X-Ray Diffraction Fibre Crystallinity and Orientation

Wide-angle X-ray diffraction (WAXD) of textile fibres (CuKα radiation λ = 0.154 nm, 2θ range 5–50°, Bragg-Brentano geometry for powder diffraction, fibre geometry for orientation measurement) characterises crystallinity, crystal size, d-spacing, and preferred orientation (Herman's orientation parameter f) that determine mechanical properties, dyeability, and shrinkage behaviour of synthetic fibres. Cotton crystallinity (Segal method, ASTM D1421): CI = (I₂₀₀ − Iam) / I₂₀₀ × 100 where I₂₀₀ = intensity at 2θ = 22.8° (cellulose I 200 plane), Iam = intensity at 2θ = 18° (amorphous halo) — native cotton CI 70–80%, mercerised cotton (cellulose II) CI 65–75%, regenerated viscose CI 25–35%. Crystal size by Scherrer equation: D = Kλ / (β cos θ) where K = 0.89 (Scherrer constant), λ = 0.154 nm, β = FWHM (full width at half maximum, radians) of peak, θ = Bragg angle — PET crystal size in (010) direction: undrawn 3.5 nm → drawn DR 5.5: 5.5 nm → heat-set 190°C: 6.5 nm; crystal size growth confirms heat-setting completeness. Herman's orientation parameter f = (3<cos²φ> − 1)/2 where φ = angle between fibre axis and crystal c-axis: f = 1 (perfect axial orientation), f = 0 (random), f = −0.5 (perpendicular orientation) — drawn PET fibre f = 0.85–0.95; undrawn PET f = 0.2–0.4; Kevlar para-aramid f = 0.96–0.99 (near-perfect orientation explains exceptional tensile modulus). SAXS (small-angle X-ray scattering, 2θ < 2°) measures long period L (stacking distance between crystalline lamellae, 10–20 nm for PET): L increases with draw ratio and heat setting temperature — L measurement verifies adequate thermal treatment in fibre production.