Electronic properties and atomic structure of (Ti, Zr, Hf)(Ni, Cu) metallic glasses

JOURNAl,

O l ~"

lllRR l,I lm ELSEVIER

Journal of Non-Crystalline Solids 180 (1995) 131-150

Electronic properties and atomic structure of (Ti, Zr, Hf) -(Ni, Cu) metallic glasses Imre Bakonyi * Research Institutefor Solid State Physics, HungarianAcademy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary Received 11 January 1994; revised manuscript received 16 February 1994

Abstract

The available experimental and theoretical data on the electronic density of states at the Fermi level, n(EF), of non-magnetic melt-quenched TEloo_xTLx amorphous alloys (TE = Ti, Zr or Hf; TL = Ni or Cu) and for the corresponding crystalline counterparts is reviewed. First, the low-temperature specific heat and superconductive data are summarized, in order to derive experimental n(EF) values. A comparison with n(EF) data from theoretical band structure calculations shows good overall agreement, both qualitative and quantitative. By taking into account recent results on the n(E F) of different structural modifications of Ti, Zr and I-If metals, an extrapolation of the composition dependence of n(E F) in TE-TL glasses to pure amorphous TE metals suggests that the local structure of these TE-TL amorphous alloys may be described by an fcc-like atomic arrangement. Some other reported results, which supply further evidence for the proposed fcc-like local structure in this type of metallic glass, are also discussed.

I. Introduction

Alloys of early transition metals (TE) with late transition metals (TL) such as Zr-Ni or Ti-Cu constitute a large class of metallic glasses. The composition range for the formation of the amorphous state by rapid quenching from the melt is usually fairly wide. In favourable cases it spans from 20 to 70 at.% of the TL component and, for a few systems, it even includes the eutectic around 90 at.% TL concentration [1]. There has been much research on these alloys in recent decades [2-4], partially because of the ability of such metallic glasses to dissolve a

* Corresponding author. Tel: + 36-1 169 9499. Telefax: + 36-1 169 5380.

significant amount of hydrogen due to the presence of the good H-absorbing TE components [5]. In the metal-metalloid type of glasses, e.g., F e - B or Ni-P, which are usually obtainable in a much narrower composition range, fairly strong chemical and topological short-range order (CSRO and TSRO, respectively) could be established [6]. This probably results from the nature of the strongly covalent bonds attributable to the presence of metalloid atoms. This SRO in the amorphous state was found, in most cases, to be similar to that of the compositionally related stoichiometric crystalline phases [7,8]. Also, in non-magnetic alloys of this type (e.g., Ni-B), the lack of long-range order did not seem to influence appreciably the average electronic density of states, n(EF), at the Fermi level, on the evidence of measurements of bulk parameters such as the electronic specific heat [9] or the Pauli susceptibility [10].

0022-3093/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved

SSDI 0 0 2 2 - 3 0 9 3 ( 9 4 ) 0 0 4 7 2 - 2

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L Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150

On the other hand, it has been found from diffraction studies and theoretical band structure calculations that the degree of SRO is weaker in T E - T L type glasses than in metal-metalloid type amorphous alloys. It may vary strongly from one alloy system to another or with alloy composition for a given alloy system [11]: the TE-rich alloys seem to show almost no CSRO whereas, depending on the alloy constituents, the CSRO may increase significantly with increasing concentration of the TL component. Since the bonding between TE and TL atoms is of metallic character, i.e., it is fairly isotropic, less constraint is imposed on the local symmetry of the atomic arrangements. Therefore, several topologically different (stable or unstable) configurations can occur for a given alloy composition. One should come to this conclusion at least when considering the experimental values of the parameters which involve the electronic density of states at the Fermi level, n(EF), and taking into account the sensitivity of n(E v) to the atomic structure as suggested by the recent analysis of experimental and theoretical data for different structural modifications of the TE metals, Ti, Zr and Hf [12]. The purpose of this work is to perform a similar analysis for the T E - T L type amorphous alloys in an effort to achieve a better understanding of their atomic structure and electronic properties. The contents of this paper are as follows. In Section 2, available data on the low-temperature specific heat (LTSH) and superconductive (SC) parameters are summarized, in order to obtain experimental values of n(E F) and to establish its composition dependence. Then the results of available theoretical band structure calculations are discussed in Section 3, with the main emphasis on n(E F) which is compared with the experimentally derived values of Section 2; the results of available relevant photoemission experiments are also briefly mentioned. Finally, a suggestion is made in Section 4 for an fcc-like local structure of these T E - T L metallic glasses, deduced from the present analysis concerning n(Er) and related parameters. This proposed structure will be contrasted with the results of experimental studies of the atomic structure and other properties in these systems. We also discuss the results of recent experimental and theoretical evidence further pointing to the possibility of de-

scribing the local structure by the proposed fcc-like atomic arrangement. In Section 5, a brief summary of the work described in this paper is given. Where appropriate, reference will also be made to the corresponding stoichiometric crystalline phases and to the pure TE metals. In this work, we shall be mainly concerned with amorphous alloys of Ti, Zr and Hf with the TL metals Ni and Cu and restrict ourselves mostly to TL concentrations < 70 at.%. Since all these alloys are Pauli paramagnets and many of them are superconductors, the LTSH and SC data can be evaluated without complications due to magnetic ordering as would be the case for TE-Fe and T E - C o alloys. A further motivation for the choice of the above alloys is that a vast amount of experimental and theoretical data on their structure and properties is available.

2. Evaluation of n(E F) from LTSH and SC measurements It has been well established previously for the metallic glasses discussed in this paper that for temperatures 1 K < T < 10 K, the LTSH can be described by the expression [13] c = 7T+

3.

(1)

Here, the first term is the electronic specific heat contribution with the coefficient 1

2

2

y = 57r kB(1 + Aep + Asf)n(EF),

(2)

and the second term is the contribution due to lattice vibrations with the parameter

= ~4R(TIOD) 3.

(3)

In these expressions, k B is the Boltzmann constant, R is the universal gas constant, O o is the Debye temperature, n(E v) is the electronic density of states (DOS) at the Fermi level and the coefficients Aep and Asf describe the enhancement of Y due to the electron-phonon interaction and spin fluctuations, respectively. To evaluate n(E F) from the measured electronic specific heat coefficient, 7, the enhancement parameters should first be determined. Since the alloy systems of interest here are weakly paramagnetic for the investigated composition ranges, we first neglect

L Bakonyi/JournalofNon-CrystallineSolids180 (1995)131-150 the spin-fluctuation parameter Ase. (Batalla et al. [14] have made a comprehensive analysis and found that /~sf ~ 0.01 for Z r - C u and A.~f< 0.1 for Z r - N i and the neglect of these small values will not qualitatively affect our conclusions.) On the other hand, most of these alloys exhibit a SC transition at a temperature, Tc, which shows up as a jump in the temperature variation of the lowtemperature specific heat. We can apply the theory of McMillan [15] which relates hep to Tc and ~gD: /~ep = [ /[Z* ln(~gD/1.45Tc) +

,

o

5.5

o °'o~

5

^

4 '~ 3.5

~

2

(5)

where n(E F) is in units of states/(eV atom). For transition metals, McMillan [15] found that /z* has values typically between 0.10 and 0.15 and for transition metals it is usually set to 0.13. In our previous work [12] we showed that for Ti, Zr and Hf the band structure calculation results indeed lead to such values of /z* through the application of Eq. (5). However, because of the form of Eq. (4), the actual choice o f / z * influences hep only moderately. An independent estimate of the electronic specific heat coefficient, which will be denoted here by 7sc, can also obtained from the measurement of the slope dHc2/dT of the upper critical field near the superconducting transition temperature through the relation [17] (6)

where M is the molar mass, Pa is the normal state resistivity near Tc, d is the density and A is a numerical factor containing fundamental constants only. This expression has been widely applied for metallic glasses, although it has also been suggested [18] that a more complete theory requires a fit to the temperature dependence of H¢2 over a large temperature range below Tc in order to arrive at a more

o

o

(4) This formula is known to give reliable results as long as the calculated value of hep does not exceed about unity [15]. The parameter, /z*, accounting for the Coulomb repulsion of conduction electrons can be derived from the isotope shift coefficient of Tc [15] or from the empirical formula [16]

•

\,

2.5

/ [ ( 1 - 0.62/z*) In(OD/1.a5T~) -- 1.04].

Ysc = A( M / p , d) [dHc2/dr ]r= rc,

Ti-(Ni Cu)

4.5

Zr-lNi,Cu)

1.04]

/~* = 0.26/[1 + H(EF)-I],

133

MQ a-TE1oo_xTLx 20

30

40

50

60

70

80

x (at.% TL)

Fig. 1. Electronic specific heat coefficient, 7, derived from LTSH measurements(see Eq. (1)) as a function of the TL content, x, in MQ amorphousTi-Ni ( 4, Ref. [19]), Ti-Cu ( ,t, Refs. [20-22]), Zr-Ni (O, Refs. [20,23-27]) and Zr-Cu (O, Refs. [20,28-30]; I , Ref. [31]; 0, Ref. [32]) alloys. The solid lines represent a linear fit to the data as given by Eqs. (7) and (8) (see text for details).

correct value of the electronic specific heat from superconductive data.

2.1. Electronic specific heat data Fig. 1 summarizes the available data on y obtained from reported LTSH measurements on meltquenched (MQ) amorphous paramagnetic T E - T L alloy systems (Ti-Ni, Ti-Cu, Zr-Ni, Zr-Cu) as a function of the composition of the TL component (Ni or Cu). Fig. 1 clearly demonstrates that y decreases approximately linearly with the increase of the TL content and the Ti-based alloys have somewhat higher values of y than the Zr-based alloys, whereas in both cases the values of y seem to be fairly insensitive to the species of the TL component (Ni or Cu). It should be noted, however, that whereas for the Ti-Ni, T i - C u and Z r - N i systems the great majority of the data are claimed to have an error of about _ 1% or even smaller, the data on y of MQ Z r - C u amorphous alloys are specified in most cases to have

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L Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150

an error of typically ___5%. Further, in evaluating the data in Fig. 1, we make the assumption that for the Ti-Cu and Ti-Ni systems the values of 3' should extrapolate to a common value when approaching pure amorphous Ti (a-Ti) and the same is expected for the Zr-based alloys as well. Therefore, we have applied first a linear fit to all the experimental data for the Ti-based alloys which yielded 3,= 6.84 - 0.0518x

[Ti-(Ni, Cu)].

(7)

The constants are in units as applied in Fig. 1 and the fit according to Eq. (7) is drawn as a straight line there through the Ti-Ni and Ti-Cu data. It can be seen that the assumption of a common 3,(a-Ti) value for the Ti-Ni and Ti-Cu systems conforms well with the available data. For the MQ amorphous Zr-Cu and Zr-Ni alloys, the situation does not appear to be so unambiguous (Fig. 1). Especially at low Cu contents, the Zr-Cu data exhibit a large scatter and, apparently, a systematic deviation downwards with respect to the much larger number of Zr-Ni datapoints. This may be partly due to the larger experimental error of the Zr-Cu data mentioned above. Another point to be made is that, in fact, only the y(Zr-Cu) values (symbols • and • in Fig. 1) of Samwer and co-workers [31,32] show a systematic deviation from the y(Zr-Ni) values and from the rest of the y ( Z r Cu) data. At the same time, these authors have also shown for the Zr-Cu system [32] that the thermal prehistory (melt temperature before quenching, annealing after quenching) of Zr-Cu amorphous ribbons may strongly influence the low-temperature specific heat and, therefore, all parameters (y, ~9D and Tc) derived from it. There have been, further, several reports [33] demonstrating that Zr-Cu glasses may undergo irreversible changes even when stored at ambient temperature and atmosphere which can have an influence on the above-mentioned parameters as well. For these reasons, we shall not make use of the 3,(Zr-Cu) data of Refs. [31,32] and we fit a common straight line to the rest of the Zr-Cu data and to all the Zr-Ni data. (This decision about selecting the 3,(Zr-Cu) data will be further justified below when discussing the 3,sc results.) In concord with the 3,(Ti-Cu) and 3,(Ti-Ni) data, this allows us

to get the same average value of y for both the Zr-Ni and Zr-Cu systems by a linear fit yielding y = 6.96 - 0.0681x

[Zr-(Ni, Cu)].

(8)

The common fits for the Ni- and Cu-based alloys are also in accordance with our general knowledge [11] about the electronic structure of TE-TL-type glasses, namely that the DOS at E F is dominated by the contribution of TE (i.e., Ti or Zr) atoms. Evidently, the smaller the TL content, the less should any parameter which reflects the electronic structure be sensitive to whether Ni or Cu is the alloying partner of the TE component. We shall now discuss available Ysc data derived on the basis of Eq. (6) for Zr-(Ni, Cu) metallic glasses. The main source of experimental error in this expression is the magnitude of the resistivity. We shall omit the 3,sc results of those papers in which the resistivity was not derived from density measurements [31,34,35]. Karkut and Hake [36] obtained Pn for Zr-Ni alloys from the measured density and achieved an accuracy of + 10% for Ysc. (They give an error of + 7% for Pn, which is probably due to the fact that they measured the resistance of a short ribbon piece which was only a few centimeters long.) On the other hand, using the same technique and measuring the resistance of a 1 m long uniform ribbon, Altounian and Strom-Olsen [17] obtained the resistivity of MQ Zr-Cu and Zr-Ni glasses with an accuracy of + 1.5%. Further, they also noted that Eq. (6) contains the product Pn d which is equal to R m / L 2, R being the resistance, m the mass and L the length of the ribbon. In this manner, they could determine the quantity pnd to within + 1 % and derived values of Ysc with an uncertainty of about + 1.5%. (Poon [18] argues that even this method may somewhat overestimate Pn if the ribbon crosssection is inhomogeneous along the length.) The Ysc data of Refs. [17,36] are shown in Fig. 2. By considering the larger error for the data of Ref. [36] (symbols /x ), the agreement of Zr-Ni data from the two studies is fairly good. Further, by considering the highly precise results of Altounian and Strom-Olsen [17] which show a linear decrease of 3,sc, one can hardly establish any difference between Zr-Cu and Zr-Ni data. This agreement gives a strong confidence in the omission of the Zr-Cu data of Samwer and co-workers [31,32] in Fig. 1 and

L Bakonyi/Journal of Non-CrystallineSolids 180 (1995) 131-150 6

4.5

-6

4

~

3.5

~_~='"" "'A,.,

LTSH (Fig. 1)

"-.. o

"',

3 2.5 2

a-Ztl00.xlNi,Culx 1.5

. 20

. 30

.

.

. 40

.

. 50

60

70

80

x (at.% TL)

Fig. 2. Electronic specific heat coefficient, 7sc, derived from superconductivitymeasurements(see Eq. (6)) as a functionof the TL content, x, in MQ amorphous Zr-Ni (©, Ref. [17]; a, Ref. [36]) and Zr-Cu (0, Ref. [17]; • , Ref. [37]) alloys. The solid line represents a linear fit to the Zr-Ni and Zr-Cu data of Refs. [17,36] as givenby Eq. (9). The dashed line representsthe average of 3,-valuesobtainedfrom LTSHmeasurementson the same alloy systems and is taken from Fig. 1. Note that the data denotedby the symbols • were derived from He2 versus T measurements over a large temperaturerange below Tc.

fitting the rest of the ~/LTSH data of Zr-(Ni, Cu) glassy alloys to a common straight line also shown in Fig. 2 (dashed line). A linear fit of the 7sc data of Refs. [17,36] gives values "Ysc = 6 . 5 0 - 0.0681x

[Zr-(Ni, Cu)]

(9)

shown by the full line in Fig. 2 which is parallel to the values determined from LTSH measurements (dashed line). Apparently, the application of Eq. (6) leads to systematically lower values of 7sc than the LTSH data. It was argued by Poon [18] that by fitting the Hc2(T) versus T curves to theoretical models yields values of (dHc2/dT)rc and 7sc some 10% higher than by simply drawing a straight line through the He2 data immediately below T¢. He applied this analysis to the He2 versus T data of Samwer and yon Lrhneysen [31] on amorphous Zr-Cu alloys and concluded that there is an enhancement of 7sc over from LTSH by about 20%. However, since, as we have shown above, the LTSH data of Ref. [31]

135

probably underestimate the actual electronic specific heat of these metallic glasses and the resistivity data on these samples are also rather uncertain, the enhancement effect suggested by Poon [18] does not seem to be confirmed by these data. Further, Nordstr/Sm et al. [37] have recently measured He2 versus T for a series of Zr-Cu amorphous alloys and applied the same analysis as suggested by Poon [18]. Since NordstrOm et al. [37] determined both the density and the resistivity of their ribbons and, further, they also considered previously reported p. and d data in order to achieve a best average value for the product pnd, they obtained 3'sc data with an uncertainty of about + 5% and their results are also shown in Fig. 2 (symbols • ) . Most of their datapoints agree within the specified 5% error limit with the 7LTSH values (dashed line). It can be concluded from this comparison that, by taking into account the He2 data over the entire available temperature range below T~, one can arrive at practically the same electronic specific heat values as derived from direct measurements of the LTSH, and the enhancement effects supposed by Poon [18] are not present in these amorphous alloy systems. It should be mentioned, however, that this point could probably be better checked on amorphous Zr-Ni alloys, by measuring Ysc and YLTSH on the same samples, since these alloys are not so susceptible to spontaneous decomposition effects as are the Zr-Cu alloys. Also, all their available 3'sc and )'LTSH data from different sources have been found to be fairly consistent with each other. In Fig. 3, the straight line fits describing the compositional variation of 7 according to Eqs. (7) and (8) in MQ amorphous TE10o_xTLx alloys are shown for all four alloy systems under study. It is noted that the extrapolated amorphous Ti (a-Ti) and Zr (a-Zr) values of "y appear as intermediate ones if we compare them with the pure metal values of 3, in the hcp and in the hypothetical low-temperature bcc phases (the pure metal values [12] are indicated by the arrows on the ordinate of Fig. 3). As to the slope of the 7 versus x plots, it is larger for Zr-based than for Ti-based amorphous alloys. Although LTSH results are available on sputtered Zr-Ni [38] and Zr-Cu [39] as well as mechanically alloyed Zr-Ni [40] amorphous alloys, the reported values of 3' in the as-prepared state were signifi-

I. Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150

136

cantly different from those obtained on the corresponding MQ alloys. Therefore, results on sputtered and mechanically alloyed samples will not be considered here. The experimental values of 3' for the crystalline stoichiometric compounds are also shown in Fig. 3. In most cases, they are fairly close to the Y data for the corresponding amorphous alloys. It should be noted, however, that tiae crystalline Zr2Cu alloy has a much smaller value of Y than the MQ amorphous Zr67Cu33 alloy. This fact can probably be attributed to a strong difference of the atomic structure between the crystalline and amorphous modifications at this composition. On the other hand, the large value of Y for the crystalline ZrNi 5 alloy already indicates a significant change in the electronic band structure around the Fermi level at such a high Ni content and the approach to ferromagnetism.

2.2. Electron-phonon enhancement

"~- "bcc" Hf "<-- "bcc" Zr ~-- "bcc" Ti

TEIOO_xTLx

""%"L-. ':22,.

4

~

"..:-.,o

am. Zr-Ni

3

"'illiiii~. ' ~

am. Zt-Cu /

',, ,,

• e

am. T i - ~

,Lo~

" ~ hcp Zr am. Ti-Cu

~=- hcp TI "~P-hcp Hf ,

The electron-phonon enhancement parameter, Aep , will be evaluated from Eq. (4) with the help of

"bcc"

Zr

"bcc" Ti

~Z am. Ti-(Ni,Cu)

hcp Ti

p-

am. Zr-~i,Cu)

o

~-~ hcp Zr "~- hcp Hf

o

o

TEIO0-xTLx

O

10

20

30

40

50

60

70

80

o

r

,

lO

20

,

T--

30

40

50

60

70

x (at.% TL)

Fig. 4. Superconducting transition temperature, Tc, as a function of the TL content, x, in MQ amorphous Zrl00_xNix ((3, data from Refs. [17,20,23-27,34-36,43-49]), Zrl00_xCUx (O, data from Refs. [28,29,31,34,35,37,43,44,46,50-52]), Til00_xNi x (zx, data from Ref. [19]) and Til00_xCu x (A, data from Refs. [20-22]) alloys and crystalline stoichiometric Zr-Ni (D, data from Refs. ]41,42,53-55]) and Zr-Cu ( • , data from Refs. [29,56]) compounds. A symbol with an attached downwards arrow ( $ ) for amorphous Zr-Ni ( O ) and Zr-Cu ( O ) alloys indicates the temperature above which superconductivity was not observed; for amorphous Ti-Ni (zx) and Ti-Cu ( • ) alloys and for crystalline Zr-Cu compounds ( • ) , all the data symbols given represent an upper limit of T~ only (for the crystalline Zr-Ni compounds, an upper limit of 1.4 K (not shown here) was obtained for XNi > 50 at.% [41,42]). The solid lines for amorphous Zr-Ni and Zr-Cu alloys represent a linear fit to the experimental data and for amorphous Ti-Ni and Ti-Cu alloys they give an upper estimate for Tc. The dashed lines are linear extrapolations of the solid lines to x = 0. The sources of Tc values for the phases of the pure TE metals can be found in Ref. [12].

x (at.% TL)

Fig. 3. Electronic specific heat coefficient, y, as a function of the TL content, x, in TE 100-xTLx alloys. D, crystalline stoichiometric Zr-Ni compounds [41,42]; • , crystalline stoichiometric Zr-Cu compounds [29]; - - , average of experimental data for meltquenched Ti-(Ni, Cu) and Zr-(Ni, Cu) amorphous alloys according to Eqs. (7) and (8), respectively; . . . . . . , linear extrapolation of solid lines to x = 0. For the sources of data on phases of the pure TE metals, see Ref. [12].

the experimental values of Tc and {~D" Fig. 4 summarizes the available SC transition temperature data for the MQ Zr-Ni and Zr-Cu alloys. In both systems, Tc decreases linearly with increasing concentration of the TL component and it is slightly higher for the Zr-Ni than for the Zr-Cu system. The

L Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150 450

composition dependence can be described by the fitting equations Tc = 5.35 - 0.0775x

(Zr-Ni),

(10)

Tc = 5.35 - 0.0893x

(Zr-Cu),

(11)

137

TEIOO-xTLx hcp Ti

4OO am.

The fits are represented by the solid lines in Fig. 4 and the dashed line extrapolations give the Tc of hypothetical amorphous Zr. For those MQ Ti-Ni and Ti-Cu amorphous alloys which have been studied up to now, superconductivity has not yet been observed; therefore, only upper limits of Tc can be given as indicated in Fig. 4. By assuming that, also for the Ti-Ni and Ti-Cu systems, Tc when extrapolated to a-Ti yields a common value and imposing the constraint that the Tc versus x data should have similar slopes for the Ti- and Zr-based alloys, we have drawn straight lines through the datapoints for the lowest TL content in the Ti-Ni and Ti-Cu systems, in order to establish an upper limit for the Tc of the Ti-based amorphous alloys. This procedure yielded the equations T~ = 3.85 - 0.0783x

(Ti-Ni),

(12)

Ti-Ni

360

o

am. Ti-Cu

................ (~3

o

~

•

hcp Zr

/

°~ am, Zt-Ni 250

~"

a

o

" b c c " Ti

/

o

o

200

~-"bcc"Zr

0

I0

o o o o

20

30

o'~ °

°

40

" /

50

60

70

80

x (at,% TL)

Tc = 3.85 - 0.0877x

(Ti-Cu),

(13)

for an upper limit of T¢ as a function of the composition. Fig. 4 also shows the values of T~ ( [ ] ) obtained for the crystalline Zr2Ni compound (for the numerous other crystalline phases of the Zr-Ni systems, T~ < 1.4 K can only be given as an upper limit [41,42]). As far as the crystalline Zr-Cu compounds are concerned, only the phases Zr2Cu and ZrTCUl0 exist for compositions up to 70 at.% Zr [57] and Fig. 4 shows the upper limits ( • ) of T c available for these phases [29,56]. It is demonstrated by Fig. 4 that the extrapolated values of T c of a-Ti and a-Zr lie well above the T~ of the hcp phases [12]. The composition dependence of the Debye temperature, OD, is shown in Fig. 5. Although there is apparently a large scatter in the data, a closer inspection of the data from a given study reveals that in most cases a linear increase of (9 D with TL content, x, was observed. Therefore, we first fitted the data for the amorphous Zr-Ni alloys by a linear composition dependence which yielded the equation OD=

150--~ 1.82x

(Zr-Ni).

(14)

Fig. 5. Debye temperature, (~D, as a function of the TL content, x, in MQ amorphous Zrl00_xNi x (O, data from Refs. [20,23-27]), Zrl00_xCux ( 0 , data from Refs. [29-32]), Til00_xNi x ( ~ , data from Ref. [19]), Til00_xCu x ( A , data from Refs. [21,22]) alloys and crystalline stoichiometric Zr-Ni (D, data from Refs. [41,42]) and Zr-Cu ( l , data from Ref. [29]) compounds. The solid lines represent a linear fit for the MQ amorphous alloys according to Eqs. (14)-(17) and the dashed lines give their linear extrapolations to x = 0. The arrows on the ordinate indicate the ~9D values for the crystalline phases of the pure TE component (for data sources, see Ref. [12]).

By assuming that tgD(a-Zr)= 150 K also holds for the Zr-Cu data, for this latter system a linear fit yields O D = 150 + 1.36x

(Zr-Cu).

(15)

With the same procedure also in the case of the Ti-based metallic glasses, we obtain first O D = 300 + 1.31x

(Ti-Ni).

(16)

(Ti-Cu).

(17)

and, then, O D = 300 + 0.36x

The extrapolated values of (9 D to a-Ti and a-Zr show the same relation as the (9 o values of the hcp

138

L Bakonyi / J o u r n a l of Non-Crystalline Solids 180 (1995) 131-150

phases of these metals although the values for the amorphous state are again considerably different from that of the hcp phase. The available O D data for the stoichiometric phases are also included in Fig. 5 and they show, in general, the same values and trend as for the amorphous alloys, except for the c-Zr2Cu compound. We can now evaluate A~p with the help of Eq. (4) and by using the averaged concentration dependence of the experimental T~ and O D values. Fig. 6 shows the composition dependence of A~p derived in this manner for different constant values of /x*. The parameter Aop decreases substantially when the ratio O D / T ~ increases and its variation with ~* is also considerable. Since 3' and therefore n ( E F) decreases with increasing concentration of the TL component, we also took into account the variation o f / z * with n(E F) as expressed by Eq. (5). To achieve this, we have chosen a value of /z* for which Aop (from Eq. (4)) and the experimental 3' data yielded, via Eq. (2) with )tee = 0, an n ( E F) value which, in turn, reproduced the starting value of /x* by using Eq. (5). These values of )tep are shown in Fig. 7, where the varia-

1

0.9

",

0.5

I upper limit only

" 0.13

0.13

0.10

/

"lq-Cu Ti-Ni Zr-Cu Zr-Ni , 0

TE100-xTLx

"bcc" Zr

0.8

"-~ "bcc" Ti

0.7

-it* = 0 . 1 6 5 ~

0.6

". "~ 0 . 5

0.4

0.3

tippet limit only" ~ ' ~ , ~ hcp Zr it only • ~

hcp Ti hcp Hf

0.1

~'ep ,

i 10

~

It * = m~°

0.2

,

_

i 20

0.152 Ti-Cu

0.149 0.1~7 0.416 Ti-Ni Zr-Cu', Zr*Ni

....... • ................. ,

, 30

,

i

,

40

i 50

,

.._.,_. . . . . . . , 60

,

, 70

, 80

x (at.% TL)

Fig. 7. Electron-phonon parameter, A~p,as a function of the TL content, x, in (Ti, Zr)-(Ni, Cu) alloys. The solid lines (and their continuation by dashed lines) refer to the MQ amorphous alloys and were obtained as described in the text, by taking into account the variation of/~* with n(E E) accordingto Eq. (5); the values of /.t* as used for the limiting concentrations are also given on each curve. The dash-dotted line represents an approximate lowest limit for any non-superconductivemetal (see text for details). The [] data refer to the crystalline ZrENi compoundand the • data to the crystalline ZrECU compound (for details and references, see text). The arrows on the ordinate indicate the values of Aep for the pure TE phases (for data sources, see Re£ [12]).

tion of /x* with TL content is also indicated at the limiting compositions considered here. For the case of the Ti-based amorphous alloys, only an upper limit of Aep could be established, based on the upper limit of Tc (see Fig. 4). A lower limit of Aep for non-superconducting alloys can be established from Eq. (4): if we take /x* = 0.10, O D = 500 K and Tc = 10 -4 K, we obtain Aep 0.20. Since T~ = 10 -5 K yields A~p = 0.18 and the decrease of A~p with further decrease of T~ becomes still smaller, we arbitrarily take ACp"= 0.20 as the approximate lower limit for a non-superconductive metal (for /x* = 0.16 and the same Tc and O D values; Aep = 0.27 and the variation of ACp with Tc is also very similar to that at /~* = 0.10). This lower limit A~" = 0.20 for the non-superconductive metals is very close to the electron-phonon enhancement parameters derived for the noble metals Cu, A g and Au by studying superconducting alloys of these -----

I~ * = 0.13

0.2

~

am. TE IO0.xTL x

2o,6 ',

0.30"4 t

I~* = 0,155 0.9

, 10

,

I 20

,

, 30

,

I

,

40

I 50

,

, 60

, 70

80

x (at.% TL)

Fig. 6. Electron-phonon enhancement parameter, Ae_, as a function of the TL content, x, in MQ (Ti, Zr)-(Ni, Cu~ amorphous alloys. The solid lines (and their continuation by dashed lines) were derived via Eq. (4) with the values of /x* as indicated on each curve and by using the average Tc and O o values as given in Figs. 4 and 5, respectively.

L Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150

elements [58]. Also, based on several different theoretical and experimental methods, Grimwall [59] suggested values of A~p slightly above 0.15 for the non-superconductive metals. For the superconductive crystalline compound, Zr 2Ni, A~p ([] in Fig. 7) was calculated in the same way as for the amorphous alloys with /~* --0.148. For the other Zr-Ni crystalline alloys, an upper limit of Tc = 1.4 K was reported [41,42] from which we can estimate that 0.20 _< h~p < 0.50. For the crystalline Zr2Cu compound, Garoche et al. [29] obtained, from a rescaling through a comparison with the superconductive amorphous Zr-Cu alloys, the h~p value as given in Fig. 7 (11). Based on their experimental result [29] that Tc < 0.3 K for c-Zr2Cu and c - Z r 7 C U l 0 , w e estimate 0.20 < hep ~ 0.40 for these two crystalline Zr-Cu compounds.

139

2.5

"x,\ ,\ \ \,

TEIOO_xTLx

\,

bcc "13THE)

"\

"bcc = Zr "bcc" Ti

'\ \ am. Ti-(Ni,Cu) [upper limit] \'\'\.\ /

,~-- fcc Ti(THE) >

i

1.5

•, am. Ti-Cu ~- bcc Zr(THEI * • • \

~'- hcp Zr

[]

~

. £3

.1

2.3. Experimental values of the electronic DOS at the Fermi level

., ,'

t~ 0.5

By knowing the Acp values, we can now derive n(E F) from the experimental electronic specific heat data (Figs. 1 and 3) via Eq. (2) and taking hsf = 0. The experimental n(E F) data derived in this manner for the (Ti, Zr)-(Ni, Cu) alloys are shown in Fig. 8. For the MQ amorphous Zr-Ni and Zr-Cu system, n(E F) is practically the same. The slight curvatures at the upper end of the investigated composition range indicate, perhaps, a slight difference in the tendencies which is expected to occur at even higher TL contents, namely, that n(E F) for pure Ni metal is much higher than for Cu [60]. The Ti-Ni and Ti-Cu values for n(E F) are rather uncertain, but they are at least 15-20% higher than for Zr-(Ni, Cu) and their upper limit with Aep = )ter~n = 0.20 is also indicated in Fig. 8 by the dash-dotted line. The n(E F) values extrapolated for a-Ti and a-Zr are well above those for the hcp phases of these metals and lie close to the n(E F) values of the fcc phases [12]. For the stoichiometric crystalline phases of the Zr-Ni and Zr-Cu system with x >_ 50, n(E F) could only be derived approximately due to the large uncertainty in the /~ep values (Fig. 8). In the case of the crystalline ZrNi 5 compound (83.3 at.% Ni), the value given in Fig. 8 is probably significantly overestimated since this alloy already exhibits weak itinerant ferromagnetism [41] and,

0

10

20

30

40

50

60

70

8O

X (at.% TL)

Fig. 8. Experimentally determined n(E F) values as a function of the TL content, x, in (Ti, Zr)-(Ni, Cu) alloys. The solid lines (and their continuation by dashed lines) refer to MQ amorphous alloys, the symbols [] and • refer to the stoichiometric crystalline Zr-Ni and Zr-Cu compounds, respectively. The n(FF) data were derived with the help of Eq. (2), by taking Ase = 0, from the experimental values of 3' as given in Fig. 3 and the values of Acp were taken from Fig. 7 (for the crystalline compounds with x _> 50, the n(E F) values given are estimates only with a typical error of about -I-0.10 states/eV atom due to the uncertainty of their Tc and, hence, Aep data). The dash-dotted line represents an approximate upper limit for the amorphous Ti-Cu and Ti-Ni alloys; the dashed and solid lines for the same alloys represent a lower limit only, but they can be considered as fairly close to the actual values. For ZrNis, because of the neglect of Asf, the value given for n(E F) is probably significantly overestimated (for a calculated value of n(EF), see Fig. 11). For the pure TE phases, the arrows on the ordinate indicate the experimentally determined (unlabeled) and theoretically calculated (labeled by THE) values of n(E F) (for data sources, see Ref. [12]).

therefore, Asf cannot certainly be neglected here (see also Fig. 11). Since all the other alloys (both amorphous and crystalline) show Pauli paramagnetism [17,41,42], the spin-fluctuation enhancement parameter, Asf, should not be large in these systems for TL contents below 70-80 at.%. There have recently

140

I. Bakonyi /Journal of Non-Crystalline Solids 180 (1995) 131-150

been some efforts [61] to determine Asf for Zr-Ni glasses also from measurements of the pressure dependence of the superconducting transition temperature, Tc, and Asf(a-ZrsoNi20)= 0.01, Asf(a-Zr75Ni25) = 0.033 and Asf(a-Zr67Ni33) = 0.043 were obtained. These data give support for the previously mentioned estimate of Batalla et al. [14] according to which A~f(Zr-Cu) < 0.01 and Asf(Zr-Ni) < 0.1 for TL contents up to about 70 at.%. (Although a recent theoretical analysis of Bose et al. [62] indicated that the pressure dependence of the spin fluctuations in Zr-Ni glasses probably plays a significant role in determining the pressure dependence of To, they have also shown that this influence may be substantial even if A~f itself is small.) In this manner, we may state that the neglect of spin fluctuations, i.e., taking A~ = 0 when applying Eq. (2) for deriving n(Ev) from experimental values of y, causes a very small ( < 1%) error only for the Zr-Cu system; for the Zr-Ni system, the error is similarly small on the Zr-rich side of the glass formation range, whereas for the Ni-rich alloys (up to about 70 at.% Ni), n(E v) reduces by at most 10% only if we take into account the spin-fluctuation enhancement as well. (For the Ti-Cu and Ti-Ni systems, the situation is expected to be correspondingly fairly similar.) This would slightly further increase the difference between the n(E F) values of the Cu-based and Ni-based amorphous alloys (Fig. 8).

3. Summary of theoretical band structure calculations and comparison with experimental data

3.1. (Ti, Zr, H)9-Cu alloys Among the T E - C u alloys, the Zr-Cu system has been studied most extensively. The results of available band structure calculations for n(E F) of amorphous Zrl00_xCU x alloys are summarized in Fig. 9. We would like first to consider the work of CyrotLackmann and co-workers [11,63,64] since they first established, for each composition investigated, the degree (o-) of CSRO at which the system is in a minimum free energy condition (O'min) and then calculated the DOS curves for the structure having a CSRO which corresponds to o'= O'mn. i They ob-

1.6 Zrloo_xCUx 1.4

E o1.2

o g " ~'o,43 am.,.~BZr-Cu(EXP)

>

ua E

•4 A° • o2

e5 •

0.8

-.5

o5

e3 e5 el

0.6

0

10

20

30

40

50

60

70

80

90

x (at.% Cu)

Fig. 9. Calculated electronic density of states at the Fermi level, n(Ev), as a function of the Cu content, x, in Zq00_xCu ~ alloys. Amorphous alloys: O, fcc-like environment, CSRO considered, stable CSRO - maximum disorder (O'mi. = 0 ) [11,63,64]; (31, fcc-like environment, CSRO considered, stable CSRO: partial ordering (O'min < 0) [63,64]; O, complete chemical disorder (O'min = 0) assumed (O1 and 0 2 , 90-atom [73] and 200-atom [74] relaxed atomic clusters with periodic boundary conditions, respectively; 0 3 , Ref. [76]; 0 4 , Ref. [78]; 0 5 , Ref. [80]; 0 6 , Ref. [81]); zx, both without CSRO and with strong CSRO [79]; ~ , 19-atom cluster [70]; *, geometrical-mean model [82]. Crystalline stoichiometric compounds: t3, chemically ordered fcc Cu3Au or CuAu structure [65,83]; II, stoichiometric Zr2Cu compound with bct structure from the theoretical calculations of Ref. [72]). The solid line and the dashed extrapolations give the experimental n(E F) data of amorphous Zr-Cu alloys from Fig. 8.

tained, for 20 _
L Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150

neighbour coordination. They were also able to show [66] that for their model calculations the topological SRO does not significantly influence the electronic structure, provided that the coordination number, Z, is sufficiently high (Z > 10). With the help of these calculations, these authors have shown [11,63] that in Zr-Cu glasses Cu gives rise to a DOS peak below E F and the DOS around E F is dominated by a Zr peak and that the width of the Zr peak decreases with increasing Cu content. The general shape and its evolution with Cu-content was found to be in fairly good agreement with previously reported photoemission spectra [67-69]. Fig. 9 also shows the calculated n(E F) values of other investigators on amorphous Zr-Cu alloys. The early calculation of Fairlie et al. [70] performed on a 19-atom model cluster also reproduced the main features of the DOS and the calculated n(E r) value (symbol ~ ) agrees well with the experimental data on the corresponding amorphous alloys. Jaswal, Ching and co-workers [71-73] have calculated the DOS of Zr-Cu glasses modelled by relaxed atomic clusters with periodic boundary conditions. These authors have shown [73] that a 90-atom cluster is already sufficiently large to represent a macroscopic Zr-Cu alloy sample and calculations for two different clusters have yielded practically the same DOS and n(EF). Their results for the 90-atom clusters [73] are included in Fig. 9 (symbol 0 1 ) whereas their data for the 39-atom clusters [71,72] have been omitted. Recently, Ching et al. [74] performed a band structure calculation for a 200-atom cluster by the same method and by using improved potentials; these data also shown in Fig. 9 (symbol 0 2 ) do not differ significantly from the results on the 90-atom clusters. Based on a relaxed DRPHS model cluster [75] of some 1500 atoms, Fujiwara [76] obtained the n(E v) data given by the symbols 0 3 in Fig. 9. (Since this paper describes the results of an improved calculation over the procedure applied in his previous work [77], the data of this latter reference are not included in Fig. 9.) Frota-Pess6a [78] started with the 39-atom cluster of Jaswal and Ching [71] and extended it to a larger cluster of about 600 atoms. The calculation of n(E F) was then performed by averaging over all atoms for a-Zr41Cu59 and over 10 different atomic sites for

141

a-Zr67Cu33; the n(E F) data are given in Fig. 9 by the symbols 0 4 . For a-ZralCu59, the error bar represents the range of n(E F) values obtained for two different clusters when allowance was made for differences in the local environment. Duarte and Frota-Pess6a [79] investigated the influence of chemical ordering on n(E v) for a-Zr34Cu66. The random structure of about 800 atoms was constructed as in Ref. [78], whereas to obtain the chemically ordered structure they started with a Cu3Au-type fcc cell of 32 atoms and constructed a cluster of about 750 atoms. For both structures, n(E v) was found to be the same (zx) although both the Zr and the Cu DOS peaks decreased in width when CSRO was introduced. The symbols 0 5 denote the results of Xanthakis et al. [80]; the details for constructing the model cluster have not been specified and the calculated n(E v) values are much smaller than the experimental data, although the composition variation of n(E F) is properly reproduced. The calculations of Krey and co-workers [81] (symbols 0 6 in Fig. 9) were performed on the model clusters of Fujiwara et al. [75]; the calculated n(E F) values, however, well exceed the experimental values at low Cu contents. Finally, we mention that Kakehashi and coworkers [82] have recently applied a geometricalmean model for calculating the electronic structure of a-Zr65Cu35. Although their simple method reproduced fairly well the main features of the DOS curve, their calculated n(E F) value (symbol *) is significantly lower than the experimental data. It can be established from Fig. 9 that most of the calculations performed for amorphous Zr-Cu model structures yield n(E F) data which are reasonably close to the experimentally derived n(E F) values. The theoretical results show especially good agreement with experiment for an amorphous model structure [11,63,64] in which an fcc local environment was assumed. For not too high Cu contents (x < 75), the most stable configuration is the completely chemically disordered state and the degree of CSRO does not seem to influence n(E F) in the amorphous state up to about 75 at.% Cu. However, for very high Cu contents (about 85 at.% Cu), some degree of CSRO develops, leading to a more rapid decrease of n(EF). The above considerations are further supported by

142

L Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150

the theoretical results of Moruzzi and co-workers [65,83]. For the crystalline Zr3Cu , ZrCu and ZrCu 3 compounds, in a completely ordered fcc structure of the Cu3Au, CuAu and Cu3Au types, respectively, these calculations yielded values given in Fig. 9 by the symbols n . For 25 and 50 at.% Cu, these assumed crystalline fcc structures apparently properly describe the main features of the local structure and the CSRO of actual Zr-Cu glasses but this is not the case of c-ZrCu 3. The two existing equilibrium crystalline stoichiometric compounds of the Zr-Cu system have also been studied to some extent. In Fig. 8, a value of n(E F) as deduced from 7 was given for c-ZrTful0 and it shows good agreement with the n(E F) of the corresponding Zr41Cu59 glassy alloy. The strong similarity of the electronic structure of this amorphous and crystalline Zr-Cu alloy has already been demonstrated by Giintherodt et al. [84] with the help of photoemission experiments. Apart from some details, the observed spectra for both structural modifications were found to be very similar both at and below the Fermi level and the n(E F) values deduced from these spectra can also be considered as identical. On the other hand, it has already been indicated by Fig. 8 that, at 33 at.% Cu content, n(E F) is substantially different for the amorphous and crystalline phases, with the crystalline value being smaller. This result is strongly supported by the theoretical calculation of Jaswal et al. [72] for bct Zr2Cu the result of which is also given in Fig. 9 (11). Because of the specific crystal structure of Zr2Cu, E F in this compound is situated in a small pseudo-gap which is smeared out upon disorder, and this gives rise to an increase of n(E F) (the Cu peak also broadens but it lies well below E F and, therefore, its broadening does not influence n(EF)). The higher n(E F) value of the glassy alloy in comparison with the crystalline compound is also observed in the NMR Knight shift [85] and spin-lattice relaxation time [86] data of both 63Cuand 91Zr nuclei. It should be mentioned finally that the theoretical calculations by Cyrot-Lackmann and co-workers [64] have been performed, not only for the Zr-Cu system but also for the Til00_xCUx and Hfloo_xCU x amorphous alloys for compositions x = 33, 50, 66 and 85. The general features of the DOS curves and the location of the Fermi level are qualitatively similar

in the investigated composition ranges for all these Cu-based systems [11,63,64]. In the composition range up to 75 at.% Cu, the Cu 3d-band exhibits a relatively sharp peak well below E F and the Fermi level is located close to the inner edge but still on the top of a relatively broad TE d-band peak [11,63,64]. For amorphous Ti-Cu alloys, photoemission experiments [87,88] from 35 to 70 at.% Cu give support for the calculated DOS curves. On the other hand, the theoretically calculated DOS curves for the TEI5Cu85 (TE = Ti, Zr and Hf) amorphous alloys [64] exhibit somewhat different features: the TE d-band peak becomes now much narrower than the almost unchanged Cu d-band peak and E F is located in the relatively flat minimum between the TE and TL peaks, close to the bottom of the TE peak. The photoemission studies of Greig et al. [89] have indeed shown that, for a-Zrl0Cu90 and a-Hfl0CU90, n(E F) is fairly small and the DOS curve is rather flat between the Cu 3d-peak and E F. Because of these differences in the location of E F for x < 75 and for x = 85, there are differences also between the two composition ranges if we compare the calculated n(E F) values in the case of the Ti-Cu, Zr-Cu and Hf-Cu alloys (Fig. 10). Namely, for 33 < x < 66, where n(E F) was calculated for all three systems, for a given Cu content n(E F) decreases in the sequence Ti ~ Zr--* Hf. (It is noted that a similar behaviour in the change of n(E F) was found in a previous theoretical work [12] also for any of the several structural modifications of these three TE metals.) Since E F here is located on the top of the TE d-band, the broadening of this latter peak in the same sequence [64] leads to a decrease of n(E F) in the same manner (Fig. 10). On the other hand, the value of n(E F) is significantly smaller and rather similar for all three discussed TE100_xCu x systems at x = 85 since E F is now shifted to the relatively deep, fiat minimum between the TE and TL peaks, leading to almost identical values of n(E F) for TE = Ti, Zr and Hr. It should still be noted that at this small TE content (15 at.%) the TE states in the TE-Cu amorphous systems appear very similar to the so-called 'virtual bound states' conventionally used in describing the electronic structure of crystalline dilute alloys. Also, the rapid decrease of n(E F) beyond 75 at.% Cu is in agreement with the small n(E F) value of pure fcc Cu metal: n(E F) =

1. Bakonyi/ Journal of Non-CrystallineSolids 180 (1995)131-150 1.8 am. "l'i-Cu (EXP)

1.6 1.4 o >

1.2

~

Zr*Cu (EXP)

~0.8

o

c 0.6 0.4 am. TE lO0.xCUx 0.2 20

40

60

80

1O0

x (at.% Cu)

Fig. 10. Calculatedelectronicdensity of states at the Fermi level, n(EF), as a function of the Cu content, x, in amorphous TE100_xCux alloys [11,63,64] for TE =Ti (zx), Zr (O) and Hf (~). The solid lines and their dashed extrapolationsare taken from Fig. 8 as the experimentaldata for the Ti-Cu and Zr-Cu system. For pure Cu (x = 100), the symbol [] gives n(EF) as calculated for the fcc phase [60].

0.29 states/eV atom [60]; since for this structure of Cu, E F lies in the flat s-band, n(E F) of amorphous Cu can be expected to be fairly close to that of the fcc structure. A recent molecular dynamics and band structure calculation [90] for liquid Cu has indeed shown a strong similarity between the DOS curves of liquid Cu and fcc Cu and the n(E F) of the liquid state was found to be approximately the same as for the fcc structure.

3.2. (Ti, Zr, Hf)-Ni alloys In describing the results of theoretical band structure calculations on the Ni-based systems, we start discussion again with the work of Cyrot-Lackmann and co-workers [11] who performed the same calculations for Zrl00_xNi x (x = 35, 50 and 60) as for the Zr-Cu system (see Section 3.1.). For these compositions of Zr-Ni amorphous alloys, they found that the minimum energy configuration is a partially ordered state (O'min < 0) and the degree of ordering increases (i.e., Ormin decreases) with increasing Ni content.

143

Since the atomic Ni 3d levels lie at higher energy than the Cu levels, the Ni 3d-band shows a stronger overlap and, therefore, a stronger hybridization with the Zr 4d-band than was in the case of the Zr-Cu system. These authors have also noted that the effect of CSRO is to increase the separation of the two d-band peaks. Further, they investigated the effect of CSRO on n(E F) for the Zr40Ni60 composition: if there is no CSRO (tr = 0), n(E F) = 1.04 states/eV atom is obtained, whereas, by taking the stable CSRO configuration (o-= o-~in < 0), the result is n(E F) = 0.88 states/eV atom. Their calculated n(E F) values for x = 60 are shown in Fig. 11 by O1 (o-= O-min) and by O1 (o-= 0) which are connected by a dashdotted line. Pasturel and Hafner [91] also calculated the CSRO for Zrl00_xNix (x = 35, 50 and 65) and also the electronic density of states for the stable configurations. Again, an increasing degree of CSRO was found with increasing Ni content and their calculated n(E F) values (symbols 0 2 ) show good agreement with the results of Cyrot-Lackmann and co-workers [11] and with the experimental data (Fig. 11). Frota-PessSa [78] calculated, as for Zr-Cu, the n(E F) for a-Zr67Ni33 and a-Zr41Ni59 ( 0 3 in Fig. 11) under the assumption of complete disorder; however, for the Zr-Ni system this assumption overestimates the values. Duarte and Frota-PessSa [79] also investigated the influence of CSRO on n(E F) for a-Zr35Ni65 ( 0 2 and 0 3 connected by a dash-dotted line): the higher value was obtained for the chemically disordered state and the lower one for an fcc-like structure with strong CSRO (neighbours of opposite kind favoured) assumed, with the latter value being fairly close to the experimental data on MQ amorphous Zr-Ni alloys. The n(E F) value of Fairlie et al. [70] ( ~ ) obtained on a 19-atom model cluster is somewhat less than the experimental data whereas most of the n(E F) values (O5) by Xanthakis et al. [80] are also significantly less than the experimental values as was also the case for the Zr-Cu alloys (Fig. 9). Jaswal [92] derived the n(E F) values ( 0 4 ) for a random packing of atoms, i.e., assuming no CSRO, and obtained good agreement with experiment for a-Zr64Ni36 whereas his calculated value for aZr41Ni49 was too large by comparison with the experimental value. This difference is in line with

I. Bakonyi/Journal of Non-CrystallineSolids 180 (1995) 131-150

144 1.8

•.

1.6

am.Ti-Ni(EXP)[lowerlimitl u,

~

1.4

1.2

t

2

o~~lolam"Zt-Ni IEXPIo3i l o4

>

.--&

.5

I

~ .

~

o2

"#',! ,~.

n

0.8

c 0.6

0.4

! 0.2 Zr1oo_xNix ' Ti1oo_xNix

oi

. . . . . . . . . . . . 0

10

20

30

i

L

. . . . 40

50

60

,_, 70

80

i 90

x (at.% Ni)

Fig. 11. Calculated electronic density of states at the Fermi level, n(Ev), as a function of the Ni content, x, in Zrl00_xNix alloys. Amorphous alloys: ©, fcc-like environment (CSRO was considered and partial ordering (O'min < 0) is the stable CSRO: ©1, Ref. [11]; 02, Ref. [91]), fcc-like structure (strong CSRO (O'min -=-0) assumed: 03, Ref. [79]) and atomic structures derived from molecular dynamics simulations (04, Refs. [100,101]); O, complete chemical disorder (O'min = 0) assumed (O1, Ref. [11]; 02, Ref. [79]; 03, Ref. [78]; 04, Ref. [92]; 05, Ref. [80]); ~, 19-atom cluster (Ref. [70]). zx and A, data calculated [62] by assuming an fcc lattice for the amorphous structure (z~, completely ordered (O'mi n = 0), ideal fcc lattice; • 1, complete chemical substitutional disorder (O'min = 0) for an ideal lattice; • 2, the same as for symbols • 1 except for allowing a lattice relaxation due to the different atomic sizes of Zr and Ni). [] and II, crystalline stoichiometric Zr-Ni compounds ([3, chemically ordered fcc Cu3Au or CuAu structures assumed [65,83]; II, actual crystal structures assumed except an MgCu2 structure for the hypothetical ZrNi3 phase [100,101]). *, calculated value for an amorphous Ti6oNi40 structure [91]. The two vertical dash-dotted lines connect calculated n(EF) data obtained at a given composition by assuming complete disorder (higher values) and strong CSRO (lower values). The solid lines and the dashed extrapolations give the experimental n(Ev) data of amorphous Ti-Ni and Zr-Ni alloys from Fig. 8.

the previously discussed findings [11,79] according to which for the amorphous Z r - N i alloys the degree

of CSRO increases (O'min decreases) with increasing Ni content and, at the same time, the value of n(E F) for the non-equilibrium, chemically disordered state is significantly higher. The increasing CSRO for the amorphous alloys indicates a tendency for the formation of unlike first neighbour atom pairs. As was the case for the Z r - C u alloys, Moruzzi and co-workers [65,83] calculated the electronic DOS also for the crystalline Zr3Ni, ZrNi and ZrNi 3 completely ordered (~r = 1) stoichiometric compounds in the fcc Cu3Au, CuAu and Cu3Au structures, respectively. Their calculated n(E F) values are given in Fig. 11 by the symbols [] which show, in most cases, a significant deviation from the experimental values for the MQ amorphous alloys. The reason for this discrepancy may lie in the fact that both the degree of CSRO and the lattice constant of the glasses are different from those assumed for the crystalline compounds. This view is supported by the band structure calculations of Bose et al. [62]. They have calculated the DOS curves of Zrt00_xNi x alloys ( x = 25, 33 and 50) with an fcc structure for several cases: (i) for completely ordered ( o - = 1) fcc Z r - N i alloys; (ii) for substitutionally disordered (~r = 0) Z r - N i alloys with an ideal fcc lattice and (iii) for substitutionally disordered Z r - N i alloys ( o - = 0) on an fcc lattice relaxed in order to accommodate the different sizes of the TE and T L atomic constituents. They also calculated, for most cases, the pressure dependence, i.e., the volume dependence of n(EF). The general result was that n(E v) always decreased with increasing pressure, i.e., with decreasing volume. Their n(E F) data for zero pressure are shown in Fig. 11 (zx, • 1 and A 2 for the above three cases, respectively) and demonstrate that whereas the chemical ordering may strongly influence n(Ev), as is the case for x = 25, for the disordered alloys the effect of lattice relaxation with respect to an ideal fcc lattice is small ( 5 - 1 0 % only). For completeness, we mention that Visnov et al. [93] performed some calculations of the local density of states of Zr 2 Ni for the bulk material with the bct structure and for several atomic clusters. For the T i - N i systems, n(E F) was calculated [91] for a-Ti60Ni4o only (* in Fig. 11). At this composition, n(E F) was found to be the same both without CSRO ( o - = 0 ) and with CSRO ( o - = 1) and the

I. Bakonyi/Journal of Non-CrystallineSolids 180 (1995) 131-150 calculated value agrees well with the lower limit of the experimental data for the corresponding amorphous alloy. As far as the crystalline Ti-Ni compounds are concerned, although there have been a few papers [94-96] reporting on their electronic structure, these results will not be discussed here since, in most cases, simultaneous theoretical and experimental data for a given phase are not available. In all the band structure calculations discussed above for either the Cu-based or Ni-based amorphous alloys, a model structure was first constructed on the basis of some assumptions about the atomic arrangement in the glassy state. Recently, Hausleitner and Hafner [97-99] have attempted to construct structural models of disordered transition-metal alloys via molecular dynamics simulation, by employing a new theoretical approach for the determination of the interatomic potentials. These structural modelling studies have led to the conclusion that the degree of CSRO increases with increasing Ni content and the local order is predominantly trigonal prismatic for low Ni contents and changes to a more polytetrahedral character for the Ni-rich alloys. Hafner and co-workers [100,101] then reported detailed band structure calculations for amorphous Zrl00_xNix model structures derived from the molecular dynamics simulation and the results are also shown in fig. 11 ( 0 4 ) . Although their calculated n(E F) values are less than the experimental data, the composition dependence for 35 < x < 65 is well reproduced and their data for x = 80 and x = 85 clearly show the expected trend, namely, that n(E F) increases as pure Ni is approached (x ~ 100). These authors have also calculated [100,101] the DOS curves for the crystalline compounds Zr2Ni, ZrNi, ZrNi 2, ZrNi 3 and ZrNi 5 in the actually existing crystal structure except for the non-existent hypothetical ZrNi 2 phase for which a MgCu 2 structure was assumed. The calculated n(E F) values (11 in Fig. 11) are all around about 1 states/eV atom except for ZrNi 3 for which a much lower value was obtained, in agreement with the previous result of Moruzzi et al. [83]. It is noted for purposes of comparison that for fcc Ni n(E F) = 1.69 states/eV atom was obtained by a spin-polarized band-structure calculation [60]. Photoemission experiments on Zr-Ni glasses [69,87,102] have also given support to the results of

145

theoretical band structure calculations in that, similarly to the Zr-Cu system, the DOS around E F is dominated by the Zr 4d-band states and the Ni 3d-band peak lies below the Fermi level. However, in the Zr-Ni system, the separation of the Zr and Ni peak is smaller, which leads to a stronger hybridization between the TE and TL states. A comparison with the crystalline Zr-Ni compounds [102,103] has revealed that the two-peaked structure of the DOS curves is not specific to the amorphous alloys but occurs in the crystalline compounds as well and that the observed DOS curves do not differ significantly for the amorphous and crystalline phases at a given composition. It should be mentioned, however, that a marked difference occurs between the T E - C u and TE-Ni glasses at sufficiently high (x > 75) TL contents. Namely, for the TE15Cu85 glasses, although E F is calculated [63,64] to be between the Cu and TE peaks, it is close to the TE peak and, therefore, there is a substantial contribution of the TE d-band states to n(Ev). Photoemission experiments [89] on the metallic glasses Zrl0Cu90 and Hfl0Cu9o have supplied support for this picture. On the other hand, the calculated DOS for ZrNi 3 [101] shows that E F is situated in the middle between the Ni and Zr peaks, whereas for ZrNi 5 E v is already on the falling edge of the DOS curve, i.e., n(E v) is already dominated by the Ni d-band. A gradual fading out of the Zr d-band states from below E v with increasing Ni content can also be seen in the photoemission experiments of Amamou [103] on the crystalline Zr-Ni compounds. Also, the calculated DOS curve of aZr15Ni85 [101] shows that E F lies on the steep side with lower binding energies of the Ni 3d-peak which is supported by photoemission experiments as well for a-Zr9Ni91 [104,105] and a-ZrsNi92 [89] alloys. This means that, at such high Ni contents, n(E F) has contributions from the Ni d-bands only.

4. Suggestions for the atomic structure from considerations of electronic DOS data

It is well known that for metals there exists a strong interrelation between a specific crystal structure and the electronic structure characteristic for that type of atomic arrangement. The question now

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arises as to whether we can learn something about the atomic structure of amorphous alloys by measuring macroscopic properties which depend on n(EF), the electronic density of states at the Fermi level. In an attempt to answer this question, we shall first briefly outline our recent results [12] on the different structural modifications of Ti, Zr and Hf metals which clearly demonstrate: (i) the dependence of n(E F) on the atomic structure, and (ii) the reliability of the extrapolation of electronic-structure-sensitive experimental quantities from binary alloy data to the pure constituent metals. Then, by considering the experimental and theoretical n(E F) data which have been reported for (Ti, Zr, Hf)-(Ni, Cu) metallic glasses, summarized in Sections 2 and 3, a suggestion is made for some aspects of the atomic structure of these systems. Finally, it will be discussed to what extent this proposed structure type conforms to other available relevant results. As discussed in Section 3, it has been shown for TE-TL alloy systems, both experimentally by photoemission studies and theoretically by band structure calculations, that n(E F) is dominated by the contribution of TE atoms. It therefore appeared worthwhile to perform a thorough analysis of the influence of atomic structure on the electronic DOS for TE metals. Specifically, the electronic band structure was calculated [12] for four crystal types (hexagonal or to, hexagonal close-packed or ct, (hypothetical) face-centered cubic and body-centered cubic or 13 phases) of Ti, Zr and Hf metals. It was found that, for each metal, n(E F) increases in the sequence to ~ ct ~ fcc ~ 13 and it is significantly higher for the cubic than for the hexagonal and hcp phases. Also, for each phase, the DOS curve exhibits a characteristic shape. Experimental n(E F) values for these metals have also been deduced [12] from available low-temperature specific heat and superconductivity data in the same manner as described in Section 2. For the stable low-temperature phase (cx) of Ti, Zr and Hf metals, the experimental n(E F) values were found to be in good agreement with the results of calculations. The 13-phase is stable at high temperatures (above 1100 K) and, therefore, experimental n(E F) values could only be obtained by extrapolating data obtained on bcc phase alloys, which are stable to lower temperatures, to the pure metals. Available magnetic

susceptibility data for the existing phases exhibited the same features as the calculations [12]. The fcc phase does not exist for these metals; however, since for the other phases the calculated n(E F) values proved to be reliable, the same should hold true for the hypothetical fcc structure data as well. It has already been noted in Section 2 that for the hcp phase of both Ti and Zr, the value of T is well below those extrapolated for the amorphous TE metals (Fig. 3) whereas the data for the hypothetical low-temperature bcc phase are much higher. For the SC transition temperature (Fig. 4) and the Debye temperature (Fig. 5), one again obtains values when extrapolated to pure amorphous TE metals which differ from those of the hcp phase of these metals. From Eq. (4), the same holds true, of course, for the electron-phonon interaction parameter as well. The electronic structure data presented in Fig. 8 indicated that the structure of pure amorphous Ti and Zr should differ from that of the hcp phase for these metals but it may resemble to some extent the structure of one of the cubic phases. According to diffraction experiments [106], for this class of amorphous alloys the average coordination number (10.4-13.7) is fairly close to its value for the fcc structure (12) and, therefore, a similarity with the bcc structure is ruled out. By invoking that in TE-TL glasses n(E F) is dominated by the TE metals, the smooth composition variation of the electronic-structure-sensitive parameters indicates that the local structure of these amorphous alloys can eventually be described in the following way. We start from an fcc-like topological arrangement of TE atoms in which structure more and more TE sites are randomly occupied by TL atoms as the concentration of the latter increases. This local structure would also correspond to the expectation that, for a disordered, close-packed and highly isotropic solid, the conditions of which are probably well fulfilled for the TE-TL glasses, the local structure should resemble an fcc structure. This feature is also manifest in the results of the band structure calculations. It has been shown for some transition metals [107] that the calculated DOS curves are very similar for the liquid state and for the fcc phase (the same was also obtained for Cu [90]). Also, it was already mentioned in Section 3 that the calculated n(EF) values are in especially good agreement (Figs. 9 and 11) with the experimental

L Bakonyi/Journal of Non-Crystalline Solids 180 (1995) 131-150

data in those cases where an fcc-like local atomic arrangement was applied as the starting configuration for the band structure calculation. Although it is admitted that this feature may eventually be merely a consequence of the fact that the electronic DOS is not particularly sensitive to such fine details of differences in the local atomic arrangements that may exist between an fcc-like and an amorphous structure, there are several other hints as well which support the idea that the local structure of Zr-Ni type glasses can be approximated by an fcc-like atomic arrangement. A further support for the fcc-like local structure of Zr-Ni type glasses comes from a study of MQ Zr-Rh and Zr-Pd alloys by Yeh and Cotts [108], who reported that at the borderline of the glass-forming range, around 80 at.% Zr, if the amorphous state could not be achieved the melt-quenched alloys exhibited an fcc structure for both systems. Further, it has been found [109] during a high-speed in situ crystallization study of an amorphous Zr67Ni33 alloy that, whereas the equilibrium crystallization product is a body-centered tetragonal Zr2Ni phase, rapid crystallization results in the appearance of a metastable fcc Zr 2Ni phase as the immediate crystallization product which may have a local structure very close to that of the starting glassy state.

5. Summary A large amount of data on the electronic structure of TE-TL type amorphous alloys has been accumulated in recent decades. In the present overview, we have summarized available experimental data on the low-temperature specific heat and superconductive properties of T E - T L glasses with TE = Ti and Zr and TL = Ni and Cu. In the paramagnetic concentration range of these alloy systems, the electronic density of states at the Fermi level could be evaluated from these data by taking into account the electron-phonon enhancement only. This analysis was performed by appropriately averaging the experimental data for the concentration dependence of the electronic specific heat, the superconducting transition temperature and the Debye temperature. From these averaged data, we derived the concentration

147

dependence of the electron-phonon enhancement parameter and the electronic density of states at the Fermi level for these systems. The latter data were then compared with n(E F) values obtained from theoretical band structure calculations on these amorphous alloys and the overall agreement was found to be satisfactorily good. Based on the results of a recent detailed band structure calculation of the TE metals Ti, Zr and Hf [12], it was found that an extrapolation of the concentration dependence of all the parameters mentioned above from about 20 at.% TL content to the pure amorphous phase of the constituent TE metals yields values significantly different from those of the hcp phases of these metals but fairly close to the corresponding values of their cubic (bcc or fcc) phases. In view of the reliability of a similar extrapolation from bcc alloys of these TE metals to their hypothetical low-temperature bcc phase [12], the local structure of such T E - T L glasses may be described by starting from an fcc-like atomic structure of TE atoms into which more and more TL atoms are substituted as their concentration increases. This suggestion is justified by the experimentally observed high coordination numbers in these T E - T L glasses, characteristic of the fcc lattice, as well as consistent with the highly isotropic character of the fcc structure. Also, the band structure calculation results for amorphous T E - T L alloys were in especially good agreement with the experimental n(E F) values in those cases where an fcc-like local atomic arrangement was chosen as the starting atomic configuration for the calculation. A recent high-speed in situ crystallization study [109] of a Zr67Ni33 glassy alloy has also given important further evidence in favour of our suggestion since the very first crystallization product observed was a metastable fcc Zr 2Ni phase different from the equilibrium bct ZrzNi structure which is the stable phase at this composition.

This work was supported by the Hungarian Research Fund (OTKA) through grant No. 2949. The constant interest and support of K. Tompa is appreciated. At the early stage of this work, the author also profited greatly from a research stay with R. Kirchheim at the Max-Planck-Institut fiir Metalforschung, Stuttgart, Germany.

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