β0023

ffiffiffiffiffi

Xc

p

¼ K

ð23:3Þ

where β002 is the full width at half maximum (FWHM) of (0 0 2) peak in degree

2θ and constant K is equal to 0.24. In XRD patterns of as-synthesized nanopowders

where any of (1 1 2) and (3 0 0) peaks were missing, FWHM values for (0 0 2) and

(3 1 0) peaks were used to compare the crystallinity. The crystallite size of

nanopowders was calculated using Scherrer’s equation (Joseph and Tanner 2005;

Clausen and Fabricius 2000):

XS ¼

0:9λ

FWHM cos θ

ð23:4Þ

where XS is the crystallite size in nm, FWHM is the broadening of diffraction line at

half of its maximum intensity in radians, λ is the wavelength of X-ray beam, and

2θ is Bragg’s diffraction angle (^). Instrument broadening was measured using

silicon standard so as to correct the value of FWHM. Three high-intensity and

well-separated peaks of XRD spectra were selected for evaluating the mean crystal-

lite size of as-synthesized nanodimensional powders. For calculating the mean

crystallite size of all heat-treated powders, three diffraction peaks (0 0 2), (2 1 1),

and (3 0 0) of XRD spectra were chosen. The mean crystallite size of β-TCP phase

was computed utilizing line broadening of (0 2 10) peak at around 31.0^ (2θ) for

heat-treated nanopowders (Ayed et al. 2001). The diffraction peaks at 25.8^ (2θ)

corresponding to (0 0 2) and 32.9^ (2θ) corresponding to (3 0 0) were examined for

calculating domain sizes along crystallographic axis “a” and “c” of nanodimensional

powders. Cell parameters were calculated using the equation given below (Webster

et al. 2004):

1

d^{2 ¼ 4=3 h2 þ hk þ k2}

a²





þ ^l2

c²

ð23:5Þ

where d is the distance between adjacent planes in a set of Miller indices (h k l).

XRD patterns of HA and cationic substituted HA nanopowders showed only HA

reflections. The reference XRD pattern is shown in Fig. 23.4. The as-synthesized

Fig. 23.4 XRD pattern of

as-synthesized HA

nanopowder

434

S. Kapoor et al.