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8/3/2019 8 X-Rays Diffraction From Fibres
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X-rays Diffractionfrom Fibres
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Typical fibre X-ray diffraction pattern
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Intensity curve-Equatorial scan of
A Nylon6 fibre
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Crystallinity by X-rays
X-ray Diffractometer
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Crystallinity by X-rays
Braggs condition for diffraction: 2dsin = n
Crystallinity:
Scattering from the sample = I(s) (s = 2sin/)
Scattering from the crystallinePart = Ic(s)
Xc = 0 Ic(s)dxs / 0
I(s) dxs
0 I(s) dxs = 4 0
s2 I(s) ds
(For spherical symmetry dxs = 4 s2 ds)
Xc = 0 s2Ic(s) ds / 0
s2I(s) ds ------------------(1)
Powered sample measurementEffect of voids no effect.
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Crystallinity by X-rays
Slope = Cc
Ic - Ia
(Iu Ia)
Crystallinity Index:
Method for materials when 100% amorphous not available
Standard Crystalline and amorphous samples:
Cellulose:-c- hydrolysed in HCl,
a- Alcohol extracted.
(Iu Ia) = Cc(Ic Ia) +B
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X-ray intensity curves of the crystalline and amorphous standards
used for the analysis of cotton cellulose.
X-ray intensity curves of the
crystallinity and amorphous standard
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Crystal Sizes
Scherrers Equation:
Size of the crystal: Lnkl =K / cos
crystal defects also give rise to broadening
hkl diff. peak
Io
I
Small angle Xray scattering for crystal sizes:
2dsin = n
Pseudo Lattice with d ~ 100 Ao, = 0o
Long Periodicity:d = C+A, X = C / (C+A)C
A
1 1.5 2
I
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Small angle Xray scattering for crystal sizes:
Diffracted X rays
Sample
Xray sound
Void Sizes Guiniers Law
lnI(s) = lnI(0) 1/3 s2 R2
I lnI(s) Slope = -1/3 R2
s2
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SASX
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Modulus of PE by X-ray diffraction
Highly oriented PE
002 = 37.379o d002 = 0.127nm
Stress of 1GN/m2, 002 = 37.226o
Strain(?)
2 * 0.127(1 +)Sin(37.226) = 0.1542
= 1/285, Modulus = 1/(1/285) =285 Gn/m2
0 0.5 1.0 1.5
I
Xc = 0.60, = 1000 kg/m3, c = 855 kg/m3
= 0.15 nm
Maximum At 2 of 0.5oLong Period is d 2dsin = n n=1
2*d sin(0.5/2) = .15nm
d =~ 20 nm
d= c+a X = c/(c+a) = 0.7
c=(c+a) * 0.7 = 20 * 0.7 = 14 nm
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Schematic Presentation of various small angle patterns
Two point pattern:
Four point pattern:
Equatorial Pattern:
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Typical Results from SAXS in Ao
PE PP Nylon PET
Long Period 90 90 150 180
Crystallite Length 60 60
Amorphous Length 30 30
Diameter 160 120 90 330-160
Nylon 6 Long Period 86, amorp = 28.7; N66 91Ao & 30.3 Ao
Nylon 6 Fibres PET Fibres
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X-ray photographs of nylon fibres
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Crystalline Orientation by X-ray diffraction
Preferred orientation Primary bonds for deformation.
Presence of arcs in diffraction pattern
Hermans Orientation function(Affine deformation):
f = [3(cos2)-1]
fc,z = [3(cos2 c,z)-1]
fa+fb+fc = 0For perfect orientation
= 0,(cos2 ) = 1, f = 1
For random orientation
(cos2) = 1/3, f = 0
For cylindrical symmetry
(cos
2
) = [o/2
I()S
incos
2
d] / [o/2
I()sin d]Experimental Measurement:
Calculate f from the following data:
I() = cos
(cos2 ) = [o /2Sin cos3 d] / [o
/2 cossind]
= o 1 x3 dx / o
1 xdx = x4 *2 / 4* x2 lo1
= [3/2 1] = 1/4
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For uniaxial orientation, a series of (hkl) planes pref. Perpendicular
to fibre direction.
Polyethylene: (110);(200);(020) to determine fa and fbOrthorhombic(a = b = c)
Polyethylene terephthalic lacks (h o o) or (o k o) reflections.
(T, o , 5) off meridian reflection.
Triclinic
cos2 hkl = e2 cos2 n + f2 cos2 + g2 cos2 + 2ef cosa cosb+2fg cosb cos c + 2ge cosa cosb..(1)
e, f, g are geometric constants of the unit cells.
In general cos2 hkl are required to determine fn(1)
Polypropylene: (110) & (040) are used for fc
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Monoclinic 2 = 14.2 2 =16.9
For PP < cos2 c, z > = 1-1.099 < cos2 110, z > -0.901 < cos
2 040, z >
For PET T05 reflection is used for fc determination.
For nylon < cos2 b, z > = 1.0-1.20 < cos2 200, z >-0.795 < cos2 202, z >
Orientation in amorphous regions:-
oriented amorphous halo observed in the case of PET
Biaxial orientation.
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Small-angle diagram of linear polyethylene
drawn to an extension ratio of approx.6:1
at 115oC.Nickel-filtered CuK radiation;
specimen-to-film distance, 400mm fibre
axis,b3
Relationship between the length of themeridian streak and the transverse
dimension of the diffraction source.
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The decomposition of the diffraction
pattern for polypropylene.
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Plot of Iu Ia versus Ic Ia for a typical cotton sample
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Relaxation time distribution controlling the width of loss peak
and length distributions are related to long peak.
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