Title The vibrational spectra of ice Ih and polar ice

Author(s) Fukazawa, Hiroshi; Mae, Shinji

Citation Physics of Ice Core Records, 25-42

Issue Date 2000

Doc URL http://hdl.handle.net/2115/32460

Type proceedings

Note International Symposium on Physics of Ice Core Records. Shikotsukohan, Hokkaido, Japan, September 14-17, 1998.

File Information P25-42.pdf

Instructions for use

Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP 25

The vibrational spectra of ice Ih and polar ice

Hiroshi Fukazawa and Shinji Mae

Department of Applied Physics, Faculty of Engineering, Hokkaido University, N13W8, Sapporo 060-8628, JAPAN

Abstract: This article reviews experimental and theoretical work on the dynamics and structure of artificial ice, ice Ih, and natural ice recovered from Antarctic and Greenland ice sheet. We focused on analyses of the vibrational spectra of artificial ice and polar ice. Based on the analyses of the vibrational spectra, which observed by Raman and inelastic neutron scattering measurements, we discussed the motion and arrangement of water molecules in Ice.

1. Introduction The study of the distribution of protons and the hexagonal arrangement of Ice Ih is ordinary ice, and the oxygen oxygen nuclei in polar ice is fundamental to nuclei in ice Ih have a hexagonal the investigation for physical properties of arrangement. The orientations of water ice core recovered from polar ice sheet. The molecules are disordered under pressure knowledge of the dynamics and structure of below about 200 MPa and at temperatures atoms and molecules in polar ice would from 0 K to the melting point. Therefore the especially lead to an understanding of the positions of the protons are disordered electrical and mechanical properties and the following the ice rules: (1) there is only one diffusion processes of water molecules and proton on each bond, and (2) there are only inclusion (chemical constituents, atmos­ two protons close to each oxygen nucleus. pheric gases, and so on) in ice sheet, which The ice rules were proposed by Pauling is essential for reconstructing the past based on the calculation of residual entropy environment. In the present review, we [1]. Neutron diffraction measurement of report dynamics and structure of molecules

D20 by Peterson and Levy [2] and of H20 and atoms in artificial ice, ice Ih, polar ice. by Kuhs and Lehmann confirmed the proton-disordered arrangement. Thus, protons in ice Ih are equally distributed 2. The vibrational spectra of ice Ih among the two possible sites on each 0-0 bond, as shown in Fig. lao The vibrational spectra, which are due to the crystal structure and atomic motions,

Physics a/Ice Core Reconls Edited by T. Hondoh Hokkaido University Press, 2000, Sapporo 26 The vibrational spectra o/ice Ih and polar ice

a b

Figure 1: (a) Location of protons in ice Ih as detennined by the neutron diffraction pattern [2]. Oxygen nuclei are represented by open circles and protons by shaded half-circles. There are two half-protons

along each 0-0 axis. (b) Structure of ice XI (space group Cmc2 j ) as detennined by the neutron diffraction pattern [20]. Open circles represent oxygen nuclei and shaded circles represent protons. have been investigated using mainly vibrations, librational vibrations and O-H infrared, Raman and neutron spectroscopy. stretching vibrations, respectively. The The infrared absorption is caused by a translational and librational vibrations are change of amount of electric dipole moment intermolecular mode of vibrations, and O-H of molecules. The Raman scattering is stretching vibration is intramolecular mode. made by a strain-dependence of the electronic polarizability. The neutron 2.1. The translational lattice vibrations scattering is made by interaction with the On the basis of the space symmetry in nuclei of the atoms. Since hydrogen has a oxygen nuclei, P6immc, the nine zero­ very large incoherent scattering cross­ wave-vector translational vibrations form

section (79.7 barns as compared with 0.01 A1g + BIg + B 2u + EIg + E2g + E2u (Fig. 3) [4]. barns of oxygen), the IINS spectrum is All these vibrations are forbidden in the

sensitive to a change of the arrangement infrared (A1g, E1g, E2g vibrations are Raman and motion of proton in ice. active). However, the forbidden vibrations Figs. 2a, b and c show the infrared, are active because the proton-disordered Raman and incoherent inelastic neutron arrangement destroys the hexagonal scattering (lINS) spectra of artificial ice, ice symmetry, so that, the infrared spectrum has I Ih, in the energy range of below 4000 cm- . the peak of the translational lattice I The spectra have peaks in the range of 150- vibrations in the region of 150-300 cm- , as I 350 cm- , 400-1000 cm-\ and 2800-3200 shown in Fig. 2a. I cm- , which assigned to translational lattice H. Fukazawa and S. Mae 27

>­ :!::: (j) C Q) -c

]000 2000 3000 4000

Figure 2: The vibrational spectra of ice Ih measured by infrared (a), Raman (b) and IINS (c) techniques [13]. The upper curve in (c) is the spectrum measured on TFXA and lower curve on RET spectrometer.

E 29 Figure 3: Displacements of the oxygen nuclei [QQI) in one unit cell in the zone-center vibration of ice Ih [4]. L {liP I 28 The vibrational spectra a/ice Ih and polar ice

Fig. 4 shows the Raman spectrum of Raman intensity lies mainly in the disorder translational lattice vibrations in ice Ih at in the location of the proton surrounding an the measurement temperature of 220-253 K, hydrogen bond. They concluded that the which has a large peak at about 220 cm-I vibrations above 240 cm-I are connected I and a small peak at 300 cm- . There is a with the vibrations in the hexagonal specific density of vibrational states for symmetry and the peak at 300 cm-I is I translational modes at 220 and 300 cm- . caused by an electrostatic interaction of the Wong and Whalley [4] discussed the theory transItIOn moments of neighboring of the Raman scattering by the translational hydrogen bonds. Marchi et al. [5] carried lattice vibrations of the proton disordered out lattice dynamics calculations for ice Ih crystals and showed that the origin of the using the SPC rigid-molecule effective pair

160 200 240 280 320

-1 Raman shift (em )

I Figure 4: Raman spectra of ice Ih in the region of translational lattice vibrations (150-350 cm- ). Measurement temperatures: (a) 220 K, (b) 238 K and (c) 253 K. The polarization plane of the incident beam was parallel to the c-axis of the sample. H Fukazawa and S. Mae 29 potential with long-range dipole-dipole increases with increases in Q, and that the interactions and calculated the density of energy at Q = 14 nm-1 is 27 meY. This states in the translational region. The result implies that the peak at 27 meV in the longitudinal-optic-transverse-optic (LO­ vibrational density of state of the ice is TO) analysis of the experimental data related to the acoustic mode. combined with the theoretical results of Marchi et al. [5] shows that the peak at 220 2.2. The librational vibrations cm-1 is due to TO vibrations and that the Bertie and Whalley [10] measured the peak at 300 cm-1 to LO vibrations. infrared spectra and absorptivity of ice Ih in J Li and Ross [6] measured the IINS the range of 350-4000 cm- , and the spectra of ice Ih and found two peaks at 27 absorption due to the librational vibrations J and 37 me V, respectively, which correspond was observed at about 850 cm- • Wong and to the peaks at 220 and 300 cm-1 in the E. Whalley [11] reported the Raman Raman spectra. They suggested that the spectrum of ice Ih, in which the peak of the strength of the hydrogen bonds in ice Ih librational vibrations at around 800 cm-J depends on the proton arrangement, and was very broad. Klug et al. [12] measured they proposed a model in which weak and the IINS spectrum of ice Ih in the range of strong hydrogen bonds exist randomly in 0-160 meV (corresponding to 1290 cm-J in ice Ih in a ratio of about I : 2. They carried the infrared and Raman spectra) and found out lattice dynamics calculations using their a large peak of librational vibrations at 80 J model, and they assigned the two peaks at meV (640 cm- ). As shown in Fig. 5, 27 and 37 meV to vibrations traveling lib rational vibrations are caused by the across the weak and strong hydrogen bonds, motion of protons, thus IINS is the respectively. measurement technique most sensitive to In contrast, according to Tse and Klug the vibrations. [7], the peaks at 26 and 35 meV in ice Ih The proton ordering greatly affects the can be reproduced by carefully shape of the spectra of librationa I vibrations. parameterized intermolecular potentials that The spectra in the proton-disordered phases, include long-range electrostatic interactions ice Ih [8, 12, 13], V [14] and VII [15], are without the weak and strong hydrogen similar, but they differ from those in the bonds. Fukazawa et al. [8] also reported proton-ordered phases, ice II [14], VIII [15, that the two peaks at 27 and 37 meV were 16], IX [14] and XI [8, 17, 18]. Ice Ih and not due to two different strengths of XI are stable below about 200 MPa, while hydrogen bond on a basis of a comparison other phases are stable over about 200 MPa. of the IINS spectrum of ice Ih and the Ice XI is formed in 0.001-0.1-mole KOH­ proton-ordered phase of ice Ih, ice XI. doped ice Ih after being maintained for The sharp peak in the IINS spectrum at about 3 days below 72 K [19]. Leadbetter et about 6 me V is assigned to transverse al. [20] measured the powder neutron acoustic vibrations. Ruocco et al. [9] diffraction of KOD-doped D20 ice (about measured inelastic the x-ray scattering 30 % transformation to ice XI) and reported spectra of ice Ih taken at the indicated that the arrangement of oxygen nuclei in ice valued of momentum transfer, Q. They XI is the same as that in ice Ih, but protons found that the energy of the acoustic mode in ice XI occupy the ordered position in 30 The vibrational spectra ofice Ih and polar ice

wag twist rock

Figure 5: The three librational modes for a water molecules: wag, twist and rock. Oxygen nuclei are represented by open circles and protons by shaded circles [25]. such a way that the spontaneous ice XI have a strong peak at about 79 meV, polarization is parallel to the c-axis (Fig. but those of ice Ih have a much lower peak, I b), thus ice XI is ferroelectric. Howe and while the difference in the translational Whitworth [21] and Line and Whitworth lattice vibrations (10-40 me V) between ice [22] measured the neutron diffraction of XI and ice Ih is small. Itoh et al. [24, 25] powdered KOH-doped H20 ice and carried out molecular dynamics simulations obtained the polar structure of the space and showed that the librational spectra of group Cmc2 1 . Jackson et al. [23] also ice XI have four sharp peaks, but those of obtained the same result in a neutron ice Ih have broad peaks. diffraction study of a single-crystal of Fukazawa et al. [8] measured the IINS

KOH-doped H20 ice. These results showed spectra of ice Ih and O.OI-mole KOH-doped that protons in ice Ih are equally distributed ice at 21 K (Fig. 6) using a crystal-analyzer among the two possible sites on each 0-0 time-of-flight (CAT) spectrometer on a bond, while protons in ice XI are fixed at pulsed spallation neutron source at the High one site on each 0-0 bond. Energy Accelerator Research Organization Using TFXA and HET spectrometers (KEK), Japan. In the CAT spectrometer, the at the Rutherford Appleton Laboratory, Li scattering angle ( fJ) is about 0° for an et al. [17] measured the IINS spectra of energy of;?: 20 me V Based on the analyses 0.02 and 0.055 mole KOH-doped ice of neutron scattering and fermi resonance in sample at 10 K, in which 30-50 % of the hydrogen bonds, Ikeda et al. [26] reported protons are ordered. They found that the the librational vibrations in ice have two IINS spectra of the librational vibrations components, so that the intensity of the (60-120 meV) of ice XI are clearly librational mode (40-150 meV) of ice Ih, different from those of ice Ih: the spectra of H. Fukazawa and S. Mae 31

IIh(s), is written as the sum of two Gaussian a functions: Ice Ih

where Al and A2 are areas, II and 12 are FWHM, and CI and C2 are energies of the peak centers. Values of parameters are determined by least square fitting (Table 1). The sample of ice XI was a mixture of ice Ih (17 %) and XI (83 %). The intensity of b the IINS spectrum of our sample, Ix/s), IS Ice XI (83%) written as

(2) -;!: C ::;) .0.... where Ixls)' is a spectrum of pure ice XI ~ and can be written as the sum of two .~ f/) c Gaussian fittings. The value of 17 is the ratio Q) E of ordered protons sample. From electric permittivity, it is estimated that '7 = 0.83. The fitting shows that II and 12 drastically decrease with decreases in 11 and that the widths of the librational mode strongly depends on the proton ordering. o 40 80 120 Ice Ih consists of four configurations Energy (meV) of pairs of molecular dipole moments (Neon! = 4), while ice XI consists of only two configurations (Neon! = 2). Fig. 7 shows the Figure 6: The solid curves represent in­ Neon}' dependence of II and 12 of ice, XI and coherent inelastic neutron scattering spectra VIII. Ice VIII consists of Bond (D) (Neon}' = from ice Ih (a) and ice XI (b) in the region of 1). This figure shows that ~ and ~ are lattice vibrations. The dotted curves are the proportional to Neon}'. resultant profiles of the Gaussian functions used for the fittings, indicated by broken curves. Measurements were made at 21 K The intensities of spectra were normalized by the integrated intensities of the elastic scattering [8]. 32 The vibrational spectra o/ice Ih and polar ice

Table 1: FWHM (fl and f 2) oftwo peaks (e 1 and e2) in the libration mode for ice Ih, IliB), and ice XI, Ix/BY [8].

£\ (meV) r) (meV) £2 (meV) r2 (meV) Temperature

71 24 91 44 21K

!xl (e)' 21K 73 15 97 41

(11=83%) After annealing

stretching vibration mode (2800-3500 em-I) and found a strong peak at 3130 em-I -- Proton order - Disorder and two weak peaks at 3246 and 3354 em-I. VIII XI 50 Ih The peak at 3130 em-I was assigned to the ...... symmetric stretching vibration mode in­ ...... 40 phase vibration, in which the molecules ---. move in phase with one another, and the >Q) g 30 peaks at 3246 and 3354 em-I were assigned ~ to the TO-LO splitting of the antisymmetric J: 20 stretching vibration mode. The Raman u..~ spectrum had a broad peak at 1653 cm-\ 10 which was assigned to the H-O-H bending mode, and a peak at 2235 em-I, which was 0 assigned to the association band of 3 Vr.. 0 2 4 (librational mode) or V2 (bending mode) + Vr.. (librational mode). Neon' Li and Ross [13] measured the spectra in the range of below 500 meV (4000 em-I). Figure 7: Proton-configuration (Neonf) depend­ ence of FWHM (fl and f 2) of ice Ih, XI and The peak of the O-H stretching vibration at VIII [8]. Open and solid circles represent f 1 and 400 meV (3200 em-I) was small in the IINS

f 2, respectively. spectrum, because the intensity of IINS decreases with increases in energy.

2.3. The O-H stretching vibrations Bertie et al. [27] measured the infrared 3. The vibrational spectra of polar ice spectra and absorptivity of ice Ih, and the absorption due to the O-H stretching 3.1. Raman spectra vibrations was observed at about 3220 em-I. Dome Fuji (DF) ice was retrieved by Wong and Whalley [28] reported the the Japanese Antarctic Research Expedition Raman spectrum of ice Ih in the O-H (JARE) at Dome-Fuji station (77°22'S, H. Fukazawa and S. Mae 33

39°37'E; elevation 3807 m) at one of the Fukazawa et al. [30, 31, 32] in­ summits in Antarctica in 1995 and 1996 vestigated the Raman and IINS spectra of (Fig. 8). Since 1992, a deep ice core drilling ice cores retrieved from Antarctic (Dome project has been carried out by the JARE at Fuji, Vostok, Mizuho and Nansen) and this site [29]. In 1997, the drilling reached Greenland (Dye-3) ice sheets, because ice over 2500 m in depth from the ice sheet in the polar ice sheets had been preserved at surface. The surface temperature is 213 K, a constant temperature for a long period and T; gradually increases with increases in (102-104 years), and they hypothesized that the depth, becoming Tc at a depth of 2060 m. it is possible to observe a very slow change The thickness of the ice at the station was in the proton arrangement in ice. An calculated to be about 3060 m by radio echo incident laser beam with a diameter of 1f..lm sounding. was focused on an appropriate crystal grain

a

o 1000km I I

b 2kmI ~--~Ti=237K (~ ==-::I Bedrock

Figure 8: (a) The drilling sites of Dome-Fuji, Mizuho and Vostok ice in Antarctica. The shaded area represents the area where Ti :s; Te = 237 K on the Antarctic ice sheet surface. (b) Schematic diagram of a cross section of the Antarctic ice sheet. The hatched area shows the area where the ice contains proton­ ordered arrangements. 34 The vibrational spectra ofice Ih and polar ice

(grain size: 0.5-7.0 mm). The crystal grain for T; ~ Te is the same as that for T; ~ Te. was pure ice, because impurities in ice are Therefore, the IR- T; relation shown in Fig. concentrated at the grain boundaries [33, 9a is considered to be caused by the proton­ 34]. They found that the ratio of peak ordered arrangement in Antarctic ice I intensities at 300 and 220 cm- (IR ) was samples at values of Ti lower than Te. independent of depth (pressure), age of the Accordingly, IR is given by Ice and temperatures at which the measurements were made. However, IR was dependent on the ice temperature in the ice sheets (TJ The dependence (Fig. 9a) was as follows: for Ti ~ Te = 237 K, IR is constant at 0.32 ± 0.01, which is the same as that of where O"ordel220) and O"ordel300) are peak I intensities at 220 and 300 cm- , respectively, the artificial ice (ice Ih); however for T; ~ Te, due to proton-ordered hydrogen-bonds; IR decreases with decreases in Ti . O"d;sorder(220) O"d;sorder(300) The IR-T; relation for T; ~ Te and the and are those due change in the T; dependence of IR at Te to proton-disordered hydrogen-bonds; and cannot be accounted for by the hypotheses '7 is the ratio of the number of the proton­ that Klug et al. [12] and Li and Ross [6] ordered hydrogen-bonds to that of all proposed on the basis of the proton­ hydrogen-bonds. For T; ~ Te, IR = 0.32 and disordered arrangement of ice Ih. A T; '7 = 0, and, therefore, O"d;sordel300) / O"disorder (220) is 0.32. IR decreases with decreases in dependence, such as the IR- T; relation, is not found in the Raman spectra of T;, and we assume that for T; == 0 K, I intramolecular vibrations (2800-3600 cm- ) O"order(300) = 0 and '7 = 1, based on of Antarctic ice. Moreover, x-ray diffraction experimental result about the decrease in I R . measurements [35] showed that the Thus, structure of oxygen nuclei in Antarctic ice

0.33 0.5 0.32 b 0.4 0.31 0.3 0.30 $::'" _CI:. 0.29 0.2 0.28 0.1 0.27 0.0 0.26 220 230 240 250 260 220 230 240 250 260 T (K) Tj(K) j

Figure 9: (a) T; dependence of IR in Antarctic and Greenland ice [32]. (b) Relation between TJ and T;.

The solid line shows '[n = ~(Tetc - T )/T for T1 -< Tc'/ and n = 0 for T>1 - TC' \\>here TC = 237 K • H. Fukazawa and S. Mae 35

3.2. IINS spectra (4) Proton ordering especially affects the shape of the IINS spectra of librational vibrations. Fukazawa et al. [32, 37] meas­ where C == O"ordel220) / O"disordel220). ured the IINS spectra of DF and Vostok ice According to the Landau theory of the using INC and CAT spectrometers at the second-order phase transition [36], '7 = KEK. The detectors in the INC are mounted ~(Tc - 1; }/Tc for Ti S Tc, and '7 = 0 for Ti ;::: in four banks, and spectra were obtained Tc, where Tc = 237 K. Theoretical values of from the detectors at () = 30.3-39.8°, and '7 are shown by the solid line in Fig. 9b. the values of () are larger than those of CAT Substituting the IR and C = 0.43 into Eq. (4), spectrometer. DF ice were measured at 21 values for '7 can be calculated, as shown in K, and the IINS spectra obtained (Ti = 213 Fig. 9b (open circles). The plotted values of K and '7 = 0.33) are shown in Fig. 10. They '7 are in good agreement with the then carried out the same measurements for theoretical values. This analysis shows that the IINS spectra of ice Ih and O.OI-mole about 33 % of the protons in DF ice (Ti :::: KOH-doped ice, for which a '7 value of 213 K) are ordered.

i' , \ , \ - OF ice (201 m) , \ I \ --- KOH-doped ice , \ (83% ice XI) , \ I \ ...... Ice Ih I \ , \ I \ -- ·00 c: ...... Q) c:

80 100 120 140 Energy (meV)

Figure 10: IINS spectra of librational vibrations (Dome-Fuji ice, ice XI, ice Ih) observed by INC spectrometer. 36 The vibrational spectra a/ice Ih and polar ice

0.83 was estimated, based on electric The order-disorder phase-transition permittivity measurements [38, 39]. Fig. 10 has not been found in experimental studies shows the IINS spectra of ice XI and ice Ih. of artificial ice (pure ice), because it is It was found that both DF ice and ice XI considered that a thermodynamic have a sharp peak at about 79 me V, but that equilibrium of protons cannot be attained in the peak of ice Ih is much lower. This result a finite period of time due to the extremely implies that proton-ordered and disordered slow cooperative process of proton arrangements coexist in DF ice. rearrangement [42]. Suga [43] roughly estimated, on the basis of results of 3.3. Ice temperature effect on vibra­ extrapolation of the relaxational heat tional spectra of polar ice capacity of ice annealed for 624 hours, that The value of 17 is independent of proton-ordering in pure ice requires about pressure (i.e., depth) but is dependent on 106 years, and he proposed that ordered ice temperature. Since the value of 17 in DF ice (pure ice) exists only on the moons of is not influenced by the measurement Jupiter and Saturn. However, on the Earth, temperature and the storage temperature of Antarctic ice has been kept at a constant 2 the ice samples after drilling, the value of 17 temperature for a long period of time (10 - 5 is considered to depend on Ti . From the 10 years). Furthermore, the proton estimation of Ti at each depth using a model rearrangement in Antarctic ice is in of bed specific heat flow [40], 17 is plotted thermodynamic equilibrium. Therefore, the

against Ti . The plotted values of 17 are in change in the librational vibration in DF ice good agreement with the relation between with depth, which indicates the phase temperature and 17 in the Landau theory of transition in Antarctic Ice sheet, IS the second-order phase-transition [36]: 17 observed.

~(Tc - 1'; }/Tc for Ti S Tc, and 17 = 0 for Ti 2:: Based on the results of proton ordering Tc, where Tc = 237 K. This agreement in Antarctic ice, Fukazawa et al. [32] suggests that the order-disorder phase­ estimated that ice slowly grown from vapor transition takes place at Tc = 237 K in the at temperatures lower than 237 K has a Antarctic ice sheet. Thus, it is reasonable to proton-ordered arrangement because the ice consider that Antarctic ice in the area where is in thermodynamic equilibrium. Su et al.

Tj S 237 K contains proton-ordered arrange­ [44] (1998) measured the sum-frequency ments. About one third of the Antarctic ice vibrational spectra of thin layers of ice mass is considered to contain proton­ grown from vapor at about 140 K and ordered arrangements. As shown in Fig. 8b, found proton ordering in the ice. ledama et the boundary between the proton-ordered al. [45] also found the proton ordering in and -disordered arrangements is at a depth ice grown from vapor at temperatures of of about 2000 m. Goodman et al. [41] 40-150 K. The results of these recent works reported that proton rearrangement imply that ice grown from vapor in the controlled the glide of ice. Since the proton­ Earth's ozone layer and atmospheric rearrangement in proton-ordered ice is aerosol over Antarctica have a proton­ extremely slow, it is thought that the ordered arrangement. flowability of ice discontinuously changes These temperatures at which a proton­ at a depth of about 2000 m. ordered arrangement in ice was found, are H. Fukazawa and S. Mae 37 higher than the transition temperature of 72 K have a large peak at 221.61 cm-I and a I K in KOH-doped ice. Analyses that explain small peak at about 300 cm- . The large the phase transition and the high transition peaks in the spectra at 238 and 253 K are at I temperatures are very important to 220.52 and 218.07 cm- , respectively. understand the hydrogen bonding of ice, but Fig. 11 shows the temperature, T, it is not clear at present. In order to obtain dependence of UTIIC and Unc, where UTIIC direct evidence of the proton ordering in ice, and Unc represent the values of the the determination of proton arrangements in frequency of the large peak at about 220 I ice by single-crystal neutron diffraction IS cm- , UT, for the polarization planes parallel important. and perpendicular to the c-axis of ice Ih, respectively. Both UTIIC and Unc decrease with increases in T, and that the rates of 4. Temperature effects on vibrational decreases in UTIIC and Unc discontinuously spectra of ice change at the measurement temperature of TC = 237 K. The following relations Ermolieff et al. [46] measured the (represent by dotted lines in Fig. 11) were Raman spectra of ice Ih over a temperature obtained: range 80-250 K in order to detect a possible anomaly in the spectrum near 100 K. T;::: T , UTIIC(cm-l) = -0. 13T(K) + 251.33, Scherer and Snyder [47] measured the c Raman scattering intensity of single crystal (6) of ice Ih at several temperatures in order to I unc(cm- ) = -0. 12T(K) + 248.41, clarify the anisotropic effects on the force constants associated with the vibrations. (7) Iohari et al. [48] reported the measurements T::; T ' UTIIC(cm-l) = -0.07T(K) + 237.11, of the Raman spectra of ice Ih from 25-273 c K and found that the change in the (8) permittivity of ice with changes in I unc(cm- ) = -0.07T(K) + 236.56, temperature is consistent with changes in the main frequency of the translational (9) lattice vibrations. We reported the Raman spectra of ice Fig. 12 shows the T dependence of Ih and Antarctic ice in the temperature UOHIIC and UOHl.C, where UOHIIC and UOHl.. C range of 198-270 K in order to observe the represent the frequency of the peak of the change in molecular polarizability due to O-H stretching vibrations, UOH, for the the change in intermolecular potential. polarization planes parallel and per­ pendicular to the c-axis of ice Ih, 4.1. Ice Ih respectively. Both UOHIIC and UOHJ..C linearly Fig. 4 shows typical Raman spectra of increase with increases in T. The following ice Ih (single crystal) at measurement relations (represented by dotted lines in Fig. temperature of 220, 238 and 253 K in the 12) were obtained: region of translational lattice vibrations I (150-350 cm- ). The Raman spectra at 220 38 The vibrational spectra o/ice Ih and polar ice

224 3145 ~."...... ~ .... a 222 .... 3140 "'1...... '7 '7- . - E '. E 3135 .£ 220 • ...... £ (.) (.) -. \ "" 3130 ...."" ;;\.. 6 ;::, 218 ;::, \ .•.•~ •.. 3125 ". 216 • 3120 224 3145 b 3140 222 .'"'1...... •• '7- '7- ...... !! .. ~ E 3135 E 220 • .£ .£ (.) (.) \~.. ..., i§'" 3130 ...... • ;::, ::::l • 218 "\ \"'- 3125 '...... ~. 216 3120 200 220 240 260 280 200 220 240 260 280 T (K) T(K) Figure 12: The T dependence of the frequency Figure 11: The measurement temperature, T, of the peak of the 0-H stretching vibrations, VOH dependence of the frequency of translational observed by Raman spectroscopy of the c-axis lattice vibrations, VT, observed by Raman parallel (a) and perpendicular (b) to the spectroscopy of the c-axis parallel (a) and polarization plane of the incident beam. perpendicular (b) to the polarization plane of the incident beam.

The linear increase in VOH is the same as the VOHIIC(cm-1) = -0.34T(K) + 3050.76, (10) T dependence of VOH reported in a previous

VOH.LC (cm -1) =-0.35T(K) + 3046.84. (11) work [27]. The lattice constants of the c- and a­ axes change with changes in T in the H Fukazawa and S. Mae 39 temperature range of 195-265 K [49]. Thus, 80 % less than those above 237 K. The the discontinuous changes in VTIIC and Vnc decrease at 237 K implies a decrease in the at Tc are caused by a temperature effect at a anharmonicity of the lattice vibrations, constant volume, (8vrl81)v, which is a non­ because (8vrl81)v is due to anharmonic linear effect in the displacement. The value term in the intermolecular potential [52]. of (8vrl81)v is divided into the effect of T Sivakumar et al. [53] estimated that the on VT at constant pressure, (8vrl81)p, and anharmonicity is mainly caused by the the constant-temperature volume effect, bending of O-H ... 0 angles. The decrease (8vrl8P)y. Thus, in anharmonicity of the lattice vibrations below 237 K is able to drive phase transitions. (8vT/8T)v =(8v T/8T)p + (a/f3X8vT/8P)T '

(12) 4.2. Polar ice Figure 13 shows temperature changes where a is the volume expansivity and f3 is in the translational lattice vibrations in DF the compressibility. The values of a and f3 ice obtained by Raman spectra, VT, of the c­ 1 1 in ice Ih are 155 MK- [50] and 12 Mbar- axis parallel (a) and perpendicular (b) to the [51], respectively, at about 255 K. 10hari et electric field [55]. There are changes at 1 al. [48] reported that (8vrl8P)y = 4.77 cm- around Tc = 237 K in the rates of decrease 1 kbar- . Thus, from Eqs. (6), (7), (8) and (9), of the frequency of the lattice vibrations. 1 (8VTIIC/81)p = -0.13 cm-1K- and (8vnc/81)p The relationship between V and tem­ 1 T = -0.12 cm-1K- for 2:: T", and (8vTl/cl81)p = perature can be written: -0.07 cm-1K-1 and (8vnc/81)p = -0.07 1 cm-1K- for::; T", where (8VTIIC/81)p and 1 T2::Tc, vT(cm- )=-0.136T(K)+252.543, (8vnc/81)p are the values of (8vrl81)p for the polarization planes parallel and (17)

perpendicular to the c-axis of ice Th, 1 T::; Tc, vT(cm- ) = -0.082T(K) + 239.985, respectively. Substituting these values into Eq. (12): (18)

Matsuoka et al. precisely measured the T2::Tc, (8vT11c /8T)v =-0.07, (13) temperature dependence of permittivities of (8vnc/8T~ =-0.06, (14) pure single-crystal [54] and DF ice (350 m in depth) [55] in the temperature range of (15) T::; Tc, (8vTIIC /8T)v = -0.01, 210-260 K. The temperature dependence of real part, s', in DF ice (Fig. 14) is given by: (8vnc /8T)v -0.01, (16) s' = 0.00 lIT + 2.8617, (19) where (8vTl/c/81)v and (8 Vnc/81)v are values of (8vrl81)v for the polarization s' = 0.0003T + 3.0620. (20) planes parallel and perpendicular to the c­ axis, respectively. The rates, (8vTllc/81)v and (8 vnc/81) v, below 237 K are about 40 The vibrational spectra o/ice Ih and polar ice

Tem p erallr e (Oe) -60 -50 -40 -30 -20 -10 3.16 (al 33GHz 3.15

i 3.14 -.a a:G.l 3.13

3.12 2.4xl0.3 (b)

The measured values of Vr and s' are Acknowledgements agreement with the Kramers-Kronig relation [48]: We would like to thank Dr. T. Hondoh, Dr. S. Ikeda, Dr. W. F. Kuhs, Dr. V. Ya. (21) Lipenkov and Dr. A. N. Salamatin for their valuable discussions. One of the authors, H. F., has been supported by a Research where nap is the refractive index at optical Fellowship of the Japan Society for the frequencies. Temperature dependence of nap Promotion of Science for Young Scientists. is governed by the continuous change in the expansivity with changes in temperature. Thus, this agreement implies that the References significant change in the rate of decrease of Vr with temperature at 237 K causes a 1. L. Pauling, J. Am. Chern. Soc., 57, 2680 change in the rate of increase of s' with (1935). temperature and also that of molecular 2. S.W. Peterson and H.A. Levy, Acta polarizability. Crystallogar, 10, 70 (1957). H. Fukazawa and S. Mae 41

3. W.F. Kuhs and M.S. Lehmann, Nature, 20. A.J. Leadbetter, R.e. Ward, I.W. Clark, 294,432 (1981). P.A. Tucker, T. Matsuo and H. Suga, J 4. P.T.T. Wong and E. Whalley, J Chern. Chern. Phys., 82, 424 (1985). Phys., 65, 82 (1976). 21. R Howe and RW. Whitworth, J Chern. 5. M. Marchi, I.S. Tse and M.L. Klein, J Phys., 90,4450 (1989). Chern. Phys., 85,2414 (1986). 22. e.M.B. Line and RW. Whitworth, J 6. J.e. Li and D.K. Ross, Nature, 365, 327 Chern. Phys., 104, 10008 (1996). (1993). 23. S.M. Jackson, VM. Nield, RW. 7. J.S. Tse and D.D. Klug, Phys. Lett., 198, Whitworth, M. Oguro and e.e. Wilson, 464 (1995). J Phys. Chern. E, 101, 6142 (1997). 8. H. Fukazawa, S. Ikeda and S. Mae, 24. H. Itoh, K. Kawamura, T. Hondoh and Chern. Phys. Lett., 282, 215 (1998). S. Mae, Physica E, 219&220, 469 9. G. Ruocco, F. Sette, U. Bergmann, M. (1996). Krisch, e. Masciovecchio, V 25. H. Itoh, K. Kawamum, T. Hondoh and Mazzacumti, G. Signorelli and R S. Mae, J Chern. Phys., 109, 4894 Verbeni, Nature, 379, 521 (1996). (1998). 10. I.E. Bertie and E. Whalley, J Chern. 26. S. Ikeda, H. Sugimoto and Y. Yamada, Phys., 40, 1637 (1964). Phys. Rev. Lett., 81, 5449 (1998). 11. P.T.T. Wong and E. Whalley, J Chern. 27. I.E. Bertie, H.I. Labbe and E. Whalley, Phys., 62, 2418 (1974). J Chern. Phys., 50, 4501 (1969). 12. D.D. KIug, E. Whalley, E.C. Svensson, 28. P.T.T. Wong and E. Whalley, J Chern. J.H. Root and VF. Sears, Phys. Rev. E, Phys., 62, (1975). 44,841 (1991). 29. O. Watanabe, W. Shimada, H. Narita, A. 13. J.e. Li and D.K. Ross, Proc. Int. Con! Miyamoto, K. Tayuki, T. Hondoh, T. Physics and Chernistry of ice, 27-34 Kawamum, S. Fujita, H. Shoji, H. (1992). Enomoto, T. Kameda, K. Kawada and 14. I.e. Li, I. D. Londono, D.K. Ross, I.L. K. Yokoyama, Proc. NIPR Syrnp. Polar Finney, J. Tomkinson and W.F. Meteorol. Glaciol., 11, 1-8 (1997). Sherman, J Chern. Phys., 94, 6770 30. H. Fukazawa, T. Ikeda, T. Hondoh, (1991). VYa. Lipenkov and S. Mae, Physica B, 15. I.e. Li and M. Adams, Europhys. Lett., 219&220,466 (1996). 34,675 (1996). 31. H. Fukazawa, D. Suzuki, T. Ikeda, S. 16. A.I. Kolesnikov, J.e. Li, D.K. Ross, Mae and T. Hondoh, J Phys. Chern. B, VV Sinitzin, 0.1. Barkalov, E.L. 101,6184 (1997). Bokhenkov and E.G. Ponyatovskii, J 32. H. Fukazawa, S. Mae, S. Ikeda and O. Phys. Lett. A, 168, 308 (1992). Watanabe, Chern. Phys. Lett., 294, 554 17. I.e. Li, VM. Nield and S.M. Jackson, (1998). Chern. Phys. Lett., 241, 290 (1995). 33. R Mulvaney, E.W. Wolff and K. Oates, 18. I.e. Li, J Chern. Phys., 105, 6733 Nature, 331, 247 (1988). (1996). 34. T. Matsuoka, S. Fujita and S. Mae, J 19. Y. Tajima, T. Matsuo and H. Suga, Phys. Chern. E, 101,6219 (1997). Nature, 299,810 (1982). 35. T. Ikeda, Master's thesis, Hokkaido Univ. (1994). 42 The vibrational spectra of ice Ih and polar ice

36. L.D. Landau and E.M. Lifshitz, 46. A. Ermolieff, P. Faure and A. Chasson, Statistical Physics, Pergamon Press, J. Phys. PariS, 37, 1457 (1976). London, 1959. 47. 1.R Scherer and RG. Snyder, J. Chern. 37. H. Fukazawa, S. Mae, S. Ikeda and Phys., 67,4794 (1977). v.Ya. Lipenkov, Polar and Meteology 48. G.P. Johari, HA.M. Chew and T.c. and Glaciology (in press). Sivakumar, J. Chern. Phys., 80, 5163 38. M. Oguro and RW. Whitworth, J. Phys. (1984). Chern. Solids, 52, 401 (1991). 49. K. R6ttger, A. Endriss, 1. Ihringer, S. 39. H. Looyenga, Physica, 31, 401 (1965). Doyle and W.F. Kuhs, Acta Cryst. E, 50, 40. A.N. Salamatin, Data of glaciological 644 (1994). studies, 83,227 (1997). 50. S.J. La Place and B. Post, Acta Crystal­ 41. D.J. Goodman, H.J. Frost and M.F. lographica, 13, 503 (1960). Ashby, Phil. Mag., 43, 665 (1981). 51. A.J. Gow and J. Williamson, J. 42. D. Eisengerg and W. Kauzmann, The Geophys. Res., 77,6348 (1972). Structure and Properties of Water, 52. G.P. Johari, Conternp. Phys., 22, 613 Oxford Univ. Press, London, 1969, (1981). 77pp. 53. TC. Sivakumar, HA.M. Chew and G.P. 43. H. Suga, Solid State Physics (in Johari, Nature, 275, 524 (1978). Japanese),20, 125 (1985). 54. T Matsuoka, S. Fujita, S. Morishima 44. X. Su, L. Lianos, YR. Shen and G.A. and S. Mae, J. Appl. Phys., 81, 2344 Somorjai, Phys. Rev. Lett., 80, 153 (1977). (1988). 55. T Matsuoka, S. Mae, H Fukazawa, S. 45. M.J. Iedema, M.J. Dresser, D.L. Fujita and O. Watanabe, Geophys. Res. Doering, 1.B. Rowland, W.P. Hess, A.A. Lett., 25, 1573 (1998). Tsekouras and J.P. Cowin, J. Phys. Chern. E, 102,9203 (1988).

Editor's comment: To better understand the arguments on the new phase transition of ice proposed in this paper, it is recommended to consider also the reviewer's comment: "It seems highly unlikely that protons could order at temperatures as high as 237 K. The Bjerrum defect mobility even in the purest ice would prevent ordering to happen. If, on the other hand, proton ordered ice would be the thermodynamically stable phase below 237 K, the proton mobility is certainly high enough that ordering should occur easily on laboratory time-scales. The anomaly at 237 K thus is very unlikely to originate in proton ordering."