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Sizestrain study of NiO nanoparticles by X-ray powder diffraction line broadening

N.S. Gonalves a,b,, J.A. Carvalho c, Z.M. Lima c, J.M. Sasaki a

a Departamento de Fsica, Universidade Federal do Cear, Campus do Pici, 60440-970, Fortaleza, CE, Brazilb Instituto Federal de Educao, Cincia e Tecnologia do Cear, Campus Acara, 62580-000, Acara, CE, Brazilc Engenharia de Materiais e Cincia de Materiais, Universidade Federal do Cear, Campus do Pici, 60440-554, Fortaleza, CE, Brazil

a b s t r a c ta r t i c l e i n f o

Article history:

Received 16 October 2011

Accepted 9 December 2011

Available online 16 December 2011

Keywords:

X-ray techniques

Nanoparticles

Microstructure

We show that the nanoparticle sizes calculated from the X-ray powder diffraction need to be analyzed morecarefully when calculated by the Scherrer equation. When nanoparticles are not perfect crystals, microstraincontributes to the line broadening of diffraction peaks. This additional width of the diffraction peak can introduce a

wrong estimateto thenanoparticle size. Inthis work,we show how to calculatedirectly the size andthe microstrainfor NiO nanoparticles using the WilliamsonHall plotting and compare with results obtained from the Scherrer

equation. In additional to these results is that the straight line obtained in the WilliamsonHall plotting shows the

homogeneity of the nanoparticles.Crown Copyright 2012 Published by Elsevier B.V. All rights reserved.

1. Introduction

Studies of materials in the nanoscale need characterization of

microstructure with emphasis in the particle size and microstrain.To estimate the particle size using X-ray powder diffraction (XRPD)measurements, the Scherrer equation is the most used method [1].According to Azaroff, the particle size (D) can be calculated using the

Scherrer equation[2]:

D k=cos 1

where k is theshape coefcient for the reciprocal latticepoint and shapecoefcient for crystal in the direct space[3],is the wavelength of the

incident radiation,is the full-width at half-maximum (FWHM) of thepeak andis the Bragg angle. In the Scherrer equation, the parameterneeds to be corrected to eliminate the so-called instrumental effects[4].A classical method to make this correction uses a standard sample with

small microstrain and great particle size so that the widths of diffractionpeaks observed are only due to instrumental effects [5]. There isa simpleapproach to separate contributions of sample andinstrumental effects tothe peak width using Gaussian prole. Letexpbe the measured width,

standardthe width due to standard sample, i.e., the instrumental width,andthe corrected one. According to Cullity[6]the best expression for

this instrumental effect correction is:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp

2standard

2q

: 2

The Scherrer equation gives us a rough estimate of particle size.

Despite the well-known accuracy of this method, it neglects theimportance of the microstrain, , and its effects in the powder diffraction

pattern[7].Differentiating the Bragg equation, the microstrain, 2 d=d, can

be written as[8]

d

d

cot

yields 2 2

d

d

tan; 3

where d is the d-spacing in the crystal and d is the fractionalvariation of this parameter. The contribution of the microstrain to theline broadening of the diffraction peak is[8]

4tan: 4

A simple method to separate the contributions of particle size

and microstrain to the line broadening in the XRPD patterns isthe WilliamsonHall (WH) plotting [9]. This analysis supposes

that particle size (D) and microstrain () contribute to the linebroadening with Lorentzian proles described by:

D ; 5

where is considered as the sum of the peak width due to themicrostrain and due to particle size. WH plotting assumes thatthose contributions to the peak width are convoluted in the Full

Width at Half Maximum (FWHM) of the diffraction peak. CombiningEqs.(1), (4) and (5), the WH equation can be written as[9]

cos k

D

4

sin: 6

Materials Letters 72 (2012) 3638

Corresponding author at: Departamento de Fsica, Universidade Federal do Cear,

Campus do Pici, 60440-970, Fortaleza, CE, Brazil. Tel.: +55 85 88520634.

E-mail address:nizomar@

sica.ufc.br(N.S. Gonalves).

0167-577X/$ see front matter. Crown Copyright 2012 Published by Elsevier B.V. All rights reserved.doi:10.1016/j.matlet.2011.12.046

Contents lists available at SciVerse ScienceDirect

Materials Letters

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m a t l e t


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The practical application of the WH plotting consists in the con-struction of a plot /cos versus sin . When the sample exhibits

homogeneous distribution of particle size and microstrain the WHplotting has a straight line. The graph can be tted by a linearfunction that provides the microstrain value from the slope andthe mean particle size from the intercept with the axis. The slope

can be positive, negative or horizontal. The positive slope indicatesa lattice expansion. The negative slope indicates a lattice compres-sion. The horizontal slope indicates perfect crystals (particles free

of microstrain).Forthis work we present the mean particles sizes for NiO calculated

from XRDP patterns by using the WH plotting method considering theeffect of microstrain and then compare with those mean particle sizesobtained with Scherrer equation. Then we use a corrected line widthinthe Scherrer equation to calculate particle size.

2. Experimental

NiO was prepared [10,11] by dissolving commercial avorlessgelatin in 30 ml of distilled water, NiCl2.6H2O and NaOH in stoichiometric

quantities. The solution was stirred constantly at 40 C through 10 minand then, dried at 100 C through 24 h. The dried gel (xerogel), with ap-pearance of a resin, was heated up at a rate of 10 C/min and calcined at350 C for 3 h in a rotating alumina tube furnace at 17 rpm using air at-mosphere. The nal powder was washed with H2O2and distilled water

to eliminate undesirable soluble phases.The X-ray powder diffraction experiments were performed in a

Rigaku powder diffractometer (DMAXB) using the BraggBrentanogeometry in a continuous mode with a scan speed of 0.25/min. ACuK radiation tube with the line focus was operated at 40 kV and25 mA. The X-ray powder diffractions (XRPD) were taken in the

range of 2090 (2) in step sizes of 0.02. The diffracted X-raybeam coming from the sample is focused into the detector slit with

a curved graphite monochromator. The crystalline phase was identi-ed using the International Center for Diffraction Data (ICDD) catalog.Rietveld renement procedures[12]were applied to diffraction pat-terns using the interface DBWS9807-Tools [13], as described by

Young et al.[14]. The FWHM was used to calculate the particle sizefor crystallographic families. The Lorentzian function was selected to

t the peak proles of the identied crystalline phase.

To correct the line broadening for the instrumental effects wehave used the approach described before in Eq.(2), where standardwas obtained from standard LaB6powder (SRM660-National Instituteof Standard Technology) using the Caglioti equation[15]

standard

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu tan2 v tan w;

q 7

where u, v and w were obtained from Rietveld renement analysiswhere u = 0.0186, v =0.0244 and w=0.0173.

3. Results and discussion

Fig. 1 shows theX-raypowder diffractionpattern of thesample. The

identied phase in the pattern is cubic nickel oxide (ICDD: 47-1049)belonging to the Fm3m space group. There exists a major quantity ofnickel oxide and a small quantity of amorphous phase peak intensity

contribution for background near 2= 20, which came from theburningof the organic gelatin precursor[10].

The average particle size and the microstrain for the sample

were calculated using the WH plotting, showed inFig. 2. The goodstraight line in the WH plotting indicates no dispersion in particle

size and microstrain suggesting that the sample has homogeneousparticle size distribution and microstrain. This method of synthesis

yields homogeneous particles in size and microstrain.

The average particle size and the microstrain were obtained asdescribed below. The procedure includes:

a. To determine the microstrain () from the slope of the straightline in the WH plotting.

b. To determine the average particle size (D) from intercept of thestraight line.

c. To calculate the line broadening due to microstrain for all the dif-

fraction peaks:= 4tan.d. To separate the line width contributions due to microstrain and

due to particle size:

D ; 8

whereDis the line width due to particle size, is the line width

due to microstrain andis the full line width correct for instru-mental effects. The plus sign is used when lattice expansion exists

and the minus sign is used when lattice compression exists.e. To calculate the particle size using the Scherrer equation consider-

ing the corrected line width (Eq.(8)).

This WH plotting method proved that average particle sizeD= 15.4 nm and microstrain is about 0.0020 to the NiO sample.This microstrain is 20 times greater than those of Si powder (0.01%,

that is almost free of microstrain [16]). The positive signal of themicrostrain indicates a lattice expansion also observed by Maia et al.[10]. These results suggest that NiO nanoparticles synthesized by

solgel proteic method are homogenous in size and microstrain.As can be seen inTable 1the average particle size obtained from

the Scherrer equation is 10 nm while the average particle size calcu-

lated using the WH plotting is 15.4 nm. Nanoparticle size estimated

20 40 60 80

{222}

{113}

{002}

{022}

Intensity

(a.u)

2(degree)

{111}

Fig. 1.X ray powder diffraction pattern of NiO.

0.3 0.4 0.5 0.6 0.7

0.0080

0.0085

0.0090

0.0095

0.0100

0.0105

0.0110

{222}

{113}

{022}

{002}

{111}

sin

cos

/

R2= 0.9999

Fig. 2.WilliamsonHall plotting to NiO (dot line is the adjusted function).

37N.S. Gonalves et al. / Materials Letters 72 (2012) 3638


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from Scherrer equation is quite different from that obtained by WH

plotting. This difference can be explained: the microstrain can inducea greater broadening in the diffraction peak while in the Scherrer

equation, the full width of the diffraction peak is considered in thecalculation. The WH procedure presents a correction for this problem.Finally, we have calculated the particle sizes using thecorrected line

widthin the Scherrer equation. This Scherrer equation only considersthe width, D, extracted from Eq.(8). With this correction, the aver-age particle size for each crystallographic direction is about 15.4 nm,that is the value obtained by the WH plotting.

4. Conclusion

This work demonstrates that the XRPD classical method of analy-sis Scherrer equation used in the characterization of crystals and,nowadays, extended to nanomaterials can induce incorrect estimatein the particle size. It is important to consider the WH plotting

when working with nanomaterials because that proved to be a char-acterization of the microstructure revealing particle size and micro-

strain. We suggest the use of a corrected line width in the Scherrer

equation to determine the particle for each crystallographic direction.This study shows that NiO nanoparticles synthesized by the solgel

proteic method and calcined in a rotating tube furnace produce sam-ple with homogeneous particle size and microstrain. The use of a ro-tating tube furnace can distribute better the energy in the calcinationsof the material to synthesize more homogeneous particles.

Acknowledgments

The authors would like to thank Brazilian funding agencies: CNPq

and CAPES for their nancial support and the Gelita for the gelatinused in the preparation of the samples.

References

[1] Vives S, Gaffet E, Meunier C. Mater Sci Eng 2004;A366:22938.[2] Buerger Azaroff. Powder method in X-ray crystallography; 1958.[3] James RW. The optical principles of the diffraction of X-rays. London: G. Bell and

Sons Ltd; 1962.[4] Weibel A, Bouchet R, Bolch'h F, Knauth P. Chem Mater 2005;17:237885.

[5] Guinier A. X-Ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bod-ies; 1994.

[6] Cullity BD. Elements of X-ray diffraction. second ed. Addison-Wesley PublishingCompany; 1978.

[7] Markmann J, Yamakov V, Weissemller J. Scr Mater 2008;59:158.[8] Burton AW, Ong K, Rea T, Chan IY. Microporous Mesoporous Mater 2009;117:

7590.[9] Williamson GK, Hall WH. Acta Metall 1958;1.

[10] Maia AOG, Meneses CT, Menezes AS, Flores WH, Melo DMA, Sasaki JM. J Non-CrystSolids 2006;352:3729.

[11] Meneses CT, Flores WH, Sasaki JM. Chem Mater 2007;19:10247.[12] Rietveld HM. Acta Crystallogr 1967;22:151.[13] Bleicher L, Sasaki JM. Paiva-Santos CO. J Appl Cryst 2000;33:1189.[14] Young RA, Sakthievel A, Moss TS, Paiva-Santos CO. J Appl Crystallogr 1995;28:366.[15] Caglioti G, Paoletti A, Ricci FP. Nucl Instrum Methods 1958;35:2238.[16] Rai SK, Kumar A, Shankar V, Jayakumar T, Rao KBS, Raj B. Scr Mater 2004;51:59.

Table 1

Particle sizes calculated by Scherrer equation, Scherrer equation (corrected line width)

and WH plotting.

Crystallographic

direction

Scherrer

equation

Scherrer

equation

(corrected

line width)

WilliamsonHall plotting

{hkl} D (nm) {hkl} D (nm) D (nm)

{111} 12.2 0.2 {111} 15.3

{002} 11.8 0.2 {002} 15.3

{022} 10.8 0.2 {022} 15.4 15.4 0.3 0.0020 0,0001

{113} 10.3 0.2 {113} 15.4

{222} 10.1 0.2 {222} 15.4

38 N.S. Gonalves et al. / Materials Letters 72 (2012) 3638

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