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Internal friction in nb-v-o alloys
Acta metall, mater. Vol. 43, No. 12, pp. 4393-4401, 1995
Pergamon 0956-7151(95)00120-4
ElsevierScienceLtd Copyright9 1995Acta MetallurgicaInc. Printed in Great Britain.All rights reserved 0956-7151/95 $9.50+ 0.00
INTERNAL FRICTION IN Nb-V-O ALLOYS N. P. KUSHNAREVA, S. E. SNEJKO and I. P. YAROSH The Institute of Metal Physics, National Academy of Sciences of Ukraine, Vernadsky Blvd 36, Kiev 252142, Ukraine (Received 3 August 1994; in revised form 24 February 1995)
Abstract--The logarithmic decrement, 6, was measured in Nb-V-O alloys with the V content of 0.5, 1.0, 1.9, 7, 12, 20 and 50 at.% using a low frequency ( f = 3-7 Hz) inverse torsion pendulum in the temperature range from 20 to 800~ The complex oxygen atom Snoek peaks were analysed with the help of a computer and individual Debye form constituent peaks-j were extracted. The parameters of these peaks were used to derive information of two sorts: (a) distribution of oxygen atoms over octahedral interstices which differ in the number j of V atoms in the nearest neighbour lattice sites (static parameter) and (b) the potential barriers for oxygen atoms diffusing from j-positions (dynamic parameter). The first was used to evaluate the binding energies of oxygen with vanadium atoms in j V 4 ) complexes, the second made understandable the structure of potential barriers for diffusion of the oxygen atoms from positions j. The differences between measurements of static and dynamic characteristics are discussed.
1. INTRODUCTION The interaction between substitutional and interstitial ( " s - i " ) solutes in b.c.c, metals influences the alloy properties to a marked degree, so far this problem is a subject of a continuous interest. Theoretical modelling and experimental measurements of diffusion, thermodynamic, mechanical and other parameters, that may be related to the macroscopic ones, are used to study this problem. Altstetter and coworkers have carried out a series of works on investigation o f " s - i " interaction in the alloys, based on VA group metals, by using the equilibrium and diffusion measurements. The review on some of these works is published in Ref. [1]. The " s - i " binding energies for V-O atoms in the N b - V - O alloys based on equilibrium data were calculated from the model of Albert et al. [2] and those based on diffusion results--from the trapping models of McLellan [3], Oriani [4] and Koiwa [5}. The binding energies thus obtained exhibited qualitative consistency but quantitative disagreement []], while in the N b - M o - O system (for M o - O atoms) they differed even in sign [2]. The similar results were obtained for the T a - V - O and T a - M o - O systems [6]. One of the reasons for the mentioned discrepancy may be, as believed by the authors, the use of the models which proceed from the definite arrangement of atoms and treat the information on an atomic scale, whereas the comparison is made with the results of the macroscopic measurements. And as concluded in [1], further experimental testing in concentrated substitutional solutions is required to make the quantitative analysis more accurate. The purpose of the present work is to investigate the interatomic " s - i "
interaction occurring in the N b - V - O system [with varying vanadium concentration (C~) in the up to 50at.%V alloys[ by using the internal friction method (i.e. Snoek relaxation peaks). The latter leads us, we believe, to the understanding of a local situation on the atomic scale, because it makes it possible to distinguish interstitial atoms, differing in the activation energies of elementary diffusion jumps. We know three works dealing with the investigation of internal friction in the N b - V - O system. Szkopiak and Smith showed that in the Nb-1 at.%V alloy the vanadium atoms acted as traps for both oxygen and nitrogen atoms [7]. The latter are located in octapores near V-atoms and the activation energy for their diffusion jumps to new locations increases, so corresponding Tmax of the peaks due to V-O and V - N in Nb shifts to higher temperatures. The peaks due to oxygen and nitrogen atoms in unalloyed niobium are absent in the alloy, this being in agreement with the fact that all oxygen and nitrogen atoms (within the experimental accuracy range) are redistributed in locations near V atoms. Later, Carlson with co-authors [8] confirmed this result for the alloys with 0.24 and 0.5 at.%V. In addition, they proved the existence of the saturation effect taking place in these low-concentration alloys: when the concentration of the oxygen atoms (Co) exceeds that of the vanadium ones, the peak P~ ( N b 4 ) ) appears in addition to the V-O peak 2. The same authors extended the concentration interval for the alloys under investigation up to l0 at.%V in [9]. A new peak (P3) due to V - O - V complexes forms in the alloys with C v ~>2.5% in addition to peak P2; thus, two peaks P2 and P3 form in the curves plotted for the alloys with 2.5 and 5at.%V, The N b - 1 0 a t . % V
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KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS
alloy exhibited a single broad peak P3, with Tm~x somewhat higher than Tm~,of P3' It was attributed to reorientation of the oxygen atoms associated with two or more vanadium atoms. The authors related the peak Pr, broadening to different crystallographic configurations of the " s - i " complexes having the same number j of the V-atoms. 2. EXPERIMENTAL
The Nb--V alloys were produced from 99.99% pure niobium and vanadium in a laboratory arc furnace with a nonconsumable tungsten electrode in a purified argon atmosphere. The investigated alloys contained 0.5, 1.0, 1.9, 12, 20 and 50at.%V. The ingots 15 mm in diameter and 120-150 mm long were remelted by the electron-beam zone method to provide the coarse-grain crystalline structure stretching along ingot axis, this being favourable for further deformation. Such ingots were cold or hot (depending on deformability of the alloy based on homogeneity of its composition) rolled into sheets 6-8 mm in thickness, cut into bars 6 • 6 mm along the length. The latter were cold drawn to a wire 0.8-1 mm in diameter. The samples 0.8-I mm in diameter and 100-120 mm long were annealed for 1 h at a temperature between 1200 and 1500~ depending on the composition. The oxygen content of the samples was varied by their annealing in vacuum of 1-10 -~ Pa at 500-800~ The logarithmic decrement (6) measurements were performed using the low frequency (3-7 Hz) torsion pendulum technique in vacuum of 10 -3 Pa in the temperature interval from 20 to 800~ The heating rate was 0.5~ The measurements were carried out in an automatic mode in steps of 2-3~ The relaxation peaks are known to have the Debye shape which can be described by an expression 6 = 6maxsech H / R ( 1 / T - l/Tin,x).
(1)
The division of the complex curves into constitutive peaksj was effected using equation (1) by specifying a set of parameters for peaks j, such as their height, 6~,~; activation energy, H, and temperature, T ~ . The most reliable of these parameters were fixed, while the others were varied until the best fitting to the experimental curve was achieved. Deviation of the peak shapes from the ideal ones due to the broadening parameter, /~, was allowed for by using the method suggested in [10]. We also used a result described in [I I], where Tm~x and H were linearly related. 3. RESULTS
The Snoek relaxation peak due to oxygen atoms in unalloyed niobium (designated as P0) is found at about 173-176~ (at frequencyf = 3.5-4 Hz) [12, 13] and its activation energy is l l2kJ/mol (different works give this value as ranging from 107 to 117 kJ/mol). Only one peak at 280~ was found in
the Nb-0.5 V alloy. This is the same V-O intera~ction peak Pz observed at about 280~ ( f = 1 Hz), as reported previously by Szcopiak et al. [7], and at about 242~ (f-----0.56 Hz), as reported by Carlson et al. [8, 9]. Its nature was accounted for by oxygen atoms located in octapores near vanadium atoms. We call it peak P~. Our numbering of peaks (Pj) coincides with the number j of vanadium atoms located in the nearest lattice sites surrounding octapores with oxygen atoms in them, whose jumps are the sources of the corresponding peaks. The shape of peak PI is close to ideal, the broadening parameter, fl, is equal to 0.25-0.3 (the ideal Debye peak has fl = 0). When Co exceeds Cv, peak P0 forms, in accordance with [9]. The character of the curves plotted for the 1%V alloy is similar, the peak P1 saturation takes place at Co>_. 1 at.%. The 6 curves for Nb--1.9 V with different oxygen contents are shown in Fig. l(a). Curve I represents the sample annealed at 1700~ (1 h) and contains two peaks at about 280 and 417~ The former is peak P~ and the latter is assumed to be, with allowance for the frequency ( f = 4 Hz), a peak forming at about 393~ ( f = 0.59 Hz) in [3], explained as being due to oxygen with two V atoms in neighbouring surrounding (i.e. a t j = 2), according to our designation--peak /)2. Curve II was obtained after doping this sample with oxygen (at 500~ in vacuum 10-~Pa) and annealing for homogenization across the sample section (at 1300~ for 1 h). For computer analysis it is necessary to know the Hmaxjvalues. The linear correlation between //max and /'max for Snoek-like peaks was first shown by Wert and Marx [11] and then confirmed in a number of works [13, 14]. We have found Hmaxjby using this correlation ( f o r f = 3-4 Hz). Carlson used the Tm~j shift by the frequency method for determining Hm~xj.The numerical values of Hm~xj, obtained by both methods, are given in Table 1 and, as seen, they correlate well enough. The computer analysis of curves II and IH with the fixed values of Tm,x~, Hm,x1, Tm~x2and Hm~x2conducted by varying 5m,xj revealed the existence of the peak with Tin,, of about 365-370~ with Hmax = 165 kJ/mol. Supposedly, the latter, by an analogy with the preceding peaks, is due to stress induced reorientation of oxygen atoms associated with three vanadium atoms, i.e. peak P3The Nb-7V alloy exhibits no oxygen part relaxation after annealing. The sample was doped with oxygen at 700~ for 1 h in the 10 -~ Pa vacuum and after that curve I [Fig. 1(b)] was plotted. The oxygen is absorbed from the sample surface. The absorption is nonequilibrium and nonhomogeneous in the bulk. Peak Pl is the biggest one in this curve, but it also has other peaks with Tm~xbetween Tmaxl and Tm~x2. Curve II corresponds to the state after homogeneous annealing at 1200~ Four peaks are present in curve II: the above peaks P~, P2, P3, as well as the fourth peak, supposedly, P4 with Tm~x= 320-325~ and H = 152 kJ/mol.
et al.:
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The situation for alloys with 12 and 20at.%V [Fig. 2(a)] is to a great degree similar to that shown above for N b - 7 at.%V. All four peaks P1, P2, P3 and P4 are present in the curves plotted for these alloys,
IN Nb-V-O
ALLOYS
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peak P2 being the highest one. Relative contributions of P1, ]92,P3 and P4 relaxations depends on annealing temperature and Cv, but does not depend on Co, The oxygen atom distribution over position j tends to
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KUSHNAREVA
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INTERNAL
Table 1. Parameters of peaks j in N b - V - O alloys ( f = 4 Hz) Peaks j 0 1 2 3 4
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be a statistical one with Cv increasing and reaches it in Nb-50 at.%V alloy. The curves plotted for this alloy with two values of Co are shown in Fig. 2(b). Peak P3 is the highest one in this alloy, so is the relative concentration of interstices with j = 3. The concentration of oxygen in position j may be determined as Cj = gj~maxj. The heights of peaks P0, P1 and /'2 for the alloys under investigation as a function of oxygen concentration are plotted in Fig. 3. Also included are appropriate data from works [2] and [3]. The "saturated" peak heights were not included. According to Fig. 3, K0 = 5.3_ 0.5, K t = 10 ___1 and K 2 = 23 _ 1.5 for the corresponding Cj in at.%. We treated the results of Fig. 3 in [9] to determine K2 (curves with 0.21, 0.38 and 0.60 at.% oxygen). The curves with 0.77 and 0.91 at.% O were not taken into consideration: they showed K2 twice as low comparing to K2 for the curves with up to 0.60 at.% O. We are of the opinion and have experimental evidence, that the considerable part of relaxation in the temperature range of peak P2 in the curves with 0.77 and 0.91 at.% O in Fig. 3 [9] has the nitrogen origin. The accuracy of the determination of K3 and K4 is low, this being accounted for by a very small height of peak P3 first formed in the Nb-l.9 V alloy, but in alloys with 7 and more at.%V peaks P3 and/'4 form simultaneously. The obtained numerical values of K3 = 17 and K4= 12 may be used with allowance for the above notes. Kj being known, it is possible to find the oxygen atom distribution in octapores with different j positions. The parameters (Tmaxi, nmax)) of peaks j in the Nb--V-O alloys at f = 3.4-4 Hz are presented in Tables 1 and 2 (Cj). 4. D I S C U S S I O N
Some questions of prime importance are to be considered prior to interpreting the results obtained. First of all, this is reliability of our treatment of the damping spectra obtained and, in particular, the conformity of peaks j to the jumps of oxygen atoms out from octahedral interstices surrounded by numberj of V-atoms. For the first time the subsidiary peaks in dilute alloys (which we call peaks Pl) with Tmaxmore than Tmaxof Snoek relaxation in unalloyed metals were received in Fe-based (Fe-Mn-C(N), Fe-V-N) alloys more than 40 years ago [15]. Their nature was associated with " s - i " interaction. One of the first reviews on this problem was published by Hasson and Arsenault [16], since then a number of works have been carried out on Fe alloys with Cr, Mo, W and other substitutional solutes and VA
FRICTION
IN Nb-V-O
ALLOYS
group metal-based alloys. In the cases of strong " s - i " interactions (such s-atoms are called traps), TmaXof peaks P~ are considerably shifted to a higher temperature, while peaks P0 and Pl are separated on the temperature scale. We know two systems (Nb-V~O [8, 9, this paper], Nb--Zr-N [17-19]), where in the next peak P2 was revealed without overlapping peaks P0 and Pl. This allows their parameters to be determined more precisely. So, as shown in [19] for the N b - Z r - N system, the height of peak P~ is in right proportion to substitutional metal concentration (Cs), as is the height of peak P2 to C~, this being a convincing proof of the Z r - N composition of the corresponding complexes for peak P~ and Z r - N - Z r for peak P2. Peaks P0, P~ and P2 in the corresponding alloys may exist in the curves simultaneously, as in the N b - Z r - N alloys [17-19], or, at some concentration intervals, form consistently, as in the present N b - V - O alloys. This depends on the relative values of the complex binding energies. So, till now we have been using a general approach, which accepts the distribution of oxygen atoms in the octapores with a different number j of the substitutional atoms. This approach has firm logical grounds and leads to reasonably consistent experimental results for the dilute alloys. Such factors as different crystallographic configuration of the complexes, as well as long range interaction, can influence the relaxation time z (H exactly). For example, complexes with j = 1 may have two configurations and those with j = 2 may have four configurations, differing in z (H). The existence of isolated peaks Pl and /'2 convinces us that these factors lead to peak spreading. The latter shows itself in the experiment: for peak P1, fl = 0.3-0.5; for/'2, = 0.5-0.6, this being not that high. It means that the higher-energy favourable crystallographic configurations for the complexes are realized, or that the difference in zj for the complexes with the same j but different configurations is rather small, compared to the difference between zj and zj_+l. In any case, the experimental evidence supports the approach on the existence of some effective z (with allowance for the spread) for /-atoms in position j. As mentioned above, we took into account the spread of individual peaks by using fl equal to 0.3-1 (the higher the j, the higher the fl). The picture becomes more complicated in the concentrated alloys. First, these alloys feature a higher probability of differences in the initial, prior to a jump, and final, after a jump, positions of interstitial atoms. We suppose that the potential barrier which an atom must overcome during each deformation half-cycle is determined by the initial configuration of j; so, the same atom can contribute to various peaks j depending on the position it occupies prior to the jump. Now, upon considering the above comments, let us come back to the results obtained. As noted above, for the alloys with Cv ~< 1 at.% the saturation of peak Pl occurs at Co > Cv. Each V
KUSHNAREVA
et al.:
INTERNAL FRICTION IN Nb-V-O ALLOYS
atom has six surrounding octapores in the first shell, twelve in the second shell and so on. Nevertheless, only one oxygen atom saturates the bonds of a vanadium atom, the latter losing its trapping quality. This is in consistency with the assumption of a chemical factor playing the predominant role in the V - O complex formation. If so, it should be noted that the electron interaction in the dilute N b - V - O alloys is of a local, rather than global, character. According
4397
to the current models, two principal factors contribute to "s i " interaction, i.e. chemical (or electron) and elastic (deformation) ones. The criterion used to determine a degree of the chemical interaction is the difference in the heat of formation of oxides, whereas the elastic interaction is controlled primarily by the size factor. One of the papers takes into account the values of modulus and first ionization potential [7]. Our opinion of the chemical origin of the V - O
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KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS
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c (at. %0) Fig. 3. 6 m a x VS at.% O for peaks P0 (t), Pi (2) and Pz (3) in the Nb-V alloys: O, A--present; Iq, A--after [9]. complex forming in the dilute N b - V - O alloys does not coincide with that mentioned in [7, 20], which consider the size factor to be the main cause. The "s-i" binding energy (AEj) may be evaluated by comparing the interstitial atom distribution in the t y p e j interstices (Cj) with the relative concentrations (hi) of the latter. In terms of the atomic configuration model and the short range interactions [21]
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(2)
Z h. e x p ( - E . / k r ) where Ej and E. are the atom potential energies in the j t h and nth positions. It can be seen that Cj = ~ e x p ( - A E / k T ) Co
(3)
where AEj = E j - E0 is the "s-i" binding energy. In [20, 21] hj was found to be h) = vA= 6! C{(l - Cs)6-j. v j(6 - - j ) !
(4)
Here, v is the total number of octahedral interstices, vj is the number of type j interstices, Cs is the concentration of substitutional solute, Cv in our case. In Refs [21, 22] the interaction between the substitutional atoms which may change the dependence (4) was neglected. The constitution phase diagram of N b - V (the full-mutual solubility, cigar-like shape, with no intermediate phases formed) does not give
grounds for it to be ignored. We are not aware of the data on the V atoms interaction in Nb, but if it existed, it would lead to the formation of regions with local heterogeneity and the presence of interstitial atoms in these regions might help to reveal them. It is this approach that was used as a basis to study local heterogeneities in the F e - C r alloys [23]. The results of calculating the binding energies for different compositions of the j complexes are presented in Table 2. Since peak P0 is absent in Nb-0.5 V alloy, first we assumed it to be equal to the background damping at the corresponding peak temperature and, second, -6m~x0 was assumed to be by an order of magnitude lower than the background level. The first assumption resulted in - 4 2 . 2 kJ/mol for the AE1 value, the second - 5 2 . 8 kJ/mol. The same AEI values were obtained for the Nb-1 V alloy. Comparison of these results with the AEI values obtained from equilibrium and diffusion experiments and summarized in Ref. [8] shows the best agreement to be with the - 4 6 . 7 k J/tool value for Nb-2.7 V alloy obtained from thermodynamic activity measurements (equilibrium experiments). The experimental internal friction curves plotted for the Nb-5 V alloy in [9] (Fig. 3, curve 4 in [9]) were also included for evaluation of AE(2_ 1) (AE2 _ 1= E2 - El ) (Table 2, line 7). The results are consistent and equal to - 15.5 kJ/mol, this providing the - 6 1 k J / m o l value for AE2 (AE2=E2-Eo) at A E I = - 4 6 k J / m o l . Only the curves plotted for the samples treated to provide the stabilized state were used for machine analysis. As can be seen, for up to 20 at.%V AE(2_ 1)remains at the level - 1 5 . 5 + 1.5 kJ/mol. The energy state of oxygen atoms in positions with j = 4 only slightly exceeds those with j = 2 (AE,_ ~= - 17 ___2 kJ/mol) and these two states are more energy-favourable than that with j = 3. This may be connected with the influence of crystallographic geometry of the responsible complexes. Besides, as can be seen, the increase in the number of V atoms in complexes does not lead to the multiple increase in binding energy value, i.e. AEj v~jAEl . The values for N b - 7 V are somewhat higher than others, but the general situation is the same. The AEu_ 1) values calculated for the Nb-50 V alloy based on the results from Fig. 2(b) are close to 0 + 2 kJ/mol. This means that oxygen atom distribution over positions j in this alloy is close to the fraction of this type j interstices, that is, close to the statistical distribution. Thus, we have no answer to the question on the character of transition from preferential to statistical distribution of oxygen atoms, whether it has abrupt or gradual dependence on Cv in the alloy. The data presented above allows us to propose a scheme of the energy variation for oxygen atoms situated in the first type traps ( j = 1) shown in Fig. 4. In a general case the potential barrier, H, an oxygen atom should overcome during its jump from a trap is: H = H, orr. - AEj - A E '
(5)
KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V~O ALLOYS
4
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where: H.o~m is ndi f for an oxygen atom in unalloyed Nb, coincides with Hmax0and equals 112 kJ/mol; AEj is the binding energy (for j = 1, it is AE1) and A E ' is the change in the saddle point energy. There are two types of the jumps: reorientation of oxygen atoms from one trap to a neighbouring one around V atoms and a jump out of traps (escaping from traps). The first one coincides with an elementary action in the internal friction experiment; that is, it explains why H is Hmax and in this case we call A E ' AE~. An escape from the t r a p is a necessary condition for a long-range diffusion to take place, in this case H coincides with ndi f and here we call A E ' AE~s. Now, evaluate some quantitative parameters. So, for the Nb--0.5 V alloy Hnorm is 112 kJ/mol, AE l = - 4 6 kJ/mol (Table 2), Hmaxl= 142 kJ/mol (Table 1) and the value of + 16 kJ/mol is obtained for AE~. In accordance with Ref. [24], ndi f of oxygen atoms in the Nb-0.5 V alloy is equal to 176 + 9 kJ/mol, in this case the value of AE~ equals - 18 kJ/mol (see Fig. 4). The value of Hdif for oxygen atoms does not coincide with H~x~ for Nb-0.5 V; the difference between them, AE~ - E~s, in this case amounts to 34 kJ/mol. This result is a convincing support of the models of Koiwa [5] and Kirhhleim [25], describing the influence of traps or antitraps on the saddle point energy. According to Kirhheim's model, the energy of the jump from a free site to a trap is lower by AQ, while the energy of the jump back from a trap to a free site--higher by AQ. The scheme similar to that shown in Fig. 4 is presented in [24] as an illustration to the Kirhheim's assumption, but in the present paper it was obtained experimentally. The authors of [24] believe the potential barrier (H) for the jump from a trap to a free site (supposedly, it is Hdif) is identical to Hm~x in the internal friction experiment (Hmax~ in the Nb-0.5 V alloy). As shown above, these two values do not coincide. That is why the value of AE 1 as calculated in [24] ( - 6 6 kJ/mol) is problematic.
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KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS
For the second-type traps (2V-O) H ~ 2 is 179 kJ/mol; AE2 = - 61 kJ/mol and calculated AE~ = - 4 kJ/mol; that is, the saddle point energy increases by 4 kJ/mol. We have no way to find E-'s for the energy of the jump of oxygen atoms from traps a t j = 2 because.of the absence of literature data o n a d i f of oxygen atoms in the N b - V alloys, where peak P2 is a predominant one. But it is clear that the energy situation in this case is different, compared to that mentioned above for the V-O traps. When calculating AE 1 and AEu_ ~) we used the C 1/Co or CflC~ concentration ratios at Tmaxof the corresponding peaks, for example Cj at Tr,axj to C~ at Tmaxj, but not Tma,j, as it should be. In this case we did not take into account the temperature dependence of C~ that should lead to a lower value of Cj at Tma,j. So, the AE(2_ ~)value for Nb-12 V was calculated as being equal to - 1 7 k J / m o l (Table 2, line 10), against -19.1 kJ/mol obtained with the allowance for the C~ temperature dependence (12% difference). The errors in determining other AEu ~) values at j = 3 must be lower, because the difference between Tm,~jand Tm~,~ decreases. So, the error in AEc4_ ~)for the same sample of N b - 1 2 V is only 3.8% ( - 1 6 . 6 k J / m o l against - 1 6 . 0 8 kJ/mol in Table 2). Consider now the reasons for the discrepancies in the AEi values obtained for the Nb- and Ta-based alloys by diffusion and thermodynamic measurements, mentioned in [1, 6]. According to [6], although both measurements indicate the V ~ ) attraction, they are not in a good quantitative agreement: the value of the binding energy derived from the equilibrium measurements is smaller than that obtained from the diffusion measurements. In the case of alloys with Mo as substitutional solutes the two values are not even in a qualitative agreement. The data obtained make it possible to understand the difference between the equilibrium (thermodynamic) and dynamic (diffusion) parameter measurements in the Nb-based alloys. The interaction energies may be obtained only in the equilibrium experiments by investigating the distribution of interstitial atoms over the positions-j octapores by the internal friction method, or by the thermodynamic measurements. The diffusion activation energy characterizes a barrier the i atom should overcome during a jump, which is a dynamic action involving, in addition to the interaction energy, the change in the saddle point energy, A E ' (Fig. 4). As shown above, A E ' varies with a kind of trap and a kind of jump, the latter being located around the traps or apart from them. In a series of the works on the diffusion and thermodynamic measurements conducted on the VA group metalbased alloys, Altstetter and co-workers employed theoretical models, which assumed A E ' to be equal to zero. This is the reason for inconsistency observed between the thermodynamic measurements and the kinetic behavior. The latter must allow for the A E ' parameters. So, in the Nb-Mo--O system the increase in Hd~f (proved by the internal friction [26] and
macrodiffusion experiments), accompanied by obtaining the positive value of the binding energy, AE (confirmed by the internal friction and thermodynamic experiments), makes it possible to conclude that the cause of an increase in ndi f in this case is an increase in the saddle point energy, A E ' . One more circumstance should be taken into account. All macroscopic methods may be useful only for the alloys with one of the trap types, i.e. the low-concentration alloys. In the case of the alloys with more than one type of the traps (Nb with 2 and more at.%V), all macroscopic methods give the average quantitative values of the effective parameters. So, the internal friction method has some advantages: the same experiment provides two types of information, i.e. on equilibrium (the distribution of i atoms over positions j ) and dynamic (Hm~xj) characteristics, as well as on the number and the types of the traps depending on an alloy concentration. We understand quite well that one may object against a too simple picture we presented, whereas the reality can be much more complicated. In this connection, one should note our remarks given at the beginning of this section. Besides, we did not consider the interaction taking place in a number of the coordinate shells. The analytical correlation given in equation (3) was excluded in terms of the atomic configuration model and the short-range (only the nearest neighbour) interactions. The short-range interaction (in the first two shells) is a typical feature of the chemical (electron) nature interaction, while that of the deformation origin has a long-range effect. According to [6] the AE value decreases as more shells of neighbours are included. But each of these alternative assumptions yielded the equally good fit to the experimental data. Therefore, it was impossible to choose between them. In the major part of our work we used a version according to which the individual peaks j do not interact with each other. But one should take into account that there are theories involving an approach based on the constituent interaction of the peaks [27, 28]. As far as the current situation is concerned, we failed to apply any of them. 5. CONCLUSIONS (1) Two types of the data were obtained by using the Snoek relaxation investigation on the N b - V - O alloys: distribution of the oxygen atoms over octahedral interstices differing in the number j of the nearest neighbouring V atoms and the potential barrier for the diffusion jumps of the oxygen atoms from positions j. The former was used for evaluation of the binding energies (AEj), the latter for evaluation of the structure of the potential barriers during i atoms jumping. (2) There is a strong interaction of a chemical nature between V-O atoms in the N b - V - O alloys with up to 5at.%V, which is determined by the
KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS binding energy ( A E v _ o = - 4 6 k J / m o l , AE2v_o= - 6 1 kJ/mol). The potential barrier for reorientation of the oxygen atoms around the V traps (Hmax) is lowered, while that for escaping from the traps (ndif) is raised due to a decrease and an increase in the saddle point energy, respectively. Thus, Hm,x does not coincide with Hair. (3) The attraction inside the j V - O complexes at j >/4 is weakened, the local effect is lost and the oxygen atom distribution with an increase in the vanadium concentration approaches the statistical one. (4) The cause of most models being inadequate lies in ignoring the changes in the saddle point energy in the constituent of the potential barrier for the dynamic diffusion processes, taking into account only one of the trap types and assuming Hdif and //max to be equivalent for all the systems.
REFERENCES, 1. J. Park and C. J. Altstetter, Acta metatt. 34, 2217 (1986). 2. E. Albert, E. Fromm and R. Kirhheim, Metall. Trans. 14A, 2117 (1983). 3. R. B. McLellan, Acta metalL 27, 1655 (1979). 4. R. A. Oriani, Acta metall. 18, 147 (1970). 5. M. Koiwa, Acta metall. 22, 1259 (1974). 6. J. S. Lee and C. J. Altstetter, Acta metall. 34, 131 (1986); 34, 139 (1986). 7. Z. C. Szkopiak and J. T. Smith, J. Phys. D: Appl. Phys. 8, 1273 (1975). 8. O. Carlson, H. Indrawirawan, C. V. Owen and O. Buck, Metall. Trans. A 18a, 1415 (1987).
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9. H. Indrawirawan, O. Buck and O. N. Carlson, Physica status solidi (a) 104, 443 (1987). 10. N. P. Kushnareva and S. M. Pechersky, Zavodskaya Laboratoria 4, 47 (1986). 11. C. Wert and J. Marx, Acta metall. 1, 113 (1953). 12. V. N. Gridnev and N. P. Kushnareva, Phys. Metals Metallography 64, 504 (1987). 13. M. Weller, J. Phys. Collogue CI0, Supplement an NI2, 46, C10-7 (1985). 14. W. Janiche, E. Stolte and J. Brauner, Technol. Mitt. Krupp. 23, 146 (1965). 15. J. D. Fast and J. L. Meijering, Phil. Tech. Rev. 8, (1953). 16. D. F. Hasson and R. J. Arsenault, Treatise on Materials Science and Technology, Vol. 1, p. 179. Academic Press, New York (1972). 17. D. Mosher, C. Dollins and C. Wert, Acta metall. 18, 797 (1970). 18. V. P. Elutin, D. G. Maksimov and E. I. Mozshuhin, Phys. Metals Metallography 38, 564 (1974). 19. V. N. Gridnev and N. P. Kushnareva, Phys. Metals 75, 32 (1979). 20. M. S. Blanter and M. I. Fradcov, Phys. Metals Metal~ lography 64, 679 (1987). 21. A. A. Smirnov, Theory of Interstitial Alloys. Nauka, Moscow (1979). 22. O. M. Barabash and A. K. Shurin, Proc. Acad. Sci. U.S.S.R., The Metals N5, 195 (1978). 23. I. A. Tomilin and M. N. Churyukanova, Proc. Higher Educational Establishments, Ferrous Metals 1, 90 (1987). 24. M. D. Tseng, H. Indrawirawan and O. N. Carlson, J. Less Common Metals 136, 312 (1993). 25. R. Kirhheim, Acta metall. 30, 1069 (1982). 26. N. P. Kushnareva, S. E. Snejko and I. P. Yarosh, Phys. Metals 12, 312 (1993). 27. H. Koiwa, Phil. Mag. 24, 1, 107 122 (1971). 28. G. Haneczok, H. Weller and J. Diehl, Physica status solidi (b) 1972, 557 (1992).
Pergamon 0956-7151(95)00120-4
ElsevierScienceLtd Copyright9 1995Acta MetallurgicaInc. Printed in Great Britain.All rights reserved 0956-7151/95 $9.50+ 0.00
INTERNAL FRICTION IN Nb-V-O ALLOYS N. P. KUSHNAREVA, S. E. SNEJKO and I. P. YAROSH The Institute of Metal Physics, National Academy of Sciences of Ukraine, Vernadsky Blvd 36, Kiev 252142, Ukraine (Received 3 August 1994; in revised form 24 February 1995)
Abstract--The logarithmic decrement, 6, was measured in Nb-V-O alloys with the V content of 0.5, 1.0, 1.9, 7, 12, 20 and 50 at.% using a low frequency ( f = 3-7 Hz) inverse torsion pendulum in the temperature range from 20 to 800~ The complex oxygen atom Snoek peaks were analysed with the help of a computer and individual Debye form constituent peaks-j were extracted. The parameters of these peaks were used to derive information of two sorts: (a) distribution of oxygen atoms over octahedral interstices which differ in the number j of V atoms in the nearest neighbour lattice sites (static parameter) and (b) the potential barriers for oxygen atoms diffusing from j-positions (dynamic parameter). The first was used to evaluate the binding energies of oxygen with vanadium atoms in j V 4 ) complexes, the second made understandable the structure of potential barriers for diffusion of the oxygen atoms from positions j. The differences between measurements of static and dynamic characteristics are discussed.
1. INTRODUCTION The interaction between substitutional and interstitial ( " s - i " ) solutes in b.c.c, metals influences the alloy properties to a marked degree, so far this problem is a subject of a continuous interest. Theoretical modelling and experimental measurements of diffusion, thermodynamic, mechanical and other parameters, that may be related to the macroscopic ones, are used to study this problem. Altstetter and coworkers have carried out a series of works on investigation o f " s - i " interaction in the alloys, based on VA group metals, by using the equilibrium and diffusion measurements. The review on some of these works is published in Ref. [1]. The " s - i " binding energies for V-O atoms in the N b - V - O alloys based on equilibrium data were calculated from the model of Albert et al. [2] and those based on diffusion results--from the trapping models of McLellan [3], Oriani [4] and Koiwa [5}. The binding energies thus obtained exhibited qualitative consistency but quantitative disagreement []], while in the N b - M o - O system (for M o - O atoms) they differed even in sign [2]. The similar results were obtained for the T a - V - O and T a - M o - O systems [6]. One of the reasons for the mentioned discrepancy may be, as believed by the authors, the use of the models which proceed from the definite arrangement of atoms and treat the information on an atomic scale, whereas the comparison is made with the results of the macroscopic measurements. And as concluded in [1], further experimental testing in concentrated substitutional solutions is required to make the quantitative analysis more accurate. The purpose of the present work is to investigate the interatomic " s - i "
interaction occurring in the N b - V - O system [with varying vanadium concentration (C~) in the up to 50at.%V alloys[ by using the internal friction method (i.e. Snoek relaxation peaks). The latter leads us, we believe, to the understanding of a local situation on the atomic scale, because it makes it possible to distinguish interstitial atoms, differing in the activation energies of elementary diffusion jumps. We know three works dealing with the investigation of internal friction in the N b - V - O system. Szkopiak and Smith showed that in the Nb-1 at.%V alloy the vanadium atoms acted as traps for both oxygen and nitrogen atoms [7]. The latter are located in octapores near V-atoms and the activation energy for their diffusion jumps to new locations increases, so corresponding Tmax of the peaks due to V-O and V - N in Nb shifts to higher temperatures. The peaks due to oxygen and nitrogen atoms in unalloyed niobium are absent in the alloy, this being in agreement with the fact that all oxygen and nitrogen atoms (within the experimental accuracy range) are redistributed in locations near V atoms. Later, Carlson with co-authors [8] confirmed this result for the alloys with 0.24 and 0.5 at.%V. In addition, they proved the existence of the saturation effect taking place in these low-concentration alloys: when the concentration of the oxygen atoms (Co) exceeds that of the vanadium ones, the peak P~ ( N b 4 ) ) appears in addition to the V-O peak 2. The same authors extended the concentration interval for the alloys under investigation up to l0 at.%V in [9]. A new peak (P3) due to V - O - V complexes forms in the alloys with C v ~>2.5% in addition to peak P2; thus, two peaks P2 and P3 form in the curves plotted for the alloys with 2.5 and 5at.%V, The N b - 1 0 a t . % V
4393
4394
KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS
alloy exhibited a single broad peak P3, with Tm~x somewhat higher than Tm~,of P3' It was attributed to reorientation of the oxygen atoms associated with two or more vanadium atoms. The authors related the peak Pr, broadening to different crystallographic configurations of the " s - i " complexes having the same number j of the V-atoms. 2. EXPERIMENTAL
The Nb--V alloys were produced from 99.99% pure niobium and vanadium in a laboratory arc furnace with a nonconsumable tungsten electrode in a purified argon atmosphere. The investigated alloys contained 0.5, 1.0, 1.9, 12, 20 and 50at.%V. The ingots 15 mm in diameter and 120-150 mm long were remelted by the electron-beam zone method to provide the coarse-grain crystalline structure stretching along ingot axis, this being favourable for further deformation. Such ingots were cold or hot (depending on deformability of the alloy based on homogeneity of its composition) rolled into sheets 6-8 mm in thickness, cut into bars 6 • 6 mm along the length. The latter were cold drawn to a wire 0.8-1 mm in diameter. The samples 0.8-I mm in diameter and 100-120 mm long were annealed for 1 h at a temperature between 1200 and 1500~ depending on the composition. The oxygen content of the samples was varied by their annealing in vacuum of 1-10 -~ Pa at 500-800~ The logarithmic decrement (6) measurements were performed using the low frequency (3-7 Hz) torsion pendulum technique in vacuum of 10 -3 Pa in the temperature interval from 20 to 800~ The heating rate was 0.5~ The measurements were carried out in an automatic mode in steps of 2-3~ The relaxation peaks are known to have the Debye shape which can be described by an expression 6 = 6maxsech H / R ( 1 / T - l/Tin,x).
(1)
The division of the complex curves into constitutive peaksj was effected using equation (1) by specifying a set of parameters for peaks j, such as their height, 6~,~; activation energy, H, and temperature, T ~ . The most reliable of these parameters were fixed, while the others were varied until the best fitting to the experimental curve was achieved. Deviation of the peak shapes from the ideal ones due to the broadening parameter, /~, was allowed for by using the method suggested in [10]. We also used a result described in [I I], where Tm~x and H were linearly related. 3. RESULTS
The Snoek relaxation peak due to oxygen atoms in unalloyed niobium (designated as P0) is found at about 173-176~ (at frequencyf = 3.5-4 Hz) [12, 13] and its activation energy is l l2kJ/mol (different works give this value as ranging from 107 to 117 kJ/mol). Only one peak at 280~ was found in
the Nb-0.5 V alloy. This is the same V-O intera~ction peak Pz observed at about 280~ ( f = 1 Hz), as reported previously by Szcopiak et al. [7], and at about 242~ (f-----0.56 Hz), as reported by Carlson et al. [8, 9]. Its nature was accounted for by oxygen atoms located in octapores near vanadium atoms. We call it peak P~. Our numbering of peaks (Pj) coincides with the number j of vanadium atoms located in the nearest lattice sites surrounding octapores with oxygen atoms in them, whose jumps are the sources of the corresponding peaks. The shape of peak PI is close to ideal, the broadening parameter, fl, is equal to 0.25-0.3 (the ideal Debye peak has fl = 0). When Co exceeds Cv, peak P0 forms, in accordance with [9]. The character of the curves plotted for the 1%V alloy is similar, the peak P1 saturation takes place at Co>_. 1 at.%. The 6 curves for Nb--1.9 V with different oxygen contents are shown in Fig. l(a). Curve I represents the sample annealed at 1700~ (1 h) and contains two peaks at about 280 and 417~ The former is peak P~ and the latter is assumed to be, with allowance for the frequency ( f = 4 Hz), a peak forming at about 393~ ( f = 0.59 Hz) in [3], explained as being due to oxygen with two V atoms in neighbouring surrounding (i.e. a t j = 2), according to our designation--peak /)2. Curve II was obtained after doping this sample with oxygen (at 500~ in vacuum 10-~Pa) and annealing for homogenization across the sample section (at 1300~ for 1 h). For computer analysis it is necessary to know the Hmaxjvalues. The linear correlation between //max and /'max for Snoek-like peaks was first shown by Wert and Marx [11] and then confirmed in a number of works [13, 14]. We have found Hmaxjby using this correlation ( f o r f = 3-4 Hz). Carlson used the Tm~j shift by the frequency method for determining Hm~xj.The numerical values of Hm~xj, obtained by both methods, are given in Table 1 and, as seen, they correlate well enough. The computer analysis of curves II and IH with the fixed values of Tm,x~, Hm,x1, Tm~x2and Hm~x2conducted by varying 5m,xj revealed the existence of the peak with Tin,, of about 365-370~ with Hmax = 165 kJ/mol. Supposedly, the latter, by an analogy with the preceding peaks, is due to stress induced reorientation of oxygen atoms associated with three vanadium atoms, i.e. peak P3The Nb-7V alloy exhibits no oxygen part relaxation after annealing. The sample was doped with oxygen at 700~ for 1 h in the 10 -~ Pa vacuum and after that curve I [Fig. 1(b)] was plotted. The oxygen is absorbed from the sample surface. The absorption is nonequilibrium and nonhomogeneous in the bulk. Peak Pl is the biggest one in this curve, but it also has other peaks with Tm~xbetween Tmaxl and Tm~x2. Curve II corresponds to the state after homogeneous annealing at 1200~ Four peaks are present in curve II: the above peaks P~, P2, P3, as well as the fourth peak, supposedly, P4 with Tm~x= 320-325~ and H = 152 kJ/mol.
et al.:
KUSHNAREVA
INTERNAL
FRICTION
The situation for alloys with 12 and 20at.%V [Fig. 2(a)] is to a great degree similar to that shown above for N b - 7 at.%V. All four peaks P1, P2, P3 and P4 are present in the curves plotted for these alloys,
IN Nb-V-O
ALLOYS
4395
peak P2 being the highest one. Relative contributions of P1, ]92,P3 and P4 relaxations depends on annealing temperature and Cv, but does not depend on Co, The oxygen atom distribution over position j tends to
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KUSHNAREVA
et al.:
INTERNAL
Table 1. Parameters of peaks j in N b - V - O alloys ( f = 4 Hz) Peaks j 0 1 2 3 4
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be a statistical one with Cv increasing and reaches it in Nb-50 at.%V alloy. The curves plotted for this alloy with two values of Co are shown in Fig. 2(b). Peak P3 is the highest one in this alloy, so is the relative concentration of interstices with j = 3. The concentration of oxygen in position j may be determined as Cj = gj~maxj. The heights of peaks P0, P1 and /'2 for the alloys under investigation as a function of oxygen concentration are plotted in Fig. 3. Also included are appropriate data from works [2] and [3]. The "saturated" peak heights were not included. According to Fig. 3, K0 = 5.3_ 0.5, K t = 10 ___1 and K 2 = 23 _ 1.5 for the corresponding Cj in at.%. We treated the results of Fig. 3 in [9] to determine K2 (curves with 0.21, 0.38 and 0.60 at.% oxygen). The curves with 0.77 and 0.91 at.% O were not taken into consideration: they showed K2 twice as low comparing to K2 for the curves with up to 0.60 at.% O. We are of the opinion and have experimental evidence, that the considerable part of relaxation in the temperature range of peak P2 in the curves with 0.77 and 0.91 at.% O in Fig. 3 [9] has the nitrogen origin. The accuracy of the determination of K3 and K4 is low, this being accounted for by a very small height of peak P3 first formed in the Nb-l.9 V alloy, but in alloys with 7 and more at.%V peaks P3 and/'4 form simultaneously. The obtained numerical values of K3 = 17 and K4= 12 may be used with allowance for the above notes. Kj being known, it is possible to find the oxygen atom distribution in octapores with different j positions. The parameters (Tmaxi, nmax)) of peaks j in the Nb--V-O alloys at f = 3.4-4 Hz are presented in Tables 1 and 2 (Cj). 4. D I S C U S S I O N
Some questions of prime importance are to be considered prior to interpreting the results obtained. First of all, this is reliability of our treatment of the damping spectra obtained and, in particular, the conformity of peaks j to the jumps of oxygen atoms out from octahedral interstices surrounded by numberj of V-atoms. For the first time the subsidiary peaks in dilute alloys (which we call peaks Pl) with Tmaxmore than Tmaxof Snoek relaxation in unalloyed metals were received in Fe-based (Fe-Mn-C(N), Fe-V-N) alloys more than 40 years ago [15]. Their nature was associated with " s - i " interaction. One of the first reviews on this problem was published by Hasson and Arsenault [16], since then a number of works have been carried out on Fe alloys with Cr, Mo, W and other substitutional solutes and VA
FRICTION
IN Nb-V-O
ALLOYS
group metal-based alloys. In the cases of strong " s - i " interactions (such s-atoms are called traps), TmaXof peaks P~ are considerably shifted to a higher temperature, while peaks P0 and Pl are separated on the temperature scale. We know two systems (Nb-V~O [8, 9, this paper], Nb--Zr-N [17-19]), where in the next peak P2 was revealed without overlapping peaks P0 and Pl. This allows their parameters to be determined more precisely. So, as shown in [19] for the N b - Z r - N system, the height of peak P~ is in right proportion to substitutional metal concentration (Cs), as is the height of peak P2 to C~, this being a convincing proof of the Z r - N composition of the corresponding complexes for peak P~ and Z r - N - Z r for peak P2. Peaks P0, P~ and P2 in the corresponding alloys may exist in the curves simultaneously, as in the N b - Z r - N alloys [17-19], or, at some concentration intervals, form consistently, as in the present N b - V - O alloys. This depends on the relative values of the complex binding energies. So, till now we have been using a general approach, which accepts the distribution of oxygen atoms in the octapores with a different number j of the substitutional atoms. This approach has firm logical grounds and leads to reasonably consistent experimental results for the dilute alloys. Such factors as different crystallographic configuration of the complexes, as well as long range interaction, can influence the relaxation time z (H exactly). For example, complexes with j = 1 may have two configurations and those with j = 2 may have four configurations, differing in z (H). The existence of isolated peaks Pl and /'2 convinces us that these factors lead to peak spreading. The latter shows itself in the experiment: for peak P1, fl = 0.3-0.5; for/'2, = 0.5-0.6, this being not that high. It means that the higher-energy favourable crystallographic configurations for the complexes are realized, or that the difference in zj for the complexes with the same j but different configurations is rather small, compared to the difference between zj and zj_+l. In any case, the experimental evidence supports the approach on the existence of some effective z (with allowance for the spread) for /-atoms in position j. As mentioned above, we took into account the spread of individual peaks by using fl equal to 0.3-1 (the higher the j, the higher the fl). The picture becomes more complicated in the concentrated alloys. First, these alloys feature a higher probability of differences in the initial, prior to a jump, and final, after a jump, positions of interstitial atoms. We suppose that the potential barrier which an atom must overcome during each deformation half-cycle is determined by the initial configuration of j; so, the same atom can contribute to various peaks j depending on the position it occupies prior to the jump. Now, upon considering the above comments, let us come back to the results obtained. As noted above, for the alloys with Cv ~< 1 at.% the saturation of peak Pl occurs at Co > Cv. Each V
KUSHNAREVA
et al.:
INTERNAL FRICTION IN Nb-V-O ALLOYS
atom has six surrounding octapores in the first shell, twelve in the second shell and so on. Nevertheless, only one oxygen atom saturates the bonds of a vanadium atom, the latter losing its trapping quality. This is in consistency with the assumption of a chemical factor playing the predominant role in the V - O complex formation. If so, it should be noted that the electron interaction in the dilute N b - V - O alloys is of a local, rather than global, character. According
4397
to the current models, two principal factors contribute to "s i " interaction, i.e. chemical (or electron) and elastic (deformation) ones. The criterion used to determine a degree of the chemical interaction is the difference in the heat of formation of oxides, whereas the elastic interaction is controlled primarily by the size factor. One of the papers takes into account the values of modulus and first ionization potential [7]. Our opinion of the chemical origin of the V - O
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KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS
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0.5
1.0
c (at. %0) Fig. 3. 6 m a x VS at.% O for peaks P0 (t), Pi (2) and Pz (3) in the Nb-V alloys: O, A--present; Iq, A--after [9]. complex forming in the dilute N b - V - O alloys does not coincide with that mentioned in [7, 20], which consider the size factor to be the main cause. The "s-i" binding energy (AEj) may be evaluated by comparing the interstitial atom distribution in the t y p e j interstices (Cj) with the relative concentrations (hi) of the latter. In terms of the atomic configuration model and the short range interactions [21]
Cj = ,_hjexp(-E]/kT)
(2)
Z h. e x p ( - E . / k r ) where Ej and E. are the atom potential energies in the j t h and nth positions. It can be seen that Cj = ~ e x p ( - A E / k T ) Co
(3)
where AEj = E j - E0 is the "s-i" binding energy. In [20, 21] hj was found to be h) = vA= 6! C{(l - Cs)6-j. v j(6 - - j ) !
(4)
Here, v is the total number of octahedral interstices, vj is the number of type j interstices, Cs is the concentration of substitutional solute, Cv in our case. In Refs [21, 22] the interaction between the substitutional atoms which may change the dependence (4) was neglected. The constitution phase diagram of N b - V (the full-mutual solubility, cigar-like shape, with no intermediate phases formed) does not give
grounds for it to be ignored. We are not aware of the data on the V atoms interaction in Nb, but if it existed, it would lead to the formation of regions with local heterogeneity and the presence of interstitial atoms in these regions might help to reveal them. It is this approach that was used as a basis to study local heterogeneities in the F e - C r alloys [23]. The results of calculating the binding energies for different compositions of the j complexes are presented in Table 2. Since peak P0 is absent in Nb-0.5 V alloy, first we assumed it to be equal to the background damping at the corresponding peak temperature and, second, -6m~x0 was assumed to be by an order of magnitude lower than the background level. The first assumption resulted in - 4 2 . 2 kJ/mol for the AE1 value, the second - 5 2 . 8 kJ/mol. The same AEI values were obtained for the Nb-1 V alloy. Comparison of these results with the AEI values obtained from equilibrium and diffusion experiments and summarized in Ref. [8] shows the best agreement to be with the - 4 6 . 7 k J/tool value for Nb-2.7 V alloy obtained from thermodynamic activity measurements (equilibrium experiments). The experimental internal friction curves plotted for the Nb-5 V alloy in [9] (Fig. 3, curve 4 in [9]) were also included for evaluation of AE(2_ 1) (AE2 _ 1= E2 - El ) (Table 2, line 7). The results are consistent and equal to - 15.5 kJ/mol, this providing the - 6 1 k J / m o l value for AE2 (AE2=E2-Eo) at A E I = - 4 6 k J / m o l . Only the curves plotted for the samples treated to provide the stabilized state were used for machine analysis. As can be seen, for up to 20 at.%V AE(2_ 1)remains at the level - 1 5 . 5 + 1.5 kJ/mol. The energy state of oxygen atoms in positions with j = 4 only slightly exceeds those with j = 2 (AE,_ ~= - 17 ___2 kJ/mol) and these two states are more energy-favourable than that with j = 3. This may be connected with the influence of crystallographic geometry of the responsible complexes. Besides, as can be seen, the increase in the number of V atoms in complexes does not lead to the multiple increase in binding energy value, i.e. AEj v~jAEl . The values for N b - 7 V are somewhat higher than others, but the general situation is the same. The AEu_ 1) values calculated for the Nb-50 V alloy based on the results from Fig. 2(b) are close to 0 + 2 kJ/mol. This means that oxygen atom distribution over positions j in this alloy is close to the fraction of this type j interstices, that is, close to the statistical distribution. Thus, we have no answer to the question on the character of transition from preferential to statistical distribution of oxygen atoms, whether it has abrupt or gradual dependence on Cv in the alloy. The data presented above allows us to propose a scheme of the energy variation for oxygen atoms situated in the first type traps ( j = 1) shown in Fig. 4. In a general case the potential barrier, H, an oxygen atom should overcome during its jump from a trap is: H = H, orr. - AEj - A E '
(5)
KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V~O ALLOYS
4
I I
I~ ~ ,777+
I I
I x x x x ~
I I
I~
I 1
I ~ ~ 7777''
where: H.o~m is ndi f for an oxygen atom in unalloyed Nb, coincides with Hmax0and equals 112 kJ/mol; AEj is the binding energy (for j = 1, it is AE1) and A E ' is the change in the saddle point energy. There are two types of the jumps: reorientation of oxygen atoms from one trap to a neighbouring one around V atoms and a jump out of traps (escaping from traps). The first one coincides with an elementary action in the internal friction experiment; that is, it explains why H is Hmax and in this case we call A E ' AE~. An escape from the t r a p is a necessary condition for a long-range diffusion to take place, in this case H coincides with ndi f and here we call A E ' AE~s. Now, evaluate some quantitative parameters. So, for the Nb--0.5 V alloy Hnorm is 112 kJ/mol, AE l = - 4 6 kJ/mol (Table 2), Hmaxl= 142 kJ/mol (Table 1) and the value of + 16 kJ/mol is obtained for AE~. In accordance with Ref. [24], ndi f of oxygen atoms in the Nb-0.5 V alloy is equal to 176 + 9 kJ/mol, in this case the value of AE~ equals - 18 kJ/mol (see Fig. 4). The value of Hdif for oxygen atoms does not coincide with H~x~ for Nb-0.5 V; the difference between them, AE~ - E~s, in this case amounts to 34 kJ/mol. This result is a convincing support of the models of Koiwa [5] and Kirhhleim [25], describing the influence of traps or antitraps on the saddle point energy. According to Kirhheim's model, the energy of the jump from a free site to a trap is lower by AQ, while the energy of the jump back from a trap to a free site--higher by AQ. The scheme similar to that shown in Fig. 4 is presented in [24] as an illustration to the Kirhheim's assumption, but in the present paper it was obtained experimentally. The authors of [24] believe the potential barrier (H) for the jump from a trap to a free site (supposedly, it is Hdif) is identical to Hm~x in the internal friction experiment (Hmax~ in the Nb-0.5 V alloy). As shown above, these two values do not coincide. That is why the value of AE 1 as calculated in [24] ( - 6 6 kJ/mol) is problematic.
+
?777
-
iii
o
I I
...e
~J ~2
>,
I x • x~mm
III
I i i
e,
I ~
~
~ ~ IIltlll
+1
?7 I I I •
o
o
4399
~
e.q
[.....,
1111
x
~~176
~2
I I t f I I I I
•215215215
,r AE't
E
o
~_~_-
o~ E
i. n
n
t
t
n
n
Fig. 4. Free activation energies for jumps of i atoms in the system with traps (AEj< 0): n--normal octahedral sites; t--trap sites; A E j = E t - E n ; Hnorm--potential barrier between normal interstices; AE'--is the change in saddle point energy.
4400
KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS
For the second-type traps (2V-O) H ~ 2 is 179 kJ/mol; AE2 = - 61 kJ/mol and calculated AE~ = - 4 kJ/mol; that is, the saddle point energy increases by 4 kJ/mol. We have no way to find E-'s for the energy of the jump of oxygen atoms from traps a t j = 2 because.of the absence of literature data o n a d i f of oxygen atoms in the N b - V alloys, where peak P2 is a predominant one. But it is clear that the energy situation in this case is different, compared to that mentioned above for the V-O traps. When calculating AE 1 and AEu_ ~) we used the C 1/Co or CflC~ concentration ratios at Tmaxof the corresponding peaks, for example Cj at Tr,axj to C~ at Tmaxj, but not Tma,j, as it should be. In this case we did not take into account the temperature dependence of C~ that should lead to a lower value of Cj at Tma,j. So, the AE(2_ ~)value for Nb-12 V was calculated as being equal to - 1 7 k J / m o l (Table 2, line 10), against -19.1 kJ/mol obtained with the allowance for the C~ temperature dependence (12% difference). The errors in determining other AEu ~) values at j = 3 must be lower, because the difference between Tm,~jand Tm~,~ decreases. So, the error in AEc4_ ~)for the same sample of N b - 1 2 V is only 3.8% ( - 1 6 . 6 k J / m o l against - 1 6 . 0 8 kJ/mol in Table 2). Consider now the reasons for the discrepancies in the AEi values obtained for the Nb- and Ta-based alloys by diffusion and thermodynamic measurements, mentioned in [1, 6]. According to [6], although both measurements indicate the V ~ ) attraction, they are not in a good quantitative agreement: the value of the binding energy derived from the equilibrium measurements is smaller than that obtained from the diffusion measurements. In the case of alloys with Mo as substitutional solutes the two values are not even in a qualitative agreement. The data obtained make it possible to understand the difference between the equilibrium (thermodynamic) and dynamic (diffusion) parameter measurements in the Nb-based alloys. The interaction energies may be obtained only in the equilibrium experiments by investigating the distribution of interstitial atoms over the positions-j octapores by the internal friction method, or by the thermodynamic measurements. The diffusion activation energy characterizes a barrier the i atom should overcome during a jump, which is a dynamic action involving, in addition to the interaction energy, the change in the saddle point energy, A E ' (Fig. 4). As shown above, A E ' varies with a kind of trap and a kind of jump, the latter being located around the traps or apart from them. In a series of the works on the diffusion and thermodynamic measurements conducted on the VA group metalbased alloys, Altstetter and co-workers employed theoretical models, which assumed A E ' to be equal to zero. This is the reason for inconsistency observed between the thermodynamic measurements and the kinetic behavior. The latter must allow for the A E ' parameters. So, in the Nb-Mo--O system the increase in Hd~f (proved by the internal friction [26] and
macrodiffusion experiments), accompanied by obtaining the positive value of the binding energy, AE (confirmed by the internal friction and thermodynamic experiments), makes it possible to conclude that the cause of an increase in ndi f in this case is an increase in the saddle point energy, A E ' . One more circumstance should be taken into account. All macroscopic methods may be useful only for the alloys with one of the trap types, i.e. the low-concentration alloys. In the case of the alloys with more than one type of the traps (Nb with 2 and more at.%V), all macroscopic methods give the average quantitative values of the effective parameters. So, the internal friction method has some advantages: the same experiment provides two types of information, i.e. on equilibrium (the distribution of i atoms over positions j ) and dynamic (Hm~xj) characteristics, as well as on the number and the types of the traps depending on an alloy concentration. We understand quite well that one may object against a too simple picture we presented, whereas the reality can be much more complicated. In this connection, one should note our remarks given at the beginning of this section. Besides, we did not consider the interaction taking place in a number of the coordinate shells. The analytical correlation given in equation (3) was excluded in terms of the atomic configuration model and the short-range (only the nearest neighbour) interactions. The short-range interaction (in the first two shells) is a typical feature of the chemical (electron) nature interaction, while that of the deformation origin has a long-range effect. According to [6] the AE value decreases as more shells of neighbours are included. But each of these alternative assumptions yielded the equally good fit to the experimental data. Therefore, it was impossible to choose between them. In the major part of our work we used a version according to which the individual peaks j do not interact with each other. But one should take into account that there are theories involving an approach based on the constituent interaction of the peaks [27, 28]. As far as the current situation is concerned, we failed to apply any of them. 5. CONCLUSIONS (1) Two types of the data were obtained by using the Snoek relaxation investigation on the N b - V - O alloys: distribution of the oxygen atoms over octahedral interstices differing in the number j of the nearest neighbouring V atoms and the potential barrier for the diffusion jumps of the oxygen atoms from positions j. The former was used for evaluation of the binding energies (AEj), the latter for evaluation of the structure of the potential barriers during i atoms jumping. (2) There is a strong interaction of a chemical nature between V-O atoms in the N b - V - O alloys with up to 5at.%V, which is determined by the
KUSHNAREVA et al.: INTERNAL FRICTION IN Nb-V-O ALLOYS binding energy ( A E v _ o = - 4 6 k J / m o l , AE2v_o= - 6 1 kJ/mol). The potential barrier for reorientation of the oxygen atoms around the V traps (Hmax) is lowered, while that for escaping from the traps (ndif) is raised due to a decrease and an increase in the saddle point energy, respectively. Thus, Hm,x does not coincide with Hair. (3) The attraction inside the j V - O complexes at j >/4 is weakened, the local effect is lost and the oxygen atom distribution with an increase in the vanadium concentration approaches the statistical one. (4) The cause of most models being inadequate lies in ignoring the changes in the saddle point energy in the constituent of the potential barrier for the dynamic diffusion processes, taking into account only one of the trap types and assuming Hdif and //max to be equivalent for all the systems.
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