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A modulation wave approach to the order hidden in disorder.

Withers R - IUCrJ (2015)

Bottom Line: The usefulness of a modulation wave approach to understanding and interpreting the highly structured continuous diffuse intensity distributions characteristic of the reciprocal spaces of the very large family of inherently flexible materials which exhibit ordered 'disorder' is pointed out.It is shown that both longer range order and truly short-range order are simultaneously encoded in highly structured diffuse intensity distributions.The long-range ordered crystal chemical rules giving rise to such diffuse distributions are highlighted, along with the existence and usefulness of systematic extinction conditions in these types of structured diffuse distributions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Research School of Chemistry, Australian National University, Building 1.38, Sullivan's Creek Road, Canberra, Australian Central Territory 0200, Australia.

ABSTRACT
The usefulness of a modulation wave approach to understanding and interpreting the highly structured continuous diffuse intensity distributions characteristic of the reciprocal spaces of the very large family of inherently flexible materials which exhibit ordered 'disorder' is pointed out. It is shown that both longer range order and truly short-range order are simultaneously encoded in highly structured diffuse intensity distributions. The long-range ordered crystal chemical rules giving rise to such diffuse distributions are highlighted, along with the existence and usefulness of systematic extinction conditions in these types of structured diffuse distributions.

No MeSH data available.


〈〉 zone-axis EDPs of (a) L3-T0 (MX-1) and (b) an incommensurate polymorph of SiO2-tridymite. The equivalent 〈〉 zone-axis EDP of high-temperature SiO2-tridymite above 250°C, with its characteristic curved diffuse intensity distribution, is superimposed in order to show that the strongest incommensurate satellite reflections in both cases fall on the characteristic diffuse distribution. Indexing in both cases is with respect to the HP P63/mmc ideal tridymite parent structure. See Withers et al. (1994 ▶) and Withers (2003 ▶) for details.
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fig7: 〈〉 zone-axis EDPs of (a) L3-T0 (MX-1) and (b) an incommensurate polymorph of SiO2-tridymite. The equivalent 〈〉 zone-axis EDP of high-temperature SiO2-tridymite above 250°C, with its characteristic curved diffuse intensity distribution, is superimposed in order to show that the strongest incommensurate satellite reflections in both cases fall on the characteristic diffuse distribution. Indexing in both cases is with respect to the HP P63/mmc ideal tridymite parent structure. See Withers et al. (1994 ▶) and Withers (2003 ▶) for details.

Mentions: SiO2-tridymite has been chosen as an illustrative example for two reasons. Firstly, its high-temperature reciprocal space features a complex curved diffuse distribution, the shape of which is by no means obvious (see e.g. Figs. 1 ▶b and 2 ▶), as well as diffuse lines, planes and points in reciprocal space [see Hammonds et al. (1996 ▶) and Dove et al. (2000 ▶)] and, secondly, it possesses extraordinary structural polymorphism (see e.g. Fig. 7 ▶). At least three distinct room-temperature polymorphic phases, as well as at least five other temperature- and/or stress-dependent polymorphic variant phases, have been reported in the literature [see, for example, Graetsch & Flörke (1991 ▶), Withers et al. (1994 ▶), Graetsch (1998 ▶), Hammonds et al. (1996 ▶) and Dove et al. (2000 ▶), and references contained therein]. Such complex polymorphism indicates a very delicate energetic and/or kinetic balance between the multitude of potential ways of combining the various possible types of correlated rotations and coupled displacements of the ideal (parent) highest temperature H1-To (HP) tri­dymite SiO4 tetrahedral framework structure to give lower temperature polymorphic structures.


A modulation wave approach to the order hidden in disorder.

Withers R - IUCrJ (2015)

〈〉 zone-axis EDPs of (a) L3-T0 (MX-1) and (b) an incommensurate polymorph of SiO2-tridymite. The equivalent 〈〉 zone-axis EDP of high-temperature SiO2-tridymite above 250°C, with its characteristic curved diffuse intensity distribution, is superimposed in order to show that the strongest incommensurate satellite reflections in both cases fall on the characteristic diffuse distribution. Indexing in both cases is with respect to the HP P63/mmc ideal tridymite parent structure. See Withers et al. (1994 ▶) and Withers (2003 ▶) for details.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4285882&req=5

fig7: 〈〉 zone-axis EDPs of (a) L3-T0 (MX-1) and (b) an incommensurate polymorph of SiO2-tridymite. The equivalent 〈〉 zone-axis EDP of high-temperature SiO2-tridymite above 250°C, with its characteristic curved diffuse intensity distribution, is superimposed in order to show that the strongest incommensurate satellite reflections in both cases fall on the characteristic diffuse distribution. Indexing in both cases is with respect to the HP P63/mmc ideal tridymite parent structure. See Withers et al. (1994 ▶) and Withers (2003 ▶) for details.
Mentions: SiO2-tridymite has been chosen as an illustrative example for two reasons. Firstly, its high-temperature reciprocal space features a complex curved diffuse distribution, the shape of which is by no means obvious (see e.g. Figs. 1 ▶b and 2 ▶), as well as diffuse lines, planes and points in reciprocal space [see Hammonds et al. (1996 ▶) and Dove et al. (2000 ▶)] and, secondly, it possesses extraordinary structural polymorphism (see e.g. Fig. 7 ▶). At least three distinct room-temperature polymorphic phases, as well as at least five other temperature- and/or stress-dependent polymorphic variant phases, have been reported in the literature [see, for example, Graetsch & Flörke (1991 ▶), Withers et al. (1994 ▶), Graetsch (1998 ▶), Hammonds et al. (1996 ▶) and Dove et al. (2000 ▶), and references contained therein]. Such complex polymorphism indicates a very delicate energetic and/or kinetic balance between the multitude of potential ways of combining the various possible types of correlated rotations and coupled displacements of the ideal (parent) highest temperature H1-To (HP) tri­dymite SiO4 tetrahedral framework structure to give lower temperature polymorphic structures.

Bottom Line: The usefulness of a modulation wave approach to understanding and interpreting the highly structured continuous diffuse intensity distributions characteristic of the reciprocal spaces of the very large family of inherently flexible materials which exhibit ordered 'disorder' is pointed out.It is shown that both longer range order and truly short-range order are simultaneously encoded in highly structured diffuse intensity distributions.The long-range ordered crystal chemical rules giving rise to such diffuse distributions are highlighted, along with the existence and usefulness of systematic extinction conditions in these types of structured diffuse distributions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Research School of Chemistry, Australian National University, Building 1.38, Sullivan's Creek Road, Canberra, Australian Central Territory 0200, Australia.

ABSTRACT
The usefulness of a modulation wave approach to understanding and interpreting the highly structured continuous diffuse intensity distributions characteristic of the reciprocal spaces of the very large family of inherently flexible materials which exhibit ordered 'disorder' is pointed out. It is shown that both longer range order and truly short-range order are simultaneously encoded in highly structured diffuse intensity distributions. The long-range ordered crystal chemical rules giving rise to such diffuse distributions are highlighted, along with the existence and usefulness of systematic extinction conditions in these types of structured diffuse distributions.

No MeSH data available.