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181 
This work is licensed under a Creative Commons Attribution 4.0 International License. 

 

   

 

 

 

 

 
 

 

Abstract  

the structural properties of the CuO nanopowder oxide prepared reflux technique without any 

templates or surfactant, using copper nitrate hydrate (Cu(NO)3 3H2O) in deionized water with 

aqueous ammonia solution are reported. The Xrd analysis data and processing in origin pro 

program used to get FWHM and integral width to study the effect of different synthesis times was 

studied on the structural properties. It was found that values of crystal sizes are 17.274nm, 

17.746nm, and 18.560nm, the size of nanoparticles is determined by Halder-Wagner, and 15.796 

nm, 15.851nm, and 16.52nm, were calculated by Size-Strain Plot (SSP) method. The Sample was 

considered to determine physical and microstructural parameters such as internal strain, 

dislocations density, surface area, and the number of unit cells and then to compare the results. 

 

Keywords: CuO, Originpro, Xrd, Halder-wagner, Size-strain plot . 

1. Introduction 

In the past few decades, nanoparticles of a variety of sizes, shapes, and compositions, have 

been found, their physical and chemical properties attract the current scientific field over bulk 

materials [1]. Quite possibly of the main boundary in the combination of these nanoparticles is the 

control of molecule size, morphology, and crystallinity and to accomplish this objective, so were 

developed different synthesis methods ; some of the most investigated approaches include the 

sonochemical ,  sol-gel method, laser removal, the electrochemical , substance precipitation and 

surfactant-based procedures [2]. Nanostructured transition metal oxides have attracted 

considerable attention from researchers in recent years [3]. Copper (II) oxide, CuO, also known as 

cupric oxide has drawn in much consideration lately due to its promising applications as CuO is 

an appealing p-type metal oxide semiconductor that has extraordinary electrical, optical and 

synergist properties, solar-cells, and  sensors espithaly gas type. [4-7]. Copper oxide is a compound 

of two elements, copper and oxygen, which are d and p block elements in the periodic table 

respectively. In a crystal, the copper ion is coordinated by four oxygen ions [8]. (CuO) is has a 

doi.org/10.30526/36.2.3024 

Article history: Received 21 September 2022, Accepted 17 October 2022, Published in April 2023. 

 

 

 

Ibn Al-Haitham Journal for Pure and Applied Sciences 

Journal homepage: jih.uobaghdad.edu.iq 

 

Effect of the Synthesis Time on Structural Properties of Copper Oxide 

 
Karrar A. Alsoltani 

Department of Physics, College of Education 

for Pure Science Ibn Al-Haitham,University of 

Baghdad, Baghdad-Iraq. 

karrar.Ameen1104a@ihcoedu.uobaghdad.edu.iq 

 

 

Khalid H. Harbbi 

Department of Physics, College of Education 

for Pure Science Ibn Al-Haitham,University of 

Baghdad, Baghdad-Iraq. 

Khalid@ircoedu.uobaghdad.edu.iq 

https://creativecommons.org/licenses/by/4.0/
mailto:karrar.Ameen1104a@ihcoedu.uobaghdad.edu.iq
mailto:Khalid@ircoedu.uobaghdad.edu.iq


IHJPAS. 36(2)2023 

182 
 

monoclinic construction and is a special monoxide compound for both essential examinations and 

commonsense applications [9]. The lattice parameters are a= 4.6850 Å, b = 3.4230 Å and c = 

5.1320 Å [10]. In this work nanopowder of CuO was prepared at different synthesis times. Samples 

for different of synthesis times 6hours, 12hours, and  24hours have studied the effect of synthesis 

times on the structural parameters by studying X-ray diffraction (XRD) and comparing and 

discussing the result. 

2. Theory 

 Method of Halder-Wagner 

In the method of Halder-Wagner where strain and crystallite size profiles are described by 

Gauss and Lorentzian [11].  

(
𝛽ℎ𝑘𝑙

∗

𝑑ℎ𝑘𝑙
∗ )

2  =  (
1

D
) (

𝛽ℎ𝑘𝑙
∗

𝑑ℎ𝑘𝑙
∗ 2

)  +  (
ε

2
)2  (1) 

Where, βhkl
∗

 = β cos 𝜃 / λ and dhkl
∗

= 2sinθ /λ and λ the wavelength of the X-ray plot was (
𝛽ℎ𝑘𝑙

∗

𝑑ℎ𝑘𝑙
∗ )

2  

against (
𝛽ℎ𝑘𝑙

∗

𝑑ℎ𝑘𝑙
∗ 2

) is a straight line. The mean diameter was obtained by the inverse slope of the line, 

while the strain distortions are obtained from y-intercept [12,13]. 

 

 Size-strain Plot Method 
This method is an advantage that peaks in the low and middle angle ranges are given more 

weight as overlap between the diffraction peaks are much less. According to the process of size-

strain plot, the relationship between lattice strain and crystal size is given by [14] 

(dhklβhklcosθ)
2  =  (

K

D
) (dhkl

2 βhklcosθ)  +  (2ε)
2  (2) 

 

Where (βℎ𝑘𝑙/ dℎ𝑘𝑙 )
2 represents X axis and (βℎ𝑘𝑙/dhkl

2
)2 represents Y axis. The mean crystal size 

value is calculated from the slope while the intersection gives the strain ε. 

3. Results and Discussion  

According to XRD patterns of Copper Oxide (CuO) NNPs developed on copper foils for various 

syntheses, times are shown in Figure1. Were observed different peaks at ( 2θ ) = 31.19° ( 110 ), 

34.72° ( 002 ), 38.51° (111 ), 50.48° ( -202 ), 56.26° ( 020 ), 62.03° ( 202 ), 66.12° ( -113 ), 71.94° 

( -311 ) and 74.23° ( 220 ) relates to various planes of the monoclinic phase of CuO [15], shows 

in situ for samples 1-3. Through a program (WebPlotDigitizer-4.5), we obtain data for intensity 

and 2θ of CuO nanoparticles to all profile lines with nine peaks. 



IHJPAS. 36(2)2023 

183 
 

 
Figure1. XRD patterns of CuO NPs prepared at different synthesis times.  [15] 

 

In addition, this data is used to draw the shape of the peaks using an analytical program 

(Origin Pro Lab) to calculate the area under the curve and the FWHM is calculated by the program 

and then calculate integral breadth was the integral breadth which is [16]: 

β = A / Io  (3) 

Where A was the area under the curve and the Io was the highest intensity of the peak for each 

sample and for the different peaks respectively. 

 By processing the data used Originpro to get the below Figures and tables. Through these 

results, the above equations will be applied to calculate each of the crystal sizes and strains by the 

above methods in order to distinguish the effect of synthesis times on it. 

 
Figure2. XRD patterns of CuO NPs prepared at 6 hour synthesis time  by Originpro. 

 
 



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184 
 

Table 1. result of CuO NPs prepared at 6 hours by Originpro. 
 

( h k l ) 2θ  Area FWHM Height β 

( 1 1 0 ) 31.089 13.235 0.104 118.134 0.112 

( 0 0 2 ) 34.597 272.214 0.246 1101.241 0.247 

( 1 1 1 ) 38.468 395.599 0.338 1166.384 0.339 

( -2 0 2 ) 50.444 109.108 0.628 172.221 0.634 

( 0 2 0 ) 56.129 24.198 0.371 62.571 0.387 

( 2 0 2 ) 61.935 53.185 0.696 74.966 0.709 

( -1 1 3 ) 66.048 76.801 0.624 121.415 0.633 

( -3 1 1 ) 71.976 120.136 0.942 126.479 0.95 

 

 
Figure3. XRD patterns of CuO NPs prepared at 12 hour synthesis time by Originpro. 

 
 

Table 2. result of CuO NPs prepared at 12 hours by Originpro. 
 

( h k l ) 2θ  Area FWHM Height β 

( 1 1 0 ) 31.154 32.701 0.563 56.325 0.581 

( 0 0 2 ) 34.718 466.623 0.62 750.63 0.622 

( 1 1 1 ) 38.468 400.479 0.492 812.328 0.493 

( -2 0 2 ) 50.444 124.019 0.659 186.672 0.664 

( 0 2 0 ) 56.25 32.861 0.549 58.027 0.566 

( 2 0 2 ) 62.013 52.383 0.735 69.919 0.749 

( -1 1 3 ) 66.169 88.908 0.693 126.774 0.701 

( -3 1 1 ) 71.976 127.039 1.031 122.195 1.04 

 



IHJPAS. 36(2)2023 

185 
 

  
Figure4. XRD patterns of CuO NPs prepared at 24 hour synthesis time  by Originpro. 

Table 3. result of CuO NPs prepared at 24 hours by Originpro. 
 

( h k l ) 2θ  Area FWHM Height β 

( 1 1 0 ) 34.839 50.105 0.524 93.699 0.535 

( 0 0 2 ) 38.589 427.655 0.651 655.394 0.653 

( 1 1 1 ) 50.565 472.581 0.631 747.106 0.633 

( -2 0 2 ) 56.394 119.626 0.759 156.365 0.765 

( 0 2 0 ) 62.137 32.325 0.754 41.566 0.778 

( 2 0 2 ) 66.133 37.797 0.647 59.963 0.63 

( -1 1 3 ) 71.855 72.658 0.847 86.946 0.836 

( -3 1 1 ) 74.395 126.554 1.097 116.241 1.089 
 

  
 

Determination of crystallite size and the lattice strain  

 Halder-Wagner method  

After calculating the integral breadth of all peaks for all three samples then we use 

equations βhkl
∗

 = β cos 𝜃 / λ and dhkl
∗

 = 2sinθ /λ where λ is the wavelength of the X-ray (0.15046) 

and plot (
𝛽ℎ𝑘𝑙

∗

𝑑ℎ𝑘𝑙
∗ )

2  against (
𝛽ℎ𝑘𝑙

∗

𝑑ℎ𝑘𝑙
∗ 2

)  then fitting the data by a straight line to compare with eq (1) by 

getting straight line equation to obtained crystallite size and the lattice strain. The results are shown 

in Table (4). 

 

 

 



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186 
 

 

 

 
Figure 5. Halder-Wagner method for each sample respectively. 

 

 



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187 
 

Table 4. result of crystallite size and the lattice strain by Halder-Wagner method for all CuO NPs sample 

Time hours D nm 𝛆 strain 

CuO 6 hour 17.274 0.002 

CuO 12 hour 17.746 0.018 

CuO 24 hour 18.560 0.023 
 

 

Size-strain plot method 

 Equation (2) In this method is used to calculate particle size for each diffraction line and 

Equation (2) represents Where (𝛽h𝑘𝑙 / 𝑑h𝑘𝑙)
2 represents X-axis and (𝛽h𝑘𝑙 /dhkl

2
)2 represents Y-axis 

and d2hklBhkl cos𝜃 calculated in radians and uses a wavelength of X-ray equal to 0.15046 as shown 
in figure 6, we can see in this method inverse relationship between crystal size and strain. The 

results were calculated and included in Table (5).  

 

 



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188 
 

 
Figure 6. Size-strain plot method for each sample respectively 

 

 

 
Table 5. result of crystallite size and the lattice strain Size-strain plot method for all CuO NPs sample 

Time hours D nm 𝛆 strain 

CuO 6 hour 15.796 0.001 

CuO 12 hour 15.851 0.003 

CuO 24 hour 16.52 0.004 
 

 
 

The surface area (S.A) can be calculated by the following equation [17]: 

S.A=6*103/Dρ 

 

(3) 

From XRD we can calculate the x-ray density of powder by using this equation [18]: 

ρ =Z Mwt/V Na (4) 

  

Where ρ: density (g/cm3), Mwt: molar mass 79.545 (g/mol) for CuO, Z: the number of atoms: unit 

cell volume (cm3), and Na: Avogadro number (1/mol) [19]. 

The dislocation density (δ) and the number of unit cells (n) are calculated using the following 

relations [20,21]: 

δ=1/D2   (5) 

n = π D3 /6 V (6) 

Their calculated values will be presented in table 6. 

Table 6.  Shows lattice parameter, X-ray and dislocations density, surface area, and number of unit cells 

 for all CuO NPs sample. 

sample CuO for 6 hours CuO for 12 hours CuO for 24 hours 

S.A (m2/g) 55.046 53.582 51.232 
δ(1/m2) *1015 3.351 3.175 2.902 

n 33928.49 36786.39 42084.26 
 

 

 



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189 
 

4. Conclusions 

We review the current knowledge about CuO and added new experimental and theoretical 

results which provide a better understanding of the structure and effect of Synthesis time.  

Increased preparation time saw that all plane peaks of CuO are marginally moved to higher angles 

indicating a little decrease in the size, more essential to notice the lower peak intensity is 

particularly in the case of prepared CuO in 24hours. The change nanoparticles size depends on the 

synthesis time. However, the size of particles increases by increasing Synthesis times, dislocation 

density, and specific surface area decreases as increasing preparation times. The number of unit 

cells steadily increases with time. These current perceptions can assist with working on how we 

might our understanding of physical properties and the formation of CuO nanoparticles. When 

comparing the two analysis methods that were used in this study noticed that the Halder-Wagner 

method gave high accuracy in results, because the equations used in this method put points in 

locations as close as possible to the straight line in the diagram. There is a convergence in the results 

of the Halder-Wagner method with the results of the ssp methods, and the two methods are also 

close because the results are within the nanoscale. 

 

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