Determination of the Structure of ZnO Powder

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Experiment #3: Determinaon of the structure of ZnO PowderAhmad Moh. Awadallah -9100030 Advanced physics lab-0352712

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Abstract

In this work, we had examined the structure of the ZnO powder sample. For this purpose, weprepared our sample by grinding a small amount of ZnO via an agate mortar and pestle untilreaching to a very fine powder could be reached. Then we pressed a small amount of it into thesample holder. The prepared sample then was studied through the XRD machine, where the used x-rays are Cu-K (=1.5406) and Cu-K2 (=1.5444). The x-ray diffraction pattern was thentreated by the Origin 9 software, and the result was presented in this report. The figures of the fittedpeaks were sited at the appendix. By treating the data, we found that the structure of ZnO containstwo phases; the major one is the wurtzite phase which has a hexagonal structure with a lattice

parameters: 3.240.03and5.190.03, in addition to a very small fcc cubicphase with the lattice parameter3.590.03. We lost an amount of accuracy due toignoring the contribution of the oxygen ions through calculating the structure factor.

1. IntroductionThe hexagonal system is one of the most important crystallite systems, it is a wide spread system inthe nature. A lot of crystals were composed from two or more basic structures. One example of thiscomposition is the Zinc oxide (ZnO); it is naturally composed from: wurtzite (B4) which is ahexagonal structure, the zinc blende (B3) which form an fcc cubic structure, and the rocksalt (orRochelle salt) (B1) as demonstrated in fig.1. The main object in this job is to calculate the latticeparameters (a) and (c) for the hexagonal structure, the crystallite size (D). They was calculated andthen compared with the Published ones. The intensities of the peaks were calculated and comparedwith the experimental (fitted) ones. The differences were explained due to the texture of the cells,they prefer to be ordered in a certain direction because of its cubic design. The collected XRDpeaks shall be divided into two categories: the 1st(main) one for the hexagonal structure, and theother for the cubic one.

In general, the following formulae are used in such a study:

To calculate the d-spacing (d):

To find the lattice parameters (a) and (c): ++ Which can be simplified to: log log log[ ] If we have 0,0,peak, Eqn. (1.3) becomes:

So we can calculate (c) directly.

If we have , ,0peak, Eqn. (1.3) becomes: So we can calculate (a) directly.

Eqn. 1.1

Eqn. 1.2

Eqn. 1.3

Eqn. 1.4

Eqn. 1.5


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To calculate the crystallite size (D): .Where B (2): the full width at half maximum (FWHM).

To calculate the intensity of a peak: ||Where F: structure factor [ 1 +]

{

0 2 3, 4 2 3, 3 2 3 1,

2 3 1 ,

}

m: multiplicity of the indices. LP (): Lorentz polarization factor +.

2.ExperimentalZnO was brought from our lab; it was prepared as a very fine powder. This fine powder then wasstuck into a sample holder stainless steel plate of 2cm diameter to fit inside the x-ray machine. Thethickness of the sample holder is about 2mm with a flat surface. The x-ray diffraction pattern wasobtained for an angular position (2) range 20.00to 95.00with 0.01step between each two

succession channels. The x-ray machine does not contain a filter for Cu-K2, so it will be taken inconsideration that the peaks are formed from a super position from both Cu-K1 and Cu-K2 tellreaching to high positions (2 6 0 ) where the peaks divided into two close peaks due to thedifferent wavelengths. Then these collected data had been analyzed. The diffraction pattern wasstudied and the intensities of the peaks were analyzed using ORIGIN 9.0.0 software. I had fitted thepeaks using the Gaussian distribution function. The splitted peaks were fitted through a multipeaksfitting routine to ensure taking in consideration the intensity of peak due to the Cu-K2 rays. Then Ihad used the Xpert HighScore (virgin 2.0a) enhance the pattern picture and to get the recordedvalue of . Microsoft excel was used to calculate and arrange our results. The Microsoft word2010 then was used to prepare this report.

3.Results and Discussiona. Fig.2 shows the XRD pattern for powdered ZnO, we can see clearly that there are 18 peaks

through the whole pattern, 4 of them are very small peaks. From the 8thpeak and go on, the peaksstarted to split into two close peaks because of the influence of Cu-K2 ray inside the XRDmachine because it appears at high positions. We can overlap this point by using Cu-K2 filter inthe XRD machine which not used in our one.

Eqn. 1.6

Eqn. 1.7

Eqn

Eqn. 1.9

Eqn. 1.10


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Fig.2: XRD paerns for the ZnO sample

Fig.1: dierent phases in ZnO


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The peak positions were determined using the Gaussian fitting, and they were listed at table 3.1.The d-spacing for the different reflections were calculated using Braggs law:

(2d sin =m) [m=1 for the first order reflection] [2dsin=]

The results were tabulated in the same table. In order to index the peaks, we calculated

logfor

each (d), and then we used the Hull-Deavy chart to index the peaks. The values of h, k, and l thatobtained from the chart were inserted to the same table. From the rectangular strip of paper and theHull-Deavy chart which will be submitted with the report-, we found that the axial ratio (c/a) isequal to: 1.6050.005and recorded at the same table. There are 4 peaks that did not fit with the chart. They did not matchwith the lines that represent the hexagonal structure, which indicates for the existence of anotherphase beside the hexagonal structure.

Using the 0,0,peaks, we calculated the value of (c) by eqn. (1.4), and with the assistance of the, ,0

peaks we calculated the value of (a) using eqn. (1.5), both were inserted into table 3.1.

We calculated to compare it with the recorded value.Peak # Position (2) d+d() log(d) ,, c

1 31.900.01 2.800.03 0.4480.01 (1,0,0) 3.23 -2 34.600.01 2.590.03 0.4140.01 (0,0,2) - 5.183 36.400.01 2.470.03 0.3920.01 (1,0,1) - -4 43.600.01 2.080.03 0.3170.01 x - -5 47.700.01 1.910.03 0.2800.01 (1,0,2) - -6 50.800.01 1.800.03 0.2540.02 x - -7 56.800.01 1.62

0.03 0.210

0.02 (1,1,0) 3.24 -

8

63.000.01

1.470.03

0.1680.02

(1,0,3) - -

9 66.500.01 1.400.03 0.1470.02 (2,0,0) 3.23 -10 68.100.01 1.380.03 0.1380.02 (1,1,2) - -11 69.200.01 1.360.03 0.1320.02 (2,0,1) - -12 72.700.01 1.300.03 0.1140.02 (0,0,4) - 5.2013 74.580.01 1.270.02 0.1040.02 x - -14 77.080.01 1.240.02 0.0920.02 (2,0,2) - -15 81.500.01 1.180.02 0.0720.02 (1,0,4) - -16 89.700.01 1.090.02 0.0380.02 (2,0,3) - -17 90.500.01 1.080.02 0.0350.02 x - -18 92.900.01 1.06

0.02 0.026

0.02 (2,1,0) 3.24 -

3.240.03 5.190.03To find the error in calculating (a) and (c):

So: [0.01]

Table 3.1: Position against d-spacing and Lattice parameters.


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Eqn. 1.11

Peak # Position (2) FWHM2(rad) Crystal size (D) 1 31.90 0.00440 3432 34.60 0.00412 3683 36.40 0.00412 3704 43.60 0.00407 384

5

47.70

0.00419

378

6 50.80 0.00559 2877 56.80 0.00461 3588 63.00 0.00290 5869 66.50 0.00269 64410 68.10 0.00267 65411 69.20 0.00278 63412 72.70 0.00210 85813 74.58 0.00382 47614 77.08 0.00208 89115 81.50 0.00255 750

16

89.70

0.00267

765

17 90.50 0.00543 37918 92.90 0.00278 757

D (average)=597

c. The last part of studying the hcp structure is to calculate the intensity. The intensity wascalculated from eqn.1.3. For this aim, we calculated the multiplicity (m) and put it in table 3.3, thenwe found the value of the structure factor (F) for each peak using eqn.1.5, we used the standardvalues of the constants ai, bi, and c from the tables at internet. The atomic form factor for Znat each

position was calculated using the following formula: /= The ZnO hcp structure (fig. 3b) contains Zn hexagonal structure bonded to the O ions hexagon. Theatomic form factor (f) should be calculated taking in consideration the two types of ions. This willmake calculating (f) more difficult. So I ignored the oxygen ions and do the job for the Zn ionsonly. This will impart more inaccuracy to my calculations, but we can balance it by the time andeffort-saving.

The values of (F) were inserted into table 3.3 too. Then I had evaluated the Lorentz PolarizationFactor (LP) using eqn.1.10, I put these values at table 3.3 to complete the required parameters tofind the intensity.

Table 3.2: The values of FWHM and crystal size with position.


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Peak # 2 fZn || ,, m LP() 1 31.90 25.1 628 (1,0,0) 6 11.8 446292 34.60 24.5 2406 (0,0,2) 2 9.9 477723 36.40 24.2 1753 (1,0,1) 12 8.9 1868934 43.60 x x x x x x

5 47.70

22.0

486

(1,0,2)

12

4.9

283146 50.80 x x x x x x

7 56.80 20.4 1671 (1,1,0) 6 3.3 327138 63.00 19.4 1128 (1,0,3) 12 2.6 350439 66.50 18.8 355 (2,0,0) 6 2.3 490110 68.10 18.6 1382 (1,1,2) 12 2.2 3632211 69.20 18.4 1017 (2,0,1) 12 2.1 2588012 72.70 17.9 1281 (0,0,4) 2 1.9 492413 74.58 x x x x x x14 77.08 17.3 298 (2,0,2) 12 1.7 618715 81.50 16.7 278 (1,0,4) 12 1.6 5285

16 89.70

15.7

739

(2,0,3)

12

1.4

1256317 90.50 x x x x x x

18 92.90 15.3 235 (2,1,0) 12 1.4 3909

The error in calculating structure Factor is coming only from reading the value of atomic formfactor (f) which is negligible. The error in calculating LP is also very small.

To compare our experimental values of intensity that obtained from the fitting routine with thecalculated ones, I normalized the calculated intensities to the second peak because it is the largerone, and so I did for the experimental values of the intensity, then I put it in table 3.4.

The difference between the normalized calculated intensities and the experimental ones are large,and that may be for several reasons. One of them is due to the hexagonal structure of our sample,the cells prefer to stack on its faces rather than the other directions, so the texture make the intensityfor the some peaks be at a great difference from the calculated one.

Another reason that make this difference between calculated and experimental intensities is that theerror in reading the integrated intensity from the fitting routine. In addition, one can get verydifferent normalized intensities if he normalizes the peaks to another one than the second. Ourcalculated intensities are close to some of the recorded patterns, fig.2 shows one of them. Ignoringthe oxygen atoms in calculating the atomic form factor added a non-small amount of inaccuracy tomy calculations.

Table 3.3: Calculated structure factor, Multiplicity, LP, and the corresponding Intensity.


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4. ConclusionsFrom the XRD pattern, we can decide that the structure of ZnO is a hexagonal structure because allthe peaks of the hcp were appeared. The lattice parameter were calculated and found to be: : 3.24 0.03 and 5.19 0.03.The crystallite size was obtained and has the order of600; it was increased when calculated from the last peaks due to the decrease in broadening of thepeaks. In addition, The ZnO structure includes another phase which is the zinc blende fcc structure

with a lattice parameter: 3.590.04.The experimental intensities of the peaks werecalculated; they are compared closely to the calculated ones.

Fig.4: A recorded XRD pattern for ZnO powder

Fig.2: XRD paerns for the ZnO (REPEATED)


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Appendix: Fied peaks with their informaon


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Determination of the Structure of ZnO Powder