Quantitative phase analysis using the Rietveld method for samples in the Ti-Cr binary systems

Transcription

1 586 Quantitative phase analysis using the Rietveld method for samples in the Ti-Cr binary systems Ofer Beeri and Giora Kimmel Nuclear Research Center Negev, P.O.Box 9001, Beer-Sheva, Israel Abstract TiCi- appears in three allotropic phases, cubic R.T. phase and two hexagonal H.T. phases. In practice it is difficult to obtain single phase materials at room temperature and quantitative phase analysis should be performed in order to determine the relative phase amounts. The diffractograms of samples from different sources showed that the major contribution to the intensities came from the cubic phase (C15) CuzMg type. A second phase was identified as the hexagonal (C36) MgNi2 type. The two phases yield complicated diffracograms in which most lines are overlapping. Thus, the quantitative phase analysis aided by the Rietveld method was adopted. The results for the TiCr2 powders showed that the weight fraction of the hexagonal was much above the contribution in integrated intensities. The conflict between the intensity contribution of the diffractograms and the actual weight fraction of the phases, comes from different structure factors and multiplicities. Introduction There are some interesting aspects in the thermodynamic system of TiCr2-I$, for example, low critical temperature, high absorption capacity and low hysteresis [ 11. According to the equilibrium phase diagram [2], there is only one intermediate phase compound TiCr2, formed concurrently at 1370 C from Ti-Cr ci2 solid solution. This intermetallic compound exists in three intermediate allotrope phases. The crystal structures of the three allotropic phases of TiCr2 are known [3,4]. The room temperature phase (a) is cubic (C15) CuzMg type, S.G. Fd3m, stable up to l%o C, and two hexagonal high temperatures phases, p (C36) MgNiz type and y (C14) MgZn, type, S.G. P6&nmc for both. There is a wide temperature range (SOO-1220 C) in which the a and p phases are overlapped. Thus, due to the slow kinetics, the as cast material is formed mainly as p phase, and the a phase is obtained after heat treatment. In practice it is difficult to obtain pure a phase at room temperature, and special prolonged heat treatments are required to reduce the amounts of the unwanted phases in these mixtures [ 11. The two phases, a and p, have the same densities and compositions, the metallography shows no contrast between the phases, thus, Quantitative X-Ray Powder Diffraction (QXRPD) is required for accomplishing complete phase analysis. Yet, the two phases yield complicated diffractograms in which most lines are overlapping. Hence, the quantitative phase analysis aided by the Rietveld method was adopted.

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3 587 Experimental procedure Materials : TiCr2 powders: In the present study, initial parent ingots of TiCr2 were prepared by weighing the appropriate amounts of Ti (99.8%) and of Cr (99.99%) then arc melting under an inert atmosphere of ultra pure Ar (99.999%). Each sample was melted 3 times, each time maintained 3 minutes as a melt. Four different samples were prepared: one as-cast sample and others with three different heat treatments, including the recommended annealing for obtaining pure cubic phase [l] (See Table 1). The annealed samples were characterized for elemental composition by wet chemical analyses and by combined SEM+EDS indicating Cr/Ti atomic ratio of 1.8 (0.05). Table 1: Heat treatments for TiCrz samples Sample Heat treatment step C 4h + W.Q C 4 weeks + F.C C 2 weeks + F.C. Heat treatment step C 2 weeks + F.C. 9OOT 3 days + F.C. X-ray Diffraction XRD svstem:automatic X-Ray Powder Diffractometer (Philips), equipped with PW 1730 generator, Bragg-Brentano O/20 PW3720 goniometer, PW37 10 microprocessor, xenonproportional detector, graphite monochromator attached to the detector (Kg remover), divergence slits O.lO, receiving slit 0.2 mm, and antiscatter slit 0.1. The sample holder was a flat plate with a rectangular storage space. Running Condition: Power: 4OKV, 40 ma, scanning method: e/28 step scanning from 16 to Typical step 0.02, time of measuring l-7 set per step. Rietveld Analysis: The program DBWS-9411 [5] has been used. The program is based on previous work [6,7]. Crystal data The crystal data used as the final input for Rietveld method is given in Tables 2-3 (the space groups are written in the computer program format [5]). Table 2: Crystal data for alpha TiCrz [3] as inserted to the Rietveld program. Phase and Space Group TiCr2 (C15) FD3M Unit cell parameters a Position 1 x y z occupancy Ti l/s l/s l/8 l/24 Position 2 x y 2 occupancy Cr l/2 l/2 l/2 l/12

4 588 Table 3: Crystal data for beta TiCr2 [4] as inserted to the Rietveld program. Results and Discussion Diffractograms The diffractograms of a and p phases are compared in Fig. 1. Whereas there are several isolated peaks of the hexagonal p phase, all diffraction peaks of the cubic a phase except one (400), are overlapping. Unfortunately this peak is weak and extremely sensitive to preferred orientation. Almost all the isolated hexagonal lines are very weak except reflection (106)h This peak is also sensitive to preferred orientation. The possibility to carry out fast quantitative analysis based on the intensities of the lines (400), and (106)h was examined in the present study. Rietveld Results Fig. 2 shows a typical Rietveld refinement plot. The crystallographic data used for the input are given in Tables 2 and 3. The quantitative analysis results are summarized in Table 4. Because the atomic scattering of Ti and Cr are similar, we could not refine the occupancies, and we assumed exact stoichiometry for both phases. Table 4: results of TiCr2 Sample Amounts expected 100% Cubic 50:50 Unknown for a phase mainly (as cast) Rietveld results for 90% 55% 45% 25% a phase

5 A 2000 _h cubiz400) hexagonal ( 106) I 45 2teta Fig. 1: Calculated diffractograms of a and p phases (based on experimental data) teta Fig. 2: Typical Rietveld refinement plot

6 590 For two phases of the same composition and same density, the traditional method is to find two diffraction lines 11 for phase A and 12 for phase B. If CA is defined as the fraction of phase A (from 0 to 1): CA=[l +m$mj (1) Where ma and ms are the mass amounts of phase A and B respectively. Then for ideal powders: ca=[l +K(Zz/Z& (2) Where K is a coefficient which is invariable for any value of CA [8]. From Eq. 2 one obtains the coefficient K from CA, Ii and 12: K=(c~-I)(hh) (3) The Rietveld refinement provides us with calculated and observed values of all intensities together with phase amount for a and p phases. On the basis on the mass amounts C,=[l+mp/m,]- (see Eq. l), which were obtained from the Rietveld refinement, the value of K was estimated for the intensity ratio I( 106)p/I(400),. The integrated intensities were derived from three sources: (i) Rietveld refinement output - calculated intensities. (ii) Rietveld refinement output - observed intensities. (iii) Line profile fitting directly from the XRD scanned data (APD method). Fig. 3 shows that in all cases the ratio I( 106)&400), is a monotonic rising function of C,. However, there is some deviation of the intensity ratio found by APD in comparison with the data derived by the Rietveld method. The distribution of K along C, is shown in Fig. 4. The average value of K was found to be Only the calculated intensities, which have been obtained from the Rietveld refinement, obey the rule of constant K (within variation of ko.05). The observed intensities yielded K between 0.1 to 0.3. Direct intensity measurements yielded K values between 0.1 to 0.5. This analysis led us to the conclusion that the ratio between two peaks cannot serve as a tool for quantitative analysis in this binary system of TiCr2 c1 and p phases. The deviation of the K factor for the direct intensity measurements (see fig. 4) indicates that without Rietveld refinement the amount of a phase is over estimated in this case. For less than 10% weight fraction of the hexagonal phase, long scans are essential, in order to provide adequate peak to background ratios of the weak peaks. Otherwise, most peaks are covered by the background and the diffractogram is almost the same as for a pure phase case. Because the Rietveld method refines also the background it improves the treatment of weak diffraction peaks. Moreover, it also takes care of the line overlapping problem. In conclusion, the Rietveld quantitative analysis method was found to be the best tool for obtaining the weight fractions of the TiCr2 phases.

7 g s z,340 - E i %mass of cubic phase by Rietveld Fig. 3: Intensities ratio as a function of %mass l APD n RTV Obs. A RTV Cal... SC 0.3 n L * I I I I I I I ?&mass of cubic phase by Rietveld Fig. 4: Derivation of coefficient K for Ihex( 106)&,b(400) 80 90

8 592 Conclusions In the TiCr2 system the Rietveld method is the only possibility to carry out accurate quantitative phase analysis. The requirement of the whole pattern treatment is because there are not enough resolved diffraction lines in the diffraction spectra for the different phases. Acknowledgments This study was supported by a grant of the US-Israel Binational Science Foundation (BSF), No References 1. J.R. Johnson and J.J. Reilly, Znorg. Chem. 17 (1978) P.A. Farrar and H. Margolin, Trans. of Metal. Sot. AZME 227 (1963) P. Duwez and J.L.Taylor, Trans. ASA (1952) P. Villars and L.D. Calve& Pearson s Handbook of Crystallographic Data for Inter-metallic Phases, American Society for Metals, R.A. Young, A. Sakthivel, T.S. Moss and C.O. Paiva-Santos, Rietveld Analysis of X-ray and Neutron Powder DifSraction Patterns, School of Physics, Georgia Institute of Technology, Atlanta, U.S.A H.M. Rietveld, J. Appl. Crystallogr. 2 (1969) R.A. Young and O.B. Wiles, J. Appl. Crystallogr. 19 (1982) L.E. Alexander and H.P. Klug, Anal. Chem. 20 (1948)