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

A critical gas boundary layer Reynolds number has been defined to indicate processing conditions under which wide glassy alloy ribbons result when processing under various gaseous atmospheres and pressures and casting onto a moving substrate at an impingement angle .alpha..

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to the production of wide glassy alloy ribbons by 
chill block melt-spinning and in particular to the critical gas boundary 
layer Reynolds number above which wide glassy alloy ribbons with serrated 
edges and surface perforations result when cast at an impingement angle 
.alpha.. 
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 edge 
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 wide 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 
wide ribbons. 
A further object of this invention is to provide a new and improved method 
for processing wide glassy alloy ribbons embodying a critical gas boundary 
layer Reynolds number for developing parameters when casting at an 
impingement angle .alpha.. 
BRIEF DESCRIPTION OF THE INVENTION 
In accordance with the teachings of this invention there is provided a 
method for producing glassy wide 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 at an impingement angle .alpha. between the melt jet and the 
tangent to the substrate surface at the impingement point. The substrate 
wheel speed S, the melt jet velocity v, the ribbon width w, the 
impingement angle .alpha. and the ambient atmospheric gas pressure P are 
adjusted to result in a gas boundary layer Reynolds number of about 
2000.+-.100. The gas boundary layer Reynolds number is empirically found 
to follow the relation: 
EQU Re =K(1-cos .alpha.)DSwP[M/.eta.] 
Re=Reynolds number 
K=constant which takes into consideration all conversion factors to obtain 
dimensional consistency 
.alpha.=impingement angle between melt jet and tangent to substrate surface 
at point of impingement 
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.-8 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) under various atmospheric 
gases and pressures using various processing conditions, ribbon edge 
deterioration invariably occurred at gas boundary layer Reynolds numbers 
of &gt;2000.+-.100 and is not exclusively dependent on ribbon width. The 
various gases in which the ribbon has been cast include helium, air, 
carbon monoxide, argon, krypton and xenon. 
The Reynolds number of the gas boundary layer interacting with the melt 
puddle made when the melt jet is cast at an impingement angle of 
90.degree. with the tangent to the substrate surface is expressed as 
follows: 
EQU Re'=KDSwP[M/.eta.] (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 
When the combination of processing parameters shown in equation (I) is such 
that the ribbon geometry is on the verge of degradation, the Reynolds 
number is said to go critical. That is, 
EQU Re'.sup.crit .perspectiveto.2000 (II) 
Preferably, Re'&lt;.about.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 a melt is cast onto a moving substrate at an 
impingement angle .alpha.. The thin gas boundary layer 10 following the 
moving substrate surface 12 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&gt;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. (III) 
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 (IV) 
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].multidot.[M/.eta.] (V) 
The first of the two factors of equation (V) relates exclusively to 
physically variable apparatus and processing parameters. The second factor 
of equation (V) is a physical constant particular to the gas in which the 
melt-spinning in 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 
__________________________________________________________________________ 
10.sup.-4 
##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## 
__________________________________________________________________________ 
Ribbon edge deterioration occurs abruptly at Re'=.about.2000. Ribbon edge 
surface deterioration is intensified with an increasing gas boundary layer 
Reynolds number. 
The impingement angle dependence of gas boundary layer Reynolds number has 
been determined by casting ribbons of various widths at fixed melt jet 
impingement angles .alpha., all other processing conditions held constant. 
This work results in the approximate expression: 
EQU Re=(K)(1-cos .alpha.)DSwP(M/.eta.) VI 
where 
K=constant which takes into consideration all conversion factors to obtain 
dimensional consistency 
and K=2.868.times.10.sup.-8 when D and w are expressed in centimeters, S is 
expressed in revolutions per minute, P is expressed in millimeters of 
mercury, M is expressed in gram per gram mole, and .eta. is expressed in 
poise. 
As previously stated in copending U.S. Patent Application, Ser. No. 
896,752, and now U.S. Pat. No. 4,144,926, the critical gas boundary layer 
Reynolds number above which serrated ribbon edges result is 2000.+-.100. 
Equation VI has been verified for various combinations of processing 
parameter values. 
Although glassy alloy ribbon has been cast with 
10.degree..ltoreq..alpha..ltoreq.100.degree., the preferred range of 
operation is 40.degree..ltoreq..alpha..ltoreq.70.degree. because of ribbon 
geometry problems occurring at either extreme. Aside from the serrated 
edges which may be found to occur at any .alpha., casting at 
.alpha.&lt;70.degree. typically imparts surface roughness and "fluid flow 
marks" on the ribbon free surface, thereby making the product undesirable. 
Casting at .alpha.&lt;.about.40.degree. results in rapid thickening of the 
sample with decreasing angle and can conceivably be the source of some 
ribbon thickness variations. Of course, sample thickening must be 
counteracted by reduced melt flow rate and/or increased substrate surface 
speed, both of which are undesirable. Finally, experiments with round melt 
jet impinged at .alpha.&lt;.about.40.degree. have revealed ribbons with 
excessively non-uniform thickness across the width of the sample. 
EXAMPLE I 
A glassy alloy ribbon of nominal composition Fe.sub.40 Ni.sub.40 B.sub.20 
3.5 millimeters in width was produced by casting from a clear fused quartz 
crucible with a 20 mil round orifice and melt ejection pressure of 80 psi 
directed at an angle .alpha.=40.degree. impingement onto the surface of a 
copper substrate wheel 7.5 centimeters in diameter rotating at a speed of 
8000 revolutions per minute. The ambient atmosphere was air at 760 
millimeters mercury pressure. The gas boundary layer Reynolds number, Re, 
as determined from equation VI was 1700. The ribbon edges were smooth and 
both the top and bottom surfaces were of excellent quality. 
EXAMPLE II 
The process of Example I was repeated except that the impingement angle was 
90.degree.. The ribbon produced was amorphous material and had good 
surface and edge qualities. However, the width of the ribbon was only 
approximately 1 mm. 
By employing the teachings of this invention and having the critical values 
for the gas boundary flow Reynolds number, Re, one is able to readily make 
good wide glassy alloy ribbon material. Glassy alloy ribbons in 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).