Off-diagonal long-range order, pair distribution function, and structure factor of the ideal Fermi gas inDdimensions and Price’s inequality

1995 ◽  
Vol 52 (1) ◽  
pp. 189-195 ◽  
Author(s):  
M. Howard Lee ◽  
Ming Long
Keyword(s):  
Distribution Function ◽  
Long Range ◽  
Structure Factor ◽  
Pair Distribution Function ◽  
Fermi Gas ◽  
Range Order ◽  
Long Range Order ◽  
The Ideal

Study on the Local Structure of PAN-Based Carbon Fiber Using Radial Distribution Function Based on XRD

2013 ◽  
Vol 664 ◽  
pp. 614-619 ◽  
Author(s):  
Xue Lin ◽  
Cheng Guo Wang ◽  
Mei Jie Yu ◽  
Zhi Tao Lin ◽  
Shan Zhang
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Long Range ◽  
Carbon Fibers ◽  
Radial Distribution ◽  
Local Structure ◽  
Range Order ◽  
Structure Evolution ◽  
Long Range Order ◽  
Rigid Rod

The local structure evolution of polyacrylonitrile (PAN) fibers during pre-oxidation and carbonization was studied using X-ray diffraction (XRD) and radial distribution function (RDF). The nearest inter-chains distance of PAN is 6.88 Å, which is close to the diameter of the “rigid rod” model proposed by Warner. The third neighbor distances of carbon fibers are greater than that of graphite, indicating the planar six-member rings are absent in the carbon fibers from 500 to 1250°C. The structure of fibers transforms from long-range order to long-range disorder during the pre-oxidation process, then transforms from short-range order to long-range order during the carbonization process.

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