SN Applied Sciences

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Comparison of average crystallite size by X-ray peak broadening and Williamson–Hall and size–strain plots for VO2+ doped ZnS/CdS composite nanopowder

  • J. MadhaviEmail author
Review Paper
Part of the following topical collections:
  1. 1. Chemistry (general)


The paper deals with the exhaustive study and analysis of VO2+ ions doped ZnS/CdS composite nanopowder with the help of X-ray peak profile analysis (XPPA). The investigation has been carried out by applying a distinct pattern of Williamson–Hall (W–H) approach viz., uniform deformation model, the uniform stress deformation model and uniform deformation energy density model, and size strain plot (SSP). Fourier transforms infrared spectroscopy (FT-IR), scanning electron microscope and energy dispersive spectra (EDS) and transmission electron microscope (TEM) techniques. The XRD study is high manipulated order and fundamental focus is on phase identification, with some analysis on advanced concepts such as crystallite size and lattice strain have been estimated using the modified form of the W–H methods. XRD pattern confirmed that the structure of the sample belongs to the cubic system. The variation of lattice constant (a) with dopant is assigned to Vegard’s law. The root means square strain was identified from the interionic separation and lattice strain assumed on W–H models. FT-IR spectrum exhibited characteristic vibrational modes of Zn and Cd ions along with other bands. EDS analysis gives information about the elemental composition in the present sample. The shape of VO2+ ions doped ZnS/CdS composite nanopowder was spherical in TEM images. The result showed that there was a good agreement in the particle size obtained from the W–H method and the SSP method with TEM images.


X-ray diffraction FT-IR Co-precipitation method W–H plots 

1 Introduction

The mechanical behavior of micro/nanoscale substance differs for their properties in terms of bulk nature, and it is familiar that “Small or nano range particles are stronger when compare to bulk materials in the present research”. Until now, electron microscopy is being used to analyze the small-scale techniques of objects placed on in situ and ex situ classification. The limitation of electron microscopy technique is a two-dimensional design of top surface from thin-sheet like foil of matter. Over the past twenty years, a large advancement is attained at third group synchrotrons that hard X-ray beam can target lowering down to the 100-nm size [1]. A synchrotron is a certain class of regular particle accelerator, which can transfer the energy of the high-speed electrons into a strong-energy poly-chromatic X-ray beam [2]. The strength of this mechanism as internal stress, research investigation for micro- and the nanoscale instrument is the estimation of stresses along with submicron clarity, the assessment of the unequal principal-stresses, and the evaluation of hydrostatic elements of the stress tensors [3]. Synchrotron diffraction contained three types of techniques namely X-ray scattering, pair distribution function (PDF), X-ray diffraction (XRD) and X-ray absorption spectroscopy (XAS) [4] which can substantially provide structural characteristics of materials with a greater conclusion and completely 3D [1]. During current research dimensions of physics, chemistry, and fabric science, transition metal oxides with nanostructure had mesmerized considerable absorption for the last couple of years concentrate of they are modern electrical and optical address with semiconductor crystals with massive binding energy (60 meV) [5]. Currently, emergent attention has been given to composite nanoparticles taking into consideration that the association of two semiconductor nanocrystals will foremost to a sequence of novel optical and digital residences [6, 7]. Nanostructured semiconductors of type II-VI which are observed to be the leading substance because they are an advantage in a lot of fields like fuel, sensors [8], photoconductors, imaging, solar cells, biological detection, UV sensors, quick wavelength laser diodes, and different luminescence instruments [9, 10]. Amongst II-VI compound semiconductors nanosize particles, Zinc, and cadmium sulfide are mostly useful for the majority part of the promising materials for greater results [11]. Zinc sulfide is a well-ordered nanoscale semiconductor compound for detecting UV [12], visible light considering that of its foremost energy gap of 3.68 eV (345 nm) and extreme reactivity. It has a wide range of possible applications in optoelectronics, optics, and solar energy devices [13, 14]. Cadmium sulfide with a direct bandgap of 2.42 eV (515 nm) [15] has a purpose in window layer materials, [16] LEDs [17] and photodetectors [18]. Its purposes in photodetectors and solar cells when used at the part of in conjunction with narrow energy gap components like CdTe CdSe, CdO etc., in a similar way the nanocomposite matching of band gaps between any two add-ones of II-VI Semiconductor NCs, for illustration of CdSe/ZnS [19] CdS/ZnS [20], CdSe/CdS [21] and ZnO/ZnS [22] has been drastically concerned for the development of the charge transfer efficiency. The doping with transition metal ion VO2+ ions brought a tremendous alteration in structural properties. Additionally, to the easier properties, VO2+ ions doped ZnS/CdS composite nanopowder illustrates reveals further promising functions in the subject of sensors, optoelectronics [23], and ferroelectric memory devices. Doped ZnS/CdS composite nanopowder particles were incorporate with the assistant of remarkable physical and chemical procedure such as spray pyrolysis, RF sputtering, electrochemical deposition, chemical vapor deposition, chemical precipitation and, sol–gel methods [24, 25, 26, 27, 28, 29, 30, 31]. Among all these methods, chemical precipitation was more appropriate and suitable procedure due to simplicity, energy-efficient and eco-friendly route to produce VO2+ ions doped ZnS/CdS composite nanopowder [32]. Secondly, comparative reviews of the suggest particle dimension from the powdered XRD, W–H models, FT-IR, SEM, EDS and TEM measurements. As the study of analytical quantity of dislocation densities are an extremely great deal with TEM investigation. The study of dislocation bend in irradiated substances is also constrained using TEM analysis [33]. The concept of Diffraction peak profile investigation is a highly useful technique to explore the dislocation density, dislocation structure, and population distribution in the technically deformed objects due to such a reason which is a foundation to be a complementary procedure to TEM analysis [34, 35].

At present, XRD was employed in three types of diffraction techniques containing, powder diffraction, single-crystal XRD, and grazing incidence angle diffraction. A black and white X-ray beam of light is used in these experiments [36]. XRD pattern is an acceptable approach to estimate the structural and phase characteristics of single crystals and/or polycrystalline components. Investigation of the mechanical action of micro-/nano size, structures of the electronic device highly essential. Crystallite size has an excellent coherent diffraction domain in XRD. Moreover, the average crystallite size of the particles varied as to the particle size as a result of the existence of grain boundaries and/or polycrystalline aggregates [37]. The formation of strain in the crystalline lattices may be created by various reasons for example lattice dislocations, crystal imperfections, triple junctions, grain boundary, sinter or contract stresses, Coherency stresses stacking faults, etc., [38]. Based on the present XRD pattern, several approaches have been employed to determine the lattice strain and crystallite dimension of elements. Under such a research scenario, we implement three models including Scherrer’s, W–H models and size–strain plot (SSP) methods. In Scherrer’s method, the crystallite size was measured using the maximum intensity of the diffraction peak in the present X-ray diffraction pattern. The Bragg width involvement produced based on crystallite size is in inverse relation to the crystallite size. Although, it should be noted that, the influence of non-uniform strain and instrumental results on the peak broadening has not been mentioned in Scherrer’s method. Thus, Scherrer’s method suggested only a lesser limitation on the average crystallite size [39]. Along with several ways to study and/or evaluate the mean crystallite size and lattice strain attention to the peak profile analysis [Warren–Averbach (W–A) method, Fourier technique, W–H models, and Rietveld refinement technique], W–H analysis is a convenient procedure to estimate the average crystallite size and lattice strain-induced peak broadening taken account into consideration the shift in peak broadening against with an deflection angle of position 2Theta.

During the current research analysis on VO2+ ions doped ZnS/CdS composite nanopowder was synthesized through co-precipitation method. It has been found that this procedure is a simple method and rapid, gentle, energy-efficient and eco-friendly route to develop VO2+ ions doped ZnS/CdS composite nanopowder. Secondly, comparable evaluations of the essential element dimension, precise information about a small volume of sample can discern crystallite shape, as well as size and weight and atomic weight percentage in the prepared sample, can be found from TEM and SEM–EDS analysis. Subsequently, the effect of single concentration (0.01 mol%) of vanadium dopant was investigated on the morphological study of ZnS/CdS composite nanopowder. Transition metal (TM) at a small concentration does not seem to produce noticeable distortions in the structure [40]. The unit cell parameters slightly change with dopant content which shows effectively built into the host lattice due to this there is no secondary diffraction peaks from other crystalline forms are noticed [41]. In the present study, the crystallite size of VO2+ ions doped ZnS/CdS composite nanopowder gives the structural parameters such as average particle size (D), microstrain (ε) and dislocation density (δ) values are evaluated from Scherrer’s method and W–H Analysis. The average crystallite size from XRD is highly correlated with TEM analysis. In extension, the lattice strain was approximated with three W–H models, specifically, (UDM), (USDM), (UDEDM), and (SSP). This analysis outperforms the study which has been made so far.

2 Experimental

2.1 Materials

All chemical reagents which are of the analytical grade, and have been purchased from pure Merck chemical supplies, India. The new synthesized route of a VO2+ ion-doped ZnS/CdS composite nanopowder were used in particular Zinc acetate Zn(CH3COO)2, Cadmium acetate Cd(CH3COO)2, Sodium sulfide (Na2S), Vanadium pentoxide (V2O5) and Ethanol were used as sources. Deionized water was used for all dilution and sample preparation. All the chemicals are above are 99% purity. All the glass wear used in this experimental was acid washed.

2.2 Preparation of VO2+ ions doped ZnS/CdS composite nanopowder

VO2+ ions doped ZnS/CdS composite nanopowder was successfully synthesized by co-precipitation method at room temperature. The powder form of a zinc acetate 0.2 mol% was dissolved in 50 mL same amount of water–ethanol matrix to an equal molar amount of Na2S aqueous solution were mixed drop by drop. The collection of sample mixture was stirred magnetically at 80 °C until a homogeneous milky white precipitate formed. This is the indication of the formation of ZnS nanoparticles. For the next step, 0.09 mol% of cadmium acetate powder was dissolved in a 50 mL equal volume of the water–ethanol matrix which is added to the above colloidal solution then stirred steadily. After 10 min, 0.1 mol% of Na2S 50 mL (prepared in a deionized water–ethanol matrix) solution was mixed dropwise in the above solution, subsequently, after 4 h of continuous stirring, the milky white solution turned to pale yellow colored voluminous precipitate appeared which indicates the composition of ZnS/CdS nanoparticles. Lastly, 0.01 mol% of V2O5 dissolved in 50 mL identical volumes of water–ethanol matrix added to the above composite solution and stirred constantly for 3 h. The obtained solution was washed several times with deionized water to remove undesirable impurities. Then the solution was kept in an ultracentrifuged at 10,000 rpm for about 30 min. The fine powder was collected and dried in a hot air oven at 120 °C for 2 h and grind with agate motor by hand milling. Finally synthesized VO2+ ions doped ZnS/CdS composite nanopowder was obtained and characterized by different techniques.

2.3 Characterization

Powder X-ray diffraction pattern (XRD) of the prepared sample is recorded on Shimadzu XRD 6100 diffractometer. Fourier Transformed Infrared (FT-IR) spectrum was recorded by using KBr pellet on Shimadzu IR Affinity-Is in the range 4000–400 cm−1. Scanning Electron Microscope (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) images were taken from ZEISS EVO 18. Transmission electron microscope (TEM) images are recorded on HITACHI H-7600 and CCD CAMERA system AMTV600 by dispersing the samples in ethanol.

3 Results and discussion

3.1 Structural properties

The X-ray diffraction pattern of the prepared VO2+ ions doped ZnS/CdS composite nanopowder was depicted in Fig. 1 all exhibited XRD peaks were listed by using ZnS and CdS structure with cubic phase, well-matched with (JCPDS) card for ZnS is (05-0566) and for CdS is (80-0019) respectively. The prepared composite nanopowder exhibits an intense as well as narrow width sharp peaks enables the good crystallinity [42]. The peak position shift with transition metal ion doping reveals the changes in the lattice parameters. The lattice constants for cubic structure (a = b = c), the cell volume obtained from the XRD pattern [43]. Apart from the X-ray peak profile evaluation (XPPA) mentioned that a very fine composite nanopowder of ZnS and CdS peaks are present in the sample. There are no observable characteristic peaks of VO2+ ions are noticed in the present X-ray diffraction; due to this, some distortion will be created in the structure of the host lattice. The broadening within the height naturally confirms the XRD outcome that tiny nanoparticles are reflected in the pattern. From Bragg’s diffraction,
$$ 2{\mathbf{dsin}}{\varvec{\uptheta}} = {\mathbf{n}}{\varvec{\uplambda}} $$
where ‘θ’ is the glancing angle, n is an integer which suggests the order of diffraction more often than not than no longer (n = 1), λ (= 1.5406 Å) is the wavelength of X-rays. The interatomic distance (d) is interrelated to the lattice constant parameter “a” and the lattice parameters <h k l> for cubic formation through the following relation [44]
$$ {\bf{d}} = \frac{\varvec{a}}{{\sqrt {\varvec{h}^{2} + \varvec{k}^{2} + \varvec{l}^{2} } }} $$
For the Estimation of the first order, n = 1;
$$ {\mathbf{sin}}^{2} {\varvec{\uptheta}} = \frac{{\lambda^{2} }}{4}\frac{{[{\text{h}}^{2} + {\text{k}}^{2} + {\text{l}}^{2} ]}}{{{\text{a}}^{2} }} $$
The lattice constant as a for simple cubic ZnS and CdS planes are <1 1 1> and <1 1 1> computed by the relation
$$ {\mathbf{a}} = \left( {\surd 3{\varvec{\uplambda}}} \right)/\left( {{\mathbf{2sin}}{\varvec{\uptheta}}} \right) $$
The lattice constant as a for the simple cubic ZnS is 5.4144 Å and CdS is 5.7726 Å corresponding unit cell volumes for simple cubic: ZnS = 158.72 cm3 and cubic CdS = 192.36 cm3. The diffraction peaks corresponding to the planes <1 1 1>, <2 0 0>, <2 2 0>, <3 1 1> and <2 2 2> are consistent with XRD data of ZnS and <1 1 1>, <2 0 0> and <2 2 2> for CdS. Comparison of (dhkl), percentage of variation of d and FWHM from XRD, JCPDS card and corresponding <h k l> planes, are shown in Table 1.
Fig. 1

XRD pattern of VO2+ ions doped ZnS/CdS composite nanopowder

Table 1

Interplanar spacing (dhkl) from XRD, JCPDS data card for corresponding <h k l> planes, percentage of variation of d, and FWHM for VO2+ ions doped ZnS/CdS composite nanopowder

<h k l>

dXRD (Å)


% of contraction in d

FWHM (°)

<1 1 1>





<1 1 1>





<2 0 0>





<2 0 0>





<2 2 0>





<2 2 2>





<3 1 1>





<2 2 2>





3.2 Debye–Scherer’s procedure

The width of the peak broadening evidence grain refinement at the side of the significant stress associated with the energy. Fixed material such as silicon is used to verify the significant broadening. The instrumental corrected enlargement (βhkl) [45] comparable to every diffraction peak of VO2+ ions doped ZnS/CdS composite nanopowder making use of the relation as follows [46]
$$ {\varvec{\upbeta}}_{{{\mathbf{hkl}}}} = {\mathbf{b}} \, [({\varvec{\upbeta}}^{2}_{{{\mathbf{hkl}}}} ) {\text{Measured}}{-}({\varvec{\upbeta}}^{2}_{{{\mathbf{hkl}}}} ){\text{Instrumental}}]^{1/2} $$
For a precise size and strain, the configurational analysis and crystallite size and identification of phase of composition sample were performed by the peak broadening as shown in Fig. 1 the evaluated grain size from the XRD peak by using the Scherer’s formula [47] is given by the following Eq. (6)
$$ {\mathbf{D}}_{{{\mathbf{sch}}}} = {\mathbf{k}}{\varvec{\uplambda}}/{\varvec{\upbeta}}_{{{\mathbf{hkl}}}} {\mathbf{cos}}{\varvec{\uptheta}} $$
For spherical shape k is equal to 0.98, βhkl is the essential half-width, λ is the wavelength of Cu-kα radiation of the incident X-ray (λ = 0.15406 nm), D is the average particle size which is in the order of nanoscale and θ is peak positions for corresponding <h k l>. For VO2+ ions doped ZnS/CdS composite nanopowder, the calculated value of the crystallite dimension is (D) 10.39 nm. Additionally, the dislocation density δ used to be calculated using Williamson and Small man’s formula in lines/m2 [48]
$$ {\varvec{\updelta}} = {\mathbf{n}}/{\mathbf{D}}^{2} $$
where n is approximately equal to 1 [49]. The dislocation density (δ) is 9.2462 × 1015lines/m2. This microstrain arises from the large fraction of exterior atoms and unsaturated affecting bonds, which may be responsible for really a lot of unique chemical and physical properties of the nanoparticles. The strain influence broadening appeared from crystal irregularity and distortion can be related in Eq. (8).
$$ {\varvec{\upbeta}}_{{\varvec{\upvarepsilon}}} = {\mathbf{C}}{\varvec{\upvarepsilon}}{\mathbf{tan}}{\varvec{\uptheta}} $$
$$ \upvarepsilon = {\varvec{\upbeta}}_{{{\mathbf{hkl}}}} /{\mathbf{4tan}}{\varvec{\uptheta}} $$

3.3 Approximation of microstrain (ε)

3.3.1 Williamson–Hall (W–H) models

W–H system [50] is dependent upon the principle which gives the knowledge about size broadening and stress broadening (βε) concerning Bragg viewpoint (θ) extent enlarge will also be interconnected to Debye-Scherer’s (βDS) method as in Eq. (6). The strain-induced broadening coming up from crystal irregularity and distortion may also be associated in Eq. (9).
$$ {\mathbf{\rm B}}{\varvec{\upvarepsilon}} = {\mathbf{C}}{\varvec{\upvarepsilon}}{\mathbf{tan}}{\varvec{\uptheta}} $$
the place, ε is examined from the determined broadening and C is the regular equivalent to 4 that is dependent upon the assumptions made involving the identity of the inhomogeneous stress [51].

3.4 Uniform deformation model (UDM)

As stated by W–H method, the enlargement of the coherent scattering neighborhood is found to be of finite and the internal stress in the arranged compound. In Williamson–Hall proposal the powder X-ay diffraction peak broadening confirms the particle dimension and strain internally. Peak profile evaluation through W–H models and SSP differentiates between strain and size broadening of the peak is considering a consequence of Bragg angle (). The strain effect broadening in composite nanoparticles are approximate distortion and imperfections were estimated by the mechanism,
$$ {\varvec{\upvarepsilon}} = {\varvec{\upbeta}}_{\text{hkl}} /{\mathbf{4tan}}{\varvec{\uptheta}} $$
The width of the peak confirms 1/cosθ varies with crystallite size and tan θ varies as strain, by adding these two present in the composite nanopowder and can be written as
$$ {\varvec{\upbeta}}_{\text{hkl}} = {\varvec{\upbeta}}_{{\mathbf{D}}} + {\varvec{\upbeta}}_{{\varvec{\upvarepsilon}}} \,\left( {{\mathbf{or}}} \right)\,{\varvec{\upbeta}}_{{{\mathbf{hkl}}}} - {\varvec{\upbeta}}_{{\varvec{\upvarepsilon}}} = {\varvec{\upbeta}}_{{\mathbf{D}}} $$
The location βD suggests crystallite dimension contribution and βε prompted through making use of brought about stress broadening and βhkl stated FWHM of instrumental broadening with corrected dimension. The X-ray powder diffraction of each peak is analyzed with the help of the instrumental broadening if the stress and particle dimension contribution are usually no longer based on each different and are independent of every extraordinary and have a Cauchy-equation [52].
From Eqs. (6) and (9)
$$ \upbeta_{\text{hkl}} = {\text{k}}\uplambda/{\text{D}}\cos\uptheta + 4\upvarepsilon\tan\uptheta $$
By way of rearranging Eq. (12), we get
$$ 4\upvarepsilon\sin\uptheta_{\text{hkl}} + {\text{k}}\uplambda/{\text{D}} = \cos\uptheta_{\text{hkl}} $$
From the linear fit of the report a plot of 4sinθhkl versus βcosθhkl, as shown in Fig. 2a the average crystallite size and the microstrain (ε) were obtained from the y-intercept. Strain due to the result of reduction inside the lattice values is ε = 3.333 × 10−3, D = 11.51 nm as summarized in Table 2.
Fig. 2

a Plot of βcosθhkl versus 4sinθhkl for VO2+ ions doped ZnS/CdS composite nanopowder. b Plot of βhkl cosθhkl versus 4sinθhkl/yhkl for VO2+ ions doped ZnS/CdS composite nanopowder. c Plot of βhkl cosθhkl versus \( 4\sin\uptheta_{\text{hkl}} \left( {2/{\text{y}}_{\text{hkl}} } \right)^{1/2} \) for VO2+ ions doped ZnS/CdS composite nanopowder. d Plot of \( \left( {{\text{d}}_{\text{hkl}}\upbeta_{\text{hkl}} \cos \theta_{\text{hkl}} } \right)^{2} \) versus \( \left( {{\text{d}}^{2}_{\text{hkl}}\upbeta_{\text{hkl}} \cos\uptheta_{\text{hkl}} } \right) \) for VO2+ ions doped ZnS/CdS composite nanopowder. e Plot of εrmsversus εhkl for VO2+ ions doped ZnS/CdS composite nanopowder. f Comparison of Scherer’s with W–H models for VO2+ ions doped ZnS/CdS composite nanopowder

Table 2

Geometric parameters for synthesized VO2+ ions doped ZnS/CdS composite nanopowder

Scherrer method

Williamson–Hall method

Size–strain plot

D (nm)




DV (nm)


σ (MPa)

D (nm)

ε × 10−3

D (nm)

ε × 10−3

σ (MPa)

D (nm)

ε × 10−3

σ (MPa)

ued (kJ m−3)

εa × 10−3

εRMS × 10−4















3.5 Uniform stress deformation model (USDM)

Inside entire crystallographic supervision, the deformation stress inside the lattice is uniform and a small microstrain is to be assumed inside the present grain. In order with Hooke’s law stated as σ = ε Yhkl where σ is the stress of the lattice, ε is anisotropic micro stress and Yhkl is the modulus of elasticity. This equation is equitable for small stress. When pressure is extended the particles depart from this correspondence. In this attainment the W–H equation [25] is reshaping through utilizing incorporating (ε) in Eq. (13) we get
$$ {\mathbf{K}}{\varvec{\uplambda}}/{\mathbf{D}} + 4{\varvec{\upsigma}}{\mathbf{sin}}{\varvec{\uptheta}}_{{{\mathbf{hkl}}}} /{\mathbf{Y}}_{{{\mathbf{hkl}}}} = {\varvec{\upbeta}}_{{{\mathbf{hkl}}}} {\mathbf{cos}}{\varvec{\uptheta}}_{{{\mathbf{hkl}}}} $$
For cubic crystal, Yhkl is given by [26]
$$ {\mathbf{Y}}_{{{\mathbf{hkl}} }}= \left( {\frac{{\left( {\left\lfloor{\mathbf{h}}^{2} + \frac{{\left({{\mathbf{h}} + 2{\mathbf{k}}} \right)^{2} }}{3} + \left( {\frac{{{\mathbf{al}}}}{{\mathbf{c}}}} \right)^{2}\right\rfloor^2 } \right)}}{{{\mathbf{S}}_{11} \left( {{\mathbf{h}}^{2} + \frac{{\left( {{\mathbf{h}} + 2{\mathbf{k}}} \right)^{2} }}{3}} \right)^{2} + {\mathbf{S}}_{33} \left( {\frac{{{\mathbf{al}}}}{{\mathbf{c}}}} \right)^{4} + \left( {2{\mathbf{S}}_{13} + {\mathbf{S}}_{44} } \right)\left( {{\mathbf{h}}^{2} + \frac{{\left( {{\mathbf{h}} + 2{\mathbf{k}}} \right)^{2} }}{3}} \right)\left( {\frac{{{\mathbf{al}}}}{{\mathbf{c}}}} \right)^{2} }}} \right) $$
The place S11, S33, S13, S44 are the elastic compliances for CdS are 2.069 × 10−11, 1.594 × 10−11 (− 0.497 × 10−11 m2 N−1), 6.412 × 10−11 m2 N−1 and for ZnS are 1.108 × 10−11, 0.86424 × 10−11, (− 0.2216 × 10−11 m2 N−1), 2.157 × 10−11 m2 N−1 [53, 54] and a, b and c are lattice parameters of VO2+ doped ZnS/CdS nanoparticles respectively [55]. The calculated value of the total Young’s modulus (Yhkl) for VO2+ ions doped cubic ZnS and CdS composite nanopowder is approximately equal to144.54 × 109 GPa which holds good with the theoretical values and is found to be 125.01 × 109 GPa. The plot is drawn between βhkl cosθhkl as a function of 4sinθhkl/Yhkl Fig. 2b. The uniform deformation stress ‘σ’ can be calculated from the slope of the linear fit and the crystallite dimension offers the y-intercept. If Yhkl of ZnS/CdS composite nanopowder can also be acknowledged, stress-energy ε can be known and evaluated given in Table 2.

3.6 Uniform deformation energy density model (UDEDM)

When ued is strain-energy density and is a function of stress is ued = (ε2Yhkl)/2 for elastic nature of a technique adopted with the aid of Hooke’s law, Eq. (14) will also be modified using [56].
$$ {\mathbf{\rm B}}_{{{\mathbf{hkl}}}} {\mathbf{cos\theta }}_{{{\mathbf{hkl}}}} = \, \left( {{\mathbf{k\lambda }}/{\mathbf{D}}} \right) \, + \, ({\mathbf{4sin\theta }}_{{{\mathbf{hkl}}}} \left( {{\mathbf{2u}}_{{{\mathbf{ed}}}} /{\mathbf{Y}}_{{{\mathbf{hkl}}}} } \right)^{{{\mathbf{1}}/{\mathbf{2}}}} $$
The Plot of βhklcosθhkl versus (4sinθhkl (2/Yhkl) 1/2) is depicted in Fig. 2c and slope of the linear fit information represents the value of ued and y-cut mentioned the average crystallite size (D). Where ued = (ε2Yhkl)/2 and linearity between stress and strain is given by σ = εYhkl where the σ was calculated from ued = (σ2/2Yhkl). By knowing Yhkl value, the lattice strain can even be calculated.

3.7 Size-strain plot (SSP)

The ‘Gaussian feature well-known shows strain’ and the “crystallite measurement” profile through Lorentzian function [57]. A different class of evaluation the dimensions stress plot specifications can also be obtained through SSP plot for anisotropic line broadening

$$ \left( {{\mathbf{d}}_{{{\mathbf{hkl}}}} {\varvec{\upbeta}}_{{{\mathbf{hkl}}}} {\mathbf{cos\theta }}_{{{\mathbf{hkl}}}} } \right)^{{\mathbf{2}}} = {\mathbf{1}}/{\mathbf{v}}_{{{\mathbf{s}}.}} \left( {{\mathbf{d}}^{{\mathbf{2}}}_{{{\mathbf{hkl}}}} {\varvec{\upbeta}}_{{{\mathbf{hkl}}}} {\mathbf{cos\theta }}_{{{\mathbf{hkl}}}} } \right) + \left( {{\varvec{\upvarepsilon}}_{{\mathbf{a}}} /{\mathbf{2}}} \right)^{{\mathbf{2}}} $$
where dhkl is the inter-planar spacing, vs is the volume-weighted acceptable size and εa is a evaluate of the apparent stress which is related to root-mean stress (RMS)
$$ \left\langle {{\varvec{\upvarepsilon}}_{{{\mathbf{rms}}}} } \right\rangle = \left( {{\varvec{\upvarepsilon}}_{{\mathbf{a}}} } \right)/{\mathbf{2}}\surd {\mathbf{2\pi }} $$
the volume-weighted actual dimension for spherical crystallites is given with the aid of
$$ {\mathbf{Dv}} = {\mathbf{Vs}}\left( {{\mathbf{4}}/{\mathbf{3}}} \right) $$
The corresponding slope for VO2+ ions doped ZnS/CdS composite nanopowder have been bought from a plot of \( \left( {{\text{d}}_{\text{hkl}}\upbeta_{\text{hkl}} \cos\uptheta_{\text{hkl}} } \right)^{2} \) versus \( \left( {{\text{d}}^{2}_{\text{hkl}} \beta_{\text{hkl}} { \cos }\uptheta_{\text{hkl}} } \right) \) as shown in Fig. 2d. For all diffraction peaks of VO2+ ions doped ZnS/CdS composite nanopowder with the cubic single-phase deflections from 2θ = (0°–70°). The particle size DV is calculated from the slope of the fitted data and the cut off from RMS value was neglected. According to the literature report, isotropic is due to line broadening and the least-squares lines through the points had a non-zero intercept and a positive slope [58]. Comparison of SSP, William, and Hall the lattice strain (ε) is in the first-rate contract with every other in Table 2. Conversely, the SSP procedure is appropriate in evaluation with W–H models for the reason that much less value is given to potential from reflections at excessive angles and the points are linearly fitted. Comparing the entire primary three W–H models, UDM confirm the homogeneous isotropic identity of the crystal whereas USDM and UDEDM confirm the anisotropic nature. In USDM and UDEDM, it most often is noted that even though every Eqs. (14) and (15) are taken into consideration within the anisotropic character of the elastic regular, they are almost specified. Equation (16) reveals deformation energy ued to be homogeneous in all crystallographic in order.

From all methods, the estimated values from the y-cut of the graphs consistent with the conventional crystallite size are found to be 11.36, 11.77, 11.12 and 8.71 nm respectively as shown in Table 2. This is almost similar and also in the order of nanoscale. From the SSP approach, the crystallite dimension value is in well-matched with Scherrer’s method and is in evaluation with W–H models. From these studies, our values are more appropriate to the literature report [30]

3.8 Estimation of RMS strain

According to the Wilson method, the maximum value (εhkl) and root-mean-square micro strains (εrms) across crystallographic planes (h k l) are related by [31, 59].
$$ {\varvec{\upvarepsilon}}_{{{\mathbf{hkl}}}} = \left( {{\mathbf{\Delta d}}_{{{\mathbf{hkl}}}} /{\mathbf{d}}_{{{\mathbf{ohkl}}}} } \right) $$
$$ \left\langle {{\varvec{\upvarepsilon}}_{{{\mathbf{rms}}}} } \right\rangle = \, \left( {{\mathbf{2}}/{\varvec{\uppi}}} \right)^{{{\mathbf{1}}/{\mathbf{2}}}} {\varvec{\upvarepsilon}}_{{{\mathbf{hkl}}}} $$
By the consideration of Gaussian microstrain distribution, RMS used to be derived from the maximum worth of the microstrain become derived from the Bragg’s law by Wilson [26, 60].
Substituting εhkl value in the Eq. (21), the RMS value is given via the relation
$$ \left\langle {{\varvec{\upvarepsilon}}_{{{\mathbf{rms}}}} } \right\rangle = \left( {{\mathbf{2}}/{\varvec{\uppi}}} \right){\mathbf{1}}/{\mathbf{2}}\left( {{\mathbf{\Delta d}}_{{{\mathbf{hkl}}}} /{\mathbf{d}}_{{{\mathbf{ohkl}}}} } \right) $$
where d0 and d represent the Observed, and calculated inter-planar distance values. Figure 2e plot of εrms versus εhkl is making an inclination of 45° to the x-axis, if the strain values hold good with the theoretical values then there is no discrepancy on the inter-planar spacing due to nature of the crystal [61]. The excess quantity of grain boundaries because of dislocations may just arise from the lattice stress in the VO2+ ions doped ZnS/CdS nanopowder particles.

The XRD peak broadening reveals crystallites size, microstrain, and instrumental broadening. In another way the cause of strain is interrelated to lattice irregularity, RMS strain gives the distortion value. The higher the value of RMS strain, the lesser is the crystallite size.

3.9 Structural parameter (texture coefficient)

The texture coefficient of each <h k l> plane is resolute from the X-ray diffraction pattern according to the following formula [62]
$$ {\text{TC}}_{\text{hkl}} = \frac{{\frac{{{\text{I}}_{{\left( {\text{hkl}} \right)}} }}{{{\text{I}}_{{0\left( {\text{hkl}} \right)}} }}}}{{\mathop \sum \nolimits_{N } \frac{{{\text{I}}_{{\left( {\text{hkl}} \right)}} }}{{{\text{I}}_{{0\left( {\text{hkl}} \right)}} }}}} $$
where Ihkl is the depth of (hkl) diffraction peak on the sample under examination; Iohkl is the intensity of (hkl) plane on an arbitrary sample taken from a powder diffraction file (PDF) card, and N is the number of diffractions considered inside the chemical analysis.
It has unique conditions
  1. 1.

    If TC(hkl) (~ 1) for every <hkl> planes, then the nanoparticles are with a randomly oriented crystalline similar to the JCPDS card reference.

  2. 2.

    TC(hkl) (> 1) implies that the VO2+ ions doped ZnS/CdS nanoparticles include a larger degree of orientation alongside C-axis.

  3. 3.

    Zero < TC(hkl) < 1 point out the lack of grains aligned in that path. Finally, the average crystallite dimension and the strain values estimated from all W–H models reveals to very suitable and intimately to interrelated Fig. 2d–f.


4 FTIR study

FT-IR spectral analysis of VO2+ ions doped ZnS/CdS composite nanopowder show a few absorption peaks between 400 and 4000 cm−1 is shown in Fig. 3. The spectrum could be explained by the characteristic bands of ZnS and CdS peaks obtained by the samples and was achieved by stirring the solution during preparation. Spectral analysis showed a small peak at 449 cm−1 corresponds to (Cd-S) metal sulfur bond confirms the configuration of CdS [63, 64]. The bands observed at a frequency 521 and 614 cm−1 are ascribed to Zn–S bond and corresponding to zinc and sulfide stretching [65, 66] and strong absorption peak at 807 cm−1 is the combination of V–O stretching modes [67]. The band at 1105 cm−1 is attributed to C-O carboxylic acid. The bands at 1631 cm−1 are ascribed to the symmetric bending mode of H2O molecule [68]. The peaks at 3433 cm−1 are assigned to the vibrational approach of O–H groups [69] as given by Table 3.
Fig. 3

FTIR spectra of Vo2+ ions doped ZnS/CdS composite nanopowder

Table 3

FTIR vibrational band assignments of VO2+ ions doped ZnS/CdS composite nanopowder

Vibrational frequency (cm−1)

Band assignments


Cd-S band

521, 614



V–O stretching


C–O carboxylic acid


Symmetric bending vibration of H2O


–OH stretching

5 Morphological studies

The SEM images of VO2+ ions doped ZnS/CdS composite nanopowder are shown in Fig. 4. The micrograph shows with uniformly distributed with spherical like structure which in the size below 50 nm were observed. It also confirms that the particles are in the order of nanosize. The detailed microstructures of the product were further investigated using EDS and TEM techniques. The EDS analysis of the VO2+ ions doped ZnS/CdS composite nanopowder is as shown in Fig. 5. To verify the stoichiometric ratios from EDS analysis, the elemental composition from Zn to S is found to be ZnS and Cd to S is CdS the doping element VO2+ ratio and also reveal the atomic weight percentages of Zn = Cd = V respectively. Spectrum confirms the elemental composition (V, Zn, S, and Cd) of composite and the information of atoms on the surface tend to migrate to the sub-surface layer [70]. TEM images of VO2+ ions doped ZnS/CdS composite nanopowder reveal that the structure of particles is in spherical as shown in Fig. 6. The average particle size of VO2+ ions doped ZnS/CdS composite nanopowder is approximately 20 nm, which confirms the order of nanosize these results are well matched with XRD data and W–H models are inter-correlated with TEM analysis.
Fig. 4

SEM images of Vo2+ ions doped ZnS/CdS composite nanopowder

Fig. 5

EDX analysis Vo2+ ions doped ZnS/CdS composite nanopowder

Fig. 6

TEM micrographs of Vo2+ doped ZnS/CdS composite nanopowder

6 Conclusion

In this paper, VO2+ ions doped ZnS/CdS composite nanopowder was successfully synthesized by co-precipitation procedure and characterized by XRD, FT-IR, SEM–EDS and TEM analysis. Generally, XRD is adapted to support the evaluation of crystallites with a broad (or) multi-modal size distribution. From the X-ray peak broadening studies, it was noticed the intensity of the X-ray diffraction line depends on the elemental composition of the sample and its preparation conditions. The set of all values of VO2+ ions doped ZnS/CdS composite nanopowder belong to the cubic structure. Observed X-ray diffraction peaks can be related to planes of atoms to assist in analyzing the atomic microstructure of a prepared sample. Both microstrain and crystallite size can be analyzed only when the broadening due to both are equivalent. The amount of microstrain is large the maximum observable crystallite size will be small. Due to vanadium ion doping causes the decrease in the crystallite size and enhanced the dislocation density, microstrain, and inter-planar spacing and also some lattice distortion will be created in the structure of the host material. Also, the estimated values of the mean particle size from the modified W–H plot and SSP methods are held a good agreement with TEM analysis.



J. Madhavi would like to thank Acharya Nagarjuna University, Guntur for providing URF. Prof. RVSSN Ravi Kumar would like to thank the UGC-DSA1 and DST-FIST, New Delhi for providing financial assistance to the Department of Physics, Acharya Nagarjuna University to carry out the present research work.

Compliance with ethical standards

Conflict of interest

The author(s) declare that they have no conflict of interests.


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Authors and Affiliations

  1. 1.Department of Physics, University College of SciencesAcharya Nagarjuna UniversityNagarjuna Nagar, GunturIndia

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