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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.


(a) A 〈110〉 zone-axis EDP typical of the (3+3)-dimensional incommensurately modulated (1−x)Bi2O3·xNb2O5 (0.06 ≤ x ≤ 0.25) solid-solution phase for x = 0.2 [see Ling et al. (1998 ▶, 2013 ▶) for details]. (b) An optical micrograph of the perfect dodecahedral symmetry of the millimetre-sized single icosahedral quasicrystal Ho8.7Mg34.6Zn56.8 [see Fisher et al. (1998 ▶); micrograph courtesy of I. R. Fisher].
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fig3: (a) A 〈110〉 zone-axis EDP typical of the (3+3)-dimensional incommensurately modulated (1−x)Bi2O3·xNb2O5 (0.06 ≤ x ≤ 0.25) solid-solution phase for x = 0.2 [see Ling et al. (1998 ▶, 2013 ▶) for details]. (b) An optical micrograph of the perfect dodecahedral symmetry of the millimetre-sized single icosahedral quasicrystal Ho8.7Mg34.6Zn56.8 [see Fisher et al. (1998 ▶); micrograph courtesy of I. R. Fisher].

Mentions: The discovery of long-range ordered incommensurately modulated structures in the early 1960s (Herpin et al., 1960 ▶; Brouns et al., 1964 ▶) and composite modulated structures in the 1970s (Johnson & Watson, 1976 ▶; Pouget et al., 1978 ▶), followed by icosohedral, octagonal, decagonal and dodecagonal quasicrystalline phases (Shechtman et al., 1984 ▶; Ishimasa et al., 1985 ▶; Steurer, 2012 ▶) from the early 1980s onwards [see Janssen (2013 ▶) for a good review of the early history of aperiodic crystals], has by now blown quite large holes in the above definition of crystalline order. For example, three-dimensional integer indexing of reciprocal lattices is no longer possible for aperiodic crystals [see e.g. Fig. 3 ▶a; see also Ling et al. (1998 ▶, 2013 ▶)]. Likewise, the constraint imposed by the original definition that true crystals should never display five-, eight-, ten- and 12-fold rotational symmetries is also clearly no longer necessarily valid [see e.g. Fig. 3 ▶b; see also Fisher et al. (1998 ▶)], although the reluctance to alter the earlier three-dimensional definition lingers on in the ‘quasi’-crystalline or aperiodic, rather than simply crystalline, name often used for these ordered crystals. In a similar manner, the description of all non-Bragg scattering as diffuse scattering in the original meaning of the word ‘diffuse’, i.e. something that does not have a regular shape or is spread out over a large volume, is far too broad and reinforces the need, in this author’s opinion, for a clear distinction between truly short-range order (≲1 nm or so)/genuine ‘diffuse’ scattering, and the rather longer range or intermediate order encoded in the highly structured diffuse intensity distributions shown in Fig. 1 ▶.


A modulation wave approach to the order hidden in disorder.

Withers R - IUCrJ (2015)

(a) A 〈110〉 zone-axis EDP typical of the (3+3)-dimensional incommensurately modulated (1−x)Bi2O3·xNb2O5 (0.06 ≤ x ≤ 0.25) solid-solution phase for x = 0.2 [see Ling et al. (1998 ▶, 2013 ▶) for details]. (b) An optical micrograph of the perfect dodecahedral symmetry of the millimetre-sized single icosahedral quasicrystal Ho8.7Mg34.6Zn56.8 [see Fisher et al. (1998 ▶); micrograph courtesy of I. R. Fisher].
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig3: (a) A 〈110〉 zone-axis EDP typical of the (3+3)-dimensional incommensurately modulated (1−x)Bi2O3·xNb2O5 (0.06 ≤ x ≤ 0.25) solid-solution phase for x = 0.2 [see Ling et al. (1998 ▶, 2013 ▶) for details]. (b) An optical micrograph of the perfect dodecahedral symmetry of the millimetre-sized single icosahedral quasicrystal Ho8.7Mg34.6Zn56.8 [see Fisher et al. (1998 ▶); micrograph courtesy of I. R. Fisher].
Mentions: The discovery of long-range ordered incommensurately modulated structures in the early 1960s (Herpin et al., 1960 ▶; Brouns et al., 1964 ▶) and composite modulated structures in the 1970s (Johnson & Watson, 1976 ▶; Pouget et al., 1978 ▶), followed by icosohedral, octagonal, decagonal and dodecagonal quasicrystalline phases (Shechtman et al., 1984 ▶; Ishimasa et al., 1985 ▶; Steurer, 2012 ▶) from the early 1980s onwards [see Janssen (2013 ▶) for a good review of the early history of aperiodic crystals], has by now blown quite large holes in the above definition of crystalline order. For example, three-dimensional integer indexing of reciprocal lattices is no longer possible for aperiodic crystals [see e.g. Fig. 3 ▶a; see also Ling et al. (1998 ▶, 2013 ▶)]. Likewise, the constraint imposed by the original definition that true crystals should never display five-, eight-, ten- and 12-fold rotational symmetries is also clearly no longer necessarily valid [see e.g. Fig. 3 ▶b; see also Fisher et al. (1998 ▶)], although the reluctance to alter the earlier three-dimensional definition lingers on in the ‘quasi’-crystalline or aperiodic, rather than simply crystalline, name often used for these ordered crystals. In a similar manner, the description of all non-Bragg scattering as diffuse scattering in the original meaning of the word ‘diffuse’, i.e. something that does not have a regular shape or is spread out over a large volume, is far too broad and reinforces the need, in this author’s opinion, for a clear distinction between truly short-range order (≲1 nm or so)/genuine ‘diffuse’ scattering, and the rather longer range or intermediate order encoded in the highly structured diffuse intensity distributions shown in Fig. 1 ▶.

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.