Long-Range Order in Two- and Three-Dimensional Smectic-BLiquid-Crystal Films

1979 ◽  
Vol 43 (10) ◽  
pp. 701-704 ◽  
Author(s):  
D. E. Moncton ◽  
R. Pindak
Keyword(s):  
Long Range ◽  
Three Dimensional ◽  
Range Order ◽  
Long Range Order ◽  
Crystal Films

Transition to long-range order in the three-dimensional random-field Ising model

1991 ◽  
Vol 66 (25) ◽  
pp. 3281-3284 ◽  
Author(s):  
J. P. Hill ◽  
T. R. Thurston ◽  
R. W. Erwin ◽  
M. J. Ramstad ◽  
R. J. Birgeneau
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Long Range ◽  
Three Dimensional ◽  
Range Order ◽  
Long Range Order ◽  
Random Field Ising Model

Mixed-morphology and mixed-orientation block copolymer bilayers

RSC Advances ◽  
2014 ◽  
Vol 4 (72) ◽  
pp. 38412-38417 ◽  
Author(s):  
Nicolás A. García ◽  
Raleigh L. Davis ◽  
So Youn Kim ◽  
Paul M. Chaikin ◽  
Richard A. Register ◽  
...  
Keyword(s):  
Block Copolymer ◽  
Long Range ◽  
Three Dimensional ◽  
Range Order ◽  
Long Range Order

Three-dimensional block copolymer structures with long-range order and mixed symmetries.

Evaluation of paracrystalline distortions from line broadening

1970 ◽  
Vol 26 (2) ◽  
pp. 272-277 ◽  
Author(s):  
W. Vogel ◽  
R. Hosemann
Keyword(s):  
Long Range ◽  
Three Dimensional ◽  
Quantitative Information ◽  
Cylindrical Symmetry ◽  
Range Order ◽  
Long Range Order ◽  
Line Broadening ◽  
Dimensional Lattice ◽  
Lattice Cell ◽  
Point Lattice

If the units building up a three-dimensional lattice have different sizes and/or shapes and are randomly distributed the long-range order of the point lattice is destroyed. The integral widths δb of the Debye–Scherrer lines increase quadratically with sin θ for a given set of netplanes. Studying the slopes for the reflexions h00, hh0 and hhh one obtains quantitative information on the paracrystalline distortions in the lattice. In the present paper these slopes are calculated for p.c., b.c.c. and f.c.c. lattices and identical coordination statistics with cylindrical symmetry and two fluctuation parameters α,β. The slopes can be conveniently normalized to the fluctuation Δxa of a lattice cell. In a logarithmic Δxa versus β 2/(α 2 + β 2) plot of all these types of paracrystalline lattices, observed Δxa values of manganese-rich spinels are fitted as well as possible. A body centred paracrystalline lattice is observed with α/β = 0.7 ± 0.1. This example may illustrate how to analyse reasonably paracrystalline lattices.

scholarly journals Three-dimensional spin systems without long-range order

1986 ◽  
Vol 265 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Francisco C. Alcaraz ◽  
Laurence Jacobs ◽  
Robert Savit
Keyword(s):  
Long Range ◽  
Three Dimensional ◽  
Spin Systems ◽  
Range Order ◽  
Long Range Order

Quasi-one dimensional magnetic interactions in the three-dimensional hyper-honeycomb framework [(C2H5)3NH]2Cu2(C2O4)3

2021 ◽  
Author(s):  
Anthony C. Jacko ◽  
Benjamin J. Powell
Keyword(s):  
Coordination Polymer ◽  
Long Range ◽  
Three Dimensional ◽  
Spin Chains ◽  
Range Order ◽  
Magnetic Interactions ◽  
Long Range Order ◽  
One Dimensional

Interference between superexchange pathways causes anisotropic magnetic interactions, leading to dimerisation and remnant quasi-one-dimensional spin chains, explaining the absence of long-range order in a 3D coordination polymer.

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