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Glass formation and crystallisation in NiSiB alloys—II. Crystal formation on annealing
km meroll Vol. 32. No. 6. pp 837-849. 1984 Prmted in Great Britain. All rights reserved
Copyght
i
0001-6160 84 53.00 + 0.00 1984 Pergamon Press Ltd
GLASS FORMATION AND CRYSTALLISATION IN Ni-Si-B ALLOYS-II. CRYSTAL FORMATION ON ANNEALING D. G. MORRIS Institut CERAC S.A.. Ecublens, Switzerland (Received
2 August
1983;
in recited form
15 December
1983)
AkMct--crystal formation in a metallic glass is a complex process that depends on the alloy composition and the crystal phase produced, the cooling rate used to prepare the glass from the liquid state. and the time and temperature of any subsequent anneal. A series of Ni-Si-B alloys has been prepared by melt spinning and the details of alloy phases produced examined. The amorphous materials produced have been annealed at low temperatures and the mechanisms of crystallisation established using transmission electron microscopy. Alloys with total metalloid contents of 22-30 at.?; have been prepared in the amorphous state by fast cooling. An alloy near the low end of this composition range subsequently crystallised on athermal, quenched-in nuclei, whilst an alloy near the upper end of the composition range subsequently crystallised by the homogeneous nucleation of crystals. Both the ability to obtain the glassy state over this range of compositions and the existence of a suitable density of quenched-in crystals can be relatively well explained using the kinetic approach to glass formation outlined in part I. R&mn&La formation de cristaux dans un verre mitallique est un phenomine complexe qui depend de la composition de I’alliage et de la phase cr-istallinc produite, des vitesses de refroidissement utilisees pour preparer le verre a partir de I’ttat liquide, et enfin de la durte et de la temperature d’un eventuel recuit ultCrieur. Nous avons fabrique une s&e d’alliages Ni-5-B par filage du bain et nous avons examine en detail les phases produites. Les materiaux amorphes ainsi obtenus etaient recuits a basses temperatures et nous avons pr6cis6 les mCcanismes de la cristallisation par microscopic Clectronique en transmission. Nous avons ptipari par trempe rapide des alliages dans 1’Ctatamorphe dont la teneur totale en metalloide ttait comprise entre 22 et 30 at.:/,. Un alliage proche du bas du domaine de composition cristallisait ensuite sur da germes athermiques trempts, alors qu’un alliage proche du haut du domaine de composition cristallisait ensuitc par germination homogine de cristaux. Gn peut expliquer relativement bien la possibiliti d’obtenir I’ttat vitreux dans tout le domaine de composition et l’existence dune densite convenable de cristaux trempts, en utilisant I’approche cinetique de la vitrification presentee dans la premiere partie. Z--Die Kristallbildung stellt in einem metallischen Glas einen verwickelten ProzeB dar. der von der Legiertmgszusammensetzung und der entstchenden Kristallphase. von der bei der Herstellung bcnutzten Abscltreckgeschwindigkeit und von Zeit und Temperature moglicher nachfolgender Temperbehandlungen abhiingt. Eine Reihe von Ni-Si-B-Legierungen wurde durch Sptitzkiihlen hcrgestellt: die entstandenen Legiertmgsphasen wurden genau untersucht. Die erzeugten amorphen Legierungen wurden bei niedrigen Temperaturen getcmpcrt. Die Kristallisationsmechanismen wurden im Durchstrahlungselektikroskop festgestcllt. Legierungen mit einem Gesamtgehalt an Metalloiden zwischen 22 und 30 Prozent wurden durch rasches Abkiihlen amorph hergestellt. Eine Legierung am unteren Ende dieser Zusammensetzung kristallisiertc danach an athcrmischen, eingeschreckten Keimcn. wohingegen einc legierung nahe dem oberen Ende durch homogenc Keimbildung kristallisicrte. Sowohl die Miiglichkeit, den Glaszustand in dicsem Bereich der Zusammcnsetzung zu erhalten. als such das Vorbcgen eina ltinreichenden Dichte eingcschrecktcr Ktistalle kann hinreichend gut mit der kinetischen Beschreibung der Glasbildung aus Teil I verstanden werden.
1. INTRODUCTION
Crystallisation of metallic glasses has been studied on many occasions [2,3]. sometimes using indirect mtasurement techniques such as resistivity changes [4] or differential scanning calorimetry [5-7], and on other occasions more direct techniques, particularly transmission electron microscopy (3,8-IO]. A wide range of crystallisation modes has been observed, ranging from continuous, homogeneous nucleation to timedependent or athermal nucleation on pm-existing nuclei. Single phases, either of the equilibrium phase
or metastable, and mixtures of phases have been seen to form. Controversy remains over several of these factors, particularly about the nucleation mechanisms during low temperature crystallisation. Indirect techniques generally make use of the Johnson-Mehl-Avrami equation [ 11,121 for analysis of crystallisation mechanisms [x = 1 - exp( - kt”)] by determination of the time exponent n in a doublelogarithmic plot. Such techniques are susceptible to significant errors, particularly at the early stages of crystallisation when simultaneous changes, for example the glass transition itself or magnetisation 837
838
MORRIS:
GLASS FORMATION IN Ni-Si-B ALLOYS-II
changes, may lead to di~culties in establishing the base-line from which to estimate crystalhnity [7]. Secondly, a wide range of possible combinations of processes may occur during crystallisation, and it is by no means evident what processes may be operating for a given value of n. There is some dispute over the values of n to be expected for particular transformation sequences [IO, 13, 141. Direct techniques for the establishment of structure are to be preferred, particularly transmission electron microscopy which offers the possibility for the measurement of both crystal number density and crystal size, hence eventually nucleation rate and growth rate [3,9,15, 161.In this case, also, great care is needed in the collection and analysis of experimental data, such as foil thickness, crystal size and number, if very large errors in the results are to be avoided. In situ measurements have been used to determine nucleation and growth rate [ 171,but the values obtained, particularly nucleation rate, must be treated with great caution because of the possibte influences of the foil surfaces. Growth rate is generally calculated from the maximum particle size D,,,, as Dmul/r,where t is the time of anneal [9, 10, 181.It was shown in Part I [I] that a small number of extremely large crystals exist in a typical, as-cast tape and growth rate determinations from the maximum observed crystal size, albeit the preferred technique, must therefore be performed with care. Also, use of the simple formula r>,, /r ignores the possibility of incubation times, that is that over some time r, growth may not have occurred and the true growth rate is D,,/(t - to). This “incubation” error will apply equally to estimations of the nucleation rate, as will errors caused by visibility problems. For example, an observed increase in crystal density may simply correspond to growth of small crystals through the size detection limit [7]. The influence of these various experimental difficulties leads to some confusion of the validity of some of the published rates. On some occasions, homogeneous crystal nucleation has been identified. This, for example, is the case for the much-studied Metglas 2826 alloy [6,9, 19,20]. In other systems the existence of large number of pre-existing crystals which can act as athermal nuclei has been demonstrated f7,18]. The number of these nuclei has been shown to vary with quench rate [7, 181 and with the alloy composition [18].It is likely that these nuclei are formed during the quench from the liquid, and that a very fast quench is more effective in suppressing such nucleation. The present study has been performed on a series of Ni-Si-B alloys to look at the influence of alloy composition and changing glass-formation parameters on the ability of an alloy to cool as a glass and on the low temperature c~s~~~tion behaviour of the glasses obtained. Transmission electron microscopy has been used such that any structural changes can be followed in detail. Also, the computer model described in Fart I [lJ, which provides a description
of the homogeneous nucleation and crystal growth occurring during the rapid cool of the initial glassforming stage, has been used to detail the structural changes taking place during tape preparation. Thereby an attempt can be made to define the likelihood of glass formation within a given ahoy and also the likelihood of athermal crystal nucleation during a subsequent low-temperatrue anneal. 2.
EXPERIMENTAL
Experiments have been performed on a range of Ni-Si-B alloys of the general composition Ni,,_, (BrSi)“. The detailed compositions studied are listed in Table I. This alloy series was chosen because it has been ext~sively studied previously [21-231 and reasonably good data on melting point and glass transition temperatures are available. The range of compositions covers a variety of equilibrium phase fields in the ternary systems and encompasses two eutectic trenches. The details of alloy preparation and melt spinning conditions were the same as described previously [ 11. High purity powders were mixed to give the desired alloy composition and twice-melted to ensure homogenisation. Alloys were heated to about 100 deg above the melting point for melt spinning and the tapes produced under otherwise identical condition for each. Tape thickness was about 30lm, corresponding to a cooling rate of about 3 x 1OSKS- ’ 1241. Annealing treatments were carrhd out by immersing a portion of tape within a salt bath. Thin foils for structural studies were prepared using a solution of 10% perchloric acid in ethanol at - 10°C with a polishing voltage of 20 V, and examined using a Philips 300 microscope at 100kV. Alloy structure identification was sometimes carried out by analysis of polycrystalline diffraction rings (because of the very small crystal sizes many crystals were included within the smallest selecting aperture), sometimes by converging beam diffraction on the Philips microscope, and otherwise using a JEOL TSEM at 200 kV in the microdiffraction mode with a beam size of about 20 nm. Crystal sizes, the number of crystals in a given area, and foii thickness were measured directly on the transmission specimens. The area fraction of crystalline material was determined using the line intersection technique of quantitative metallography. Foil thickness was deduced, as outlined in Part I flJ, from the electron intensity ratio-
Table I. AJioy compositions mtudied (at. %) Alloy designation
Nickel
Silicon
it;lzs 19:x ‘If.5 14.5 70 55
i.25 6.75 7.5 8.3
A : D 5 G
I!
Boron 10 12.5 13.5 15 :(: 30
MORRIS:
GLASS FORMATION
IN Ni-Si-B
ALLOYS -II
passing intensity through the area of interest/intensity recorded in the absence of a foil. A foil thickness-intensity ratio relationship had previously been established based on foils of thicknesses measured by noting the relative motion during tilting of small gold islands deposited on the two sides of the foil or by counting the number of thickness fringes within penetrated large crystals in the amorphous foil. The number of crystals per unit area in a given material, N,,, was measured from the foil. The number of crystals per unit volume. N,, may then be calculated as N, =-
N.4 t+b
where t is the foil thickness and b the average crystal size [25,26]. In a similar way the area function of the projected image containing crystalline materiat, ,f,, may be related to the true volume fraction of crystalline material as [25]
In order to achieve significantly precise values for these parameters, it is important that large areas are studied. In a typical foil, areas of about lo-” rn’ were examined. The number of crystals varied slightly from area to area and it is estimated that the area density and area fraction were probably correct to k 207;. Taking account of errors in the estimations of foil thickness and particle diameter, the number of crystals per unit volume and the volume fraction crystallised are considered to be correct to about +3OY& Very small crystals, less than 20-40 nm, are difhcult to detect and at such small crystal sizes the errors in measurement may be significantly larger. Estimations of the crystal size distribution within a given foil area can provide useful information about changes in the nucleation rate during the annealing. When the crystal sizes involved are much smaller than the foil thickness, the estimation of size distribution is trivial and reduces to a simple collection of a sufficient quantity of data. For crystal sizes larger than the foil thickness. however, sectioning effects become important and it is more difficult to deduce the true particle size distribution from that observed. In this case, the same sectioning effects can be assumed as for optical reflection microscopy and the corresponding analysis used [26]. 3. RESULTS 3.1. As-fast .Wuflure
The alloys containing IO”, boron-?; silicon, 12.5T0 boron-6.259, silicon, 13.59, boron-6.7%; silicon and 309; boron-l ST.,silicon, designated A, B, C and G in Table 1. were obtained in the crystalline
Fig. 1. As-cast structure of the 85Ni-IOB-5% alloy. (a) Large primary dendrites and microcrystalline material. (h) Primary dendrites and interdendritic eutectic material. state. Alloys in the range 159~ boron-7.5’, silicon to 209; boron-10S; silicon, alloys, D, E and F in Table 1. were obtained in the fully amorphous state. Alloy A contained a mixture of large primary dendrites and the remainder as either a microcrystalline or a eutectic material, Fig. I, The dendrites were identified, by diffraction analysis, as the f.c.c. nickel phase which may have been supersaturated in metalloids. The microcrystalline and eutectic materials appeared to be mixtures of the same f.c.c. nickel and a cubic phase with the structure of Ml,m,. namely N&(B.Si), here. A phase having this structure is somewhat unusual for this alloy system, but has, nevertheless, been observed recently during the decomposition of an amorphous nickel-based alloy [4]. Alloy B contained the same phases as those observed for alloy A, but in different proportions. Only a few primary dendrites of the f.c.c. nickel phase were observed and the majority of the alloy was a microcrystalline mixture of the nickel and NL;(B.Si), phase. In alloy C, no large. primary phase structure was observed. Instead. a microcrystalline mixture of the same phases as for the previous alloys was observed. Occasionally, small volumes of amorphous phase were found, occupying in total about 25”, of the material. Alloy G typically contained a few large.
MORRIS: GLASS FORMATION IN Ni-Si-B ALLOYS-II 3.2. CrystaNisation qf amorphous alloys Alloy D. This alloy was prepared in the fully amorphous state by melt-spinning and on heating in the range 350-45O’C crystallisation took place. The crystals forming had a lobed, or butterfly morphology and contained some internal faults, Fig. 2. When about 40-50x of the material had crystallised a eutectic mixture was formed which led to complete crystallisation. The changes taking place during such crystallisation are illustrated in Fig. 2. This crystallisation sequence may indicate that a small composition difference exists between the butterfly crystals and the amorphous matrix which leads to a change in the matrix composition as crystallisation continues. The butterfly crystais were identified as having the orthorhombic N&B phase structure. The volume percentage crystallised as a function of time at temperature is shown in Fig. 3. Crystallisation begins rapidly, at short annealing time, with no evidence of an incubation period. and the transformation rate decreases continuously until the eutectic phase nucleates. The eutectic mixture first appears when about 40-5Oyb of the material has crystallised and this proportion does not appear to change, significantly at least, with the annealing temperature. The eutectic lamellae spacing is very small, of the order IO-15 nm. The fraction crystallised-annealing time data lead to an exponent on the Johnson-Mehl-Avrami Plot of 1.0, Fig. 4. This exponent suggests a crystallisation process on pre-existing nuclei with considerable restriction on the growth process. The variation of crystal number density with annealing time is shown in Fig. 5. There is some evidence to suggest that the crystal density decreases initially to reach a constant value fairly early during
*Or 2 3 a
0 45O’C l
4GPc
x
35O’C *
aso-
; z
x
Fig. 2. Crystaiiisation of the 7?.5Ni-15B-7.5Si alloy during annealing at 350-C: (a) 8 h; (b) 250 h; (c) 930 h.
primary crystals with a microcrystalline phase mixture occupying most of the volume. Occasional regions of eutectic material were found. The phases present were, in all cases studied, complex intermetallics and, in some cases, were not identified. The major phase appeared to have a Ni,Br structure, probably with silicon replacing some of the boron. The orthorhombic N&B structure was also identified, apparently with silicon replacing boron to form a superlattice on some occasions.
I
0
/ 60
I 40
/ 20
500
400’C(h) / IOCO
350°C
Fig.
3.
Percentage
77.5Ni-15B-75%
I 90
I ISOC
(h)
crystallised material in the alloy as a function of annealing time.
MORRIS:
GLASS FORMATION
IN Ni-Si-B
841
ALLOYS-II
o-
.
-1 -
-
.
2:
L -C
-2
.
LL +
/
-3-
-4 t
/
5
l
6
0
20
1
The value of the crystal density decreases as the annealing temperature decreases. The influence of crystal invisibility is unimportant in this case because the crystal size soon becomes very much larger than the resolution limit (2043nm). The variation of crystal size with annealing time and temperature is shown in Fig. 6. While the scatter in data is too great to make precise analysis possible, reasonably good fit to a growth relationship of the form D” = KI is obtained 3.1 + 1. Classical with m taking values diffusion-controlled particle growth [13] should lead to a growth exponent of 2. The higher exponent observed is not fully understood: it may stem from the inapplicability of assumptions in the classical growth theory, for example that phase composition or chemical profile shape may change in time or that the diffusional parameters may be changed in a complex way during continued growth. As an example, the loss of free volume trapped during the glass
,
0
1
L
I
40
1
0
80
5co
I
I
I
40
60
80
4OOT(h) 1
1000
I
1500
35O’C (h) Fig. 5. The number of crystals per unit volume during crystallisation of the 77.5Ni-15B7SSi alloy.
preparation may lead to anomalous diffusion rate decreases during annealing. Figure 7 shows an Arhenius plot of the growth constant K, and also of the long-term, steady state crystal number density N,,, seen in Fig. 5. Both parameters are consistent with the Arhenius relationship and activation energies of about 160 kJ/mol and 65 kJ/mol are deduced for the growth process and the crystal number density, respectively. It should be noted that the activation energy of the number density is near one third that obtained from the Dm-f growth relationship. It is possible that there is a connection between the growth mechanism and the process establishing the stable crystal density and
15
0
x I
40
I
I
crystallisation.
45OWd I
2u
0
x x
I
0 Fig. 4. Johnson-Mehl-Avrami plot obtained from the data of Fig. 3.
x
Kxp x-x
4OO'C(h)
g, 1
1
500
loo0
350e (h) Fig. 6. Variation of crystal size during crystallisation of 77.5Ni-15B7.5Si
alloy.
MORRIS:
842
13
14
103/T
GLASS
15
FORMATION
IN Ni-Si-B
ALLOYS-II
16
(K-II
Fig. 7. Arhenius plot of the growth constant K. and the steady state crystal number density N, Fig. 9. Crystals formed in the glassy 73.5Ni-17B-5Si alloy on low temperature heating.
that the same activation process, related through the growth exponent, may control nucleation and growth. The crystal size distribution observed after partial crystallisation at 45O’C is shown in Fig. 8. The crystal sizes are generally very much larger than the foil thickness and it is necessary to use the reflection metallographic analysis to deduce details of the time dependence of the nucleation process leading to the observed size distribution, it is clear that most of the crystals must have nucleated very early during the annealing treatment and that most of the crystals have about the same, large size. Many of the apparently small crystal sizes recorded can be explained on the basis of sectioning effects. Alloy E. This alloy was prepared in the fully amorphous state and crystallised by heating at a range of temperatures. A complete crystallisation study has been performed at 35O’C only. However, the major observations have been confirmed by additional studies at 400 and 45OC. The first crystals to form were irregular/near-spherical and identified as the othorhombic Nir B phase, Fig. 9. After about 75’/,
Crystal stze (pm) Fig. 8. The size distribution of crystals in the 775Ni-15B-7.5Si alloy after annealing at 45O.C to about 30% crystallisation.
crystallisation had occurred. a eutectic phase mixture formed and led to complete crystalhsation. The volume fraction crystallised. crystal size. and crystal number density as a function of the annealing time are shown in Fig. 10. Again. the volume fraction crystallised increased rapidly with time with no evidence of an incubation period. The Avrami exponent had a value of about 2 for annealing times less than about 10 min. where limited data was obtained. and about 1.0 _t 0.1 for annealing times in excess of IOmin. The interpretation of these exponents is difficult and in essence impossible without further process information. The implication of these exponents is that there is a compositional difference between the crystals and the amorphous matrix and growth is diffusionally-controlled [ 131. The crystal number density increases about linearly with annealing time up to a value of 3-4 x IO’” crystals,m3
Time lmin) 01 35O’C Fig. 10. Percentage cr)stallisrd. crystal size and crystal number density for the 74.5X1-1 7B-X.5Si alloy as a function of time at 350 C.
MORRIS:
GLASS FORMATION
IN Ni-Si-B
ALLOYS--II
843
after a time of IO-20 min. At this time the crystallised volume is onl) about S’, of the total. At longer annealing times the number of crystals remains constant. For this material. the resolution limit for detection of crystals (2040 nm) may lead to an underestimation of the crystal density at the first annealing time considered (1 min) for which the observed crystal size was about 35 nm. Nevertheless, this visibility criterion should not be important for any of the subsequent data. The growth rate of the crystals decreases continuousI> throughout crystallisation. The crystal sizes obe) a relationship D”’ rr
55O’C (s) 0
10
0
I 5
0
I 20
500°C
(rnln)
I 10
450°C
(h)
440000°C
thl
l
, ?5 , 800
I
I
4000 350°C
/ 30
aooc (h )
Fig. 12. Volume percentage transformed on annealing the 70Ni-20B-10Si alloy.
b
Fig. 11. Crystalllsation of the 70N1-IOB-10% alloy on annealing at 450 C: (a) 3 h: (b) 5 h. (c) JO h.
with m having a value of 2.8 f 0.5. While this dependence is again not consistant with classical diffusion-controlled growth theory, it seems likely that diffusional chemical transport between crystal and amorphous matrix is the controlling step with some additional change in diffusivity of chemical profile taking place. Alloy F. Crystallisation studies on this alloy were carried out in the temperature range 35&550 C. Approximately spherical crystals formed. which increased in number and size until almost all the material had crystallised. At about 909,, crystallinity a eutectic phase mixture formed, see Fig. Il. The near-circular crystals were not unambiguously identified, showing sometimes diffraction patterns characteristic of the orthorhombic Ni, B structure and other times of the face centred cubic Ni,,B, structure. These may correspond to an intermediate phase structure or to a mixture of two phases. On some occasions the crystals exhibited a speckle contrast suggesting that some phase change or precipitation process occurred within them. The volume fraction crystallised at each temperature. as a function of the annealing time, is shown in Fig. 12. The curves now show the standard S shapes with a slow initial growth stage followed by an acceleration in the rate of transformation and a slow final transformation rate as crystal impingements become significant. Fitting the data to the Avrami relationship let to the determination of ex-
844
MORRIS:
4
0
I
0
10
0
1 5
GLASS FORMATION
8
55O’C(s)
I
20
500°C I
xl
(min)
d&c
I 15
(II)
0
I
I
a00
400
400°C
(h)
SO’(m) Fig. 13. The number of crystals per unit volume during
crystallisation of the 70Ni-20B-10Si alloy. ponents of 2.9 + 0.4 over the range of annealing temperatures. An experiment conducted to follow resistance changes during annealing at 470°C was difficult to interpret because of the influences of the glass transition. Fitting this data to an Avrami relationship led to an exponent of about 2.6, in good agreement with the results from the structural observations. The variation in crystal number density with annealing time is shown in Fig. 13. The crystal number
IN Ni-Si-B
density rises rapidly with the time of anneal to reach a steady state. This steady state value increases rapidly with the annealing temperature, ranging from about 10’8/m3 at 350°C to more than 102’/m3 at 550°C. The steady state value is reached when only about 20% of the total volume has crystallised for each of the temperatures examined. When the crystal number densities are plotted on linear plots evidence for a clear transient period is seen. During this time the nucleation rate is either zero, as suggested in Fig. 14(a), or increases continuously, as in Fig. 14(b). The nucleation process is here approximated as a constant nucleation rate stage, preceded by a transient or incubation period (listed in Table 2 for each temperature studied), and followed by a saturation stage, when nucleation essentially stops. The transient stage, or incubation period, becomes shorter as the temperature increases. These times remain consistant, however, corresponding to about 5% of the total time to full crystalhsation of each temperature. The rate of increase of crystal density becomes greater at higher temperatures, illustrated in Fig. 14, and this increase obeys an Arhenius relationship with an activation energy of 270 kJ/mol. The crystal size increases with time at ail temperatures, with a faster increase at higher temperatures, see Fig. 15. The crystal size data can be fitted to an expression of the type D” = K(I - to), where r,, is the transient or incubation time. The values of m obtained are 1.8 k 0.4 for the range of temperatures studied. Some of the data are shown in Fig. 16 where, after the incubation period (when no crystals were detected), the crystal size squared is related to the annealing time. Values for the incubation period deduced in this way are also shown in Table 2 and seen to be very similar to those determined from the nucleation plots. The growth rate proportionality factor, K, increases with increasing temperature according to the Arhenius relationship with an activation energy of 250 kJ/mol. This value is close to that for the nucleation process and suggests that the same diffusive process controls both the nucleation and growth steps.
Table 2. Transient or incubation times for the start of crystaliisation Annealing temperature (“C) Incubation time deduced from nucleation plots (Fig. 14) Incubation time deduced from growth plots Growth rate K (D*lAr) (m’/s) Incubation time deduced from K and nslbd~ty criterion (D ==20-4Omn)
ALLOYS-II
in the 70Ni-20B-10Si alloy
400
450
500
550
15@2OOh
lh
1.5 min
1.5s
5Oh
2h
3 min
1.2s
5.6 x l0-M
6.2 x IO-”
1.6 x IO-l6
7.8 x lo-l6
Sh
3 min
7s
1.2s
MORRIS:
GLASS FORMATION
IN Ni-Si-B
845
ALLOYS-II
(h)
Fig. 14. Crystal number density during crystallisation of the 7ONi-2OB-1OSi alloy: (a) at 45OT; (b) at 4OO’C.
Based on the experimentally-deduced growth rate constant K, it is possible to examine the influence of the visibility criterion on the recorded incubation times. Assuming, for example, that crystals smaller than 20-40 nm will not be detected, the time required for a just-nucleated crystal (size -0) to grow to visibility can be calculated. These values are shown in Table 2. With the possible exception of the results at 55O”C, the experimentally-deduced incubation periods are much greater than those values calculated from the visibility criterion. This analysis confirms
(h)
Fig. 16. Increase in size of crystals when annealing the 70Ni-20B-10Si alloy. Growth occurs after an incubation period, according to a D2 = Kr relationship: (a) at SSO’C:(b) at 450 C.
that the incubation are true effects and The distribution been examined for more uniform than some tendency to
periods seen (in Figs 14 and 16) not simply observational artifacts. of crystals of different sizes has this alloy. The distribution plot is that of the alloy D, but still shows be skewed to larger crystal sizes. 4. DlSCUSSlON
34 -
-03
-
E a. al s
0.2 -
0 E t
01 -
ooj/y- , 4
55o*c
1
0
5
0
I s
e
(s)
I
15
(min)
450.C
(h)
4OOT
(h)
1 400
4.1. As-cast
structure
4
5CXYZ I 10
It has on many occasions been noted that an easy glass-forming tendency may often be associated with an alloy composition of low melting point T,,,, and high glass transition temperature T,. The need for a high value of the ratio T,/T, has accordingly been used as one of the rules-of-thumb in the search for new amorphous alloys. Below, an attempt is made to quantify the relationship between T8, TM and the cooling rate and to evaluate the extent to which this quantitative model is in accordance with the experimental observations. Furthermore, since the quantitative model provides a description of the distribution of small crystals present in any nominally amorphous alloy, it should be possible to interpret the subsequent low temperature crystallisation behaviour based on the hypothesis of the small crystals acting as embryos or nuclei for subsequent growth.
I IS
I 800
Fig. 15. Increase in size of crystals during annealing the
70Ni-20BlOSi alloy.
Figure 17 shows a part of the Ni-B,Si section through the ternary diagram from which subsequent quantitative analysis is made. Data on glass temperature or, as a near approximation, the crystallisation temperature and the melting point are taken from the literature (21-231. Liquidus lines, an approximate eutectic solidus line, and the glass transition temperature line have been drawn on the figure.
846
MORRIS: GLASS FORMATION IN Ni-Si-B
/ 400
n/
t
’
10
1 50
EC
D
E
?5
F 20
Boron content (otomlc)
I
75 S~llcon
100
content
I 25
I 12 5
(atomic)
Fig. 17. Part of the Ni-B2Si section through the Ni-B-Si termary diagram. See text for details. In addition, as an aid to discussion, approximate positions for To lines have been shown. The T, temperature is that below which a given alloy can solidify without any compositional change occurring (27,281. The r, lines illustrated here are nothing more sophisticated than approximate bisectors of the liquidus lines and the vertical direction, starting from the maximum in the liquidus. From an equilibrium diagram such as that of Fig. 17 several solidification sequences can be envisaged: (i) The alloys may crystalhse with a large amount of diffusional chemical segregation to produce phases very close in composition to those of the equilibrium solidus. (ii) A slight modification of the previous possibility; a certain amount of diffusion and segregation may take place to give supersaturated phases. (iii) Combinations of equilibrium or supersaturated phases may be produced, as by eutectic solidification, in such a way that the distances over which chemical segregation must occur are greatly reduced. (iv) The temperature falls rapidly below the T, line and solidification can take place without the need for any change of chemical composition. The easiest case to analyse is the final one, where no composition change occurs’as the crystals form. This is the basis for the homogeneous nucleation and growth model described in Part I [1], and the application of this model to the present case will now be considered. Summarising, the model assumes that thermally-activated homogeneous nucleation takes place on the steady-state distribution of embryos,
ALLOYS-II
diffusional crystal growth takes place without change of chemical composition between the amorphous matrix and the crystal. The model developed in Part I [I] calculates the changes in structure during cooling at a given cooling rate and thereby describes the structure present, as fraction crystallised, size and distribution of sizes of crystals. The temperature dependence of the activation energy for formation of the critical nucleus is best described using the Thompson-Spaepen relationship [ 1,291. Other factors used here to evaluate the influence of alloy composition on glass formability were as follows: the critical free energy was taken as AG*/kT = 40 for AT, = 0.20, where AG* is the free energy required to form the nucleus of the critical size, k is the Boltzman constant, T the temperature, and AT, the relative undercooling (TM - T)/T,, where T,,, is the melting point of the given alloy. This value has been shown to more correctly describe crystal formation during cooling in the 74.5 Ni-17B-8.5 Si alloy [I]. Viscosity data were established from data available for this 74.5 Ni-17B-8.5 Si alloy [30] and assuming that the viscosities rt obey the Vogel-Fulcher. relationship, namely q = A exp B/( T - T, ). The parameters A, B and T, were evaluated for each alloy composition by assuming a viscosity of 0.1 P (IO-*Nsm-*) at the melting point, lO’-‘P(lO” Nsm-*) at the glass transition temperature, and the same variation of viscosity with temperature above the melting point (equivalent to assuming an activation energy of about 120 kJ/mol for the viscosity of the liquid just above the melting point). A cooling rate of 3 x 105Ks-’ was used, based on the tapes produced which had a thickness of 30pm [24]. The results of this model simulation are summarised in Table 3 and compared with the experimentally established as-cast structure. The model predicts that the three alloys D, E and F should be obtained in the “fully-amorphous” state, that is with very small fractions of crystalline material. The alloy A is predicted to crystallise completely. Both these results are in agreement with experimental observations. The intermediate alloys, B and C, however, are predicted to contain only about 10% and < l”//,of crystalline material, in contrast to the experimental observations of 100 and 75%. Also shown in Table 3 are the temperatures at which, according to the model, crystallisation begins. Comparison with the schematic To lines of Fig. 17 suggests that the glassforming alloys D, E and F should be below the To temperatures when crystallisaton starts, whilst the alloys A, B and C may be above their To temperatures at this stage. This provides further confidence in the use of this unicornpositional model for the analysis of alloys D, E and F and raises futher doubts of its applicability to the other alloys. Of additional interest in Table 3 is the presence of large numbers of small crystals and a few large crystals within each alloy. even those nominally amorphous. Very obviously a large amount of chemical redistribution has taken
MORRIS:
GLASS FORMATION
Table 3. Predictions of homogeneous nucleation-diffusive
Crystalline Fraction Maximum crystal size (pm) Number of crystals larger than 2 x lo+ m(/m’) Number of crystals larger than - 10-s m(/m’) Temperature crystakation begins (K) as-cast struCtuTe
847
IN Ni-Si-B ALLOYS-II
Alloy designation C
growth model D
E
F
3 X 10-1
4 X 10-b
2 X 10-l
IO-’
5
3
2.3
2.1
1.5
2 X 1010
5 X 10”
5 X 1020
1 X 1on’
4 X 10’9
1 X 10”
2x IoN
2 X 102’
I x ION
1 x 10’9
4 X 10”
5 X 10’6
1050
1075
1000
A
B
1
0.1
10
when 1200 Crystalline dendritic
1150
Crystalline
place during the crystallisation of alloys such as A and B. In this case the previous model requires modification, as follows: the diffusion rate may be taken as reduced proportionately to the concentration of the solidifying elements in the matrix [31,32], for example if Nickel crystals form in a matrix containing 85% Nickel and 15% metalloids the diffusion rate can be taken as 0.85 D, where D is the diffusion rate applicable within the matrix as a whole. This factor applies to both the nucleation frequency and to the crystal growth rate, but is not a major correction for the crystals and alloy compositions considered here. Of greater importance is the rejection of solute as the crystals form, leading to a high solute (metalloid) concentration in the glass in contact with the crystal. The build-up of concentration leads to a decay in growth rate which obeys a (diameter)2 a time relationship rather than the linear diameter a time seen in the absence of compositional changes [18,33]. Modification of the model to include these compositional effects leads to such a restriction on crystal growth that crystallisation is largely avoided for all the alloys (for alloys A, B and C the fractions crystallised after cooling at a rate of 3 x l@ KS-’ are 10e2, lo-’ and 10S6). Clearly this restriction on growth does not lead to a realistic description of the solidification behaviour. Further analysis of the behaviour of the alloys A, B and C is difficult for a variety of reasons. As just described, neither a model completely ignoring compositional changes nor a model including the parabolic decrease of growth rate with time can adequately explain the results. Clearly, dendritic solidification takes place for some of the alloys and growth can continue much faster than implied by the restrictive parabolic reltionship. Also, a second phase can nucleate in the high solute region leading to a co-operative or eutectic phase mixture. Finally, the glass transition temperature is so low for these alloys that any amorphism retained by the rapid quench
1050 Mostly crystalline some amorphlsm
Fully amorphous
may subsequent tallisation.
be lost by low temperature
crys-
4.2. Low temperature crystallisation Alloy D. The low temperature crystallisation behaviour of this alloy is fully in accord with crystal growth taking place on a number of pre-existing nuclei. In Fig. 5, the crystal number density has been seen to remain constant, after an initial decrease at fairly short times. This decrease is possibly the result of the dissolution of some of the original embryos which were formed during the quench. The relationship noted between the activation energies for the growth process and the nucleus number may support this idea. The number of embryos which are stabihsed to become growing nuclei changes with the temperature (10” - 5 x 10” - 10’*/m3 at 350-400-45O’C, see Fig. 5) in a way that is not completely understood. The proposal that crystallisation takes place on pre-existing nuclei is also supported by the change of the fraction crystallised with time (Fig. 3) where there is no evidence of an incubation time before crystallisation. Furthermore, the Avrami exponent of about 1 can be seen to be in full accordance. The Avrami exponent of the total crystallisation process, nlOUI?can be related to the time dependences of the crystal density, nnr,, , and of the crystal volume growth, kl, or the crystal diameter growth, Q,,, as
nloul = a,,, + nVol= n,,l+
3nd,, .
(3)
Here, taking the crystal density to remain constant (n,,, = 0) and the crystal diameters to grow accordtimem. ing to a relationship, hence G_, = 0 + (3 x 0.27) = 0.81, in reasonable agreement with the measured exponent. Finally, of course, the observed distribution of crystal sizes provides additional support for early nucleation of all the crystals present. Alloy E. During the crystalhsation of this alloy the
848
MORRIS:
GLASS
FORMATION
crystal number density increases linearly with time initially to reach a stable volume when only about 5% of the alloy has crystallised (shown in Fig. 10). This behaviour suggests that a sort of continuous, probably thermally-activated nucleation process occurs initially. However, nucleation stops when such a small fraction of volume has transformed that it Seems unlikely that a true, equilibrium distribution of embryo sizes is achieved at the crystallisation temperatures. It is proposed that a distribution of embryo sizes, corresponding to the higher temperatures seen during glass preparation, is frozen in to the glass during rapid quenching. These embryos are not sufficiently large, or of stable chemical composition, to act as quenched-in crystal nuclei. However, they represent an attractive metastable embryo distribution on which thermally-activated stabilisation processes can occur leading to nucleation. The Avrami exponent deduced from the variation of crystallised fraction with time was about 2 initially and about 1 later. Here again, this exponent can be related to the time dependence of nucleation, nnuc,= 1, initially becoming nnucl= 0 later, and to that of crystal growth, namely about ndln= l/2.8 = 0.35. Hence, from equation (3), ntora,= 1 + (3 x 0.35) = 2.1 1.1 later. initially, becoming nlora,=0+(3x0.35)= Alloy F. The number of crystals per unit volume increases during the early crystallisation of this alloy. After about 20% crystallisation the number remains constant at a value that depends on the annealing temperature and varies between about 10’*/m3 at 350°C and about 3 x 102’/m3 at 55OC. As for alloy E, the approximately linear rate at which crystals appear on annealing, and the variation of this rate with temperature, imply that a thermallyactivated process for crystal stabilisation is operating. However, the apparent lack of nucleation after about 20% volume crystallisation implies that a true, homogeneous nucleation mechanism cannot be considered. It is inconceivable that a steady-state embryo distribution can be created, homogeneous nucleation begin, only to halt when still 80% of the material is still amorphous. Equally, it is not consistent with the results to consider that quenched-in nuclei are present. It follows therefore that some quenched-in structure, which is metastable at the annealing temperature, is utilized as a metastable embryo distribution on which stabilisation processes leading to crystal formation will occur. This quenched-in structure may be in the form of crystal embryos, metastable at the annealing temperature, as suggested by an earlier publication [I], or may be in the form of short range order, e.g. (341. According to this hypothesis, the number of crystals than can form will be related to the number of quenched-in, metastable embryos. However, since the embryo distribution is metastable it will decay at the annealing temperature and the ultimate crystal density will depend both on the rate of embryo growth to stable crystals and on the rate of metastable embryo decay. It is this conflict which
IN Ni-S-B
ALLOYS-II
is believed responsible for the variation in the number of crystals produced at saturation as the annealing temperature changes (see Fig. 13). The Avrami exponent deduced directly from the change of fraction crystallised with time, 2.9 + 0.4. can be shown to be in agreement with the suggestion of continuous nucleation during the initial stage. Assuming continuous nucleation, i.e. nnuc,= 1, and taking the measured value of ndla= 0.56 for the time dependence of the crystal diameter, we obtain n ,0,,l= 1 + 3 x 0.56 = 2.7, in good agreement with the deduced Avrami exponent. In Table 3 the typical numbers of small crystals which are calculated on the basis of the homogeneous nucleation and growth model to be present in the as-cast ribbons are shown. The same calculation also shows that the critical nucleus size is about 1.3-2 nm over the range of annealing treatments performed on the alloys D, E and F. Accordingly, the number the quenched-in crystals suitable to act as nuclei are predicted to be about 1020/m3 for alloy D, about 4 x 10’9/m3 for alloy E, and about l-2 x lO’*/m for alloy F. (These are the number of crystals having sizes greater than the critical sizes quoted above.) Within alloy D there are sufficient quenched-in crystals to act as nuclei for low temperature crystallisation. Apparently, many of the nuclei may dissolve during the early stages of crystallisation and this loss by dissolution is more important at low temperatures. Within alloy E the calculated number of quenched-in crystals is identical to that observed during crystallisation at 350°C. These quenched-in crystals should be able to act as stable nuclei for growth, and crystallisation of this alloy should then take place by growth alone on these quenched-in nuclei. It does not appear, on the basis of the experiments performed. that this is the case. Rather it seems that quenched-in. sub-critically sized embryos are produced which require thermally-activated stabilisation. Within alloy F the number of quenched-in crystals (Table 3) is less than the number observed to form during low temperature crystallisation (with the possible exception of annealing carried out at 350-C where about the same number of crystals have been observed). In this case thermally-activated stabilisation must take place on sub-critically sized embryos that are characteristic of the detailed metastable, quenched structure of the amorphous alloy. At each annealing temperature, thermally-activated stabilisation takes place on the limited number of embryo sites which, because of their quenched-in, metastable nature, tend to disappear or change to that characterising the annealing temperature. Once these metastable embryos have been used, nucleation almost stops since the true, homogeneous nucleation rate is much slower. Details of embryo formation and distribution, mechanisms of stabilisation to crystal or modification to steadystate embryos, are unclear, and the simple homogeneous crystallisation model is not useful. An alternative hypothesis for nucleation rate vari-
MORRIS:
GLASS FORMATION
ations should be considered. This hypothesis would assume that homogeneous nucleation on an equilibrium embryo distribution takes place (e.g. alloys E and F), perhaps preceded by a transient as the equilibrium distribution is built up (alloy F). However, the diffusivity of the amorphous phase can be supposed to gradually decrease, for example as free volume annihilation occurs. This explanation may apply to alloy E, where an anomalous crystal growth rate exponent (LIZ* zr) was seen, but does not seem to be consistant with the growth data on alloy F (D’ %r) which is interpreted as diffusional growth at constant diffusivity.
5. CONCLUSIONS
The processes of crystal nucleation and growth occurring during the preparation of a series of nickel-silicon-boron alloy tapes by melt spinning have been studied and related to the thermal properties of the alloys. The kinetic model of glass formation evaluated in a previous report [l] has been used to describe the nucleation and growth taking place during cooling and shown to provide a good description for those alloys which can solidify without change of composition. In the present case these alloys were those where crystal formation could fairly readily be avoided and amorphous tapes prepared. Alloys which may solidify with significant redistribution of solutes as crystallisation occurs cannot be described by the model in its present form. The low temperature crystallisation of three amorphous alloys has been studied in detail. For one, crystallisation took place by the growth of quenchedin crystals. For the other two, crystal formation was a thermally-activated process which took place on some quenched-in metastable sites. These metastable embryos may be analogous to the crystal nuclei predicted by the kinetic model, or may be related to the short range order structure of the glass. The Avrami exponent deduced from the change in fraction crystallized with time is very well explained by the nucleation and growth rates determined by direct observation. However, it is not possible to deduce, unambiguously, the crystallisation mechanisms from the exponent alone. The change from athermal nucleation on quenched-in nuclei to thermally-activated embryo stabilisation is perfectly in accord with the predictions of the kinetic model which points to the existence of small crystals within the rapidly cooled tape. If a suitable number of sufficiently large crystals is present, then subsequent crystallisation can take place using these crystals as nuclei. On the other hand, if there are few quenched-in crystals, the quenched-in metastable embryo distribution will be important in acting as sites for thermally-activated crystal formation.
IN .Ni-Si-B
ALLOYS-II
849
REFERENCES 1. D. G. Morris. Acta metall. 31, 1479 (1983) 2. M. G. Scott. Rapidlv Quenched Merals. Proc. 3rd Inr. Conf,. p. 198. Metals Sot.. London (1978). 3. U. Koster and U. Herold. Topics in Applied Physics (edited by H. J. Guntherodt and H. Beck). Vol. 46. p. 225 Sorineer-Verlan. Berlin (198 1). 4. R. P.‘Mi;galski. 0’. T. Inal. F. G. boost and M. M. Kamowsky. J. Mater. Sci. 16, 3357 (1981). Mater. Sci. 5. M. G. Scott and P. Ramachandrarao, Engng
29, 137 (1977).
6. M. G. Scott. J. marer. Sci. 13, 291 (1978). 7. A. L. Greer, Acta metal/. 30, 171 (1982). 8. T. Watanabe and M. G. Scott, J. marer. Sci. 15, 1131 (1980). 9. R. S. Tiwari, S. Ranganathan and M. v. Heimendahl. Z. Merallk. 72, 563 (1981). IO. M. von Heimendahl and G. Kuglstatter. J. marer. SCI. 16, 2405 (1981). 11. W. A. Johnson and R. F. Mehl, Trans. metall. Sot. A.I.M.E.
135, 4(6 (1939).
12. M. Avrami, J. them. Phys. 7, 1103(1939). in 13. I. W. Christian, The Theory of Transformations Metals and Alloys. Part I. 2nd edn. Pergamon Press. Oxford (1975). 14. B. Ilschner, Archir. Eissenhiirr. 26, 59 (1955). 15. M. von Heimendahl and G. Maussner, J. morer. Sci. 14, 16. 17. 18.
19. 20.
21. 22. 23. 24.
1238 (1979). U. Kdster and U. Herold. Rapid/J, Proc. 4rh Inr. Cor~f. (edited by T.
Quenched
Metals.
Masumoto and K. Suzuki). p. 719. Japan Inst. Metals (1982). P. H. Shingu. K. Shimomura, K. Kobayashi and R. Ozaki. Mater. Sci. Engng 23, 183 (1976). U. KBster. U. Herold and A. Becker. Rapid/v Quenched Metals, Proc. 4th lnr. Con/. (edited by T. Masumoto and K. Suzuki), p. 587. Japan Inst. Metals (1982). D. G. Morris, Acra merall. 29, 1213 (1981). Y. Limoge and A. Barber. RapidIT Quenched Memls. Proc. 4th Inr. Co& (edited bv T. Masumoto and K. Suzuki), p. 739. Japan Inst. ietals (1982). 1. W. Donald and H. A. Davies, J. mater. Sci. 15, 2754 (I 980). A. Inoue, T. Masumoto. M. Kikuchi and T. Minemura. Sci. Rep. R.I.T.U. 27a, 127 (1979). S. Ohmori. Y. Hashimoto. K. Shoji. K. Kidaka and Y. Kohira. J. Japan Sot. Po1t.d. Meroll. 18, 316 (1972). H. A. Davies. N. Shohji and D. H. Warrington. Rapid Solidificarion
Processing,
Principles
and Technologies
II
(edited by Mehrabian. B. H. Kear and M. Cohen). p. 153. Claitors. Baton Rouge (1980). 25. J. W. Cahn and J. Nutting, Trans. merall. Sot. A.I.M.E. 215, 526 (1959). Merallograph,v, p. 221. 26. R. T. DeHoff. Quantitative 01 27. J. C. Baker and J. W. Cahn, Thermodvnamics Solidification. Solidificarion, p. 23. Am. Sbc. Metal;. Metals Park, OH (1971). 28. T. B. Massalski, Rapid& Quenched Metals, Proc. 4th Inr. Co& (edited by T. Masumoto and and K. Suzuki). p. 203. japan Inst.- Metals (1982). 29. C. V. Thompson and F. Spacpen. Acra merall. 27, 1855 (1979).
30. H. A. Davies. Rapidly Quenched Merals. Proc. 3rd Int. Con/. Brighton. p. 1, Metals Sot., London (1978). 31. J. W. Christian, The Theory of Transformarions in Metals and Allo.vs, Part I, 2nd edn. Pergamon Press. Oxford (1975). 32. C. N. R. Rao and K. J. Rao, Phase Transitions in Solids. McGraw-Hill, New York (1978). 33. H. B. Aaron, D. Fainstein and G. R. Kotler. J. appl. Phys. 41, 4404 (1970). 34.
D. M. Kroeger. C. C. Koch. D. G. McKamey and J. 0. Scarbrough. Proc. LAMl Los Angeles (1983).
Copyght
i
0001-6160 84 53.00 + 0.00 1984 Pergamon Press Ltd
GLASS FORMATION AND CRYSTALLISATION IN Ni-Si-B ALLOYS-II. CRYSTAL FORMATION ON ANNEALING D. G. MORRIS Institut CERAC S.A.. Ecublens, Switzerland (Received
2 August
1983;
in recited form
15 December
1983)
AkMct--crystal formation in a metallic glass is a complex process that depends on the alloy composition and the crystal phase produced, the cooling rate used to prepare the glass from the liquid state. and the time and temperature of any subsequent anneal. A series of Ni-Si-B alloys has been prepared by melt spinning and the details of alloy phases produced examined. The amorphous materials produced have been annealed at low temperatures and the mechanisms of crystallisation established using transmission electron microscopy. Alloys with total metalloid contents of 22-30 at.?; have been prepared in the amorphous state by fast cooling. An alloy near the low end of this composition range subsequently crystallised on athermal, quenched-in nuclei, whilst an alloy near the upper end of the composition range subsequently crystallised by the homogeneous nucleation of crystals. Both the ability to obtain the glassy state over this range of compositions and the existence of a suitable density of quenched-in crystals can be relatively well explained using the kinetic approach to glass formation outlined in part I. R&mn&La formation de cristaux dans un verre mitallique est un phenomine complexe qui depend de la composition de I’alliage et de la phase cr-istallinc produite, des vitesses de refroidissement utilisees pour preparer le verre a partir de I’ttat liquide, et enfin de la durte et de la temperature d’un eventuel recuit ultCrieur. Nous avons fabrique une s&e d’alliages Ni-5-B par filage du bain et nous avons examine en detail les phases produites. Les materiaux amorphes ainsi obtenus etaient recuits a basses temperatures et nous avons pr6cis6 les mCcanismes de la cristallisation par microscopic Clectronique en transmission. Nous avons ptipari par trempe rapide des alliages dans 1’Ctatamorphe dont la teneur totale en metalloide ttait comprise entre 22 et 30 at.:/,. Un alliage proche du bas du domaine de composition cristallisait ensuite sur da germes athermiques trempts, alors qu’un alliage proche du haut du domaine de composition cristallisait ensuitc par germination homogine de cristaux. Gn peut expliquer relativement bien la possibiliti d’obtenir I’ttat vitreux dans tout le domaine de composition et l’existence dune densite convenable de cristaux trempts, en utilisant I’approche cinetique de la vitrification presentee dans la premiere partie. Z--Die Kristallbildung stellt in einem metallischen Glas einen verwickelten ProzeB dar. der von der Legiertmgszusammensetzung und der entstchenden Kristallphase. von der bei der Herstellung bcnutzten Abscltreckgeschwindigkeit und von Zeit und Temperature moglicher nachfolgender Temperbehandlungen abhiingt. Eine Reihe von Ni-Si-B-Legierungen wurde durch Sptitzkiihlen hcrgestellt: die entstandenen Legiertmgsphasen wurden genau untersucht. Die erzeugten amorphen Legierungen wurden bei niedrigen Temperaturen getcmpcrt. Die Kristallisationsmechanismen wurden im Durchstrahlungselektikroskop festgestcllt. Legierungen mit einem Gesamtgehalt an Metalloiden zwischen 22 und 30 Prozent wurden durch rasches Abkiihlen amorph hergestellt. Eine Legierung am unteren Ende dieser Zusammensetzung kristallisiertc danach an athcrmischen, eingeschreckten Keimcn. wohingegen einc legierung nahe dem oberen Ende durch homogenc Keimbildung kristallisicrte. Sowohl die Miiglichkeit, den Glaszustand in dicsem Bereich der Zusammcnsetzung zu erhalten. als such das Vorbcgen eina ltinreichenden Dichte eingcschrecktcr Ktistalle kann hinreichend gut mit der kinetischen Beschreibung der Glasbildung aus Teil I verstanden werden.
1. INTRODUCTION
Crystallisation of metallic glasses has been studied on many occasions [2,3]. sometimes using indirect mtasurement techniques such as resistivity changes [4] or differential scanning calorimetry [5-7], and on other occasions more direct techniques, particularly transmission electron microscopy (3,8-IO]. A wide range of crystallisation modes has been observed, ranging from continuous, homogeneous nucleation to timedependent or athermal nucleation on pm-existing nuclei. Single phases, either of the equilibrium phase
or metastable, and mixtures of phases have been seen to form. Controversy remains over several of these factors, particularly about the nucleation mechanisms during low temperature crystallisation. Indirect techniques generally make use of the Johnson-Mehl-Avrami equation [ 11,121 for analysis of crystallisation mechanisms [x = 1 - exp( - kt”)] by determination of the time exponent n in a doublelogarithmic plot. Such techniques are susceptible to significant errors, particularly at the early stages of crystallisation when simultaneous changes, for example the glass transition itself or magnetisation 837
838
MORRIS:
GLASS FORMATION IN Ni-Si-B ALLOYS-II
changes, may lead to di~culties in establishing the base-line from which to estimate crystalhnity [7]. Secondly, a wide range of possible combinations of processes may occur during crystallisation, and it is by no means evident what processes may be operating for a given value of n. There is some dispute over the values of n to be expected for particular transformation sequences [IO, 13, 141. Direct techniques for the establishment of structure are to be preferred, particularly transmission electron microscopy which offers the possibility for the measurement of both crystal number density and crystal size, hence eventually nucleation rate and growth rate [3,9,15, 161.In this case, also, great care is needed in the collection and analysis of experimental data, such as foil thickness, crystal size and number, if very large errors in the results are to be avoided. In situ measurements have been used to determine nucleation and growth rate [ 171,but the values obtained, particularly nucleation rate, must be treated with great caution because of the possibte influences of the foil surfaces. Growth rate is generally calculated from the maximum particle size D,,,, as Dmul/r,where t is the time of anneal [9, 10, 181.It was shown in Part I [I] that a small number of extremely large crystals exist in a typical, as-cast tape and growth rate determinations from the maximum observed crystal size, albeit the preferred technique, must therefore be performed with care. Also, use of the simple formula r>,, /r ignores the possibility of incubation times, that is that over some time r, growth may not have occurred and the true growth rate is D,,/(t - to). This “incubation” error will apply equally to estimations of the nucleation rate, as will errors caused by visibility problems. For example, an observed increase in crystal density may simply correspond to growth of small crystals through the size detection limit [7]. The influence of these various experimental difficulties leads to some confusion of the validity of some of the published rates. On some occasions, homogeneous crystal nucleation has been identified. This, for example, is the case for the much-studied Metglas 2826 alloy [6,9, 19,20]. In other systems the existence of large number of pre-existing crystals which can act as athermal nuclei has been demonstrated f7,18]. The number of these nuclei has been shown to vary with quench rate [7, 181 and with the alloy composition [18].It is likely that these nuclei are formed during the quench from the liquid, and that a very fast quench is more effective in suppressing such nucleation. The present study has been performed on a series of Ni-Si-B alloys to look at the influence of alloy composition and changing glass-formation parameters on the ability of an alloy to cool as a glass and on the low temperature c~s~~~tion behaviour of the glasses obtained. Transmission electron microscopy has been used such that any structural changes can be followed in detail. Also, the computer model described in Fart I [lJ, which provides a description
of the homogeneous nucleation and crystal growth occurring during the rapid cool of the initial glassforming stage, has been used to detail the structural changes taking place during tape preparation. Thereby an attempt can be made to define the likelihood of glass formation within a given ahoy and also the likelihood of athermal crystal nucleation during a subsequent low-temperatrue anneal. 2.
EXPERIMENTAL
Experiments have been performed on a range of Ni-Si-B alloys of the general composition Ni,,_, (BrSi)“. The detailed compositions studied are listed in Table I. This alloy series was chosen because it has been ext~sively studied previously [21-231 and reasonably good data on melting point and glass transition temperatures are available. The range of compositions covers a variety of equilibrium phase fields in the ternary systems and encompasses two eutectic trenches. The details of alloy preparation and melt spinning conditions were the same as described previously [ 11. High purity powders were mixed to give the desired alloy composition and twice-melted to ensure homogenisation. Alloys were heated to about 100 deg above the melting point for melt spinning and the tapes produced under otherwise identical condition for each. Tape thickness was about 30lm, corresponding to a cooling rate of about 3 x 1OSKS- ’ 1241. Annealing treatments were carrhd out by immersing a portion of tape within a salt bath. Thin foils for structural studies were prepared using a solution of 10% perchloric acid in ethanol at - 10°C with a polishing voltage of 20 V, and examined using a Philips 300 microscope at 100kV. Alloy structure identification was sometimes carried out by analysis of polycrystalline diffraction rings (because of the very small crystal sizes many crystals were included within the smallest selecting aperture), sometimes by converging beam diffraction on the Philips microscope, and otherwise using a JEOL TSEM at 200 kV in the microdiffraction mode with a beam size of about 20 nm. Crystal sizes, the number of crystals in a given area, and foii thickness were measured directly on the transmission specimens. The area fraction of crystalline material was determined using the line intersection technique of quantitative metallography. Foil thickness was deduced, as outlined in Part I flJ, from the electron intensity ratio-
Table I. AJioy compositions mtudied (at. %) Alloy designation
Nickel
Silicon
it;lzs 19:x ‘If.5 14.5 70 55
i.25 6.75 7.5 8.3
A : D 5 G
I!
Boron 10 12.5 13.5 15 :(: 30
MORRIS:
GLASS FORMATION
IN Ni-Si-B
ALLOYS -II
passing intensity through the area of interest/intensity recorded in the absence of a foil. A foil thickness-intensity ratio relationship had previously been established based on foils of thicknesses measured by noting the relative motion during tilting of small gold islands deposited on the two sides of the foil or by counting the number of thickness fringes within penetrated large crystals in the amorphous foil. The number of crystals per unit area in a given material, N,,, was measured from the foil. The number of crystals per unit volume. N,, may then be calculated as N, =-
N.4 t+b
where t is the foil thickness and b the average crystal size [25,26]. In a similar way the area function of the projected image containing crystalline materiat, ,f,, may be related to the true volume fraction of crystalline material as [25]
In order to achieve significantly precise values for these parameters, it is important that large areas are studied. In a typical foil, areas of about lo-” rn’ were examined. The number of crystals varied slightly from area to area and it is estimated that the area density and area fraction were probably correct to k 207;. Taking account of errors in the estimations of foil thickness and particle diameter, the number of crystals per unit volume and the volume fraction crystallised are considered to be correct to about +3OY& Very small crystals, less than 20-40 nm, are difhcult to detect and at such small crystal sizes the errors in measurement may be significantly larger. Estimations of the crystal size distribution within a given foil area can provide useful information about changes in the nucleation rate during the annealing. When the crystal sizes involved are much smaller than the foil thickness, the estimation of size distribution is trivial and reduces to a simple collection of a sufficient quantity of data. For crystal sizes larger than the foil thickness. however, sectioning effects become important and it is more difficult to deduce the true particle size distribution from that observed. In this case, the same sectioning effects can be assumed as for optical reflection microscopy and the corresponding analysis used [26]. 3. RESULTS 3.1. As-fast .Wuflure
The alloys containing IO”, boron-?; silicon, 12.5T0 boron-6.259, silicon, 13.59, boron-6.7%; silicon and 309; boron-l ST.,silicon, designated A, B, C and G in Table 1. were obtained in the crystalline
Fig. 1. As-cast structure of the 85Ni-IOB-5% alloy. (a) Large primary dendrites and microcrystalline material. (h) Primary dendrites and interdendritic eutectic material. state. Alloys in the range 159~ boron-7.5’, silicon to 209; boron-10S; silicon, alloys, D, E and F in Table 1. were obtained in the fully amorphous state. Alloy A contained a mixture of large primary dendrites and the remainder as either a microcrystalline or a eutectic material, Fig. I, The dendrites were identified, by diffraction analysis, as the f.c.c. nickel phase which may have been supersaturated in metalloids. The microcrystalline and eutectic materials appeared to be mixtures of the same f.c.c. nickel and a cubic phase with the structure of Ml,m,. namely N&(B.Si), here. A phase having this structure is somewhat unusual for this alloy system, but has, nevertheless, been observed recently during the decomposition of an amorphous nickel-based alloy [4]. Alloy B contained the same phases as those observed for alloy A, but in different proportions. Only a few primary dendrites of the f.c.c. nickel phase were observed and the majority of the alloy was a microcrystalline mixture of the nickel and NL;(B.Si), phase. In alloy C, no large. primary phase structure was observed. Instead. a microcrystalline mixture of the same phases as for the previous alloys was observed. Occasionally, small volumes of amorphous phase were found, occupying in total about 25”, of the material. Alloy G typically contained a few large.
MORRIS: GLASS FORMATION IN Ni-Si-B ALLOYS-II 3.2. CrystaNisation qf amorphous alloys Alloy D. This alloy was prepared in the fully amorphous state by melt-spinning and on heating in the range 350-45O’C crystallisation took place. The crystals forming had a lobed, or butterfly morphology and contained some internal faults, Fig. 2. When about 40-50x of the material had crystallised a eutectic mixture was formed which led to complete crystallisation. The changes taking place during such crystallisation are illustrated in Fig. 2. This crystallisation sequence may indicate that a small composition difference exists between the butterfly crystals and the amorphous matrix which leads to a change in the matrix composition as crystallisation continues. The butterfly crystais were identified as having the orthorhombic N&B phase structure. The volume percentage crystallised as a function of time at temperature is shown in Fig. 3. Crystallisation begins rapidly, at short annealing time, with no evidence of an incubation period. and the transformation rate decreases continuously until the eutectic phase nucleates. The eutectic mixture first appears when about 40-5Oyb of the material has crystallised and this proportion does not appear to change, significantly at least, with the annealing temperature. The eutectic lamellae spacing is very small, of the order IO-15 nm. The fraction crystallised-annealing time data lead to an exponent on the Johnson-Mehl-Avrami Plot of 1.0, Fig. 4. This exponent suggests a crystallisation process on pre-existing nuclei with considerable restriction on the growth process. The variation of crystal number density with annealing time is shown in Fig. 5. There is some evidence to suggest that the crystal density decreases initially to reach a constant value fairly early during
*Or 2 3 a
0 45O’C l
4GPc
x
35O’C *
aso-
; z
x
Fig. 2. Crystaiiisation of the 7?.5Ni-15B-7.5Si alloy during annealing at 350-C: (a) 8 h; (b) 250 h; (c) 930 h.
primary crystals with a microcrystalline phase mixture occupying most of the volume. Occasional regions of eutectic material were found. The phases present were, in all cases studied, complex intermetallics and, in some cases, were not identified. The major phase appeared to have a Ni,Br structure, probably with silicon replacing some of the boron. The orthorhombic N&B structure was also identified, apparently with silicon replacing boron to form a superlattice on some occasions.
I
0
/ 60
I 40
/ 20
500
400’C(h) / IOCO
350°C
Fig.
3.
Percentage
77.5Ni-15B-75%
I 90
I ISOC
(h)
crystallised material in the alloy as a function of annealing time.
MORRIS:
GLASS FORMATION
IN Ni-Si-B
841
ALLOYS-II
o-
.
-1 -
-
.
2:
L -C
-2
.
LL +
/
-3-
-4 t
/
5
l
6
0
20
1
The value of the crystal density decreases as the annealing temperature decreases. The influence of crystal invisibility is unimportant in this case because the crystal size soon becomes very much larger than the resolution limit (2043nm). The variation of crystal size with annealing time and temperature is shown in Fig. 6. While the scatter in data is too great to make precise analysis possible, reasonably good fit to a growth relationship of the form D” = KI is obtained 3.1 + 1. Classical with m taking values diffusion-controlled particle growth [13] should lead to a growth exponent of 2. The higher exponent observed is not fully understood: it may stem from the inapplicability of assumptions in the classical growth theory, for example that phase composition or chemical profile shape may change in time or that the diffusional parameters may be changed in a complex way during continued growth. As an example, the loss of free volume trapped during the glass
,
0
1
L
I
40
1
0
80
5co
I
I
I
40
60
80
4OOT(h) 1
1000
I
1500
35O’C (h) Fig. 5. The number of crystals per unit volume during crystallisation of the 77.5Ni-15B7SSi alloy.
preparation may lead to anomalous diffusion rate decreases during annealing. Figure 7 shows an Arhenius plot of the growth constant K, and also of the long-term, steady state crystal number density N,,, seen in Fig. 5. Both parameters are consistent with the Arhenius relationship and activation energies of about 160 kJ/mol and 65 kJ/mol are deduced for the growth process and the crystal number density, respectively. It should be noted that the activation energy of the number density is near one third that obtained from the Dm-f growth relationship. It is possible that there is a connection between the growth mechanism and the process establishing the stable crystal density and
15
0
x I
40
I
I
crystallisation.
45OWd I
2u
0
x x
I
0 Fig. 4. Johnson-Mehl-Avrami plot obtained from the data of Fig. 3.
x
Kxp x-x
4OO'C(h)
g, 1
1
500
loo0
350e (h) Fig. 6. Variation of crystal size during crystallisation of 77.5Ni-15B7.5Si
alloy.
MORRIS:
842
13
14
103/T
GLASS
15
FORMATION
IN Ni-Si-B
ALLOYS-II
16
(K-II
Fig. 7. Arhenius plot of the growth constant K. and the steady state crystal number density N, Fig. 9. Crystals formed in the glassy 73.5Ni-17B-5Si alloy on low temperature heating.
that the same activation process, related through the growth exponent, may control nucleation and growth. The crystal size distribution observed after partial crystallisation at 45O’C is shown in Fig. 8. The crystal sizes are generally very much larger than the foil thickness and it is necessary to use the reflection metallographic analysis to deduce details of the time dependence of the nucleation process leading to the observed size distribution, it is clear that most of the crystals must have nucleated very early during the annealing treatment and that most of the crystals have about the same, large size. Many of the apparently small crystal sizes recorded can be explained on the basis of sectioning effects. Alloy E. This alloy was prepared in the fully amorphous state and crystallised by heating at a range of temperatures. A complete crystallisation study has been performed at 35O’C only. However, the major observations have been confirmed by additional studies at 400 and 45OC. The first crystals to form were irregular/near-spherical and identified as the othorhombic Nir B phase, Fig. 9. After about 75’/,
Crystal stze (pm) Fig. 8. The size distribution of crystals in the 775Ni-15B-7.5Si alloy after annealing at 45O.C to about 30% crystallisation.
crystallisation had occurred. a eutectic phase mixture formed and led to complete crystalhsation. The volume fraction crystallised. crystal size. and crystal number density as a function of the annealing time are shown in Fig. 10. Again. the volume fraction crystallised increased rapidly with time with no evidence of an incubation period. The Avrami exponent had a value of about 2 for annealing times less than about 10 min. where limited data was obtained. and about 1.0 _t 0.1 for annealing times in excess of IOmin. The interpretation of these exponents is difficult and in essence impossible without further process information. The implication of these exponents is that there is a compositional difference between the crystals and the amorphous matrix and growth is diffusionally-controlled [ 131. The crystal number density increases about linearly with annealing time up to a value of 3-4 x IO’” crystals,m3
Time lmin) 01 35O’C Fig. 10. Percentage cr)stallisrd. crystal size and crystal number density for the 74.5X1-1 7B-X.5Si alloy as a function of time at 350 C.
MORRIS:
GLASS FORMATION
IN Ni-Si-B
ALLOYS--II
843
after a time of IO-20 min. At this time the crystallised volume is onl) about S’, of the total. At longer annealing times the number of crystals remains constant. For this material. the resolution limit for detection of crystals (2040 nm) may lead to an underestimation of the crystal density at the first annealing time considered (1 min) for which the observed crystal size was about 35 nm. Nevertheless, this visibility criterion should not be important for any of the subsequent data. The growth rate of the crystals decreases continuousI> throughout crystallisation. The crystal sizes obe) a relationship D”’ rr
55O’C (s) 0
10
0
I 5
0
I 20
500°C
(rnln)
I 10
450°C
(h)
440000°C
thl
l
, ?5 , 800
I
I
4000 350°C
/ 30
aooc (h )
Fig. 12. Volume percentage transformed on annealing the 70Ni-20B-10Si alloy.
b
Fig. 11. Crystalllsation of the 70N1-IOB-10% alloy on annealing at 450 C: (a) 3 h: (b) 5 h. (c) JO h.
with m having a value of 2.8 f 0.5. While this dependence is again not consistant with classical diffusion-controlled growth theory, it seems likely that diffusional chemical transport between crystal and amorphous matrix is the controlling step with some additional change in diffusivity of chemical profile taking place. Alloy F. Crystallisation studies on this alloy were carried out in the temperature range 35&550 C. Approximately spherical crystals formed. which increased in number and size until almost all the material had crystallised. At about 909,, crystallinity a eutectic phase mixture formed, see Fig. Il. The near-circular crystals were not unambiguously identified, showing sometimes diffraction patterns characteristic of the orthorhombic Ni, B structure and other times of the face centred cubic Ni,,B, structure. These may correspond to an intermediate phase structure or to a mixture of two phases. On some occasions the crystals exhibited a speckle contrast suggesting that some phase change or precipitation process occurred within them. The volume fraction crystallised at each temperature. as a function of the annealing time, is shown in Fig. 12. The curves now show the standard S shapes with a slow initial growth stage followed by an acceleration in the rate of transformation and a slow final transformation rate as crystal impingements become significant. Fitting the data to the Avrami relationship let to the determination of ex-
844
MORRIS:
4
0
I
0
10
0
1 5
GLASS FORMATION
8
55O’C(s)
I
20
500°C I
xl
(min)
d&c
I 15
(II)
0
I
I
a00
400
400°C
(h)
SO’(m) Fig. 13. The number of crystals per unit volume during
crystallisation of the 70Ni-20B-10Si alloy. ponents of 2.9 + 0.4 over the range of annealing temperatures. An experiment conducted to follow resistance changes during annealing at 470°C was difficult to interpret because of the influences of the glass transition. Fitting this data to an Avrami relationship led to an exponent of about 2.6, in good agreement with the results from the structural observations. The variation in crystal number density with annealing time is shown in Fig. 13. The crystal number
IN Ni-Si-B
density rises rapidly with the time of anneal to reach a steady state. This steady state value increases rapidly with the annealing temperature, ranging from about 10’8/m3 at 350°C to more than 102’/m3 at 550°C. The steady state value is reached when only about 20% of the total volume has crystallised for each of the temperatures examined. When the crystal number densities are plotted on linear plots evidence for a clear transient period is seen. During this time the nucleation rate is either zero, as suggested in Fig. 14(a), or increases continuously, as in Fig. 14(b). The nucleation process is here approximated as a constant nucleation rate stage, preceded by a transient or incubation period (listed in Table 2 for each temperature studied), and followed by a saturation stage, when nucleation essentially stops. The transient stage, or incubation period, becomes shorter as the temperature increases. These times remain consistant, however, corresponding to about 5% of the total time to full crystalhsation of each temperature. The rate of increase of crystal density becomes greater at higher temperatures, illustrated in Fig. 14, and this increase obeys an Arhenius relationship with an activation energy of 270 kJ/mol. The crystal size increases with time at ail temperatures, with a faster increase at higher temperatures, see Fig. 15. The crystal size data can be fitted to an expression of the type D” = K(I - to), where r,, is the transient or incubation time. The values of m obtained are 1.8 k 0.4 for the range of temperatures studied. Some of the data are shown in Fig. 16 where, after the incubation period (when no crystals were detected), the crystal size squared is related to the annealing time. Values for the incubation period deduced in this way are also shown in Table 2 and seen to be very similar to those determined from the nucleation plots. The growth rate proportionality factor, K, increases with increasing temperature according to the Arhenius relationship with an activation energy of 250 kJ/mol. This value is close to that for the nucleation process and suggests that the same diffusive process controls both the nucleation and growth steps.
Table 2. Transient or incubation times for the start of crystaliisation Annealing temperature (“C) Incubation time deduced from nucleation plots (Fig. 14) Incubation time deduced from growth plots Growth rate K (D*lAr) (m’/s) Incubation time deduced from K and nslbd~ty criterion (D ==20-4Omn)
ALLOYS-II
in the 70Ni-20B-10Si alloy
400
450
500
550
15@2OOh
lh
1.5 min
1.5s
5Oh
2h
3 min
1.2s
5.6 x l0-M
6.2 x IO-”
1.6 x IO-l6
7.8 x lo-l6
Sh
3 min
7s
1.2s
MORRIS:
GLASS FORMATION
IN Ni-Si-B
845
ALLOYS-II
(h)
Fig. 14. Crystal number density during crystallisation of the 7ONi-2OB-1OSi alloy: (a) at 45OT; (b) at 4OO’C.
Based on the experimentally-deduced growth rate constant K, it is possible to examine the influence of the visibility criterion on the recorded incubation times. Assuming, for example, that crystals smaller than 20-40 nm will not be detected, the time required for a just-nucleated crystal (size -0) to grow to visibility can be calculated. These values are shown in Table 2. With the possible exception of the results at 55O”C, the experimentally-deduced incubation periods are much greater than those values calculated from the visibility criterion. This analysis confirms
(h)
Fig. 16. Increase in size of crystals when annealing the 70Ni-20B-10Si alloy. Growth occurs after an incubation period, according to a D2 = Kr relationship: (a) at SSO’C:(b) at 450 C.
that the incubation are true effects and The distribution been examined for more uniform than some tendency to
periods seen (in Figs 14 and 16) not simply observational artifacts. of crystals of different sizes has this alloy. The distribution plot is that of the alloy D, but still shows be skewed to larger crystal sizes. 4. DlSCUSSlON
34 -
-03
-
E a. al s
0.2 -
0 E t
01 -
ooj/y- , 4
55o*c
1
0
5
0
I s
e
(s)
I
15
(min)
450.C
(h)
4OOT
(h)
1 400
4.1. As-cast
structure
4
5CXYZ I 10
It has on many occasions been noted that an easy glass-forming tendency may often be associated with an alloy composition of low melting point T,,,, and high glass transition temperature T,. The need for a high value of the ratio T,/T, has accordingly been used as one of the rules-of-thumb in the search for new amorphous alloys. Below, an attempt is made to quantify the relationship between T8, TM and the cooling rate and to evaluate the extent to which this quantitative model is in accordance with the experimental observations. Furthermore, since the quantitative model provides a description of the distribution of small crystals present in any nominally amorphous alloy, it should be possible to interpret the subsequent low temperature crystallisation behaviour based on the hypothesis of the small crystals acting as embryos or nuclei for subsequent growth.
I IS
I 800
Fig. 15. Increase in size of crystals during annealing the
70Ni-20BlOSi alloy.
Figure 17 shows a part of the Ni-B,Si section through the ternary diagram from which subsequent quantitative analysis is made. Data on glass temperature or, as a near approximation, the crystallisation temperature and the melting point are taken from the literature (21-231. Liquidus lines, an approximate eutectic solidus line, and the glass transition temperature line have been drawn on the figure.
846
MORRIS: GLASS FORMATION IN Ni-Si-B
/ 400
n/
t
’
10
1 50
EC
D
E
?5
F 20
Boron content (otomlc)
I
75 S~llcon
100
content
I 25
I 12 5
(atomic)
Fig. 17. Part of the Ni-B2Si section through the Ni-B-Si termary diagram. See text for details. In addition, as an aid to discussion, approximate positions for To lines have been shown. The T, temperature is that below which a given alloy can solidify without any compositional change occurring (27,281. The r, lines illustrated here are nothing more sophisticated than approximate bisectors of the liquidus lines and the vertical direction, starting from the maximum in the liquidus. From an equilibrium diagram such as that of Fig. 17 several solidification sequences can be envisaged: (i) The alloys may crystalhse with a large amount of diffusional chemical segregation to produce phases very close in composition to those of the equilibrium solidus. (ii) A slight modification of the previous possibility; a certain amount of diffusion and segregation may take place to give supersaturated phases. (iii) Combinations of equilibrium or supersaturated phases may be produced, as by eutectic solidification, in such a way that the distances over which chemical segregation must occur are greatly reduced. (iv) The temperature falls rapidly below the T, line and solidification can take place without the need for any change of chemical composition. The easiest case to analyse is the final one, where no composition change occurs’as the crystals form. This is the basis for the homogeneous nucleation and growth model described in Part I [1], and the application of this model to the present case will now be considered. Summarising, the model assumes that thermally-activated homogeneous nucleation takes place on the steady-state distribution of embryos,
ALLOYS-II
diffusional crystal growth takes place without change of chemical composition between the amorphous matrix and the crystal. The model developed in Part I [I] calculates the changes in structure during cooling at a given cooling rate and thereby describes the structure present, as fraction crystallised, size and distribution of sizes of crystals. The temperature dependence of the activation energy for formation of the critical nucleus is best described using the Thompson-Spaepen relationship [ 1,291. Other factors used here to evaluate the influence of alloy composition on glass formability were as follows: the critical free energy was taken as AG*/kT = 40 for AT, = 0.20, where AG* is the free energy required to form the nucleus of the critical size, k is the Boltzman constant, T the temperature, and AT, the relative undercooling (TM - T)/T,, where T,,, is the melting point of the given alloy. This value has been shown to more correctly describe crystal formation during cooling in the 74.5 Ni-17B-8.5 Si alloy [I]. Viscosity data were established from data available for this 74.5 Ni-17B-8.5 Si alloy [30] and assuming that the viscosities rt obey the Vogel-Fulcher. relationship, namely q = A exp B/( T - T, ). The parameters A, B and T, were evaluated for each alloy composition by assuming a viscosity of 0.1 P (IO-*Nsm-*) at the melting point, lO’-‘P(lO” Nsm-*) at the glass transition temperature, and the same variation of viscosity with temperature above the melting point (equivalent to assuming an activation energy of about 120 kJ/mol for the viscosity of the liquid just above the melting point). A cooling rate of 3 x 105Ks-’ was used, based on the tapes produced which had a thickness of 30pm [24]. The results of this model simulation are summarised in Table 3 and compared with the experimentally established as-cast structure. The model predicts that the three alloys D, E and F should be obtained in the “fully-amorphous” state, that is with very small fractions of crystalline material. The alloy A is predicted to crystallise completely. Both these results are in agreement with experimental observations. The intermediate alloys, B and C, however, are predicted to contain only about 10% and < l”//,of crystalline material, in contrast to the experimental observations of 100 and 75%. Also shown in Table 3 are the temperatures at which, according to the model, crystallisation begins. Comparison with the schematic To lines of Fig. 17 suggests that the glassforming alloys D, E and F should be below the To temperatures when crystallisaton starts, whilst the alloys A, B and C may be above their To temperatures at this stage. This provides further confidence in the use of this unicornpositional model for the analysis of alloys D, E and F and raises futher doubts of its applicability to the other alloys. Of additional interest in Table 3 is the presence of large numbers of small crystals and a few large crystals within each alloy. even those nominally amorphous. Very obviously a large amount of chemical redistribution has taken
MORRIS:
GLASS FORMATION
Table 3. Predictions of homogeneous nucleation-diffusive
Crystalline Fraction Maximum crystal size (pm) Number of crystals larger than 2 x lo+ m(/m’) Number of crystals larger than - 10-s m(/m’) Temperature crystakation begins (K) as-cast struCtuTe
847
IN Ni-Si-B ALLOYS-II
Alloy designation C
growth model D
E
F
3 X 10-1
4 X 10-b
2 X 10-l
IO-’
5
3
2.3
2.1
1.5
2 X 1010
5 X 10”
5 X 1020
1 X 1on’
4 X 10’9
1 X 10”
2x IoN
2 X 102’
I x ION
1 x 10’9
4 X 10”
5 X 10’6
1050
1075
1000
A
B
1
0.1
10
when 1200 Crystalline dendritic
1150
Crystalline
place during the crystallisation of alloys such as A and B. In this case the previous model requires modification, as follows: the diffusion rate may be taken as reduced proportionately to the concentration of the solidifying elements in the matrix [31,32], for example if Nickel crystals form in a matrix containing 85% Nickel and 15% metalloids the diffusion rate can be taken as 0.85 D, where D is the diffusion rate applicable within the matrix as a whole. This factor applies to both the nucleation frequency and to the crystal growth rate, but is not a major correction for the crystals and alloy compositions considered here. Of greater importance is the rejection of solute as the crystals form, leading to a high solute (metalloid) concentration in the glass in contact with the crystal. The build-up of concentration leads to a decay in growth rate which obeys a (diameter)2 a time relationship rather than the linear diameter a time seen in the absence of compositional changes [18,33]. Modification of the model to include these compositional effects leads to such a restriction on crystal growth that crystallisation is largely avoided for all the alloys (for alloys A, B and C the fractions crystallised after cooling at a rate of 3 x l@ KS-’ are 10e2, lo-’ and 10S6). Clearly this restriction on growth does not lead to a realistic description of the solidification behaviour. Further analysis of the behaviour of the alloys A, B and C is difficult for a variety of reasons. As just described, neither a model completely ignoring compositional changes nor a model including the parabolic decrease of growth rate with time can adequately explain the results. Clearly, dendritic solidification takes place for some of the alloys and growth can continue much faster than implied by the restrictive parabolic reltionship. Also, a second phase can nucleate in the high solute region leading to a co-operative or eutectic phase mixture. Finally, the glass transition temperature is so low for these alloys that any amorphism retained by the rapid quench
1050 Mostly crystalline some amorphlsm
Fully amorphous
may subsequent tallisation.
be lost by low temperature
crys-
4.2. Low temperature crystallisation Alloy D. The low temperature crystallisation behaviour of this alloy is fully in accord with crystal growth taking place on a number of pre-existing nuclei. In Fig. 5, the crystal number density has been seen to remain constant, after an initial decrease at fairly short times. This decrease is possibly the result of the dissolution of some of the original embryos which were formed during the quench. The relationship noted between the activation energies for the growth process and the nucleus number may support this idea. The number of embryos which are stabihsed to become growing nuclei changes with the temperature (10” - 5 x 10” - 10’*/m3 at 350-400-45O’C, see Fig. 5) in a way that is not completely understood. The proposal that crystallisation takes place on pre-existing nuclei is also supported by the change of the fraction crystallised with time (Fig. 3) where there is no evidence of an incubation time before crystallisation. Furthermore, the Avrami exponent of about 1 can be seen to be in full accordance. The Avrami exponent of the total crystallisation process, nlOUI?can be related to the time dependences of the crystal density, nnr,, , and of the crystal volume growth, kl, or the crystal diameter growth, Q,,, as
nloul = a,,, + nVol= n,,l+
3nd,, .
(3)
Here, taking the crystal density to remain constant (n,,, = 0) and the crystal diameters to grow accordtimem. ing to a relationship, hence G_, = 0 + (3 x 0.27) = 0.81, in reasonable agreement with the measured exponent. Finally, of course, the observed distribution of crystal sizes provides additional support for early nucleation of all the crystals present. Alloy E. During the crystalhsation of this alloy the
848
MORRIS:
GLASS
FORMATION
crystal number density increases linearly with time initially to reach a stable volume when only about 5% of the alloy has crystallised (shown in Fig. 10). This behaviour suggests that a sort of continuous, probably thermally-activated nucleation process occurs initially. However, nucleation stops when such a small fraction of volume has transformed that it Seems unlikely that a true, equilibrium distribution of embryo sizes is achieved at the crystallisation temperatures. It is proposed that a distribution of embryo sizes, corresponding to the higher temperatures seen during glass preparation, is frozen in to the glass during rapid quenching. These embryos are not sufficiently large, or of stable chemical composition, to act as quenched-in crystal nuclei. However, they represent an attractive metastable embryo distribution on which thermally-activated stabilisation processes can occur leading to nucleation. The Avrami exponent deduced from the variation of crystallised fraction with time was about 2 initially and about 1 later. Here again, this exponent can be related to the time dependence of nucleation, nnuc,= 1, initially becoming nnucl= 0 later, and to that of crystal growth, namely about ndln= l/2.8 = 0.35. Hence, from equation (3), ntora,= 1 + (3 x 0.35) = 2.1 1.1 later. initially, becoming nlora,=0+(3x0.35)= Alloy F. The number of crystals per unit volume increases during the early crystallisation of this alloy. After about 20% crystallisation the number remains constant at a value that depends on the annealing temperature and varies between about 10’*/m3 at 350°C and about 3 x 102’/m3 at 55OC. As for alloy E, the approximately linear rate at which crystals appear on annealing, and the variation of this rate with temperature, imply that a thermallyactivated process for crystal stabilisation is operating. However, the apparent lack of nucleation after about 20% volume crystallisation implies that a true, homogeneous nucleation mechanism cannot be considered. It is inconceivable that a steady-state embryo distribution can be created, homogeneous nucleation begin, only to halt when still 80% of the material is still amorphous. Equally, it is not consistent with the results to consider that quenched-in nuclei are present. It follows therefore that some quenched-in structure, which is metastable at the annealing temperature, is utilized as a metastable embryo distribution on which stabilisation processes leading to crystal formation will occur. This quenched-in structure may be in the form of crystal embryos, metastable at the annealing temperature, as suggested by an earlier publication [I], or may be in the form of short range order, e.g. (341. According to this hypothesis, the number of crystals than can form will be related to the number of quenched-in, metastable embryos. However, since the embryo distribution is metastable it will decay at the annealing temperature and the ultimate crystal density will depend both on the rate of embryo growth to stable crystals and on the rate of metastable embryo decay. It is this conflict which
IN Ni-S-B
ALLOYS-II
is believed responsible for the variation in the number of crystals produced at saturation as the annealing temperature changes (see Fig. 13). The Avrami exponent deduced directly from the change of fraction crystallised with time, 2.9 + 0.4. can be shown to be in agreement with the suggestion of continuous nucleation during the initial stage. Assuming continuous nucleation, i.e. nnuc,= 1, and taking the measured value of ndla= 0.56 for the time dependence of the crystal diameter, we obtain n ,0,,l= 1 + 3 x 0.56 = 2.7, in good agreement with the deduced Avrami exponent. In Table 3 the typical numbers of small crystals which are calculated on the basis of the homogeneous nucleation and growth model to be present in the as-cast ribbons are shown. The same calculation also shows that the critical nucleus size is about 1.3-2 nm over the range of annealing treatments performed on the alloys D, E and F. Accordingly, the number the quenched-in crystals suitable to act as nuclei are predicted to be about 1020/m3 for alloy D, about 4 x 10’9/m3 for alloy E, and about l-2 x lO’*/m for alloy F. (These are the number of crystals having sizes greater than the critical sizes quoted above.) Within alloy D there are sufficient quenched-in crystals to act as nuclei for low temperature crystallisation. Apparently, many of the nuclei may dissolve during the early stages of crystallisation and this loss by dissolution is more important at low temperatures. Within alloy E the calculated number of quenched-in crystals is identical to that observed during crystallisation at 350°C. These quenched-in crystals should be able to act as stable nuclei for growth, and crystallisation of this alloy should then take place by growth alone on these quenched-in nuclei. It does not appear, on the basis of the experiments performed. that this is the case. Rather it seems that quenched-in. sub-critically sized embryos are produced which require thermally-activated stabilisation. Within alloy F the number of quenched-in crystals (Table 3) is less than the number observed to form during low temperature crystallisation (with the possible exception of annealing carried out at 350-C where about the same number of crystals have been observed). In this case thermally-activated stabilisation must take place on sub-critically sized embryos that are characteristic of the detailed metastable, quenched structure of the amorphous alloy. At each annealing temperature, thermally-activated stabilisation takes place on the limited number of embryo sites which, because of their quenched-in, metastable nature, tend to disappear or change to that characterising the annealing temperature. Once these metastable embryos have been used, nucleation almost stops since the true, homogeneous nucleation rate is much slower. Details of embryo formation and distribution, mechanisms of stabilisation to crystal or modification to steadystate embryos, are unclear, and the simple homogeneous crystallisation model is not useful. An alternative hypothesis for nucleation rate vari-
MORRIS:
GLASS FORMATION
ations should be considered. This hypothesis would assume that homogeneous nucleation on an equilibrium embryo distribution takes place (e.g. alloys E and F), perhaps preceded by a transient as the equilibrium distribution is built up (alloy F). However, the diffusivity of the amorphous phase can be supposed to gradually decrease, for example as free volume annihilation occurs. This explanation may apply to alloy E, where an anomalous crystal growth rate exponent (LIZ* zr) was seen, but does not seem to be consistant with the growth data on alloy F (D’ %r) which is interpreted as diffusional growth at constant diffusivity.
5. CONCLUSIONS
The processes of crystal nucleation and growth occurring during the preparation of a series of nickel-silicon-boron alloy tapes by melt spinning have been studied and related to the thermal properties of the alloys. The kinetic model of glass formation evaluated in a previous report [l] has been used to describe the nucleation and growth taking place during cooling and shown to provide a good description for those alloys which can solidify without change of composition. In the present case these alloys were those where crystal formation could fairly readily be avoided and amorphous tapes prepared. Alloys which may solidify with significant redistribution of solutes as crystallisation occurs cannot be described by the model in its present form. The low temperature crystallisation of three amorphous alloys has been studied in detail. For one, crystallisation took place by the growth of quenchedin crystals. For the other two, crystal formation was a thermally-activated process which took place on some quenched-in metastable sites. These metastable embryos may be analogous to the crystal nuclei predicted by the kinetic model, or may be related to the short range order structure of the glass. The Avrami exponent deduced from the change in fraction crystallized with time is very well explained by the nucleation and growth rates determined by direct observation. However, it is not possible to deduce, unambiguously, the crystallisation mechanisms from the exponent alone. The change from athermal nucleation on quenched-in nuclei to thermally-activated embryo stabilisation is perfectly in accord with the predictions of the kinetic model which points to the existence of small crystals within the rapidly cooled tape. If a suitable number of sufficiently large crystals is present, then subsequent crystallisation can take place using these crystals as nuclei. On the other hand, if there are few quenched-in crystals, the quenched-in metastable embryo distribution will be important in acting as sites for thermally-activated crystal formation.
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849
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