies o 1 Alg , v 1BIg and o3Eg in Ice VIII (fig. 1), (B)a strong decrease in the intensities of all the Raman-active stretching modes from ten times the intensity of the VT(Blg + Eg) lattice modes at 3 GPa to below their intensity at 30 GPA, (C) the disappearance of these last lattice modes of Ice VIII around 50 GPa and the appearance of a new lattice made around 38 GPa, and (D) an isotope frequency ratio of 1.05 for these lattice modes in Ice VIII and of 1.0 for the new lattice mode attributed to Ice X. Since the pressure is not hydrostatic in these experiments, the local pressure may deviate by +10% from the average pressure measured by a ruby manometer. Therefore, the presence of Raman lines for both Ice VIII and the new phase lee X in a finite range of the nominal pressure (fig. 1) could result just from inhomogeneous stresses. Finally, (E) it can be noticed, that the decrease in the mode frequencies by 26% from the VT(BI~ + Eg) modes of Ice VIII to the OTT2g modes o~ Ice X (fig. 1) corresponds at least qualitatively to what one expects from the dispersion of the phonon branches in Ice I [6], which indicates that these Raman active OT(Blg + Eg) modes of Ice 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 101A, number 3
PHYSICS LETTERS =
2500 -
.
!
|
|
v
Vl Big
6~_
X~x---X_ x _ "X"--X ~x~x.__ "~ ~X"x"X~X X
ZOOO" r~
!
19 March 1984
~"-"---"
x~
-~.~.~.,~
1500'
-xx-x-_._~xV3 Eg ~---~-~--. Vl Alg
D20 of 100 K
N ¢-
VR2 B2g
<3
~,~ttc=~_Tr~. . . . . . ,
"r
..... V-----TB,g + VT Eg ...
10
:__?R
E g VT T2g
,
20
30
Pressure (GPo) Fig'. 1. Variation of Raman-active mode frequencies of D2 O-Ice VIII (crosses) and Ice X (circles) under pressure.
VIII correspond to zone boundary modes of this OTT2g branch of Ice X as a result of the increase in the unit cell at the transition from Ice X to Ice VIII. The pressure dependence of the IR-active modes of Ice VII was determined up to 12 GPa also just recently [7]. A linear extrapolation of the VRE13u- and the o2Alu-mode frequencies with pressure suggests that these modes become degenerate in both H20 and D20 Ices at around 22 GPa as required in the transition to the high symmetry phase Ice X. However, there is no reason to trust in such a linear extrapolation to twice the pressure of the experimental data. Furthermore, the Ice V I I - X transition may occur at room temperature also at some lower pressure than the Ice V I I I - X transition at 100 K, and nothing is known yet about the triple point between the phases V I I VIII-X. A model for the hydrogen bonds in Ice VIII can be based on one a priori symmetric double well potential [3] for the correlated motions of all the protons in any of the stretching modes (o I Alg , o 1 Blg and u3Eg ) at the F point if one takes the slight differences between these mode frequencies into account by additional small proton-proton coupling parameters. In a first approximation, each side of this symmetric double well potential can be represented by an effective Morse potential Z(x) = A(eZ~x
_ 2e~x) ,
where A represents the barriere height between the two wells. This very crude approximation has the essential advantage that it gives closed quantum mechanical solutions [8] for the energy levels
En
= -A
[1 - (hoo/A)(n + -~)] ,
with the "harmonic" frequency
%
=
(~121r)V'-'~lm.
For the first Raman frequency, one obtaines u 1 = o0(1 - hoo/2A), where A is considered now to depend on the oxygen-oxygen distance d. For o0, one can take the "harmonic" value from the free water molecule since the experimentally observed value for the isotope ratio of the pressure dependences [2]
dvi(H20)/dP dui(D20)/dP
=
1.8
ensures that u0 depends only very weakly on d. In fact, the value of 2 for this ratio would require a constant value of u0 within this model. If one assumes a decrease of A(d) which corresponds to a Landau-type expansion of the free energy [9], one finds a variation of the type A ( d ) = A**(d - de)/(d - do) whereA** = 9.6 X 10-19 Nm represents the value of A for the OlAlg mode of the free molecule [10]. d e and d o are free parameters which are determined by a fit to the experimental data, fig. 2. The best fit for the o 1 Alg mode gives a critical oxy143
Volume 101A, number 3 o
!
PHYSICS LETTERS t
|
i
i
2500!
"'~°'eo-o.~... °o..~ V3Eg -%b. " ~ Vl A1g °~'oo ~
2250 E
0
2000 E > 1750
.£3 D
1500
219
I
28
t
27
216
O-0 Bindingdistonce{A)
215
Fig. 2. Variation of stretching frequencies of D2 O-Ice VIII with respect to the bond length. The continuous lines represent two-parameter fits to the experimental data. gen--oxygen distance d e = 2.32 A where A ( d c ) = 0, whereas the best fit for the o3Eg mode corresponds to the slightly smaller value o f 2.26 A with d o = 0.35 A in b o t h cases. We are aware o f the fact, that this model must be regarded as a crude approximation, however, it represents reasonably the steep decrease in the barrier for the proton in the hydrogen bonds o f Ice VIII as the bondlength d approaches a critical value o f d e ~- 2.3 A. The deviations o f the fitted curves in fig. 2 from the experimental data at low pressures (d > 2.9 A) are attributed to b o n d bending [5] which appears to be significant only in the low pressure region and has been neglected also in the present considerations.
144
19 March 1984
It can be noticed, further more, that a stiffening in the equation o f state of Ice VII and VIII at d e had been predicted theoretically [3] and this stiffening has been observed in fact in recent Brillouin scattering experiments [11] on Ice VII at a pressure o f about 42 GPa which corresponds to a d e ~ 2.5 A in reasonable agreement with the present results. Finally, one should be aware o f the possibility that gradual disorder o f the protons in Ice X could cause at elevated temperatures a strong protonic conduction prior to melting and possibly could lead also to one more cubic phase of Ice with complete proton disorder and the "average" space group O2h(Pn3n).
References [ 1 ] B. Kamb, Crystallography of ice, in: Physics and chemistry of ice, eds. E. Whalley, S.I. Jones and L.W. Gold (Royal Soc. of Canada, Ottawa, 1973). [2] B. Kamb and B.L. Davis, Proc. Nat. Acad. Sci. USA 52 (1964) 1433. [3] W.B. Holzapfel, J. Chem. Phys. 56 (1976) 712. [4] R.W.G. Wyckoff, Crystal structures col. 1 (Wiley, New York, 1963). [5 ] K.R. Hirsch, Dissertation, University of Paderborn (1983); K.R. Hirsch and W.B. Holzapfel, to be published. [6] H. Bilz and W. Kress, Phonon dispersion relations in insulators, in: Solid state science, Vol. 10 (Springer, Berlin, 1979) p. 187. [7] W.B. Holzapfel, B. Seiler and M.F. Nicol, Lunar Planet. Sci. XIV (1983) 321. [8] L.D. Landau and E.M. Lffschitz, Lehrbuch dot theor. Phys, Vol. 3 (Akademie-Verlag, Berlin, 1974). [9] W. Dultz and E. Rehaber, Phys. Rev. B28 (1983) 2114. [10] R. Chidambaram, J. Chem. Phys. 36 (1962) 2361. [11 ] A. Pollan, private communication (1983).