microscopic mechanisms of metastable phase formation during ball milling of intermetallic tial...

Pergamon Acta mater. Vol. 45, No. 9, pp. 3935-3948, 1997

C 1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved

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MICROSCOPIC MECHANISMS OF METASTABLE PHASE FORMATION DURING BALL MILLING

OF INTERMETALLIC TiAl PHASES

T. KLASSEN, M. OEHRING and R. BORMANN Institute for Materials Research, GKSS Research Centre, Max-Planck-Str.,

D-2 1502 Geesthacht, Germany

(Received 13 August 1996)

Abstract-Powders of the intermetallic equilibrium phases oc*-TixAl, i -I-TiAl and TiAl3 were ball milled in order to investigate the microscopic origins of the energetic destabilization and the transformation into metastable phases during the milling process. It was found that the intermetallic phases were chemically partially disordered on milling followed by the transformation into solid solution phases after long milling. In detail, for the y phase, the formation of numerous deformation twins, thin h.c.p. lamellae and iamellae of the 9R phase formed by an antitwin operation was observed by TEM. The disordering of the D022-TiAIJ phase occurred inhomogeneously in the material via the formation of antiphase boundaries on (001) planes, resulting in an f.c.c. solid solution in the final state. In summary, it can be concluded that the formation of the observed metastable phases results from chemical disordering, whereas the excess enthalpy of grain boundaries plays only a minor role for the energetical destabilization of the intermetallic compounds during milling in this case. 0 1997 Acta Metallurgica Inc.

Zusammenfassung-Pulver, die die intermetallischen Gleichgewichtsphasen cr2-T&Al, y-TiAl bzw. TiAl, enthielten, wurden in einer Kugelmiihle gemahlen, urn die mikroskopische Ursache der energetischen Destabilisierung und der Umwandlung in metastabile Phasen beim Mahlen zu untersuchen. Es zeigte sich, daI3 der chemische Fernordnungsgrad der intermetallischen Phasen abnimmt, gefolgt von einer Umwandlung in Mischkristallphasen nach langem Mahlen. In der y-Phase wird elektronenmikroskopisch die Bildung zahlreicher Verformungszwillinge, diinner hdp-Lamellen und Lamellen der 9R-Phase, die durch eine Antizwilhngsoperation entsteht, beobachtet. Die Entordnung der TiAlj-Phase mit DO&truktur in den kfz-Mischkristall erfolgt inhomogen im Material iiber die Bildung von Antiphasengrenzen auf (OOl)-Ebenen. Zusammenfassend kann geschlossen werden, da8 die Bildung der beobachteten metastabilen Phasen beim Mahlen auf eine chemische Entordnung zuriickgeht und die in Korngrenzen gespeicherte Exzess-Enthalpie fiir die energetische Destabilisierung der intermetallischen Phasen in diesem Fall nur eine geringe Rolle spielt

I. INTRODUCTION

In recent years mechanical alloying has extensively been investigated showing that preferably metastable amorphous phases or disordered supersaturated solid solutions are formed upon ball milling of elemental powder blends [l]. For the formation of metastable phases, two different explanations have mainly been discussed.

First, nucleation and growth problems have been claimed to be the reason for the suppression of the equilibrium intermetallic phases [2, 31, in analogy to metastable phase formation during early stages of thermal reactions observed in artificially layered thin films [4]. The comparison with multilayered samples is near at hand because often lamellar micro- structures develop upon mechanical alloying. This explanation is supported by the TEM investigations of Petzoldt et al. [5], Eckert et al. [6] and Klassen et al. [7], which demonstrate that metastable phases are already formed in the early stages of

phase formation at the interface between both components.

However, the explanation based on kinetic constraints for the suppression of the intermetallic equilibrium phases might not hold for the final state of milling. In particular, it contradicts with results obtained after milling of equilibrium phases [8]. If similar milling conditions are chosen, in most cases intermetallic compounds transform into the same metastable phases as observed during milling of the elemental components. Obviously, such a trans- formation cannot be explained by constraints of nucleation and growth of the stable phases. Instead, the energetical destabilization of intermetallic phases upon milling has to be considered [9].

To allow a transformation into metastable phases, considerable amounts of energy are required to be stored in intermetallic phases. Concerning the types of defects by which enough energy could be stored, grain boundaries [lo, 1 l] and chemical disorder are discussed in particular. For example, the energy

3935

3936 KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE

stored in grain boundaries has been claimed to drive the amorphization rection upon milling of the intermetallic NiTi [l 11. On the other hand, chemical disordering has been suggested to play a key role in the destabilization of ordered intermetallic phases, not only upon ball milling [12, 131 but also upon electron irradiation [14]. In fact, in quite a number of studies chemical disordering has been found on milling, e.g. for NiTi> [15], AlRu [16], Nb,Al [17], Ni,AI [18] and NbiAu [19] but in many cases the defects responsible for the chemical disordering could not be identified.

It is important to note that the experimental research has predominantly concentrated on systems where amorphous phases form upon milling of intermetallic compounds. However, in these systems, the contributions of disordering and grain boundaries to the stored energy cannot be separated. Therefore, the Ti-Al system was chosen for this study, because the metastable solid solutions have a higher thermodynamic stability than the amorphous phase. Indeed, upon mechanical alloying of elemental Ti/Al powder blends, the formation of the h.c.p. solid solution is observed up to 60 at.% Al, while for 75 at.% Al the f.c.c. solid solution is obtained [20, 211. These results suggest that intermetallic compounds in the Ti-Al system should transform into an h.c.p. or f.c.c. solid solution and the influence of the excess energy of the grain boundaries with respect to chemical disorder can be investigated and quantified.

In this paper, the phase formation as well as the microstructural evolution were studied by X-ray diffraction (XRD) and transmission electron mi- croscopy (TEM) for different titanium aluminides in order to determine the microscopic mechanisms of metastable phase formation.

2. EXPERIMENTAL PROCEDURE

For the milling experiments, two different preal- loyed powders with overall compositions of T&,AI,, and TizsAlT5 were chosen. While the latter is a single phase material of the intermetallic equilibrium phase TiAl, with DOZ2 structure, the TiS1AL9 powder particles exhibit a two phase microstructure, consist- ing predominantly of the intermetallic phase y-TiAI (Ll, structure) and a small amount of the az-TizAl phase (DO,, structure). Milling was carried out in a planetary ball mill (Fritsch P5) in intervals of 15 min to allow cooling down of the vials, which heated up typically to about 5O’C during milling. The milling tools consisted of Cr steel and a ball-to-powder weight ratio of 10 was chosen. All handling of the powders including milling was performed inside a glove-box under an argon atmosphere, which was continuously purified to keep the oxygen and water level each below 1 ppm. Therefore, oxidation of the powders could be minimized. After 100 h of milling, typical impurity contents of 0.30 wt% and

0.60 wt% 0 were detected by chemical analysis for TiS1AL9 and TiZ5Ab5, respectively, arising mainly from the initial oxygen content of the powders. Fe contamination due to abrasion of the milling tools amounted to less than 0.05 wt%. Structural evolution of the milling process was characterized using a Siemens D 5000 X-ray diffractometer with CuK, radiation and a graphite monochromator. TEM investigations were performed on a Philips EM 400 T operating at 120 kV to follow the microstructural development upon milling. For sample preparation the ball milled powders were blended with Al powder and cold-compacted. Specimens were then thinned electrochemically by a jet-polishing technique using an electrolyte which consisted of 18 ml perchloric acid (70%) 430 ml butanol and 230 ml methanol

WI.

3. RESULTS

3.1. Milling of TiA13 intermetallic powder

Figure 1 shows XRD patterns of the intermetallic TiAI, phase after different milling times. The equilibrium structure of TiAI? is D02*. Below 35” the corresponding superlattice lines are found, which decrease with increasing milling time until they have completely vanished after 5 h of milling. The tetragonal DOzz structure with a c/a ratio of 2.23 is based on the f.c.c. lattice, consisting of cubes which

15 min

/&___J__

45 min

Fig. 1. X-ray diffraction patterns of intermetallic T-TiAlj powder after different milling times.

KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE 3937

hypothetical structure W23 L’P

introduction of anti-phase boundaries (APB)

Fig. 2. Possible cell arrangements for TiAh.

are tetragonally distorted due to the ordering (Fig. 2). This results in the splitting of the (2001 peak of f.c.c. lattices into the (004) and the (200)/(020) Bragg reflections between 42” and 48”. Synchronously to the reduction of DOZ2 order, a broad intensity plateau develops between these two peaks and finally the (200) reflection of the f.c.c. solid solution evolves, which is the final state of milling, as it does not change anymore even after 50 h of milling. Again, as in the experiments for mechanical alloying of elemental powders of the same composition [7], a low degree of LIZ ordering can be detected. Also, the lattice parameter of a = 0.3997 nm is in good agreement with the corresponding value of mechani- cally alloyed TiZ5A1,, and with literature data [20]. Evaluation of the peak broadening [23] reveals a crystallite size of (9 f 2) nm. The milling time necessary to transform the equilibrium DOj2 structure into the metastable f.c.c. solid solution is remarkably short compared to the 50 h milling time needed for mechanical alloying of the elemental components under the same milling conditions.

TEM investigations of the TiAl, powder demon- strate that DOZz-TiAls transforms inhomogeneously, as can be seen in Fig. 3(a), which shows the microstructure after 2 h of milling: a DOZ2 ordered crystallite approximately 100 nm in size is surrounded by small crystallites with only about 10 nm diameter, which cannot be imaged under the same conditions using the (1 IO) superlattice reflection of DO>*-TiA&. Therefore, they must have been transformed into another structure already. Aside from the point reflections of the DOzl ordered larger crystallite, the corresponding diffraction pattern shows superlattice reflection rings, which match the (008) and (110) lattice spacings of D021-TiAl, [24]. Superlattice reflections of other phases could not be detected. However, in analogy to the XRD results, the second fundamental reflection ring exhibits a broad intensity distribution, with a variety of spots between the reflection ring doublet of D023-TiAI,, indicating the presence of a small fraction of additional phases with lower c/a ratio. Aside the few remaining larger DO?>-TiAh crystallites, the crystallite size is already as low as about 10 nm after this first structural

transformation, comparable with the size after long mechanical alloying of the elemental components [7]. This indicates, that the crystallite size decreases during the transformation. As can be seen in Fig. 3(b), there are groups of several small crystallites, which have still about the same orientation and probably belonged to the same initial DO**-TiAh crystallite.

In addition to the results of the X-ray measure- ments, the TEM investigations demonstrate that in an intermediate stage, the equilibrium phase trans- forms into the metastable DOZ3-TiAl, structure, before the f.c.c. solid solution with a low degree of LIZ ordering is finally achieved. The broad diffraction intensity between 42” and 48” indicates that the transformation of the tetragonally distorted phases into the f.c.c. structure possibly involves additional intermediate phases with a smaller c/a ratio. The smallest grain size is found in the final state of milling.

3.2. Milling of two phase TiSIA14ppowder consisting of y-TiAl and a2-Ti3Al

Figure 4 shows XRD patterns of a two phase powder with an overall composition of Tis,AL9 after different milling times. The initial material exhibits the reflections of two intermetallic phases, mainly y-TiAl and a small amount of a2-Ti3A1. The L10 crystal structure of y-TiAl is based on the f.c.c. structure, which is slightly tetragonally distorted due to the chemical ordering; cr?-T&Al has the ordered hexagonal DOI structure.

After 1.5 h of milling the peaks have already broadened significantly, indicating a substantial reduction in grain size. Further, the intensities of the superlattice lines, located below 20 = 35”, decrease continuously with increasing milling time until they cannot be detected any more after 50 h of milling. Synchronously, the intensities of the y-TiAl funda- mental peaks, e.g. the (002)/(200) doublet, also decrease continuously, while the fraction of the disordered h.c.p. tc phase increases, as derived from the changing intensity ratio between the y(lll)/ ~(002)/a(OO2) reflection and the a2(201)/a(01 1) reflection. Finally, only the peaks of the disordered h.c.p. solid solution with lattice constants a = 0.2878 nm and c = 0.4626 nm are present after 50 h milling time, identical with the final state after mechanical alloying of elemental powders of the same overall composition [20].

In the case of the hexagonal cc>-T&Al, this result can simply be explained by disordering into the cr-Ti(A1) solid solution, as the fundamental lattice itself does not change. However, continuous disordering of y-TiAl would result in an f.c.c. solid solution for structural reasons.

In order to elucidate this transformation, the (relative) long-range ordering parameter and the phase fraction of the y-TiAl phase were determined. For the determination of the phase fractions the

3938 KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE

(c> (b) 5nm

Fig. 3. TEM micrographs of intermetallic r-TiAli powder after 2 h of milling. (a) Dark field image, g = (1 10)Da,,; (b) dark field image using intensity of the (111) reflection ring; (c) corresponding selected

area diffraction pattern.

KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE 3939

20” 30” 40” 50” 60” 28

Fig. 4. X-ray diffraction patterns of Tii,Aldg powder consisting of the intermetallic y-TiAl and a2-TisAl phases

after different milling times.

integral intensities of the (002)/(200) reflections for the y-TiAl phase were related to the (201)/(011) reflections of the ccl-T&Al phase and the solid solution, respectively, assuming that this intensity ratio is proportional to the phase fraction of the y-TiAl phase. For the initial material the phase fraction was calculated by the Lever rule using the phase diagram.

Analogously, the (relative) long-range ordering parameter s of the y-TiAl phase was determined by relating the integral intensity of the (110) superlattice line to the sum of the intensities of the (200) and (002) Bragg reflections and normalizing with the corre- sponding ratio of the initial material.

The (relative) ordering parameter and the phase fraction of the y-TiAl phase are displayed in Fig. 5. While the phase fraction of the y-TiAl phase is continuously decreasing, the ordering parameter is lowered only to 0.88 and stays constant upon further milling [21]. This allows the conclusion that complete disordering of the y-TiAl phase is energetically unfavorable. Instead, the energy stored by the small reduction of the ordering parameter obviously is already sufficient to allow for a transformation into the disordered h.c.p. solid solution.

To characterize the structural defects which are formed during milling of the y-TiAl phase, TEM investigations were performed after selected milling times. In the undeformed state, the two phase y/a2

microstructure consists mainly of y and CQ lamellae arranged in parallel with fixed orientation relation- ships [e.g. 2.5, 261. Figure 6 shows the microstructure and corresponding selected area diffraction pattern (SADP) in (OIi]-orientation after 30 min of milling. Although dynamical effects cannot be excluded, the SADP indicates the presence of two additional y-variants and two a2-variants as well as a new ordered modification called 9R [27, 281. The origin of these features will be discussed in the following.

Steveral studies show that twinning of the type (1 lz]( 111) is one of main deformation mechanisms of the y-TiAl phase [2.5,29-311. Twins of this type do not destroy the L10 ordering and are therefore energetically favored in contrast to (21 l](l 11) twins, which would lead to an APB. In the powder milled for 30 min only deformation twins of the true twin type are found [Fig. 6(c),(d)], which enclose angles of 70.53” with the initial y-lamellae [Fig. 6(a),(b)]. However, the intersection of these deformation twins with the former twin interfaces leads to disordering and may account for the decrease of the long-range order parameter as observed in the X-ray investi- gations (Fig. 5).

The SADP also includes (011) reflections, that indicate the presence of an h.c.p. phase in addition to the initial crz-phase [Fig. 6(e)]. The corresponding dark field image [Fig. 6(f)] shows thin lamellae parallel to the y-deformation twins. However, the expected (101) superlattice reflections corresponding to cc*-ordering cannot be detected.

While twins are formed by shifting every (111) lattice plane, a shift of every second lattice plane would result in an h.c.p. structure. A remaining chemical order could subsequently be destroyed during further deformation. The formation of h.c.p. lamellae in y-TiAl has also been reported by Feng ef al. [32-341 upon extruding.

A similar mechanism leads to the formation of the 9R structure, which was reported by Appel et al.

[27] and by Singh and Howe [28]. While primary

000 0

x x 0 L . . “‘.I x

0 50 100 200 500 1000

milling time [min]

Fig. 5. Phase fraction (x) and relative long-range order parameter s (0) for y-TiAl as a function of milling

time.

3940 KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE

(a> (h)

Fig. 6(a)p(d)-Caption on p. 3942.

(4 200 nm

KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE 3941

(e> (0

3942 KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE

0)

Fig. 6. TEM micrographs of Tis,A149 powder consisting of the intermetallic y-TiAl and ccz-Ti,Al phases after 30 min of milling. (ah(h) Dark field images of a lamellar region in (Oli) orientation; (a) g = ~~‘(022); (b) g = gL2(1 1 I); (c) g = ~~~(200); (d) g = yX2(il 1); (e) g = c&(200); (f) g = h.c.p.X’(200); (g) g = 9Rx’(l/3yL’(iii)); (h) g = 9RX2(1/3yL2(1 11)); (i) corresponding selected area diffraction pattern; 6) schematic pattern for indexing-spots marked L are related to lamellae oriented in the longitudinal

direction, X refers to the cross direction, as can be seen in the corresponding dark field images.

twinning can be described by a (1 l?.](l 11) shearing, an inverse twinning of type (ii2](i 11) on every third lattice plane creates the 9R structure, giving rise to Bragg reflections at l/3 dclll)g. Corresponding dark field images show thin lamellae in the initial direction as well as in the directions of both kinds of deformation twins [Fig. 6(g),(h)]. The formation of the 9R phase is especially favorable for higher degrees

of deformation, because it provides a shearing of double the distance of regular twinning [35]. The chemical ordering is not affected by the formation of the 9R phase, though it contributes to the refinement of the microstructure.

Although the formation of the 9R phase is not surprising, it has to be mentioned here that the observed l/3 d(,,,); reflections could also be due to

KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE 3943

00 0) 63 200 nm Fig. 7. TEM micrographs of TiilA149 powder consisting of the intermetallic y-TiAl and ocz-Ti,Al phases after 5 h of milling. (a) Bright field image; (b) dark field image [conditions as indicated in (c)l;

(c) corresponding selected area diffraction pattern.

double reflections. Therefore, the existence of the 9R phase in the milled material could unambiguously only be proven by high resolution TEM.

The microstructure of the powder after 5 h of milling can be viewed in Fig. 7. The lamellae, characteristic of the initial stages, have transformed into spherical crystallites with a diameter of about 15-20 nm, a fraction of which is still L10 ordered. Some of the crystallites have kept their orientation, so that the former lamellae can still be recognized. This also gives rise to the strong texture observed in the SADP. However, the reflections extend into rings and the former preferred orientations get more and more lost. In particular, some closed reflection rings corresponding to the disordered h.c.p. solid solution can already be observed.

In addition, a part of the powder is nearly fully transformed into the h.c.p. solid solution, exhibiting a homogeneous microstructure, which consists of spherical crystallites with a diameter of about 15-20 nm (Fig. 8). The corresponding SADP shows fairly homogeneous ring reflections and nearly no texture can be detected.

Summarizing, the microstructure of the y-TiAl/cc2- Ti?Al two phase powder is more and more refined upon milling by the formation of twins, thin h.c.p.

lamellae and the 9R phase, which are based on the shifting of { 111 j, lattice planes. The domains of these phases are often only a few nanometers thin and could serve as nucleation centers for spherical crystallites of the h.c.p. solid solution, the lamellae of disordered h.c.p. phase formed within the y-TiAl lamellae being of particular interest.

4. DISCUSSION

The investigations show that the equilibrium intermetallic phases are energetically unstable under the chosen milling conditions. The final states reached are identical to those obtained if starting from the elemental components with the same overall concentration [20].

Investigations on the deformation behavior of the intermetallic TiAI, phase [29,3638] show that the main deformation mechanism at room temperature is twinning of type [I lz]( 111) caused by 1/6[ 1 I?] Shockley partial dislocations, which does not disorder the DOzl structure. However, with increasing temperature a second mechanism occurs, which disorders the DOZ2 structure and could therefore be important for the process of phase transforma- tion during mechanical milling. Instead of (1 lo]

3944 KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE

(b) 5nm

Fig. 8. TEM micrographs of a different area of the same material as shown in Fig. 7. (a) Bright field image; (b) dark field image [conditions as indicated in (c)l; (c) corresponding selected area

diffraction pattern.

KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE

Table 1. Possible crystal structures of TlAl,

3945

Phase structure Svmmetrv a (nrn~ c (nm) rin Ref , I ~ I ~ ,

Ti>AL DOx Tetragonal 0.38537 0.42920 x 2 I.1137 x 2 L461 (equil.) 0.3x51 0.4306 x 2 I.118 x 2 [241 TLAI,? DO?? Tetragonal 0.3890 0.4206 x 8 I.081 x 8 [241 TilhAk - Tetragonal 0.3892 0.4165 x 16 1.070 x 16 I401 WTIAII LI? Cubic 0.398 0.398 I I411

0.397 0.397 1 ~241

superlattice dislocations. which are energetically unfavorable, corresponding partial dislocations of type l/2( 1101 are formed, which are separated by antiphase boundaries (APBs) on the (001) lattice planes. The energy required to form these APBs is low as indicated by full-potential linearized aug- mented plane-wave (FLAPW) calculations [39]. As Fig. 2 elucidates, the introduction of l/2( 110](002) APBs on every cube plane changes the structure from DOzz towards Ll, which is the simplest type of ordering for the given stoichiometry. Other periodic arrangements of APBs result in more complex superstructures, like the DO>? ordered T&All2 high temperature phase or the T&All8 superlattice consisting of eight DO:? cells. These derivatives of the TiAli structure have been already observed in diffusional reactions between Ti and Al [40-42].

Concomitantly, with increasing number of APBs the ratio c/a decreases, which is in the following referred to the tetragonally distorted f.c.c. subcell of the different structures. This decrease is attributed to the change in bonding character. Model calculations of Eberhart et al. 1431 reveal that the pronounced tetragonality of the DO?> structure is due to anisotropy of the bonding in the direction of the a and c axes. This anisotropy can be reduced by introduction of defects, i.e. changing the distribution of electrons, as e.g. by APBs. In consequence, the energy of the DOS1 phase rises with respect to the LIZ structure [44], resulting in the destabilization of the equilibrium phase. Below a c/a ratio of about 1.02, the Liz phase has the lower energy and transformation becomes favorable. These theoretical calculations are supported by experimental results [36,45], showing that adding small amounts of a third component to TiAl, leads to the formation of the LIZ instead of the D022 phase.

It is near at hand that partial disordering by APBs or occupation of sublattice sites by the wrong species also contribute to the decrease in subcell tetragonality and the destabilization of the DOZ2 equilibrium structure. Table 1 [24,40, 41, 461 lists lattice con- stants and c/a ratios of different structures, which can be formed by introduction of APBs into the D022 structure. Here, the ratios of the strongly tetragonally distorted DOzz and the cubic LIZ lattices are the extremes; all other periodic arrangements of APBs result in structures with c/a ratios in between these values. Consequently, for a random distribution of APBs in the direction of the c-axis a broad distribution of lattice plane spacings follows, which

explains the formation of the broad intensity plateau between the two DOZ2 peaks (004) and (200) in the diffraction patterns. The TEM results confirm the presence of intermediate phases, in particular DOZ3-TiAl?. These results indicate that the DOZ2-TiAl? is chemically disordered and therefore energetically destabilized by the introduction of APBs. Finally, the equilibrium phase is transformed into the metastable Ll, structure, involving a variety of intermediate metastable phases.

It is interesting to note that the described phase transformation sequence is observed in the opposite direction by thermal reaction of multilayered thin films [47] of the elemental components in the appropriate ratio, as well as by annealing of mechanically alloyed L12-TiAl? [24, 481. In the latter case, the LIZ phase transforms at about 753 K into the metastable DOzi phase, before finally the equilibrium DO*? ordering is achieved at about 1073 K.

In the case of the y-TiAl phase, a slight decrease in the long-range order parameter is found, which is attributed to numerous intersecting twains and lamellae of the 9R phase. The development of APBs by a dislocation mechanism could also contribute; however, this has not yet been confirmed. For y-TiAl alloys predominant occurrence of ordinary dislo- cations has been reported [31, 49, SO], but also superdislocations have been observed [31, 511 which split to form an APB and a superlattice intrinsic stacking fault [52]. The transformation of the L10 structure into the h.c.p. structure is concluded to occur via shifting of (11 I)-lattice planes, which of the major deformation mode for y-TiAl. Finally, dynamic recrystallization leads to spheroidization of the thin lamellae and randomly oriented equiaxed crystallites are obtained.

In the following, we will estimate the free energy stored by the partial disordering and compare it to the transformation enthalpies determined experimen- tally. For simplicity, homogeneous disordering is assumed and entropy effects are neglected, because they are usually small compared to the differences in enthalpy. According to the Bragg-Williams theory [53], the ordering enthalpy AHord for an equiatomic alloy is given by-

AHord = 1/4Nzes2 = 1/2AHrs2

where N is the number of atoms, = the number of next nearest neighbors, e the pair exchange energy and s the long-range ordering parameter.

3946 KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE

Using the enthalpy of formation AHr = -35 kJ/(g atom) as derived from CALPHAD calculations [54], which is in reasonable agreement with theoretical calculations [55], this leads to an ordering enthalpy of - 17.5 kJ/(g atom), in very good agreement with a value of - 17.2 kJ/(g atom) determined by ab initio calculations [56].

Consequently, an enthalpy of AH = 4.0 kJ/(g atom) is stored by disordering from s = 1 to s = 0.88, which supplies enough energy for the observed transformation, as the difference in free energy between y-TiAl and the h.c.p. solid solution is only 3.9 kJ/(g atom). It should be mentioned here that the ordering parameter of the initial material might already be slightly lower than s = 1 owing to processing conditions during the powder produc- tion. Nevertheless, this would make the free energy of the y-TiAl phase even higher with respect to the disordered h.c.p. solid solution.

The results on milling of the different titanium aluminides stress the importance of chemical disordering for the transformation into metastable states. However, not only disordering but also thermal relaxation and reordering kinetics have to be considered, which try to re-establish lower energy states. In the case of TiAl, this might explain the remaining low degree of L12 ordering, as the result of a certain reordering rate.

Therefore, the final state of milling is determined by the dynamical equilibrium between the thermal relaxation on one side and the external forcing, which drives the system away from its equilibrium state, on the other side, analogous to the mode1 developed by Bellon and Martin [57]. These two factors are represented by the rate at which defects are introduced vs the rate at which these defects are annealed out.

Finally, a certain amount of energy is stored in the material corresponding to the particular steady state.

Consequently, the phase formation can be ex- plained using the relative free energies of the competing phases. Phase transformations are ex- pected to occur during ball milling, if the difference in free energy between the competing phases is smaller than the energy which can be stored by the introduction of defects. In particular, chemical defects like APBs play an important role, since their energy varies for the competing phases and might reach significantly high values.

For titanium aluminides, the enthalpy stored in grain boundaries has only a minor influence on the transformation. The stored enthalpy should be similar or even enhanced in the case of a transformation from the intermetallic compound into a solid solution phase as the grain sizes do not differ essentially or even decrease in the course of the transformation.

The free energies of the competing phases were calculated by the CALPHAD method based on the

available thermodynamical data of the system. It reveals that exclusively those disordered metastable solid solutions are formed during ball milling, that have the lowest free energy for the particular concentration, i.e. the h.c.p. solid solution for Al concentrations up to 60 at.% and the f.c.c. solid solution for higher Al contents. This is understand- able, as the introduction of topological defects would increase the free energies or both solution phases by roughly the same amount, so the relative free energies of h.c.p. and the f.c.c. solid solution are not substantially affected. It is interesting to note that in cases where the free energy difference between the intermetallic and a solid solution or amorphous phase is smaller than the enthalpy of ordering, only partial disordering on milling can be observed before a transformation occurs, as for y-TiAl and the Al5 phase Nb3A1 [ 171, whereas in the opposite case, which has been reported for the Al5 Nb,Sn phase [58], complete disordering is found. This observation again emphasizes that the phase selection on milling of intermetallic phases is determined by free energy differences, with chemical disordering contributing substantially to the destabilization.

However, with respect to the formation of amorphous phases the energy stored in grain boundaries of crystalline phases has to be considered additionally. Obviously, the grain size finally achieved under the described milling conditions is not small enough to allow for a further destabiliza- tion of the crystalline solid solutions with respect to the amorphous phase. However, milling of TiAl alloys under different milling conditions leads to a smaller crystallite size of down to 7 nm allowing for partial amorphization [20]. CALPHAD calculations give an enthalpy difference of about 3 kJ/(g atom) between the h.c.p. solid solution and the amorphous phase for an Al concentration of 50 at.%. By assuming a grain boundary energy of 0.5 J/m*, an enthalpy of 2.1 kJ/(g atom) can be estimated for an average grain size of 7 nm, supporting the conclusion that the transformation of the solid solutions into the amorphous phase is mainly driven by the grain refinement.

For other systems, where the amorphous phase has a lower free energy than the solid solutions and consequently amorphization is observed upon milling of intermetallic compounds, crystallization enthalpies of more than 5 kJ/(g atom) are often measured [59], which is more than would be expected from grain boundary energies alone. Therefore it can be concluded, that chemical disordering also has to be considered as an additional contribution in these systems.

5. CONCLUSIONS

TiAl powders of equilibrium intermetallic phases were ball milled in order to investigate the origins of energetic destabilization and the transformation

KLASSEN et al.: MICROSCOPIC MECHANISMS OF METASTABLE PHASE 3941

of ordered intermetallic equilibrium phases into metastable phases during the milling process. The structural and microstructural evolution during milling was analyzed by XRD and TEM. The following conclusions can be drawn.

1. All intermetallic phases, the xz-Ti3Al with D0,9, the y-TiAl phase with L10 and the TiAl,-phase with DOZ2 equilibrium structure are chemically disordered during milling and transformed into metastable phases.

2. For the final milling stage the equilibrium phases have been fully transformed into an h.c.p. solid solution for the Ti49 at.% Al powder and a slightly Ll? ordered f.c.c. phase for the composition Ti-75 at.% Al, respectively. The final phase selec- tion can be understood by considering the free energy curves for different metastable phases which were quantitatively calculated by the CALPHAD method.

3. Due to the milling process, the long-range order degree of the ;l-phase is reduced to s = 0.88 which results in a stored enthalpy of 4.0 kJ/(g atom) in this phase. This energetical destabilization is sufficient to explain the transformation into the metastable h.c.p. solid solution.

4. The defects observed during ball milling are the same defects that are observed during plastic deformation and differ for each intermetallic compound. The TiA13 phase is disordered by the formation of APBs on (001) planes, involving the formation of various transitional phases and finally leading to a transformation into the metastable f.c.c. solid solution with a low degree of LIZ ordering. In the case of the y-TiAl phase, a slight decrease in the long-range order parameter is found by XRD, which is attributed to numerous intersecting deformation twins and lamellae of the 9R phase. APBs might also contribute, although they have not been observed. The transformation into the h.c.p. solid solution is concluded to occur via shifting of (111) lattice planes and subsequent dynamic recrystallization.

5. In general, it can be concluded that the phase selection is determined by the free energies of the competing phases. Under given milling conditions different stable and metastable phases can store different amounts of energies which shift their free energies. Ordered phases are especially prone to be substantially destabilized by chemical disordering on heavy plastic deformation during milling if the enthalpy of ordering is large, i.e. in the case of large negative enthalpies of formation. The energy stored in grain boundaries is found to play only a minor role on the destabilization of titanium aluminides because the metastable phases present in the final milling stage are nanocrystalline and hence a similar amount of energy is stored in grain boundaries before and after the transformation. However, a subsequent amorphization reaction on milling can be substantially supported by the grain boundary

energy, if the free energy difference between the solid solution and the amorphous phase amounts only to a few kJ/(g atom).

Acknowledgements-We would like to thank C. Michaelsen, S. Wiihlert, Z. H. Yan, C. Gente, U. Lorenz and G. Miillauer for stimulating discussions and experimental help throughout this work. In addition, we are very grateful to P. A. Beaven, F. Appel and M. H. Yoo for valuable comments and discussions, and to H. Schmelzer and D. Potrykus for chemical analyses. This research has been supported by the Bundesministerium fiir Forschung und Technologie under Grant No. 03M0040 and by the Deutsche Forschungsgemeinschaft (Leibniz-Programm). One of us (TK) also would like to acknowledge partial financial support by the U.S. Department of Energy under Grant No. DEFG 02-91 ER-45439.

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