Short-range atomic order in TbCu2 and DyCu2 metallic glasses

/ O U R N A L OF

ELSEVIER

Journal of Non-Crystalline Solids 167 (1994) 255--262

Short-range atomic order in TbCu 2 and D y C u 2 metallic glasses V. Petkov

*, A . A p o s t o l o v

Department of Solid State Physics, Sofia University, Sofia 1126, Bulgaria

(Received 28 May 1993; revised manuscript received 8 July 1993)

Abstract

The total pair correlation functions for RECu 2 metallic glasses (RE = Tb, Dy) have been determined using X-ray diffraction. A proper model for the R E C u 2 glassy structure has been selected by comparing the experimental pair correlation functions with model ones for disordered crystalline structures. It has been established that the local atomic arrangement in RECu 2 glasses can be described as a dense packing of trigonal prisms similar to that found in the RECu 2 crystalline compounds with A1B2-type structure. 1. Introduction

A number of studies on the short-range atomic order in amorphous alloys of chemical composition R E T 2 have been carried out in the past two decades ( R E is rare-earth metal, T is transition metal). The earlier structural studies have found similarities between the local atomic arrangement of sputtered R E T 2 glasses (T = Fe, Ni) and that of the corresponding crystalline counterparts belonging to the Laves phases family [1,2 and refs. therein]. A structural model based on a dense random packing of hard spheres has been proposed, however, to describe the atomic ordering in vapour quenched R E - C o glasses, including that in R E C o 2 [3]. The subsequent detailed studies on sputtered R E F e 2 amorphous alloys and YCo 2 glass p r e p a r e d by ball milling have also found that their structure is characterized by a

* Corresponding author: Tel: +359-2 62 3015. Telefax: + 359-2 46 35 87.

topologically random arrangement of the constituent atoms [4,5]. The results of these structural studies show that the R E T 2 glasses (T = Fe, Co, Ni) can be generally subdivided into two groups with respect to the type of short-range atomic order. R E T 2 glasses, for example, GdCo2, HoCo2, G d F e 2, DyFe 2 [3,4], the structure of which can be described as a dense random packing of the constituent R E and T atoms fall into one of these groups. The other group is formed by the R E T 2 glasses, the local atomic ordering of which is well approximated by a tetrahedral dense packing of R E and T atoms similar to that observed in the crystalline Laves phases. YNi 2 and TbFe 2 are typical members of this structural group [1,2]. The results also suggest that the specific conditions of preparation influence the local atomic ordering of R E T 2 glasses since different types of short-range order have been found in chemically identical R E T 2 glassy samples obtained by different techniques [1,4]. It is interesting to change the preparation technique and, further, to replace the transition

0022-3093/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0022-3093(93)E0249-8

256

1/. Petkou, A. Apostolou /Journal of Non-Crystalline Solids 167 (1994) 255-262

metallic component, T, in R E T e glasses (T = Fe, Co, Ni) by a non-transition one, for example by Cu which belongs to the group of noble metals, in order to check whether the type of atomic ordering would modify upon these changes, i.e., whether R E C u 2 glasses would fall into one of the structural groups defined above. An answer to this question will be given in the present p a p e r by studying the type of short-range atomic order of melt-spun R E C u 2 metallic glasses (RE = Tb, Dy) in detail and by comparing the specific structural features found with those exhibited by the R E T 2 glasses (T = Fe, Co, Ni).

data for counter dead time, polarization, absorption, background and Compton scattering, the total reduced interference functions

F(S)

:S{[I

c°h-

Ecifi2(s)l//[ ECifi(S)12), (1)

and their Fourier transforms, the total reduced radial distribution functions,

G(r) = (2/~rT)fS=SmaXF(s) sin(sr)

ds,

(2)

~s=0

where all symbols have the usual meaning, were computed. All corrections were carried out according to the scheme described in Ref. [7].

2. Experimental

2.1. Sample preparation and characterization The T b C u 2 and DyCu 2 master alloys were prepared from commercially available constituent elements by arc melting. A m o r p h o u s ribbons were produced from them by single-wheel rapid quenching in a protective argon atmosphere. The chemical composition of the amorphous samples corresponds to the overall formula RE33Cu67 a s checked by electron microprobe m e a s u r e m e n t s ( R E = Tb, Dy). Due to the relatively small amount of the fully amorphous samples obtained, their density was not experimentally measured. It was estimated via the method described in Ref. [6] and was found to be 8.39 and 8.89 g / c m 3 for the TbCu 2 and for the DyCu 2 glass, respectively.

3. Results Experimental F(s) and the corresponding G(r) for R E C u 2 glasses ( R E = Tb, Dy) are shown in Figs. 1 and 2, respectively. Both F(s) curves have a sharp first peak, a second peak with a shoulder on its small-s side and subsequent decaying peaks on which small amplitude ripples, due to the insufficient X R D data statistics, are superimposed. The moderate X R D data statistics at high

5.0

%4.0

I, 3.0

2.0

2.2. X-ray diffraction inuestigation

I ~

1.0 V The X-ray diffraction ( X R D ) measurements were performed on a U R D 6 diffractometer in a transmission geometry using filtered Mo K~ radiation. The samples scattering was multiply scanned in steps of 0.2 ° from 20 = 9-65 ° and in steps of 0.4 ° from 20 = 65-120 ° in order to accumulate at least 10000 counts for each step. The background scattering was measured in the same way as the sample scattering, with the only difference that the sample holder was empty. After the appropriate corrections of the experimental X R D

~

-

DyCu2

~

o.o

- 1 .o

.

J

.

TbCu2

~

i i [ it i l l i [hi i l l l l l l l l l u n n n

-2.0

0.0

F i g . 1. R e d u c e d

5.0

10.0

interference

functions,

I I 1 1 1 II I I I I I I

15.0

F(s),

for

20.0

(,+,-b

WbCu 2 a n d

DyCu z metallic glasses: - - , experimental results; --model calculations for AIBz-type disordered crystalline structure.

V. Petkov, A. Apostolot, /Journal of Non-CrystaUine Solids 167 (1994) 255-262 4.0 "Z" c~

.3.0

2.0~ ~

DyCu2

1.0

O0

257

their separation. This observation indicates the existence of a short-range atomic order only in RECu 2 glasses (RE = Tb, Dy). This short-range order is obviously the same for both glasses since the details of their G(r)s are quite similar.

4. Discussion ~,~

~

'

~

TbCu2

-1 .o

-2,o 0.0

i ii i l l l l [ ] i l l l ] i i i [11111 i i i ii1,11 ii i l l [11 ii ii ii 5.0 10,0 15.0 20.0 25.0

r (1) Fig. 2. Experimental reduced radial distribution functions, G(r), for TbCu z and DyCu z metallic glasses.

Generally, a knowledge of the structural building units as well as of the partial coordination numbers and the partial coordination distances is needed for clarifying the type of short-range atomic ordering in metallic glasses. In order to extract this knowledge from the total radial distribution functions which are only available for the RECu 2 glasses investigated, their pair correlation functions (PCF)s, g(r),

g(r) = (]/4wrpo)G(r) + 1 =p(r)/po, diffraction angles and some factors in the X R D data processing that are unaccountable for, including the termination effect in the Fourier transformation, have caused high frequency spurious oscillations in both experimental G(r)s at small values of r (below approximately 0.2 nm). The oscillations are of rapidly decaying amplitude, so that they do not distort the experimental atomic distribution functions in the region above their first peak (see Fig. 2). That is why no attempt has been made to remove these by manipulating the experimental X R D data. The combined effect of all experimental deficiencies on the final G(r)s was checked by estimating the latter on the basis of various F(s) data sets differing in the upper limit of s. Since no qualitative changes in both G(r)s have been observed, one might conjecture that all important features of them are structurally relevant and are not experimental artifacts. The examination of the experimental G(r)s shows that their peaks rapidly decrease in height with the increase of the interatomic distance, r, and vanish almost completely at approximately 0.1 nm. The fact reflects the rapid decrease of the correlation between the positions of the constituent R E and Cu atoms with the increase of

(3)

where p(r) and P0 are the local and the average atomic density, respectively, have been compared with model functions for disordered crystalline structures.

4.1. Determination of the type of" building structural units and their arrangement in RECu 2 glasses The method of comparing the experimental PCFs with calculated ones for disordered crystalline structures has proved to be very efficient in selecting a model for the local atomic arrangement in metallic glasses [8-10 and refs. therein]. The method consists of a destroying the longrange spatial order in the perfect crystal by approximating the g-peaks of its PCF with Gaussians, the widths of which increase with the interatomic distances, and a subsequent search for an agreement between thus-calculated PCF and the experimental one. The presence of such an agreement indicates that the short-range atomic order in both the metallic glass and the disordered crystal considered exhibits similar features and, consequently, both are built up of similar structural units arranged in identical coupling schemes. Since similarities are only found when a comparison is made with crystalline structures of corresponding composition, the structures of RET~

V. Petkov, A. Apostolov / Journal of Non- Crystalline Solids 167 (1994) 255-262

258 3.0

v

(o)

2.5

I

l l

2.0

I

1.5

I

/x\

1.0

0.5

0.0

1.0

;3.0

5,0

7.0

9.0 r

(A)

2.0

"D

(b)

v

1.5 [\

1.0

0.5

0.0

1.0

3.0

5.0

7.0

9.0 r

(1)

2.0

(4 1.5

1.0

crystalline compounds were used as trial ones (T = Fe, Co, Ni, Cu). The crystal structure of Laves phase R E T 2 ( T = F e , Co, Ni) is of MgCu2-type [11]. The structure of RECu 2 compounds can be of two types: AIBz-type and its distorted variant KHgz(CeCuz)-type. The former structural type occurs with R E = La only, while the remainder of the rare earths form the latter type when alloyed with a proper amount of Cu [11]. The calculated PCFs for MgCuz-type, KHgz-type and A1Bz-type disordered crystalline structures are shown in Figs. 3(a), 3(b) and 3(c), respectively, along with the experimental PCF for DyCu 2 glass. The model PCFs were computed with the use of data for the crystalline structures of these representatives of the three structural types under consideration which are as close to DyCu 2 glass in chemical composition as possible. These are the structures of DyFe 2, DyCu 2 and LaCu 2 crystalline compounds, respectively [11-14]. In all trial perfect crystalline structures, the long-range spatial disorder was introduced by increasing the widths of the peaks of their PCFs proportionally to a square root of the corresponding interatomic distances. To map the experimental PCF for DyCu 2 glass and the model PCF for LaCu 2 disordered crystalline compound onto the same scale, the r-scale data of the model PCF were multiplied by a factor of 0.9---rDy/rLa. Similar scaling procedures have been successfully applied to obtain a better correspondence between model and experimental PCFs [9,10 and refs. therein]. All calculations were performed with the use of the program C R Y S R D F [15]. As can be seen from Fig. 3(a), the model and the experimental PCFs do not agree. The peaks of the model PCF are too high by comparison with those of the experimental one and, further, the finer details of the latter are not reproduced by the former at all. This disagreement shows that the short-range atomic order in RECu z

0.5

0.0

Y ii

1.0

J i 1 , 1 , 1

iii

3.0

ii

, , , , , i , l l

5.0

i i i i

i i i 1 , , 1 1 1 1 1 1

7.0

9.0

r (I)

Fig. 3. Comparison between the pair correlation function for DyCu 2 metallic glass, ( ) and the model pair correlation function ( . . . . . ) for: (a) MgCu2-type, (b) KHg2-type and (c) A1B2-type disordered crystalline structures.

V. Petkov, A. Apostolot' /Journal of Non-Crystalline Solids 167 (1994) 255-262

glasses differs from that in the Laves phase R E T 2. The structure of Laves phases can be considered as built of close-packed tetrahedral units [16]. Evidently, the structure of RECu 2 glasses cannot be described on the basis of a dense packing of tetrahedra. Fig. 3(b) shows that there is not a good correspondence between the model PCF for KHg2-type disordered crystalline compounds and the experimental PCF for DyCu 2 glass. This lack means that the structure of KHg2(CeCu2)-type crystalline compounds, similarly to that of the Laves phases, cannot serve as a model for the RECu 2 glassy structure. Inspection of Fig. 3(c) reveals that there is a satisfactory agreement between the model and the experimental PCFs. The model PCF well reproduces the positions and heights of all main peaks in the experimental PCF up to 0.9 nm. The characteristic details in the experimental PCF, including the pronounced splitting of its first peak, are also reproduced. Interference functions calculated from disordered A1B2-type arrangement also agree well with the experimental interference functions for R E C u 2 glasses (see the dashed lines in Fig. 1). The observed similarities indicate that the local atomic arrangement in RECu 2 glasses investigated resembles that in AIB2-type crystalline compounds. The structure of these compounds can be considered as built of close-packed trigonal prisms sharing all their faces [16] (see

Fig. 4. Fragment of the crystalline lattice of RECu 2 compound with the A1B2-type structure, o , RE atoms; o, Cu atoms.

259

Fig. 4). Clearly, the structure of RECu 2 glasses can be approximated by an ensemble of densepacked trigonal prisms. On the basis of this result, one can conclude that the type of short-range atomic ordering of melt-spun RECu 2 metallic glasses is completely distinct from that of R E T 2 glasses (T = Fe, Co, Ni) obtained by sputtering and mechanical alloying, i.e., that the change in preparation technique and the substitution of the transition metallic component, T, for the noble metal Cu, changes the type of short-range atomic order in R E T 2 glasses. To verify this conclusion, the partial atomic distances and the partial coordination numbers for RECu 2 glasses (RE = Tb, Dy), which are structural parameters sensitive to the type of short-range atomic order, were obtained by a profile analysis of the experimental PCFs and compared with the corresponding structural parameters of R E T 2 glasses (T = Fe, Co, Ni).

4.2. Determination of the partial atomic distances and partial coordination numbers for RECu 2 glasses The profile analysis of a PCF consists of it approximating by a sum of Gaussians, each pertaining to a particular peak in its profile [8,17]. The parameters of the individual Gaussians, which are adjusted until a good approximation is achieved, are structurally relevant: the positions of the Gaussians correspond to frequently occurring interatomic distances and the areas correspond to the corresponding number of atomic pairs. Thus a successful profile analysis of an experimental PCF yields a set of characteristic parameters of the amorphous structure under study. The choice of the number and the positions of Gaussians approximating the PCFs for RECu 2 glasses is, however, far from straightforward since the individual peaks in the experimental PCFs are not well resolved. That is why the characteristic structural data of A1Ba-type crystal structure, namely the positions of the first few coordination spheres and the corresponding coordination numbers of LaCu 2 crystalline compound, have been used as initial values of the structural parameters

K Petkov, A. Apostolov /Journal of Non-Crystalline Solids 167 (1994) 255-262

260

2.0

varied in the profile analysis of the PCFs for RECu z glasses (RE = Tb, Dy). This approach ensures that reliable structural data are obtained for the RECu 2 glasses investigated since, as was shown in the previous section, their local atomic arrangement resembles that in the A1B2-type disordered crystalline compounds. The results of the profile analysis of PCFs for the TbCu 2 and the DyCu 2 glass are shown in Figs. 5 and 6, respectively. The reliability, R factor, defined in Ref. [18], which indicates the quality of the profile analyses performed, is 5.22% for the TbCu 2 and 3.96% for the DyCu 2 case. The computations were performed with the help of the program FIT [181. The first three Gaussians, approximating the profile of the experimental PCFs in the region from 0.18 to 0.42 nm, correspond to the contributions of C u - C u , R E - C u and R E - R E atomic pairs to the first coordination shell of RECu 2 glasses (RE = Tb, Dy), respectively. The partial coordination numbers and the partial coordination radii, estimated on the basis of the parameters of these Gaussians, are listed in Table 1. The corresponding structural parameters of the MgCuz-type, KHgz-type, A1B2-type crystal structures, TbFe z glass, with local atomic arrangement similar to that of the tetrahedrally close-packed Laves phases, and DyFe 2 glass, the local atomic arrangement of which similar is to that in the

"C"

1.0

L'

o.s

'v', 7-,, / / " ,

.^ v

/?, t / // ~ \

,,

/ /~ \/ ,'\ \

',

~<~ <;'C\

",,"\

-0.5

-1.0 1.0

2.0

3.0

4.0

5.0

6.0

(~) Fig. 5. Profile analysis of the pair correlation function for TbCu 2 metallic glass. The residual difference between the experimental PCF ( ) and the Gaussians ( . . . . ) approximating its profile is shown in the lower part. r

computer modelled assemblies of randomly packed hard spheres, are also listed in Table 1. The obtained first-neighbour C u - C u distance in RECu 2 glasses is shorter than that observed in Ybz2Cu78 glass [6] and longer than that in Gd57Cu43 [9]. The obtained first-neighbour T b Tb and D y - D y separations correspond to those encountered in other R E - T glasses of similar chemical composition [1-6,8,9]. All first-

Table 1 Partial atomic distances, rip (in nm) and partial coordination numbers, Zi? for R E C u 2 ( R E = Tb, Dy) and R E F e 2 ( R E = Tb, Dy) glasses, and for the MgCuz-type, KHgz-type and AIBz-type crystalline structures all with chemical composition of the type , 5 ~ 2 ,~,_,~

J-~,

rij TbCu 2 DyCu 2 DyFe 2 b TbF% c MgCu 2 KHg 2 d AIB2 a

0.242(2) 0.241(2)

a

za¢_,~¢'

[Ref.]

Zij

rij

Zij

rij

Zij

3.6(5) 3.6(5) 5(1) 6.4

0.296(2) 0.297(2)

9.1(5) 9.1(5) 8(1) 10.3

0.359(2) 0.356(2)

4.5(5) 4.3(5) 6(1) 6.3

[this work] [this work] [4,5] [1]

4 4 or 6 4 or 6

[11-14] [11-14] [11-14]

6 4 or 7 3 or 5

12 12 12

a The n u m b e r s in parentheses represent the error in the last digit of the experimental values reported. b With a structure build up of randomly dense-packed Dy and Fe atoms. c With a structure build up of tetrahedrally dense-packed Tb and Fe atoms. d The n u m b e r of first neighbour ~-~¢" and ..~-~' atoms depends on the definition for the spatial extent of the first coordination sphere adopted.

K Petkoc, A. Apostoloc/Journal of Non-Crystalline Solids" 167 (1994) 255-262 2.0

ED

1.5

!.0

I;

',,, , -

/~l

o.~

I"

f):

t

j~ ,/

,

\

\,

/

."

", ,

,

-0.5

-1.0

1.o

2.0

3.0

4.0

5.0

6.0

(~,) Fig. 6. Profile analysis of the pair correlation function for D y C u 2 metallic glass. The residual difference between the experimental PCF ( ) and the Gaussians (. . . . ) approximating its profile is shown in the lower part. r

neighbour distances in R E C u 2 glasses are close to the sum of the corresponding Goldschmidt atomic radii [16]. The survey of Table 1 also shows that the number of Cu and R E atomic pairs in R E C u 2 glasses is less than the number of the corresponding Fe and R E atomic pairs in both the TbFe 2 glass and the DyFe 2 glass. Further, the partial coordination numbers of R E C u 2 glasses are closer to those of the AIBz-type, related to the KHg2-type crystalline structure, than to those of the MgCu2-type structure. (These results are not predetermined by the use of the coordination numbers of A1B2-type structure as initial values for the parameters varied in the profile analysis of the experimental PCFs since they are reproduced in general when other sets of such initial values are used.) These observations indicate that the local atomic arrangement in R E C u 2 glasses resembles that in AIBz-type crystalline compounds and corroborates the suggestion that the type of short-range atomic order in R E C u 2 glasses (RE = Tb, Dy) is different to that in R E T 2 glasses (T = Fe, Co, Ni). To clarify the reason for this difference, the Warren chemical short-range order parameter, o~ = 1 - - Z R E _ T / [ C T ( Z ) ] ,

(4)

26l

where ( Z ) = CTCNRE + CRECN v, C, is the atomic concentration and CN i the average number of nearest neighbours of the /-type atom (CNRE = ZRE-RE + ZRE T) [19], for the glasses presented in Table 1 was calculated. The values obtained are a = - 0 . 1 9 for the TbCu 2 and DyCu 2 glasses, a = - 0 . 0 5 for the TbFe 2 glass and a = +0.01 for the DyFe 2 glass. It is clearly seen that there is a well pronounced preference between the unlike atoms in RECu 2 glasses (RE = Tb, Dy) whereas the R E T 2 glasses ( R E = T b , Dy; T = Fe) are almost fully chemically disordered. It is thus not surprising that the structure of R E T 2 glasses (T = Fe, Co, Ni) is approximate to either a random or a tetrahedral dense packing of the constituent atoms. It is shown by computer simulations that both random atomic packings almost free of tetrahedral structural units and packings with quite a high degree of tetrahedrality can be obtained in the absence of chemical and symmetrical constraints [20,21]. The presence of preferential interactions between the R E and Cu atoms constituting the RECu 2 glasses (RE = Tb, Dy) is most probably the reason for the formation of specific structural units of a trigonal-prismatic-type with them. This specific local atomic arrangement of melt-spun RECu 2 glasses is assumed to be responsible for the observed peculiarities of their magnetic behaviour which will be reported elsewhere [22].

5. Conclusion

The structure of melt-spun RECu 2 glasses (RE = Tb, Dy) can be neither a random nor a tetrahedral dense packing of the constituent atoms both encountered in the R E T 2 glasses (RE = Fe, Co, Ni). It can be well described as an ensemble of trigonal prisms dense packed in a way similar to that found in the AlBz-type crystalline compounds.

The authors are indebted to Mr L. Bozukov from Sofia University, Bulgaria, for preparation of the samples.

262

1I..Petkou, A. Apostolov /Journal of Non-Crystalline Solids 167 (1994) 255-262

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Rare-Earth Alloys (Visha Shkola, Lvov, 1982) (in Russian). R. Mansey, G. Raynor and I. Harris, J. Less-Comm. Met. 14 (1968) 329, 337. D. Debray, J. Less-Comm. Met. 30 (1973) 237. A. Storm and K. Benson, Acta Crystallogr. 16 (1963) 701. V. Petkov, A. Aspostolov, S. Neov, E. Gerasimova and B. Sidjimov, in: Proc. 3rd Nat. Conf. on X-ray Diffraction Methods, Nesebar, Bulgaria, 1989, p. 113 (in Bulgarian). W. Pearson, in: Crystal Chemistry and Physics of Metals and Alloys (Wiley, New York, 1972). F. Hajdu, Phys. Status Solidi A60 (1980) 365. V. Petkov and N. Bakaltchev, J. Appl. Crystallogr. 23 (1990) 138. C. Wagner, J. Non-Cryst. Solids 42 (1980) 3. T. Ichikawa, Phys. Status Solidi A29 (1975) 293. C. Briant and J. Burton, Phys. Status Solidi B85 (1978) 393. L. Bozukov, IEEE Trans. Magn. (1993) in press.