The crystallization temperature of amorphous transition-metal alloys

The crystallization temperature of amorphous transition-metal alloys

Volume 9, number MATERIALS I2 .August 1990 LETTERS THE CRYSTALLIZATION TEMPERATURE OF AMORPHOUS TRANSITION-METAL ALLOYS R. DE REUS and F.W. SARIS...

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Volume 9, number

MATERIALS

I2

.August 1990

LETTERS

THE CRYSTALLIZATION TEMPERATURE OF AMORPHOUS TRANSITION-METAL ALLOYS R. DE REUS and F.W. SARIS FOM-Institute for Atomic and Molecular Received

15 March

Physics, Kruislaan

407, 1098 SJAmsterdam,

The Netherlands

1990; in final form 17 May 1990

Comparison of the formation enthalpy of the amorphous phase (AW’“) to the formation enthalpy of simple solid solutions (AW”) shows that diffusionless polymorphic crystallization occurs at low temperatures if AWm > AH”‘. In the composition range where AHBm
The unique properties of amorphous materials make them useful for a variety of applications. Because of their high wear and corrosion resistance amorphous alloys are used as protective coatings. Specific magnetic and optical properties are used in magnetic and optical recording. The absence of grain boundaries, which act as fast diffusion paths at moderate temperatures, makes amorphous alloys almost ideal diffusion barriers in IC technology. Also, new materials can be formed with amorphous phases as a starting point. However, an amorphous phase is metastable. A key parameter characterizing the stability of amorphous alloys is the crystallization temperature ( TX). In the recent past the description of general trends in the behavior of TXhas received considerable interest. For binary alloys it has been shown by Buschow [ 1 ] that the heat of compound formation and TX do not correlate, whereas the formation enthalpy of holes the size of the smaller constituent AHVsma,,and TXdo correlate. The background of Buschow’s model is that crystallization occurs when the smaller constituent of the alloy becomes mobile. This happens at a temperature TX, which is proportional to the activation energy for the diffusion process, represented by AH V.fn.11. Barbour et al. [ 21 have pointed out that Buschow’s model is in contradiction with observa0167-577x/90/$

03.50 0 Elsevier Science Publishers

B.V.

tions of solid-state amorphization reactions, in which an amorphous phase forms by diffusion of I he smaller constituent. Apparently, crystallization via a diffusion-controlled process requires mobility of both constituents. Therefore, Barbour et al. [ 21 modified Buschow’s model and correlated TX with the formation enthalpy of holes the size of the larger constituent (ivI,,, ). Clearly, if crystallization occurs via a polymorphic transition long-range diffusion is not required and much lower values for TX are found [ 31. Using Miedema’s macroscopic atom approach [ 4 1, Loeff et al. [ 5 ] calculated formation enthalpies of random amorphous alloys (AH”“) and crystalline solid solutions (AH”). They showed a tendency towards high crystallization temperatures, according to Buschow’s model [ 11, for the composition range in which the Gibbs free energy of the amorphous phase is lower than the Gibbs free energy of the solid solution, approximated by AH’“” and AHss, respectively. For the composition range in which AHran
( North-Holland

)

487

Volume 9, number 12

MATERIALS LETTERS

more atomic distances) and relatively high values of TX are expected. For the composition range in which AH’“” > AH”“, polymorphic transitions are possible and TX will be low. The same model was applied by van der Kolk et al. [ 61 to predict the glass-forming range for a number of systems. In their calculations of AH’“” Loeff et al. [5] treated the amorphous alloy as a statistically disordered system, whereas Weeber [ 71 showed that a certain degree of chemical short-range order should be taken into account. The heat of formation of the amorphous phase (APm) calculated according to Weeber [ 71, in some cases differs substantially from AH”“. Therefore, when predicting the glass-forming range based on the Miedema model, one should compare AH”” to AH”” rather than to AH’““. In the case AH”” < AH’“, crystallization will occur through long-range diffusion and TX is predicted by the Barbour approach [ 2 1. In this paper we will first show how AH”” and AH”” are calculated. Then TX will be correlated to AHYlaac in the amorphous alloy, assuming the same degree of chemical short-range order as in the calculation of AH”“. Let us start to point out how the different heats of formation are calculated in the Miedema model [ 46]. The formation enthalpy of the amorphous alloy is calculated by AH”” = AHchem + O.O035r,,, (kJ/mole)

,

(1)

in which Tm is the averaged melting temperature of the solids (in Kelvin). The term comprising T,,, reflects the disordered nature of the amorphous phase and compares with the heat of fusion for liquids. The chemical contribution (mchem) for a binary alloy A,B, _-x is determined by AHchem=xftAHSO’(Ain

B) ,

(2)

in which x is the fraction of A atoms, fg the degree to which A atoms are surrounded by B atoms, and AHsol(A in B) the solution enthalpy of A in B (tabulated in ref. [ 41). In regular liquids or solid solutions fg is given by

fki=G,

(3)

where cf, represents the surface concentration atoms and is defined by cs, = (1 -x)

488

V;‘3/[xV;‘3+

(1 -x)

Vi’31 )

of B

(4)

August 1990

where VA and V, are the molar volumes of pure A and B, respectively. Using eq. (3) for fg, one obtains AEP”. However, to calculate AH”“, one should not use fi as given in eq. (3) but the following calculation of ft recommended by Weeber [ 7 ] : j-g=c&[

1+5(cftci)*]

.

(5)

The formation enthalpy of the solid solution prises three contributions and is given by ~SS =

mchem

_+ &pastic

+

~structural

.

com-

(6)

The first term (APhem ) is given by eq. (2) in which (4) and ( 5 ) are substituted, assuming that the same degree of chemical short-range order is present as in the amorphous phase. The elastic contribution of the ( AHelastic ) arises from the size mismatch constituents, which occupy equivalent lattice sites in the solid solution. The structural contribution ( AHstructura’) reflects the energy associated with the simple hcp, fee, and bee crystal structures and is determined as a function of the average number of valence electrons of the metal alloys. Both AHelastic and APtlUCtUra’ are described in detail elsewhere [ 4-61. Hole formation enthalpies in the amorphous alloy can be calculated in the Miedema model [4] according to AH”,::=(l

-fi:)~~"+f~(vA/v~)5/6M:: (7)

for holes the size of A atoms. AHfv and AH:: are the monovacancy formation enthalpies for pure A and B, respectively. For fg one should use eq. (5). To obtain formation enthalpies of holes the size of B atoms the indices A and B should be interchanged. In the following we will evaluate the Re-W system as an example using the calculations described above. In the middle part of fig. 1 crystallization temperatures (TX) are given measured as a function of composition. The data are from Collver and Hammond [ 8 ] (circles) and from Denier van der Gon et al. [ 3 ] (squares). Also indicated are the crystalline phases observed directly after crystallization [ 3 1. A strong composition dependence is observed. The W-rich alloys crystallize by a polymorphic transition into a bee solid solution of W (Re) at relatively low temperatures. The Re-rich alloys show similar behavior and the crystalline phase observed is a hexagonal Re( W) solid solution. The alloys with a composition around 60 at.% Re crystallize into the complicated o phase

Volume 9, number

MATERIALS

12

bee

.

0 3800

G t1800 atomic

% Re

100

Re

Fig. 1. Top: calculated formation enthalpies for the amorphous phase (AH”“), the random alloy (AH”“), and the bee and hexagonal solid solutions (AH”“) in the Re-W system as described in the text. Middle: crystallization temperatures for various amorphous Re-W alloys. Data are taken from ref. [ 31 (squares) and ref. [ 81 (circles). Also indicated are the crystalline phases detected after crystallization. The arrow indicates that the Re,,W,, alloy was crystalline at room temperature, which is taken as an upper limit of TX. Bottom: phase diagram of the Re-W system (afterref. [9]).

and exhibit the highest values for TX. Comparison with the phase diagram (bottom part of fig. 1, after ref. [ 91) shows that also an equilibrium x phase exists, which is not observed in the present experiments, even though one of the amorphous alloys has the exact stoichiometry. In all cases crystallization resulted in a single-phase material, irrespective of whether the composition was in a single- or a twophase region of the phase diagram. We now compare the formation enthalpy of the amorphous phase (AH”” ) to the formation enthalpy of the solid solution (AH”“). The values AH”” for the amorphous phase, and AH”” for the bee solid solution W( Re) and the hexagonal solid solution Re( W), were calculated as a function of composition using relationships ( 1 ), ( 5), and (6). The results are depicted in the top part of fig. 1. In the re-

LETTERS

4ugust

1990

gions where AH”” is lower in energy than AH”” diffusionless crystallization is possible. Indeed, these are the regions where TX is low and crystallization was observed into single-phase solid solutions. In the composition range where AH””
Volume 9, number

I2

MATERIALS

LETTERS

August

1990

Table I Alphabetical list of several binary transition-metal alloys and the highest crystallization temperature reported for each system as well as heats of formation calculated as described in the text. The systems for which an upper limit of TXis given are crystalline as prepared. For details the reader is referred to the text and the references quoted. Tis in Kelvin and AH values arc in kJ/molc System

Large element

IX

7

7

Au Au La

7 21 I2 I4 -41

25 I3 I6 -45

25 I6 I8 -34

1101 IlO1 1121 111

148 I50 I54 123 199

Au Au Zr cu Hf

I3 -38 -60 12 -24

I5 -49 -75 I4 -31

I9 -55 -75 9 -20

I131 1141 [lOI [I21

189 190 212 176 215

205 186 209 I81 205

La MO Ta Ti W

-II

-15

-I

642 833 i 350 < 300 1350

172 221 108 129 140

180 225 III 132 142

Cul,,Ta80 C~MTI,S

920 831 280 1070 700

154 173 167 212 I41

Cu‘MVw, CboW,o Cu90ZrIo Fe,oHf,, Fe&o,”

280 450 877 866 870

Fe,OPt,o Fe,,Ti,, Fe50W,, Fc~oYw Fe&r, 3

Audi50 .Au,JTi,s Auj5Zr63 Co&r,0 CowHfb” Co,OLa,o CowMow C%Ta,o CoTsTi,,

360 < 300 470 813 453

I IO 128 164 I50 130

II6 139 I79 165 131

Al3

<300 670 820 < 300 823

137 140 I56 II8 196

473 1170 II20 873 1070

Ag

1121

[lOI

1121 [13,151

3

2

7

8

-22 - 19 7

-9 - 19 I3

[I51 III [I61

Y Zr cu Cr Pd

-13 -II 19 0 -8

-16 - 13 23 -2 -12

7 - 12 I8 -II -20

[I21 [I21 (171 I181 1191

I56 I71 157 210 139

Ti Hf

-3 -16 32 II -5

-3

Ta Ti

0 -II 26 II -3

I201 [I21 I211 1111 1221

138 196 168 196 183

132 179 168 199 179

V W Zr Hf MO

I1 31 -5 -II 6

I3 38 -5 -16 5

9 37 -I - IO 6

121 I Ill.121

< 300 930 II50 741 882

168 170 218 186 218

170 177 208 201 224

Pt Ti W Y Zr

-6 -10 IO 5 -6

-10 -I5

- I8 -10 15 25 -3

1251 WI 1121 1121 I23271

Hfd’h HLV,, Ir,J% h5Ta5, Ir25W75

923 808 1133 1283 < 350

201 200 202 224 240

208 206 208 223 238

Hf Hf Nb Ta W

-34

-46

-33 13 -60 -49 4

[ W81

hpNi3, MoPJbw Mo,oNl,o MeoReo MomRh,s

443 75 900 I020 155

I57 189 187 224 197

160 189 183 230 197

La Nb MO MO MO

-8 -3 -2

111 [81 II31 [81 1121

Co5sW,, Co4oYt.0 CowZr,o Cr,0Cu50

Cr4,Ni,, Crd’dso CrSOT150 Cud% hoMo~o

490

MO

-15 -15

9 5 -8

6 -43 -41 0 -14

5 -60 -56 -2 -16

8 I 6 I

8 -2 4 0

0 32 7 -4

4 0

1231 1121 1241

III 1121 1291 [301

Volume 9, number

MATERIALS

12

August

LETTERS

1990

Table 1. Continued Large element

System

AH””

AH”

-5

-9

-8

Ref.

800 910 920 850 1093

201 183 187 169 190

201 183 187 164 192

MO Zr Nb Nb Nb

-22 -45 -36

-32 -61 -49

-27 -69 -49

[12.13]

150

195 213 166 228 158

203 210 171 223 161

Zr Ta Ti W Y

12 -19 -28 8 -17

14 -26 -39 7 -19

12 -15 -38 12

I81 [15,18]

-41 -26

-55 -37

-42 -36

-40 -58

-54 -78

-54 -85

-28 -68

-39 -91 -1 -66 -12

-49 -98

1020 822 920 591 886 1220 1220 1050 750

200 234 244 198 149

209 237 243 191 148

Zr Ta W Ta Ti

570 720 1070 768 1220

152 159 236 180 247

158 162 234 181 252

Pd Ti Pt Zr Ta

1070 1118 758 450 1070

245 214 188 181 236

244 211 191 190 233

W Ta Zr Ti W

670 210 870 1170

191 251 196 226

194 259 204 240

Zr Ta Zr Zr

a) 350 A thick amorphous Pt-W alloys were coevaporated by transmission electron microscopy after isochronal alloys with a composition between 77 at.% W and 82 occurred into a mixture of fee W and an unidentified b, As a). Amorphous V,,ZrSO crystallized at 600°C into

,

5

4

0 -59 -8

7

3 -33

-1

8

3

[311 (361 a) [II [301

4 -41 -59 -57

0

7

3 3

-26 -12 II 0

-38 5 4 1

(321 [331 [341 [?21 [301 [301 [311 1351

-75 -18

-47 -59 -49

[81 [311 [I21

I

3

8 -34 -50 -35

(8,131 6

5

[31 [I21 [II [371 [31 [371 [81 [381b' [331

in the composition range between 75 at.% W and 82 at.% W. TXwas determined annealing for 15 min in a vacuum better than I X lo-’ mbar. TX was 800°C for at.% W. Amorphous Ptz4W,, crystallized at 775°C. For all alloys crystallization bee phase with lattice parameter a = 6.85 ( 15 ) A. an unidentified phase.

symbols represent systems for which AHam> AH”“. The arrows indicate alloys which were crystalline as prepared. For the alloys which are believed to crystallize via diffusion, i.e. the alloys for which AHam < AH”” (tilled symbols), the relationship found between TX and AH?!, is T, = 4.7M%,,,

AH’“”

(8)

in which TX is given in Kelvin and AHa;lme in k_I/ mole. This relationship is indicated by the solid line in fig. 2. A few exceptions seem to be encountered when AH””
alloys for which TX can be predicted using relationship (8 ). However, for most of these systems the differences AH”” - AH”” do not exceed the error limit of 4 kJ/mole. This is illustrated, e.g., by amorphous Au&o,~, which crystallized into a single-phase solid solution [ lo], and a AusoNiso alloy, prepared at LN2 temperature, which appeared to be a solid solution instead of an amorphous phase [ lo]. Apparently, for these alloys AH”” - AHSS> 0, whereas a negative value was calculated (see table 1). In fig. 2 a few open symbols, which belong to systems with AH”” > AH”“, still show high TX.Also, for these systems the dif491

Volume 9, number 12

MATERIALS LETTERS

August 1990

the thermal stability of amorphous alloys in the range of compositions not yet measured.

AH,&

The authors would like to thank R.J.I.M. Koper, G.P.A. Frijlink, and H. Zeijlemaker for their assistance with the deposition of the V-Zr and Pt-W alloys. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on Matter) and was financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organization for Scientific Research) and the Stichting Technische Wetenschappen (Netherlands Technology Foundation ).

(kJ/mole)

Fig. 2. Crystallization temperatures (T,) versus formation enthalpy of holes the size of the larger constituent (M$E_) for the amorphous alloys compiled in table 1. Closed symbols represent systems for which AH”” - AH” < 0 kJ/mole. Open symbols represent systems for which AH”” -AH”> 0 kJ/mole. Systems indicated with arrows were crystalline as prepared and the preparation temperature is given as an upper limit for T,. The line T,=4.?AH;y_ gives a rough estimate of T, for the systems represented by almost all closed symbols, i.e. for systems which are expected to crystallize via diffusion.

are less than the error limit. ferences AH”” -AH” For instance, the Re-W system, as discussed above, or amorphous CuzoTaso, which crystallizes into Cu and /3-Ta at 1070 K by phase separation [ 111. This requires diffusion and relationship ( 8 ) applies. The proportionality constant 4.7 in relationship (8 ) appears slightly larger than the value of 4.2 determined by Barbour et al. [ 2 1. The difference between the proportionality constants does not arise from the fact that in Barbour’s model AHE*= was because the difference beused instead of AH;!+ tween AHKme and m$!‘_

is relatively

small, as can

be seen in table 1. The major difference is that in our least-squares determination of the proportionality constant each system is only included once, whereas in Barbour’s case systems exhibiting positive heats of formation were excluded and, moreover, several systems were included many times for various compositions. From the deviations between the measured values of TX and the values predicted by relationship (8) it is clear that only an indication of TXcan be given this way. Yet, this may still be useful in order to predict 492

References [ 1] K.H.J. Buschow, Solid State Commun. 43 ( 1982) 171. (21 J.C. Barbour, R. de Reus, A.W. Denier van der Gon and F.W. Saris, J. Mater. Res. 2 (1987) 168. [3] A.W. Denier van der Gon, J.C. Barbour, R. de Reus and F.W. Saris, J. Appl. Phys. 61 (1987) 1212. [4]F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema and A.K. Niessen, in: Cohesion in metals, eds. F.R. de Boer and D. Pettifor (North-Holland, Amsterdam, 1988). [ 5] PI. Loeff, A.W. Weeber and A.R. Miedema, J. LessCommon Met. 140 (1988) 299. [6] G.J. van der Kolk, A.R. Miedema and A.K. Niessen, J. LessCommon Met. 145 (1988) 1. [ 71 A.W. Weeber, J. Phys. F 17 (1987) 809. [ 81 M.M. Collver and R.H. Hammond, J. Appl. Phys. 49 ( 1978) 2420. [ 91 T.B. Massalski, ed., Binary alloy phase diagrams (American Society for Metals, Metals Park, 1986). [lo] J.W. Mayer, B.Y. Tsaur, S.S. Lau and L.S. Hung, Nucl. Instr. Methods 182/183 (1981) 1. [ 111 M. Nastasi, F.W. Saris, L.S. Hung and J.W. Mayer, J. Appl. Phys. 58 (1985) 3052. [ 121 R. Wang, Bull. Alloy Phase Diagrams 2 ( 198 1) 269. [ 131 B.-X. Liu, W.L. Johnson, M.-A. Nicolet and S.S. Lau, Nucl. Instr. Methods 209/2 10 ( 1983) 229. [ 141 R. de Reus, A.M. Vredenberg, A.C. Voorrips, H.C. Tissink and F.W. Saris, Nucl. Instr. Methods B, submitted for publication. [ 15 ] L.S. Hung, F.W. Saris, S.Q. Wang and J. W. Mayer, J. Appl. Phys. 59 (1986) 2416. [ 161 S.Q. Wang, L.H. Allen and J.W. Mayer, in: Tungsten and other refractory metals for VLSI applications, Vol. 4, eds. R.S. Blewer and CM. McConica (MRS, Pittsburgh, 1989) p. 269. [ 171 SM. Shin, M.A. Ray, J.M. Rigsbee and J.E. Greene, Appl. Phys. Letters 43 (1983) 249.

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[IX] L.S. Hung. S.Q. Wang, J.W. Mayer and F.W. Saris. MRS Symp. Proc. 54 ( 1985) 159.

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593.

(24

L.J. Huang. Q.M. Chen. B.-X. Liu. Y.D. Fan and H.-D. Li, MRS Symp. Proc. 128 (1989) 225.

[25

G. Battaglin. S. LoRusso. P. Mazzoldi and D.K. Sood. presented at the CODEST Conference on Investigation and Application of Metastablc Materials, Groningen. The Netherlands. July 7-l I. 1986.

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[ 271 Z. Altounian, E. Batalla and J.O. Strom-Olsen. 1. Appl. Phys. 59 (1986) 2364. [ ZS] K.H.J. Buschow, J. Non-Cryst. Solids 68 ( 1984) 43. [ 29) S. Davis. M. Fischer. B.C. Gicsscn and D.E. Polk, in: Rapidly quenched metals Ill. Vol. 2. cd. B. Cantor (Chameleon Press. London, I978 ) p. 425. [30 G.J. van der Kolk. J. Mater. Kes. 3 ( 1988) 209. 131 G.J. van der Kolk. T. Mincmura and J.J. \an der Broek. J. Mater. Sci. 24 ( 1989) 1895. K.H.J. Buschow. J. Phys. F I3 (1983) 563. M.F. Zhu. F.C.T. So. ET.-S. Pan and M.-A. Nicolct. Phys. I:: Stat. Sol. 86 ( 1984) 47 I. 134 C. Colinet. A. Pasture1 and K.H.J. Buschow. J. Appl. Phys. 62 (1987) 3712. 135 J.R. Thompson and C. Polrtis. Europhys. Letters 3 ( 1987 I 199. I36 L.S. Hung and J.W. Mayer. J. Appl. Phys. 60 ( 1986) 1002. [37 Y.-T. Cheng. W.L. Johnson and M.-A. Nicolet. MRS Symp. Proc. 37 (1985) 365. [ 381 A.W. Weeber and H. Bakker. in: Proceedings of the 6th International Conference on Liquid and Amorphous Metals, Vol. 2. eds. W. Gliser, F. Hensel and E. L&her (Oldenburg, Munich, 1987) p. 221.

U. Scheuer, L.E. Rehn and P. Baldo, MRS Symp. Proc. I28 (1989) 213.

493