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Thermal stability of amorphous rare earth-iron alloys
Journal of the Lea-Common
FERN
Met&
79 (1981) 9 - 18
STARILITY OF ~O~HOUS
9
RARE EARTH-IRON ALLOYS
K. H. J. BUSCHOW
Philips &search Labomtorfes,
Eindhoven (The Netherlands)
(Received August 29,198O)
Amorphous alloys RssFe= (R = Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu), Tbl,Fe, (x = 0.31,0.40,0.45,0.50f and Eq,Fe, (3~= 0.25,0.31,0.33, O-37,0.40) were prepared by melt spinning.The electricalresistivityp of the alloys based on terbium was studied as a function of temperature (4.2 300 K). Negativevalues of the temperature coefficient of resistivitywere observed in the alloys with iron concentrations correspondingto x = 0.40, x = 0.45 and x = 0.50. The crystallizationbehaviour of the variousalloys was studied usingdifferential scanningcalorimetry (DSC) and X-ray diffraction. In generaltwo exothermic heat effects were observed in the DSC traces. The heat effect occurring at the lower temperatureT1 was identified as being caused by precipitation of the rare earth metal. The heat effect occurring at the higher temperature I; corresponds to the crystallizationof the Cl5 phase RFez. For the heavierrare earth elements (R = Dy - Lu) the temperature TX co~espond~g to the lower ~~zation peak increaseswith increasingatomic number of the rare earth and follows closely the R dependence observed in amorphous R&o3 and R,Nis alloys. For rare earth elements lighterthan dysprosium the temperatureT1 in Rs9Fes, has a tendency to be much lower than the first crystallizationtemperaturein the corresponding R&o3 and R,Nis amorphous alloys. Furthermore,Tz no longer increases with increasingatomic number of R. A discussion is given in terms of the heat of alloying and the heat of vacancy formation.
1. Introduction In severalprevious investigations[l, 2 ] we have analysedthe thermal stability of a variety of amorphous alloys between two metals in terms of a model in which the crystallizationtemperature7”, scales linearlywith the corresponding hole formation enthalpy A&, where A&, refers to a hole the size of the smallertype of atom in the alloy. In most of the amorphous alloys the relation 7’, w 7A&, is obeyed [I]. Much higher values of TX than those correspondingto this relation have been found in severalamorphous calcium alloys, e.g. C&&s6 [ 33 . Recent calculationsmade by Hafner [ 41 using the pseudopotential method have shown that, on alloying, the @ Elsevier ~uoia~n~ed
in The Netherlands
10
radius ratio between calcium and its partner element may become considerably smaller (RCa/BM = 1.15) than the radius ratio based on the pure metals or on Gold~hmidt radii (Rca/& = 1.40). The hole formation enthalpies depend markedly on the radius ratio (or better on the ratio of atomic volumes) so that the enthalpy values calculated on the basis of the smaller radius ratio are comparatively larger. This removes to a great extent the aforementioned discrepancy between T, values observed and those expected from the relation T, = 7A&. A second group that does not behave in agreement with this relation comprises the amorphous alloys between the elements gold or silver and iron or cobalt [ 51. As in amorphous Gdss Fesl , the crystallization temperature is much lower than expected from TX = 7A&. As a possible origin of this discrepancy we have mentioned [l] the fact that the heat AH, of mixing in these alloys is positive. The purpose of the present ~vest~ation is to assess more clearly the role played by AH, in the thermal stability. For this reason the investigation of amorphous Rs9Feal will be extended to both lighter and heavier rare earth elements (R q Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu). This alloy series is well suited for this purpose since A&, changes from small positive values to comparatively larger negative values along the lanthanide series [ 61.
2. Experimental The amorphous R-Fe alloys were prepared by melt spinning under purified argon gas using arc-melted alloy buttons as starting materials. X-ray diffraction patterns were obtained with Cu Kol radiation in combination with an X-ray monochromator. The thermal behaviour of the alloys was studied using a DuPont 910 differential scanning calorimeter and purified argon during the measurements. In amorphous DyssFeal the transformations occurring during the heating of the samples were studied in more detail by varying the heating rate between :0.5 and 100 K mine1 , At the highest heating rates it was found that the temperature of the specimens lagged behind that recorded by the differential scanning calorimetry (DSC) unit. In these cases the necessary corrections were determined from the lead solid-liquid transition recorded under similar circumstances. The origin of the heat effects observed in the DSC traces was correlated with the results of the X-ray examination by heating the ribbons to distinct stages in the crystallization process followed by quenching and X-ray diffraction. The electrical resistivity measurements were performed using a four-probe technique while the temperature was slowly increased or decreased at a constant rate.
3. Experimental results Amorphous alloys of the type RssFe,, could not be prepared by melt spinning when the element R was a light rare earth element having an atomic
11
number smaller than that of samarium. Some examples of DSC traces obtained on various amorphous Rss Fear alloys with a heating rate of 50 K mm-’ are shown in Fig. 1. Most of the alloys (R - Dy, Ho, Er, Tm, Lu) give rise to two strong exothermic heat effects, preceded by a relatively small endothermic effect. This endothermic effect corresponds to the glass transitions. As has been already observed [7] in ErssFesa, X-ray diffraction shows that the first exothermic effect at Tl corresponds to the crystallization of the pure rare earth component. X-ray diffraction also shows that small diffraction peaks due to the precipitation of the pure rare earth metal or a metastable intermetallic phase occur below Tl without a pronounced heat effect. From a comparison of the intensities of these diffraction lines and the intensity of the diffuse amorphous (principal) halo it can be inferred that the precipitations occurring below Tl are only minor. These minor precipitations are probably the result of small inhomogeneities present in the amorphous ribbons. They will not be considered in the following. In some cases the precipitation corresponding to Tl involves a metastable phase. For instance in the amorphous erbium and lutetium alloys the X-ray diagrams obtained after quenching from above TX were composed of the X-ray pattern of the pure rare earth component plus single diffraction lines corresponding to the spacings d = 2.92 A and d = 2.89 A for erbium and lutetium respectively. These lines were no longer present in the X-ray diagrams of alloys quenched from temperatures T > Tz. This and the fact that such diftiction lines are absent in ascast (crystalline) alloys are taken as an indication of the metastable nature of the corresponding compounds. The peak at Tz could be shown by X-ray diffraction to correspond to the crystallization of the cubic Laves phase compound RFea . The X-ray patterns of alloys quenched from above Tz consist of the set of lines corresponding to the cubic RFez type together with a set of lines belonging to the pure rare earth metal. For compositions Rsa Feal the simultaneous presence of both these phases is expected at thermal equilibrium according to the R-Fe phase diagrams [8]. The alloys SmssFesl and TbssFeal each give rise to only a single exothermic peak (see Fig. 1) corresponding to the crystallization of SmFez and TbFes. In this respect these alloys behave in very much the same way as GdssFeal does; this alloy has been studied previously [9] . In each of these three cases it could be shown by X-ray diffraction that crystallization of the pure rare earth element occurs over quite an extended temperature range comprising temperatures only slightly above room temperature. As far as they could be observed in the various R6sFesl alloys we plotted the temperatures corresponding to the thermal events at Tl and Tz as a function of the rare earth component (Fig. 2). It is clear that amorphous alloys of comparatively high iron concentrations are less supersaturated with respect to the rare earth component. Hence the first crystallization process corresponding to Tl will become relatively less important if the iron concentration of the alloy increases. This is in agreement with the experimental results shown in Fig. 3. When studied as a function of iron concentration the crystallization behaves as shown for the Erl,Fe, alloys in Fig. 3. In all four cases the two-
12
Tb
Tm
I
I
200
I
1
300
I
,
I
LOO
,
600
,
6 0
TI’CI
Fig. 1. DSC traces of various amorphous rate, 50 K min-l).
R-Fe alloys of composition
RaFea
(heating
Fig, 2. Dependence of the transformation temperatures TX and T2 observed in DSC experiments (heating rate, 60 K miner) on the rare earth component in ReeFe31; - - -, mean of the TX values found in the alloys R6sNi31 and ReaCoal.
step crystal&&ion behaviour (TXand T2) is preserved.The distance between the two thermal eventsis seen to become smalleras the iron concen~tion is increased,whilst the relativeintensityof the thermal event at T1 becomes much reduced in the same sense. In amorphous DyseFeai we studied the crystallizationprocesses in more detail by applying different heatii rates, varyingfrom 0.5 to 100 K min-’ . It was found that the peak temperaturescorrespondingto the exothermic heat effects at Tl and T2 both increasemarkedly with increasing heatingrate. Measurementsof the temperaturedependence of the electricalresistivity p were made on several amorphous Tbr , Fe, alloys, The room temperature resistivitieswere found to be quite high, typically of the order of a few hundred microohms centimetres.In all alloys investigated(IC= 0.31,0.40, 0.45,0.50) p -provedto be almost independentof temperature.As an example Fig. 4 givesthe p(T) cme of TbrioFem(broken line), Insteadof p it is more appropriateto plot the more sensitiveresistivityratio r = {p(T) - p (300)}/ ~(300). From such plots it is found that the temperaturecoefficient of the resistivity(TCR) is positive in Tb7eFeaeand is negativein the three more
13
!QO
200
300
LOO
TI’CI
500
600
TIK)
Fig. 3. DSC traces of various amorphous Erl-% Fe, alloys (heating rate, 60 K min-’ ). Fig. 4. - - -, left-hand scale, temperature dependence of the resistivity in amorphous Tb Few;right-hand scale, temperature dependence of the resistivity ratio r = % (T) - p( 30b)}/p( 300) in three amorphous Tbl-, Fe, alloys.
iron-rich alloys. Plots of F for these three alloys are included in Fig. 4. In TbsOFeM the TCR is almost independent of the temperature, whereas in the alloys with x = 0.45 and x = 0.50 the TCR is somewhat higher below about 100 K than it is above this temperature. 4. Discussion In previous investigations [9, lo] of the thermal stability of amorphous R-Ni or R-Co alloys it has been found that the crystalhxation temperature TX, defined as the first peak temperature in the DSC traces, increases continuously along the lanthanide series from lanthanum to lutetium. For a fixed rare earth component there is hardly any difference between the TX values of the nickel alloys and those of the cobalt alloys. The mean TX values of the cobalt and nickel alloys, plotted as a function of the rare earth component R, are included in Fig. 2 and are represented as a broken line. It can be seen that the crystallization temperature in amorphous R-Fe alloys behaves in almost the same manner as in the corresponding nickel or cobalt alloys when R belongs to the group of heavy rare earth elements beyond R = Tb. In previous investigations [ 1,2] it has also been shown that the increase in TX with 3d atom concentration or with atomic number of the rare earth component can satisfactorily be explained in terms of a kinetic approach where the activation energy for crystallixation is taken to be proportional to the formation enthalpy AHh of a hole the size of the corresponding 3d atom. Thus it would seem from the results just described that the crystallization of the RssFesl alloys with R = Sm, Cd, Tb does not proceed in conformity with this model since crystallixation was observed to occur at temperatures close to room temperature or, in any case, at temperatures much lower than those indicated by the broken line in Fig. 2. The experimental results obtained for these three alloys could also be characterized
by stating that the crystallization which gives rise to a sharp heat effect at T1 in the alloys with the heavier rare earth components is shifted to lower temperatures and is smeared out considerably. This fact, together with the observation that T2 for these rare earth alloys deviates in the opposite direction (to higher temperatures, see Fig. 2), needs further discussion. As a first correction to the description in which the activation energy for crystallization is taken to be proportional to the hole formation enthalpy, it can be taken into account that there is a positive or a negative interaction between the rare earth and 3d atoms. As mentioned previously [ 1,9], it might be expected that it will be more difficult to create a hole in the alloy if there is a strongly attracting interaction between the rare earth and 3d atoms and it will be easier if there is a repulsive interaction. As measured from the heat AH, of mixing of rare-earth-rich R-Fe alloys, the former situation applies to alloys in which the rare earth component belongs to the elements at the end of the lanthanide series (AH, < 0) whereas the interaction is repulsive for rare earth components occurring at the beginning of the lanthanide series (AH, > 0) [6] . Qualitatively the inclusion of a positive AH, value (or negative, as the case may be) is in keeping with the observation of comparatively low (high) crystallization temperatures in the Re9Fesl alloys. As a second and more drastic correction to the description in terms of hole enthalpies, the effect of differences in the atomic arrangement of the amorphous alloys might be considered. Comparisons of the physical properties of amorphous alloys are usually made on the basis of the tacit assumption that the atomic arrangements in all these alloys are similar and can be represented by, for instance, a random dense packing of atoms or by equivalent arrangements. In our opinion this is rather improbable. In all cases where there is mutually attractive or repulsive interaction between the two types of atoms (AH, # 0) some degree of compositional short-range order will exist. If AH, > 0 there will be clustering between like atoms; if AH, < 0 there will be clustering between unlike atoms. In particular, in amorphous alloys prepared by continuous cooling from the liquid state the clustering already present in the liquid state will be frozen in and will be retained in the amorphous alloy. The positive value of AH, in alloys involving rare earths at the beginning of the lanthanide series in fact means that there is a tendency to phase separation in the liquid state. It is therefore not surprising that the corresponding alloys cannot be prepared in the amorphous state by melt spinning. For Rs9Fes1 alloys involving rare earths from the middle of the lanthanide series this tendency to phase separation is reduced, although regions with relatively high concentrations of like atoms in the liquid state and hence also in the amorphous ribbons might still be expected. If these regions are large, basically the same situation as would be encountered in amorphous alloys of higher rare earth concentration exists. The crystallization temperature in these areas will be relatively low, which agrees with experimental observation. The smearingout of the crystallization is probably a result of the presence of regions of different sizes. The presence of such
15
regions is not expected when R is a heavy rare earth occurring at the end of the lanthanide series. Here AH,,, < 0 and a behaviour similar to that observed in the corresponding cobalt or nickel alloys is expected. It has been shown [7] by transmission electron microscopy (TEM) examination that the low temperature crystallization in amorphous TbssFeal involves cu-Tb and some yet unidentified Tb-Fe inter-metallic compound. That clustering between like atoms is more pronounced for the light rare earth elements is shown by the TEM observation [9] that in Gd6aFesl the low temperature crystallization involves cu-Gdand pure a-Fe instead of some R-Fe compound as in TbssFes, . A consequence of this complete phase separation into the parent metals is that formation of the compound RFe2 at T2 will be rather difficult. Not only will there be difficulties in nucleation [9] of the RFez crystals in the matrices of a-Fe or a-Gd but also the growth of the RFes crystals will involve a comparatively large diffusion length. This may explain why the decrease in T2 in going from R = Lu to R = Tb is not continued for R - Gd. Instead T2 increases again. It should be noted that in Sm6sFesl the tendency to phase separation into the parent metals is even more pronounced than in GdssFeal , leading to an even larger T2 value. It will be clear from the foregoing that the transformations occurring at the temperatures Tl and T2 in R6aFes1 are different in nature. In general the transformation at Tl can be characterized as an amorphous-tocrystalline transformation and that at T2 can be characterized as a recrystallization between crystalline phases. Since the rate of both types of transformation is diffusion controlled it would be interesting to compare the magnitude of the corresponding activation energies. These activation energies can be derived from the dependence of the transformation temperatures Tl and T2 on the heating rate(s). Using the Kissinger [ 111 method we plotted semilogarithmically the values of sTlm2 (sT~-~) found in Dy,Feal against the corresponding values of T1-l (TzP1). As can be seen in Fig. 5, a straight line is obtained in both cases. This can be taken as evidence that both transformations can be described by a single activation law. From the slopes of these lines the values 2.42 eV and 2.28 eV are found for the activation energies of the transformations at TI and T2 respectively. These values are rather close to each other and, roughly speaking, it might be said that they do not support the view that diffusion in amorphous materials proceeds more easily than diffusion in atomically well-ordered crystalline materials does. However, that the iron concentration in the crystalline phases is different from that in the original amorphous alIoy has to be taken into account. Since cr-Dy is one of the crystalline phases that precipitates at T,, the second (metastable) Dy-Fe phase is necessarily richer in iron than DyssFesl is. For this reason the comparison described is not free of ambiguity. It was shown in Fig. 4 that the resistivity of the Tbl,FeX alloys investigated is rather high and nearly temperature independent when compared with crystalline materials where p 0: T6 over a large temperature range. The magnetic properties of these alloys have been studied previously [12]. Magnetic ordering occurs in the range 200 - 300 K. It can be seen from the
16
data given in Fig. 4 that the occurrence of magnetic ordering does not show up in the resistivity behaviour. Apparently, in view of the already high atomic disorder, the effect on the conduction electron scattering of the spin disorder can be neglected. The occurrence of a negative TCR has currently been explained [13 - 151 in terms of extensions of the Ziman model (high temperature limit). It is quite generally observed in amorphous alloys when the condition 2kr = Q, + SQ, is met. Here kv represents the Fermi wavevector of the conduction electrons and Q, is the wavenumber corresponding to the principal peak in the X-ray interference function I(Q). The quantity SQ, can be estimated from the width of the principal peak and is roughly equal to 0.15 A-l. The experimental values of QP were plotted as a function of composition (Fig. 6); the concentration dependence of kF calculated using the free-electron model was also plotted. In the concentration range considered the number of conduction electrons contributed by the iron atoms (0.6 electrons atom-‘) [ 141 is not very critical. For terbium we adopted three different values (3,2 and 1) for the number 2 of conduction electrons per terbium atom. It can be inferred from the results shown in Fig. 6 that the condition 2kF = QP * 0.15 is met only for the case where the terbium atoms contribute about two conduction electrons. This is intermediate between the value 2 = 3 derived from measurements on liquid rare earth alloys by Waseda et al. [ 161 and the value 2 = 1 found by Delley and Beck [17]. In the extended Ziman model the magnitude of p depends very critically on the number of conduction electrons when 2kF approaches the Q values corresponding to the principal peak in the interference function
10-s. 3.0
to-91 13
1.L
1.5 -
1.6
1.7
1.8
1.9
201 0.2
_--
__---
0.L x
T-'lK)-'K")
Fig. 5. Kissinger plots of the transformations various heating rates s.
_
observed
in DyeaFear
at Tr and Tz at
Fig. 6. Concentration dependence of the wavenumber QP of the principal amorphous conpeak of the X-ray interference function in amorphous Tbl,Fe, alloys ( -); centration dependence of k~ calculated on the assumption of the freeelectron model and 3 (upper), 2 (middle) and 1 (lower) conduction electrons contributed by the terbium atoms.
17
[18]. In view of the uncertainties in kF mentioned earlier we restricted ourselves to analysing only the temperature dependence of p . If we compare the p data obtained on the amorphous Tbl,Fe, alloys with those of the corresponding cobalt alloys [lo] we find that the region of negative TCR values comprises the lower 3d atom concentrations in the cobalt alloys. The alloy Tb6sCosl still has a negative TCR whereas in Tbs9 Feal the TCR is positive. In view of the low 3d atom concentration in both alloys it is unlikely that this is the result of the somewhat smaller number of conduction electrons contributed by cobalt than by iron. We believe rather that the positive TCR in TbssFesl is caused by the occurrence of some clustering between like atoms, which is also responsible for the deviating crystallization behaviour described earlier (see Fig. 1). We cannot, however, exclude the possibility that the low crystallization temperature of this alloy (see Section 3) leads to a small layer of microcrystalline material on the side of the ribbon which is not in contact with the copper wheel during melt spinning. Such a small microcrystalline layer is not easily detected by standard X-ray diffraction techniques. Since crystalline material, at low temperatures in particular, has a conductivity several orders of magnitude larger than the conductivity of amorphous material, the small microcrystalline layer may carry a relatively large portion of the current (with a positive TCR) and hence may mask the presence of a negative TCR for the remaining amorphous part of the ribbon. 5. Concluding remarks In an earlier investigation [7,9] it has been suggested that the glassforming ability depends to a certain extent on the heat of mixing between the two constituent metals. The present results obtained on alloys of heavy rare earth metals of the type R6aFes1 show that, once quenched into the amorphous state, the crystallization temperatures of these alloys are similar to those of the corresponding cobalt or nickel alloys, even though the cobalt or nickel alloys have considerably larger negative AH, values. This indicates that the absolute value of the (negative) heat of mixing has only a small influence on the crystallization temperature, although its effect on the ease of glass formation may be important [9] . Exceptions are encountered when AH, becomes positive. In these cases the corresponding amorphous alloys have crystallization temperatures that fall considerably below those of their nickel or cobalt counterparts. The effect of the positive value of AH, on TX is not to be sought, however, in a substantial reduction in the hole formation enthalpy AH, (TX = 7AH,). It leads rather to a different microstructure of the corresponding alloys and entails a tendency to phase separation into the parent metals on crystallization. In this respect the amorphous alloy SmaaFesi resembles closely the amorphous alloys of silver and gold with iron and cobalt. In these cases also the AH, values are positive and crystallization is expected to occur at temperatures considerably lower than those expected from the general relation TX = 7AH,.
Acknowledgment The author wishes to express his gratitude to N. M. Beekmans for performing the resistivity measurements.
References 1 K. H. J. Buschow and N. M. Beekmans, Solid State Commun., 35 (1980) 233;Phys. Rev. B, 19 (1979) 3843. 2 K. H. J. Buschow, J. Phys. (Park), Colloq., CS, 41 (1980) 559. 3 R. St. Amand and B. C. Giessen, Ser. Metall., 12 (1978) 1021. 4 J. Hafner, Phys. Rev. B, 21 (1980) 406. 5 H. A. Davies, Phys. Chem. Glasses, 17 (1976) 159. 6 A. R. Miedema and P. F. de Ch%el, in L. H. Bennett (ed.), Theory of Alloy Phase For-
mation, Rot. American Metallurgy Society Meet., New Orkan8, LA, 1979. 7 K. H. J. Buschow and A. G. Dirks, Electrochemical Society Conf. Proc., 1980, Vol. 8 9 10 11 12 13 14 15 16 17 18
80-2, Electrochemical Society, Princeton, NJ, 1980, p. 514. K. H. J. Buschow and A. S. van der Goot, Phys. Status Solidi, 35 (1969) 515. K. H. J. Buschow and A. G. Dirks, J. Phys. D, 13 (1980) 251. K. H. J. Buschow and N. M. Beekmans, Phys. Statue Solidi, 60 (1980) 193. H. E. Kissinger,AnaZ. Chem., 29 (1957) 1702. K. H. J. Buschow and A. M. van der Kraan, J. Magn. Magn. Mater., in the press. H. Beck and R. Oberle, in B. Cantor (ed.), Proc. 3rd Znt. Conf. on Rapidly Quenched Metak, Brighton, 1978, Metals Society, London, 1978, p. 416. H. J. Giintherodt, M. Miiller, R. Oberle, E. Hauser, H. U. Kiinzli, M. Liard and R. Miiller, Inst. Phys. Conf. Ser. 39 (1978) 436. L. V. Meisel and P. J. Cote,Phys. Rev. B, 17 (1978) 4652. Y. Waseda, A. Jain and S. Tamaki, J. Phys. F, 8 (1978) 125. B. DeBey and H. Beck, J. Phys. F, 9 (1979) 517. E. Esposito, H. Ehrenreich and C. D. Gelatt, Jr., Phys. Rev. B, 18 (1978) 3913.
FERN
Met&
79 (1981) 9 - 18
STARILITY OF ~O~HOUS
9
RARE EARTH-IRON ALLOYS
K. H. J. BUSCHOW
Philips &search Labomtorfes,
Eindhoven (The Netherlands)
(Received August 29,198O)
Amorphous alloys RssFe= (R = Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu), Tbl,Fe, (x = 0.31,0.40,0.45,0.50f and Eq,Fe, (3~= 0.25,0.31,0.33, O-37,0.40) were prepared by melt spinning.The electricalresistivityp of the alloys based on terbium was studied as a function of temperature (4.2 300 K). Negativevalues of the temperature coefficient of resistivitywere observed in the alloys with iron concentrations correspondingto x = 0.40, x = 0.45 and x = 0.50. The crystallizationbehaviour of the variousalloys was studied usingdifferential scanningcalorimetry (DSC) and X-ray diffraction. In generaltwo exothermic heat effects were observed in the DSC traces. The heat effect occurring at the lower temperatureT1 was identified as being caused by precipitation of the rare earth metal. The heat effect occurring at the higher temperature I; corresponds to the crystallizationof the Cl5 phase RFez. For the heavierrare earth elements (R = Dy - Lu) the temperature TX co~espond~g to the lower ~~zation peak increaseswith increasingatomic number of the rare earth and follows closely the R dependence observed in amorphous R&o3 and R,Nis alloys. For rare earth elements lighterthan dysprosium the temperatureT1 in Rs9Fes, has a tendency to be much lower than the first crystallizationtemperaturein the corresponding R&o3 and R,Nis amorphous alloys. Furthermore,Tz no longer increases with increasingatomic number of R. A discussion is given in terms of the heat of alloying and the heat of vacancy formation.
1. Introduction In severalprevious investigations[l, 2 ] we have analysedthe thermal stability of a variety of amorphous alloys between two metals in terms of a model in which the crystallizationtemperature7”, scales linearlywith the corresponding hole formation enthalpy A&, where A&, refers to a hole the size of the smallertype of atom in the alloy. In most of the amorphous alloys the relation 7’, w 7A&, is obeyed [I]. Much higher values of TX than those correspondingto this relation have been found in severalamorphous calcium alloys, e.g. C&&s6 [ 33 . Recent calculationsmade by Hafner [ 41 using the pseudopotential method have shown that, on alloying, the @ Elsevier ~uoia~n~ed
in The Netherlands
10
radius ratio between calcium and its partner element may become considerably smaller (RCa/BM = 1.15) than the radius ratio based on the pure metals or on Gold~hmidt radii (Rca/& = 1.40). The hole formation enthalpies depend markedly on the radius ratio (or better on the ratio of atomic volumes) so that the enthalpy values calculated on the basis of the smaller radius ratio are comparatively larger. This removes to a great extent the aforementioned discrepancy between T, values observed and those expected from the relation T, = 7A&. A second group that does not behave in agreement with this relation comprises the amorphous alloys between the elements gold or silver and iron or cobalt [ 51. As in amorphous Gdss Fesl , the crystallization temperature is much lower than expected from TX = 7A&. As a possible origin of this discrepancy we have mentioned [l] the fact that the heat AH, of mixing in these alloys is positive. The purpose of the present ~vest~ation is to assess more clearly the role played by AH, in the thermal stability. For this reason the investigation of amorphous Rs9Feal will be extended to both lighter and heavier rare earth elements (R q Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu). This alloy series is well suited for this purpose since A&, changes from small positive values to comparatively larger negative values along the lanthanide series [ 61.
2. Experimental The amorphous R-Fe alloys were prepared by melt spinning under purified argon gas using arc-melted alloy buttons as starting materials. X-ray diffraction patterns were obtained with Cu Kol radiation in combination with an X-ray monochromator. The thermal behaviour of the alloys was studied using a DuPont 910 differential scanning calorimeter and purified argon during the measurements. In amorphous DyssFeal the transformations occurring during the heating of the samples were studied in more detail by varying the heating rate between :0.5 and 100 K mine1 , At the highest heating rates it was found that the temperature of the specimens lagged behind that recorded by the differential scanning calorimetry (DSC) unit. In these cases the necessary corrections were determined from the lead solid-liquid transition recorded under similar circumstances. The origin of the heat effects observed in the DSC traces was correlated with the results of the X-ray examination by heating the ribbons to distinct stages in the crystallization process followed by quenching and X-ray diffraction. The electrical resistivity measurements were performed using a four-probe technique while the temperature was slowly increased or decreased at a constant rate.
3. Experimental results Amorphous alloys of the type RssFe,, could not be prepared by melt spinning when the element R was a light rare earth element having an atomic
11
number smaller than that of samarium. Some examples of DSC traces obtained on various amorphous Rss Fear alloys with a heating rate of 50 K mm-’ are shown in Fig. 1. Most of the alloys (R - Dy, Ho, Er, Tm, Lu) give rise to two strong exothermic heat effects, preceded by a relatively small endothermic effect. This endothermic effect corresponds to the glass transitions. As has been already observed [7] in ErssFesa, X-ray diffraction shows that the first exothermic effect at Tl corresponds to the crystallization of the pure rare earth component. X-ray diffraction also shows that small diffraction peaks due to the precipitation of the pure rare earth metal or a metastable intermetallic phase occur below Tl without a pronounced heat effect. From a comparison of the intensities of these diffraction lines and the intensity of the diffuse amorphous (principal) halo it can be inferred that the precipitations occurring below Tl are only minor. These minor precipitations are probably the result of small inhomogeneities present in the amorphous ribbons. They will not be considered in the following. In some cases the precipitation corresponding to Tl involves a metastable phase. For instance in the amorphous erbium and lutetium alloys the X-ray diagrams obtained after quenching from above TX were composed of the X-ray pattern of the pure rare earth component plus single diffraction lines corresponding to the spacings d = 2.92 A and d = 2.89 A for erbium and lutetium respectively. These lines were no longer present in the X-ray diagrams of alloys quenched from temperatures T > Tz. This and the fact that such diftiction lines are absent in ascast (crystalline) alloys are taken as an indication of the metastable nature of the corresponding compounds. The peak at Tz could be shown by X-ray diffraction to correspond to the crystallization of the cubic Laves phase compound RFea . The X-ray patterns of alloys quenched from above Tz consist of the set of lines corresponding to the cubic RFez type together with a set of lines belonging to the pure rare earth metal. For compositions Rsa Feal the simultaneous presence of both these phases is expected at thermal equilibrium according to the R-Fe phase diagrams [8]. The alloys SmssFesl and TbssFeal each give rise to only a single exothermic peak (see Fig. 1) corresponding to the crystallization of SmFez and TbFes. In this respect these alloys behave in very much the same way as GdssFeal does; this alloy has been studied previously [9] . In each of these three cases it could be shown by X-ray diffraction that crystallization of the pure rare earth element occurs over quite an extended temperature range comprising temperatures only slightly above room temperature. As far as they could be observed in the various R6sFesl alloys we plotted the temperatures corresponding to the thermal events at Tl and Tz as a function of the rare earth component (Fig. 2). It is clear that amorphous alloys of comparatively high iron concentrations are less supersaturated with respect to the rare earth component. Hence the first crystallization process corresponding to Tl will become relatively less important if the iron concentration of the alloy increases. This is in agreement with the experimental results shown in Fig. 3. When studied as a function of iron concentration the crystallization behaves as shown for the Erl,Fe, alloys in Fig. 3. In all four cases the two-
12
Tb
Tm
I
I
200
I
1
300
I
,
I
LOO
,
600
,
6 0
TI’CI
Fig. 1. DSC traces of various amorphous rate, 50 K min-l).
R-Fe alloys of composition
RaFea
(heating
Fig, 2. Dependence of the transformation temperatures TX and T2 observed in DSC experiments (heating rate, 60 K miner) on the rare earth component in ReeFe31; - - -, mean of the TX values found in the alloys R6sNi31 and ReaCoal.
step crystal&&ion behaviour (TXand T2) is preserved.The distance between the two thermal eventsis seen to become smalleras the iron concen~tion is increased,whilst the relativeintensityof the thermal event at T1 becomes much reduced in the same sense. In amorphous DyseFeai we studied the crystallizationprocesses in more detail by applying different heatii rates, varyingfrom 0.5 to 100 K min-’ . It was found that the peak temperaturescorrespondingto the exothermic heat effects at Tl and T2 both increasemarkedly with increasing heatingrate. Measurementsof the temperaturedependence of the electricalresistivity p were made on several amorphous Tbr , Fe, alloys, The room temperature resistivitieswere found to be quite high, typically of the order of a few hundred microohms centimetres.In all alloys investigated(IC= 0.31,0.40, 0.45,0.50) p -provedto be almost independentof temperature.As an example Fig. 4 givesthe p(T) cme of TbrioFem(broken line), Insteadof p it is more appropriateto plot the more sensitiveresistivityratio r = {p(T) - p (300)}/ ~(300). From such plots it is found that the temperaturecoefficient of the resistivity(TCR) is positive in Tb7eFeaeand is negativein the three more
13
!QO
200
300
LOO
TI’CI
500
600
TIK)
Fig. 3. DSC traces of various amorphous Erl-% Fe, alloys (heating rate, 60 K min-’ ). Fig. 4. - - -, left-hand scale, temperature dependence of the resistivity in amorphous Tb Few;right-hand scale, temperature dependence of the resistivity ratio r = % (T) - p( 30b)}/p( 300) in three amorphous Tbl-, Fe, alloys.
iron-rich alloys. Plots of F for these three alloys are included in Fig. 4. In TbsOFeM the TCR is almost independent of the temperature, whereas in the alloys with x = 0.45 and x = 0.50 the TCR is somewhat higher below about 100 K than it is above this temperature. 4. Discussion In previous investigations [9, lo] of the thermal stability of amorphous R-Ni or R-Co alloys it has been found that the crystalhxation temperature TX, defined as the first peak temperature in the DSC traces, increases continuously along the lanthanide series from lanthanum to lutetium. For a fixed rare earth component there is hardly any difference between the TX values of the nickel alloys and those of the cobalt alloys. The mean TX values of the cobalt and nickel alloys, plotted as a function of the rare earth component R, are included in Fig. 2 and are represented as a broken line. It can be seen that the crystallization temperature in amorphous R-Fe alloys behaves in almost the same manner as in the corresponding nickel or cobalt alloys when R belongs to the group of heavy rare earth elements beyond R = Tb. In previous investigations [ 1,2] it has also been shown that the increase in TX with 3d atom concentration or with atomic number of the rare earth component can satisfactorily be explained in terms of a kinetic approach where the activation energy for crystallixation is taken to be proportional to the formation enthalpy AHh of a hole the size of the corresponding 3d atom. Thus it would seem from the results just described that the crystallization of the RssFesl alloys with R = Sm, Cd, Tb does not proceed in conformity with this model since crystallixation was observed to occur at temperatures close to room temperature or, in any case, at temperatures much lower than those indicated by the broken line in Fig. 2. The experimental results obtained for these three alloys could also be characterized
by stating that the crystallization which gives rise to a sharp heat effect at T1 in the alloys with the heavier rare earth components is shifted to lower temperatures and is smeared out considerably. This fact, together with the observation that T2 for these rare earth alloys deviates in the opposite direction (to higher temperatures, see Fig. 2), needs further discussion. As a first correction to the description in which the activation energy for crystallization is taken to be proportional to the hole formation enthalpy, it can be taken into account that there is a positive or a negative interaction between the rare earth and 3d atoms. As mentioned previously [ 1,9], it might be expected that it will be more difficult to create a hole in the alloy if there is a strongly attracting interaction between the rare earth and 3d atoms and it will be easier if there is a repulsive interaction. As measured from the heat AH, of mixing of rare-earth-rich R-Fe alloys, the former situation applies to alloys in which the rare earth component belongs to the elements at the end of the lanthanide series (AH, < 0) whereas the interaction is repulsive for rare earth components occurring at the beginning of the lanthanide series (AH, > 0) [6] . Qualitatively the inclusion of a positive AH, value (or negative, as the case may be) is in keeping with the observation of comparatively low (high) crystallization temperatures in the Re9Fesl alloys. As a second and more drastic correction to the description in terms of hole enthalpies, the effect of differences in the atomic arrangement of the amorphous alloys might be considered. Comparisons of the physical properties of amorphous alloys are usually made on the basis of the tacit assumption that the atomic arrangements in all these alloys are similar and can be represented by, for instance, a random dense packing of atoms or by equivalent arrangements. In our opinion this is rather improbable. In all cases where there is mutually attractive or repulsive interaction between the two types of atoms (AH, # 0) some degree of compositional short-range order will exist. If AH, > 0 there will be clustering between like atoms; if AH, < 0 there will be clustering between unlike atoms. In particular, in amorphous alloys prepared by continuous cooling from the liquid state the clustering already present in the liquid state will be frozen in and will be retained in the amorphous alloy. The positive value of AH, in alloys involving rare earths at the beginning of the lanthanide series in fact means that there is a tendency to phase separation in the liquid state. It is therefore not surprising that the corresponding alloys cannot be prepared in the amorphous state by melt spinning. For Rs9Fes1 alloys involving rare earths from the middle of the lanthanide series this tendency to phase separation is reduced, although regions with relatively high concentrations of like atoms in the liquid state and hence also in the amorphous ribbons might still be expected. If these regions are large, basically the same situation as would be encountered in amorphous alloys of higher rare earth concentration exists. The crystallization temperature in these areas will be relatively low, which agrees with experimental observation. The smearingout of the crystallization is probably a result of the presence of regions of different sizes. The presence of such
15
regions is not expected when R is a heavy rare earth occurring at the end of the lanthanide series. Here AH,,, < 0 and a behaviour similar to that observed in the corresponding cobalt or nickel alloys is expected. It has been shown [7] by transmission electron microscopy (TEM) examination that the low temperature crystallization in amorphous TbssFeal involves cu-Tb and some yet unidentified Tb-Fe inter-metallic compound. That clustering between like atoms is more pronounced for the light rare earth elements is shown by the TEM observation [9] that in Gd6aFesl the low temperature crystallization involves cu-Gdand pure a-Fe instead of some R-Fe compound as in TbssFes, . A consequence of this complete phase separation into the parent metals is that formation of the compound RFe2 at T2 will be rather difficult. Not only will there be difficulties in nucleation [9] of the RFez crystals in the matrices of a-Fe or a-Gd but also the growth of the RFes crystals will involve a comparatively large diffusion length. This may explain why the decrease in T2 in going from R = Lu to R = Tb is not continued for R - Gd. Instead T2 increases again. It should be noted that in Sm6sFesl the tendency to phase separation into the parent metals is even more pronounced than in GdssFeal , leading to an even larger T2 value. It will be clear from the foregoing that the transformations occurring at the temperatures Tl and T2 in R6aFes1 are different in nature. In general the transformation at Tl can be characterized as an amorphous-tocrystalline transformation and that at T2 can be characterized as a recrystallization between crystalline phases. Since the rate of both types of transformation is diffusion controlled it would be interesting to compare the magnitude of the corresponding activation energies. These activation energies can be derived from the dependence of the transformation temperatures Tl and T2 on the heating rate(s). Using the Kissinger [ 111 method we plotted semilogarithmically the values of sTlm2 (sT~-~) found in Dy,Feal against the corresponding values of T1-l (TzP1). As can be seen in Fig. 5, a straight line is obtained in both cases. This can be taken as evidence that both transformations can be described by a single activation law. From the slopes of these lines the values 2.42 eV and 2.28 eV are found for the activation energies of the transformations at TI and T2 respectively. These values are rather close to each other and, roughly speaking, it might be said that they do not support the view that diffusion in amorphous materials proceeds more easily than diffusion in atomically well-ordered crystalline materials does. However, that the iron concentration in the crystalline phases is different from that in the original amorphous alIoy has to be taken into account. Since cr-Dy is one of the crystalline phases that precipitates at T,, the second (metastable) Dy-Fe phase is necessarily richer in iron than DyssFesl is. For this reason the comparison described is not free of ambiguity. It was shown in Fig. 4 that the resistivity of the Tbl,FeX alloys investigated is rather high and nearly temperature independent when compared with crystalline materials where p 0: T6 over a large temperature range. The magnetic properties of these alloys have been studied previously [12]. Magnetic ordering occurs in the range 200 - 300 K. It can be seen from the
16
data given in Fig. 4 that the occurrence of magnetic ordering does not show up in the resistivity behaviour. Apparently, in view of the already high atomic disorder, the effect on the conduction electron scattering of the spin disorder can be neglected. The occurrence of a negative TCR has currently been explained [13 - 151 in terms of extensions of the Ziman model (high temperature limit). It is quite generally observed in amorphous alloys when the condition 2kr = Q, + SQ, is met. Here kv represents the Fermi wavevector of the conduction electrons and Q, is the wavenumber corresponding to the principal peak in the X-ray interference function I(Q). The quantity SQ, can be estimated from the width of the principal peak and is roughly equal to 0.15 A-l. The experimental values of QP were plotted as a function of composition (Fig. 6); the concentration dependence of kF calculated using the free-electron model was also plotted. In the concentration range considered the number of conduction electrons contributed by the iron atoms (0.6 electrons atom-‘) [ 141 is not very critical. For terbium we adopted three different values (3,2 and 1) for the number 2 of conduction electrons per terbium atom. It can be inferred from the results shown in Fig. 6 that the condition 2kF = QP * 0.15 is met only for the case where the terbium atoms contribute about two conduction electrons. This is intermediate between the value 2 = 3 derived from measurements on liquid rare earth alloys by Waseda et al. [ 161 and the value 2 = 1 found by Delley and Beck [17]. In the extended Ziman model the magnitude of p depends very critically on the number of conduction electrons when 2kF approaches the Q values corresponding to the principal peak in the interference function
10-s. 3.0
to-91 13
1.L
1.5 -
1.6
1.7
1.8
1.9
201 0.2
_--
__---
0.L x
T-'lK)-'K")
Fig. 5. Kissinger plots of the transformations various heating rates s.
_
observed
in DyeaFear
at Tr and Tz at
Fig. 6. Concentration dependence of the wavenumber QP of the principal amorphous conpeak of the X-ray interference function in amorphous Tbl,Fe, alloys ( -); centration dependence of k~ calculated on the assumption of the freeelectron model and 3 (upper), 2 (middle) and 1 (lower) conduction electrons contributed by the terbium atoms.
17
[18]. In view of the uncertainties in kF mentioned earlier we restricted ourselves to analysing only the temperature dependence of p . If we compare the p data obtained on the amorphous Tbl,Fe, alloys with those of the corresponding cobalt alloys [lo] we find that the region of negative TCR values comprises the lower 3d atom concentrations in the cobalt alloys. The alloy Tb6sCosl still has a negative TCR whereas in Tbs9 Feal the TCR is positive. In view of the low 3d atom concentration in both alloys it is unlikely that this is the result of the somewhat smaller number of conduction electrons contributed by cobalt than by iron. We believe rather that the positive TCR in TbssFesl is caused by the occurrence of some clustering between like atoms, which is also responsible for the deviating crystallization behaviour described earlier (see Fig. 1). We cannot, however, exclude the possibility that the low crystallization temperature of this alloy (see Section 3) leads to a small layer of microcrystalline material on the side of the ribbon which is not in contact with the copper wheel during melt spinning. Such a small microcrystalline layer is not easily detected by standard X-ray diffraction techniques. Since crystalline material, at low temperatures in particular, has a conductivity several orders of magnitude larger than the conductivity of amorphous material, the small microcrystalline layer may carry a relatively large portion of the current (with a positive TCR) and hence may mask the presence of a negative TCR for the remaining amorphous part of the ribbon. 5. Concluding remarks In an earlier investigation [7,9] it has been suggested that the glassforming ability depends to a certain extent on the heat of mixing between the two constituent metals. The present results obtained on alloys of heavy rare earth metals of the type R6aFes1 show that, once quenched into the amorphous state, the crystallization temperatures of these alloys are similar to those of the corresponding cobalt or nickel alloys, even though the cobalt or nickel alloys have considerably larger negative AH, values. This indicates that the absolute value of the (negative) heat of mixing has only a small influence on the crystallization temperature, although its effect on the ease of glass formation may be important [9] . Exceptions are encountered when AH, becomes positive. In these cases the corresponding amorphous alloys have crystallization temperatures that fall considerably below those of their nickel or cobalt counterparts. The effect of the positive value of AH, on TX is not to be sought, however, in a substantial reduction in the hole formation enthalpy AH, (TX = 7AH,). It leads rather to a different microstructure of the corresponding alloys and entails a tendency to phase separation into the parent metals on crystallization. In this respect the amorphous alloy SmaaFesi resembles closely the amorphous alloys of silver and gold with iron and cobalt. In these cases also the AH, values are positive and crystallization is expected to occur at temperatures considerably lower than those expected from the general relation TX = 7AH,.
Acknowledgment The author wishes to express his gratitude to N. M. Beekmans for performing the resistivity measurements.
References 1 K. H. J. Buschow and N. M. Beekmans, Solid State Commun., 35 (1980) 233;Phys. Rev. B, 19 (1979) 3843. 2 K. H. J. Buschow, J. Phys. (Park), Colloq., CS, 41 (1980) 559. 3 R. St. Amand and B. C. Giessen, Ser. Metall., 12 (1978) 1021. 4 J. Hafner, Phys. Rev. B, 21 (1980) 406. 5 H. A. Davies, Phys. Chem. Glasses, 17 (1976) 159. 6 A. R. Miedema and P. F. de Ch%el, in L. H. Bennett (ed.), Theory of Alloy Phase For-
mation, Rot. American Metallurgy Society Meet., New Orkan8, LA, 1979. 7 K. H. J. Buschow and A. G. Dirks, Electrochemical Society Conf. Proc., 1980, Vol. 8 9 10 11 12 13 14 15 16 17 18
80-2, Electrochemical Society, Princeton, NJ, 1980, p. 514. K. H. J. Buschow and A. S. van der Goot, Phys. Status Solidi, 35 (1969) 515. K. H. J. Buschow and A. G. Dirks, J. Phys. D, 13 (1980) 251. K. H. J. Buschow and N. M. Beekmans, Phys. Statue Solidi, 60 (1980) 193. H. E. Kissinger,AnaZ. Chem., 29 (1957) 1702. K. H. J. Buschow and A. M. van der Kraan, J. Magn. Magn. Mater., in the press. H. Beck and R. Oberle, in B. Cantor (ed.), Proc. 3rd Znt. Conf. on Rapidly Quenched Metak, Brighton, 1978, Metals Society, London, 1978, p. 416. H. J. Giintherodt, M. Miiller, R. Oberle, E. Hauser, H. U. Kiinzli, M. Liard and R. Miiller, Inst. Phys. Conf. Ser. 39 (1978) 436. L. V. Meisel and P. J. Cote,Phys. Rev. B, 17 (1978) 4652. Y. Waseda, A. Jain and S. Tamaki, J. Phys. F, 8 (1978) 125. B. DeBey and H. Beck, J. Phys. F, 9 (1979) 517. E. Esposito, H. Ehrenreich and C. D. Gelatt, Jr., Phys. Rev. B, 18 (1978) 3913.