Structure and spectra of H2O in hydrated β-aluminaa)

Structure and spectra of H2O in hydrated βalumina@fa@f)J. B. Bates, N. J. Dudney, G. M. Brown, J. C. Wang, and R. Frech Citation: J. Chem. Phys. 77, 4838 (1982); doi: 10.1063/1.443725 View online: http://dx.doi.org/10.1063/1.443725 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v77/i10 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Structure and spectra of H20 in hydrated p-alumina8)

J. B. Bates,b) N. J. Dudney,b) G. M. Brown,e) J. C. Wang,b) and R. Frechd)

Solid State and Chemistry Divisions, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 (Received 1 June 1982; accepted 29 July 1982)

!he structure a~d spectra of hydrated Li and Na p-alumina were investigated using neutron diffraction, Infrared absorption, and Raman scattering. The dimensions of the hexagonal unit cell of a hydrated Li Palumina crystal containing 1.55 H20 molecules per unit cell are a = 5.591 A and c = 22.715 A. The oxygen atoms of the water molecules are located in the conduction plane between the mO, and the aBR sites; the protons, located above the below the plane, form bent hydrogen bonds with the 0(4) oxygen ions. The HOH ~nd angle of water in Li p-alumina is 114' and the IO-HI bond distance is 0.992 A. Based on polarized Infrared spectra, H20 adopts a similar structure and orientation in Na P -alumina. Spectra of absorbed HP, 0 20: and HI>? species show that water molecules dissociate in Li p-alumina to form OH- and H(H20): Species. No eVidence was found for the dissociation of water in Na p-alumina. The absorption coefficients determined for OH- and Hp in Lip-alumina include local field corrections. A large local field anisotropy at the protons of H20 is responsible for the large ratio of the intensities of v 3 and v I observed for water in Li and Na P -alumina.

I. INTRODUCTION

The reaction of water with {3-alumina is a potentially serious problem in the application of this material as a solid electrolyte in the sodium-sulfur battery. The results of experiments conducted over the last decade suggest that water diffuses into the conduction layers of Na {3-alumina and causes a marked decrease in conductivity and a degradation of mechanical strength (see citations in Refs. 1 and 2). Until recently, the nature of the hydration reaction of {3-alumina and the properties of the hydrated compounds were largely unknown. Our initial investigations of the reaction of water with single crystals of Na1_xLix {3-alumina (O:::ox:::o 0.9) using infrared and Raman techniques provided additional evidence that H20 molecules diffuse into the conduction layers and form strong electrostatic bonds with the mobile cations.1

In more recent studies, we have investigated the kinetics and thermodynamics of the reaction of water with Na and Li {:l-alumina and the effect of absorbed water on the ionic conductivities of these materials. Since these investigations rely on infrared absorption spectroscopy as a quantitative analytical tool, it is essential to understand the structure and vibrational spectra of H20 in hydrated {3-aluminas.

Most of our studies have been made on Li {3-alumina because it absorbs larger quantities of water and reacts with H20 at a much greater rate than does Na {3-alumina. In this paper we will: (i) describe the structure of hydrated Li {3-alumina determined by neutron crystallography, (ii) analyze the infrared and Raman spectra of hydrogen and deuterium species in Li {3-alumina, and (iii) discuss the experiments and calculations undertaken to determine the absorption coefficients of H20 and OHin Li {3-alumina, including the corrections for local

alResearch sponsored by the Division of Materials Science, U. S. Department of Energy, under contract W-7405-eng-26 with Union Carbide Corporation.

blSolid State Division. clChemistry Division. dlDepartment of Chemistry, University of Oklahoma, Norman,

Oklahoma.

fields. The infrared spectra of H20 in Na {3-alumina will also be discussed. The thermodynamics of the reaction of Li and Na l3-alumina with water are described in the following paper. 2

II. EXPERIMENTAL PROCEDURES

A. Sample preparation

Single crystals of Na {3-alumina were cut from a large boule obtained from Union Carbide Crystal Products DiviSion. Based on repeated measurements of the weight change as a result of ion exchange, the composition of this boule was determined to be 1. 19N~O . llA120 3• Specimens for the infrared measurements using unpolarized light were cut as discs measuring 5 mm in diameter and 0.5 to 1 mm in thickness, with the c axis perpendicular to the base of the disc. Crystals for the neutron diffraction and Raman measurements were cut as rectangular parallelepipeds. The edges of the Raman specimens were polished using 10 j.J. alumina powder. Li {3-alumina samples were prepared from these various specimens using a two-step ion exchange process (Na - Ag - Li) described previously.1 Two crystals for the infrared polarization measurements were cut from the parent boule such that one large face contained the crystallographic c axis. These faces required polishing since they are perpendicular to

the natural (001) cleavage plane. One crystal about 4 mm thick was used for the polarization measurement on H20 in Na {3-alumina. Another large crystal about 8 x 3 x 2 mm thick was treated several times in LiN03 to a constant weight corresponding to 7CfYo exchange of Na+. The intermediate treatments of this crystal in AgN03

were avoided to minimize the risk of delamination. Eventually a small section of the crystal separated from the main piece, and this small crystal was reexchanged to Na {3-alumina and then to 10CfYo Li {3-alumina using the two-step process.

The crystals of Li {3-alumina were treated under various conditions of water vapor pressure and temperature depending on the equilibrium concentration of H20 required for a particular measurement. Crystals containing high

4838 J. Chern. Phys. 77(10),15 Nov. 1982 021-9606/82/224838-19$02.10 © 1982 American Institute of Physics


Bates et al.: H20 in hydrated t3-alumina 4839

concentrations of water (~ 1. 5 H20 per unit cell) were prepared for the neutron diffraction and Raman scattering measurements by heating the specimens at 235°C in aboutBO kPa of H20 for over 200 h. Hydrated crystals containing relatively low concentrations of water (0.005 to 0.5 per unit cell) were prepared for the infrared measurements under conditions in which the water vapor pressure (PH20 ) could be carefully controlled by saturating flowing N2 with water contained in a constant temperature bath. With this technique a homogeneous distribution of H20 could be achieved at low concentrations by proper selection of PH20 and treatment temperature. Crystals containing Hoo were prepared by treatment in mixtures of 9:1 H20:DP and 9:1 D20:H20. Because of their much slower rate of reaction with water, crystals of Na j3-alumina were treated for periods as long as 800 h at 235°C in 80 kPa of H20. Even after this extended treatment, the equilibrium concentration of water had not been reached; the average concentration was about O. 3 molecules per unit cell. By contrast, an equilibrium concentration of about 1. 7 H20 molecules per unit cell was reached in a Li j3-alumina crystal of comparable size after about 200 h of treatment under the same conditions.

The total water content of various hydrated samples was determined from weight-change measurements using a Cahn 2000 electrobalance. The weight of one or more crystals was measured before and after the hydration reactions and after dehydration of the samples in flowing N2. The weight measurements were accompanied by infrared measurements of each specimen so that a correlation of absorption intensities and total H20 concentration could be made.

B. Neutron diffraction measurements and data analysis

The specimen of hydrated Li j3-alumina used in the neutron diffraction experiments had the dimensions O. 46x2. 6x3. 0 mm and weighed 11.2 mg. It was found by preliminary x-ray precession photography to be a single crystal of good quality displaying the Laue symmetry P6/mmm, corresponding to the expected space group, P63/mmc.

The neutron-diffraction data, comprising one complete set of independent reflections, were collected by the 8 - 28 step-scan method to a 28 limit of 1300 (A = 1. 0153 .A) using the computer-controlled diffractometer at the Oak Ridge High Flux Isotope Reactor. The indices of the 756 independent reflections recorded were chosen so that their reflection vectors were scattered randomly in the 24 equivalent solid angles of the limiting sphere of reflection for the space group P63/mmc. This unusual procedure was adopted so that later in the leastsquares refinement reliable anisotropiC extinction corrections could be made without having to record (at great expense of time) a number of different complete sets of independent data. In the preliminary processing of the data, absorption corrections were applied, based on an absorption coefficient 0.415 cm-1 calculated for the composition 1. 19 Li20· llA120 3 ' 2H20. The absorption calculation also provided the mean path lengths needed later in the calculation of extinction corrections.

For use in least-squares refinement the standard errors of the observations were calculated by the equation

( 1)

where Fo is the observed structure factor, a!(F~) is the variance from counting statistics, and the second term on the right is an empirical addition to make some allowance for deficiencies in the model and for instability in the generator and counter circuitry.

The analysis of the data was started using the fractional coordinates of the isomorphous Na j3-alumina (furnished by Reidinger3) for all of the atoms except Li and the atoms of the water molecule. The nuclear scattering lengths used in the calculations were taken from a compilation of Shu1l4: 0, 0.5803; AI, 0.3449; H, - 0.374; and Li, - O. 214, in units of 10-12 cm. Using standard Fourier, difference-map, and leastsquares methods, we have been able to locate water in the structure with some confidence. However, we have not been able to place the lithium ions, presumably because of their small scattering power and diffuse distribution.

In the course of the analysis peaks were found that could be interpreted as representing the hydrogen and oxygen atoms of a water molecule in threefold disorder about the line OOz, with the fractional oxygen atoms O(w) in 6-h-mm sites and the fractional hydrogen atoms H in 12-j-m sites. Subsequently these atoms were included in a least-squares refinement in which coordinates, thermal parameters, and occupancy factors were adjusted. Initially, when the Hand O(w) occupancy factors were independently adjusted, their values were found to be identical within experimental error, indicating about 1. 5 water molecules per cell. Accordingly, the two occupancies were constrained to be equal in the final refinement cycles. The original corrections for absorption were modified to correspond to 1. 54 molecules of H20 per cell instead of the 2.0 molecules originally assumed.

At an advanced stage of the analysis all atomic occupancies were adjusted while the scale factor was held fixed. Apart from the atoms of the water molecule, the only atoms for which there were significant indications of occupancies other than unity were AI(1) and AI(3i), the so-called interstitial aluminum. 3.5 The occupancies of these two atoms summed to untiy within experimental error. Subsequently they were constrained to sum to unity, and the other occupancies except those of water were fixed at unity.

The discrepancy index R(F) for the 674 reflections included in the final refinement was 0.060, and the standard deviation of an observation of unit weight is 1. 75. Reflections were rejected if F~ < O'(F~) and F~ > a(F~). The measures of agreement are poorer than usually attained for neutron data from a hard crystal. This is consistent with the fact that a final partial difference Fourier map, which for the atoms included in the calculations should show only the H, O(w), and AI(3i) peaks, has background features of height almost comparable to the heights of the expected peaks.

J. Chern. Phys., Vol. 77, No. 10, 15 November 1982


4840 Batesetal.: ~O in hydratedJ3-alumina

The final partial difference map shows significant positive density at the 4/ (Beevers-Ross) site, t, t, ~, which may indicate that there is more H20 present in the structure than accounted for in this analysis. Also, there is significant positive density at the 0(5) sites, suggesting that the 0(5) thermal motion is not described quite satisfactorily. There are volume elements of negative density here and there, some of which may correspond to the presence of lithium (a negative scatterer).

Part of the "noise" in the partial difference map may be the result of residual effects of extinction not taken care of by the Type I anisotropic extinction corrections6

applied. Experience suggests, however, that the extinction effects are minimal. Thus, only 17 reflections are calculated to have had their intensities reduced by more than 1~, four more than 20%, and two more than 30%. The greatest reduction was 36% (for reflection 002).

C. Infrared and Raman measurements

Infrared spectra were measured with an FTS-20 Fourier transform spectrometer. In this instrument, the interferometer, sample compartment, and detector are enclosed in a vacuum box which is evacuated to about 1 kPa pressure during a measurement. Typically 400 to 800 single beam interferograms of the sample were collected, and reference interferograms were collected under identical conditions without the sample. Using the transformed single beam sample and reference spectra, the data could be plotted as percent transmittance, absorbance, or as reciprocal extinction length (absorbance/sample thickness). Taking into account the degradation of resolution resulting from triangular apodization of the interferograms, the resolution was about 2 cm- t for spectra measured at 77 K and about 6 cm- t for the room temperature measurements.

For the infrared measurements at room temperature, the samples were placed in a 4x beam condenser. Circular masks were used to allow the incident light to pass only through regions of O. 5, 1. 0, 2.0, or 4.0 mmdiam. from the center of a sample. The homogeneity of the H20 distribution could be checked by comparing the spectra measured with different masks. Measurements at 77 K were made with the samples placed over a 2 mm aperture on the cold finger of a liquid nitrogen cryostat. The transmission-type polarizer consisted of a gold wire grid on a AgBr substrate.

Polarized Raman spectra were measured using the computer-controlled spectrometer and techniques described previously. t. 7 Either the 476.5 or the 514.5 nm line from an argon ion laser, operating at 800 mW, was the excitation source. The choice of exciting line wavelength was dictated by the need to avoid interference due to luminescence from Cra. in the samples. Measurements at low temperatures were made by COOling the samples using a closed cycle refrigerator. The sample temperature, nominally between 40 and 50 K, was determined by the Stokes/anti-Stokes intenSity ratio of the 112 cm- t phonon line of Li j9-alumina. The resolution for the 300 K and low-temperature mea-

surements was about 5 cm-t • The scattering geometry is described using the orthogonal coordinates a, a' and c, where c is coincident with the crystal c axis.

III. RESULTS AND DISCUSSION

A. Structure and composition

The structure of Na {:l-alumina was first solved by Peters et al. 8 from x-ray diffraction data. It has the symmetry of the hexagonal space group P63/mmc (D~,,) and consists of densely packed layers of aluminum and oxygen ions having a spinel-like structure separated by loosely packed planes which contain the Na- ions and bridging O' ions. The structure of other alkali-metal {:l-aluminas are isomorphous with that of the sodium compound, with small differences occurring in the distribution of ions on the Beevers-Ross (BR), antiBeevers-Ross (aBR), and mid-oxygen (mO) sites. The locations of the Lr ions in anhydrous Li {:l-alumina are not well determined, but from preliminary analysis of recently obtained neutron diffraction data, we find an indication that some of the ions are located about 1 A above and below the BR sites.

The structural parameters and composition of the hydrated Li (:l-alumina crystal are summarized in Table I(A). The unit-cell dimenSions, determined by the method of least squares from angle data of 12 carefully centered reflections in the 28 range 53_101°, are: a = b = 5. 591(± 0.001) A and c = 22. 715(± 0.004) A. A comparison with the cell parameters determined for the same crystal after dehydration in flowing N2 at 400°C, a = 5. 594 (± 0.001) A and c = 22. 556 (± 0.004) A, shows that the water at a concentration of about 1. 55 molecules per unit cell causes a nearly O. 7% expansion along the c direction but essentially no change in the a direction. The position, occupation, and thermal parameters of the atoms of the hydrated crystal, determined from the least-squares refinement, are listed in Table I(B). The apparent number of interstitial aluminum atoms denoted by Al(3i), 12xO. 083= 1. 0 per unit cell, is much larger than that expected from the known compOSition. If there are approximately 0.2 excess O' ions per unit cell and if two Al(3i) atoms are required for each compensating O· ion to form the V A1Al(3i)-0-Al(3i) VAL defect,5 then we expect no more than 0.4 AI(3i) per unit cell. This would give an occupancy factor of 0.967 for the AI(l) atoms rather than the value of O. 917 determined in the refinement.

Potential energy calculations9 as well as the diffraction data mentioned above indicate that at least some of the Li- ions in anhydrous Li j9-alumina are about 1 A above and below the BR sites. It is of interest, therefore, that the final difference Fourier map of the hydrated sample has small negative peaks about O. 5 A above and below the BR sites that might be due to Liions. However, the peaks could also be due to noise.

A perspective drawing of H20 and the surrounding ions of the host lattice is given in Fig. 1. The water molecules in Li {:l-alumina are disordered, and the dotted outline in Fig. 1 shows the three equivalent pOSitions around the aBR site which a molecule can occupy. The

J. Chern. Phys., Vol. 77, No. 10,15 November 1982


Bates et al.: ~ 0 in hydrated l3-alumina 4841

TABLE I. Results of neutron diffraction analysis of hydrated Li ,6-alumina.

(A) Structural parameters

a = 5.591(1) A <HOH=114° d[0(4) ···HI=1.671 A

c= 22.715(4) A d[O-H] =0. 992 A d[0(4)" ·0(w)]=2.623 A

space group: P63/mmc <0(4) ···H-0=159.3"

1. 55 (± O. 4) H20 per unit cell

(B) Positional, occupancy, and thermal parameters with estimated standard errors. a

Equlvalentb Occupancy Fractional coordinatesC Thermal parametersd

positions factor " z /3 11 ,622 ,633 f323

0(11 12 k m 1.0 0.15731(10) 0.04964(4) 0.0064(2) 0.0040(3) 0.00028(1) - O. 000 07(5) 0(2) 12 k m 1.0 0.50290(14) 0.14609(4) 0.0050(2) 0.0065(3) 0.00055(1) -0.00019(6) 0(3) 4 f 3m 1.0 2/3 0.05486(8) 0.0049(3) ,611 0.00023(2) 0.0 0(4) 4 e 3m 1.0 0.0 0.14166(7) 0.0043(3) /311 0.00029(2) 0.0 A I (1) 12 k m 0.917(5)' 0.83170(20) 0.10488(6) 0.0056(4) 0.0039(5) 0.00028(2) - O. 000 08(9) Al(2) 4 f 3m 1.0 1/3 0.02443(11) 0.0038(5) 0.0038 0.00023(3) 0.0 Al(3) 4 f 3m 1.0 1/3 0.17549(14) 0.0101(6) /311 0.00016(3) 0.0 Al(4) 2 a 3m 1.0 0.0 0.0 0.0049(7) f3 11 0.00016(4) 0.0 Al(3i) 12 k m 0.08a' 0.8429(22) 0.1747(8) 0.0056' 0.0039' 0.00028' - O. 000 08' 0(5) 6 h mm 1/3 0.2980(13) 1/4 0.046(4) 0.060(9) 0.00021(5) 0.0 O(w) 6 h mm 0.258(3)11 0.9075(25) 1/4 0.081(8) 0.109(16) 0.00020(9) 0.0 H 12 k m 0.258' 0.963(11) 0.2134(6) 0.109(27) 0.19(10) 0.0013(2) -0.005(4) Li 4 f 3m no value 1/3h 0.22~

astandard errors are given by the numbers in parentheses, whose digits correspond to the least significant digits in the cor-responding parameters. No errors are given for fixed or dependent parameters.

J>rhis composite column gives the number of positions, the Wyckoff notation, and the point symmetry. cFor every atom y = 2x. dThe temperature factor is of the form exp(-h2/311 -k2/322 _l2/333 - 2hk(:l12- 2hl/313 - 2kl(3 23 ). For each atom, /3 12 = 1/2,622 and ,613 = 1/2,623'

'The sum of occupancy factors for Al(l) and Al(3i) was constrained to be unity. 'Each thermal parameter of A1(i) was constrained bo be equal to the corresponding one of Al(lI. liThe occupancy factors of O(w) and H were constrained to be equal. hpossible position parameters from a difference map.

water oxygen atom is located in the conduction plane between the aBR and mO sites (0. 72 A from the mO site), while the protons are located above and below the plane. The line between the protons is parallel to the c axis and intersects the conduction plane at a point about 0.36 A from the aBR site. The protons from bent hydrogen bonds with the 0(4) oxygen ions which are located directly above and below the :lBR site. The intramolecular O-H distance of 0.992 A is typical for water in a solid,10 but the HOH angle of 114° is larger than the typical value of 109° observed in hydrates. 10 (The gas phase value l1 is 104.5°.)

The schematic drawing of the conduction plane in Fig. 2 shows several possible arrangements of H20 molecules and single and paired Li+ ions. The radius of the H20 molecule was taken to be the same as that of the O· ions (1. 4 A) •. If all of the available sites for water were filled, there would be two H20 molecules per unit cell. If the excess Li+ ions are compensated by extra 0= ions in the conduction layer as suggested by Roth et al. ,5 then there are about O. 2 O· ions per cell which we assume to be located near the same position occupied by H20. Thus the maximum number of H20 molecules in the unit cell would be 1.8. Concentrations as high as 1. 7 H20 per unit cell have been detected from weight-change measurements of Li fJ-

alumina equilibrated in water vapor at 235°C, and we believe that 1. 8 H20 per unit cell is a reasonable value for the saturation limit.

Although the predominant H20 species in hydrated Li fJ-alumina are oriented as shown in Fig. 1, we estimate from the infrared spectra described below that, for a water concentration of about O. 2 molecules per unit cell, about 3% of the molecules have their molecular planes parallel to the conduction plane. In addition, an appreciable fraction of the water molecules dissociate to produce OH- ions and H(H20): ions. The residual positive denSity seen in the difference Fourier maps could be due to the oxygen atoms of these other protoncontaining species and to the excess O· ions which were not included in the refinement procedure.

B. Infrared and Raman spectra

1. General features

Examples of the infrared absorption spectra of Li and Na fJ-alumina single crystals recorded before and after treatment in water vapor are compared in Fig. 3. The disc-shaped samples were heated at 235°C in about 80 kPa of H20, and measurements were made at room temperature immediately following treatment for the times specified in the figure. The electric field of the



4842 Bates et at.: ~ 0 in hydrated J3-alumina

Ill)

All

BR

05r---------~~ __ ~

Ib) FIG. 1. Perspective drawing of hydrated Li {3-alumina. (a) Portion of a unit cell showing H20 molecules in the conduction plane. The position of the Li' ion is schematic. (b) Detailed structure of H20 and surrounding ions. The dotted outlines represent the two other equivalent positions a water molecule may occupy.

incident unpolarized radiation was perpendicular to the c axis. The absorption intensities in Fig. 3 are given in units of reciprocal extinction length, which is proportional to concentration. The major absorption bands near 3175 cm-I , as shown below, are due to the VI sym-

metric stretching vibration of H20 molecules with the orientation shown in Fig. 1. The fact that these bands appear in the spectrum of as-prepared crystals of Li i3-alumina (0 h curve) with a larger intensity than found in the parent sodium compound shows that water is absorbed from the molten salt during ion exchange. I By comparing the two sets of curves in Fig. 3, it is apparent that Li i3-alumina absorbs water much more rapidly than does Na i3-alumina. Moreover, a crystal of L i 13 -alumina saturated with water at 235°C contained about 1. 7 molecules per unit cell whereas a crystal of Na i3-alumina treated Similarly for over 800 h contained only about O. 2 molecules per unit cell. 12 The spectrum observed after treating Li (:3-alumina for 10 h corresponds to about O. 3 molecules per unit cell. It can also be seen in Fig. 3 that the spectra of hydrated Li 13-alumina contain considerably more structure than those of hydrated Na i3-alumina. These differences will be discussed below.

After treatment of Li or Na i3-alumina crystals in water vapor, we occasionally observed the infrared spectrum shown in curve (a) of Fig. 4. This spectrum, obtained after treatment of aNa i3-alumina crystal, is due to absorption by a thin layer of liquid water that is physically trapped between partially delaminated pieces of the crystal. After the initial measurement, the two pieces were separated, and subsequent infrared measurements on each piece showed no evidence of the liquid like absorption. Comparison with the absorption band of chemically bound H20 in Na i3-alumina [curve (b) of Fig. 4] clearly illustrates the difference between the spectra of the trapped liquid layer and absorbed H20.

The absorption spectra of hydrated Li i3-alumina contain far more structure than those of hydrated Na 13-alumina. The complexity of the former is demonstrated by the low temperature measurements shown in Fig. 5. In addition to the major feature due to H20, the spectrum of hydrated Li i3-alumina [Fig. 5(a)] also contains peaks above 3350 cm- I that are attributed to OW ions and bands below 2700 cm-I that are attributed to H30' and H50i species. The OH- and H(H20)~ ions are produced as a

consequence of the dissociation of H20 in the crystal, H20 - W + OH-. The H' ions either bind with 0= ions of the host lattice to form additional OH- groups, or they combine with H20 molecules to form H(H20)~ species. These reactions are discussed in Ref. 2. By contrast only the bands attributed to H20 have been observed in spectra of hydrated Na i3-alumina measured at room temperature or below. Understanding the spectra of hydrated Li i3-alumina is further complicated by the variations that result from different treatment conditions. Namely, the peak positions of several infrared and Raman features shift, and new features appear with changes in the concentration of water and with prolonged treatment. Therefore, caution must be exercised in comparing spectra of samples with widely different water concentrations and/or treatment histories.

2. Assignments

To assist in the analysis of the infrared and Raman spectra discussed in this section, sets of these spectra

J. Chem. Phys., Vol. 77, No. 10,15 November 1982


Bates et al.: H20 in hydrated (3-alumina 4843

Li f3-ALUMINA

.O'IO(S)I aBR

• • FIG. 2. Schematic drawing of the conduction plane illustrating possible arrangements of single and paired Li- ions near H20 molecules. The water molecule was drawn with the same radius as the 0(5) oxygen ions.

• The Beevers-Ross (BR), mid-oxygen (mO) and antiBeevers-Ross (aBR) sites are indicated. The dashed circles illustrate the positions of the 0(2) and 0(4) oxygen ions above and below the conduction plane.

were resolved by fitting the observed contours to the function a+ bll+ ~FI(II), where a and b are constants which describe the background, and F j (lI) is a Lorentzian peak. Recognizing the inherent pitfalls in such a procedure, we used only the number of Lorentzian components that corresponded to clearly defined peaks or shoulders. An example of a fitted contour and individual components is given in Fig. 6. The fitted values of peak position (II), full-width at half-peak maximum (6) and peak amplitude (A) for the various hydrated crystals are listed in Table II. The area under a peak is given by the product 1. 57A6.

In order to simplify the nomenclature describing the hydrated crystals, we adopt the abbreviations Lit!· nH20, Lit!· nD20, etc., where Lit! = 1. 19Li20· llAl20 3• The hydration number n (number of H20 per unit cell) is specified for each type of sample in Table II and the figure captions. In many instances we refer to the spectral features of either the protonated or the deuterated species and include parenthetically the results for the corresponding features of the other isotope, where such a correspondence is obvious. Since the widths of the infrared and Raman peaks of the deuterated species are as much as two times smaller than those of their proton counterparts, the spectra of the deuterated compounds are better resolved.

a. OH-. The sharp peaks above 2500 cm- t in the Lit!· D20 spectra (Fig. 5) are assigned to OD- ions based

on the observation that these features did not shift position in the spectra of Lit!. nHDO (Table II). By correspondence the sharp peaks above 3400 cm- t in the Lit!· nH20 spectra are attributed to OH- ions. For example, as illustrated in Fig. 7, the peaks at 2608 and 2534 cm- t in the spectrum of Lit!· nD20 occur at the same position in the Lit!. nHDO spectrum. However, the stronger peaks at 2352 and 2247 cm- t of Lit!· nD20 shift to higher wave numbers in the spectrum of Lit!· nHDO. In general, a shift of the OH(OD) stretching frequencies usually occurs after partial isotope exchange of molecules containing two or more protons as a result of coupling among the proton displacements in the normal modes. For example, the stretching frequencies of HDO usually occur about midway between the symmetric (lit) and antisymmetric (113) stretching frequencies of the respective H20 and D20 molecules.t3 The absence of a frequency shift after partial deuteration in a peak known to be due to vibration of a proton is strong evidence that the molecule in question contains a single proton.

In the infrared spectra presented here, we aSSign seven peaks to OH- ions. These are numbered in Table II. Not all of these peaks are observed in the same spectrum, and in fact we attribute four of them (3-7) to two types of OH- whose frequencies depend on the total H20 concentration. The weak peak at 3629 (2678) cm- t [curve (a) of Fig. 8] was observed only in the Eo II c spectrum indicating that the O-H bond is



Bates et at.: H20 in hydrated Jl-alumina

5 f---- __ 22_2~

____ ~o~

o ~----~----~------~----~ 4000 3500 3000 2500 2000

WAVE NUMBER (em-')

FIG. 3. Absorption spectra of single crystal Li and Na~alumina measured at 25·C with Eolo before and following treatment in 80 kPa H20 at 235°C for the specified times. Ordinate in units of reciprocal extinction length.

parallel to the c axis. The high frequency and narrow width of this feature compared to the others suggest that the OH- ion in question is only weakly coupled to the surrounding lattice. The broader peak at 3596 (2659) cm -1 is observed predominantly for Eo 11 c. A very weak peak at this position can also be seen in the Eo 1 c spectrum [curve (b) of Fig. 8], but its intensity is so small that the uncertainty in the fitted amplitude is about ± 25%. Assuming equivalent absorption coefficients for all of the OH- ions, we estimate that those giving rise to the 3629 and 3596 cm- i peaks amount to less than 3% of the total number of hydroxyl species in Lil3 . nH20.

The OH- ions which produce infrared peaks 3-7 constitute the bulk of these species in Lil3 . nH20. Peaks 3 and 4 are attributed to one type of OH- whose stretching frequency increases smoothly from 3514 to 3537 cm-i

as the water concentration increases from "'0.005 to "'0.5 molecules per unit cell. This change with H20 concentration can be seen by comparing curves (b) and (d) of Fig_ 8. Likewise, we believe that peaks 5 (3472 cm- i )

and 6 (3438 cm- i ) are due to one type of OH- ion. Peak 7 (3415 cm- i

) is not observed in initially hydrated samples, but it develops slowly with increasing treatment time. This behavior is discussed in detail in the following paper. 2 The position of peak 7 does not change Significantly with the total water concentration. The positions of peaks 3-7 shift with changes in sample temperature. When the sample temperature is lowered from 300 to 77 K, peak 4 moves downward by about 5 cm-1, peaks 5 and 6 move downward by about 10 cm-t, but peak 7 shifts upward by about 10 cm-1• As illustrated by curves (b) and (c) in Fig. 8, the proximity of peaks 6 and 7 at low water concentrations (n '" 0.005) and their opposite shifts with temperature causes them to nearly coalesce at 77 K. This effect is more pronounced for OD-: at 300 K two overlapping peaks are evident in the spectrum and are resolved into components at 2553 and 2527 cm-1 (Table II). At 77 K only a single symmetric peak is seen at 2541 cm-!, the midpoint of the two components at 300 K. At high H20 concentrations (n'" O. 5), peaks 5 and 7 are sufficiently separated to be well resolved at 77 K [Fig. 5 and curve (d) of Fig. 8].

t w u z <{ aJ a:: o en aJ <{

4000 3500 3000

WAVE NUMBER (em -1)

2500

FIG. 4. Absorption spectra of a thin layer of water physically trapped between two partially delaminated pieces of a Na/3-alumina crystal, curve (a), and water chemically bound in the conduction plane of Na /3-alumina, curve (b). (Eol. 0).

J. Chem. Phys., Vol. 77, No. 10, 15 November 1982


Bates et al.: H20 in hydrated /3-alumina 4845

Prominent bands due to OH- and on- ions also appear in the Raman spectra of Li{:l' nH20 and Li{:l· nDzO (Fig. 9). Several of these occur near the same positions as the infrared peaks and are therefore attributed to the same type of OH-(On-) ions. Thus peaks 3', 5', and 7' are associated with their infrared counterparts 3, 5, and 7. Although the Raman peak at 3622 (2676) cm- t is close to the weak infrared band seen at 3629 cm- t , its width (6 = 16 cm- t ) is considerably larger than that of the infrared feature (6 = 4 cm-t). Therefore it is not clear that these two features can be ascribed to the same type of ion. Moreover, the strongest of the OH- Raman peaks, which occurs at 3571 (2642) cm- t in a(a' a')c

t w u z

li .a-ALUMINA

T=77K (0) H20

T 0.37

1

~ 3800 3500 3200 2900 2600 2300 2000 a:: o en CD « (b) D20

T 0.25

1

2800 2600 2400 2200 2000 1800 1600 WAVE NUMBER (em -1)

FIG. 5. Absorption spectra of Li,B • O. 6HzO and Li,B' O. 7DzO measured at 77 K with Eo.L o. The inset in (a) shows the spectrum observed at 300 K in the bending mode region of HzO. Sample thickness d = O. 028 cm.

1 w u z ct CD rr: &l CD ct

2700

Li /3·ALUMINA: 020 T= 17K -+ Ele

2500 2300 WAVE NUMBER (em-')

2100

FIG. 6. Examples of a curve resolution of Li,B • O. 3DzO measured at 77 K with Eo.LO [curve (b) of Fig. 71 using Lorentzian functions and a linear background. The solid curve through the data points is the sum of the Lorentzian components. The baseline is moved down for the graphs of the individual components. Sample thickness d = 0.054 cm.

spectrum, was not seen in the infrared data. It is not surprising to find marked differences between the Raman and infrared spectra due to the large differences in H20 concentration; the Raman samples contained about 1. 6 H20 molecules per unit cell (close to the saturation limit) while the highest concentration of water in the infrared samples was =0.6 molecules per unit cell.

The locations of the OH- ions in Li{:l· nHzO are not known precisely, but we speculate that there are two major types of hydroxyl groups. (i) Interstitial OHions which, after formation by dissociation of H20, H20- OIr + H+, remain near the positions formerly occupied by the water molecules. These are denoted by OfW, The protons produced in the dissociation could bond to excess (J' ions to form additional O,W. As a result of hydrogen bonding with 0= ions in the spinel block, we expect that the O-H bond of OfW is located out of the conduction plane. (ii) Bonding of W to 0(5) oxygen ions produces a second type of hydroxyl group which is denoted by OuW. The O-H bond of this species is expected to be parallel to the conduction plane as a result of the symmetric environment of neighboring (J' ions (Fig. O.

The angle between the O-H bonds of the hydroxyl groups and the crystallographic c axis can, in prinCiple, be determined from the infrared polarization measurements. As shown in the Appendix, this angle 8e is given approximately by

(2)

where E:'oc and Etoc are the local electric field components parallel and perpendicular to the c axis, respectively, and A" and A~ are the measured peak amplitudes for the respective polarizations. The local field



4846 Bates et 81.: H20 in hydrated j3-alumina

TABLE II. Summary of results from the curve resolution of the infrared and Raman spectra of hydrated Li and Na.B -alumina. a

Peak positions (v) and bandwidths (6=FWHM) in cm-t • Infrared peak heights (A) in units of absorbance xIOO. Sample thickness din cm. Raman peak heights in counts/so

(1)

(2) (4)

(6)

(A) Infrared (unpolarized, Eo.l C, T = 77 K)

(3)

(4)

(5)

(7)

Li.B ·0.6Hp (d=0.028)

II {, A

OR"

3537 30 61 (3537 35 45)b

3472 50 34 (3466 57 23) 3415 40 134

(3407 58 74)

HP

vt 3168 180 145

"f, II~ 2941 170 50

n = 1

n =2

n = 1

2762 101 15

2577 33 61 2533 113 95 2379 131 41

Eo II c (d' 0.248)

Li.B'O,7DP (d = 0, 028)

II {, A

OD-

2614 20 25

2571 42 16

2535 26 41

2468 78 8

2361 71 69 [2307 92 25]0

2235 78 25

D(D20)~

2114 27 6 2091 49 7 1975 15 9 1962 32 14

Li.B '0,3 DP (d=0.054)

II I> A

OD-

2608 20 31

2534 42 16

2463 57 14

2352 73 90

2247 77 47

(B) Infrared (polarized, 77 K)

Li.B • O. 005 H20 Li.B·O,007 Dp Li.B '10-3 HDO ([H20] ~ O. 005) Li.B ·0.005Hp

II {, A

OW

3629 4 10 3596 51 28 3514 31 96

v {, A

OD-

2678 3.4 8 2659 29 27 2603 23 71

[3272 295 88] 2438 80 69

(3176 209 180) (2398 112 129) 3151 105 71 2363 60 92

II {, A

OD-

2657 3.3 4.5

2603 30 18

HDO

(2380 108 37) (11) 2361 51 59

II {, A

OW

[3592 36 410

3513 26 13 (3522 67 14)b 3438 47 25

(3449 75 16) 3416 26 25

(3408) 53 25

3257 151 9 (3179 222 16)

3H8 116 20 2972 199 1(i

N~ '0.01 H,O (300 K) (<I ~ O. 371)

Eollc

Ii A " A

v~ :127:1 121< 8:\ v~ 1:1235 197 51 "~ :1l5(i 159 15R "'I 1:1121< 17H 71

Li/3 'HDO [(H20]=0.3) (d=0.054)

II {, A

OD-

2608 21 5

2535 32 2

HDO

[2455 58 2.3] [2401 72 3]

('1) 2366 50 10

(II~) 2253 62 8

N~·O.OIHp

(d=0.040)

II {, A

Hp

3244 87 11 (3237 131 17) 3122 79 38

(3135 205 37) 3059 178 23

(2907 181 3)

Li.B • O. 007 D20 Li/3 '10-3 HDO ([HP] = 0, 005)

II {, A II {, A

OD-

[2662 28 5] 2602 30 18

(2608 35 10)

(2553 41 35) 2541 36 9

(2527 31 23)

2445 110 12 (2380 126 10)

2:153 65 2:1 2255 73 R

OD-

2603 17 3

2541 36 9

HDO

(,,~) 2435 67 1. 5

(11) 23GO 53 5.4

(11) 2255 61 2.6



Bates et al.: H20 in hydrated ~-alumina 4847

TABLE II (Continued)

(e) Polarized Raman spectra (50 K)

ala 'a 'le a(ca)c a(cc)a'

LiP '1.6 H2O LiP '1.6 Dp LiP '1.6 H2O LiP '1.6 D20 LiP '1.6 H2O LUi·1.6Dp

V Ii A v Ii A v Ii A v Ii A v () A v Ii A

OW OD- OR" OD- OW OD-

3622 16 178 2676 15 119 3622 16 66 3622 21 743 3571 40 398 2642 25 333 3567 37 90

(3') 2614 10 37 3544 53 54 2626 38 111 3555 45 556 2627 41 47-1

(5') 3472 42 97 3473 52 110 2573 50 94 2563 49 110

3445 32 70 (7') 3409 74 226 2529 40 49

H2O DzO HzO H2O DzO

3388 132 148 3380 125 2316 I{ 3246 104 360 [2434 38 3661°

vf 3212 191 121 3204 104 6674

vt 3178 152 642 2382 123 896

t1 3116 113 87 2356 125 515 3117 170 6274 2351 124 ()280 vf. vf 2947 177 127 2228 127 177

H(HzO)~ D(D20)~

n =1 2740 57 38 2102 49 386 n =2 2572 64 326 1972 26 643

"Standard deviations u of the fitted parameters for the infrared data were estimated from analysis of four crystals treated under identical conditions. For medium to strong features, a{v) "=' o. 02%, u(6) "=' 2% and u (A) "='8%. For weak and strongly overlapped features, a{v) "" o. 05%, u(6) "" 5%, and u(A) "" 10%. Uncertain assignments are indicated by (?).

bparameters enclosed in brackets correspond to features appearing as shoulders or to very weak components. CParameters enclosed in parentheses from fit of 300 K data.

anisotropy E~oc/El~OC is appreciable in Fl-alumina and depends on the location at which the fields are calculated. 14

For example, for d[ O-H]= O. 992 A and 9c = 45°, (E~oc/Etoc)2 at the proton varies from 2.34 to 3.64 as the oxygen is moved from the mO 'site to the O(w) position. Therefore, as can be seen from Eq. (2), ignoring the local field correction will lead to errors in 9 c' For example, if the dichroic ratio AII/2A~ = 2. 8 (a value close to those observed for O;H-), then at the O(w) site, including the local field correction in Eq. (2) gives 9c = 48°, whereas assuming (E~oc/Etoc)2 = 1 gives 9c= 31°.

Using the procedures outlined in the Appendix, dichroic ratios were calculated for a range of assumed pOSitions of the oxygen and hydrogen atoms for d [O-H] = O. 992 A. At each oxygen position, the ratios were calculated at 2° intervals of 9c from 65 to 25°C. By interpolation we obtained the value of 9c which gives a calculated ratio equal to the observed ratio. The observed dichroic ratios were taken as the average values from several sets of fitted data for Li/3 ·nH20 and LiJ1· nD20. From measurements at 300 K, the average observed ratios are 2.78 for peak 2 and 2.81 for peak 4. Both values give 9c = 48° for oxygen at the O(w) poSition and 9c = 40° for oxygen at the mO pOSition.

In order to test the validity of 9c determined above, we calculated the electrostatic potential energy for various orientations of the OH- ion at the O(w) site. The methods employed to calculate the electric fields and induced dipole moments on the ions in the lattice were

described elsewhere. 15.16 The potential energy due to these charges and induced dipoles of the lattice ions was calculated for various orientations of OH-, assuming that the oxygen atom remains fixed at the O(w) site and that d [OH]= O. 99 A. The minimum energy occurs for 9 c = 50° with the O-H bond pointing toward a point on the line between the aBR site and the 0(4) oxygen ion. The calculated angle is in good agreement with the value of 48° determined from the dichroic ratio. Given this result, we assign peaks 2 and 4 to interstitial O;H- ions located near the O(W) site with their O-H bonds tilted out of the conduction plane by about 42° and with their protons hydrogen bonded to the 0(4) oxygen ions. The difference in stretching frequencies of these ions could be due to a difference in local coordination from single and paired alkali ions or to a small difference in R o_o•

The dichrOic ratios for peaks 6 and 7 are close to zero (Table II and Fig. 8). IT the O-H bond is parallel to the conduction plane, then All should be zero. The small value of All observed can easily be attributed to a slight misalignment of the crystal. We therefore asSign peaks 6 and 7 to hydroxyl ions which lie in the conduction plane. A reasonable assumption is that one or both of these ions is of the 0.,11" type described above. To test this assumption the electrostatic potential energy for a proton bound to an O( 5) oxygen ion was calculated for various orientations of the proton. The calculated minimum energy occurs when the proton is in the conduction plane and the O-H bond lies on the line between



4848 Bateset 81.: H2 0 in hydrated ~·alumina

the 0(5) oxygen ion and the aBR site, placing the proton in a symmetric environment of oxygen ions. The intense Raman peak at 3571 (2642) cm-1 was observed for a(a' a')c scattering only implying that the O-H bond of this species also lies in the conduction plane.

Hayes et ai. 17 have reported measurements of the infrared spectra of hydrogen ~-alumina at 77 K. They aSSigned peaks observed at 3548 and 3510 cm-1 to OHspecies which we calIO.,H-, i. e., hydrogen attached to the 0(5) oxygen ion. Bands observed at 3430 and 3385 cm-1 were attributed to O.,H- species perturbed by hydrogen bonding to H20. There is no certain correlation between these features and the OH- peaks we report.

f w u z « !Il 0:: o (f) !Il «

Li .a-ALUMINA

f 0.09

i

020( 77 K)

f 0.16

!

f 0.04

i

020(300 K)

(0)

HOO(77K)

2800 2600 2400 2200 2000 WAVE NUMBER (em-I)

FIG. 7. Absorption spectra of LIP ·0.3D20 measured at 300 K, curve (aI, and at 77 K, curve (b): (c) spectrum of LiP 'H~ containing 10% UOO measured at 77 K. Eo.!.C in each case. Sample thickness d=0.054 cm.

I w U z « CD 0:: o

(a)

~ (b) «

(e)

(d)

3700 3600 3500 3400 WAVE NUMBER (cm- 1 )

FIG. 8. Absorption spectra in the OH- region of hydrated LiJ:Ialumina. (a) LIP '0.005 H20 with Eo II c measured at 77 Ki (bl same crystal with Eo.!.c measured at 77 K, and (c) at 300 Ki (dl LIP '0.6 H20 with Eo.l.c and measured at 77 K.

The 3510 cm-1 peak is close to the band we observe at 3514 cm-1 (no. 4), and the peak at 3430 cm- t is close to the peak resolved at 3438 cm-1 in the Eol c spectrum when measured at 77. The polarization characteristics of these corresponding features, however, appear to differ in the two cases, leading to different assignments.

b. H20. The major infrared absorption and Raman scattering lines near 3170 cm-1 in the spectra of Li~. nH20 and near 2350 cm-1 in the spectra ofLi~. n020 are attributed to the water molecules identified by neutron diffraction. Because of the special orientation, the induced moment of Vt is perpendicular to the c axis, and the induced moment of v3 is parallel to the c axis. Examples of the infrared spectra of Li~ . O. 007D20 measured with polarized light at 300 and 77 K are shown in Fig. 10.

From the analysis of the low temperature data, v1 is resolved at 3148 (2353) cm -1 in the Eo 1 c spectra and v3

is resolved at 3152 (2363) cm-1 in the Eo II c spectra. These modes are referred to as vf and Vs in Table II, where the superscript "a" distinguishes this type of molecule. The positions of vf and Vs depend on sample temperature and water concentration (Table II). For



Bates et al.: H20 in hydrated p-alumina 4849

t u ~ ...

1 > ~ VI Z ~ Z ....

U ~-ALUMINA

t:i20 \

T=50K

T 2000 i

i 200

T

3800 3400

o(eole

3000 2600 2300

x2

2800 2600 2400 2200 2000 lSOO WAVE NUMBER (em-I)

FIG. 9. Polarized Raman scattering from LI/3 '1. 6H20 and the a(a' a 'Ie spectrum of Li.8 '1. 6D20. Measurements at 50 K.

example. "1 of D20 increased about 10 cm-1 when the water concentration was increased from'" O. 3 to '" O. 6 D20 molecules per unit cell. Peaks at higher wave numbers than the main absorption bands appear at 3257 (2445) cm-t in the Eo 1 c spectra and at 3272 (2429) cm-1 in the Eo II c spectra. These are aSSigned to IIf and II~, respectively. of water molecules which have the same orientation but a different local environment than the molecules of set a. At 300 K. the a and b components merge into a single broad peak located between the positions of a and b.

We also attribute the band in the Eo 1 c spectra at 2972 (2255) cm-1 to water based on its change in intensity with PK20 as described in the following paper. 2 If this assignment is correct, these molecules evidently lie in the conduction plane. since a corresponding peak in the Eo II c spectra was not observed. We assume that the lit and 113 modes overlap because only one peak was observed and because. within the error of the curve resolution, no shift in the peak's position was seen in the HDO spectrum (Fig. 7). This band is labeled by lIf. lIg in Table II. By correspondence with the results for Lij3 . nH20. the two sets of peaks observed in the polarized absorption spectra of Na,8' nH20 are assigned to lit and "3 of two types H20 molecules that have the same orientation as the principal H20 species in Li~ . nHp.

The large shift to lower wave numbers of the lit and "3 modes of water in hydrated Li and Na ~-alumina com-

1 UJ u Z <t co 0: 0 VI co <t

LiO.7NaO.3

~·ALUMINA

°2° T

0.21

1

17K

E lie

2800 2400 WAVE NUMBER (cm- 1 )

2000

FIG. 10. Polarized absorption spectra of Li,8 '0.007 D20 measured at 300 and 77 K. The Eo.!.c curves are multiplied by ax. Sample thickness d = O. 248 cm.



4850 Bates et al.: H20 in hydrated {3-alumina

pared to the gas phase values1B of 3657 (2671) and 3756 (2788) cm-1, respectively, is evidently caused by hydrogen bonding. The positions of these modes in Li (3-alumina occur at the low end of the range of frequencies observed for vl and 113 in other hydrates. 19,20 There is known to be a correlation between the R o- o distance in a hydrogen bond and the O-H stretching frequency: the frequency decreases as Ro_o decreases. Falk and Knop19 discuss earlier correlations and propose one of their own based on the OD stretching frequency of HOO (112) in hydrates and ices. Using the value of R o- o = 2.6 'A between O(w) and the 0(4) oxygen ions in Li{3· nH20, their linear least-squares relation21 between Ro-o and 112 gives v2 = 2254 cm-1 compared to the observed value of 2360 cm-1. The agreement between the observed and predicted v2 frequency is quite good considering that Ro-o and 112 in Li (3-alumina are well below the range of the respective values used by Falk and Knop in their analysis.

Another consequence of hydrogen bonding of water in solids is the reduction13 ,22 in the splitting between 113

and 111' all3 ,l = 113 - vl' In the gas phase, all3, 1 = 117 cm-1

for Dp and 100 cm-1 for H20. Schiffer et al. 13 have found that all3,l decreases linearly with 1I0D' where 1I0D is taken either as the mean value of the 113 and vl frequencies of D20 or as the observed v2 frequency of HOO. From the data in Table lIB, for the principal HOO molecules at 77 K, 112 = 2360 cm-1. Assuming 2(113 - 1I0D) = all3,l' Eq. (18) of Ref. 13 gives aV3,l = 58 cm-t for D20 compared to the observed splitting of 10 cm-1 between the v3 and IIi components. At 300 K, the major D20 and HOO peaks appear at higher wave numbers: 113 = 2398, vl = 2360, and 112 = 2380 cm-1. Thus, all3,t = 38 cm-t compared to a calculated value of 60 cm-t. The discrepancy between the observed and calculated splittings using our data are considerably larger than the differences obtained for the data analyzed by Schiffer et al. 13 However, the values of 1I0D in Li{3' nHOO are well below the range of their analysis. Somewhat better agreement is obtained for H20. Using the polarization data at 77 K in Table II and VOR = 1/2(v3+ vt> = 3150 cm-1, the calculated splitting is aV3,l = - 12 cm-t while the observed splitting is 4 cm-t . As in the case for D20, the H20 peaks shift to higher wave numbers at 300 K, but at this temperature v3 = 111 = 3180 cm-1 so that the observed splitting is zero whereas the calculated splitting is - 6 cm-1. From Eq. (17) of Ref. 13, v3 = Vt when 1I0R = 3209 cm -1.

We have not explored possible causes for the poor agreement between the observed and calculated aV3.1

splittings. Perhaps part of the discrepancy is due to the strong hydrogen bonding of water in {3-alumina and the consequent large HOH bond angle. t3 We can conclude, however, that our data for the principal type of H20 and D20 molecules in Li {3-alumina agree qualitatively with the predicted correlations, and furthermore it is true that for all of our samples, aV3,t for H20 is smaller than aV3,t for D20, which appears to be a fundamental property of water.

In the spectra of hydrated Li and Na {3-alumina, two sets of peaks, distinguished by a and b, were attributed

to the stretching modes of two principal types of water molecules, i. e., molecules with the orientation shown in Fig. 1. The splitting between the corresponding pairs of components vf - vf and V3 - v~ for H20 and D20 and V2 - v~ for HOO is within the range of 70-120 cm-1

(Table II). We speculate that this splitting is caused by interactions of the molecules with Single and paired alkali ions. If second nearest neighbors are considered, then there are several possible configurations of single and paired ions about a water molecule. But if we assume that only nearest neighbor interactions are important, then these are reduced to two types: H20 molecules near paired ions and H20 molecules near single ions (Fig. 2). The distribution of molecules next to paired and single ions then depend on the temperature, the number of each type of site available, the difference in binding energy of water at the two kinds of sites, and the total water concentration. Because there is more room for a molecule next to paired ions than next to a single ion (Fig. 2), especially in the case of Na+ ions, it is reasonable to suppose that the O(w) sites next to paired ions are preferred. Potential energy calculations using Coulomb interaction and a point charge model for H20 (see Ref. 2) indicate that the location of a water molecule next to paired Na+ ions on mO sites is more favorable by about 0.07 eV than the configuration in which water is located next to a single Na+ ion on a BR site. If we assume that for Na {3-alumina vf is due to H20 near paired ions and vf is due to H20 near single ions, then from the relative peak areas and the number of sites of each type, we estimate the difference in binding energies to be 0.06 eV at 300 K, in good agreement with the calculated value. This energy difference is only about a factor of two larger than kT at 300 K, and it is considerably smaller than the enthalpies of hydration, which are equal to about -1 eV (Ref. 2). In the case of Li /3-alumina, the a and b components are resolved only at low temperatures; from the relative intensities of v2 and v~ components of HOO, we estimate an energy difference of only about 0.02 eV at 77 K. If our interpretation is correct, then because of the small difference between the binding energies, rapid interchange of the single-ion water and paired-ion water configurations can occur at room temperature. This might explain the very large increases in the bandwidths that are observed between 77 and 300 K (Table II).

The inset in the top portion of Fig. 5 shows the spectrum of Lifj. nH20 in the bending mode region of H20. This graph is the ratio of a single beam spectrum of a crystal containing a high concentration of water to that of the same crystal containing a low concentration of water. Similar plots at intermediate compositions show that the intensity of 1515 cm-t peak is proportional to that of the H20 peak at ::::3170 cm- t. If this peak is due to v2 of H20, the bending mode of D20 should occur near 1115 cm-t, which is well below the wave number limit (:::: 1200 cm-t) for total absorption by our samples. The bending mode for the principal water species should appear in the infrared spectrum for Eol c but not for. Eo II c. We were not able to verify the polarization characteristics of this band because the dichroism sample



Bates et al.: ~ 0 in hydrated J3-alumina 4851

was to thick to permit measurements below 1700 cm-I•

The v2 mode of H20 in hydrates typically occurs above the gas phase position at 1595 cm- I , but values below 1595 cm- I have been reported. 19 The 1515 cm-I peak in Li{:l· nli20 occurs at the low end of the distribution of bending frequencies in hydrates shown by Falk and Knop.19

The selection rules governing Raman scattering from water molecules in Li t!-alumina are derived in the Appendix (Table V). For the principal type of molecule (Fig. 1), the rules predict that the Vt mode is active in (a' a'), (a' a) and (ee) scattering while the va mode is active only in (ca) scattering. The strongest scattering was observed for a(ce)a' geometry (Fig. 9). The two strong peaks resolved at 3204 and 3117 cm- I in this spectrum (Table II) are assigned to Vt of two types of water molecules. Two components were also resolved in the a(a'a')e spectrum at 3212 and 3116 cm-t. Because of the large uncertainty in the fitted position of these peaks, we assume that they are the same components resolved in the a(ce)a' spectrum. In the a(ea)a' spectrum, two peaks resolved at 3246 and 3178 cm- I are assigned to v3 components corresponding to the Vt components at 3204 and 3117 cm- I , respectively. The two sets of VI - v3 components are distinguished by upper case letters in Table II. These probably correspond to the a and b components observed in the infrared spectra, but close agreement in the peak positions cannot be expected because of the large difference in water concentration between the Raman and infrared samples. In the a(ee)a' spectrum of Lit! . nli20 a broad peak appears at 3380 cm- I • A weak feature near this position was also resolved in the a(ca)e spectrum (Table II). A corresponding band was not resolved in the Raman spectra of Lit!· nD20 nor was any feature identified near this pOSition in the infrared spectra. Because of the large width of the 3380 cm- I peak, Il = 125 cm-t, it is unlikely to be due to OH-. Possibly it is due to another type of H20 molecule or to an H(H20); speCies which becomes evident only at high water concentration.

The Raman peak at 2947 (2228) cm- I observed in the a(a' a')e spectrum appears to correspond to the infrared feature at 2972 (2255) cm-I observed in the E 1 c infrared spectra. The fact that this peak is observed only in the a(a' a')e spectrum is consistent with the assignment to overlapping VI and Vs components of in-plane H20 molecules.

e. H(H20)~. The infrared and Raman bands observed below 2800 (2200) cm-t are assigned to the stretching modes of HsO· and H50i species (Table II). The strongest support for these assignments is the change observed in the infrared intensities with changes in water vapor pressure. 2 The peak positions are within the range of values reported23 for HsO· and H50; in monoand dihydrates of HCI. In the case of H50i, the bands in question are assigned to the terminal O-H stretching modes. The central O-H-Q stretching vibration occurs at much lower frequencies (1000-1200 cm- I). 23.24 The isotope frequency ratios VK/VD also support the assignments. The ratios for the H30· and H50; stretching modes reported by Gilbert and Sheppard23 are be-

tween 1. 27 and 1. 29. The ratios for the peaks in Table II that we assign to HsO· and H50i range from 1. 29-1. 31. Typically for H20 in hydrates VK/VD = 1. 35 to 1. 36 for va and vI' (We observe 1. 34 for the vf components of H20.)

The Raman bands assigned to HsO· and H50; (Fig. 9) appear only in the a(a' a')e and a(a' a)e spectra. This implies that the basal plane of HsO·. and the plane of the terminal HOH groups of H50i are parallel to the conduction plane, since the largest change in polarizability in a stretching mode of an OH group is expected to occur along the O-H bond. From simple arguments based on the packing of H20 molecules in the conduction plane using the diagram in Fig. 2, it is possible to construct several modelS for HaO· and H50i species with the required orientation. Some of these modelS involve hydrogen bonding of interstitial HsO· and H50i with 0(5) oxygen ions. In view of the fact that H(H20)~ ions constitute only a minor fraction of the proton containing species in Lit! . nli20 and that only H20 molecules were identified in the analysis of the diffraction data, it is unlikely that direct structural evidence for such models can be obtained.

It can be seen in Figs. 5 and 9 that there are differences in relative intensities between several corresponding infrared and Raman peaks in the respective spectra of Lit! . nli20 and Lit!· nD20. In the most extreme case, the peak at 2379 cm-t in the infrared spectrum of Lit! . nH20 was seen only as a very weak feature near 1830 cm-I in the deuterated sample. These differences are probably due to isotope effects on the equilibrium constants of the reactions which lead to the formations of OH- and H(H20); species.

Infrared and Raman spectra of hydrated hydronium t!-alumina have been reported by Colomban et al. 25.26

The Raman spectrum of this compound26 closely resembles the a(a' a')c Raman spectrum of Lit!· 1. 6H20 in Fig. 9. The peaks reported by Colomban et al. 25 were aSSigned to stretching vibrations of HaO" H5e>; or H703. In particular, two infrared bands observed at 3520 and 3508 cm-t were assigned to HsO·. These peaks occurred at the same poSition in a deuterated sample containing 5% hydrogen, suggesting that they should be aSSigned to OH- as in the case of Lit! . nli20. The assignments of other peaks between 3400 and 2300 cm-t

to specific HsO· ions or to specifiC stretching modes of the H50i species are plausible but not proved. The uncertainty of such assignments based only on optical data arises because of the sensitivity of the frequency and width of an O-H stretching vibration to hydrogen bonding. The weak feature we observed at 2160 cm-I

in the Eo II c spectrum of Lij9· 0.007020 (Fig. 10) is close to the peak at 2150 cm-t reported for 0(020)~ {3-. alumina. 26 The latter was assigned to the central deuterium stretching mode of Oop;. This assignment is unlikely for the 2160 cm- I feature in our spectra because the polarization data show that the 0-0 bond is parallel or nearly parallel to the e axis. The pOSition of this peak in the Eo II c spectrum of Lit!· nHDO (Fig. 11) occurs at 2157 cm-I (:I: 5 cm-I ), which, considering the uncertainty, indicates no frequency shift from the fully deu-



4852 Bateset al.: ~O in hydrated ~-alumina

t w u z ~ a:: o (/) al <l

LiO.7 NOO.3 (3 -ALUMINA

HDO T= 77 K

T 0.1

i

2800 2600 2400 2200 WAVE NUMBER (cm- I )

x2

2000

FIG. 11. Polarized absorption spectra of LI/3 ·0. 005 H20 containing 2~ HDO. The Eo.lo curve is multiplied by 2x. Sample thickness d=0.248 cm.

terated sample. At present we are unable to suggest a reasonable assignment for this peak.

3. Absorption coefficients

There is a paucity of information in the literature on the absolute intensities or absorption coefficients of the vibrational modes of water in solids. The lack of such data for the stretching modes is probably due in part to the complexity of the spectra which result from the overlap of v1' vs, and 2v2' It is known that appreciable changes occur in the infrared intensities of water from the gas phase to condensed states as a result of hydrogen bonding. Furthermore, local fields can alter the absorption intensities from one condensed medium to another. In principle the absorption intensities of water in Li tl-alumina can be determined from a combination of infrared absorption and weight measurements following hydration and dehydration. However, because H20 dissociates to form OH- and other protonated species, it is necessary to account for the fraction of dissociated water in order to make an accurate determination. At low water concentrations, OH- ions are predominantly formed, so as a first step the absorption coefficients for hydroxyl species in Li tl-alumina were calculated. In all of our calculations we have used a unit cell volume of 6. 15 x 10-22 cmS based on the unit cell dimensions of Litl· 1. 55H20 in Table I. Using this value to calculate the water or OH- content at low water concentration where the cell parameters are smaller in-

troduces less than a 1% error into the results.

The integrated intensity or line strength of an infrared transition in units of timol cmz (cm/m mol) is defined by

S = (l/Cd) f In[lo/l(v) ]dv ,

where C is the concentration in mol/f, d is the sample thickness in cm, and 10 and I are the incident and transmitted intensities of the light, respectively. In much of the literature on water, the infrared intensity is represented by the molar absorption coefficient €(f/mol cm), where E = (l/Cd) log 10(10/1), and Ip is the intenSity of the transmitted light at the peak of the band. In the analysis of our data, the absorbance spectra, given by values of log (10/1) measured as a function of v, are fit to the expression a+bv+:E;Fj(v), where a and b are constants, and Fj(v) is a Lorentzian function. The linear baseline term, a+ bv, accounts for the intensity loss due to reflection and background absorption in the sample. Using the fitted values of amplitude A and bandwidth /) given in Table II, the quantities

f In[lo/l(v) ]dv = 3.617 X 10-2 A6

and

10g(lo/lp) =A x 10-2 ,

are obtained for each peak. In the discussion below, the units of S(timolcmz) and E(timolcm) will usually be omitted.

The absorption coeffiCient for OH- in Ti02 was measured by Johnson et ale 27 In the units of S used here, their value for the line strength is SOH = 3. 48 X 104• In order to correct this value for the effect of the Ti02 lattice, we use the approximation

<cos20) (n2+2)2 SOH = --n- -3- SOH' (3)

where n is the refractive index and 0 is the angle between the electriC field and the O-H bond. The factor (n2 + 2)/3 is the Lorentz local field correction for a cubic site. 28 From infrared dichroism measurements29 it is evident that the Ok bonds in Ti02 are perpendicular to the c axis and lie in the isotropiC (001) plane. In this case (see the Appendix) <cos2 O)=~. Using no = 2.37 for Ti02 at A= 4~ as reported by Cronemeyer,30 we obtain from Eq. (3), S~H = 2. 56 X 104• This value represents the line strength for an OH- group that inCludes the effect of hydrogen bonding in the Ti02 lattice but eXCludes the effect of the local fields. In order to determine a similar quantity for OH- in Lit!· nH20, the effects of hydrogen bonding in this lattice must be taken into account. It was found in early studies by Huggins and pimente131

that a strong correlation exists between the line strength and bandwidth of H-bonded OH groups. From the tabulation of bandwidths and integrated intensities of the OH stretch of pyrole, methanol and phenol in several organic solvents given in Ref. 31, the ratios S/6 are seen to be remarkably constant, although 6 ranges from 22-275 cm-1 and S ranges from 5xl03 to 75x103• This suggests that we can use the ratio of bandwidths as an approximate scaling factor to calculate S'OH in hydrated Li tl-alumina



Bateset al.: ~O in hydrated ~-alumina 4853

TABLE m. Molar absorption coefficients (~) and integrated intensities (8) for OW and H20 in hydrated Li .a-alumina at 300 K.

(A) OW

Species (cm-I )

O.W(9 c =4S") 3525

O.H-(9 c =0") 3424 3408

0.,Ir(9c =0") 3424 3408

0.498 0.088

0.210 0.026

0.166 0.035

Averages VI (Eo.L 0)

E 50 (±8)

S 42 (±6) x 103

"Concentration in molecules/unit cell.

S(l/mol cm2) x 10-3

Eo.LC Eo II"

11.1 62.1

32.3 0.0

21. 5 0.0

((1)1) (l/molcm), Eo.Lc

High Low

48.7

46.0

61.6

490 (±74)

45.0

44.0

56.8

417 (±62)X103

lIconcentration of H20 which dissociated for form Oil"". [H20]OH =! [OWl. Average of values for two choices of assignment of 3400 cm-I peaks to O.H- or O"W.

°E and S for v3 were obtained by multiplying the respective quantities for VI by the intensity ratio of v3 and VI measured at 300 K.

based on the value determined in Ti02• In Ti02, 6 = 20 cm-t at 300 K. 32 In hydrated Li il-alumina, the major OH- peaks have widths of about 40 cm- t (no. 3) and about 60 cm-I (nos. 5 and 7) at 300 K, so S~H = 5. 12 X 104 for peak 3 and S'OH = 7.68 X 104 for peaks 5 and 7. Using these values of S~H' the integrated intensities for the three major OH- peaks for Eo II c and Eol c were calculated using the expressions for SOH given in the Appendix. These quantities are listed in Table III. Notice that, as a consequence of the variation in the local electric fields at different positions in the conduction plane, the intensities of peaks 5 and 7 depend on whether the hydroxyl is assumed to be an in-plane OiH- or an O...Hspecies. The amount of dissociated H20 was determined from the observed intensities of the three OH- peaks using the line strengths listed in the table. This quantity is given by [OH- 112.

It is also necessary in determining the absorption intensities of vf and va to account for the fraction of water molecules which lie in the conduction plane. This was estimated using the following assumptions: (i) the peak at 2960 cm-I assigned to in-plane H20 molecules consists of overlapping VI and v3 components; (ii) in the absence of local field effects, the absorption intensities of VI and v3 are the same as those of the principal H20 species, and (iii) the local electric field at these molecules is within the range of the two values calculated for the in-plane OH- ions. Assumption (ii)

is reasonable since the 3180 and 2960 cm-t bands have similar widths so we can expect similar intensities. Using the observed intensity ratio for v3 and Vt of the principal H20 species and Eqs. (A5) and (A6) in the Appendix, S' (v3) = O. 77 S' (Vt); The total intenSity for the 2960 cm-t band is then S'r -1. 77 S' (Vt). Since the bandwidths of Vt and v3are equal within the error of the curve resolution, then !~=1. 77!'(Vl)' As above the prime denotes quantities that include the effects of hydrogen bonding but exclude the effects of local fields.

The results of the infrared and weight change measurements on crystals of Li !3-alumina following hydration-dehydration under different conditions are summarized in Table III. The absorption coefficient and line strength for VI were determined from each of the three sets of data using the expressions

(4a)

and

(4b)

where AI and A2 are the amplitudes of the 3180 and 2960 cm- I peaks, respectively, obtained from the curve resolution of the spectra, [H20.loH is the concentration of H20 that dissociated to form OH-, [H201- is the total H20 concentration obtained from the weight-change measurements, and LJ. is the ratio of the local field correction for the in-plane H20 molecules to that for the principal type of molecule. The two values of ! for each data set in Table III are the maximum and minimum of the four fesults obtained for the two choices of local field for the OH- ion and for the in-plane H20 molecules. Errors in the determination of [HaC]r and in the curve resolution yield an uncertainty of about ± 12l> in the absorption coeffiCient for each data set. This error is really a measure of the precision of the determinations since we are not able to estimate the uncertainty introduced by the assumptions made in arriving at Eq. (4a). The consistency among the values of ! is reassuring, especially in view of the fact that the total H20 concentration and the relative concentration of OH- were considerably different in the three sets of measurements (Table III). If we assume that the uncertainties in line strengths for OH-and the in-plane H20 molecules are as large as :I: 5~, the uncertainties in the average values of ! and S are about ±1~.

It is interesting to compare the integrated intensities of VI and v3 for H20 in Li!3 . nH20 with those reported for water in the gas, liquid, and solid phases. Because the H20 molecules were randomly oriented in the samples of ice (polycrystalline films were used) as well as in the vapor and liquid, the intenSities in Li!3' nH20 must be scaled to make this comparison: S(VI) = ~ S(VI) and S(v~ =tS(V3)' The scaled quantities are listed in Table IV with the vapor phase intensities reported in the compilation by Pugh and Rao, 33 the liquid intensities reported by Motojima et al. ,34 and the intensities of ice measured by Ikawa and Maeda. 35 In water and ice, it is not feaSible to measure the separate intensities of VI

and v3 because of the strong overlap of these modes. The values reported are the sum of the intensities of VI



4854 Bates et al.: H20 in hydrated t3-alumina

TABLE IV. Integrated intensities (llmol cm2) of H20 stretching

modes in different substances.

Vapora

Liquidb (VI and vs)

Iceb (VI and v3)

Li,B 'nH2Oc

aReference 32. ~eference 33.

S (observed) x 10'3

VI Va

0.25 4.23

89.9

140

28 139

5' (corrected)d x 10'a

VI Va (Sum)

0.25 4.23 (4.48)

75.8 (75.8)

118 (118)

88 67 (I 55)

cs (VI) =~S(vl); S(vs) =is(v3), where S(Vt) and S(v3) are the experimentally determined quantities.

dIntensities corrected for local field and refractive index.

and v3 and of 2V2 as well. It can be seen in the table that there is a large increase in the total intensity S(Vt)

+S(V3) from the vapor to the solid phase. This increase has been attributed primarily to hydrogen bonding (see Ref. 35, e. g. ,) but local fields also contribute to the intensity change. The intensities corrected for local field effects (denoted by S') are also listed in Table IV. The corrections for water and ice were made36 using the factor (n2 + 2)2/9n, where the index n was taken to be 1. 3 for the liquid37 and the sOlid. 38 For H20 in L~· nH20 the corrected values were obtained from (see the Appendix): S'(Vt)=S(vl)/O.32 and S(vs)=S(v3)/2. 09. Local fields have an appreciable effect on the relative intensities of Vt and va in Lij3 . nH20, but the largest contribution to the increase in the sum of the absolute intensities of Vt and va, 155, compared to the sum of the gas phase intensities, 4.48, is derived from hydrogen bonding.

IV. CONCLUSIONS

When Li /3-alumina is exposed to water vapor, H20 molecules diffuse into the conduction layers. The concentration of water can be varied continuously, depending on the treatment condition, up to a saturation limit which, in units of H20 per unit cell, is given by 2-t no. per unit cell of excess Li+ ions (1. 8 H20 per unit cell for our samples). The oxygen atoms of the majority of the water molecules occupy one of three equivalent positions between the mO and aBR sites in the conduction plane. The protons are located symmetrically above and below the plane and form bent hydrogen bonds with the 0(4) oxygen ions that are directly above and below the aBR sites. Water molecules in hydrated Na /3-alumina evidently have the same orientation and occupy similar pOSitions. There is evidence that a small fraction of the water molecules in Li/3 . nH20 (less than ~) are oriented such that their protons lie in the conduction plane. In Li and Na /3-alumina, we speculate that the two types of H20 molecules which have the same orientation but different OH stretching frequencies are associated with single and paired alkali ions. The difference in energy between the two types of configurations appears to be small.

A fraction of the water molecules in hydrated Li /3-

alumina dissociate to form OH' ions and hydrated proton species HsO+ and HsOi. Two major types of OH' ions are identified. These are proposed to be (i) O/Hinterstitial ions with the O-H bond pointing out of the conduction plane and (ii) 0)1- ions in which the proton is possibly bound to an 0(5) oxygen ion and in which the O-H bond is parallel to the conduction plane. No evidence was found for dissociation of H20 in Na j3-alumina measured at 300 K or below.

A large local field anisotropy in the conduction plane of /3-alumina is responsible for the large difference in the infrared intensities of OH- and H20 measured with E II C and E lc. Using calculated absorption coeffiCients for OH- and the results of absorption and weight-loss measurements following hydration and dehydration of Li /3-alumina, the integrated intenSities for Vt and va were determined to be 42 (± 6) x lOa and 417 (± 62) x lOa limol cm2

, respectively, at 300 K. The large increase in the total absorption from Vt and V3 compared to that in the gas phase is attributed to hydrogen bonding of H20 in Li /3-alumina.

ACKNOWLEDGMENT

We thank the referee for his (her) very careful review of this paper.

APPENDIX

The integrated intensity for absorption of polarized light by the fundamental stretching mode of an isolated OH group in a condensed medium can be expressed as39 •40

S - 1 (EIOc)2 (A A)2 41T2NvOH I (11 I 12

OH - ~ Eo e loc ' YOH lie POH 0) ,

(AI) where n is the index of refraction, E loc and Eo are the magnitudes of the local and applied fields, respectively, eloc is a unit vector in the direction of the local field, r OH is a unit vector in the direction of the induced dipole moment of the OH group POH' and N in Avogadro's number. The index of refraction was assumed to be n = ~ = 1. 68, where E:c is the high-frequency dielectric constant of Na /3-alumina reported by Barker et al. 4t

The magnitude and direction of the local field in Li /3-alumina depend on the polarization of the incident light and on the location at which the field is calculated. t4

At the general pOSitions above and below the conduction plane, E loc has components both parallel and perpendicular to the c axis for either polarization direction of the incident light, but the deviation of E loc from the direction of Eo is small. If we neglect this deviation, and let

~ = 41T2NvOD l(llp 10) 12 OH lie OH,

then from Eq. (AI),

(A2)

and

_ 1 (E10c )2 SOH . 2 S. - '2 Et 1. 68 sm Be , (A3)



Bates et al.: ~ 0 in hydrated j3-alumina 4855

where ec is the angle between YOH and the c axis and where the symbols II and .1 denote components of E loe and Eo parallel and perpendicular to the c axis, respectively. The factor of ~ in Eq. (A3) takes into account that the induced moment p of any oscillator in the conduction layer can point along anyone of three equivalent directions that are related by a threefold rotation about an axis parallel to the crystallographic c axis. If cP is the angle between the direction of E~ and Pv the component of p in the plane, Eq. (AI) will contain a factor

1 2

<cos2 cp)= 3" ~ cos2[cp+ 120n]=~. n=O

The same result is obtained for unpolarized radiation with Eo in the plane:

1 l' <cos2 cp)= - cos2CPdCP=~. 7T 0

The polarized absorbance spectra for Eo.1 c shown above were multiplied by a factor of two when compared directly with the Eo II c spectra.

Equation (2) in the text which gives the relationship between ec and the dichroic ratio for OH- absorption was derived from Eqs. (A2) and (A3). The values of ec reported in the text are those which give the best agreement between the measured values of A,,/2A~ and the ratio

R = [(Eloc),,(E\oe.rOH)" J2 calc (Eloe)~(eloe.YOH)~ ,

(A4)

which was calculated for various assumed orientations of OW. The II and .1 symbols distinguish the magnitude (E loe) and direction (e IOe ) of the calculated local field at the proton for incident light polarized parallel and perpendicular to the c axis, respectively. Equation (A4) is more exact than Eq. (2) in the text since the actual local fields used in Eq. (A4) are not restricted to be aligned with the incident field.

The absorption coefficients and line strengths for the OH- ions listed in Table III were calculated using Eq. (A 1) and the local fie Ids calculated at the protons for the appropriate orientation determined by ec. The expressions for S are:

SOH = O. 22S~H' Eo.tc

and

SOH = 1. 21 S~H' Eo II C ,

(ii) OiH-(ec= 90j ,

SOH = O. 42S'OH' Eo .tc ,

and

(iii) O.,Ir(e c = 90°)

SOH = O. 28S~H' Eo.tc.

The integrated intensities for III and 113 of the principal type of H20 species in Lij3. nH20 were obtained from Eq. (AI) using the local fields calculated at the observed positions of the protons. These intensities are given by

TABLE V. Raman scattering tensor elements for the fundamental modes of H20 in ,a-alumina. R,b

Mode (a., 4,)2 (a.,.,)2 a;c a~c

VI or V2 i-a!x 3 9 2 +4 axxa ... + '8 a .. } (a",,_a .. )2 0 3a;"

113 0 0 l.a 2 2 ~ ..

aCalculated for the H20 molecules oriented as in Fig. 1. lIscattering geometry denoted in text by a(a ' a ')e. etc •• where the outer symbols a and e indicate the direction of the incident and scattered light, respectively, and the inner symbols a' and a' e. g., indicate the polarization of the incident and scattered light.

(A5)

and

(A 6)

where S' (113) and S' (III) are defined in the same manner as S~H' The coefficient 0.16 in Eq. (A6) includes the factor of ~ to account for the average dipole orientation as discussed above [Eq. (A3)]. In calculating the geometric factors, (e IOe ' rOH) , it was assumed that the protons move along the two O-H bonds of the H20 molecule. The appropriate phases were chosen for the III

and 113 modes so that the net dipole moment was parallel to c for 113 and perpendicular to c for III' as required by symmetry.

The polarization data for HDO (Fig. 11) provide the best check on our local field calculations, since in this case we can compare the intensities for the same mode. From Table II A" /2A~ = 5. 5 for the 112 stretching mode at 2360 cm-I • The orientation of the transition moment of 112 was calculated from a point charge model14 on HDO, giving ec = 37.6°. For this angle, Reale = 5.4. The good agreement between Reale and the observed dichroic ratio gives us a measure of confidence in the calculated local fields and underscores the importance of local field effects on the absorption spectra of water and other proton species in j3-alumina.

In order to analyze the polarized Raman spectra of Lij3' 1. 6H20 and Lij3· 1. 6D20, we calculated the form of the Raman tensors for H20 using the methods developed previously for NH4 in j3-alumina. 7 The major type of H20 molecules in Li j3-alumina occupy C2v sites, with the C2 rotation axis perpendicular to the crystallographic c axis. The molecular scattering tensors for the Al and B2 species of the C 2v point group, a~1 and a! 2, are given in Eq. (7) of Ref. 7. The crystal scattering tensor elements calculated from the specified transformations using ei = 1200 in Eq. (10) of Ref. 7 are given in Table V. It can be seen from this table that Raman bands due to III will apeear in (a' a'), (d a) and (cc) scattering, while Raman bands due to 113 should appear only in (a' c) or (ac) scattering.

For the small fraction of molecules which lie in the conduction plane, a calculation of the Raman scattering tensors assuming the molecules occupy C 2v sites gives the following results: III is allowed in (a' a'), (aa), (a' a) or (aa'), and (cc) scattering, and 113 is active in (a'a'),



4856 Bates et at.: H2 0 in hydrated j}-alumina

(a a) and (a' a) scattering. Neither of the modes is active in (ca) scattering.

IJ. B. Bates, R. Frech, H. Engstrom, J. C. Wang, and T. Kaneda, Solid State lonics I, 15 (1980).

2N. J. Dudney, J. B. Bates, and J. C. Wang, J. Chern. Phys. 77, 4857 (1982).

3F. Reidinger, Ph. D. dissertation, State University of New York at Albany, 1979.

'C. G. Shull (privately distributed, 1972). OW. L. Roth, F. Reidinger, and S. LaPlaca, in Superionic

Conductors, edited by G. D. Mahan and W. L. Roth (Plenum, New York, 1976), p. 223.

Sp. Coppens and W. C. Hamilton, Acta CrystaUogr. Sect. A 26, 71 (1970).

7J • B. Bates, T. Kaneda, J. C. Wang, and H. Engstrom, J. Chern. Phys. 73, 1503 (1980).

BC. R. Peters, M. Bettman, J. W. Moore, and M. D. Glick, ActaCrystallogr. Sect. B 27,1826 (1971).

9T • Kaneda, J. B. Bates, and J. C. Wang, Solid State Commun. 28, 469 (1978).

lOG. Ferraris and M. Franchini-Angela, Acta Crystallogr. Sect. B 28, 3572 (1972).

11D• Eisenberg and W. Kauzmann, The Structure and Properties of Water (Oxford, New York, 1969).

12The water concentration in the Na f3-alumina crystal had not reached the equilibrium value.

13J. Schiffer, M. Intenzo, P. Hayward, and C. Calabrese, J. Chern. Phys. 64, 3014 (1976).

14J. B. Bates, J. C. Wang, and N. J. Dudney, Phys. Rev. B (to be submitted).

15J. B. Bates, J. C. Wang, and R. A. Perkins, Phys. Rev. B 19, 4130 (1979).

16J. C. Wang, Phys. Rev. B 22, 2725 (1980). 17W. Hayes, L. Holden, and B. C. Tofield, J. Phys. C 13,

4217 (1980). 18W• S. Benedict, N. Gailar, and E. K. Plyler, J. Chem. Phys.

24, 1139 (1956). 19M• Falk and O. Knop, in Water, a Comprehensive Treatise,

edited by F. Franks (Plenum, New York, 1972), Vol. 2,

Chap. 2. 20 B• K. Srivastav'a, D. P. Khandelwal, and H. D. Bist, Chern.

Phys. Lett. 39, 366 (1976). 21The equation given by Falk and Knop on p. 105 of their paper

(Ref. 19) applies to VOD and not to A,vOD as stated. 22R. A. Fifer and J. Schiffer, J. Chern. Phys. 52, 2664 (1970). 23A. S. Gilbert and N. Sheppard, J. Chern. Soc. Faraday Trans.

2, 69, 1628 (1973). 2'J. B. Bates and L. M. Toth, J. Chern. Phys. 61, 129 (1974). 25Ph. Colomban, G. Lucazeau, R. Mercier, and A. Novak, J.

Chern. Phys. 67, 5244 (1977). 26 Ph. Colomban and A. Novak, Solid State Commun. 32, 467

(1979). 270. W. Johnson, J.DeFord, andJ. W. Shaner, J. Appl. Phys.

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Structure and spectra of H2O in hydrated β-aluminaa)

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