X-ray Scattering and O-O Pair-Distribution Functions of Amorphous Ices

Abstract

The structure factor and oxygen-oxygen pair-distribution functions of amorphous ices at liquid nitrogen temperature ( T = 77 K) have been derived from wide-angle X-ray scattering (WAXS) up to interatomic distances of r = 23 Å, where local structure differences between the amorphous ices can be seen for the entire range. The distances to the first coordination shell for low-, high-, and very-high-density amorphous ice (LDA, HDA, VHDA) were determined to be 2.75, 2.78, and 2.80 Å, respectively, with high accuracy due to measurements up to a large momentum transfer of 23 Å^-1. Similarities in pair-distribution functions between LDA and supercooled water at 254.1 K, HDA and liquid water at 365.9 K, and VHDA and high-pressure liquid water were found up to around 8 Å, but beyond that at longer distances, the similarities were lost. In addition, the structure of the high-density amorphous ices was compared to high-pressure crystalline ices IV, IX , and XII, and conclusions were drawn about the local ordering.

Figure 1

Example of data treatment using an HDA sample. (A) Scaling of the background (blue) to the sample I(Q) (red). (B) I(Q) (red) shown after subtraction of the background (see A) and Compton scattering (blue) plotted together with the molecular form factor (green). (C) Comparison of total structure factor S(Q) (red) and the oxygen–oxygen interaction S_OO(Q) (black). To visualize the differences at higher Q, S(Q) is multiplied by Q.

Figure 2

Structure factors at short and intermediate ranges for HDA (=eHDA), LDA (=LDA-II), and VHDA, averaged from individual runs within the same batch (see the SI). (A) First and second maximum in S(Q). (B) Full-range structure factor multiplied by Q. All data are averaged over five sample positions.

Figure 3

Partial distribution function for oxygen–oxygen interactions for LDA (blue, LDA-II), HDA (red, eHDA), and VHDA (green), averaged from individual runs within the same batch (see the SI). (A) First coordination shell. (B) Short-range correlations. (C) Intermediate-range correlations at 7–15 Å. (D) Intermediate-range correlations at 15–23 Å.

Figure 4

Running O–O coordination number of LDA (blue), HDA (red), and VHDA (green). (A) Short-range. (B) Full range.

Figure 5

Oxygen–oxygen distribution function of amorphous ice (solid line) compared with crystalline ice (dashed) calculated from structure models. (A,B) LDA and hexagonal ice. (C,D) HDA, ice IX, and ice IV. (E,F) VHDA and ice XII. In panels (B), (D), and (F), the crystalline data are scaled by a factor of 1/3 and shifted upward by 0.7 for better comparison.

Figure 6

Liquid water comparison with LDA and HDA. (A) Structure factor. (B) Short-range PDF. (C) Intermediate-range PDF. At short range, the liquid water data was multiplied by 3 and at intermediate range the liquid water was multiplied by 5 in order to magnify the structures for better visibility.

Figure 7

Comparison of experimental high-pressure liquid water from Skinner et al. with HDA data. (A) Structure factor. (B) Short-range PDF. (C) Intermediate-range PDF.