Oxygen as a Site Specific Probe of the Structure of Water and Oxide Materials

The method of oxygen isotope substitution in neutron diffraction is introduced as a site specific structural probe. It is employed to measure the structure of light versus heavy water, thus circumventing the assumption of isomorphism between H and D as used in more traditional neutron diffraction methods. The intramolecular and intermolecular O-H and O-D pair correlations are in excellent agreement with path integral molecular dynamics simulations, both techniques showing a difference of $\simeq 0.5\%$ between the O-H and O-D intramolecular bond distances. The results support the validity of a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intramolecular and intermolecular quantum contributions.

Figure 1

(a) The first difference functions $\Delta F_{\mathrm{D}}(Q)/\mathrm{b}=0.0059(2)[S_{\mathrm{OD}}(Q)-1]+0.00262(8)[S_{\mathrm{OO}}(Q)-1]$ and $\Delta F_{\mathrm{H}}(Q)/\mathrm{b}=-0.0033(1)[S_{\mathrm{OH}}(Q)-1]+0.00263(8)[S_{\mathrm{OO}}(Q)-1]$ and (b) the second difference function $\Delta F_{\mathrm{OX}}(Q)$ which is constructed by subtracting $\Delta F_{\mathrm{H}}(Q)$ from $\Delta F_{\mathrm{D}}(Q)$ and is equal to $S_{\mathrm{OD}}(Q)$ [or $S_{\mathrm{OH}}(Q)$] if the O-O correlations cancel (see the text). In (a) and (b) the vertical bars give the statistical errors on the measured data points and the solid (black) curves give spline fits that were used to generate the corresponding real space functions shown in Fig. 2. The broken (red) curves show the path integral molecular dynamics results.

Figure 2

(a) The first difference functions $\Delta G_{\mathrm{D}}(r)/\mathrm{b}=0.0059(2)[g_{\mathrm{OD}}(r)-1]+0.00262(8)[g_{\mathrm{OO}}(r)-1]$ and $\Delta G_{\mathrm{H}}(r)/\mathrm{b}=-0.0033(1)[g_{\mathrm{OH}}(r)-1]+0.00263(8)[g_{\mathrm{OO}}(r)-1]$, where $g_{\alpha \beta }(r)$ denotes a partial pair distribution function. The O-H correlations in $\Delta G_{\mathrm{H}}(r)$ have a negative weighting factor because $b_{\mathrm{H}}<0$. The first peak or trough arises from intramolecular O-D or O-H correlations and gives a measured coordination number of 1.9(1) or 2.0(2), respectively. (b) The second difference function $\Delta G_{\mathrm{OX}}(r)$ which is equal to $g_{\mathrm{OD}}(r)$ [or $g_{\mathrm{OH}}(r)$] if the net quantum effects are sufficiently small that the O-O correlations cancel (see the text). The measured function gives a first peak at 0.987(5) Å with a coordination number of 2.0(1). In (a) and (b) the solid curves were obtained by Fourier transforming the spline fitted data sets presented in Fig. 1 before and after the application of a Lorch modification function. The data obtained from the first procedure were joined with the data obtained from the second procedure after the first peak or trough. The path integral molecular dynamics results are shown by circles.