Relaxation Mechanisms in Fe-Al-C Alloys I.S. GOLOVIN, T.V. POZDOVA, N.Y. ROKHMANOV, and D. MUKHERJI The relaxation spectrum of Fe-Al alloys has been studied as a function of Al content and ordering reaction in Fe-Al. Three types of relaxation peaks are observed, with activation energies between 0.8 and 3 eV. Snoek-type relaxation is studied in Fe-(0 to 50 at. pct)Al and compared with the Snoek relaxation in pure iron (C in a -Fe), chromium (C in Cr), and niobium (O in Nb). The snoek-type relaxation peak in iron (at 314 K for 1 Hz) shifts to higher temperatures with increasing Al content in iron. Significant changes in the peak parameters occur when a -Fe is alloyed with Al, because of the ordering reaction in Fe-Al. Peculiarities of the carbon-atom distribution in ordered and disordered Fe-Al alloys are discussed using an atom-interaction model, in which the elastic interaction is supplemented by the chemical C-Al interaction. Two other peaks are observed only when a certain Al content is exceeded: a Zener peak for Fe-(. 10 pct)Al and an X peak for Fe-(. 26 pct)Al. Parameters of these peaks are discussed with respect to alloy structure. Three hypotheses are discussed for the X-peak mechanism with an activation energy about 1.7 eV. A map of relaxation peaks in the Fe-Al system is constructed.
I.
INTRODUCTION
IRON-RICH alloys of the Fe-Al system are widely used because of their favorable combination of mechanical, magnetic, and dissipative properties. Besides their application as a functional material, Fe-Al alloys are attractive for structural applications because they show higher strength than iron, high corrosion resistance, and are relatively inexpensive. Binary Fe-Al alloys containing sufficient Al content may produce long-range ordering of two types: D03 (Fe3Al) and B2 (FeAl). The Fe3Al phase is stable at lower temperatures, while the FeAl phase is stable at higher temperatures for Al , 35 pct. At high temperatures, Fe-Al is a disordered bcc solid solution (designated A2). In contrast to the many studies of long-range ordering in binary Fe-Al alloys (e.g., References 1 through 4), a limited number of articles have examined carbon-atom short-range ordering accompanying D03 or B2 ordering[5,6,7] and the corresponding dissipative properties. The use of an internal-friction method allows a study of the parameters of carbon-atom diffusion and shortrange order caused by the Fe-Al order-disorder transition.[8 – 11] The loss maximum (Q2 1) for the relaxation peak and, in particular, for stress-induced jumps of interstitial atoms in bcc metals (known as Snoek relaxation[12] ), is described by the Debye equation:[13] Q2
1
5
D?
11
vt (vt )2
where D is the relaxation strength, v 5
[1]
measuring frequency. In practice, it is usual to measure Q2 1 vs T (T being the temperature). The jump of carbon (C) atoms under stress in Fe-based alloys is the elementary step of carbon diffusion, and its temperature dependence is described by the well-known Arrhenius equation: t 5 t0 1 exp (H/kBT ), where H is the activation energy and, kB is the Boltzman’s constant. Some differences in the carbon Snoekpeak parameters in a -Fe are reported in the literature: the peak temperature is 314 K[14] or 308 K[13,15] for 1 Hz, and the corresponding activation energy for C in a -Fe is about 0.87 6 0.01 or 0.835/0.83 eV, respectively. A value of H 5 0.84 6 0.04 eV was determined by magnetic after-effect spectroscopy.[16] A Zener peak caused by stress-induced reorientation of solute metallic atom pairs in solid solution is observed in Fe-Al alloys, with an activation energy of about 2.5 eV (H depends on the percentage of Al). Another relaxation peak between the Snoek and the Zener effects has been recently reported in the literature, but its origin is not well explained. All relaxation peaks in Fe-Al are broader than the single Debye peak.[5 – 11] In Fe-Al, as in other alloys, there is a set of nonequivalent energy positions for the interstitial (e.g., carbon) atoms because of their interaction with substitute atoms. In such a case, the lognormal spectrum of the relaxation-time (t ) distribution for continuous spectra is almost always used.[13,17– 19] In that case, the Snoek peak measured at different temperatures for a fixed frequency is described as[18,19]
2pf, and f is the Q2
I.S. GOLOVIN, Professor, is with the Materials Science Department, Russian State Technology University MATI, Moscow, 121552 Russia, now with the Institute for Materials, Technical University of Braunschweig. Contact e-mail:
[email protected] D. MUKHERJI, Scientist, is with the Institute for Materials, Technical University of Braunschweig, 38106 Germany. T.V. POZDOVA, Scientist, is with the Physics of Metals Department, Tula State University, Tula, 300600 Russia. N.Y. ROKHMANOV, Senior Researcher, is with the School of Physics, Kharkiv National University, Kharkiv, 61077 Ukraine. Manuscript submitted November 1, 2001. Dedicated to the memory of our colleague and friend Alexandr B. Lebedev. METALLURGICAL AND MATERIALS TRANSACTIONS A
1
(T ) 5
Q2m 1 cosh2
1
1
1
H 1 2 k B r2 ( b ) T
1 Tm
22
[2]
where Q2m 1 is the peak height, Tm is the peak temperature, B is the width of the relaxation-time distribution, r2(b ) 5 DT 2 1(b )/DT 2 1(b 5 0) is the corresponding relative peak breadth, and DT 2 1(b 5 0) is the width of a single Debye peak in terms of temperature. Broadening of the Snoek peak with respect to a Debye peak with a single relaxation time (for a single relaxation time of b 5 0 and r2(b ) 5 1) is calculated on the assumption that symmetrical broadening is caused by a lognormal distribution of relaxation times[13] VOLUME 34A, FEBRUARY 2003—255
Table I. Al and C Content in Different Fe-Al Alloys At. pct Al At. pct C
11.7 0.03
16.3 0.03
19.6 0.04
21.7 0.03
22.5 0.04
28.4* (1 2.7 pct Cr) 0.16
31.5 0.075
35.0 0.03
40.0 0.4
*Al28.44, Cr2.65, Mn0.40, and Ce0.02 (at. pct).
due to a distribution of C atoms in different positions in solid solution. For an analytical description of the broadened relaxation peak, one should know the activation energy, peak height, and width parameter. The methods used for evaluation of C-atom energies and distribution on the basis of Snoek relaxation have been discussed.[13– 16] The purpose of this article is to bring the results on internal friction together with structural study and computer simulation for specimens with different compositions in binary FeAl alloys that undergo different order-disorder reactions on heating. The aim is to explain quantitatively the parameters of the relaxation peak observed by corresponding shortrange atom distributions. Special attention is paid to the question of peak stability during measurement. In addition, the experimental results of this article are compared with available data from the literature. II. MATERIALS, EXPERIMENTAL TECHNIQUE, AND CALCULATION METHOD Most of the Fe-Al specimens used this article (Table I, all concentrations are given in atomic percent) were vacuum melted in an induction furnace using refined iron and A99grade aluminium, annealed, and spark machined. Then, the specimens were water quenched* after tempering for 60 *Temperatures of heat treatment in this article are in degrees Celcius (8 C).
minutes in a protective atmosphere at different temperatures between 720 8 C and 1100 8 C, followed by aging at different temperatures (200 8 C to 560 8 C, depending on Al content). The specimens used might be roughly divided into three groups, namely, 12 and 16 pct Al with an A2 structure and short-range ordering at low temperatures (so-called K1 state); 20 to 22 pct Al with an A2-D03 ordered structure; and 28 to 35 pct Al with A2-B2H-B2L-D0 3 transitions, depending on temperature. “Pure” chromium and niobium specimens were also used for comparison with Fe-Al alloys. Internal-friction measurements were carried out by means of low-frequency free-decay vibration in (1) an inverted torsion pendulum ( f 5 1 to 4 Hz, magnetic field of 2 ? 104 A/m, pressure of ’3 Pa, and heating rate of 2 K/min) using thin bars measuring 80 3 1 3 1 mm3 under a surface deformation of g0 ’ 3 3 102 5, and in (2) a torsion pendulum ( f 5 30 to 90 Hz, magnetic field of 2.4 ? 104 A/m, pressure of ’0.01 Pa, and heating rate of 2 to 4 K/min) using doubleblade-shaped specimens with a working diameter of 2.5 mm and working length of 18 to 25 mm, under a surface deformation of g0 ’ 3 3 102 5. Activation energies of relaxation peaks were determined by the temperature-frequency (T-f ) shift: H5
(RTm1Tm2 ln ( fm2 /fm1))/(Tm2 2
Tm1)
[3a]
and by the Marx–Wert equation: H5
RTm ln (kBTm /hfm) 1
256—VOLUME 34A, FEBRUARY 2003
Tm DS
[3b]
where R and h are the universal gas and Planck constants, respectively. Equation [3a] is used to deduce the activation energy only in the case where the peak-temperature shift caused by change in frequency does not change the specimen microstructure. This is not always true for the Fe-Al system. The Snoek relaxation is treated in terms of an atominteraction model, in which a long-range strain-induced interatomic interaction according to the Khachaturyan method[20] is supplemented by a short-range “chemical” CAl interaction and a screened Coulomb C-C repulsion.[21– 24] This approach is helpful for internal-friction studies when the “first-principle” calculations of energy distribution are absent. This has been applied for an internal-friction application in different bcc[9,25– 27] and fcc[22,28,29] alloys by Blanter and Golovin. Coupling effects from C-C atom interaction, considered in References 30 and 31, are neglected because of the low carbon content in the present alloys. The C-Al interaction influences the distribution of C atoms and creates a short-range order around the Al atoms. This changes the energy of C atoms in the octahedral interstices. A shortrange chemical interaction, i.e., the interatomic chemical forces, must be assumed, because it is not known for real materials. For this reason, the Lennard–Jones potential (the pairwise-additive interaction potential U(rpm ),r 2pm6 where rpm is the distance between C and Al atoms) is employed as the best simple potential for qualitative insight into the phenomena,[32] and the value of the C-Al chemical interaction in the first shell (Hch (1)) is the single fitting parameter of this model. Energies of strain-induced (elastic) pair interactions were computed for five coordination shells in Reference 24. The atom energies and distribution in the lattice are calculated by the Monte Carlo method. The change in the energies of dissolved atoms in a solid solution caused by atom interactions influences the diffusion and relaxation parameters. Interstitial atoms (in our case, C atoms) create a distortion field of tetragonal symmetry in octahedral interstices in the bcc lattice, which are characterized by the values l1 and l2, used for internal-friction simulations.[13] Transmission electron microscopy (TEM) samples were prepared from 3 mm discs punched out from thin slices (150 mm) cut from the specimen. The discs were electrochemically thinned by twin-jet polishing using an electrolyte containing 640 ml methanol, 300 ml glycerine, and 600 ml perchloric acid. Thinning was carried out at -20 8 C at a voltage of 27 V. Specimens were examined in a PHILIPS* *PHILIPS is a trademark of Philips Electronic Instruments Corp., Mahwah, NJ.
CM12 microscope operating at 120 kV. Dark-field imaging with {111} reflections in the ^110& beam direction was used to image the ordered domains of Fe3Al. The thermal analyses were done using a Perkin-Elmer DSC7 differential scanning calorimeter with a heating-cooling rate of 5 K/min in the temperature range up to 700 8 C. METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 1—Internal friction in (a) Fe-(, 25 pct) Al and (b) Fe-(. 25 pct) Al alloys vs temperature (1 to 2 Hz, after subtraction of background at 300 K: Q 2 1 values for Fe-40 pct Al are 3 times lowered for reason of better visualization); (c) the carbon Snoek peak temperature in a -Fe, Fe-21.7 pct Al (in A2 and B2) and Fe-40 pct Al (in B2, also X peak) vs frequency; (d ) heat flow in Fe-(16 to 40 pct) Al alloys vs temperature (all specimens 0.3 g). Dotted line is the interpolated baseline, i.e., it connects the heat flow curve before and behind the peaks in a way as if no peaks appeared. All exothermic reactions point in the negative Y direction.
III.
RESULTS AND DISCUSSION
2 1
The Q vs T and corresponding heat-flow vs T curves for a -Fe and a few Fe-Al alloys with Al contents from 11.7 to 40 at. pct are presented in Figure 1. Three types of relaxation peaks, marked as S, X, and Z, are observed and discussed in connection with point-defect reorientation under applied stress. A. Map of Relaxation Peaks The activation energies for the S, X, and Z peaks and the peak temperatures (in this case, the resonance frequency is 1 to 2 Hz) are generalized in Figure 2 on the basis of results available from the literature and our own results. Activation energies are plotted either according to the authors of cited articles or, in the case where only experimental curves for one frequency were published, we made an estimation of the activation energy using Tmax and f by Eq. [3b]. The activation energy for the carbon Snoek peak in a -Fe, determined on the basis of our experimental data, is 0.83 6 0.02 eV when estimated from four frequencies in the T-f plot (Figure 1(c)) and varies from 0.84 to 0.86 eV when the Marx–Wert equation ([3b]) with DS 5 1.1 3 102 4 eV K2 1 is used. The estimation of the activation energy in Fe-Al METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 2—“Maps” of (a) temperature (at 1 to 2 Hz) and (b) activation energy of internal friction peaks vs Al content. Snoek peak is marked by circles; X peak, by triangles; and Zener peak, by squares. The horizontal dash line in (a) separates, by temperature, two states: above—dash line alloys are close to equilibrium state; and below—corresponds to quench-in state.
alloys is complicated if the use of the T-f shift method shifts the measuring peak from one range of the Fe-Al equilibrium diagram to another (e.g., refer to Figure 1(c) for Fe-21.7 pct VOLUME 34A, FEBRUARY 2003—257
Al). This aspect of structural influence on activation energy is shown in Figure 4. That is why we used two methods and different frequencies. To avoid the problem of structure instability during measurements at elevated temperatures, we have additionallycarried out a few Q2 1 vs f measurements of an S-type peak in Fe-Al.[33] The isothermal measurements are more reliable than temperature scanning, because, in the latter, the microstructure may change during temperature increase. There is some minor discrepancy between activation energies derived from the Q2 1 vs T and Q2 1 vs f measurements: by the first method, the H value for the carbon Snoek relaxation in quenched-in and aged Fe-21.7 pct Al specimens, is about 1.17 and 1.05 eV, respectively, while by the second method, H is about 1.3 and 1.2 eV (in both cases, the T-f shift (Eq. [3a]) is used). This difference is a result of the S-peak instability at high temperatures (444 K at 2 Hz and 501 K at about 87 Hz), contrary to the stable peak’s behavior during Q2 1 vs f tests at T , 270 K. The maps which display the peak temperature (’1 Hz) vs Al pct and the activation energy vs Al pct (Figure 2) show that all relaxation peaks observed in the Fe-Al system (with activation energies between 0.8 and 2.8 eV) might be distinguished into three groups and relates to different phenomena discussed in this article. The Snoek peak in a -Fe is inherited by Fe-Al alloys as the Snoek-type phenomena; its temperature and activation energy smoothly increase with Al content. The X peak appears in Fe-Al when Al . 25 at. pct and might be sometimes splitted into low-temperature (XL) and hightemperature (XH) components. The Zener peak is pronounced when Al . 10 at. pct. Peaks 1 through 4, presented in Reference 33, seem to fit this general scheme as well. The peak temperatures (for 1 to 2 Hz) are plotted (Figure 2(a)) together with the lines of the Fe-Al phase diagram. The Snoek-type peak is mainly located below the temperature of ordering and corresponds to the quenched-in state of alloys (this temperature is indicated in Figure 2(a) by a horizontal dashed line, according to the data presented in Figure 1(d)). The temperatures of the X and Zener peaks are observed in the range where ordering is completed (above the dashed line) and, in the first approximation, can be compared with the equilibrium-phase diagram. B. The Carbon Snoek-Type Peak This peak (marked as “S”) in Fe-Al is observed between 310 and 470 K at 1 Hz. This peak retains the main features of a carbon Snoek peak in a -Fe and can be called a Snoektype peak. The nitrogen content in the alloys used is at least one order lower than the carbon content; also, the nitrogen atoms in Fe-Al cannot contribute to Snoek-type relaxation, as they are trapped by Al atoms. The peak temperature increases with an increase in the Al content and the frequency of measurements. The carbon Snoek-type peak in Fe-Al is smoothly shifted to higher temperatures with respect to a Fe, due to an increase in the activation energy of the C atom’s diffusion under stress when iron is alloyed by Al. At the same time, an increase in the lattice parameter with increasing in Al content is observed (Figure 3(a)). Generally, such a tendency is not typical: an increase in the lattice parameter should make jumps of carbon atoms easier, i.e., it should decrease its activation energy. The correlation between the lattice parameter and activation energy for carbon diffusion observed shows that alloying 258—VOLUME 34A, FEBRUARY 2003
(a)
(b) Fig. 3—Influence of Al content in Fe on (a) lattice parameter (Pearson, 1967) and activation energies of the carbon Snoek peak, (b) on the b width of relaxation time distribution (Snoek peak).
iron with Al leads to local lattice distortions and, possibly, contribution of vacancies. The influence of ordering is stronger than the increase in the lattice parameter. The effect of Al on carbon-atom distribution is also seen from the increase in the peak width (Eq. [2] and Figure 3(b)). The increase in b values for Snoek relaxation (the width of the peak with respect to a single Debye peak with b 5 0 (Eq. [2]) in the quenched-in specimen takes place with the increase in Al content in iron within the A2 range of the phase diagram. This is a result of nonequivalentpositionsfor C-atom appearance in octahedral interstices. With an increase in atomic order, the value of the b parameter decreases. The ordering can be achieved either by aging (for 12 to 16 pct Al, shortrange ordering; for 19 to 32 pct Al, a D03 order, and for 35 pct Al and higher, a B2 order) or by an increase in Al content (. 27 pct Al) in the alloy, which finally leads to quenching from the B2 range of the Fe-Al phase diagram. Contrary to the 0 to 20 pct Al and . 30 pct Al ranges, a large “scattering” of activation energies is observed in the range of 20 to 30 pct Al (Figure 3(a)). In fact, it is not only real scattering, but also an effect either of the specimen aging or of a change in the frequency of measurements. With an increase in the frequency of measurements, the relaxation-peak location METALLURGICAL AND MATERIALS TRANSACTIONS A
(a) Fig. 4—The Snoek peak for Fe-21.7 pct Al quenched-in (from 720 8 C) and quenched-in 1 aged (290 8 C, 30 min) states measured at two frequencies (2 and 87 Hz) and heat flow; dash line—Snoek peak in “pure” Cr.
shifts to a higher temperature, i.e., into the range of intensive ordering. In the case in which the ordering of quenched-in specimens takes place (A2 to D03 or B2 to D03), the activation energy decreases. The increase in measuring frequency or annealing of a specimen both lead to this effect. Most of the experimental points for the activation energy in Figure 3(a), which lay lower, were measured either at relatively high frequency or after annealing. Annealing of the 20 to 30 pct Al quenched-in specimen leads to a decrease in b (Figure 3(b)) and, according to Pearson’ data, to a decrease in the lattice parameter as well. The carbon Snoek-peak height in Fe-Al alloys is proportional to the annealing temperature before water quenching,i.e., to the C content in solid solution. Such a dependence is the result of proportionality between the relaxation strength (D 5 2Q2m 1) and carbon content in solid solution:[19] Ds , C(l1 2 l2)2/kBT, where C is the fraction of carbon atoms, * l1 2 l2* ’ 0.83 for C in a -Fe. For better visualization of the peak broadening, the Snoek peak in an Fe-21.7 pct Al alloy (,2 Hz) is compared with the carbon Snoek peak in “pure” chromium (Figure 4). The corresponding activation energy in Cr is the same as in Fe-21.7 pct Al in the quenched state (1.17 eV), but in pure Cr, there is only one type of octahedral interstice, and one relaxation time is available for carbon-atom jumps. The decrease in b values for Snoek relaxation in Fe-Al alloys with the increase in measurement temperature occurs nearly as ,1/kT (for 21.7 pct Al, b 5 3.6 if f 5 2 Hz and b 5 2.2 if f 5 85 Hz; for 32 pct Al, b 5 1.8 if f 5 2 Hz and b 5 1.5 if f 5 47 Hz), indicating, according to Reference 13, that the broadening is due to a distribution in activation energy and not the frequency factor of atomic jumps (or relaxation time). At the same time, it is necessary to remember that the increase in peak temperature shifts the peak in the unstable range of measurements with respect to ordering processes, and ordering leads to the peak narrowing as well. This problem with the structural instability during measurements at higher frequency is clearly shown in Figure 4. When the peak is measured at a higher frequency (,85 Hz), it relates to at least a partly ordered structure and not to a disordered quenched-in structure. The peak temperature in the ordered structure is lower than in the disordered one, and the estimation of activation energy by the T-f shift is influenced by this change. METALLURGICAL AND MATERIALS TRANSACTIONS A
(b) Fig. 5—X peak in Fe-31.5 pct Al (a) in different states and (b) in 35 pct Al and 28Al3Cr after aging.
Taking into account a potential instability of quenched FeAl alloys during measurement, the accumulated equivalent aging time[15] for the employed heating rate of 2 K/min up to 470 K is estimated to be less than 1 minute of aging at 470 K. According to data given in References 6, 8, and 9, such “aging” is acceptable, considering that our specimens remain in the “as-quenched” state during the measurement. Most of our measurements were carried out at about 1 to 2 Hz; thus, the Snoek peak remains below 470 K. According to the heat-flow measurement (Figures 1(d) and 4), we do not observe an ordering reaction below ’470 K for Fe20 pct Al and greater (i.e., in the range of Snoek-peak observations for low-frequency measurements. With the increase in measuring frequency, the peak temperature increases to 543 to 553 K. Measurements of the Snoek peak at a frequency of ’85 Hz shift the peak position to a range of well-pronounced ordering (Figure 4). It means that for any quantitative estimation of ordering influence on the peak parameters, it is necessary to use a low-frequency technique in order to avoid an ordering influence on internal-friction measurements. The heat flow vs temperature curve (Figure 1(d)) shows the beginning of a broad exothermic peak (D03 ordering) at 470 to 500 K for the quenched specimen with 16 to 40 pct Al. This peak is due to a gradual improvement of the D03 or B2 (in Fe-40 pct Al) order in the specimen. The magnitude of the peak (for the 0.3-g specimens used) increases with VOLUME 34A, FEBRUARY 2003—259
increasing Al content. This peak is not observed if the specimen is preliminarily aged at 290 8 C,[27] because the ordering reaction has been completed during aging at this temperature. From the maximum of the exothermic peak up to the maximum of the endothermic peak (at about 720 K for Fe-21.7 pct Al, Figure 1(d)) the structure is D03, according to the equilibrium-phase diagram.[1] The exo- and the endothermic peak parameters relate to the degree of the ordering kinetics. Then, disordering for alloys with 11.7 to 21.7 pct Al or the transition to the B2 phase for 30 to 40 pct Al takes place at higher temperatures. That is why the measurements of the Snoek peak at this frequency range are disturbed by this microstructural instability and, sometimes, give confusing results for the activation energy by the T-f shift. For 11.7 and 16.3 pct Al, the long-range ordering was not observed by TEM, but, according to thermal analyses and internal friction,[8] a short-range ordering is possible. Possible contribution of vacancies to the S peak will be discussed elsewhere. C. The X Peak This peak is observed in our tests in Fe-30 pct Al, Fe-32 pct Al at 615 K (at 1.69 Hz) or at 672 K (at 45 Hz), in Fe28Al3Cr at 668 K (2.2 Hz), in Fe-35 pct Al at ’620 K (2.28 Hz), and in Fe-40Al at 716 or 760 K for 354 and 1838 Hz, respectively.[34] Peaks with similar parameters were earlier reported in Fe with 34, 37.5, 39, 45 and 50 at. pct Al by Damson et al.,[35,36] , in Fe-31 pct Al by Rokhmanov,[11] and in 26.3 pct Al by Nagy et al.,[37] and are marked in this article as the “X” peak. Its nature is still not clear. Three hypothesis may be considered, as follows. (1) As proposed in Reference 11, a Snoek-type effect (i.e., jumps of carbon atoms) in the presence of an additional phase other than the equilibrium D03 phase. (2) As proposed in References 35 and 36, a reorientationrelated effect of two vacancies[36] or VFe-Fe complexes.[35] The main argument favoring this approach is that the activation energy for vacancy (V) migration and the activation energy deduced from the X peak are rather similar. (3) Stress-induced jumps of carbon atoms trapped by vacancies or vacancy complexes in an ordered solid solution Fe-Al-C-V with high vacancy concentration are responsible for the X peak (the difference between the activation energy of the X peak and the Snoek peak is a reasonable value for the binding energy between carbon atoms and vacancies in iron, which is about 0.4 to 0.5 eV, according to Reference 39). Thermal vacancies in Fe-Al are formed readily[38] because of a low enthalpy (’1 eV), which is even lower than the migration enthalpy (1.5 to 1.8 eV) of vacancies. Consequently, there is a high thermal-equilibriumvacancy concentration in the measured temperature range. The wide range of concentrations (26 to 50 pct Al) in which similar peaks have been observed,[11,34– 37] as well as our recent results with about 28, 32, and 35 pct Al and 40, 45, and 50 pct Al in Fe,[34,40] makes the hypothesis regarding the influence of vacancies on the Q2 1 vs T spectrum a very attractive explanation for the X peak. The recent study of vacancy migration in Fe-Al[41] makes distinction between single vacancy defects in alloys with , 35 at. pct Al with D03, B28, and A2 structures (six-jump diffusion cycle) and triple 260—VOLUME 34A, FEBRUARY 2003
defects (with two Fe vacancies as next-nearest neighbors and one Fe-antistructure atom) in the low-temperature B2L phase (Al . 35 pct) supplied with additional divacancies from the high-temperature B2H phase in quenched-in conditions. The aforementioned vacancy types are characterized by different activation energies for vacancy migration and distortion fields (values of l1 and l2) below and above 35 at. pct Al. The concentration of vacancies, the activation energy for vacancy migration, and the activation energy of the X peak as a function of the Al content in Fe-Al alloys are summarized in Table II. The activation energy for vacancy migration, measured by different methods is similar to the activation energy of the process which is responsible for the X peak. But, the peak height does not correlate with the vacancy concentration, with a maximum at about 34 pct, which should correspond to the vacancy-migration mechanism of the X peak. The relative X-peak height with respect to the S-peak height (Q2X 1 /Q2S 1) increases with increase in Al content from 26 to 40 pct.* The influence of Cr and C also can hardly be *I.S. Golovin: Proc. of IIAPS-10 Conf. “Int. Conf. on Imperfections Interaction and Anelasticity Phenomena in Solid,” Tula State University, Tula, Russia, Nov. 13–15, 2001, 2002, pp. 47-54.
explained by a pure vacancy approach. Clearly, a high vacancy concentration is important for this relaxation effect, probably playing the role of a background for carbon-atom jumps under applied stress in solid solution in the stress field enforced by vacancies. The vacancy hypothesis is also used in Reference 36 to explain the S peak in Fe-(34 to 50)pct Al by a two-jump reorientation of the tetragonal dipole VFe-Fe-VFe. But, decarburizationexperiments[5,6] give evidence of the dependence of the peak height on the carbon content in Fe-(22 to 25)pct Al. The influence of carbon content was recently reported in Reference 37, which showed that an increase in C from 0.008 to 0.028 at. pct (Fe-26 pct Al) leads to an increase in the S-peak height from 3 3 102 4 to 13 3 102 4. It means that vacancy contributes to S peak in case of high Al concentration only. At this stage, it is only possible to point out the important features of the X peak. This is a relaxation peak, and its behavior with respect to different treatment regimes is rather similar to the S peak. The X peak is mostly observed in the temperature range where D03 or B2 phases are stable, according to the Fe-Al equilibrium diagram. Tentatively, the X peak may be decomposed into two low- and hightemperature relaxation peaks, XL and XH . This tendency is stronger in Fe-35 pct Al and in the ternary alloy Fe-28Al3Cr. A smaller peak appears at the high-temperature side of the main peak. Long-term low-temperature aging up to 300 hours smoothly decreases the X-peak height, but it is more unstable at higher aging temperatures: both the S and X peaks disappear after 30 minutes of aging at 500 8 C and 540 8 C (Fe-40 pct Al) or at ’600 8 C (Fe-28 pct Al-3 pct Cr). The activation enthalpy associated with the reaction of vacancy elimination in Fe-50 pct Al is between 1.19 6 0.27 (isochronal annealing) and 1.22 6 0.06 eV (isothermal annealing) using magnetic measurements and is 1.2 6 0.1 using isochronal calorimetric measurements[42] and should be compared in the future with the same measurements for carbon-atom elimination from a quenched solid solution. Cold working of an Fe-26 pct Al alloy[37] influences the carbon Snoek peak: an additional amplitude-dependentpeak METALLURGICAL AND MATERIALS TRANSACTIONS A
Table II. The Concentration of Vacancies Cv at 700 K,[41] the Activation Energy for Vacancies Migration,[36,41] and the Activation Energy of X Peak (References 35 through 37 and This Article) as a Function of Al At. Pct Al Cv , 105 Hmigr, eV[41] structure At. Pct Al Hmigr, eV[36] At. Pct Al HX(low), eV HX(high), eV Structure
26.4
29.3
32.4
35.9
0.9 1.0 1.2 — 0.45 ,1 ,1.2 1.7 ¬—————–— B28 ————–——® 23
25
1.31 26.3
1.5 28.4+Cr
37 1.7 31.5
[37]
1.75 1.77 1.65/1.72 — 1.94 — ¬————— D03 —————®
38.5 1.57 34
39.3
43.1
46.5
50
0.4 0.8 1.1 1.5 15 1.0 1.15 1.55 1.65 ,2 ¬—————————— B2L ——————————® 39 1.7 35
40 1.62 37.5
44
47
1.67 39/40
1.75 45
50 2.41 50
1.69[36] 1.63 1.65[36] 1.74[37]/1.78[36] 1.79[35] — — 1.82 — — 1.7[36] 1.79[36] ¬————————————— B2L —————————————®
appears at the high-temperature side of the S peak, but, practically, it does not change the X peak, probably because of the annealing effect during measurement. Alloying FeAl by Cr shifts the S and X peaks to higher temperatures and also increases the activation energy (S peak: 1.32 eV, and X peak: 1.77 eV). The Z peak nearly remains unchanged in temperature and activation energy. Substitution of Al by Cr atoms (28 pct Al, 3 pct Cr) shifts the X peak to a higher temperature as compared to the alloy Fe-31.5 pct Al, which has nearly the same content of substitute atoms in iron (DTS/TS 5 0.065, DTX/TX 5 0.079, and DHS/HS 5 0.054, DHX/HX 5 0.068) and even as compared to Fe-35 pct Al (HS 5 1.23; HX 5 1.62, and HZ 5 2.15 eV). The ternary Fe-AlCr alloy has the highest carbon content (0.16 at. pct C) among other binary alloys studied (except the alloy with 40 pct Al) and exhibits a higher S- and X-peak height. The effect of Cr on the increase of the carbon Snoek-peak temperature has been studied earlier and can be explained by the strong CCr chemical attraction.[10,25] A similar influence of Cr and C content on the S and X peaks in Fe-Al–based alloys is difficult to explain by the pure-vacancies hypothesis—neither the Cr nor C content significantly influence the vacancy concentration. If carbon is a participating element in the relaxation process, then a similar shift of the S and X peaks looks reasonable. The TEM study does not give a clear answer to an earlier proposal[11] of the presence of a metastable phase being responsible for the X peak. Taking into account the significant role of both carbon atoms and vacancies in the formation of the mechanical properties of Fe-Al alloys,[43] the study of the problem will be continued.* *After this article was submitted, some additional experiments were carried out. A more-systematic study of Fe-28 pct Al-Cr-Ti alloys (refer to previous note in text) shows (1) the systematic influence of Cr content (from 2 to 4 at. pct) on the increase in activation energy of the S and X mechanisms, (2) a nearly 10 times decrease in the S- and X-peak heights if 0.8 pct Ti is added to the alloy, (3) a very similar change of the S- and X-peak heights and widths, caused by different heat treatments (annealing temperature and quenched aging regimes), and a contribution of vacancies to the S peak for Fe-Al alloys with high Al content.
D. Zener Peak At a higher temperature range, the well-known Zener peak (denoted as “Z”) is observed for all alloys studied, as a result of stress-induced ordering (Figures 1 and 6). For better visualization, the peak heights in Figure 6 are plotted METALLURGICAL AND MATERIALS TRANSACTIONS A
35.9
Fig. 6—Zener peak height vs Al concentration.
together with lines of the A2 ÖB2, A2 ÖD03, and B2 ÖD03 transitions. The fit between peak heights and equilibriumdiagram lines gives only a rough illustration of this effect and should not be considered quantitatively. Peak temperatures are also indicated in Figure 6. According to References 13 and 19, the relaxation strength (DZ ) for the Zener peak should be increased with an increase in Al concentration as DZ , CAl2 /(T 2 T0), where CAl is concentration of Al, and T0 is the temperature of alloy ordering. The increase in Al content in the A2 range of the Fe-Al diagram leads to the increase in relaxation strength as DZ , CAl2, even far above the range of dilute solid solution predicted by theory. For compositions with less than 20 pct Al, i.e., in the range of random distribution of Al atoms in the lattice (A2), heat treatment (quenching or aging) is not important. The experimental results of Tanaka[6] and those in this article are rather similar, but the peak heights observed by Shyne and Sinnott[44] are higher. For . 22 pct Al, the Z peak is close to the A2-D03 boundary when measured at about 2 Hz (778 K) and is mostly in the A2 range only, when measured at about 82 Hz (873 K). The increase in frequency in this case leads to an increase in the peak height, because the peak is shifted to a higher temperature. The influence of aging on the peak parameters might be also expected for low-frequency measurements for 22 pct Al. The Zener-peak height for the 28, 32, and 35 pct Al alloys is lower than that in the 22 pct alloy, in spite of an increase VOLUME 34A, FEBRUARY 2003—261
E. Effect of Ordering and Ordering Kinetics
(b) Fig. 7—Dark-field TEM image with {111} reflection in [110] zone axis showing ordered domains of (a) Fe3Al in the 21.7 pct Al alloy after 290 8 C aging and (b) Fe3Al in the 31.5 pct Al alloy.
in Al content, because the Zener peak for 28 to 35 pct Al is observed in the temperature range of an Fe-Al ordered solution (T , T0). In a perfectly ordered alloy, the “stressinduced ordering damping” is eliminated, but, in the compositions studied, some deviations from perfect order lead to the Zener peak below T0. In the concentration range of the D03 phase, the peak height decreases, having a minimum value at 25 to 28 pct Al, i.e., near the stoichiometric composition Fe3Al. An increase in Al concentration to 32 to 35 pct, i.e., to the boundary between the D03 and B2 ranges, leads to a relative increase in the peak height. According to References 36 and 40, the peak height decreases with an increase in Al within the B2 range of the diagram. The activation energy for Zener relaxation is close to the activation energy of self diffusion,[13] and the results are presented in Figure 2. Additional alloying of Fe-Al by Cr does not significantly influence the Zener-peak parameters. This is contrary to the situation with the S and X peaks. In the latter case, the chemical attraction between C and Cr atoms is the main factor, but, in the case of Zener relaxation, where an elastic dipole is created by two neighboring atoms, the role of Cr is lower. 262—VOLUME 34A, FEBRUARY 2003
Some kinetics aspects of ordering for the 21.7 and 31.5 pct Al alloys have been discussed earlier with the help of heat-flow data. A transmission electron microscope was used to check the state of ordering in different Fe-Al alloys with varying Al contents. Alloys with low Al (, 12 pct) do not show long-range ordering; however, it has been reported that these alloys may contain short-range ordering.[7] The microstructure from an Fe-21.7 pct Al alloy specimen after aging at 290 8 C for 3 hours is shown in Figure 8(a). The dark-field micrograph shows an ordered-domain structure, in the size range of 5 to 10 nm. The domain-size estimation in the present study agrees with that reported earlier.[3,4] The superlattice reflections in the selected-area diffraction (SAD) pattern from the ^110& zone axis, shown in the inset of Figure 8(a), clearly indicate that the ordering is D03 type and not B2 type. When the same alloy was quenched from 720 8 C in cold water (5 8 C), no super lattice reflection was seen in the ^110& zone-axis pattern, suggesting the absence of any ordering after this heat treatment. The microstructure of the Fe-31.5 pct Al alloy after aging at 290 8 C and a diffraction pattern from the ^113& zone axis are shown in Figure 8(b). The ordered domains (of ’ 10 nm in size) are also seen in this alloy. The diffraction patterns examined in different orientations indicate the presence of D03 ordering. It is, however, not easy to distinguish a mixture of B2 and D03 ordering from the SAD patterns, as B2 reflections (fundamental and superlattice) are superimposed by the D03 spots and, therefore, are indistinguishable. The presence of additional peaks in the X-ray diffraction patterns in similar alloy compositions have been found recently.[46] They have suggested that this phase may have a tetragonal crystal structure. From the TEM investigation, we did not find direct evidence of the metastable phase proposed in Reference 11 to be responsible for the X peak, so the question of the third phase remains open. Aging of quenched specimens leads to ordering and to a decrease in the Snoek-peak temperature (DT ), to the peak narrowing (b /bmax ), and to an increase in the peak height (Qm2 1 /Qm.wq2 1) (Figure 8). Such an effect of ordering is absent in a -Fe, very small (if any) for 11.7 pct Al (only a short-range ordering is possible[7] ), well defined in 20 to 30 pct Al alloys (A2-D0 3), and weak in the 31.5 pct Al alloy (B2-D03) (Figure 3(b)). The decrease in b with aging indicates a decrease in distribution in the activation energy, which is the result of a decrease in the different interstitial positions available for carbon atoms due to ordering. The change in H and b values correlates with ordering parameters for Fe-23 pct Al, as reported in Reference 4, which, in particular, means that the change in Q2 1 values does not directly reflect a change in the carbon content in solution, because its activation energy and width depend on the aging time and temperature. F. Simulations The change in activation energy for carbon diffusion in a -Fe due to alloying by Al and ordering is explained using the Khachaturyan theory of strain-induced interaction[20] and the simulation method[21 – 29] for internal-friction interpretation as a change in the distribution of C-atom energies due METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 8—Influence of aging on the carbon Snoek peak: left—experiment; and right—simulations. The oxygen Snoek peak in Nb with activation energy 1.11 eV is plotted in left figure to be compared with aged Fe-21.7 at. pct Al with nearly the same activation energy
to C-Al interaction. In fact, a simulation of the X peak by the same approach is also possible in a framework of the hypothesis of C-vacancy interaction. In this article, we have applied the Khachaturyan–Blanter approach to the Snoek carbon peak only. The C-Al interaction changes the energy of C atoms in the octahedral interstices by a value of DEp , where “p” denotes the number of all C atoms in solid solution. This leads to the change in diffusion barrier for each individual C atom (Hp 5 HD 2 DEp , where HD 5 0.84 eV is the activation energy of C-atom diffusion in a -Fe), the pth C atom having the energy of interaction (DEp) with Al atoms and other C atoms:
1o W
DEp 5
(C-C)
1
j
o m
W
(C-Al)
(rp 2 (rp 2
rj ) ? C(rj ) rm) ? C(rm)
[4]
2
where the vectors rp and rj describe the positions of the octahedral interstices, rm describes the positions of the crystalline lattice points, W(C-C) (rp 2 rj) and W(C-Al))(rp 2 rm) are the energies of C-C and C-Al pair interactions, and C(r) represents the occupation numbers for the octahedral interstices and lattice points. Here, C(r) 5 1, if the interstitial or lattice point is occupied by a solute atom, and C(r) 5 0 if the interstitial or lattice point is not occupied. The “elastic” C-Al attraction significantly increases the peak temperature by an increase in the * DEp* value, and the chemical C-Al repulsion, according to the Lennard–Jones potential, compensates this increase, but not completely: the carbon Snoek-peak temperature in Fe-Al is higher than in a -Fe. Contrary to the Fe-C-Cr system,[25] where one value of chemical interaction between carbon and substitute atoms (Fe or Cr) fits well to all the concentrations studied, the situation in Fe-Al-C is more complicated, and it is not possible to describe the concentration range from 0 to 50 at. pct Al by one Hch (1) value. The higher values of Hch (1) better fit to lower Al concentrations, and vice versa. However, a reasonable agreement with experiment and simulation is observed for alloys with about 20 pct Al if Hch (1) ’ 0.2 eV, and, for alloys with 30 to 35 pct Al, if Hch (1) ’ 0.1 eV. Absolute values for the activation energies evaluated from METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 9—Simulations of Al concentration influence on DE (av) value for A2, P B2, and D03 structures (in case Al . 25 pct, Al atoms were distributed in D03 structure first, and the rest in B2) for Hch 5 0.2 eV. Dotted lines show corresponding changes in DE (av) in the ranges where related structures are P not observed according to Fe-Al equilibrium diagram.
the experiment and the simulation might both be improved in the future using better testing conditions (e.g., a Q2 1 vs f scan) and extended simulations, probably with a better potential for Hch . A major restriction for the accuracy of simulations is the limited size of the model crystal (i.e., 12 3 12 3 12 a03, where a0 is the lattice parameter) with periodic boundary conditions[9] used. But, even with the previously mentioned restrictions, the model explains the experimental results. Simulations (Figure 9) for different ordered structures show the influence of ordering on carbon mobility in solid solution. The activation energy for carbonatom diffusion is decreased for a given temperature, in the order of the A2 ® B2 ® D03 1 B2 ® D03 phases; simulated values depend on the value of the fitting parameter H(1) ch . I. Alloys with 20 to 25 at. pct Al. The A2 structure can be obtained at room temperature by water quenchingfrom high temperatures, and the D03 structure can be obtained by subsequent aging. A certain amount of B2 phase can be produced in a structure, according to the equilibrium diagram for the 22 to 23 pct Al alloys, by aging at 555 8 C. The positions of C atoms in the five coordination VOLUME 34A, FEBRUARY 2003—263
Table III. Energies of the Pair Interaction (Strain-Induced 1 Chemical Interaction at Hch(1) 5 0.2 eV) of Carbon Atom Located in the Octahedral Interstice ri with Al Located in the Lattice Point rm 5 (0, 0, 0), Averaged Values of D Ep (eV), and Numbers of C-Al Interactions (n) per One C Atom at 450 K in Ordered and Disordered Alloy with 22 At. Pct Al (ri 2
Hch (1) 5
0.2 eV
rm)/(a/2) Shell * ri 2 rm* /a DEp* W(C-Al) (rp 2 structure nA2 2 0.350 nB2 2 0.274 nD03 2 0.225
rm)
100 1 0.5 0.049 0.4 0.05 0.25
110 2 0.71 2 0.1468 2.46 2.97 1.46
120 3 1.19 2 0.027 2.82 1.43 1.06
211 4 1.22 1 0.038 1.91 2.95 2.57
300 5a 1.5 2 0.022 0.54 0.15 0.26
122 5b 1.5 1 0.006 1.78 0.15 0.95
Fig. 10—Activation energies for C atom diffusion in different structural states for Fe-22 pct Al alloys as compared with quenched (nearly A2) and aged (555 8 C, i.e., A2 1 B2 1 D03 ; and 300 8 C, i.e., D03 1 A2 structure) and distribution of energy (DEp value) for carbon atoms due to its interaction with solute atoms (Gauss fit to simulated values is given for better visualization).
shells and the corresponding energies of Hch(1) 5 0.2 eV are listed in Table III (energies of elastic interaction at Hch(1) 5 0 eV[9] and for Hch(1) . 0 eV, according to the Lennard–Jones potential). The A2 ÖB2 ÖD03 transitions have an influence on the short-range carbon-atom order and change the number of C-Al interactions (n) in different coordination shells, especially in the third and fourth shells. Table III quantitativelyillustrates that ordering redistributes C atoms around Al atoms (the C short-range order). The shortrange redistribution of C atoms due to ordering depends on ordering degree, temperature, and energy of the C-Al interaction. For the calculations, we used T 5 450 K, which is the average temperature at which the peaks were observed. The simulations done for the disordered and the ordered states of the 22.5 pct Al alloy (according to thermal analyses, the Fe22.5 pct Al composition has A2, B2, and D03 structures at different temperatures) shows a reasonable agreement with the experimental values if Hch (1) 5 0.2 eV (Figure 10). The simulation for the Snoek peak in Fe-Al alloys cannot be fit simultaneously to disordered and double-ordered states simply because the structure is a mixture of A2 1 (B2) 1 D03 phases, while the calculations are performed for a single A2, B2, or D03 phase. That explains the weaker effect of ordering observed in experiments compared to simulations (Figures 8) as a possible “mixture” of peaks from these structures. The ordering-induced decrease in H value leads to a higher rate of carbon diffusion in ordered states as compared to that in the disordered state. The C and Al atom interaction brings about the short-range order in the alloy. 264—VOLUME 34A, FEBRUARY 2003
Fig. 11—Atom positions in Fe-Al ordered alloys.
The degree of C-Al short-range order depends on the energy of the chemical repulsion:[15] if Hch(1) . 0, the number of the C-Al pairs decreases in the second, third, and fifth shells, but increases in the fourth shell. As a result of the changes taking place in the second and third shells, DHpav falls in value. In the ordered D03 structure, there are two types of octahedral interstices. One type is located in the first, third, and fifth, coordination shells, with respect to Al atoms, and the other type is located in the second and in the fourth coordination shells (Figure 11). The sum of the energies of C-Al interactions in the interstices in the five coordination shells of the first type for Fe-22.5 pct Al (the probability of 90 pct of Al atoms in the Fe3Al superlattice, according to Al content and Hch(1) 5 1 0.2) of interstices W1 1 4W3 1 2W5b is 1 0.14 eV; in the second type of interstices, the C-Al interaction energy 2W2 1 4W4 is 2 0.05 eV. The C atoms occupy positions of the second type, mainly leading to the Snoek-peak narrowing. This effect decreases with a decrease in Al content from the stoichiometric Fe3Al composition. In the B2 structure, Al atoms may occupy the neighboring bcc units. That leads to the Snoek-peak broadening with respect to D03 and an intermediate position for the carbon Snoek peak with respect to the A2 and D03 phases (Figure 10). METALLURGICAL AND MATERIALS TRANSACTIONS A
Table IV. Energies of the Pair Interaction (Strain-Induced 1 Chemical Interaction at Hch(1) 5 0.1 eV) of Carbon Atom Located in the Octahedral Interstice ri with Al Located in the Lattice Point rm 5 (0, 0, 0), Averaged Values of D Ep (eV), and Numbers of C-Al Interactions (n) per One C Atom at 450 K in Ordered and Disordered Alloy with 32 At. Pct Al (ri 2
Hch (1) 5
0.1 eV
rm)/(a/2) Shell (ri 2 rm)/a DEp * W(C-Al) (rp 2 structure nA2 2 0.452 nB2 2 0.396 nD031 B2 2 0.343
rm)
100 1 0.5 2 0.051 1.01 0.17 0.27
2. Alloys with about 30 to 40 at. pct Al. The B2 and D03 structures are mainly observed in these alloys, dependent on temperature range. It is, practically, very difficult to obtain an A2 structure at room temperature because of the high transition temperature for the A2 to B2 reaction and the corresponding ordering during cooling at lower temperatures. That is why, in most cases, the B2 structure is obtained after quenching,the B2 to D03 transition takes place at lower temperatures if Al , 35 pct. For the simulations in that case, we distribute the Al atoms in the D03 sublattice first, and the rest of the Al atoms are randomly distributed in the B2 sublattice. Results of simulations (Figure 9 and Table IV) show only a small difference in carbonatom energies and distributions in this case, and they lead to a rather small change in Snoek-peak parameters (activation energy and width) due to aging of quenched specimens. Results of the simulation are in agreement with experimental data. IV.
CONCLUSIONS
Three types of relaxation peaks in Fe-Al, with activation energies in the ranges of 0.8 to 1.3, 1.6 to 1.8, and 2.1 to 2.9 eV, are observed in Fe-(0 to 50 pct)Al alloys. The peak heights, widths, and activation energies depend on Al content and thermal history of the specimen, and these parameters are discussed with respect to the temperature ranges of ordering. Our experimental results and the experimental results available from the literature are plotted together to show three different relaxation effects caused by different point defects that can be distinguished in Fe-Al alloys: namely, a Snoek-type effect, vacancy-related effect (X peak), and Zener relaxation. The carbon Snoek-type relaxation is due to carbon diffusion under stress. Parameters of the corresponding peak depend on Al content and on the A2 ÖB2 ÖD03 transitions. The most pronounced effect of ordering is observed for 19 to 23 at. pct Al, caused by the A2 Ö D03 reaction, where the peak shifts to a lower temperature (DT # 30 K) and increases in height. A similar effect for lower Al concentrations (11 to 16 pct Al) is smaller, because of the lower degree of ordering (short-range ordering). Alloys with 28 to 35 pct Al exhibit mostly B2 ÖD03 transitions due to aging after quenching, which leads to relatively small changes in the peak parameters. These peculiarities of the carbon Snoek relaxation in the disordered and ordered states are interpreted in terms of an atom-interaction model, in which the C-Al long-range elastic interaction is supplemented by the shortrange chemical C-Al interaction. Ordering of Al atoms in Fe solid solution appears to prevent the occupation of some METALLURGICAL AND MATERIALS TRANSACTIONS A
110 2 0.71 2 0.147 3.58 3.45 3.06
120 3 1.19 2 0.027 3.43 0.60 1.01
211 4 1.22 1 0.038 1.49 3.30 3.77
300 5a 1.5 2 0.022 0.73 0.15 0.24
122 5b 1.5 1 0.006 2.42 0.50 0.92
interstitial positions around Al atoms by C atoms, leading to the decrease in the activation energy of carbon diffusion. The X peak, with an average activation energy of about 1.7 eV, is observed in the 26 to 50 pct Al alloys in the ascast, quenched, and aged states. The peak is rather stable with respect to heat treatment, but might be split into lowand high-temperature components. The features of this peak cannot be completely explained by existing models.[11,32,33] Our tentative explanation for the X-peak origin is that it is related to the stress-induced jumps of carbon atoms when trapped by vacancies or vacancy complexes. The height of the Zener peak as a function of Al content in Fe has two maxima: the first in the disordered A2 structure at about 22 pct Al (i.e., at the maximal Al concentrationin the disordered state) and the second, smaller increase near the B2 Ö D03 boundary (i.e., for 32 to 34 pct Al alloys). ACKNOWLEDGMENTS The authors are grateful to Professors H. Neuha¨user, K. Tanaka, V. Udovenko, and Dr. J. Kopecek for the specimens, to Professors M.S. Blanter, S.A. Golovin, and D.G. Morris for discussions, to Professor A. Rivie`re and Mr. A. Strahl for help with measurements, and to Mrs. Cr. Grusevski for the help with TEM analyses. REFERENCES 1. P.R. Swann, W.R. Duff, and R.M. Fisher: Metall. Trans., 1972, vol. 3, pp. 409-19. 2. S.M. Allen and J.W. Cahn: Acta Metall., 1975, vol. 23, pp. 1017-26. 3. D.G. Morris and S. Gunter: Acta Mater., 1996, vol. 44, pp. 2847-59. 4. D.G. Morris and S. Gunter: Acta Mater., 1997, vol. 45, pp. 811-22. 5. J.A. Hren: Phys. Status Solidi, 1963, vol. 3, pp. 1603-18. 6. K. Tanaka: J. Phys. Soc. Jpn., 1971, vol. 39, pp. 404-11; K. Tanaka and K. Sahashi: Trans. Jpn. Inst. Met. (Trans. JIM), 1971, vol. 3, pp. 130-35. 7. N.P. Kulish, V.M. Mandrika, and P.V. Petrenko: Fiz. Met. Metalloved., 1981, vol. 51, pp. 1229-37 (in Russian). 8. I.S. Golovin, T.V. Pozdova, and S.A. Golovin: Mater. Sci. Heat Treatment, 1998, vol. 4, pp. 3-9 (in Russian). 9. I.S. Golovin, M.S. Blanter, T.V. Pozdova, K. Tanaka, and L.B. Magalas: Phys. Status. Solidi (a), 1998, vol. 168, pp. 403-16. 10. I.S. Golovin: J. Alloys Compounds, 2000, vol. 310 (1–2), pp. 356-62. 11. N.Y. Rokhmanov: Proc. IV Int. Conf. EDS ’98, Barnaul, p. 34; Functional Materials 2000, Barnaul State University, Barnaul, Russia, vol. 7, pp. 235-39. 12. J.L. Snoek: Physica VIII, 1941, No. 7, pp. 711-29. 13. A.S. Nowick and B.S. Berry: Anelastic Relaxation in Crystalline Solids, Academic Press, New York, NY, 1972. 14. M. Weller: J. Phys. IV, 1996, vol. 6, pp. 63-72. 15. W. Pascheto and G.P. Johari: Metall. Mater. Trans., A, 1996, vol. 27A, pp. 2461-69. 16. H.J. Blythe, H. Kronmuller, A. Seeger, and F. Walz: Phys. Status VOLUME 34A, FEBRUARY 2003—265
Solidi (a), 2000, vol. 181, pp. 233-45. 17. R.S. Lakes: Viscoelastic Solids, CRC Press, Boca Raton, London,1998. 18. Internal Friction Method in Materials Science, Reference Book, M.S. Blanter and U.V. Piguzov, eds., Metallurgia, Moscow, 1991 (in Russian). 19. Mechanical Spectroscopy Q-1 2001 with Applications to Materials Science, R. Schaller, G. Fantozzi, and G. Gremaud, eds., Trans Tech Publications Ltd., Aedermannsdorf, Switzerland, 2001. 20. A.G. Khachaturyan: Theory of Structural Transformations in Solids, Willey, New York, NY, 1983. 21. M.S. Blanter and M.Y. Fradkov: Acta Metall. Mater., 1992, vol. 40, pp. 2201-08. 22. M.S. Blanter and A.G. Khachaturyan: Phys. Status Solidi (a), 1980, vol. 60, pp. 641-49. 23. M.S. Blanter: Phys. Rev. B, 1994, vol. 50, pp. 3603-08. 24. M.S. Blanter: Fiz. Met. Metalloved., 1981, vol. 51 n(3), pp. 609-19 (in Russian). 25. I.S. Golovin, M.S. Blanter, and R. Schaller: Phys. Status Solidi (a), 1997, vol. 160, pp. 49-60. 26. I.S. Golovin, M.S. Blanter, and A.V. Vasiliev: J. Phys. IV, 1996, vol. 6, pp. 107-10. 27. I.S. Golovin, D. Mukherji, and T.V. Pozdova: Materials Week 2000, Munich, Sept. 25–29, 2000 (published in electronic form: http:// www.materialsweek.org/proceedings/index.htm). 28. M.S. Blanter and L.B. Magalas: Scripta Mater., 2000, vol. 43, pp. 435-40. 29. M.S. Blanter, I.S. Golovin, and R. De Batist: Phys. Status Solidi (a), 2000, vol. 178, pp. 621-32. 30. K.L. Ngai. and C.T. White: Phys. Rev. B, 1979, vol. 20, pp. 2475-79. 31. G. Haneczok, M. Weller, and J. Diehl: Phys. Stat. Sol. B, 1992, vol. 172, pp. 557-72.
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32. C.H. Bennett in Diffusion in Solids, A.S. Nowick and J.J. Burton, eds., Academic Press, Inc. (London) LTD, London, 1975, p. 74. 33. A. Rivie`re and I.S. Golovin: ENSMA LMPM, F-86961,France, unpublished research, 2001. 34. A. Strahl and I.S. Golovin: Technical University, Braunschweig, Germany, unpublished research, 2001. 35. H.E. Schaefer, B. Damson, M. Weller, and E. Arzt: Phys. Status Solidi (a), 1997, vol. 160, pp. 531-40. 36. B. Damson: Ph.D. Dissertation, Universitat Stuttgart, Stuttgart, 1998, p. 105. 37. A. Nagy, U. Harms, F. Klose, H. Neuha¨user: Mater. Sci. Eng., 2002, vol. A324, pp. 68-72, and private communication with H. Neuha¨user and A. Nagy, Technical University, Braunschweig, Germany, 2001. 38. G. Sauthoff: Intermetallics, VCH Weinheim, 1995. 39. M.S. Blanter and A.G. Khachaturyan: Metall. Trans. A, 1978, vol. 9A, pp. 753-62. 40. I.S. Golovin, R.V. Zharkov, T.V. Pozdova, and S.A. Golovin: Mater. Sci. Heat Treatment (MiTOM), 2002, No. 6, pp. 16-22 (in Russian). 41. T. Hehenkamp, P. Scholy, B. Ko¨hler, and R. Kerl: Def. Diffus. Forum, 2001, vols. 194–199, pp. 389-94. 42. S. Zaroual, O. Sassi, J. Aride, J. Bernardini, and G. Moya: Def. Diffus. Forum, 2001, vols. 194–199, pp. 357-62. 43. Garcia Oca C., D.G. Morris, and M.A. Munos-Morris: Scripta Mater., 2001, vol. 44, pp. 561-68. 44. J.C. Shyne and M.J. Sinnott: Trans. AIME, 1960, vol. 218, pp. 861-65. 45. G. Thomas and M.J. Goringe: Transmission Electron Microscopy of Materials, Wiley-Interscience Publication, New York, NY, 1979. 46. N.Y. Rokhmanov: J. Condensed Matter Interphase Boundaries, 2001, vol. 3, pp. 281-85 (in Russian). 47. W.B. Pearson: A Handbook of Lattice Spacings and Structures of Metals and Alloys, Pergamon Press, vol. 2, 1967.
METALLURGICAL AND MATERIALS TRANSACTIONS A
