<
p id="
p-1">Dumo
rtie
rite,
ca. (Al,□)Al
6(BO
3)Si
3O
13(O,OH)
2, has a com
plex and unusual c
rystal st
ructu
re that is sha
red by seve
ral mine
rals and an inc
reasing numbe
r of synthetic mate
rials, which we g
rou
p togethe
r as dumo
rtie
rite-like mate
rials (DLMs). Dumo
rtie
rite has a st
rongly
pseudo-hexagonal o
rtho
rhombic st
ructu
re based on
rod-like double-chains of Al octahed
ra in a f
ramewo
rk based on the {6·4·3·4} semi-
regula
r plana
r tiling. The la
rge hexagonal channels contain chains of face-sha
ring Al octahed
ra attached to the f
ramewo
rk by
rings of SiO
4 tet
rahed
ra. Smalle
r t
riangula
r channels contain
plana
r BO
3 g
rou
ps, while in othe
r mate
rials the t
riangula
r channels a
re occu
pied by tet
rahed
ral o
r py
ramidal g
rou
ps. Holtite and magnesiodumo
rtie
rite a
re isost
ructu
ral with dumo
rtie
rite, while ellenbe
rge
rite,
phos
phoellenbe
rge
rite, ekatite, and the synthetic mate
rials have ve
ry simila
r st
ructu
res to dumo
rtie
rite, but with hexagonal symmet
ry. These mine
rals and mate
rials diffe
r f
rom one anothe
r in the identity of the metal cations occu
pying the f
ramewo
rk and face-sha
ring chains, and in the tet
rahed
ral,
py
ramidal, o
r t
riangula
r g
rou
ps within the hexagonal and t
riangula
r channels. We w
rite the following st
ructu
re-gene
rating function, which desc
ribes both to
pological and stoichiomet
ric
pro
pe
rties of DLMs:
pan class="disp-formula" id="disp-formula-1">
rmula" src="1197/embed/mml-math-1.gif" /> pan>
p><
p id="
p-2">whe
re X is the face-sha
ring hexagonal channel octahed
rally coo
rdinated site, M is the f
ramewo
rk octahed
rally coo
rdinated site, T
p>hp> and T
p>tp> a
re th
ree- to fou
r-coo
rdinate cation sites in the hexagonal and t
riangula
r channels, Φ is a fou
r-coo
rdinate anion site, Θ
p>hp> and Θ
p>tp> a
re th
ree-coo
rdinate basal anion sites, and θ
p>hp> and θ
p>tp> a
re one- to th
ree-coo
rdinate a
pical anion sites. We discuss va
rious st
ructu
ral and c
rystal chemical
pro
pe
rties of DLMs, illust
rating thei
r commonalities as va
riations on the theme desc
ribed by the st
ructu
re-gene
rating function. We also discuss th
ree closely
related st
ructu
res which involve modifications of diffe
rent geomet
rical o
r to
pological as
pects of the DLM st
ructu
re: the st
ructu
re of
lyonsite and its synthetic analogues, the st
ructu
re of satte
rlyite and holtedahlite, and the st
ructu
re of the AB
polyty
pe of the canc
rinite g
rou
p of felds
pathoids.
p>