Quantitative Analysis of Synthetic Diamond by X-Ray Diffraction

QUANTITATIVE ANALYSIS OF SYNTHETIC DIAMOND BY X-RAY DIFFRACTION

Rashmi*, Nahar Singh and K.N.Sood

National Physical Laboratory Dr. K. S. Krishnan Marg, New Delhi 110 012, India * Email: [email protected]

ABSTRACT

Diamonds are non-reactive material, have excellent physical and chemical properties and have a large number of applications ranging from cutting and grinding to high technology applications. Compositional analysis is, therefore, important as it affects the properties and suitability for applications. Quantitative analysis of synthetic diamond powder has been carried out by x-ray diffraction (XRD). The crystalline phases identified were diamond, corundum and silicon carbide and these were quantified by Rietveld refinement of the XRD profile. Correlation of the quantitative results by XRD and chemical analysis brought out some interesting results such as presence of amorphous material in the sample and that silicon is present not only as silicon carbide but also in other forms.

Key Words:Quantitative Analysis; Synthetic Diamond; XRD; Rietveld Method; Chemical Analysis.

1. INTRODUCTION

Diamonds have been cherished as the most precious gemstone historically. Among natural minerals, diamond is the hardest material followed by corundum /I/. Diamonds have excellent physical and chemical properties and have a large number of applications ranging from cutting and grinding to high technology applications /2,3/. Analysis of purity and composition is, therefore, important as it affects the properties and suitability

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for applications. As diamond is a precious material it is preferable to characterize it by nondestructive techniques. Powder x-ray diffraction (XRD) is a powerful non-destructive tool to obtain qualitative as well as quantitative information from polycrystalline materials /4/. It analyzes the components of the mixtures in the form as present in the sample and not as elements, ions, functional groups, etc. Quantitative phase analysis (QPA) by XRD finds use in research and many industries. Quantitative phase analysis by XRD is based on the facts that (a) each crystalline component of the mixture has a unique diffraction pattern, (b) the diffraction patterns overlap with out interference, and (c) the intensity of each pattern is proportional to the amount of the component present in the mixture. In an earlier study Hull /5/ indicated the possibility of QPA by XRD but the first published results are by Clark and Reynolds on QPA of mine dust 161. A number of methods were developed for QPA by XRD which were standard based, required pure phases and were time consuming as calibration curves and or reference intensity ratios needed to be defined for each phase. With the advancements in the automation of diffractometers, numerical methods utilizing full diffraction profile could be developed. The Rietveld method, one of the whole pattern methods, is a powerful tool for the determination of crystal structure as well as for QPA of powder samples /7,8,9,10/. Rietveld quantitative phase analysis (RQPA) consists of least squares refinements until a best fit is obtained between the observed and the calculated powder diffraction patterns. It has a number of advantages over the standard based methods. It gives more accurate results due to the use of a wide range of data. It can deal with complex mixtures, does not require pattern decomposition and overlapping of reflections is not a problem as the calculated pattern considers full diffraction profiles of all contributing phases. Sample related effects on diffraction profile such as preferred orientation; peak broadening can also be modeled. The Rietveld method is nowadays the most preferred approach for QPA of polycrystalline mixtures. The Rietveld method therefore has more advantage in compositional analysis in comparison to other nondestructive/destructive techniques like Neutron Activation Analysis and chemical based destructive analysis. In continuation of our work on quantitative analysis by powder x-ray diffraction /11,12/, the results on synthetic diamond powder are reported in this paper. The results of XRD and chemical analyses have been correlated

66 Rashmi, Ν. Singh and K.N. Sood Reviews in Analytical Chemistry

and additional information on amorphous material in the sample has also been discussed.

2. THE RIETVELD METHOD

The Rietveld method /7,10/ consists of least squares refinements until a best fit is obtained between the observed and the calculated powder diffraction patterns. The calculated pattern is based on a refinable crystal structure model, diffraction optics, instrumental and other specimen characteristics as may be desired. Quantitative phase analysis by the Rietveld method is based on the following normalization equation:

(1) j

where Wt is the weight fraction of the phase j in the mixture. The mixture pattern is calculated by considering contribution of each phase/.

y,:(i) = Sj£Yc,j(i) +Yh(i) (2)

where Sf is the Rietveld scale factor for the / phase, YcJi) is the calculated intensity at each step i in the pattern due to the phase j and Yh(i) is the background intensity at that point. Weight fraction of each phase is calculated from the refined scale factor S)

(3)

where M, and V, are the unit cell mass and volume of each phase j.

67 Vol. 26, No.l, 2007 Quantitative Analysis of Synthetic Diamond by X-ray Diffraction present study. The powder was of light gray color. Scanning electron micrographs were recorded on a Leo 440 scanning electron microscope. The micrographs showed particles of irregular shapes and angular cuts. The particles were of varying sizes up to about ΙΟμπι. A representative micrograph is shown in Fig. 1.

Fig.l: Scanning electron micrograph of the synthetic diamond powder sample showing particles of various shapes and sizes.

3.2 XRD

The powder X-ray diffraction data were collected on a Bruker AXS D8 Advance Diffractometer (with Diffracplus software) using CuKa radiation. The specimen for diffraction measurements were front-loaded pressed powder. Instrumental and measurement details are given in Table I. Rietveld quantitative phase analysis was performed using Siroquant software /13/.

3.3 Chemical Analysis

The carbon content in the sample was determined gravimetrically. Other

68 Rashmi, Ν. Singh and K.N. Sood Reviews in Analytical Chemistry

elements in the sample were determined by flame atomic absorption spectrometry (FAAS). The details of chemical analysis have been already reported elsewhere /14/.

Table I Instrument Parameters for Bruker AXS D8 Advance X-ray diffractometer.

Target Copper Tube rating 40kV / 40mA Incident beam optics 0.5° divergence slit, 2.5° vertical soller slit Diffracted beam optics 0.5° antiscatter slit, 2.5° vertical soller slit Monochromator Graphite, diffracted beam, 0.1mm monochromator slit Detector Scintillation detector, 0.6mm detector slit Scan range 15° to 95° (2Θ) Scan mode Step scan Scan speed 0.0274s Sample rotation 30 r.p.m.

4. RESULTS AND DISCUSSION

4.1 Crystalline Phases

Figure 2 shows the X-ray diffraction pattern of the synthetic diamond powder in the 2Θ range from 15° to 95° using CuKa radiation. The main phases have been identified as diamond (PDF # 6-675) and corundum (PDF # 46-1212), marked as D and C respectively in Fig. 2. A small amount of cubic silicon carbide is also present (PDF # 29-1129), marked as S in Fig. 2. In addition, a small peak at about 36.8° 2Θ (d~0.2346nm) remained unidentified.

4.2 Quantitative Analysis

Quantitative phase analysis was done by Rietveld refinement of the background subtracted diffraction profile. The phases considered for quantification were diamond, corundum and cubic silicon carbide. The diffraction peaks were fitted using Pearson 7 profile function. The initial unit cell parameters were taken from the powder diffraction file (PDF).

69 Vol. 26, No. 1, 2007 Quantitative Analysis of Synthetic Diamond by X-ray Diffraction

Absorption correction was done according to Brindley /15/.

r: cö 3 TO s ΪΙ Ο ο CΛ C CI Φ Ο c^t ο «-".υ α ο Jj II ΊΓ 60 2 Theta / degree

Fig. 2: XRD pattern of the synthetic diamond powder sample in the 2Θ range 15° to 95° using CuKa radiation. The phases have been marked as - D: diamond; C: corundum; S: silicon carbide.

Figure 3 shows the observed, calculated and difference profiles after Rietveld refinement of the background-subtracted diffraction profile of the mixture. The upper profile is the measured pattern, dots represent the calculated profile, and the lower one is the difference profile. There is a reasonable correspondence between the calculated and the observed patterns. 2 The agreement indices /10/ are: Rp=0.394, R,.Xp=0.304 and χ =1.7. The refined parameters are compiled in Table II. The figures in parentheses are the Rietveld refined esds. The quantitative results are compiled in Table III. The figures in parentheses are the errors obtained by multiplying the Rietveld refined esds by χ. /13/. The diamond and corundum phases estimated are in comparable amounts and the amount of silicon carbide estimated is very small. The results of chemical analysis are shown in Table IV. Carbon and aluminum are in major amounts followed by silicon and small amount of iron. Other impurities are in trace amounts. The estimated amounts of Al and

Si have been given as A1203 and SiC/Si02 also in Table IV in order to facilitate correlation with the XRD results.

70 Rashmi, Ν. Singh and K.N. Sood Reviews in Analytical Chemistry

Fig. 3: Rietveld refinement with the synthetic diamond powder sample diffraction profile. Upper solid line represents the observed pattern. The dots are the calculated fit. The lower solid line represents the difference profile.

It may be noted that only the crystalline phases have been quantified by XRD. Though the XRD pattern indicates that the sample has good crystallinity, there may be some amount of amorphous material in the sample. The presence of amorphous material in the sample is suggested when quantitative results by XRD are correlated with those of the chemical analysis. Assuming that the carbon, aluminum and silicon estimated by chemical analysis correspond to the diamond, corundum and silicon carbide phases, it may be noted that the results of XRD are on the higher side except that for silicon carbide. This suggests that (i) there is some amount of amorphous material in the sample, (ii) not all of the silicon estimated by chemical method is in silicon carbide form, and some of it may be in other form such as non-crystalline silica. About 0.6% iron in the sample has been estimated by chemical analysis. It is quite common that metallic impurities are found in synthetic diamond 121. These may arise from the solvent-catalyst

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Table II Refined values of crystal and profile parameters, refinement indicators and other parameters.

Parameters Refined Values Zero error (in °2Θ) -0.0028(7) Rexp 0.304 Ro 0.394 x2 1.7 Phase Diamond Corundum Silicon carbide Scale 9.24(9)xl0"3 2.29(l)xl0"4 3.6(3)xl0"5

Profile shape 1.14(4) 1.02(2) 1.4* parameter 1 Profile shape 2.82(2) 1.79(2) 1.4* parameter 2 Profile width 0.012(1) 0.009(1) 0.015* Parameter Preferred Orientation 0.86(1) 1* 1* Parameter Unit cell parameter a = 0.35667(2 a = 0.47594(2) a = 0.43589* (in nm) c= 1.29931(3) •indicates that the parameter is not refined.

Table III Relative phase composition of the synthetic diamond powder sample by Rietveld method.

Phase Amount (wt.%) Diamond 50.8±0.4 Corundum 48.610.4 Silicon carbide 0.610.1

72 Rashmi, Ν. Singh and K.N. Sood Reviews in Analytical Chemistry

Table IV Chemical analysis of the synthetic diamond powder sample.

Analytes analyzed by Gravimetric Amount (Wt.%) method C 40.92± 0.25 Al 21.8± 0.9 as AI2O3 41.19 Si 5.0± 0.09

as Si02 10.69 as SiC 7.14 Fe 0.59± 0.10 Analytes in mg/kg analyzed by Flame Atomic Absorption Spectrometer Ni 95.413.8 Ca 75.412.4 Na 105.413.6 Mg 95.412.6 W 0.8510.06 Co 3.610.6 * Reported values are the average of ten replicate measurements and figures in parentheses are the standard deviation.

metal used for diamond synthesis. These impurities could be in metallic form or carbide form. Metallic impurities in the oxide form could also be present as impurities in corundum /l/. The amounts of diamond (50.8%), carbon from silicon carbide (0.2%) and corundum (48.6%) add up to 99.6%, Table III. The amounts of carbon (40.9%) and aluminum oxide (41.2%) estimated by chemical analysis add up to 82.1%, Table IV. Rescaling the concentrations of carbon and corundum to a total of 82.1%, one gets diamond as 41.90% and corundum as 40.1%. These figures compare reasonably well with the chemical analysis results.

5.CONCLUSIONS

Quantitative phase analysis of a synthetic diamond powder has been done

73 Vol. 26, No.l, 2007 Quantitative Analysis of Synthetic Diamond by X-ray Diffraction by XRD using the Rietveld method. The sample has been found to have diamond and corundum as the major crystalline phases and they are present in almost equal amounts. It has been possible to quantify a very small amount of silicon carbide in the presence of strongly diffracting phases diamond and corundum. A correlation of the quantitative phase analysis by XRD and the elemental analysis by chemical methods suggests the presence of some amount of amorphous material also in the sample, and that silicon is present not only as silicon carbide but also in some other form.

6. ACKNOWLEDGEMENTS

The authors are grateful to Professor Vikram Kumar, Director, N.P.L., India, for encouragement and permission to publish this work. The authors would like to thank Dr S.K. Gupta, Head, Materials Characterization Division. The authors are also thankful to Delta Exports, India for providing the sample used in this study.

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1. M.B. Bever; Editor in Chief,. Encyclopedia of Mater. Sei. & Engg., Vol.1, Pergamon, Oxford, 1986. 2. J.E Field; Editor, The Properties of Natural and Synthetic Diamonds (Academic Press, London), 1992. 3. G.L. Trigg; Editor. Encyclopedia of Applied Physics (VCH Publisher, NY) 1993. 4. H.P. Klug and L. E. Alexander. X-ray Diffraction Procedures (Wiley, New York), 1974. 5. A.W. Hull,. J. Amer. Chem. Soc. 41,1168 (1919). 6. G.L Clark and D. H. Reynolds. Ind. Eng. Chem. Anal. Ed. 8, 36-40 (1936). 7. H.M. Rietveld. J. Appl. Crystallogr. 2,65-71 (1969). 8. R.J. Hill and C.J. Howard, J. Appl. Crystallogr, 20,467-474 (1987). 9. D.L. Bish and S.A. Howard.. J. Appl. Crystallogr 21, 86-91 (1988). 10. R.A. Young,; Editor, The Rietveld Method, (Oxford University Press, Oxford) 1993. 11. Rashmi, Nahar Singh and A. K. Sarkar,. Powder Diffr. 19, 141-

74 Rashmi, Ν. Singh and K.N. Sood Reviews in Analytical Chemistry

144(2004). 12. Rashmi and Nahar Singh, 5th International Conference on Advances in Metrology, February 23-25, 2005, NPL, New Delhi. 13. J.C. Taylor. Powder Diffr. 6,2-9(1901). 14. Nahar Singh, Rashmi and A. K. Sarkar. J.Mater. Sei. 39, 1665-1669 (2004). 15. G.W. Brindley. Philos. Mag. 3, 347-369 (1945).