Diffusion Phenomena of the Oxygen and Nitrogen in Niobium by Mechanical Spectroscopy

O. Florêncio1, a, P.S. Silva Jr1,b and C. R. Grandini2,c 1Federal University of São Carlos, São Carlos, São Paulo, CEP13565-905, BR

2São Paulo State University, Bauru, São Paulo, CEP17033-360, BR aodila@ufscar.br, bpsergio@df.ufscar.br, cbetog@fc.unesp.br

Keywords: Niobium, Internal Friction, Oxygen, Nitrogen, Diffusion Coefficient

Abstract. The short-range diffusion phenomenon (Snoek Effect) was investigated by mechanical spectroscopy measurements between 300 K and 650 K, in a polycrystalline niobium sample, containing oxygen and nitrogen, using a torsion pendulum. Experimental spectra of anelastic relaxation were obtained under three conditions: as-received sample; annealed sample and subsequently annealed in an oxygen atmosphere for three hours at 1170 K in partial pressure of 5x10-5mbar. The experimental spectra obtained were decomposed in elementary Debye peaks and the anelastic relaxation processes were identified. With anelastic relaxation parameters and the lattice parameters, the interstitial diffusion coefficients of the oxygen and nitrogen in niobium were calculated for each kind of preferential occupation (octahedral and tetrahedral). The results were compared with the literature data, and confirmed that the best adjustment is for the preferential occupation octahedral model for low concentrations of interstitial solutes, but at higher concentration of oxygen were observed deviations of experimental data for the interstitial diffusion coefficients of oxygen in niobium when compared with the literature data, this could be related to the possible occurrence of a double occupation of interstitial sites in the niobium lattice by oxygen interstitials.

Introduction

Mechanical relaxation measurements have been used to obtain information about many aspects of the behavior of solutes in metals, such as matrix-solute interactions [1], interstitial-interstitial and substitutional-interstitial interactions [2-5], interstitial diffusion [6-7], etc. The application of mechanical spectroscopy measurements to diffusion studies in body-centered cubic (BCC) metals has been used in the last decades. In the BCC lattice, mobile point defects (such as oxygen and nitrogen) with strain fields with symmetry lower than the lattice symmetry give rise to a relaxation process of the Snoek type [1]. Point defects in solids can give rise to anelastic relaxation provided that these defects behave as elastic dipoles. Elastic dipoles represent atomic defects and produce an anisotropic local distortion of the crystal lattice [8]. Heavy interstitial atoms, such as oxygen and nitrogen, in BCC metals induce elastic dipoles with tetragonal symmetry. Matyash et al. [9] have studied the location of oxygen dissolved in a niobium single crystal using the proton channelling method, it being observed that the oxygen occupies interstices of octahedral-type. Several techniques can be used to measure the internal friction [5, 10-11]. The torsion pendulum is the best suited to the study of metals-interstitial solute interactions (such as carbon, oxygen and nitrogen). In the present work, the short-range diffusion phenomenon (Snoek effect) was investigated by mechanical spectroscopy (internal friction and oscillation frequency) measurements in the niobium sample, containing oxygen and nitrogen, using a torsion pendulum. With the anelastic relaxation parameters obtained and the lattice parameters, the interstitial diffusion coefficients of the oxygen

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and nitrogen in niobium were calculated for each kind of preferential occupation (octahedral and tetrahedral). The results were compared with the literature data, and confirmed that the best adjustment occurs with preferential occupation for an octahedral model for low concentrations of impurities, but it did not occur for higher content of oxygen.

Experimental Procedure

The polycrystalline Nb sample was obtained by electron-beam zone melting and was supplied in the form of a swaged rod of 3mm in diameter, by FAENQUIL/Lorena/SP/Brazil. The 50mm long Nb samples which had been chemically polished to 1 mm diameter, in a mixture of nitric and fluoric acids, were used for the anelastic relaxation and X-ray diffraction measurements. The values of internal friction and frequency were obtained with a torsion pendulum of the Kê-type [11] which was set to give rise the oscillation frequencies between 1Hz and 10Hz, with a heating rate of 1K/min and pressure lower than 2x10-5 mbar. The internal friction was determined from the amplitude decay, and the frequency was determined from the period of oscillation. The spectra of anelastic relaxation were obtained for three conditions of the Nb sample: (a) as-received sample, (b) annealed sample, during two hours, in a temperature of 1170K and pressure of 2.5x10-8 mbar and (c) with subsequent treatment in an oxygen atmosphere during three hours, in a temperature of 1170 K and partial pressure of 5x10-5 mbar. Immediately before the measures of mechanical relaxations and of the thermal treatments the sample was submitted to an etching solution, for cleaning of the metallic surface. The lattice parameters of the Nb samples were determined by X-ray diffraction by powder method. The internal friction curves as a function of temperature were resolved into elemental Debye peaks [12] using the method of successive subtraction (in the present work, Peak Fitting Module of Origin). The anelastic processes were identified, and the relevant parameters (activation energy, relaxation strength, peak temperature, relaxation time) of each of the process were obtained and the interstitial diffusion coefficients of the oxygen and nitrogen in niobium were calculated for each kind of occupation (octahedral and tetrahedral).

Results and Discussion

When the redistribution of process is characterized by a relaxation time (τ) the anelastic relaxation of point defects can be described in the ideal case by a Debye peak [12]:

( )

+∆=−

21

1 ωτωτ

Q (1)

centered at ωτ = 1. The maximum height peak is ∆/2, where ∆ is relaxation strength and ω is angular frequency of oscillation (ω = 2πf.). For a BCC metal, the interstitial atoms migration is given by jumps into energetically equivalents sites. For these materials, whose jumps are possible just between octahedral sites, the interstitial diffusion coefficient (D) may be determined by [6,7,12]:

τ36

2aD = (2)

where a is the lattice parameter of material. For jumps possible between tetrahedral sites, the interstitial diffusion coefficient (D) may be determined by [6,12]:

τ72

2aD = (3)

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Experimental spectra of anelastic relaxation as a function of temperature were obtained for the Nb sample, under three distinct conditions of sample. The analyses of the total impurities were determined using a TC-436 DR equipment (Leco Co.) and X-ray diffraction spectra revealed only peaks related to the BCC structure for all conditions (see Table 1). Table 1: Analysis of the total amounts of oxygen and nitrogen and lattice parameter for distinct Nb sample conditions.

Sample Condition Oxygen [at-%] "itrogen [at-%] Lattice Parameter [Å] (a) 0.42±0.06 0.21±0.05 3.295±0.002 (b) 0.40±0.05 0.17±0.06 3.297±0.002 (c) 1.23±0.05 0.13±0.03 3.301±0.003

Fig. 1. shows the anelastic spectrum of Nb sample, after annealling, which was decomposed into two relaxation processes, associated with the matrix-interstitial interactions: Nb-O and Nb-N.

Figure 1. Anelastic relaxation as a function of temperature for Nb sample, for (b) condition,

resolved into constituent peaks corresponding to the interactions: Nb-O and Nb-N. Fig. 2 shows the internal friction and the oscillation frequency as a function of temperature for the Nb sample, after treatment in an oxygen atmosphere. This experimental spectrum of anelastic relaxation was resolved into four elemental Debye peaks, for a better mathematical adjustment, and associated with the Nb-O, Nb-O-O, Nb-O-O-O and Nb-N matrix-interstitial interactions. These data were obtained with an oscillation frequency about 2.4 Hz (at room temperature).

1348 Diffusion in Solids and Liquids V

Figure 2. Internal friction and oscillation frequency as a function of temperature for Nb sample, after treatment in an oxygen atmosphere, resolved into constituent peaks corresponding to the interactions Nb-O, Nb-O-O, Nb-O-O-O and Nb-N. The resolution of the mechanical relaxation spectra as a function of temperature into their constituent Debye peaks was criticized by Weller and et al. [13,14]. They contested the results of Powers and Doyle [6,15] who proposed the existence of pairs of oxygen atoms in an interstitial solid solution in tantalum to explain the observed asymmetric broadening of the anelastic relaxation peak. According to Weller and et al. [13,14], the asymmetric broadening and the shifting to higher temperatures of the anelastic relaxation peak are related to the variation of the measured frequency as a function of temperature (through changes of the modulus), and also to the temperature dependence of the relaxation strength. The asymmetry would disappear if these values were modified to consider these temperature dependences. In addition, Weller et al. [14] argue oxygen atoms would also occupy interstitial tetrahedral positions, for high oxygen contents, as also argued Kê [16]. This double occupancy would then cause the shifting and broadening of the peak, justifying again the existence of a single anelastic relaxation process. The curves of internal friction as a function of temperature obtained in present work for Nb sample for (c) condition, however, are clearly asymmetric. The correction proposed by Weller et al. [13,14] was tested for these values, but the asymmetry continued to be evident with no possibility of fitting a single calculated curve. Assuming that the peaks are true Debye peaks, one can compute the activation energies (E) for the processes, measuring the width at half of the peak height. Using the condition of Debye peak (ωτ = 1), the relaxation time (τ) was determined for each relaxation process. Interstitial elements in solid solution of metals with BCC lattice are responsible for the Snoek peaks in the relaxation spectrum of internal friction, due to the stress-induced ordering, i.e. diffusion process. The evaluation of interstitial diffusion coefficients of oxygen and nitrogen in Nb, using Eq. 2 and Eq. 3 indicates the preference of the solute atoms for octahedral or tetrahedral sites. Beshers [17] carried out a detailed study of interstitial sites in the BCC lattice, discussing the distortions caused by interstitial solutes and associated elastic strain energies, concluding that oxygen and nitrogen in niobium and tantalum should occupy mainly the tetrahedral sites.

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Boratto and Reed-Hill [18] accomplished a comparison between the octahedral and tetrahedral models of occupation for oxygen and nitrogen in niobium and tantalum through elastic after-effect measurements. They verified that the octahedral model gives a better fit than the tetrahedral model. Therefore, the kind of preferential occupation of the interstitial solutes in BCC metals, such as oxygen and nitrogen in niobium is still controversial. Fig. 3 shows the interstitial diffusion coefficients for oxygen in niobium for two models of preferential occupation of the interstitial sites in metallic matrix, for (b) sample condition, where it can be observed that for low oxygen concentration, a good adjustment for octahedral occupation model when compared with literature data[19], similar results were obtained for (a) sample condition.

Figure 3. Interstitial diffusion coefficients for oxygen in niobium, for Nb sample in (b) condition.

The diffusion curve of oxygen in niobium (D = 8x10-2exp[-116320/RT]) used was obtained by E. Fromm and E. Gebhardt [19], being valid for a large temperature range, showing that even for a small range of temperatures of the experimental data, the results obtained are coherent. Fig. 4 shows the interstitial diffusion coefficient for nitrogen in niobium for two models of preferential occupation of the interstitial sites in metallic matrix, for the (c) condition, where it can be observed that for low nitrogen concentration, a good adjustment for octahedral occupation model when compared with literature data [20]. For (a) and (b) conditions the results for the interstitial diffusion coefficients of the nitrogen in niobium show similar behaviours as the (c) condition.

1350 Diffusion in Solids and Liquids V

Figure 4. Interstitial diffusion coefficients for nitrogen in niobium, for Nb sample in (c) condition.

The diffusion curve of nitrogen in niobium (D = 2.6x10-2exp[-152300/RT]) used was obtained by G. Hörz et al. [20], being valid for a large temperature range, showing that even for a small range of temperatures of the experimental data, the results obtained are coherent. Comparing the results obtained with the literature data [19,20]; the coherence of the obtained values can be verified, confirming the validity of the technique for the determination of interstitial diffusion coefficient, for a diluted solid solution. The octahedral preferential occupation sites of oxygen and nitrogen in niobium were confirmed for low concentrations of these solutes. Fig. 5 shows the interstitial diffusion coefficients for oxygen in niobium for two models of preferential occupation of the interstitial sites in metallic matrix, for the (c) sample condition, where it can be observed that for a high oxygen concentration, there is not adjustment either for the octahedral occupation model or for the tetrahedral occupation model when compared with literature data [19].

Figure 5. Interstitial diffusion coefficients for oxygen in niobium, for Nb sample in (c) condition.

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The experimental data deviations for the interstitial diffusion coefficients of oxygen in niobium for high concentration of oxygen ((c) sample condition) when compared with the literature curve [19] can be related with the possible occurrence of double occupation of the interstitial sites in niobium lattice. This result confirms that the asymmetric broadening of the peak is related to the double occupation of interstitial sites in niobium for a high concentration of interstitial solute oxygen, revealing that no clear physical model is available to explain all the features of the Snoek relaxation in BCC metals[21].

Conclusions

1 - The anelastic relaxation spectra for an Nb sample containing different amounts of interstitial elements were obtained as a function of temperature with a torsion pendulum at oscillation frequency in the hertz bandwidth, for two conditions of the Nb sample. 2 - X-ray diffraction revealed only peaks related to the cubic structure for all conditions of the Nb sample, and the lattice parameter was determined for Nb. 3 - The anelastic relaxation spectrum for Nb sample was resolved into two interactions processes: Nb-O and Nb-N, for all conditions. With the parameters of anelastic relaxation for each kind of interaction (peak temperature, activation energy and relaxation time) and lattice parameter the determination of interstitial diffusion coefficient of oxygen and nitrogen in Nb was possible. 4 - The octahedral preferential occupation sites of oxygen and nitrogen in Nb was confirmed for low concentrations of the interstitial solutes. 5 - For high concentration of oxygen in niobium, deviations of experimental data were observed for the interstitial diffusion coefficients of oxygen in niobium when compared with the literature data. This phenomenon is related to the possible occurrence of a double occupation of interstitial sites in niobium lattice.

Acknowledgments

We would like to thank the following Brazilian agencies: FAPESP and CNPq for financial support.

References

[1] J. L. Snoek: Physica Vol. 6 (1939), p. 591. [2] P.M. Bunn, D.G. Cummings and H.W. Leavenworth Jr: J. Appl. Phys. Vol. 33 (1962), p. 3009. [3] M.S. Ahmad and Z.C. Szkopiak: J.Phys.Chem.Solids Vol. 31 (1970), p. 1799. [4] Z.C. Szkopiak and J.T. Smith: J.Phys.D. Vol. 8 (1975), p. 1273. [5] W.J. Botta F., O. Florêncio, C.R. Grandini, H. Tejima and J.A.R. Jordão: Acta Metall. Mater. Vol. 38 (1990), p. 391. [6] R.W. Powers and M.V. Doyle: J. Appl. Phys. Vol. 30 (1959), p. 514. [7] G. Haneckzok, and J. Rasek: Defect and Diffusion Forum Vol. 3 (2001), p. 188. [8] M.Weller: J. de Physique IV Vol. 6 (1996), p. C8. [9] P.P. Matyash, N.A. Skakun and N.P. Dikii: JETP Lett. Vol. 19 (1974), p. 18. [10] O. Florêncio, D.G. Pinatti and J.M.Roberts: J. Physique Vol. 46 (1985), p. C10. [11] T.S. Kê: Phys. Rev. Vol. 71 (1947), p. 533. [12] A.S. Nowick and B.S. Berry: Anelastic Relaxation in Crystalline Solids (Academic Press, New York 1972). [13] M. Weller, G.Y. Li, J.X. Zhang, T.S. Kê and J. Diehl: Acta Metall. Vol. 29 (1981), p. 1047. [14] M.Weller, J.X. Zhang, G.Y. Li, T.S. Kê and J. Diehl: Acta Metall. Vol. 29 (1981), p. 1055.

1352 Diffusion in Solids and Liquids V

[15] R.W. Powers and M.V. Doyle: Trans. Metall. Soc. A.I.M.E. Vol. 215 (1959), p. 655. [16] T.S. Kê: Phys. Rev. Vol. 74 (1948), p. 9. [17] D.N. Beshers: J. Appl. Phys. Vol. 36 (1965), p. 290. [18] F.J.M. Boratto and R.E. Reed-Hill: Scripta Met. Vol. 12 (1978), p. 313. [19] E. Fromm: in Gase und Kohlenstoff in Metallen, edited by E. Fromm and E. Gebhardt, Berlin Springer (1976). [20] G. Hörz et al.: Gases and Carbon in Metals, Physics Data, (1981). [21] F. Povolo and O.A. Lambri: Mater. Trans. JIM Vol. 34 (1993), p. 33.

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DOI References

[1] J. L. Snoek: Physica Vol. 6 (1939), p. 591.

doi:10.1016/S0031-8914(39)90061-3 [3] M.S. Ahmad and Z.C. Szkopiak: J.Phys.Chem.Solids Vol. 31 (1970), p. 1799.

doi:10.1016/0022-3697(70)90170-8 [13] M. Weller, G.Y. Li, J.X. Zhang, T.S. Kê and J. Diehl: Acta Metall. Vol. 29 (1981), p. 1047.

doi:10.1016/0001-6160(81)90056-0 [17] D.N. Beshers: J. Appl. Phys. Vol. 36 (1965), p. 290.

doi:10.2307/2060142 [18] F.J.M. Boratto and R.E. Reed-Hill: Scripta Met. Vol. 12 (1978), p. 313.

doi:10.1016/0036-9748(78)90120-5 [19] E. Fromm: in Gase und Kohlenstoff in Metallen, edited by E. Fromm and E. Gebhardt, Berlin Springer

(1976).

doi:10.1515/bgsl.1976.1976.98.325