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Neutron Diffraction Study on the Structure of Hydrated Li in Dilute Aqueous Solutions +

Yasuo Kameda, Shunya Maeda, Yuko Amo, Takeshi Usuki, Kazutaka Ikeda, and Toshiya Otomo J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b12218 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018

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The Journal of Physical Chemistry

Neutron Diffraction Study on the Structure of Hydrated Li+ in Dilute Aqueous Solutions Yasuo Kameda,*† Shunya Maeda,† Yuko Amo,† Takeshi Usuki,† Kazutaka Ikeda,‡ Toshiya Otomo‡

†

Department of Material and Biological Chemistry, Faculty of Science, Yamagata University,

Yamagata 990-8560, Japan ‡

Institute of Material Structure Science, KEK, Tsukuba, Ibaraki 305-080, Japan

KEYWORDS: Li+ hydration, Neutron diffraction, 6Li/7Li isotopic substitution

ABSTRACT Neutron diffraction measurements have been carried out for 6Li/7Li isotopically substituted aqueous 1.0 mol% (0.5 mol/kg) LiCl and 1.1 mol% (0.56 mol/kg) LiClO4 solutions in D2O to obtain structural insight concerning hydration structure of Li+ in more dilute electrolyte solutions. The first-order difference function, ∆Li(Q), was analyzed by means of the least squares fitting procedure to obtain short-range structural parameters around the Li+. It was revealed that the nearest neighbor Li+…O(D2O) distance, rLiO, and the coordination number, nLiO, for the aqueous 1.0 mol% LiCl solution are 2.01 ± 0.02 Å and 5.9 ± 0.1, respectively. The values, rLiO = 1.97 ± 0.02 Å and nLiO = 6.1 ± 0.1, are obtained for aqueous 1.1 mol% LiClO4 solution. These results indicate that the hydration number of Li+ in dilute solution is close to 6, which is much

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larger than 4 that has long been believed. A possible explanation is that the hydration number of Li+ varies with the solute concentration.

INTRODUCTION The hydration structure of Li+ has long been a standing problem for extensive fields of chemical, physical and biological sciences. Physical properties of aqueous solutions involving Li+ have been important research subjects at present in both experimental1-5 and theoretical6-11 studies. Especially, the structure of hydrated Li+ is regarded as an important touchstone for estimating better interaction potential between Li+ and O atom in the theoretical studies. The hydration structure and contact ion pair formation of Li+ are of great importance for understanding physical properties of aqueous solutions. Detailed structural properties of hydrated Li+ have been experimentally obtained by neutron diffraction with 6Li/7Li isotopic substitution method.12 Newsome et al. first conducted the 6Li/7Li isotopic substitution experiments on 6.7 mol% and 16.7 mol% *LiCl-D2O solutions. Hydration number of Li+ was determined to 5.5 ± 0.3 and 3.3 ± 0.5 for 6.7 mol% and 16.7 mol% *LiCl solutions, respectively,13 which implies hydration number of Li+ has concentration dependence. Hydration number reported from neutron diffraction studies on concentrated aqueous 20 mol% LiBr (nLiO = 3.9 ± 0.5)14 and 16.6 mol% LiCl (nLiO = 4 ± 1)15 solutions indicate that the hydration number of Li+ is close to 4 in accordance with that reported by molecular dynamics (MD) simulations.6 On the other hand, concentration dependence of the hydration number of Li+ was examined by Howell and Neilson employing samples with wider LiCl concentration range (2, 6.7, and 22 mol% LiCl).16 Obtained hydration number was 3.2 ± 0.2, 6.0 ± 0.4, and 6.5 ± 1 for 22, 6.7 and 2.0 mol% LiCl solutions,


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respectively,16 indicating that the hydration number of Li+ at the lower-concentration limit should be ca. 6 in contradiction with that obtained from most of MD simulation studies. Neutron diffraction study on 10, 25 and 33 mol% LiBr-D2O solutions also represented that the hydration number of Li+ is concentration dependent and the value determined for the 10mol% LiBr solution being 5.6 ± 0.2.17 Main difficulties in adopting the 6Li/7Li isotopic substitution method emerge from extremely large absorption cross section of 6Li nucleus. In order to obtain scattering data with excellent statistical accuracy, the use of high-performance diffractometer is therefore necessary. Recently, Mason et al. reported 6Li/7Li isotopic substitution experiments on more diluted 2 mol% (1 mol/kg) LiCl-D2O solutions using D4c multi-detector high performance diffractometer install at high flux reactor in ILL.18 The obtained hydration number of Li+ (4.8 ± 0.3) is obviously smaller than that reported earlier (6.5 ± 1).16 On the other hand, concentration dependence of Li+ hydration in aqueous LiNO3 solutions has recently been investigated using new-generation high-performance time-of-flight (TOF) neutron total scattering diffractometer installed at high intensity pulsed neutron source. The lower-limit of the solute concentration was extended to 1 mol% (0.5 mol/kg) LiNO3,19 which corresponds to half of that employed by Mason et al. The hydration numbers determined by the least squares fitting analyses were 4.12 ± 0.06, 5.18 ± 0.03, and 6.0 ± 0.2, for 10, 5 and 1 mol% LiNO3-D2O solutions, respectively.19 These results are clearly contradict to those obtained by Mason et al. In order to solve these problems, new experimental data with higher statistical accuracy obtained for more diluted solutions are therefore indispensable. Furthermore, the isotopic difference method for diluted solutions requires careful examination of the normalization constant to be applied for observed scattering cross sections before taking subtraction between isotopically distinct sample solutions. The overall normalization factor of the observed scattering cross section should be determined from


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the internal standard, i.e. the amplitude of the intramolecular interference term of the D2O molecule involved in the observed scattering cross section in the high-Q region. Another difficulty in applying 6Li/7Li isotopic substitution method is extremely large absorption by 6Li nucleus. Since the magnitude of absorption cross section of sample is known to be proportional to the incident neutron wavelength,20 the TOF total scattering experiment with short incident neutron wavelength is considered to be the most suitable experimental technique. Further, since the troublesome inelasticity effect on neutron scattering becomes smaller at the smaller scattering angles,21 the TOF method using small scattering angle detectors is again regarded as the most preferable experimental technique. In the present paper, we report the results of neutron diffraction with 6Li/7Li isotopic substitution method applied for 1 mol% (0.5 mol/kg) LiCl in D2O in order to clarify the hydration structure of Li+ in dilute solutions. Experiments on the 1.1 mol% (0.56 mol/kg) LiClO4 solutions have also been carried out. Since ClO4- is known to exhibit weak interaction with cations in aqueous solutions, the hydration structure obtained from the LiClO4 solutions is expected to that free from the effect of the contact ion pair formation. In the data analysis procedures, the overall normalization factor of observed scattering cross sections was carefully checked by employing the least squares fitting procedure of the observed intramolecular interference term. The structural parameters concerning the hydrated Li+ were determined form the least squares fitting analysis of the observed first-order difference function to avoid uncertainties arising from the truncation error associated with the Fourier transform.


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EXPERIMENTAL 6

Li- and 7Li-enriched lithium chloride and lithium perchlorate were prepared by reacting 6Li2CO3

(95.6% 6Li) and 7LiOH.H2O (99.99% 7Li) obtained from Tomiyama Chemical Co. Ltd. Tokyo with a slightly excess amount of concentrated aqueous HCl and HClO4 solutions (Nacalai Tesque, guaranteed grade). The dehydration of the product solutions were achieved by heating at 120 °C under vacuum for more than a day. The weighted amount of enriched anhydrous *LiCl and *LiClO4 were dissolved into D2O (99.9% D, Aldrich Chemical Co.) to prepare 1 mol% *LiCl and 1.1 mol% *LiClO4 solutions with different 6Li/7Li isotopic compositions. Densities of the sample solutions were determined picnometrically. The sample parameters are listed in Table 1. The sample solution was introduced into a thin-walled cylindrical V-Ni null alloy cell (6.0 mm in inner diameter and 0.1 mm in wall thickness) and sealed by an indium seal. Neutron diffraction measurements were carried out at 25°C using the NOVA total scattering spectrometer22 installed at BL21 of the MLF pulsed neutron source in J-PARC, Tokai, Japan. Incident beam power of the proton accelerator was 200 and 300 kW in measurements for 1 mol% LiCl and 1.1 mol% LiClO4 solutions, respectively. Scattered neutrons (neutron wave band of 0.1 ≤ λ ≤ 8.7 Å) were detected by ca. 900 of 20 atm 3He position sensitive proportional counters (1/2 inch φ, 800 mm in active length with 5 mm in positional resolution) installed at 20° (13.1°27.9°), 45° (33.6°-54.9°), 90° (72.7°-107.4°) and back scattering (136.5°-169.0°) detector banks. The data accumulation time was ca. 3 h for each sample. Measurements were made in advance for 8 mm in diameter vanadium rod, empty cell and instrumental background. Observed scattering intensities for the sample were corrected for instrumental background, absorption of sample and cell23, multiple24 and incoherent scatterings. The coherent scattering


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lengths, scattering and absorption cross sections for the constituent nuclei were referred to those tabulated by Sears.20 The wavelength dependence of the total cross sections for H and D nuclei was estimated from the observed total cross sections for H2O and D2O, respectively.25 The inelasticity correction for the observed self-scattering term was applied by the use of the observed self-scattering intensities from the null-H2O.26 The first-order difference function, ∆Li(Q),27,28 is derived from the numerical difference between scattering cross sections observed for two solutions that are identical except for the scattering length of Li. Inelasticity distortion of the observed scattering cross section is cancelled out by the subtraction.27,28 The ∆Li(Q) normalized for stoichiometric units, (LiCl)x(D2O)1-x and (LiClO4)x(D2O)1-x, can be written as linear combination of partial structure factors, aLij(Q), involving correlations form the Li-j pair:

∆Li(Q) = A[aLiO(Q) - 1] + B[aLiD(Q) - 1] + C[aLiCl(Q) - 1] + D[aLiLi(Q) - 1]

(1)

where, A = 2x(1-x) (b6Li - b7Li) bO, B = 4x(1-x) (b6Li - b7Li) bD, C = 2x2 (b6Li - b7Li) bCl, D = x2 (b26Li - b27Li) for (LiCl)x(D2O)1-x solution, and A = 2x(1+3x) (b6Li - b7Li) bO, B = 4x(1-x) (b6Li - b7Li) bD, C = 2x2 (b6Li - b7Li) bCl, D = x2 (b26Li - b27Li) for (LiClO4)x(D2O)1-x solution, respectively. Numerical values for coefficients, A-D in eq 1 are summarized in Table 2. Since the observed ∆Li(Q) from forward angle detector pixels located at 13.1 ≤ 2θ ≤ 54.9° agree well within the statistical uncertainties, they were combined at the Q-interval of 0.1 Å-1 and used for subsequent analyses.


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The distribution function around Li+, GLi(r), is deduced from the Fourier transform of ∆Li(Q):

Qmax

∫

GLi(r) = 1 + (A + B + C + D)-1(2π2ρ0r)-1 Q∆Li(Q) sin(Qr) dQ 0 = [AgLiO(r) + BgLiD(r) + CgLiCl(r) + DgLiLi(r)] (A + B + C + D)-1

(2)

The upper limit of the integral was set to 20 Å-1 in the present study. Structural parameters concerning the hydration shell of Li+ were obtained through the leastsquares fitting procedure of the following function:29-31

∆Limodel(Q) = Σ2cLinLijbj(b6Li – b7Li) exp(-lLij2Q2/2) sin(QrLij)/(QrLij) + 4πρ0(A + B + C + D) exp(-l02Q2/2) [Qr0 cos(Qr0) – sin(Qr0)]Q-3

(3)

where, cLi and nLij are the number of Li+ in the stoichiometric unit and the coordination number of atom j around Li+, respectively. Parameters, lLij and rLij denote the root-mean-square amplitude and internuclear distance of the Li+…j pair, respectively. In the present analysis, the nearest neighbor Li+…D coordination number, nLiD, was fixed to 2nLiO. The long-range parameter, r0, is the distance beyond which continuous distribution of atoms around Li+ can be assumed. The parameter, l0, describes the sharpness of the boundary at r0. Structural parameters,


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nLij, lLij, rLij, l0, and r0 were determined from the least-squares fit to the observed ∆Li(Q). The fitting procedure was performed in the range of 0.1 ≤ Q ≤ 20 Å-1 with the SALS program.32 In the least-squares fitting calculation, the Marquardt method was employed. The dynamical biweight procedure was used for the weight adjustment of the observed data.32 Prior to the fitting analysis, correction for the low-frequency systematic error involved in the observed ∆Li(Q) was adopted.33

RESULTS AND DISCUSSION In the isotopic substitution method, it is essential that the observed scattering cross sections are properly corrected and accurately normalized. The overall normalization factors for sample solutions can be determined through the least squares fitting of the observed interference terms in the high-Q region, where the interference amplitudes are regarded as the intramolecular interference term of D2O for (*LiCl)0.010(D2O)0.990 solution and the sum of those of D2O and ClO4- for (*LiClO4)0.011(D2O)0.989 solution. The intramolecular interference term, iintra(Q), for the *

LiCl and *LiClO4 solutions are respectively represented by the following equations.

iintra(Q) = (1 – x)β[4bObDexp(-lOD2Q2/2)sin(QrOD)/(QrOD) + 2bD2exp(-lDD2Q2/2)sin(QrDD)/(QrDD)],

(4)

for *LiCl solution,


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iintra(Q) = (1 – x) β[4bObDexp(-lOD2Q2/2)sin(QrOD)/(QrOD) + 2bD2exp(-lDD2Q2/2)sin(QrDD)/(QrDD)] + xβ[8bClbOexp(-lClO2Q2/2)sin(QrClO)/(QrClO) + 12bOO2exp(-lOO2Q2/2)sin(QrOO)/(QrOO)],

(5)

for *LiClO4 solution, respectively. β denotes the overall normalization factor. In the fitting procedure, the normalization factor and structural parameters for D2O molecule were treated as independent parameters, while, molecular parameters for ClO4- in eq 5 were fixed to the literature values34 because of its smaller contribution in the observed interference term. The fitting was performed using the SALS program32 in the Q-range of 10 ≤ Q ≤ 40 Å-1. The results of the least squares fitting analyses for LiCl and LiClO4 solutions are indicated in Fig. 1. Structural parameters determined are summarized in Table 3. The present values of O-D distance (rOD = 0.971 – 0.974 Å) within the D2O molecule is somewhat shorter than that reported for pure liquid water (0.983 ± 0.008 Å,35 0.983 ± 0.005 Å,33 0.989 Å,36 0.979 ± 0.004 Å,37 and 0.987 ± 0.005 Å38), while in good agreement with those observed for aqueous LiNO3 solutions in D2O (rOD = 0.970 – 0.976 Å).19 The overall normalization factor, β, was determined to be 1.01 ± 0.01 ~ 1.05 ± 0.02. These values are very close to unity, implying that correction and normalization procedures have been adequately adopted. In the present study, renormalization of observed scattering cross sections for sample solutions was achieved by applying determined normalization factor β.


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The first-order difference function, ∆Li(Q), was then obtained from the difference in the renormalized scattering cross sections observed for 6Li and 7Li sample solutions. The ∆Li(Q) observed for 1 mol% LiCl solutions is shown in Fig. 2. The first diffraction peak at Q ~ 3.2 Å-1 and oscillatory features extending to higher-Q region can be obviously identified. The ∆Li(Q) function observed for 1.1 mol% LiClO4 solutions is also represented in Fig. 2. Although data points are somewhat scattered in the higher-Q region, interference features are clearly identified in the range of Q < 10 Å-1. Distribution function, GLi(r), indicating the distribution of water molecules around Li+, observed for 1 mol% LiCl and 1.1 mol% LiClO4 solutions are shown in Fig. 3. The first and second peak located at r ~ 2 and 2.6 Å observed in GLi(r) for both solutions are assigned to the nearest neighbor Li+…O(D2O) and Li+…D(D2O) interactions, respectively. The Li+…D peak for the LiClO4 solution seems slightly asymmetric probably due to ripples associated with the statistical uncertainties involved in the observed ∆Li(Q). The third peak appearing at r ~ 4.3 Å clearly indicates that the second hydration shell of Li+ is present in these solutions. The second hydration shell in the LiClO4 solutions seems more pronounced, suggesting that ClO4- might be involved in the second hydration shell of Li+. In the present analysis of the ∆Li(Q) for the LiCl solution, the contribution of the second hydration shell was treated as a single interaction between Li+ and D2O with the bj value in eq 3 being 2bD + bO. The structural parameters were determined by the least squares fitting analyses of the observed ∆Li(Q) to avoid the uncertainties caused from truncation effect associated with the Fourier transform. In the preliminary analysis, it has been found that the second hydration shell of Li+ in the LiClO4 solution cannot be reproduced by a single interaction. Then, two Li+…D2O interactions for the second hydration shell were involved in the model function for LiClO4 solution. The best-fit of calculated ∆Li(Q) is compared with observed ones in Figs. 2. Satisfactory


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agreement was obtained for observed and calculated ∆Li(Q) in the whole Q-range employed. The results of the least squares fitting analyses of the ∆Li(Q) observed for LiCl and LiClO4 solutions are summarized in Tables 4 and 5, respectively. The present values of the nearest neighbor Li+…O(water) distances, rLiO = 2.01 ± 0.02 and 1.97 ± 0.02 Å determined for LiCl and LiClO4 solutions are slightly longer than that reported for concentrated LiCl solutions (1.95 ± 0.02 Å for 16.7 mol% LiCl,13 1.95 ± 0.02 Å for 6.7 mol% LiCl,16 and 1.96 ± 0.02 Å for 22 mol% LiCl16 solutions). On the other hand, the present rLiO value is in good agreement with that reported for more dilute 1 mol% LiNO3 solution (2.00 ± 0.02 Å).19 The hydration number of Li+ for the LiCl and LiClO4 solutions was determined to 5.9 ± 0.1 and 6.1 ± 0.1, respectively. The present hydration number is obviously larger than that reported by Mason et al.(4 ~ 5),18 and suggesting that the lower-concentration limit of nLiO is close to 6. In order to discuss the concentration dependence of the nearest neighbor Li+…O distance and coordination number, the present results of rLiO and nLiO are compared with those reported for various aqueous Li-salt solutions. Figure 4a summarizes literature values of the nearest neighbor Li+…O distance against the mole fraction of LiX which have been obtained from neutron diffraction studies with 6Li/7Li isotopic substitution method.13-19, 39-44 The rLiO value seems constant at 1.95 - 1.96 Å in the range of x > 0.05 and slightly increases to ~ 2 Å in more dilute region. On the other hand, the hydration number of Li+ exhibits strong concentration dependence as shown in Fig. 4b. The nLiO in the lower concentration limit approaches to ~ 6 which is in accordance with the present results. The hydration number of Li+ gradually decreases to ca. 4 at solute concentration of ~ 15 mol% LiX, where no indication of contact ion pair formation has been suggested from the neutron experiments. Li…X contact ion pair formation has been reported for concentration range above ~ 20 mol% LiX.17, 39-41 On the other hand, the hydration number of Li+ predicted from most of


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classical45-48 and ab initio7, 49 MD simulation studies is concentration independent and close to 4. More recently, the reduced charge model of ions has been examined for interaction potential employing in the MD simulation to reproduce the experimentally obtained hydration structure of alkali metal and halogenide ions,50,51 however, the simulated hydration number of Li+ shows apparent discrepancy, i.e. ca. 451 and ca. 6.50 Ibuki and Bopp have recently proposed interaction potentials for MD simulation of aqueous LiCl solutions that well reproduce hydration structure of Li+ as well as Li+…Cl- ion pair formation in wide solute concentration range,52 however, simulated cation-cation distribution functions exhibit unrealistic short-distance peak even in very dilute solutions. Obviously, more sophisticated potential models for the MD simulation of aqueous LiCl solutions are necessary. The results of the present study clearly indicate that the concentration dependence of the hydration number of Li+ exists. In order to establish the hydration structure of Li+ in more dilute aqueous solutions, neutron diffraction study on aqueous Li-salt solutions of concentration range below 1 mol% LiX should be necessary. The experimental information of interionic distribution functions such as gLiLi(r), gClCl(r),53 and gLiCl(r) as well as partial structure function between water molecules14,54,55 in the intermediate concentration range (5 – 10 mol% LiCl) is also necessary to deduce full description of the structure of aqueous electrolyte solutions. These will be a future experimental subject by using high-intensity neutron diffractometer.

CONCLUSIONS Neutron diffraction with 6Li/7Li isotopic substitution method has been extended for dilute aqueous 1 mol% LiCl and 1.1 mol% LiClO4 solutions by using high-performance pulsed neutron


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diffractometer NOVA. The normalization of observed scattering intensities was carefully examined by employing the least squares fitting analysis of intramolecular interference term of D2O as an internal standard. The structural parameters concerning the first hydration shell of Li+ were determined through the least squares fitting analysis of the observed first-order difference function, ∆Li(Q). The hydration number of Li+ was determined to 5.9 ± 0.1 and 6.1 ± 0.1 for 1 mol% LiCl and 1.1 mol% LiClO4 solutions, respectively. The present results clearly indicate that the hydration number of Li+ in the lower concentration limit is close to 6.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Y. Kameda)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors thank members of the NOVA experimental group for their help during neutron diffraction measurements. Neutron scattering experiments were approved by the Neutron Scattering Program Advisory Committee of IMSS, KEK (Proposal No. 2014S09). All calculations were performed at Yamagata University Networking and Computing Service Center. This work was partially supported by Grant-in-Aid for Scientific Research (C) (Nos.


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20

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Figure Captions Figure 1. Total interference term observed for 1.0 mol% LiCl- and 1.1 mol% LiClO4-D2O solutions (red dots). The best-fit of the calculated intramolecular interference term (blue line). The residual functions are indicated below.

Figure 2. First-order difference functions, ∆Li(Q), observed for 1.0 mol% LiCl- and 1.1 mol% LiClO4-D2O solutions (red dots). The best-fit of the calculated intramolecular interference term (blue line). The residual functions are indicated below.

Figure 3. Distribution function, GLi(r), around Li+ observed for 1.0 mol% LiCl- and 1.1 mol% LiClO4-D2O solutions (black dots). Short-range Li+…O(D2O) and Li+…D(D2O) interactions in the first hydration shell are indicated by red and blue lines, respectively. Contribution from the second hydration shell is denoted by green lines. The long-range random distribution of atoms is indicated by purple lines.

Figure 4. Concentration dependence of a) the nearest neighbor Li+…O distance and b) hydration number of Li+ observed by means of neutron diffraction with 6Li/7Li isotopic substitution method.


21


Page 22 of 31

Table 1 Isotopic composition, average neutron scattering length of Li, total cross section and number density of sample solutions scaled in the stoichiometric unit, (*LiCl)0.01(D2O)0.99 and (*LiClO4)0.0111(D2O)0.9889, σt and ρ0, respectively

Sample

6

(6LiCl)0.01(D2O)0.99

95.6

(7LiCl)0.01(D2O)0.99

0

Li/%

(6LiClO4)0.0111(D2O)0.9889 95.6 (7LiClO4)0.0111(D2O)0.9889

0

7

Li/% 4.4

bLi/10-12 cma

σt/barnsb ρ0/Å-3

0.182

17.684

0.3330

100.0

-0.222

12.696

0.3330

4.4

0.182

18.442

0.3318

100.0

-0.222

12.917

0.3318

a

Taken from Ref. 20.

b

For incident neutron wavelength of 1.0 Å.


22

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Table 2 Values of the Coefficients in eq 1 Sample

A/barns

(*LiCl)0.010(D2O)0.990

0.00464 0.01066 0.00008 0.00000

B/barns

C/barns

D/barns

(*LiClO4)0.011(D2O)0.989 0.00538 0.01182 0.00010 0.00000


23


Page 24 of 31

Table 3 Results of the least squares fitting analysis of total interference term observed for (*LiCl)x(D2O)1-x and (*LiClO4)x(D2O)1-x solutions (Q-range: 10 – 40 Å-1)a

x

solute

rOD/Å

lOD/Å

rDD/Å

lDD/Å

β

0.010

6

LiCl

0.972(1)

0.064(1)

1.548(7)

0.119(5)

1.05(1)

0.010

7

LiiCl

0.974(1)

0.062(1)

1.547(7)

0.120(5)

1.01(1)

0.011

6

LiClO4

0.971(1)

0.064(1)

1.564(9)

0.122(6)

1.05(2)

0.011

7

LiClO4

0.972(1)

0.060(1)

1.561(7)

0.119(4)

1.02(1)

a

Estimated standard deviations are given in parentheses.


24

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Table 4 Results of the least squares fitting analysis of ∆Li(Q) observed for (*LiCl)0.010(D2O)0.990 solutionsa

Interaction Li+…D2O(I)

i…j Li+…O Li+…D

rij/Å 2.01(2) 2.57(1)

lij/Å 0.08(2) 0.18(1)

nij 5.9(1) [11.8]b

Li+…D2O(II)

Li+…D2O

4.4(2) r0/Å

0.48(2) l0/Å

12(4)

Long-range

Li+…X

5.3(3)

0.5(3)

a


b

Fixed to 2nLiO.


25


Table 5

Page 26 of 31

Results of the least squares fitting analysis of ∆Li(Q) observed for

(*LiClO4)0.0111(D2O)0.9889 solutionsa

Interaction Li+…D2O(I)

i…j Li+…O Li+…D

Li+…D2O(II) Li+…D2O Li+…D2O(III) Li+…D2O Long-range a

Li+…X

rij/Å 1.97(2) 2.64(2)

lij/Å 0.12(2) 0.16(1)

nij 6.1(1) [12.2]b

4.2(4) 5.0(5) r0/Å

0.25(8) 0.5(4) l0/Å

8(2) 11(7)

6.0(5)

0.4(7)


b

Fixed to 2nLiO.


26

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(6LiCl)0.010(D2O)0.990

δ(Q)

(7LiCl)0.010(D2O)0.990

δ(Q)

(6LiClO4)0.011(D2O)0.989

δ(Q)

(7LiClO4)0.011(D2O)0.989

δ(Q)


27


Page 28 of 31

Figure 1 Kameda et al.

(*LiCl)0.010(D2O)0.990

δ(Q)

(*LiClO4)0.011(D2O)0.989

δ(Q)

Fig. 2 Kameda et al.


28

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(*LiCl)0.010(D2O)0.990

(*LiClO4)0.011(D2O)0.989



29


Page 30 of 31

b



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Table of Contents


31

in Dilute Aqueous Solutions - American Chemical Society

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