The Influence of β Phase Aging on the Martensitic Transformation Temperatures of CuMnAl Alloys

Scripta Materialia, Vol. 38, No. 3, pp. 375–383, 1998 Elsevier Science Ltd Copyright © 1998 Acta Metallurgica Inc. Printed in the USA. All rights reserved. 1359-6462/98 $19.00 1 .00

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THE INFLUENCE OF b PHASE AGING ON THE MARTENSITIC TRANSFORMATION TEMPERATURES OF CuMnAl ALLOYS Miguel O. Prado Centro Ato´mico Bariloche (Comisio´n Nacional de Energı´a Ato´mica) and Instituto Balseiro (Comisio´n Nacional de Energı´a Ato´mica and Universidad Nacional de Cuyo), 8400 S.C. de Bariloche, Argentina (Received July 30, 1997) (Accepted September 11, 1997) 1. Introduction Alloys with the composition along the line Cu3Al-Cu3Mn2 retain their high temperature b phase when quenched into water at room temperature from the homogenization temperature 1123K. During the quenching the b phase orders with the sequence A27B27L21 [1]. These alloys transform from b (bcc) to 2H or 18R martensite as has been reported before [2]. The equilibrium temperatures (T0) between b and martensite phases can be determined by measuring the martensitic transformation temperatures Ms and Af in the as quenched condition, without or with aging at room temperature, at 373K and at 423 K. It is possible to calculate the order parameters, minimizing the Helmholtz free energy of the ternary CuMnAl alloy in b phase with respect to a heterogeneous mixture of the pure elements in the bcc phase, which allows us to characterize the disorder in terms of first neighbor (nn) and second neighbor (nnn) disordered pairs as proposed by Rapacioli and Ahlers [3]. It is known from several works that the T0 temperature depends upon the thermomechanical history of the alloy. In CuZnAl Abu Arab and Ahlers [4] have shown that the stabilization of martensite can be deduced from the difference of the energy of formation of disordered pairs in b and in martensite. Matsushita et al. [5] studied the evolution of T0 with aging in CuMnAl alloys at high temperatures and found that the precipitation of stable phases interfered with the growth of martensite plates and made the transformation hysteresis larger. In this work it will be shown that the Ms (temperature at which martensite starts to form) measured in the as quenched alloys are quite different from those corresponding to ordered alloys. Measured differences between the Ms temperature after room temperature aging and after 373K aging will be presented, and these values will be compared with calculated differences in terms of energies of reordering of atomic pairs in CuMnAl alloys. 2. Experiments and Results The composition of the Cu-Mn-Al specimens used are listed in Table 1. They were all prepared by melting in an alumina crucible under argon atmosphere a Cu-35 at% Mn eutectic with the appropriate 375

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TABLE 1 Composition of Samples in at% Alloy

cCu

cAl

cMn

HM10 HM105 HM1125 HM1190 A13

0.713 0.711 0.708 0.705 0.701

0.188 0.184 0.180 0.176 0.169

0.100 0.105 0.112 0.119 0.13

Cu and Al quantities. They were kept five minutes at 1123K for b homogenization and then quenched into water at room temperature. Immediately after quenching the Ms was measured by the electric resistance method. For samples aged at room temperature the Ms was measured until it reached a saturation value. Ms values were also measured after a 24 hours aging at 373K and 423K. In Table 2 the Ms and Af values for the as quenched and aged samples are shown. 2.1. Ms Temperature Dependence on the Quenching Temperature The homogenization temperature, 1123 K in this case, was chosen to have a stable b phase according to the phase diagram along the composition line Cu3Al-Cu3Mn2 [6]. Nevertheless, one alloy of composition 10.5%at Mn was quenched from temperatures in the range 1050 –1200K (corresponding to the width in temperature of the b phase region at that composition). Ms decreases slightly with increasing homogenization temperature, and 1123K seems a proper election. 2.2. Aging Effects Four aging conditions are studied in this work: As quenched, room temperature, 373 K and 423K annealing. The Ms in the as-quenched state was that obtained just some minutes after quenching from 1123K to water at room temperature. Room temperature aging produced a decrease of the Ms temperature in all samples, it was of about 12K for 10.5 at% Mn as shown in Figure 1. The Ms decreased slowly until a final value was reached approximately at the fifth day. Aging at 373K produced a marked increase in the Ms temperature as Figure 2 shows. For 10.5%at Mn it is about 60K. The aging time required for a final Ms value is approximately 24 hs. For different aging temperatures, the final Ms values are depicted in Figure 3. Increasing the aging temperature up to 423K generated a completely new electrical behavior during TABLE 2 Measured Ms and Af, and Calculated T0 Values; T0 5 (Ms 1 Af)/2 As Quenched

Aged 24 Hs at 373K

Alloy

MS(K)

AF(K)

T0(K)

MS(K)

AF(K)

T0(K)

HM10 HM105 HM1125 HM1190 A13

246.3 189.0 162.8 128.0 46.5

259.2 201.0 173.2 136.2 74.7

252.7 195.0 168.0 132.1 60.6

294.5 255.0 248.6 189.0 143

303.1 264.1 257.2 197.4 166

298.8 260.0 252.9 193.2 154.5

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Figure 1. Evolution of MS with time at room temperature [8].

the martensitic transformation. Figures 4, 5 and 6 compare the electrical transformation cycle corresponding to different aging processes for the 10%, 11.25% and 13 at.%Mn respectively. The 10at.% Mn alloy seems to transform in two stages. The first stage has an Ms value of 300K, where most of the alloy transforms, and in the second stage a fraction of the alloy transforms at approximately 200K. The fact of having two Ms values in the same sample indicates the presence of two compositions by decomposition. For this sample it is also noted that the total change in resistivity during the martensitic transformation is lower than that observed for aging at lower temperatures. The 11.25 at%Mn alloy shows a much wider hysteresis cycle after a 423K aging and the overall change in resistivity is about 1/5 of that obtained for lower aging temperatures. The alloy with 13% at. Mn showed only slight changes after 423K aging, but in the same direction as the other two alloys. That during aging at 473K decomposition occurs is supported by the results by Bouchard and Thomas [7]. By aging treatments at and below 373K decomposition is avoided, and only these results will be discussed in the following.

Figure 2. Evolution of MS with time for aging at 383K [8].

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Figure 3. Final Ms for different aging temperatures [8].

3. Calculations and Results 3.1. Beta Phase The Helmholtz free energy for a ternary CuMnAl alloy in b phase with respect to a heterogeneous mixture of the pure elements in the bcc phase is written in Equation 1 [9]: F52

O (W

(1) AB

A,B

1

T 4

1 3W(2) AB)cAzcB 1

O (4W

A,B

(1) AB

2 3W(2) AB)xAzxB 1

O 1.5W

A,B

(2) AB

(yAzyB 1 zA.zB)

(1)

O p .ln p

A,B

j A

j A

Where the sum is over all atom species A, B5 Cu, Mn, Al, the cA the atomic fraction, the pJA the occupation probabilities of species A on one of the four sublattices J5I to IV to describe L21 order, and xA, yA and zA are the order parameters [10].

Figure 4. Ms resistivity cycles for as quenched, 373K aged and 423K aged alloy 10% at Mn alloy.

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Figure 5. Ms resistivity cycles for as quenched, 373K aged and 423K aged alloy, 11.25 at % Mn.

The W(s) AB are the b phase chemical interchange energies between atomic species A and B in the s51,2 coordination sphere (first or second neighbors) which are taken from [1] and are: (1) WCu-Al 5 (1605 6 35)K (1) WCu-Mn 5 (1266 6 130)K (1) WAl-Mn 5 (2144 6 35)K

(2) WCu-Al 5 (856 6 25)K (2) WCu-Min 5 (343 6 130)K (2) WAl-Mn 5 (1168 6 35)K

(where to obtain the W(s)ij in Joule/mole units, one has to multiply by 8.3143 Joule/(mol * K)). For the occupation probabilities at T5550K the following values are obtained. pMn(I) 5 2.2240549*1024 1 0.0022166345*cMn 2 1.1757812*c2Mn pMn(III) 5 23.795.1024 1 0.0320087*cMn 2 5.82e-5 2 c2Mn

Figure 6. Ms resistivity cycles for as quenched, 373K aged and 423K aged alloy 13% at Mn alloy.

(2)

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pMn(IV) 5 26.514*1025 1 0.003561*cMn 1 2.9307*1024*c2Mn pAl(I) 5 6.865*1025 1 7.3969*1024*cMn 2 2.3677*1025*c2Mn pAl(III) 5 3.619*1024 1 .00406*cMn 2 1.26586*1024*c2Mn pAl(IV) 5 0.97314 2 .02615*cMn The F function (Equation 1) was minimized for compositions along the line Cu3Al- Cu3Mn2 at a temperature of 550K, since it was shown for CuZnAl alloys that diffusion effects on order were not important for lower temperatures [11]. The resulting occupation probabilities are given in Equation 2. From Equation 2 we see that the order obtained after quenching is not a perfect L21 order since if this were the case we should have pMn(I)5 pMn(II)5 pMn(IV)5 pAl(I)5 pAl(II)5 pAl(III)50. It is worth to remind that this model does not take into account short range order. Therefore we are overestimating disorder with the occupation probabilities here calculated. This partial disorder can be described in terms of disordered atomic pairs. The different possibilities are: Cu(I) 7 Mn(III) Cu(IV) 7 Mn(III)

Cu(I) 7 Al(IV) Cu(IV) 7 Al(IV)

Al(IV) 7 Mn(III)

Where Cu (I)7Mn (III) stands for a Mn atom that changes from a site at sublattice III to a site at sublattice I and its original place is occupied by a Cu atom from a site at sublattice I. The corresponding energies of formation for these disordered atomic pairs are: e

II III I (1) (1) (1) IV II [Cu(I) 2 Mn(III)] 5 (2(pIV Al 2 pAl) 1 1.5(pAl 2 pAl))(WCuMn 2 WAlMn 1 WCuAl) 1 . . . 1 (4(pMn 2 pMn) I (1) IV II (2) (2) (2) 1 3(pIII Mn 2 pMn))WCuMn 1 . . . 1 3(pAl 2 pAl)(WAlMn 2 WCuAl 1 WCuMn) II (2) 2 6(pIV Mn 2 pMn)WCuMn

e

III (2) IV III IV III (2) [Cu(IV) 2 Mn(III)] 5 2.5.[(pIV Al 2 pAl ).WCuAl 1 (2(pMn 2 pMn) 1 pAl 2 pAl )WCuMn III (2) 2 (pIV Al 2 pAl )WAlMn]

e

III (2) IV III IV III (2) [Al(IV) 2 Cu(III)] 5 2.5.[(pIV Mn 2 pMn).WCuMn 1 (2(pAl 2 pAl ) 1 pMn 2 pMn)WCuAl III (2) 2 (pIV Mn 2 pMn)WAlMn]

e

III (2) IV III IV III (2) [Al(IV) 2 Mn(III)] 5 2.5.[(pIV Cu 2 pCu).WCuMn 1 (2(pAl 2 pAl ) 1 pCu 2 pCu)WAlMn III (2) 2 (pIV Cu 2 pCu)WCuAl]

e

II IV I (1) (1) (1) [Cu(I) 2 Al(IV)] 5 (2(pIII Mn 2 pMn) 1 1.5(pMn 2 pMn))(WCuAl) 2 WAlMn 1 WCuMn) 1 . . . II IV I (1) 1 (4(pIII Al 2 pAl) 1 3(pAl 2 pAl))WCuAl 1 . . . II (2) (2) (2) III II (2) 1 3(pIII Mn 2 pMn)(WAlMn 2 WCuMn 1 WCuAl) 2 6(pAl 2 pAl)WCuAl]

As example for the HM105 alloy, we obtain: eb[Cu(IV)-Mn(III)] 5666 K, eb [Cu(I)-Mn(III)] 5 2577 K, eb[Al(IV)-Cu(III)] 5 3114 K, eb [Al(IV)-Mn(III)] 5 3780 K, eb [Cu(I)-Al(IV)] 5 4110 K.

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3.2. Martensitic Phase The values of the nearest neighbor chemical interchange energies in the martensite phase, M(1) AB were determined from the known b phase values. Ahlers [12] has found that the interchange energies are not structure dependent but distance dependent. An exponential function was fitted to the known data in b phase, also with the condition that the chemical interchange energies are negligible at long distances, (1) for example 30 nm. The interpolated values in martensite phase are: M(1) CuAl 5 1404 K, MCuMn 5 1019 (1) K, MAlMn 5 1939K. For martensite next nearest neighbors the exponential approximation could not be used because the Ruderman-Kittel [13] oscillations invalidate this approach. Second neighbor interchange energies were chosen as the lower values compatible with experimental observations, as shown. M(2) CuAl 5 0 K,

M(2) CuMn 5 0 K,

M(2) AlMn 5 150K

Since disorder is inherited from the beta phase during the diffusionless martensitic transformation, the corresponding energies of formation of the disordered atomic pairs can be deduced and are: (1) (2) Mn eM F (CuIV 2 MnIII) 5 (3MCuMn 1 2MCuMn)pIII

S

D

(1) (1) M(1) AlMn 2 MCuAl 2 MCuMn (2) (2) IV 1 2 M(2) CuMn 1 MAlMn 2 MCuAl pAl 2 (1) Mn (2) (2) (2) IV eM F (CuI 2 MnIII) 5 MCuMn pIII 1 3(2MCuMn 1 MAlMn 2 MCuAl)pAl

The remaining energy expressions can be obtained by analogy with the two above. 3.3. Calculation of dT0 It is proposed in this work that after quenching reordering processes occur in the b phase, since the alloys try to minimize their free energy. A similar approach has been proposed before to explain stabilization in CuZnAl alloys [3]. From thermodynamic considerations we can calculate the change in T0 (dT0) due to the effect of ordering: DHb3 M 5 T0zDSb3 M

d(DHb3 M) 5 dT0zDSb3 M dT0 5

b b b b M M n(eM 1 n.eM d(DHb3 M) dHM 2 dHb (H(0) F 2 H(0))2(H(0) 1 n.eF 2 H(0)) F 2 eF 5 5 5 DSb3 M DSb3 M DSb3 M DSb3 M

Where D refers to changes in the thermodynamic quantities due to the martensitic transformation and d to changes due to ordering. DS is taken from [2]. n, the number of reordered atomic pairs can be also defined as the number of disordered pairs at 550K, since we suppose that at the 373K aging process all these pairs are reordered and was calculated from the occupation probabilities shown in Equation 2. Calculated values of dT0 for alloy HM105, are shown in Table 3. 4. Discussion The problem of the dependence of T0 with the thermal history of the sample must be resolved in order to assign a correct chemical order state to the sample whose transformation temperatures are being

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TABLE 3 Calculated Values of dT0 for HM105 Alloy. Only Cu(IV)-Mn(III) Disordered Pairs are Considered. Cu(I,II)Mn(III) Disordered Pairs Concentration is Overestimated by a Factor 3 Approximately Ordering pair

n (disordered pairs/mol) (*)

eM F (K) ordering energy

eFb(K) ordering energy

DSb3M (joule/mol K)

dT0 (K)

Cu(IV)-Mn(III) Cu(I,II)-Mn(III) Al(IV)-Cu(III) Al(IV)-Mn(III) Cu(I,II)-Al(IV)

9.043*1021 3.172*1021 2.930*1021 1.440*1021 1.570*1021

2913 21441 22444 21370 23169

2390 22334 22839 23229 23858

21.23 21.23 21.23 21.23 21.23

53.2 231.9 213 230 212

measured. It is of actual importance when these measured values are used as input for physical models that suppose a certain ordered state (for example L21). In this work the variation of T0 with aging has been analyzed in terms of the reordering of disordered atomic pairs. These disordered atomic pairs are due to the fact that the ordering produced during quenching is not total. It is a main feature of martensite that it inherits the disordered pairs that were present in its parent beta phase. In part 3. we showed that two types of disordered pairs are possible: first neighbor (I-III or I-IV) and second neighbor (III-IV) pairs. Moreover, first neighbor reordering causes a decrease of T0 and second neighbor reordering mainly a T0 increase. If reordering is vacancy assisted it is probable that at room temperature mainly first neighbor ordering contributes. This is supported by the decrease experimentally found in T0 for specimens aged at room temperature (Figure 2). At higher aging temperatures, say 373K, second neighbors ordering also plays a role and the change in T0 is mainly due to Cu(IV)-Mn(III) reordering (Figure 3). Figure 7 shows measured and calculated values of dT0. Here the M(2) ij have been chosen to make the best fit to measurements. The dispersion of measurements is mainly due to deviations from the nominal composition and to the fact that the quantities that are plotted are differences of transformation temperatures which involve a diffusion process between them. From all considered disordered pairs, Cu(IV)-Mn(III) should be, because of its lower energy of formation, the most probable at 550K.

Figure 7. Calculated and measured values of dT0.

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Others should be improbable except Cu(I,II)-Mn(III) which in the case of being the responsible of the room temperature decrease of T0, would be present in a concentration 3 times lower than that indicated in Table 3. 5. Conclusions In spite of the simplicity of the model here used, we can draw the following conclusions: The decrease of T0 during room temperature aging can be explained by first neighbor reordering. The increase of T0 due to 373K temperature aging is consistent with first and second neighbor reordering. The tendency of dT0 to increase with Mn content agrees with calculations. To get the best match (2) (2) between measurements and calculations the following M(2) ij are obtained: MCuAl 5 0 K, MCuMn 5 0 K, (2) MAlMn 5 150K. These values are small quantities as predicted by Ahlers [11]. Decomposition has been observed at 423K, preferably at lower Mn content. These results bring confidence to previously calculated chemical interchange energies in b phase, and the models involved. Acknowledgments The author gratefully acknowledges helpful discussions and the reading of the manuscript to Dr. Manfred Ahlers. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

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