GRD Journals- Global Research and Development Journal for Engineering | Volume 5 | Issue 12 | November 2020 ISSN- 2455-5703
Relationship between the Diffraction Peak Intensity and Composition in (Ti1-xWx)C Powders Mohsen Mhadhbi Assistant Professor Department of Chemical Engineering Laboratory of Useful Materials, National Institute of Research and Physical-chemical Analysis
Abstract In this work, nanostructured (Ti1-xWx)C (0 ≤ x ≤ 0.2) powders were synthesized through solid state mechanical alloying (MA) process in a high-energy planetary ball mill (Fritsch Pulverisette 7) using Ti, W, and C powders mixture. Thus, MA was performed at room temperature under argon atmosphere to avoid oxidation. The relationship between the changes in diffraction peaks intensity and the composition of obtained powders was determined by using the structure factor calculations. However, the obtained results were compared with the theoretical ones. Keywords- X-Ray Diffraction, Carbide, Diffraction Peak, Composition, Nanostructure, Mechanical Alloying
I. INTRODUCTION Titanium carbides (TiC) are a materials of great industrial importance due to its excellent properties such as good wear resistance, high hardness, high thermal conductivity, etc. However, they possess some limitations like transverse rupture strength and low density [1]. These special characteristics allow for various applications like high temperature structural materials, in electrical discharge machining, and as abrasive for cutting tools and grinding wheels [2, 3]. Recently, several studies have focused on the investigations of nanostructured titanium carbide synthesized through mechanical alloying technique [4-10]. Mechanical alloying (MA) is a simple powder processing method that is employed to fabricate alloy powders, both in equilibrium and non-equilibrium, in the solid state. In fact, MA technique makes it possible to produce and control a refined, homogenous, and nanostructured microstructures [11, 12]. Furthermore, MA of elemental powder mixtures, with desired compositions, corresponding to the stoichiometry of intermetallic phases, which lead to the formation of powders with partially ordered or disordered solid solutions [13, 14]. Hence, MA is a significant process that contains cycle of cold welding followed by fracturing and re-welding, which cause an excellent inter-diffusion between powders particle [15, 16]. In this paper, a nanocrystalline (Ti,W)C powder was produced by MA. The morphology and microstructure of the refractory MA powder were studied. Hence, the relationship between the diffraction peak intensities and the composition of (Ti 1xWx)C solid solution was also studied based on structure factor calculations from the data of X-ray diffraction.
II. EXPERIMENTAL WORK A mixture of elemental powder Ti (< 40 μm, 99.9 %), C (5 μm, 99.9 %), and W (< 5 μm, 99.9 %) was sealed into a stainless steel vial (45 mL in volume) with 5 stainless steel balls (15 mm in diameter and 14 g in mass) in a glove box filled with purified argon to prevent oxidation. The ball to powder weight ratio was 70:1. The mechanical alloying (MA) procedure of 20 h was performed at room temperature using a high-energy planetary ball mill (Fritsch Pulverisette 7). The formed powders were characterized by X-ray diffraction using a Panalytical XPERT PRO MPD diffractometer with Cu Kα radiation. The High Score Plus program was used in order to analyze the XRD patterns and to obtain the position, the full-width at half maximum and the intensity of various peaks. The existing phases were determined based on the ICDD PDF2 data base. The XRD patterns were analyzed by the Fullprof program [17] using the Rietveld method [18]. The intensity of the diffraction peaks was measured from the measured raw data by integrating the area under the diffraction peak. The analytical functions relating the (111) and (200) diffraction peak intensities to the solid solution composition were deduced from the structure factor calculations. Assuming that the intensity of the diffraction peak can be determined only from the structure factor we can have a small variation that depends on other factors. In this context, we determined the powders diffraction patterns by computer calculations taking into account other parameters, such as instrumental broadening, strain factor.
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Relationship between the Diffraction Peak Intensity and Composition in (Ti1-xWx)C Powders (GRDJE/ Volume 5 / Issue 12 / 002)
III. RESULTS AND DISCUSSION A. Analytical Approach Fig.1 shows the X-ray diffraction patterns of TiC and Ti0.8W0.2C powders MA for 20 h. As it can be seen for the case of TiC powder (Fig. 1a) the XRD pattern consists of a new formed phase with a face center cubic NaCl type structure and correspond to the TiC phase. Thus, the peaks are broadened due to the refinements of grains and the introduction of defects during milling. At the same time, an additional small peak related to the Fe element as contamination resulted from the wear between the milling media (vial and balls). For the case of Ti0.8W0.2C powder (Fig. 1b) the XRD pattern consists of broadened peaks of (Ti,W)C solid solution, with a face center cubic NaCl type structure. In addition, a small peak related to the Fe element appeared.
Fig. 1: X-ray diffraction patterns of (a) TiC and (b) Ti0.8W0.2C powders MA for 20 h
In this study, we suppose that the change in intensity of the diffraction peaks is a function of the structure factor alone, the intensity of the two main peaks of TiC powder can be written as follows:
F(111) 4( fT i f C )
(1)
F( 200) 4( f 'Ti f 'C )
(2)
In the case of (Ti1-xWx)C powders, the intensity of the diffraction peaks increase. This is explained by the fact that W has more electrons than Ti and consequently the atomic scattering factor of Ti is smaller than that of W (as given in Table 1). So, we used new analytical functions [19] to determine the atomic scattering factors for the different elements (Ti, C, and W). Table 1: Calculated scattering factors for the different elements f(Ti) f(C) f(W) (111) peak 17.140 3.686 62.652 (200) peak 14.433 3.581 60.798
In the case where tungsten replaces titanium, the mole fraction is x, the above structure factors will be:
F(111) = 4[(1 - x) f Ti + x f W - f C ]
(3)
F( 200) = 4[(1 - x) f '´Ti + x f ' W - f 'C ]
(4) However, as shown in Fig. 1, there is a difference between the intensities of the (111) and (200) peaks due to the different X-ray scattering factors of Ti and W. The general equation relating the absolute intensity of (111) peak with the scattering factors of Ti, W, and C is defined as:
I (111) C111 F(111)
2
(5)
Substitution of Equation (3) into Equation (5) we find:
I (111) C111 ( f T i f C ) ( f W f Ti ) x (6) 2
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Relationship between the Diffraction Peak Intensity and Composition in (Ti1-xWx)C Powders (GRDJE/ Volume 5 / Issue 12 / 002)
The equation relating the absolute intensity of (200) peak with the scattering factors of Ti, W, and C is defined as:
I ( 200) C 200 F( 200)
2
(7)
Substitution of Equation (4) into Equation (7) we find:
I ( 200) C111 ( f 'T i f 'C ) ( f 'W f 'Ti ) x
2
(8) where C111 and C200 are constants obtained from the intensities of (111) and (200) peaks of pure TiC having a known structure. However, the peak (111) of pure TiC is more intense than the peak (200) (see Fig. 1). In fact, the absolute intensities are normalized by the highest intensity peak. We multiply by 100 to calculate the intensity of each second main peak as following:
I (111) 100
I W(111) I W( 200)
(9)
W
I ( 200) 100
I ( 200) I W(111)
(10) Substitution of both Equations (6) and (8) into Equations (9) and (10) we obtain:
I (111)
C 100 111 C 200
I ( 200) 100
C111 C 200
( f W f Ti ) x ( f Ti f C ) ( f 'W f 'Ti ) x ( f 'Ti f 'C ) (11) 2 ( f 'W f 'Ti ) x ( f 'Ti f 'C ) ( f W f Ti ) x ( f Ti f C ) 2
(12)
B. Comparison with Experimental Results During the fitting, only the C111/C200 ratio was adjusted because the slope was invariant. Fig. 2 shows the relative intensity of (111) and (200) diffraction peaks as a function of the composition (comparison between experimental and theoretical results). As it can be seen from the figure, for the experimental the C111/C200 ratio is equal to 0.612 while for the case of theoretical the C111/C200 ratio is equal to 0.526. This explains that there is no dependency between the experimental results and XRD measurements conditions. Further, the intensity values depend on several factors such as the step, the scan speed, and the scan mode. Unlike the intensity ratio which does not depend on these factors. Hence, we can mention that all of these obtained results are related to the carbon stoichiometry of the studied carbide (Ti1-xWx)C.
Fig. 2: Variation of the relative intensity of (111) and (200) diffraction peaks as a function of the composition
IV. CONCLUSIONS In this paper, the relationship between the diffraction peak intensities and the composition of (Ti1-xWx)C solid solution was studied based on structure factor calculations from the data of X-ray diffraction. Furthermore, the experimental results are in agreement with theoretical calculations. This approach can be used to study the composition of the (Ti1-xWx)C solid solution. All rights reserved by www.grdjournals.com
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Relationship between the Diffraction Peak Intensity and Composition in (Ti1-xWx)C Powders (GRDJE/ Volume 5 / Issue 12 / 002)
ACKNOWLEDGMENT Author would like to acknowledge the support of Global Research and Development Journals.
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