SYNOPSISWide-angle X-ray diffraction studies of crossbreed silk fibers and fibers annealed at various temperatures for different periods of time were carried out to evaluate the crystal size and lattice distortion parameters, as these determine the properties of silk fibers. Also, minimum enthalpy for the formation of these fibers has been estimated and compared.
I NTRO DUCT10 NSilk, which is a fibrous protein, is one of the industrially important fibers. Wide-angle X-ray scattering studies (WAXS) by earlier investigators of silk fibers have shown that they are partially crystalline.' For a perfect crystal, the diffraction pattern would comprise of an array of very small spots. For silk fibers, the spots are made into arcs that are caused by two types of defects present in the silk fibers: first, the lattice distortion, and, second, the effect of the crystal size.' Using Fourier analysis of the scattered X-ray reflections, we determined the crystal size and lattice distortion parameters for (210) equatorial reflections of crossbreed silk fiber and the effect of annealing on these parameters has been studied. Also, we determined the minimum enthalpy for the formation of these fibers. Such studies have not been reported earlier except for determining the cell p a r a r n e t e r~~-~ and percentage of crystallinity6 for natural silk fibers.Both multiple-and single-order methods used to separate crystal size and distortion parameters are derived from the theory of Warren-Averbach7 utilizing the Fourier cosine coefficients of the intensity profile. Somashekar et al? and Hall and Somashekar' considered various aspects of multiple-and single- CCC 0021-8995/93/060949-04 order methods. Recently, we extended a single-profile method to natural polymers.1°
THEORYThe intensity profile of the X-ray reflection from a partially crystalline sample like natural silk fibers is a function of the distribution of crystal sizes and of the lattice distortion g, and these are related through the Fourier coefficients A ( n ) to the profile intensity I ( S) by the equationHere, So is the value of S ( = sin B / h ) at the peak of the profile; d , the mean d-spacing of the lattice planes causing the reflection; and n , the harmonic number.The Fourier coefficients can be factorized into size As ( n ) and disorder coefficients Ad ( n ) :These are not normalized. By taking the exponential distribution function for crystal sizes, which gives fairly reliable results, lo we have the following relations for As( n ) :