I I, I I I. I s I s I s I s I s I s (Eq 1) s I I I π θ λ i s (Eq 2) f rG r si s (Eq 3) r r r s s s s s s s s s s s, si s s. s Ann. Phys., Z. Phys., X-ray Diffraction, X-ray Diffraction, s I s, s θ I s s s I I I I s W n s a n b n ds e (Eq 4) W n d e a n b n c n i s si s N ij f i f j s sr ij /r ij f (Eq 5) r ij i j N ij l ij s l ij s rG r s rG r (Eq 6) (Eq 7) (Eq 8) (Eq 9) (Eq 10) r ij l ij N ij a n b n c n K uc sd; A I (Eq 11) p q u v w a, b, A I K, r ij l ij and N ij si s si s si s I r ij l ij K, A, I Table 1 Initial and final short-distance parameters for the silica glass refinement Material Cycle r ij , l ij 0.03 0.06 0.10 0.10 0.10 si s s I uc uc NT NT NT NT NT j f j if j i f i f j f i F j f i f j A ij IP IP ij k,m s sr k,m sr k,m (Eq 12) k,m i j. I s i s I s I s A ij IP ij (Eq 13) N N A ij N N N IP ij Acta Cryst., J. Appl. Cryst., Advances In X-ray Analyses, r r w i w j f i f j r r ij r ij l ij f (Eq 14) i j i j r,R (Eq 15) r,R r R (Eq 16) t. (Eq 17) F rG r rG r dr (Eq 18) J. Appl. Cryst., [...]... X-ray diffraction: Small-Angle Scattering of X-rays, Small-Angle X-ray Scattering, X-rays in Theory and Experiment, X-ray Diffraction Procedures, Newer Methods of Polymer Characterization, Direct Analysis of Diffraction by Matter, J Appl Crystallogr., J Appl Crystallogr., J Appl Crystallogr., Mater Sci Eng., x, y λ λ Small-Angle Scattering of X-rays, Newer Methods of Polymer Characterization, Acta Crystallogr.,... in Applied Physics, J Non-Cryst Solids, J Appl Crystallogr., J Appl Crystallogr., Poly Eng Sci., J Poly Sci Poly Phys., J Poly Sci Poly Phys., J Appl Poly Sci., J Poly Sci Poly Phys., J Poly Sci Poly Phys., Appl Phys Lett., Small-Angle Scattering of X-rays, Small-Angle X-ray Scattering, X-rays in Theory and Experiment, X-ray Diffraction Procedures, Newer Methods of Polymer Characterization, Direct... Cristobalite 0.26 0.28 0 .10 1.00 0.46 0.44 -0 .17 0.00 -0 .32 0.31 0.33 0.76 1 8-2 0 0.75 0.40 0.70 0.72 r s s I I s π ρ π ρ a b b a b b b a rG r r F F rG r rG r dr (Eq 19) rG r dr Table 3 Comparison of the correlation functions F(calc,exp) and F'(calc,exp) for carbon with five models Range Å b-ribbon bent Layer bent (a) (a) (a) b-ribbon Layer (b) (b) (b) a (a) (a) (b) 0.85 0.88 F F b J Non-Cryst Solids, Carbon,... dridrj r (Eq 6) (Eq 7) r r (Eq 8) a (Eq 9) a I h r R, r (Eq 10) (Eq 11) h, (Eq 12) h Small-Angle Scattering of X-rays, X-rays in Theory and Experiment, J Math Phys., J Appl Phys., Kolloid Zh., Acta Metall., x T I I I I d (Eq 13) d I I h I d (Eq 14) x Table 1 Some applications of SAS techniques Materials Subject Technique(s) 32, 33, 34 2, 9, 10 35, 36 18 2, 7 37 18, 38 18, 39, 40, 41, 42 41, 42, 43 44... Phys., X-ray Diffraction, X-ray Diffraction, Phys Rev., J Non-Cryst Solids, Acta Cryst., J Appl Cryst., Advances In X-ray Analyses, J Appl Cryst., J Non-Cryst Solids, Carbon, General Uses • • Examples of Applications • • • • • Samples • • Form: Size: Limitations • • Estimated Analysis Time • Capabilities of Related Techniques • Scanning electron microscopy: • Transmission electron microscopy: • X-ray... Techniques • X-ray or neutron diffraction: • • • X-ray anomalous scattering: Electron energy loss spectroscopy: Magic-angle spinning nuclear magnetic resonance: I I I x (Eq 1) I x hv E E, E hv E (Eq 2) hv x k Physics of Non-Crystalline Solids, Phys Rev., Z Phys., Z Phys., Sci Rep Tohoku Univ., Rev Mod Phys., Phys Rev B, Phys Rev., Phys Rev Lett., Non-Crystalline Solids, Phys Rev., Advances in X-ray Spectroscopy,... 18 2, 7 37 18, 38 18, 39, 40, 41, 42 41, 42, 43 44 19, 21, 31 20, 31 24, 25, 26 24, 25, 26 45 11, 46 46, 47 48, 49 28, 30, 50, 51 29 26 Polymer molecules Configuration SANS 27 Small-Angle Scattering of X-rays, Small-Angle X-ray Scattering, J Appl Crystallogr., J Appl Crystallogr., Mater Sci Eng., Acta Crystallogr., Appl Phys Lett., J Phys., J Am Ceram Soc., Phys Chem Glasses, Phys Chem Glasses, J Mater... Poly Sci Poly Lett., Z Metallkd., Philos Mag A, J Nucl Mater., Phys Status Solidi, Acta Metall., Phys Status Solidi (A), J Phys., Philos Mag A, Philos Mag A, IEEE Trans., Topics in Applied Physics, J Non-Cryst Solids, J Appl Crystallogr., J Appl Crystallogr., Poly Eng Sci., J Poly Sci Poly Phys., J Poly Sci Poly Phys., J Appl Poly Sci., J Poly Sci Poly Phys., J Poly Sci Poly Phys., Appl Phys Lett., General . microscopy: • X-ray diffraction: Small-Angle Scattering of X-rays, Small-Angle X-ray Scattering, X-rays in Theory and Experiment, X-ray Diffraction Procedures, Newer Methods of Polymer Characterization, Direct. alt="" b J. Non-Cryst. Solids, Carbon, Ann. Phys., Z. Phys., X-ray Diffraction, X-ray Diffraction, Phys. Rev., J. Non-Cryst. Solids, Acta Cryst., J. Appl. Cryst., Advances In X-ray Analyses, J text Range, 1412 atom model Tridymite Cristobalite 0.26 0.28 0 .10 1.00 0.46 0.44 -0 .17 0.00 -0 .32 0.31 0.33 0.76 1 8-2 0 0.75 0.40 0.70 0.72 r s s I I s