Physica B 405 (2010) 4256–4261

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Physica B

0921-45

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/physb

X-ray peak broadening studies of nanocrystalline hydroxyapatiteby Williamson–Hall analysis

K. Venkateswarlu a,b, A. Chandra Bose b, N. Rameshbabu a,n

a Department of Metallurgical and Materials Engineering, National Institute of Technology, Tiruchirappalli 620 015, Tamilnadu, Indiab Department of Physics, National Institute of Technology, Tiruchirappalli 620 015, Tamilnadu, India

a r t i c l e i n f o

Article history:

Received 4 June 2010

Received in revised form

8 July 2010

Accepted 10 July 2010

Keywords:

Hydroxyapatite

Microwave synthesis

Crystal structure

X-ray diffraction

Anisotropy

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016/j.physb.2010.07.020

esponding author. Tel.: +91 431 2503464; fa

ail addresses: rameshrohith@gmail.com, nrb@

a b s t r a c t

Hydroxyapatite (HA) nanoparticles were prepared by microwave synthesis method and the obtained

powder is annealed at 800 1C for 2 h. The annealed HA particles were characterized by X-ray diffraction

(XRD) and Fourier transform infrared (FTIR) spectroscopy methods. The HA size and morphology were

examined using a transmission electron microscope (TEM). The XRD results reveal that the diffraction

peaks of the annealed HA were of well crystalline and correspond to the hexagonal crystal structure.

The XRD and FTIR results confirm the absence of secondary phases such as b-tricalcium phosphate

(b-TCP) and calcium oxide in annealed HA particles. The TEM result confirms the hexagonal structure of

annealed HA and the particles were observed to be of ellipsoid-like shaped morphology with less

agglomeration. The lattice strain, crystallite size, lattice deformation stress and deformation energy

density for annealed (800 1C) HA nanoparticles were estimated by Williamson–Hall-isotropic strain

model (W–H-ISM), W–H-anisotropic strain model (W–H-ASM) and W–H-energy density model (W–H-

EDM) based on Williamson–Hall (W–H) plot from powder X-ray diffraction data. The results of

estimated average crystallite size of annealed HA by Scherrer and W–H plot methods were compared

with TEM results. It is found that the average crystallite size measured by W–H plot methods is in good

agreement with TEM results.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

Hydroxyapatite [HA, Ca10(PO4)6(OH)2], a major mineral com-ponent of natural bone, has been successfully applied inorthopedic and dental implant applications for several years dueto its excellent biocompatibility [1]. It has also been applied innon-medical fields, such as gas sensors, catalysis and hostmaterial for lasers [2]. In most of the cases in nanomaterials(such as hydroxyapatite), in comparison with micron sizematerials, the densification and fracture toughness are higher[3]. It has also been found that nanoscale particles (1–100 nm)usually have physical properties different from those of bulkparticles (10–100 mm). They exhibit a variety of interestingproperties including magnetic, optical and other physical proper-ties as well as surface reactivity depending on particle size [4].Hence for complete understanding of nanoscale material proper-ties, the crystallite size need to be calculated correctly. Out of allthe methods available for the calculation of crystallite sizeScherrer’s method is a well known method that uses X-raydiffraction patterns to predict the size of crystallites based on the

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width of the diffraction peak. But Scherrer’s formula under-estimates or provides only lower bound to the crystallite sizebecause it has not taken account of peak broadening resultingfrom other important factors such as inhomogeneous strain andinstrumental effects. If the peak broadening contributions fromthese other factors were zero, then the peak width would bedetermined solely by the crystallite size and the Scherrer’sformula would be applicable. If the other contributions to thewidth were non-zero, then the crystallite size can be larger thanthat predicted by the Scherrer’s formula. Unlike Scherrer’smethod, X-ray diffraction peak profile analysis takes into accountpeak broadening resulting from the above said other importantfactors and has been widely used to calculate the grain size, latticedistortion, twinning, stacking fault probabilities and long-rangeand root mean square stresses in nanocrystalline materials [5–7].Apart from these, various analytical methods are being used toestimate the crystallite size and lattice strain present in thematerial from X-ray peak broadening [8].

In nanomaterials both crystallite size and lattice strain havetheir own contribution to X-ray diffraction peak broadening andthe peak broadening contributed by lattice strain is due tolarge volume of grain boundaries [9,10]. Hence the strain presentin the nanomaterial affects the crystallite size measurement. Inorder to measure the crystallite size correctly and to study the

K. Venkateswarlu et al. / Physica B 405 (2010) 4256–4261 4257

modifications introduced by strain in the properties of nanoma-terials, strain calculations are required [11]. However, fitting thepowder diffraction data completely and accurately is complicatedand hence it attracts many indirect methods such as Williamson–Hall method and Warren–Averbach analysis for estimating thelattice strain and crystallite size [12,13]. In Warren–Averbachanalysis the intensity of the diffracted X-ray beam is calculated inFourier space and this intensity is considered as a value given bythe convolution of size and strain broadening [14]. Whereas W–H

analysis is a simplified method that clearly differentiates betweensize induced and strain induced peak broadening by consideringthe peak width as a function of 2y [15].

The objective of this work is to calculate the crystallite size ofnanocrystalline annealed HA particles more accurately frompowder X-ray diffraction data by considering the contributionsof other important factors, namely instrumental and lattice straineffects to the X-ray peak broadening. In addition, other micro-structural parameters such as lattice strain, lattice deformationstress and deformation energy density present in the annealed HAnanoparticles were estimated based on conventional W–H plotusing W–H-ISM, W–H-ASM and W–H-EDM models. From thecrystallite size values obtained from Scherrer and W–H methods,it is observed that there is significant effect of lattice strain oncrystallite size estimated from X-ray diffraction data, which isfurther confirmed by the good agreement between the crystallitesize values obtained from W–H and TEM analyses.

2. Experimental

2.1. Synthesis of HA nanoparticles

Analytical grade calcium hydroxide [Ca (OH)2, E. Merck,Germany] and di-ammonium hydrogen phosphate [DAP,(NH4)2HPO4, E. Merck, Germany] were used for the preparation ofHA nanoparticles by microwave synthesis method. The amount ofthe reactants is calculated based on the Ca/P molar ratio of 10/6. The0.3 M DAP solution in a glass beaker is added to the 0.3 M calciumhydroxide aqueous suspension in 1000 ml glass beaker in 1 minunder high-speed stirring conditions. This 1000 ml glass beakercontaining the precursor mixture with pH of about 11 (Orion 3 star,Thermo electron, USA) is immediately subjected to the microwaveirradiation for an optimized time of 30 min [16] in a domesticmicrowave oven (Samsung India, 2.45 GHz, 850 W power). Themixing, crystallization of HA and its aging occur under themicrowave irradiation in a shorter period. The product obtainedafter filtration is dried at 80 1C for 24 h and the cake obtained afterdrying was powdered with agate mortar and pestle. The as-synthesized HA powder particles were annealed at 800 1C for 2 h.

2.2. Characterization of prepared powder

The X-ray diffraction is carried out for these powder particlesusing a Rigaku Ultima III X-ray diffractometer with Cu Ka1

Table 1Young’s modulus and strain calculation of annealed HA nanoparticles.

hkl Ehkl (GPa) W–H-ASM W–H-EDM

Strain�10�3 Strain�10�3

210 133 0.3909 0.1819

202 175 0.2971 0.1382

310 133 0.3909 0.1819

113 120 0.4333 0.2016

213 140 0.3714 0.1728

004 91 0.5714 0.2659

radiation (l¼1.54056 A) over the 2y range of 20–601, using a stepsize of 0.021 and step time of 4 s. The diffraction pattern ofannealed HA sample consists of well defined peaks. The isolatedand preferred high intensity peaks (shown in Table 1)corresponding to higher diffraction angle were chosen toestimate crystallite size and lattice strain by various modelsbased on the W–H plot. The functional groups present in as-synthesized and annealed HA were ascertained by Fouriertransform infrared spectroscopy (FTIR, Perkin Elmer, SpectrumOne, USA) over the region 450–4000 cm�1 in pellet form for thepowder samples of 1 mg mixed with spectroscopic grade KBr(Merck) of 200 mg. Spectra were recorded at 4 cm�1 resolution,averaging 80 scans. The size and the crystal structure of theannealed HA powders were analyzed by transmission electronmicroscope (TEM, Philips, CM12 STEM, Netherlands). For TEManalysis, the powder sample was ultrasonically dispersed inethanol to form dilute suspensions, and then few drops weredeposited on the carbon-coated copper grids. Electron diffractionpatterns were obtained in microprobe mode with 10 mm selected-area aperture.

3. Results and discussion

3.1. XRD and FTIR analyses of HA nanoparticles

The XRD pattern of annealed HA sample is shown in Fig. 1(a).The annealed HA sample exhibits several diffraction peaks, whichcan be indexed as hexagonal HA. Since the HA nanoparticles wereprepared using precursor materials with stoichiometric Ca/Pmolar ratio of 10/6 and in favorable synthesis conditions[17,18], such as basic pH (pH�11), temperature above 90 1C,suitable microwave irradiation power (850 W) and irradiationtime (30 min), no impurity peaks such as calcium oxide (CaO) orb-TCP were detected in the diffraction pattern after annealing.The presence of impurities, if any, was below the detection limitand hence the annealed HA is greater than 95 wt% phase pure andis acceptable for surgical implant applications as per standards(ASTM F 1185-03). Generally the favorable synthesis conditionsincrease the Ca/P molar ratio of the precipitated HA, which in turnincreases its thermal stability at high temperatures. This suggeststhat the prepared HA particles were thermally stable under theperformed annealing conditions. As compared to the broad X-ray

Fig. 1. X-ray diffraction pattern of hydroxyapatite annealed at 800 1C for 2 h

(a) and as-synthesized hydroxyapatite (b).

Fig. 2. FTIR spectra of as-synthesized hydroxyapatite (a) and hydroxyapatite

annealed at 800 1C for 2 h (b).

Fig. 3. W–H-ISM plot of annealed nanocrystalline hydroxyapatite.

K. Venkateswarlu et al. / Physica B 405 (2010) 4256–42614258

diffraction peaks of HA nanoparticles in as-synthesized condition(Fig. 1(b)), the diffraction peaks of the annealed HA particles(Fig. 1(a)) were narrow and well separated. It confirms that thesample is of improved crystallanity and increased crystallite size.The absence of impurities and an increase in crystallinity ofannealed HA nanoparticles are also proved by FTIR analysis. TheFTIR spectra of as-synthesized and annealed HA were shown inFig. 2(a) and (b), respectively. The characteristic bands for HAwere exhibited in both the spectra: 900–1200 cm�1 forphosphate bending and stretching; 602 cm�1 for phosphatebending; and 632 cm�1 and 3571 cm�1 for librational andstretching modes of hydroxyl vibrations. The intensities of boththe hydroxyl bands and the band at 962 cm�1 for phosphate canbe used to indicate the crystallinity of HA [19]. The intensities ofthese bands increased with annealing treatment and this resultcoincides with the XRD results as shown in Fig. 1. In addition, theabsence of the broad bands at 1630 and 3400 cm�1 in annealedHA is due to the removal of adsorbed water with the annealingtreatment. The broadening of the phosphate characteristic bandsnear 1040 and 1090 cm�1 is due to low crystallinity and smalldimensional effect of as-prepared HA particles [20]. In the case ofannealed HA particles, the phosphate characteristic bands near962, 1040 and 1090 cm�1 and hydroxyl band at 632 cm�1 arecomparatively sharp, which indicates improved crystallinity. Noabsorption bands at 873, 1421 and 1455 cm�1 corresponding tothe presence of carbonate ions, which may come from a reactionbetween carbon dioxide in air and high pH precursor solution[21], were found in the annealed HA compared to as-synthesizedHA particles. It is found that the human bone or synthetic HAwhen heated above 700 1C readily lose their carbonate ions [22].The absence of carbonate bands in sample, annealed at 800 1C inthe present study, is also due to the loss of carbonate ions duringheating in air.

3.2. Determination of crystallite size by Scherrer analysis

Generally, the X-ray diffraction peak broadening is due to theinstrumental broadening, broadening due to crystallite size andlattice strain present in the material. The contributions of each ofthese effects are convoluted causing an overall broadening of thediffraction peaks. Before estimating the crystallite size andlattice strain, it is necessary to correct the instrumental effect.

The instrumental corrected broadening bhkl [23] correspondingto the diffraction peak of HA was estimated using the equation

bhkl ¼ ½ðbh k lÞ2measured�ðbÞ

2instrumental�

1=2 ð1Þ

It is well known that the Scherrer’s formula provides only thelower bound to the crystallite size. Here the crystallite size valueis calculated using Scherrer’s formula to compare with the valuesobtained from the W–H models and TEM analysis results.

The crystallite size Dv of annealed HA is estimated from theScherrer’s equation [24] as

Dv ¼kl

bhkl cosyhklð2Þ

where Dv is the volume weighted crystallite size (nm); k is theshape factor (k¼0.9), l is the wave length of the X-rays(l¼0.154056 nm for Cu Ka radiation); yhkl is Bragg diffractionangle (1) and bhkl is the broadening of the hkl diffraction peakmeasured at half of its maximum intensity (in radians). Thevolume weighted crystallite size Dv measured using Scherrer’sformula is found to be 65 nm.

3.3. Estimation of lattice strain (e) and crystallite size (Dv)

by W–H-ISM

In addition to the instrumental X-ray peak broadening, latticestrain and crystallite size are the other two independent factorsthat contribute to the total peak broadening. The strain inducedline broadening bs is given by the relationbs ¼ 4etanyhkl. Now thetotal peak broadening is represented by the sum of thecontributions of crystallite size and strain present in the material.Assuming that the strain present in the material is uniform, thusconsidering the isotropic nature of the crystal, the W–H equation[25] for the total peak broadening is given by

bhkl cos yhkl ¼KlDvþ4esin yhkl ð3Þ

where K is the shape factor and Dv is volume weighted crystallitesize. A plot is drawn by taking 4sinyhkl along X-axis andbhkl cosyhkl along Y-axis as shown in Fig. 3. In W–H-ISM model,the strain present in the material and the crystallite size are,respectively, extracted from the slope and the intercept of thelinear fit made to the plot. The estimated values of the strainand the crystallite size are given by 4.9436�10�4 and 97 nm,respectively. From Fig. 3, it seems that the conventional

Fig. 4. W–H-ASM plot of annealed nanocrystalline hydroxyapatite. Fig. 5. W–H-EDM plot of annealed nanocrystalline hydroxyapatite.

K. Venkateswarlu et al. / Physica B 405 (2010) 4256–4261 4259

W–H-ISM model is an appropriate approach for the estimation oflattice strain due to less scatter of data points from the linear fit.The better fit of the experimental data points confirms theuniformity of the lattice strain.

3.4. Estimation of lattice deformation stress (s) and crystallite size

(Dv) by W–H-ASM

According to Hook’s law, within elastic limit, there exists linearproportionality relation between stress and strain and is given bys¼Ee where E is the constant of proportionality being the modulusof elasticity or Young’s modulus. This equation is merely anapproximation that is valid for significantly small strain. Assuminga small strain to be present in the annealed HA particles, Hook’slaw can be applied to estimate the lattice deformation stress to areasonable approximation. Beyond the elastic limit or with afurther increase in strain, the stress in the particles deviate fromthis linear proportionality. Hence by assuming that the latticedeformation stress is uniform in all crystallographic directions, thestrain factor in the second term of Eq. (3) is replaced by e¼s/Ehkl

and the modified equation is given by

bhkl cosyhkl ¼KlDvþ

4ssinyhkl

Ehklð4Þ

Here Ehkl is Young’s modulus in the direction normal to the set of(h k l) crystal lattice planes.

The crystallographic direction dependent Young’s modulus inhexagonal crystals [26] is given by

Ehkl ¼½h2þððhþ2kÞ2=3Þþðal=cÞ2�2

s11ðh2þðhþ2kÞ2=3Þ2þs33ðal=cÞ4þð2s13þs44Þðh2þðhþ2kÞ2=3Þðal=cÞ2

ð5Þ

Here s11, s33, s44 and s13 are the elastic compliances and theirstandard hand book values are 7.49�10�12, 10.9�10�12,15.1�10�12 and �4.0�10�12, respectively [27]. A plot is drawnby taking 4sinyhkl=Ehkl along X-axis and bhkl cosyhkl along Y-axis asshown in Fig. 4. The lattice deformation stress and crystallite sizewere, respectively, extracted from the slope and intersection ofthe linear fit made to the plot. The crystallite size estimated byW–H-ASM is 92 nm and the estimated deformed stress is 52 MPa.Under the assumption of uniform lattice deformation stress madeearlier, the anisotropic strain can be estimated using the relationehkl ¼ s=Ehkl. From Fig. 4, it can be observed that though there is asmall scatter of experimental data points nearer to the linear fit, it

allows the uniformity of the stress to a reasonable approximation.Here, the scatter of data points from the linear fit is due to theintroduction of anisotropic Young’s modulus in Eq. 4.

3.5. Estimation of deformation energy density by W–H-EDM

In Eq. (3), it is considered the homogeneous isotropic nature ofthe crystal which, in many cases, is not fulfilled. Moreover, all theconstants proportionality associated with the stress–strain rela-tion are no longer independent when the lattice strain energydensity u is considered. According to Hook’s law u¼ e2Ehkl=2, andtherefore, the modified W–H-ASM equation can be expressed as

bhkl cosyhkl ¼KlDvþ4 sinyhkl

2

Ehkl

� �1=2" #

u1=2 ð6Þ

The graph drawn between bhkl cosyhkl and 4½sinyhklð2=EhklÞ1=2�

is shown in Fig. 5.The uniform lattice deformation energy density u is estimated

from the slope and the crystallite size is estimated from theintersection of the linear fit made to the graph. From Eqs. (4) and(6), the deformation stress and energy density are relatedasu¼ s2

hkl=2Ehkl. It can be noted that in both Eqs. (4) and (6)the anisotropic nature of the elastic constants has been taken intoaccount. In Eq. (4), it is assumed that the lattice deformationstress has the same value in all crystallographic directionsallowing the deformation energy to be anisotropic whereas inEq. (6), the deformation energy density is assumed to havethe same value in all crystallographic directions allowing thedeformation stress to be anisotropic. However, W–H plots drawnusing Eqs. (4) and (6) are virtually the same. For a given sample,W–H plots can be plotted using Eqs. (3), (4) and (6) and theappropriate model can be chosen based on the best fit of theexperimental data. In the present study the root mean squareerror (RMSE) or standard deviation (SD) of experimental datapoints from the ideal linear fit for W–H-ISM (Fig. 3), W–H-ASM(Fig. 4) and W–H-EDM (Fig. 5) is given by 1.44�10�5, 8.32�10�5

and 7.54�10�5, respectively. Though the data points seem to bevisually scattered from the W–H plots, the standard deviationdata show that the scatter from the linear fit is of the orderof 10�5 in case of the three W–H models. This much less signifi-cant SD from the linear fit of the three models supports thatthe assumptions made in the present analysis are acceptable ina reasonable approximation. However, the scattering of the

K. Venkateswarlu et al. / Physica B 405 (2010) 4256–42614260

experimental data pointing away from the linear fit is very muchless significant in W–H-ISM (Fig. 3) compared to W–H-ASM(Fig. 4) and W–H-EDM (Fig. 5). This confirms that the uniformityof the lattice strain is more than that of lattice deformation stressand deformation energy density. Since the data points are close tothe linear fit in all the three models, the estimated crystallite sizeis in agreement with the TEM results as discussed in Section 3.6.The crystallite size, lattice strain, deformation stress and defor-mation energy density are estimated by following the linear fitprocedure in all the three models. Especially the crystallite size isestimated from the intercept made by the linear fit with Y-axis.The intercept value depends on the distribution of the data points,which in turn affects the crystallite size to be estimated. Also, thedistribution of data points with respect to the linear fit dependson its number of points. It suggests that the estimation of thecrystallite size by linear fit procedure depends on the number ofpeaks taken for the analysis [23]. The calculated anisotropicYoung’s modulus and lattice strain values are listed in Table 1 andthe estimated crystallite size, lattice strain, lattice deformationstress and deformation energy density values from W–H analysisare listed in Table 2.

3.6. TEM analysis of nanocrystalline hydroxyapatite

In TEM, the transmitted electron beam is used to create animage of the sample. Elastic or inelastic scattering occurs when

Table 2The estimated microstructural parameters of annealed HA nanoparticles.

Method Parameter (unit) Estimated values

Scherrer analysis Dv (nm) 65

W–H analysis

W–H-ISMDv (nm) 97

e�10�3(no unit) 0.4943

W–H-ASMDv (nm) 92

s (MPa) 52

W–H-EDMDv (nm) 95

u (kJ m�3) 12

TEM analysis Dv (nm) 95710

Fig. 6. TEM micrograph (a) and SAED pattern (b)

the electron beam interacts with matter. Elastic scattering can beboth coherent with a phase relationship and incoherent without aphase relationship among the scattered electrons. Elastic scatter-ing occurring from well-ordered arrangements of atoms as in acrystal results in coherent scattering and gives spot pattern. If thecrystals in the material were randomly oriented as in the caseof a polycrystalline material, the elastic scattering results in a ringpattern. The TEM micrograph and the selected area electrondiffraction (SAED) pattern of annealed HA particles were shown inFig. 6(a) and (b), respectively. It is observed that the annealed HAis of ellipsoid-like shaped morphology. The crystallite size ofannealed HA is estimated from TEM images by image analysisdone with a freely available IMAGE J software and the estimatedaverage crystallite size is 95710 nm (mean7SD). The SAEDpattern confirms the crystalline structure of hexagonal HA and isin agreement with the XRD results.

4. Conclusions

Pure nanocrystalline HA is successfully synthesized by micro-wave method using precursor materials with calcium:phosphor-ous molar ratio of 10:6. There is a significant difference betweenobtained crystallite size value by the Scherrer analysis and theTEM analysis. There is a good agreement between the crystallitesize values obtained by W–H-ISM, W–H-ASM and W–H-EDMmodels and that obtained by TEM analysis. Hence, W–H analysisby the three models results in more accurate estimation ofcrystallite size compared to Scherrer analysis. Therefore it issuggested that the contribution from instrumental effects andlattice strain effect to the X-ray peak broadening need to beconsidered while calculating the crystallite size value of nano-materials. Within the materials elastic limit, the W–H models canbe applied to estimate other microstructural parameters such aslattice strain, lattice deformation stress and lattice deformationenergy density in a reasonable approximation. The crystallite sizeand the lattice strain values obtained from the W–H-ISM modelcan be further extended to estimate the dislocation densitiespresent in the material with more accuracy.

of annealed nanocrystalline hydroxyapatite.

K. Venkateswarlu et al. / Physica B 405 (2010) 4256–4261 4261

Acknowledgements

The authors would like to acknowledge the grants fromDepartment of Biotechnology, New Delhi (BT/PR-11731/MED/32/99/2008, dated 19-08-2009) and Department of Science andTechnology, New Delhi (SR/NM/NS-27/2008, dated 25-02-2009).The authors would also like to thank Dr. M. Chidambaram,Director, National Institute of Technology, Tiruchirappalli, for hisconstant support and encouragement.

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