Critical gas boundary layer Reynolds number for enhanced processing of glassy alloy ribbons

A critical gas boundary layer Reynolds number has been defined to indicate conditions under which glassy alloy ribbons with serrated edges and surface perforations result when processing under various gaseous atmospheres and pressures.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to producing glassy alloy ribbons by chill block 
melt-spinning and in particular to a critical gas boundary layer Reynolds 
number above which glassy alloy ribbons with serrated edges and surface 
perforations result. 
2. Description of the Prior Art 
Relationships between processing parameters and dimensions of glassy alloy 
ribbons formed by melt-spinning have been discussed by Chen and Miller in 
Material Research Bulletin 11, 49 (1976), Liebermann and Graham, Jr., 
I.E.E.E. Transactions Mag-12, No. 6, 921 (1976) and Kavesh, Metallic 
Glasses, ed. J. J. Gilman, A.S.M. (1978), Ch. 2. However, the nature of 
the gas boundary layer associated with the motion of the substrate wheel 
and its effects on the melt puddle and resultant ribbon geometry have not 
been quantitatively considered in the literature. Although relatively 
narrow glassy alloy ribbons may be cast satisfactorily without special 
care regarding the prevalent atmosphere in which melt-spinning is 
conducted, the fabrication of wider ribbons with good surface finish and 
smooth edges is found to be difficult or impossible without controlling 
the gas boundary layer on the circumferential surface of the rotating 
substrate wheel. Failure to control this boundary layer typically results 
in ribbons with serrated edges and possible longitudinal slits. 
It is therefore an object of this invention to provide a new and improved 
method for processing glassy alloy ribbons. 
Another object of this invention is to provide a new and improved method 
for processing glassy alloy ribbons wherein substantially higher than 
prior art substrate speeds are employed in the manufacture of very thin 
ribbons. 
A further object of this invention is to provide a new and improved method 
for processing glassy alloy ribbons embodying a critical gas boundary 
layer Reynolds number for developing casting parameters. 
Other objects of this invention will, in part, be obvious and will, in 
part, appear hereinafter. 
BRIEF DESCRIPTION OF THE INVENTION 
In accordance with the teachings of this invention there is provided a 
method for producing glassy alloy ribbons. The method includes controlling 
the thin gas boundary layer established on the rapidly moving substrate 
surface immediately adjacent to the melt puddle from which the ribbon is 
produced. The melt puddle is produced by impinging a molten alloy jet onto 
the circumferential surface of a rotating substrate wheel of diameter D. 
The substrate wheel speed S, the melt jet velocity resulting in a melt 
puddle of width w on the substrate wheel surface, and the ambient 
atmospheric pressure P are adjusted to predetermined values. The glassy 
alloy ribbon is produced from the melt puddle while maintaining the 
Reynolds number Re for the gas boundary layer flow about the melt puddle 
less than a critical value Re.sup.crit of about 2000 .+-. 100. The gas 
boundary layer Reynolds number is expressed by the following formula: 
EQU Re = KDSwP M/.eta.! 
wherein 
Re = Reynolds number 
K = constant which takes into consideration all conversion factors to 
obtain dimensional consistency 
D = substrate wheel diameter 
S = substrate wheel speed 
w = ribbon or puddle width 
P = ambient atmospheric pressure under which casting is conducted 
M = molecular weight of ambient gas in which casting is conducted 
.eta. = viscosity (20.degree. C.) of ambient gas in which casting is 
conducted 
The value of K is 2.868 .times. 10.sup.-9 when D and w are each expressed 
in centimeters, S is expressed in revolutions per minute, P is expressed 
in millimeters of mercury, M is expressed in grams per gram-mole, and 
.eta. is expressed in poise.

DESCRIPTION OF THE INVENTION 
It has been discovered that in the casting of glassy alloy ribbons 
(commonly referred to as amorphous ribbons) in various types of gaseous 
atmospheres and at various pressures ribbon edge deterioration invariably 
occurred at gas boundary layer Reynolds numbers of > 2000 .+-. 100 and was 
not necessarily dependent on ribbon width. The various gases in which the 
ribbon was cast were helium, air, carbon monoxide, argon, krypton and 
xenon. 
The critical Reynolds number of the gas boundary layer interacting with the 
melt puddle is expressed as follows: 
EQU Re.sup.crit = KDSwP M/.eta.! .apprxeq. 2000 (I) 
where 
Re = Reynolds number 
K = constant which takes into consideration all conversion factors to 
obtain dimensional consistency 
D = substrate wheel diameter 
S = substrate wheel speed 
w = ribbon (puddle) width 
p = ambient atmospheric pressure under which casting is conducted 
M = molecular weight of ambient gas in which casting is conducted 
.eta. = viscosity (20.degree. C.) of ambient gas in which casting is 
conducted 
Preferably, Re < .apprxeq. 2000 .+-. 100 in order that ribbon edge 
deterioration and surface perforations are avoided and the product is 
useable for product manufacture. 
A thin boundary layer in which the gas molecules essentially move with the 
same velocity as the casting surface of a substrate wheel, upon which a 
melt is cast, is established because of frictional forces between the 
substrate surface and the adjacent gas molecules. It is the nature of this 
thin boundary layer and its interaction with the alloy melt puddle, from 
which glassy alloy ribbon is continuously drawn, which determines whether 
or not serrated ribbon edges and surface perforations will occur under a 
given set of casting conditions. 
With reference to FIG. 1, the thin gas boundary layer 10 following the 
moving substrate surface and immediately adjacent to the melt puddle at 
its interface with the substrate surface 12 does not adversely affect 
changes in the melt puddle width. The thin gas flow boundary layer 10 
remains nonturbulent for a gas boundary layer Reynolds number Re less than 
some critical value Re.sup.crit. Referring now to FIG. 2, turbulence 
occurs in the thin boundary layer 10 when Re > Re.sup.crit and modulates 
melt puddle width, thereby causing serrated edges. 
The gas boundary layer Reynolds number appears to follow the relationship: 
EQU Re = vw/.nu. (II) 
wherein 
Re = the Reynolds number 
v = gas velocity (assumed equal to substrate surface velocity) 
w = ribbon width (assumed equal to melt puddle width at interface with the 
substrate wheel) 
.nu. = .eta./.rho. = kinematic gas viscosity 
and 
.eta. = static gas viscosity 
.rho. = gas density 
Assuming ideal gas behavior, 
EQU .rho. = nM/V = PM/RT (III) 
wherein 
n = moles of gas 
M = gas molecular weight 
V = gas volume 
P = gas pressure 
R = ideal gas constant 
T = gas temperature 
by substitution: 
EQU Re = vwp/RT .pi. .multidot. M/.eta.! (IV) 
the first of the two factors of equation (IV) relates exclusively to 
physically variable apparatus and processing parameters. The second factor 
of equation (IV) is a physical constant particular to gas in which the 
melt-spinning is conducted. The following Table records the physical 
constant and propensity for serrated edge formation for various gases, all 
of which have been used in melt-spinning experiments except for H.sub.2 
and Ne. 
TABLE 
______________________________________ 
Gas He H.sub.2 
Ne Air CO Ar CO.sub.2 
Kr Xe 
______________________________________ 
##STR1## 
2.06 2.30 6.49 
15.8 
16.0 
18.1 
29.7 
34.1 
58.1 
order of increased propensity for serrated ribbon edge formation 
##STR2## 
______________________________________ 
With reference to FIG. 3, glassy alloy ribbons of Fe.sub.40 Ni.sub.40 
B.sub.20 were produced under various gas boundary layer Reynolds numbers. 
The ribbon edge deterioration occurred abruptly at Re = .apprxeq. 2000. 
Ribbon edge and surface deterioration intensified with an increasing gas 
boundary layer Reynolds number. 
By application of Equation (I) one is able to determine apparatus and 
processing conditions necessary for the fabrication of uniform wide glassy 
alloy ribbons with smooth edges. Glassy alloy ribbons in the systems such 
as Fe-B, Fe-B-C, Fe-Ni-B, Fe-B-Si, Nb-Ni, Cu-Ti, Ni-Zr, and Cu-Zr are 
successfully cast with smooth edges when the processing parameters conform 
to the limitations expressed in Formula (I). The following is an example 
of the manner in which equation (I) may be used to define processing 
parameters for the fabrication of glassy alloy ribbons with good, uniform 
geometry. If glassy alloy ribbon is melt-spun at 20.degree. C. using a 
substrate wheel diameter of 7.5 cm, the critical ambient atmospheric 
pressure for casting the glassy alloy ribbon of given width with good 
edges in air at several substrate wheel speeds is given in the graph of 
FIG. 4. The use of ambient atmospheric pressure greater than critical will 
cause the gas boundary layer Reynolds number to become hypercritical and 
serrated-edge ribbon will result. 
EXAMPLE I 
Glassy Alloy Ribbon Manufacture With Re > Re.sup.crit 
A glassy alloy ribbon of nominal composition Fe.sub.40 Ni.sub.40 B.sub.20 3 
millimeters in width was produced by casting on the surface of a substrate 
wheel 7.5 centimeters in diameter rotating at a speed of 9000 revolutions 
per minute. The ambient atmosphere was xenon at 150 millimeter mercury 
pressure. The gas boundary layer Reynolds number, Re, as determined from 
equation (I) was 5000. The ribbon edges were serrated and the ribbon 
surface showed fine perforations. 
EXAMPLE II 
Glassy Alloy Ribbon Manufacture With Re < Re.sup.crit 
A glassy alloy ribbon of nominal composition Fe.sub.80 B.sub.18 Si.sub.2 7 
millimeters in width was produced by casting on the surface of a substrate 
wheel 7.5 centimeters in diameter rotating at a speed of 10000 revolutions 
per minute. The ambient atmosphere was air at 70 millimeters mercury 
pressure. The gas boundary layer Reynolds number, Re, as determined from 
equation (I) was 1700. The ribbon edges were smooth and both the top and 
bottom surfaces were of excellent quality. 
EXAMPLE III 
Glassy Alloy Ribbon Manufacture With Re << Re.sup.crit 
A glassy alloy ribbon of nominal composition Fe.sub.40 Ni.sub.40 B.sub.20 
2.5 centimeters in width was produced by casting on the surface of a 
substrate wheel of 25 centimeters diameter rotating at a speed of 3000 
revolutions per minute. The ambient atmosphere was air at 0.10 millimeters 
mercury pressure. The gas boundary Reynolds number, Re, as determined from 
equation (I) was 8. The ribbon edges were smooth and both the top and 
bottom surfaces were of excellent quality.