Characterization of metastable crystalline phases in the AlGe alloy system

kro twroll. Vol 33. 50 2. pp. 191-203. 1985 Prinrcd III Great Bmam. All rights resewed

Cop>nght

~~-6140 85 5300+000 < 1985 Pergamon Press Ltd

CHARACTERIZATION OF METASTABLE CRYSTALLINE PHASES IN THE AI-Ge ALLOY SYSTEM M. J. KAUFMAN+ and H. L. FRASER Department of Metallurgy and the Materials Research Laboratory. University of Illinois, Urbana. IL 61801. U.S.A. f Received 19 MQJ

1984: in ret%ed form 4 September 1984)

Abstract-Metastable crystalline phases have been produced in Al-Ge alloys by melt spinning liquid alloys and by rapidly heating thin films which are inittally amorphous. The structures and compositions of these nonequilibrium phases have been characterized using convergent beam electron diffraction and energy dispersive X-ray spectroscopy. The results of these studies are compared directly with those of previous authors in order to resolve the controversy which has existed in the literature concerning the identity of the metastable phases which form in AI-Ge alloys when processed by novel techniques such as rapid solidification. RhmG-Nous avons fabrique des phases cristallines mitastables dan des alliages AI-Ge par trempe sur rouleau et par chauffage rapide de films minces initialement amorphes. Nous avons caracterise la structure et al composition de ces phases hors d%quilibre par diffraction d’electrons en faisceau convergent et par spectroscopic de rayons X a dispersion d’energie. Nous comparons directement Ie r&.ultat de ces etudes avec ceites d’auteurs antirieurs afm d-essayer de resoudre la controverse qui existe dans la litterature et qui conceme l’identiti des phases metastables qui se forment dam les alliages Al-Ge &labor&s par des techniques nouvelles telles que la solidification rapide. Zuaammenfaaaung-Metastabile kristalline Phasen wurden ir Al-Ge-Legierungen durch Schmelzspinnen und Abschrecken diinner. anfangs amorpher Filme hergestellt. Struktur und Zusammensetzung dieser Nichtgleichgewichtsphasen wurden mit der Beugung im konvergenten Elektronenstrahl und mit energiedispersiver Rontgenanalyse untersucht. Die Ergebnisse werden mit denen anderer Autoren verglichen. Ziel ist. den in der Literatur bestehenden Widerspruch aufzukllren. der in der ldentifizierung der durch neue Techniken (wie rasche Erstarrung) in Al-Ge-Legierungen entstehenden Phasen vorliegt.

The development of novel and unique microstructures has been a central aim of the application of rapid solidification processing (RSP) for improving the properties of metals and alloys. Among these microstructures are those which contain a significant amount of metastable alloy phases, i.e. those which do not exist on equilibrium phase diagrams [1,2]. It is anticipated that the properties of alloys containing metastable phases will be related closely to the structures of the various phases (i.e. types of crystal structure and whether ordered or disordered) and to the mo~hologies and distributions of these phases within the microstructures. As a result, it is extremely important that both the structures of such phases be characterized as thoroughly as possible and the important experimental conditions required to produce such microstructures be determined conclusively. This paper presents the characterization of the nonequilibrium crystalline structures produced in Al-Ge alloys by different tPresent address:MetallurgyDivision. National Bureau of Standards, Gaithersburg.

MD. 20899. U.S.A.

ex~rimental methods. A refated paper [3] will describe the results of an ex~~mental determination of the important factors controlling the formation of the various structures produced in this alloy system, Such determinations are especially relevant in light of the recent attempts directed towards constructing metastable phase diagrams [4-71. As was pointed out by Sinha ef al. [2], only in a limited number of instances has detailed characterization of the crystal structures and compositions of metastable alloy phases been performed. Consequently, there has been a considerabIe delay in the progress of this ~tentiaIly exciting area. In fact, in many cases such attempts at identifi~tion, using conventional methods, have proven very difficuk and often incorrect determinations have resulted. The most probable reason for these difficulties is the fact that, while the microstructures have been refined increasingly by such novel processing methods, the characterization techniques normally utilized have not been refined accordingly. For example, X-ray diffraction has been the most commonly employed method for such characterization attempts. either alone or in conjunction with other techniques such as electron diffraction and differential thermal analysis

191

192

KAUFMAN and FRASER:

METASTABLE CRYSTALLINE PHASES

(DTA). As might be expected. it is extremely difficult, in most cases. to obtain single crystal X-ray diffraction patterns from the very small phases char-

acteristic of materials produced by these novel processing techniques. This dificultg is compounded when more than one nonequilibrium phase exists and contributes to the diffraction pattern. Consequently, it is essential that these types ofmaterials be analyzed using state-of-the-art analysis techniques, e.g. anafytical transmission electron microscopy (AEM). In this way. it should be possible to obtain structural and compositional information from areas where only one phase exists. The Al&e system has been the subject of a number of investigations (8-191and is an example of a system in which a significant controversy has arisen concerning the accurate characterization of the metastable phases produced by different processing techniques Many different metastable crystalline phases have been reported ranging from simple cubic to complex monoctiaic and most determinations were made using X-ray diffraction, sometimes in combination with electron diffraction [Il. 191,DTA f 17, 181or both [ 131.A summary of the crystal structures which have been reported is given in Table I and includes the techniques utilized in these dete~inat~ons. In an effort to explain the large number of phases reported in this alloy system. it has been proposed that the different phases might form as a function of cooling rate which is likely to vary from one quenching device to the next {e.g. 161.However, this argument is oversimplified somewhat since, generally, it is accepted that, for most RSP experiments. there is a range of cooling rates experienced by the solidification products [ 181.Thus. a more likely explanation for the occurrence of the various metastable phases formed using essentially equivalent experimental techniques involves structure determinations which are incorrect. This explanation is supported by the fact that the X-ray diffraction data (i.e. number and positions of lines) appear to be similar in the different studies. it should be mentioned here that Sinha et al. [Z]referred $5 unpublished work in which a metastable single crystal phase had been identified, using X-ray diffraction, as A&Ge? with a monoclinic structure similar to the hexagonal (PJm 1)structure of Mg,B&. It was claimed that this phase, though very different from those determined by the other investigators (Table I). could account for most of the X-ray diffraction lines reported in the various studies. The purpose of the present paper is to describe mctastable phase characterization in AI&e alloys using two analytical electron microscopy (AEM) techniques, namely convergent beam electron diffraction (CBED) PO. 211 and energy dispersive X-ray spectroscopy (EDXS) 122-241. These techniques were chosen because they permit microstructural and micr~om~sitiona~ info~ation to be obtained from very smaft volumes (defined by probe sizes down to z 5 nm in diameter).

KAUFMAN

and FRASER:

METAST ZBLE CRYSTALLINE

2. EXPERIMENTAL Melt spun ribbons

Al-20. 30. 36, 42 and SOGet alloy ingots were prepared from pure starting materials by induction melting under Ar and chill casting in Cu molds. Subsequently. ingot sections were induction melted in graphite and heated to a temperature of approximately 50 C above the melting point before being forced through a small nozzle. using a pressure of Ar gas. onto a Cu wheel rotating with a surface velocit> of approximately 24m,‘s. The AI-30. 36 and 42Ge ribbons were produced in air while those of the AI-20 and 50Ge alloys were made in a vacuum of approximately iO_’ torr. Initially. the ribbons were analyzed using X-ray diffraction in order to determine whether metastable crystalline or amorphous phases had been produced. Since all of the X-ray patterns from the various allo> ribbons contained a significant number of crystalline peaks which could not be attributed to either face centred cubic Al (r-Al) or diamond cubic Ge (&-Ge). those which appeared to have the largest volume fraction of metastable crystalline phases. namely Al-36Ge and Al-42Ge. were chosen for microstructural analysis using AEM. Thin foiis from these two compositions were prepared. initially by standard electropolishing techniques and finally by Ar ion thinning where the latter procedure was found to produce more satisfactory samples. Microstructurai characterization of the samples was performed it-, either a Philips EM 400T or a Philips EM 420 TEhl both equipped with EDAX energy dispersive X-ray spectrometers and 9160 data analysis systems. ~i?lor~jto~s film pr~dMct~oi~ und ~r~.stull~~at~t~t~

Amorphous alloy films were produced by the molecular beam epitaxy technique at liquid He temperatures.: Alloy films of nominal composition Al-30. 40 and 50Ge were produced from high purity elements which were housed in individual cryoshielded furnaces. Compositional variations were controlled by separate shutters and monitored by mass spectrometers. The alloy films. typically 200-400nm thick, were deposited on rock salt substrates and then removed from the rock salt by immersing in water. Subsequently, small pieces of the films were collected on 3 mm Cu grids and inserted into the microscopes for analysis. Metastable. as well

PHASES

193

a> rtable, phases were produced by rapid11 heating the films with the eiectron beam causing crpstallization. The various structures which were produced were characterized using the analytical capabilities of the microscopes. 3. RESULTS Melt spun ribbons

As mentioned in the previous section, the AI-36Ge and A1-42Ge alloy ribbons appeared to contain the largest volume fraction of the nonequilibrium crystalline structures and. therefore, were chosen for analysis by AEM. Also. the X-ray lines from these tn (\ ~110~sencompassed all of those observed for the othm the Al-36Ge alloy ribbon. As is evident, there exist5 a dendritic structure surrounded by either an interdendritic second phase or an eutectic mixture. SAD patterns obtained from this primary dendritlc phase could not be indexed as either Z-AI or P-Ge indicating that it is a metastable crystalline phase. Convergent beam patterns (CBP’s) were obtained from the primary dendritic phase and the zone axis patterns used to determine the crystal point and space croups are shown in Fig. 2. In the [IOO] and [ini] CBP’s$ [Fig. 2(a) and (b)] the projection diffraction and whole pattern symmetries’ are 2~ut1 and ~1, respectively. From Table 2 in Buxton ct d. [20] it ma) be deduced. based on this symmetry information. that the diffraction group for these two zone axes is Z,mm,. Also. when the specimen was tilted through large angles alor;g the mirror line of the whole pattern. no zone .ixes of higher symmetry \vere observed ruling out as possibilities the 1773777. 6 177177tf7. 377. 4, ~WVNand 777f77777point groups (see Tables 3 and 4 in Buxton et ul. [20]). As a result. only the 6 117.4 777

tAl1 compositions are in at. “O. :The films were kindly prepared by Dr J. E. Cunningham Jr of the Materials Research Laboratory at the University of Illinois. gin all CBP’s the indices of the zone axis and certain reflections are included even though these were not known until after the space group determinations were complete. CThese terms are the same as those used by Buxton cf al. [20]where it was shown that these symmetries are related directly to the actual symmetry of the diffracting crystal.

Fig I Bright field electron micrograph of a typical region in the Al-X&e melt spun ribbon.

194

KAUFMAN

m

and FRASER:

METASTABLE CRYSTALLINE

PHASES

a

m

m

b

c Fig. 2. CBP’s obtained from the dendritic phase in the Al-36Ge ribbon: fa) [lOOI.(b) [IOr] and Ic) [OlO].

KAUFMAN

and FRASER:

METASTABLE

CRYSTALLINE

PHASES

195

Table 2. Zone axis symmetries required by the three point groups 6:m. 4 M and 2:m. Note that one needs to find either a 61 R. 41 R or 21 R diffraction group to determine the point group unambiguously Possible crystal point group

Zone axis symmetries (diffraction groups)

6/m

K@O]l

[uv.O] &mm,?

4m

[:A;]

2,m

[04lox1 ?I,

[Ut.O] Z,mm, [WOW] 2,mm,

[W.H.] 28 [UW] 2, [ULW) 2,

and 2;m point groups remain as possibilities. The diffraction groups expected for the different zone axes of these three point groups are listed in Table 2 from which it is evident that it is only necessary to find a CBP with either the 61 R, 41 R or 21 Rdiffraction group to determine the point group unambiguously. The [OlO) CBP [Fig. 2(c)] is the required pattern since it may be noted that the projection diffraction and whole pattern symmetries are both 2 and the resulting possible diffraction groups are either 2 or 21 R (Table 2 in Buxton et al. [20]). Since only the 21R diffraction group is consistent with the other zone axis symmetries the point group must be 2/m (monocIinic). The space group is determined most readily by considering the dynamic absences present in CBP’s (e.g. the [loo] and [IOT] CBP’s in Fig. 2). Thus, if a systematic row exhibits reflections with dynamic absences, the crystal structure contains either a two-fold screw axis, parallel to the systematic row, and/or a glide plane, whose normal is perpendicular to both the electron beam direction and the systematic row [25,26]. Before examining the dynamic absences, it is important to consider the symmetry elements which are possible for a crystal with the 2/m point group. A stereo~am (b-axis unique) depicting these elements is shown in Fig. 3 and it is clear that only a (010) ghde plane and a [OIO] two-fold screw axis are possible. Thus, upon examining the [loo] CBP [Fig. 2(a)] it can be seen that dynamic absences exist along the 010

010

oio

2/m

Fig. 3. Stereogram (b-axis unique) displaying the possible symmetry elements for crystals with the 2/m point group. Heavy lines (-) represent mirror planes (possible glide planes) and symbols (0) represent diads (possible two-fold screw axes).

Fig. 4. 010 projection (solid lines) of the monoclinic crystal (b-axis unique) proposed by Koster (old) along with the 070 projection (dashed fines) of the monoclinic ceil identified in the present work (new). The new cell was chosen to comply with the convention adopted in Ref. [27] where fl > 90’ and the glide is of the c-type. and 001 systematic rows. The symmetry element responsible for the absences along the 001 systematic row must be a (010) glide plane since the alternative, a [OOl] two-fold screw axis, is impossible (cf. Fig. 3). Likewise, the symmetry element responsible for the absences along the 010 systematic row is a [OlO] two-fold screw axis since a (001) glide plane is not possible. Identical results are obtained by analyzing the dynamic absences in the [lOI] CBP [Fig. Z(b)]. This information may be combined with that concerning forbidden reflections in order to determine the space group. However, for crystals with the 2im point group it is difficult to determine the indices of the hO/ reflections because the a and c axes and the angle fl are not known a priori and are dictated both by the symmetry elements, if any, which are present and by the convention adopted. To illustrate this complication a 010 projection of the monoclinic unit cell determined by KLister (Table 1) is shown in Fig. 4. According to the indexing scheme used by Koster, the CBP’s in Fig. 2(a), (b) and (cf would be indexed as [tOOI, [OOl] and [OIO], respectively. For this indexing scheme to be consistent with the observed kinematically forbidden reflections, it would be necessary for the glide translation to be of the diagonal (n) type (i.e. a glide translation of a/2 + c/2) as shown in the figure. However, the convention usually adopted is that an n-glide is not permitted in monoclinic systems since the indices can be altered such that either the a or c axis is chosen to he along the diagonal (glide) direction [e.g. 27]. Thus, if the c-axis is placed along the former diagonal and fl is chosen to be obtuse 1281, the new lattice parameters become a = 0.6734 nm, b = 0.5818 nm, c = 0.8045 nm and #3= 147.85” (Fig. 4). For this choice of lattice parameters there are two possible space groups, C2/c and P2,/c [28]. By analyzing the reflections in the higher order Laue zones (holz) of the CBP’s in Fig. 2, it appears that the reciprocal lattice is primitive corresponding to a primitive real lattice (211 and the resulting space group is P2,/c. Confirmation of this choice is afforded by comparing directly the reflections expected for the two different space groups with the line

196

KAUFMAN

and FRASER:

METASTABLE

PHASES

this phase was performed, using both standard and standardless methods (221, and the resulting composition was found to lie in the range 43-45 Ge. When the AI-42Ge alloy ribbon was examined in the microscope the microstructure which was observed most frequently appeared somewhat similar to that in the AI-36Ge alloy and consisted of a primary cellular phase surrounded by intercellular r-Al particles (Fig. 5). However, closer examination using CBED revealed that the primary phase was not the monoclinic (PZ,/c) phase, determined above for the more dilute alloy. or either of the stable phases (r-Al and fl-Ge) and, therefore, must be another metastable crystalline phase. Figure 6 displays the CBP’s used to perform the point and space group analyses of this phase. In the [OOOI]CBP [Fig. 6(a)] the projection diffraction and whole pattern symmetries are 6~2 and 3m, respectively. while those in both the [flOl] CBP [Fig. 6(b)] and [Ii021 CBP [Fig. 6(c)] are 2na71 and m, respectively. Again. by utilizing the tables in Buxton et al. (201 it is possible to deduce the diffraction

Fig. 5. Bright field electron micrograph of a typical region in the AL42Ge melt spun ribbon. positions measured in the X-ray diffraction patterns as will become evident in Section 4. Thus, the space group is P2,;c with the lattice parameters mentioned above. Quantitative EDXS analysis from

,rn -

m

CRYSTALLINE

b Fig. 6. a and b

KAUFMAN and FRASER:

METASTABLE CRYSTALLINE PHASES

present in some of the CBP’s. Again. it is useful initially to consider a stereogram which depicts the possible symmetry elements for crystals with the ?m point group (Fig. 7). From this stereogram it can be seen that only (1120) glide planes and (11~0) twofold screw axes are possible. Now. in the [Ii021 CBP [Fig. 6(c)]. dynamic absences occur along the ilO systematic row. From Fig. 7 it becomes evident immediately that the responsible symmetry element is a (1120) glide plane since the alternative. a [ilOl] two-fold screw axis, is impossible. From the tables in Ref. [28] it is found that. for the Jrn point group, the only space groups which have { 11201 glide planes are P3c 1 and Rk. Closer examination of the d-spacings obtained from the [OOOI]CBP reveals that the TlOO and 2200 type reflections are absent and the conditions are such that for l’ihO0reflections. the equality

groups (6,mm, for [OOOl]and 2,mm, for [ilOll and [lT02]) corresponding to these CBP’s and, furthermore, the two possible point groups, m3m (cubic) and 3m (rhombohedral). Since no zone axes were observed which displayed the higher symmetries expected for a cubic (m3m) structure, this possibility can be rejected and the point group must be 3rn. Confirming evidence is obtained from the [ 11201CBP [Fig. 6(d)] in which the projection diffraction and whole pattern symmetries are both 2 and the corresponding diffraction group is either 2 or 21,. Since the diffraction group 2 is not allowed for either 3m or m3m and since the diffraction group 21 R is not allowed for m3m (Table 3 in Buxton et al. [20]) then the only consistent point group is 3~. The space group analysis of this phase is performed, as before, by analyzing the dynamic absences

m

m

197

C

d FIN. 6. CBP’S from the primary phase in the Al42Ge ribbon: (a) [OOOll.(h) [Ttotl. (c) ]tTOziand (d) ]I 1201.

198

KAUFMAN

and FRASER:

METASTABLE

CRYSTALLINE

PHASES

ioio

izio

Fig, 7. Stereogram displaying the possible symmetry elements for crystals with the 3m point group. Lines and symbols have the same meaning as in Fig. 3.

/I = 3n (n = integer) must be satisfied for the reflection to be allowed. Only the Rfc space group has such restrictions and, as a result, the space group has been determined unambiguously. The lattice parameters for this crystal structure are a 2 7.67 nm and z z 96.5’ (rhombohedral indices) in accord with Kiister’s earlier analysis (Table 1). Again, quantitative EDXS analysis was used and the resulting composition range was determined as 49-51 Ge. The monoclinic (P2,/c) and rhombohedral (R3c) phases were the only nonequilibrium crystalline phases observed in the various alloys when processed by melt spinning. The possibility of other phases being present in these or the other rapidly quenched materials of previous studies will be discussed further below. Rapidly heated films Figure 8 displays a typical microstructure of an Al-4OGe alloy film which was heated rapidly with the electron beam (in situ) to cause crystallization. The microstructure consists of regions of stable (Z-AI + P-Ge) phases (marked A) together with regions of metastable ones. Two different metastable phases (marked B and C) are present in Fig. 8 and these could not be identified as either of those characterized in the melt spun ribbon studies above. As a result, it was decided to attempt to characterize these phases using AEM techniques. For the metastable phase in the region marked C in Fig. 8, CBP’s necessary for characterization were obtained and are shown in Fig. 9. The [ 1001CBP [Fig. 9(a)] has 2mm projection diffraction and whole pattern symmetries and the corresponding diffraction group is either 2mm or 2mm 1R (Table 2 in Buxton et al. [20]). Both the [ lOl] and [ 1IO] CBP’s in Fig. 9 display 2mm projection diffraction symmetry and m whole pattern symmetry and, therefore, belong to the

Fig. 8 Bright field electron micrograph of an AI-40Ge MBE film which was crystallized by heating rapidly with the electron beam in the microscope. Region A corresponds to z + p while regions B and C contain metastable phases.

2,gnm, diffraction group. From Table 3 in Buxton et al. [20], it is evident that the possible crystal point groups having these diffraction groups are ~~VIV~I. 4/mmm, 6/mmm, m3 and 0131~. However. all point groups other than mn~~ can be rejected bj, noting that no CBP’s were observed which had the higher symmetries required by the other possibilities (Table 4 in Buxton et al. [20]). Thus, the point group is /WWU (orthorhombic). Due to the large number of space groups (i.e. 28) with the n~mm point group [28]. it is necessar! initialI> to determine the nature of the unit cell. This is accomplished most readily by considering the [ IOO] and [I IO] CBP’s (Fig. 9). By projecting the holz reflections back onto the zero layer. a primitive reciprocal lattice unit cell can be constructed. Thus. the real lattice unit cell is also primitive. xext. it is necessary to consider the dynamic absences observed in the various CBP’s. Since. for crystals hating the mmm point group, only jOO1i glide planes and (001) two-fold screw axes are possible (Fig. 10). then the absences in the [IO11 and [I lo] CBP’s are the easiest to interpret. For example. the [IOI] CBP [Fig. 9(b)] contains dynamic absences along both the 010 and TO1 systematic rows. Those along the 010 ro\h. can only be due to a (OIO] two-fold screw axis since a (701) glide plane is impossible. Similarly. those along the TO1 systematic row must be due to a (010) glide plane since a [TO11two-fold screw axis is not possible. By similar reasoning, the dynamic absences along the 001 systematic row in the [1 IO] CBP [Fig. 9(c)] must be caused by a [OOl] two-fold screw axis. while those along the IT0 systematic row must be due to a (001) glide plane. By combining this information. it is possible, using the tables in Ref. [28]. to determine the

KAUFM.19

and FRASER:

METASTABLE

CRYSTALLINE

PHASES

m

m

b

m

I

m Fig. 9. CBP’s from the unknown

C phase (marked C) in Fig. 8: (a) (lOO]. (h) {lOI] and (t) [I iO].

200

KAUFMAN

and

FRASER:

METASTABLE

Fig. IO. Stereogram displaying the possible symmetry elements for crystals with the N~~~WI point group. Lines and symbols have the same meaning as in Fig. 3

space group as Pbcu with lattice parameters a ~0.78 nm. b -Y 0.57 nm and c n. 0.73 nm. Quantitative EDXS analysis was p~rfo~ed on this phase and the composition was determined to fie in the range 41-43 Ge. SAD patterns (e.g. Fig. ii) from the other metastable phase produced in these films (marked B in Fig. 8) could not be indexed on the basis of any of the phases previously determined and, therefore, this phase represents the fourth such nonequilibrium crystalline phase produced in this alloy system in the present study. CBED analysis was attempted with little success because, firstly, the structure tended to have very localized strains and, secondly, the gspacings in the di~raction patterns were very closely spaced resulting in significant overlap of the disks produced in CBP‘s. However, by examining more closely the SAD patterns obtained from this structure, it is found that this phase is identical to that produced and characterizied in a previous study of

submicron powders of the eutectic composition [29]. In that study, the structure was determined to be hexagonal, P6/mmm space group (6itnmm point

CRYSTALLINE

PHASES

Fig. I 1. SAD pattern from the unknown phase (marked B) in Fig. 8.

group), with lattice parameters a z 1.4nm and c = 0.72 nm. Quantitative compositional analysis. using EDXS, was performed in the present study and revealed that the hexagonal phase composition was in the range 42-45 Ge. The microstructures produced in the Al-5OGe films by heating rapidly with the beam contained the same two metastable phases while those produced in the AI-30Ge films contained only the hexagonal phase in addition to the stable (r-Al + /3-Ge) phases. It should be noted. however, that the lattice parameters of the orthorhombic phase in the AI-5OGe films were slightly larger. i.e. a = 0.80nm, b 1: 0.59nm. and c z 0.75 nm, indicating a dependency of the lattice constants on composition and an enrichment of Ge up to approximately 50”,. 4. DISCUSSlOK

Table 3 summarizes the results of the present study, As noted above only four metastable crystalline structures were produced using the two experimental approaches. A comparison of these results with those

Table 3. Summary of the microstructural and microcompositional information obtained for the four metastable crystalline phases characrerized in this study Crystal slructure

Space group

Monoclinic

P2, <

Lattice parameters (nm) a = 0.6734 b =0.5818

c = 0.8045

fl = 147.85 Rhombohedral Orthorhombic

Hexagonal

RJC

a = 0.7672

Pbrrr

z = 96.55 a = 0.78

P61mmm

b c a (’

I 0.57 z 0.73 z 1.40 10.72

Forbidden reiktions (general)

Composition range (at. OLtGel 43-4s

ItOl:l=2n+l OkO:k = 2n +

I

hhl:i=Zn+l 0kl:k =2n + I hO/:/=2n+ I hkO:h = 211 + I None

49-51 41-50

42-4s

The lattice parameters of the monoclinic and rhombohedral phases are taken from the values proposed by K(ister (Table I) and. therefore. are considerably more accurate than those determined using electron diffraction.

201

KAUFMAN and FRASER: METASTABLE CRYSTALLINE PHASES of previous investigations reveals that Koster was the first to establish correctly the crystal structures of the monoclinic, rhombohedral and hexagonal phases. The discrepancy between the lattice parameters of the monoclinic phase determined by Koster and those identified in the present study is a direct consequence of our space group analysis. As mentioned above, the n-glide using the lattice parameters of Koster must be replaced by a c-glide using our indices in order to concur with the convention established by crystallographers. Otherwise, the unit cells are equivalent. It is of interest to note that the tetragonal phase, reported by Koster (Table 1) to form upon heating initially amorphous films with the electron beam in a microscope, has very similar lattice parameters to the b and c values obtained for the orthorhombic (Pbca) phase identified in the present study. This would seem to imply that the same phase was produced in both studies and that the tetragonal structure determined by Koster was indexed incorrectly. A further disagreement exists between the compositions determined by Koster and those measured in the present study. However, in our analysis, precautions were taken to avoid any problems in the EDXS analyses and, as a result, the composition ranges quoted here should be reasonably close ( f 39,) to the actual values. Closer examination of Table 3 reveals one of the major problems encountered when employing X-rays to characterize the crystal structures of Complex nonequilibrium phases. Except for the hexagonal structure, the other three metastable phases have space groups with many restrictions thereby limiting

Table 4. Summary

of the allowed reflections and d-spacings for the monoclinic and rhombohedral relation of these values IO previously published dam

Present study Rhom. Mono. IOT I10

Ill 200

IO? 100 20f 011 202 2ff 210 211 t12 110 212 020 201 211 212 121

%

213 021 2lT 311 310

considerably the number of allowed reflections and adding to the complexity of such analyses. However. in the present study, it has been demonstrated that microstructural analysis using CBED for crystal structure determination is relatively straightforward and simple. As pornted out by Laridjani er al. [18] and later by Ramachandrarao et al. 1191 and mentioned in the Intr~uction, there is considerable overlap in the interplanar spacings determined in all of the previous investigations of this alloy system, even though the crystal structures identified are at such variance. This observation combined with the present results would seem to imply that only the monoclinic. ThOmbohedral and hexagonal metastable crystalline phases can be produced by quenching from the liquid and that the first two of these most probably account for the metastable phases observed in the various splat quenching studies. Proof of this premise is afforded by tabulating the kinematically allowed reflections for these two phases and comparing these values with the d-spacings determined in the previous experimental investigations (Table 4). As is evident from this table, most of the experimentally determined d-spacings can be accounted for as arising from these two phases. Thus, the other metastable phases reported previously (Table I), as well as the monoclinic phase proposed by Sinha et al. [2]. appear to have been determined incorrectly. The formation of these two phases in rapidly cooled materials in preference to the metastable (hexagonal and orthorhombic) and stable (r-Al and /?-Ge) phases will be discussed in greater detail in Ref. [3].

d..,. 0.5726 0.503 I 0.4402 0.3779 0.3643 0.3583 0.3569 0.3448 0.3366 0.3306 0.3219 0.3154 0.3087 0.3051 0.2914 0.2909 0.2863 0.2800 0.2677 0.2670 0.2516 0.2488 0.2427 0.2406 0.2391 0.2306 0.2303

1111

iI81

3OGe

ll81

6Ge

Previousstudies II81 1131

I191

3OGe+

phases and the

1151

191

0.5728

0.4402

0.4393

0.4393

0.4385

0.3643 0.3583

0.3635 0.3591

0.3636 0.3589

0.3630

0.3451 0.3366 0.3307 0.3221 0.3155

0.3444 0.3360 0.3300 0.3214 0.3150 0.3086 0.3028

0.3444 0.3361 0.3299

0.3465

0.305 I 0.2915

0.291 0.2860 0.2800 0.2677 0.2671 0.2516 0.2486 0.2427 0.2406 0.2391 0.2307

0.2796

0.3299 0.3214 0.3148 0.3029

0.3029 0.291

I

0.3296 0.3215 0.3142 0.303

I

1

0.4396 0.3740 0.3643 0.3579

0.4399 0.3982

0.3447 0.3374 0.3310 0.3223 0.3122

0.3484

0.3062 0.2917

0.3589

0.3299 0.3215 0.3153 0.3089 0.3049 0.29 I3 0.2859 0.2796

0.2675 0.2670

0.2669 0.2514

0.2513 0.2423 0.2406 0.2391

0.2425 0.2406 0.2391 0.2303

0.2302

0.2303

0.2664 0.2584 0.2509 0.2432

0.2669 0.2649 0.2515 0.2487 0.2427

0.3026

0.2802 0.2653

0.241

0.2410 0.2339 0.2300

0.3225 0.3130

0.2892

0.2906 0.2792

0.2792

0.4367 0.3987

0.2384 0.2313

0.2385 0.2305 0.2303

i

202

KAUFMAN and FRASER:

Presentstudy Khom. Mono. 222

122 I20

302 222 ST2 002 312 313 012 3oa UT 320 ;z 322 22T 222

I13 IlT

303 314 401 400 4TT ::: 313 321 204 4lT 200 402 410 323 031 4r5 214 022 412 210 130 323 z 411

422

123 12T 324

332 32:! 421

403

414

g 413 233

421

::i: 220 413

42J 31T 423 333 424

d,, 0.2282 0.2273 0.2258 0.2233 0.2201 0.2164 0.2141 0.2120 0.2094 0.2OoQ 0.2003 0.2002 0.1983 0.1973 0.1967 0.1956 0.1948 0.1946 0.1934 0.1916 0.1909 0.1894 0.1891 0.1890 0.1878 0.1869 0.1&i 0.1851 0.1842 0.1821 0.1794 0.1792 0.1785 0.1780 0.1777 0.1767 0.1761 0.1738 0.1724 0.1714 0.1712 0.1706 0.1704 0.1683 O.IMIO 0.1677 0.1676 0.1664 0.1653 0.1650 0.1641 0.1633 0.1630 0.1617 0.1615 0.1609 0.158% o.is77 O,lS70 O.lS69 O.lSSQ 0.1544 0.1526 0.1524 O.ISO4 O.lSOO 0.1484 0.1470 0.1467 0.1457

IllI

0.2274

METASTABLE CRYSTALLINE

PHASES

Previousstudies

WI

3cGe

[ISI

6Gc

Ilf4

3oGet

if31

1191

0.2274

0.2273

1151

IQ1

0.2268 0.2227

0.2166 0.2141

0.2164 0.2140

0.2oQ3

0.20% 0.2009

0.2140

0.2186 0.2145

0.2095

0.2174 O.tlSI 0.2107 0.2041 0.201s

0.2009 0.1996

0.2002

0.2207 0.2163 0.2140 0.2116 0.2108 0.2083

0.2169 0.2125

0.1999 0.1979

0.1973 0.1967

0.1970 0.1965

0.1970 O.I%S

0.1948

0.1947

0.1947

0.193s

0.1933 0.1915 0.1908

0.1939

0.1909

0.1933 0.1915 0.1908

0.1890 0.1876

0.1890 0.187s

O.lBQO

0.188s

0.1878 0.1865

0.1865

0.1966

0.1968 0.1958

0.1960

0.1945

0.1909 0.1895 0.1892

0.186s

0.1905

0.1936 0.1915 0.1902

0.1906

0.1876

0.1890 0.1875

O.ISS8

0.1g57 0.I849

0.1842

0.1840

0.1793 0.1792

0.1841 0.1822 0.1792

0.1792

0.1780 0.1777 0.1767 0.1761 0.1738

0.1776 0.1767 0.1759 0.1737

0.1776 0.1766

0.1841

0.1839

0.1802

0.1793

0.1792

0.1777

0.1778

0.1748

0.1759 0.1737

0.1777 0.1767 0.1758 0.1738

0.1840 0.1821 0.1791

0.1759 0.1738

0.1736

0.1710 0.1708

0.1708

0.1708 0.1699 0.1693

O.lMiO

0.1681

0.1653

0.1676 0.1663 0.1652

0.1678

0.1678

0.1675

0.1676 0.1663 0.1658

0.1652

0.1653 0.1649 0.1639 0.1628

0.1610

0.1607

0.1607

0.1611

0.1607

0.1604

0.1577

0.1575

O.ISfS

0.1574

0.1574

O.lS72

O.IS40

O.lS40

0.1519

O.lSlQ

0.1521

O.ISO2 0.1483 0.1466 0.1458

0.1556

0.1518 O.lSOl 0.112

0.1467

0.1519

0.151s

0.1483 0.1469

0.14S8

Note the considmbk overkp in the ruportaitits of the diITerent studies. The value cakukted are based on the lattice pnrumcten givenby Kortcr(Tsbk I).It ispossible thatthem purumeten mightchange withcompositionand should be in:erpreted carefully. tHutal to 52OK in I diierentiel scanningcalorimeter [I7].

KAUFMAN

and FRASER:

METASTABLE

SUMMARY

Metastable alloy phases have been produced in AI-Ge alloys by either melt spinning alloys or rapidly heating initially amorphous films. Four such nonequilibrium crystalline phases have been identified and characterized using analytical electron microscopy and compared to earlier investigations in order to resolve the controversy which has existed over proper phase identification in this alloy system. These phases are tabulated in Table 3. It has been demonstrated that the CBED technique is an extremely valuable tool for characterizing the crystal structures of unknown nonequilib~um phases produced by novel processing techniques, especially when combined with quantitative EDXS methods to determine the composition ranges of such phases. Acknow~ledgements-This work was sponsored by the U.S. Department of Energy, Division of Materials Science, under contraet No. DE AC02 76EROll98. The electron microscopy studies were performed in the Center for Microanatysis of Materials in the Materials Research Laboratory at the University of Illinois. REFERENCES I. 3. C. Giessen. Proc. brd InI. Conf. on Rapid@ Quenched Metals (edited by N. 1. Grant and 8. C. Giessen). p. 119. MIT Press. Cambridge, MA (1976). 2. A. K. Sinha. B. C. Giessen and D. E. Polk. Frearise on Sold Slale bhemisrry III (edited by N. B. Hannay). p. I. Plenum Press, New York (I 976). 3. M. J. Kaufman and H. L. Fraser. In?. J. Rapid Solid@curion.

1, 27 (3984-85). III, Phase Diagrams,

4. T. P. Seward

Marerials

Science and

(edited by A. M. Alper). p. 295. Academic Press, New York (I 970). 5. J. H. Perepezko and W. J. Boettinger, Murer. Res. Sot. Symp. on Alloy Phase Diagrams (edited by L. H. Bennett, T. B. Massalski and B. C. G&en), Vol. 19. p. 223. Elsevier, Nosh-Holland (1983). Technology.

f

CRYSTALLINE

203

PHASES

6. J. L. Murray ibid. p. 249. 7. J. L. Murray. Metal/. Trans. HA, 261 (1984). 8. P. Predecki. B. C. Giessen and N. J. Grant. T.M.S.-A.I.M.E.

233,

Trans.

1438 (1965).

9. A. K. Kushnereva and I. V. Salli. IX. Akad. hbuk SSSR, Nears. Mafer. 6. 1867 (1970). IO C. Suryanarayana and T. R. Anantharaman. J. Marer. sci. 5, 992 ( 1970). II U. Koster, Z. Metallk. 63. 472 (1972). 12 U. Kdster. &a merall. 20, 1361 (1972). 13 P. Ramachandrarao, M. G. Scott and G. A. Chadwick. Phil. Mag. 5, 961 (I 972). I4 C. Suryanarayana and T. K. Anantharaman. Z. Merall&. 64, 800 (1973).

B. Predel and G. Schluckebier, Z. Meralik. (1972). 16 M. G. Scott. Z. Metallk. 65, 563 (1974). 17 M. Laridjani and R. W. Chan. Marer. Sci. I5

63,

198

Enann .r I 23.

125 (1976).

18, M. Laridjani, K. D. Krishnanand and R. W. Cahn. J. Mawr. Sri. 11, 1643 (1976). 19. P. Ramachandrarao. L. Lai. A. Singhdeo and K. Chattopadhyay. Mater. Sri. Engng 41, 259 (1979). 20. B. F. Buxton. J. A. Eades. J. W. Steeds and G. M. Rackham, Phil. Trans. R. Sot.. Land. A2%1, 171 ( 1976). 21. 1. W. Steeds, inrroducrion IO Analyfical Electron Microscopy (edited by J. J. Hren. J. I. Goldstein and D. C. Joy), p. 387. Plenum Press. New York (1979~. 22. M. E. Twigg and H. 1. Fraser. SEM. In press. 23. N. J. Zaluzec, Ref. 21, p. 121. 24. J. I. Goldstein, ibid. p. 83. 25, J. GJonnes and A. F. Moodie. Acra cryrallogr. 19, 65 (1965). 26. J. W. Steeds, G. M. Rackham and M. D. Shannon. Elecvon Drrracrion 1927-1977. Inr. Co@ on Electron Diffracrion. London, 1977 (hsl. Phys. CoqY Ser. No. 41; 0305-2346) (edited by P. J. Dobson, J. B. Pendry

and C. J. Humphreys). p, 135. Inst. of Physics. Bristol (1978). 27. M. J. Buerger. inrroducrion to Crysral Geometry. p. 123. McGraw-Hill. New York t 1971). Tables ,for X:ray ~r~,s~allograph~ (edited 28. Internationul by N. F. M. Henry and K. Lonsdale) Vol. 1. Kynoch Press. Bi~ingham. England f 1965). 29. M. J. Kaufman and H. 1. Fraser. Morer. Sri. Engnn 57, Ll? (1983).