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Embrittlement of some metallic glasses by Sb, Se, and Te
EMBRITTLEMENT
OF SOME METALLIC BY Sb, Se, AND Te
GLASSES
H. H. LIEBERMANN and F. E. LUBORSKY General Electric Corporate Research and Development Schenectady, NY 12301 U.S.A. (Received
9 February
1981)
Abstract-Some metallic glasses have been found to embrittle after annealing at low temperatures, much as do some steels. In phosphorus-bearing alloys, phosphorus has been found to segregate during annealing and result in sample embrittlement. The present report describes the effects of the steelcmbrittling elements Sb, Se, and Te on metallic glasses in which the primary metallic constituents are Fe and/or Ni. Bend ductility and stress relaxation measurements of as-cast and annealed glassy alloy ribbons have been used to study embrittkment resulting from less than 0.2 at.‘):, Sb. Se, and Te addition to the base alloys XRD, DSC, and magnetic measurements have been used to further characterize the samples and to check for changes in magnetic properties which may accompany embrittlement. Results show that P is a very weak embrittler compared with Sb, Se, and Te. Furthermore, the embrittling power of these three ekmettts varies in the sequence Te > Se B Sb, the same sequence as found in steels. The effect of a given embrittler is enhanced when substituting Fe in place of Ni. No substantial changes in DSC or magnetic measurements have been found as a result of substituting the small amount of embrittler into the base alloys investigated. R&m&Nous.avons trouvC que certains verres metalliques ttaient fragilises par un recuit a basse tempCrature, comme certains aciers. Dans les alliagcs pour paliers au phosphore, le phosphore sCgrtge au tours du*recuit, de qui conduit a une fragilisation de l’tchantillon. Dans cet article, nous prtsentons les effets de l’addition de Sb, Se and Te, qui sont des elements fragilisant des aciers, sur des verres metalliques dont les constituents mttalliques principaux sont Fe et/au Ni. Des mesures de ductilite en flexion et de,relaxation de contrainte sur des rubans d’alliages vitreux bruts de coulee et recuits ont permis de mettre en Cvidmce une fragilisation provenant de l’addition de moins de 0.2 at”/, de Sb, Se et Te aux alliages de base. Des mesures de diffraction X, de DSC et magnttiques ont ensuite permis de caracteriser plus prtcistment Ies tchantillons et d’observer une tventuelle variation des proprittts magnCtiques ‘qui pourrait accompagncr la fragilisation. Nos resultats montrent que le P est beaucoup moms fragilisant que,Sb, Se et Te. De plus, Ie pouvoir fragilisant de ces trois elements varie selon la sequence Te > Se # Sb, c’est 4 dire la m8me que dans Ies aciers. On augmente l’egect dun element fragilisant en remplacartt du Ni par du Fe. Nous n’avons pas vu de changement notable du DSC ou des propri6ti.s magnttiques B la suite de la substitution dune faible quantite d’eltment fragilisant dans l’alliage de base. Zusammeufasamg-Einige metallische Glliser vcrspri%en wiihrend der Auslagerung bei niedrigen Temperaturen wie gewisse Stlihle. In phosphorhaltigen Legierungen wurde gefunden, dal3 Phosphor wiihrend der Auslagerung segregiert und dadurch die Versprtiung verursacht. Die vorliegende Arbeit beschreibt den EinfluB der Stahl-verspr6denden Elemente Sb, Se und Te auf metallische Cl&r mit den metallisthen Hauptkomponenten Fe und/oder Ni. Mit Messungen der Biegeduktilitgt und der Spannungsrelaxation an frisch hergestellten und ausgelagerten Biindern metallischer Gliser wurde die Verspradung untersucht, die von Sb-, Se- und Te-Zugaben in Mengen von weniger als 42 At.-“/:, verursacht wird. Mit XRD-, DSG und magnetischen Messungen wurden die Proben weiterhin untersucht, urn mogliche, mit der Verspradung einbergehende Anderungen der magnetischen Eigenschaften aufzufinden. Die Ergebnisse xeigen, daD P im Vergleich tu Sb, Se und Te sehr schwach verspradend wirkt. Die Wirksamkeit dieser Elemente gindert sich in der Folge Te > Se % Sb wie in den Stiihlen. Der EinfluB eines versprodenden Elementes wird verstiirkt, wenn Ni durch Fe ersetzt wird. Es wurden keine bedeutenden Anderungen bei DSG und magnetischen Messungen gefunden, die als Folge der Einfiihrung des kleinen Anteils versprtiender Elemente in die Basislegierung auftraten.
INTRODUCTION The embrittkment of some metallic glasses may occur without the onsct of crystallization during annealing at temperatures well below those required to cause crystallization. This embrittlement is analogous to that found in steels Cl, 23, except that it is irreversible. Phosphorus is a metalloid used in the formation of
some metallic glasses and the discovery of embrittlement in glassy alloys containing this element has prompted numerous investigations [3-81. It has been suggested that P enrichment occurs on a highly localized scale in these alloys during annealing, resulting in sample embrittlement because of sharply reduced ductility in the segregated regions and the extent to which the ductile-brittle transition temperature is
1413
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LI~BERMANN
ABD
LUBORSKY:
~~~BRITTL~M~NT
suppressed varying directly with phosphorus content [7]. Elements such as Sb, Se and Te are much more potent embrittlers of steel than is P[9J. The current investigation deals with the nature of temper embrittlement in metallic glasses of nominal composition Fe a,.5B,,.5Si4, Fe&%&~. and Nial.&.& containing 0.2 at.% or less of the embrittling agents Sb, Se or Te. The alloy compositions have been selected to be phosphorus-free so that properties measured will not be the result of P segregation. Furthermore, the nominal compositions chosen permit a comp~ison of embrittlement as Ni and Fe are interchanged in the base alloy. Embrittlement of a metallic glass is not only dependent upon the addition of embrittling alloying elements but is also determined by processing conditions with which the sample is manufactured. For example, it has been found that glassy afloy embrittlement increases with decreased ribbon-substrate contact distance during chill block melt-spinning [lo]. A similar correlation has been established between glassy ribbon stress relaxation and ribbon-substrate contact distance [l 1J. Increased tendency for embrittlement has also been demonstrated with increased as-cast ribbon thickness [12]. Whether by reduced ribbonsubstrate contact distance or by excessive ribbon thickness, the increased embrittlement and reduced stress relaxation result from the ‘self-anneal’ of the ribbon when departing from the substrate surface without having undergone sufficient heat removal during melt-spinning. EXPERIMENTAL Master aIloys of the compositions investigated were premelted using high purity constituent alloying elements in an alumina crucible atmosphere and poured into a split copper mold under Ar atmosphere. The resultant ingots were then crushed and pieces chili block melt-spun in vacuum [t33. A 125 mm diameter copper substrate wheel was used at 2, 4, 6, and 12 krpm to result in a set of ribbons having average thicknesses of from 8 pm to 45 pm for each alloy composition investigated. Ribbon-substrate sticking distance was not found to vary with the alloy compositions studied for a given geometric crosssection and substrate velocity. Although the embrittling elements studied are also surface active and reduce liquid iron and nickel surface tension [14]. no significant change in ribbon geometry was noted when casting embrittler-bearing samples. This is presumably because of substantial melt puddle turbulence during casting and suggests a uniform distribution of the embrittler elements in the ribbons. Ribbons of various thicknesses for each composition were examined by transmission Laue X-ray diffraction (Charles-Supper precession camera with a GE XRD-4 power generator) to check for indications of crystallinity. These samples were also subjected to
OF METALLIC
GLASSES
bend ductility testing in which a ribbon sample is gradually bent (shiny side out) to a decreasing radius of curvature between the platens of a micrometer drive and the platen separation at sample fracture converted to a relative maximum strain to fracture [43 using micrometer (maximum) ribbon thickness for calculation. The degree to which atomic motion is possible was monitored through stress relaxation measurements on all of the ribbons formed. Stress relief data were obtained by annealing ribbon segments in 1 cm i.d toroidal cans for two hours at 498 K and me~uring the degree of spring-back exhibited by each sample on removal from the can [15]. Ductile, glassy ribbons of about 25 pm average thickness were sealed in evacuated glass tubes and subjected to 1 h anneals at 373,473, 573 and 673 K. The relative strain to fracture for these annealed ribbon samples was then remeasured and embrittlement assessed. Differential scanning calorimetry (DSC) using a Perkin Elmer DSC II at 4OK/min heating rate was used to compare crystallization temperatures of some ribbon samples with and without embrittler alloy additions. Magnetic coercivity measurements using an 8OOAm-’ (IOOe) drive fietd have also been used to examine the annealing response of Fe*eNi,eBzo base metallic glass containing small amounts of Sb and Se. RESULTS AND DISCUSSION
The embritfiement of alI ribbons in the as-cast state has been measured by the relative maximum strain to fracture of U-shaped samples [4], a typical data set of which is shown in Fig. 1 for the Fe,eNi4eBzo base alloys, The sharp increase in fracture strain with decreasing ribbon thickness has been drawn to comply with this kind of variation typically exhibited by glassy alloys [73. The dashed portion of the Fe40Ni4,,Bt9,9Tee.1 data curve is an extrapolation to a maximum relative strain of 1.0. Fracture strain data scatter is well-masked by the steepness of the curves drawn. From such plots, the maximum ductile sample thickness (f$ for each composition is obtained by reading the thickness at which the maximum relative strain to fracture drops below unity. Note that the r$ values obtained are particular to the melt-spinning apparatus and conditions (such as ribbon-roller contact distance) used and may vary when using other equipments. A summary of Q for all the glassy alloy compositions investigated is given in Table 1. From this data, it is seen that as-cast Feal,sB,&i4 ribbons show less embrittlement (can be made thicker yet ductile) than either Fe,N,i~OBle or Nie,.,B,&i, ribbons. This is pr~umably because of the greater thermal stability of the Fe-based metallic glass, as shown by the DSC data in Table 4. The right-hand column in Table I lists the ratio of maximum as-cast ductile ribbon thickness for a given base composition (G) to the equivalent thickness for an embrittler-containing
LIEBERMANN
AND
LUBORSKY:
EMBRITTLEMENT
Fig. 1. Relative maximum strain to fracture data for as-cast samples as a function of &ssy alloy ribbon micrometer (maximum) thickness for the Fe40NiiBz0 base alloy and samples containing small amounts ofthe embrittlers Sb, Se or Te.
alloy (c). This ratio eliminates the diierence in thermal stability of the three base alloy compositions and gives an indication of relative embrittlement, with 1.00 corresponding to. that of the embrittler-free base alloy. The sequence of elements in order of increased embrittling power in FeMNiiBzo glassy alloy data shown in Fig. 1 is Sb, Se, Te for 0.1 at.% ~b~~Ier addition. The resutts also show that increased quantt ties of Sb in Fe4eNi,+&s0 result in increased embrittlement. This increased embrittling strength with
Table I. Maximum as-cast glassy alloy ribbon micrometer thickness at which completely ductile bending is possible (4) and ratio of ductile base alloy to ductile embrittlercont~ning alloy ribbon thickness ~~/~). Composition
II: pm
Wt;
Fe~I.~Br4.& Fea~.,B,~.,gt~.~gh,.~ Fe~~.~B~~.~Si,.~Se~.~ Feel.sB14.~SiJ.9Teo.1 F%.oNL&0 ~~~~~i~~~,9.~~~ho.~~ ~~~~~i~~~~9.~~h~~~~ Fe4~NL&9.agho.2~ f+&&B19.~9ge~.~~
58 40 420
1.45 * 2.90 * 2.90 1.00 1.05 2.33 1.00
Fe,oNi40B19.&eo.t~
28 42 c25 40 40 :
Fe~oNi~~B,9.99Teo.o~ Fe40Ni40B19.9Teo.l~
Nk9k& Nis~.~Blr.sSi,.9Sbo.l Nk~Bl&iJ.&%.~ Nier.~B&%.9Teo.,
420
42 42 40 18 42
1.50 1.00 > 1.68 1.00 1.00 1.00
OF METALLIC GLASSES
1415
lh 11. I(
Fig. 2. Relative maximum strain to fracture data as a function of one hour isochronal annealing temperature for the Ni ~I.5B,I.SSi~ base alloy and sample containing 0.1 at.% of the embrittler Sb, Se, or Te.
concentration of embrittler would presumably also be the case for the other base alloys as well. In the
Ni81.sBt4.&?i4glassy alloy system, there seems to be no embrittling effect due to Sb, Se or Te at the 0.1 at.% concentration in any of the as-cast ribbons. Relative maximum strain to fracture of ribbons as a function of 1 h isochronal ~n~~rng temperature is exemplified by the data for the NiaI.,B,,,Si4 base metallic glass shown in Fig. 2. The 1 h embrittlement temperature is defined as that at which the relative maximum strain to fracture drops below unity and the sample begins to show loss of bend ductility. Fracture strain data scatter is more obvious in the less steep portions of the curves drawn. As in Fig. 1, the shape of the data curves has been drawn to comply with that typically found for glassy alloys [7]. Note that for the -25 pm thick ribbon samples annealed and tested, an embrittlement of the NiB1.5B,4.5Sil base composition samples is only found for samples containing 0.1 at.% Se or Te. It is interesting that a 0.1 at.% Sb addition causes no detectable embrittlement beyond that of Nisl,sB14.&. The embrittling Rower of the three agents used follows the same sequence in each of the three base alloys: Te > Se >>Sb. A summary of 1 h embritttement temperatures and the ratio of one hour embrittlement temperature for the base alloy to that of the embrittlercontaining alloy (T’,/T,) for the three base compositions appears in Table 2. An illustration of the embrittlement data in Table 2 is shown in Fig. 3 for the three base alloy compositions. The dashed curves are extrapolations. The TbfT,trends
I4lh
AND
LIEBERMANN
LUBORSKY:
EMBRITTLEMENT
OF METALLIC
GLASSES
?‘;thlc 2. One hour annealing temperature above which . 15 pm thick glassy ribbons show a loss in ductility on hcntfing und ratio of one hour embrittlement tem~rature fq)r the h;~sc;tllny to that of the embritt~er-containing alloy T,/T,. Composition
F‘o8, 5B1dL Fcal.JB,*.ISi3.9Sbo., Fcsi.~Bil.,Si3.9Seo.1
Fe~i.AG%.9Teo.t Fer&.J& ~e~oNi~oB,9,9Sb~., Fel&iloBI&k~ Fe&Ji.&9.9Teo.t Ni~l.A4.& Nisl.IB,4.1Si).9SbO.l Nisl.,Bl~.sSi3.9Seo., Nis,.AG&Teo.~
1h Tmt.,(K) 600 510 CRT
TdTe 1.18
> 2.01 > 2.01 1.09 1.50 > 2.01
p
0.6 -
d
l "'61.6~14.6%.~t
0.2 -
1G 1.47 1.67
shown are not believed to be very much affected by the slight variations in transition metal: metalloid ratio or Si:B ratio in the three base alIoy compositions and show apparently increased embrittlement as Ni is replaced by Fe. Stress relaxation Stress relaxation of ribbon samples was conducted as described by Luborsky et al. [15]. The results are an indication of the extent to which atomic rearrangement occurs during a given annealing treatment. A stress relief fraction of 1.0 corresponds to complete relaxation of the ribbon. As an example, the data taken for the Nisl.sB1,&G, alloy series as a function of average ribbon thickness is shown in Fig. 4. The decrease in stress relief with increased ribbon thick-
3’w Itlf__// 3.50 -
1.00
Fig. 3. Relative embrittlement (T&/T.) as a function of base alloy composition and 0.1 at.% tmbrittlcr species.
Fig. 4. Stress relaxationdata for the NisI.sBI,.sSi+ giassy alIoy series is a function of aveqe ribbon thickness. Sampleswere annealed 2 h at 498K for relaxation.
ness is presumably the result of self-annealing of the ribbon during casting, as discussed earlier. By determining the stress relaxations for a given sample thickness on the data curves shown in Fig. 4, the dependence of ribbon stress relaxation on embrittler ~on~ntration for various ribbon thicknesses may be plotted, as shown in Fig. 5. Note that these plots are linear because only two data points arc available per ribbon composition and thickness. Table 3 lists the Table 3. Linearized dependence of stress relaxation on embrittler content as a function of embrittler spccics and average sample thickness. Base alloy
Embrittler
TC Sb Se TC Sb se Te Sb se Te Sb Se Te Sb Se Te Sb Se Te Sb se :; Se Te
S,pm
-d(oR)/dC
20 20 20
0.0 0.0 0.0
:
1.5
1.5
: 35 35 $ 20 30 30 :: 35 35 IO 10 10 20 :: 30 :
iI; 2.1 >5 0.8 0.8 3.4 3.1 1.9 >5 >5 3.5 .“>5 0.0 0.0 0.8 0.0 0.0 3.3 1.5 3.2 5.7
LIBBERMANN AM) LUBORSKY:
EMBRITTLEMENT
1.0
1
OF METALLIC GLASSES
-
%s4
0.04 AlMCF%fkXNTE~E~
0.00
Fig.5. Stressrelaxation
ments occur on annealing with the addition of the three embrittlers to the base alloys. For a given ribbon thickness, a large negative value of du/dC indicates a system for which the stress relaxation depends greatly on embrittler content.
Differential ~g’calorimetry (DSC) has been used to obtain start-of-crystallixation temperatures, T:, and crystallization peak temperatures, I’:, for sample compositions as &ted in Table ‘4.The results show a slight decrease ,in ‘crysta&ation temperature of the Fesr.sBr&~ alloy when replacing 0.1 at% Si with Te. The scatter in the Fe,,Ni&, base alloy data shows no systematic trend. The Nisr.sBr&~ metallic glass temperatures are given for comparison with those of the other two base alloys. As-cast ductile glassy alloy ribbons having nominal compositions Fe4eNi4,,Bse, FeMN&Br9.sSb0.s, and Fe40Ni19$e0.r with similar cross-sections (- 12p x 0.9 mm) all were measured to have a magnetic coercivity of - 1.3Am-’ (160mOe) in a longitudinal drive field of 800 Am" (IOOe). A subsequent 1.5 hour anneal of these samples at 623 K reduced the magnetic coercivity to - 0.6 Am- ’ (70 mOe). After Table 4. Crystallization start, T: and peak temperatures, T,P, as obtained by DSC at 40 K/min. 7% (K) T,c, (K) 7% (K) Z,(K)
ii 108 loo 703
0.12
799 793 121 134 132 720
this annealing treatment, only the Sb and Se-bearing samples showed embrittlement. tonger annealing times resulted in substantial embrittlement due to crystallization and a corresponding coercive field increase.
CONCLUDING
Thermal and magntftic’measuments
Fe~l.,Bt&& Fesl.sB14,~Si~.9Teo.l Fe,oNi4oBzo Fe,oNi40Bt9.9Sbo.l Fe,ONi4OB,9,9Seo., Ni 81.~B&ji4
0.06
as a function of glassy alloy embrittler content and average ribbon thickness for the Ni SI.sB,4,5Si, alloy series.
slopes of the lines geuerated in such a fashion and thereby gives the extent to which atomic rearrange-
Composition
1417
820 813 -
833 821 -
REMARKS
Enhanced temper embrittlement in Fe and/or Nibased metallic glasses by small additions of Sb, Se and Te has been found in the present investigation. The precise embrittlement mechanism remains to be defined. From the present work, it appears that the embrittling strength of the elements investigated scales as Te > Se $=Sb, which is the same sequence found in steels [l]. Furthermore, the embrittling strength of P is feeble by comparison. For all of these embrittling elements, loss of metallic glass ductility is accelerated with increased embrittler content, as is exemplified in Table 1 for the case of Sb in FetiN&Blo base metallic glass. Walter et al. [6] have proposed an embrittlement model based on fast diffusion of the smaller metalloid atoms to form highly localized clusters which embrittle the sample. While such a concept perhaps seems feasible for explaining the temper embrittlement of metallic glasses containing P and smaller metalloids, it seems unlikely that atoms as large as the embrittlers studied in the present investigation would be capable of extensive diffusion at the annealing temperatures and times used. Furthermore, it is remarkable that the embrittling strength of these elements is as strong as has been shown in view of the relatively low atomic mobility anticipated. Unlike the contention by Chen (163 that glassy alloy embrittlement comes about through incomplete filling of transition metal 3d electron shells, and the
1418
LIEBERMANN
AND
LUBORSKY:
EMBRITTLE‘MENT OF METALLIC GLASSES
Walter et ul. concept of long ,range metalloid diffusion, it seems that embrittlement by an individual species of atom in a metallic glass depends on a combination of aspects such as embrittler electronegativity and ionic size. The embrittler strength scales with neither electronegativity nor size alone. Figure 1 shows that similar embrittlement behaviors may be exhibited by Sb-bearing and Se and Te-bearing glassy alloys by simply increasing the content of the weaker embrittling element. Thus, embrittlement in metallic glasses most likely is based on the ability of embrittler atoms to localize electrons from the matrix. Embrittlement of metallic glasses occurs as the result of annealing, whether intentionally by heat treatment or unintentionally by fabricating ribbon samples which are very thick and/or departing prematurely from the substrate surface on which they are cast. Nevertheless, the ribbons used in the present investigation may be viewed as having undergone varied degrees of heat treatment during casting, depending on the particular process conditions and sample composition used. Evidence for this appears in
stress relaxation is the densification (reduction in free volume) found when metallic glasses are annealed. Thus, the contribution to stress relaxation due to embrittler atoms is rather small when the prominent contribution due to densification is subtracted out. The DSC and magnetic measurements show that although glassy alloy embrittlement may occur as a result of low temperature annealing, the crystallization characteristics and structure-sensitive magnetic coercivity are relatively unaffected by small additions of embrittling elements. Finally, since the samples
annealed to embrittlement show no detectable coercivity changes, the embrittler-induced atom localization is probably on a very fine scale. Acknowledgements-The authors are grateful to
N. A. Marotta for the DSC runs, S. J. Kelly for the magnetic measurements, and to C. L. Briant for helpful discussions and critical reading of the manuscript.
REFERENCES
1. C. J. McMahon, Grain Boundarks in Engineering Table 1, in which the c of only the Nisl.sBt,.sSi, Materials (Edited by J. L. Walter et al) p. 525, Claitor’s metallic glasses are independent of embrittler adPublishing (1975). ditions. Both the FesI.sB,,,sSi4 and the Fe40Ni40B2,, 2. C. L. Briant and S. K. Bane@, Int. Metal/. Rev. 23, 164 (1978). base glassy alloys show a variation in maximum as3. D. G. Ast and D. Krenitsky, Mater. Sci. Engng. 23,246 cast ductile ribbon thickness which depends on the (1976). embrittler and its concentration. Thus, the anneal to 4. F. E. Luborsky and J. L. Walter, J. appl. Phys. 47, 3648 which the ribbon is subjected during casting is suf(19763. ficient to cause some ductility loss in FetiN&,BZO 5. R. S. Williams and T. Egami, IEEE km. Msg. MAGl2,927 (1976). and Fesl.sB14.sSi4ribbons having thickness >$. The 6. J. L Walter, F. Bacon and F. E. Luborsky, Mater. Sci. ribbons selected for the 1 h annealing embrittlement Engng. 24,239 (1976). treatments have therefore intentionally been selected 7. J. L. Walter and F. E. Luborsky, Mater. Scf. Engng. 33, to have a maximum thickness of less than Q in order 91 (1978). 8. R. S. Williams and T. Egami, Rapidly Quenched Metals to have a fully ductile starting sample. However, the III Vol. I, p. 214, The Met& Society, London (1978). varying susceptibility of the various metallic glasses to 9. M. Guttmann and D. McLean, Intcrfcrcrrr~Segregation embrittlement during casting should be considered in (Edited by W. C. Johnson and J. M. Blakely) p. 261 the interpretation of the results. ASM (1979). The trends in the stress relaxation data mirror 10. G. C Chi, H. S. Chen and C. E. Miller, J. appl. Phys. 49.1715 (1978). those of the embrittlement data, although fractional 11. H. H. Liebcrmana, J. Mater. Sci. liZi (1980). change in stress relaxation is not as great as fractional change in bend ductility after a given anneal. This correspondence between stress relaxation and embrittlement data exists because the reduced stress relaxation observed during embrittlement indicates reduced atomic motion and presumably results from reducedatomicmobilitycaused by theembrittleratoms. A concurrent atomic mechanism resulting in redbced
12. F. E. Luborsky, H. H. Li&rmann and J. L. Walter. Pm. Con/. Merallic Gkuses, Budapest (1980). 13. H. H. Liebcrmann, Mater. Scl. Engng 43,203 (1980). 14. P. Kozakeviteh, Su&ee Pherwmenaof Metals, p. 223.
S.C.I. Monograph No. 28, Society of Chemical Industry, London (1968). 15. F. E. Luborsky, J. J. Becker and R. 0. MeCary, IEEE 7h1~. Mug. MAGll, 1644 (1975). 16. H. S. Chen, Mater. Sci. Engng. 26, 79 (1976).
OF SOME METALLIC BY Sb, Se, AND Te
GLASSES
H. H. LIEBERMANN and F. E. LUBORSKY General Electric Corporate Research and Development Schenectady, NY 12301 U.S.A. (Received
9 February
1981)
Abstract-Some metallic glasses have been found to embrittle after annealing at low temperatures, much as do some steels. In phosphorus-bearing alloys, phosphorus has been found to segregate during annealing and result in sample embrittlement. The present report describes the effects of the steelcmbrittling elements Sb, Se, and Te on metallic glasses in which the primary metallic constituents are Fe and/or Ni. Bend ductility and stress relaxation measurements of as-cast and annealed glassy alloy ribbons have been used to study embrittkment resulting from less than 0.2 at.‘):, Sb. Se, and Te addition to the base alloys XRD, DSC, and magnetic measurements have been used to further characterize the samples and to check for changes in magnetic properties which may accompany embrittlement. Results show that P is a very weak embrittler compared with Sb, Se, and Te. Furthermore, the embrittling power of these three ekmettts varies in the sequence Te > Se B Sb, the same sequence as found in steels. The effect of a given embrittler is enhanced when substituting Fe in place of Ni. No substantial changes in DSC or magnetic measurements have been found as a result of substituting the small amount of embrittler into the base alloys investigated. R&m&Nous.avons trouvC que certains verres metalliques ttaient fragilises par un recuit a basse tempCrature, comme certains aciers. Dans les alliagcs pour paliers au phosphore, le phosphore sCgrtge au tours du*recuit, de qui conduit a une fragilisation de l’tchantillon. Dans cet article, nous prtsentons les effets de l’addition de Sb, Se and Te, qui sont des elements fragilisant des aciers, sur des verres metalliques dont les constituents mttalliques principaux sont Fe et/au Ni. Des mesures de ductilite en flexion et de,relaxation de contrainte sur des rubans d’alliages vitreux bruts de coulee et recuits ont permis de mettre en Cvidmce une fragilisation provenant de l’addition de moins de 0.2 at”/, de Sb, Se et Te aux alliages de base. Des mesures de diffraction X, de DSC et magnttiques ont ensuite permis de caracteriser plus prtcistment Ies tchantillons et d’observer une tventuelle variation des proprittts magnCtiques ‘qui pourrait accompagncr la fragilisation. Nos resultats montrent que le P est beaucoup moms fragilisant que,Sb, Se et Te. De plus, Ie pouvoir fragilisant de ces trois elements varie selon la sequence Te > Se # Sb, c’est 4 dire la m8me que dans Ies aciers. On augmente l’egect dun element fragilisant en remplacartt du Ni par du Fe. Nous n’avons pas vu de changement notable du DSC ou des propri6ti.s magnttiques B la suite de la substitution dune faible quantite d’eltment fragilisant dans l’alliage de base. Zusammeufasamg-Einige metallische Glliser vcrspri%en wiihrend der Auslagerung bei niedrigen Temperaturen wie gewisse Stlihle. In phosphorhaltigen Legierungen wurde gefunden, dal3 Phosphor wiihrend der Auslagerung segregiert und dadurch die Versprtiung verursacht. Die vorliegende Arbeit beschreibt den EinfluB der Stahl-verspr6denden Elemente Sb, Se und Te auf metallische Cl&r mit den metallisthen Hauptkomponenten Fe und/oder Ni. Mit Messungen der Biegeduktilitgt und der Spannungsrelaxation an frisch hergestellten und ausgelagerten Biindern metallischer Gliser wurde die Verspradung untersucht, die von Sb-, Se- und Te-Zugaben in Mengen von weniger als 42 At.-“/:, verursacht wird. Mit XRD-, DSG und magnetischen Messungen wurden die Proben weiterhin untersucht, urn mogliche, mit der Verspradung einbergehende Anderungen der magnetischen Eigenschaften aufzufinden. Die Ergebnisse xeigen, daD P im Vergleich tu Sb, Se und Te sehr schwach verspradend wirkt. Die Wirksamkeit dieser Elemente gindert sich in der Folge Te > Se % Sb wie in den Stiihlen. Der EinfluB eines versprodenden Elementes wird verstiirkt, wenn Ni durch Fe ersetzt wird. Es wurden keine bedeutenden Anderungen bei DSG und magnetischen Messungen gefunden, die als Folge der Einfiihrung des kleinen Anteils versprtiender Elemente in die Basislegierung auftraten.
INTRODUCTION The embrittkment of some metallic glasses may occur without the onsct of crystallization during annealing at temperatures well below those required to cause crystallization. This embrittlement is analogous to that found in steels Cl, 23, except that it is irreversible. Phosphorus is a metalloid used in the formation of
some metallic glasses and the discovery of embrittlement in glassy alloys containing this element has prompted numerous investigations [3-81. It has been suggested that P enrichment occurs on a highly localized scale in these alloys during annealing, resulting in sample embrittlement because of sharply reduced ductility in the segregated regions and the extent to which the ductile-brittle transition temperature is
1413
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LI~BERMANN
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LUBORSKY:
~~~BRITTL~M~NT
suppressed varying directly with phosphorus content [7]. Elements such as Sb, Se and Te are much more potent embrittlers of steel than is P[9J. The current investigation deals with the nature of temper embrittlement in metallic glasses of nominal composition Fe a,.5B,,.5Si4, Fe&%&~. and Nial.&.& containing 0.2 at.% or less of the embrittling agents Sb, Se or Te. The alloy compositions have been selected to be phosphorus-free so that properties measured will not be the result of P segregation. Furthermore, the nominal compositions chosen permit a comp~ison of embrittlement as Ni and Fe are interchanged in the base alloy. Embrittlement of a metallic glass is not only dependent upon the addition of embrittling alloying elements but is also determined by processing conditions with which the sample is manufactured. For example, it has been found that glassy afloy embrittlement increases with decreased ribbon-substrate contact distance during chill block melt-spinning [lo]. A similar correlation has been established between glassy ribbon stress relaxation and ribbon-substrate contact distance [l 1J. Increased tendency for embrittlement has also been demonstrated with increased as-cast ribbon thickness [12]. Whether by reduced ribbonsubstrate contact distance or by excessive ribbon thickness, the increased embrittlement and reduced stress relaxation result from the ‘self-anneal’ of the ribbon when departing from the substrate surface without having undergone sufficient heat removal during melt-spinning. EXPERIMENTAL Master aIloys of the compositions investigated were premelted using high purity constituent alloying elements in an alumina crucible atmosphere and poured into a split copper mold under Ar atmosphere. The resultant ingots were then crushed and pieces chili block melt-spun in vacuum [t33. A 125 mm diameter copper substrate wheel was used at 2, 4, 6, and 12 krpm to result in a set of ribbons having average thicknesses of from 8 pm to 45 pm for each alloy composition investigated. Ribbon-substrate sticking distance was not found to vary with the alloy compositions studied for a given geometric crosssection and substrate velocity. Although the embrittling elements studied are also surface active and reduce liquid iron and nickel surface tension [14]. no significant change in ribbon geometry was noted when casting embrittler-bearing samples. This is presumably because of substantial melt puddle turbulence during casting and suggests a uniform distribution of the embrittler elements in the ribbons. Ribbons of various thicknesses for each composition were examined by transmission Laue X-ray diffraction (Charles-Supper precession camera with a GE XRD-4 power generator) to check for indications of crystallinity. These samples were also subjected to
OF METALLIC
GLASSES
bend ductility testing in which a ribbon sample is gradually bent (shiny side out) to a decreasing radius of curvature between the platens of a micrometer drive and the platen separation at sample fracture converted to a relative maximum strain to fracture [43 using micrometer (maximum) ribbon thickness for calculation. The degree to which atomic motion is possible was monitored through stress relaxation measurements on all of the ribbons formed. Stress relief data were obtained by annealing ribbon segments in 1 cm i.d toroidal cans for two hours at 498 K and me~uring the degree of spring-back exhibited by each sample on removal from the can [15]. Ductile, glassy ribbons of about 25 pm average thickness were sealed in evacuated glass tubes and subjected to 1 h anneals at 373,473, 573 and 673 K. The relative strain to fracture for these annealed ribbon samples was then remeasured and embrittlement assessed. Differential scanning calorimetry (DSC) using a Perkin Elmer DSC II at 4OK/min heating rate was used to compare crystallization temperatures of some ribbon samples with and without embrittler alloy additions. Magnetic coercivity measurements using an 8OOAm-’ (IOOe) drive fietd have also been used to examine the annealing response of Fe*eNi,eBzo base metallic glass containing small amounts of Sb and Se. RESULTS AND DISCUSSION
The embritfiement of alI ribbons in the as-cast state has been measured by the relative maximum strain to fracture of U-shaped samples [4], a typical data set of which is shown in Fig. 1 for the Fe,eNi4eBzo base alloys, The sharp increase in fracture strain with decreasing ribbon thickness has been drawn to comply with this kind of variation typically exhibited by glassy alloys [73. The dashed portion of the Fe40Ni4,,Bt9,9Tee.1 data curve is an extrapolation to a maximum relative strain of 1.0. Fracture strain data scatter is well-masked by the steepness of the curves drawn. From such plots, the maximum ductile sample thickness (f$ for each composition is obtained by reading the thickness at which the maximum relative strain to fracture drops below unity. Note that the r$ values obtained are particular to the melt-spinning apparatus and conditions (such as ribbon-roller contact distance) used and may vary when using other equipments. A summary of Q for all the glassy alloy compositions investigated is given in Table 1. From this data, it is seen that as-cast Feal,sB,&i4 ribbons show less embrittlement (can be made thicker yet ductile) than either Fe,N,i~OBle or Nie,.,B,&i, ribbons. This is pr~umably because of the greater thermal stability of the Fe-based metallic glass, as shown by the DSC data in Table 4. The right-hand column in Table I lists the ratio of maximum as-cast ductile ribbon thickness for a given base composition (G) to the equivalent thickness for an embrittler-containing
LIEBERMANN
AND
LUBORSKY:
EMBRITTLEMENT
Fig. 1. Relative maximum strain to fracture data for as-cast samples as a function of &ssy alloy ribbon micrometer (maximum) thickness for the Fe40NiiBz0 base alloy and samples containing small amounts ofthe embrittlers Sb, Se or Te.
alloy (c). This ratio eliminates the diierence in thermal stability of the three base alloy compositions and gives an indication of relative embrittlement, with 1.00 corresponding to. that of the embrittler-free base alloy. The sequence of elements in order of increased embrittling power in FeMNiiBzo glassy alloy data shown in Fig. 1 is Sb, Se, Te for 0.1 at.% ~b~~Ier addition. The resutts also show that increased quantt ties of Sb in Fe4eNi,+&s0 result in increased embrittlement. This increased embrittling strength with
Table I. Maximum as-cast glassy alloy ribbon micrometer thickness at which completely ductile bending is possible (4) and ratio of ductile base alloy to ductile embrittlercont~ning alloy ribbon thickness ~~/~). Composition
II: pm
Wt;
Fe~I.~Br4.& Fea~.,B,~.,gt~.~gh,.~ Fe~~.~B~~.~Si,.~Se~.~ Feel.sB14.~SiJ.9Teo.1 F%.oNL&0 ~~~~~i~~~,9.~~~ho.~~ ~~~~~i~~~~9.~~h~~~~ Fe4~NL&9.agho.2~ f+&&B19.~9ge~.~~
58 40 420
1.45 * 2.90 * 2.90 1.00 1.05 2.33 1.00
Fe,oNi40B19.&eo.t~
28 42 c25 40 40 :
Fe~oNi~~B,9.99Teo.o~ Fe40Ni40B19.9Teo.l~
Nk9k& Nis~.~Blr.sSi,.9Sbo.l Nk~Bl&iJ.&%.~ Nier.~B&%.9Teo.,
420
42 42 40 18 42
1.50 1.00 > 1.68 1.00 1.00 1.00
OF METALLIC GLASSES
1415
lh 11. I(
Fig. 2. Relative maximum strain to fracture data as a function of one hour isochronal annealing temperature for the Ni ~I.5B,I.SSi~ base alloy and sample containing 0.1 at.% of the embrittler Sb, Se, or Te.
concentration of embrittler would presumably also be the case for the other base alloys as well. In the
Ni81.sBt4.&?i4glassy alloy system, there seems to be no embrittling effect due to Sb, Se or Te at the 0.1 at.% concentration in any of the as-cast ribbons. Relative maximum strain to fracture of ribbons as a function of 1 h isochronal ~n~~rng temperature is exemplified by the data for the NiaI.,B,,,Si4 base metallic glass shown in Fig. 2. The 1 h embrittlement temperature is defined as that at which the relative maximum strain to fracture drops below unity and the sample begins to show loss of bend ductility. Fracture strain data scatter is more obvious in the less steep portions of the curves drawn. As in Fig. 1, the shape of the data curves has been drawn to comply with that typically found for glassy alloys [7]. Note that for the -25 pm thick ribbon samples annealed and tested, an embrittlement of the NiB1.5B,4.5Sil base composition samples is only found for samples containing 0.1 at.% Se or Te. It is interesting that a 0.1 at.% Sb addition causes no detectable embrittlement beyond that of Nisl,sB14.&. The embrittling Rower of the three agents used follows the same sequence in each of the three base alloys: Te > Se >>Sb. A summary of 1 h embritttement temperatures and the ratio of one hour embrittlement temperature for the base alloy to that of the embrittlercontaining alloy (T’,/T,) for the three base compositions appears in Table 2. An illustration of the embrittlement data in Table 2 is shown in Fig. 3 for the three base alloy compositions. The dashed curves are extrapolations. The TbfT,trends
I4lh
AND
LIEBERMANN
LUBORSKY:
EMBRITTLEMENT
OF METALLIC
GLASSES
?‘;thlc 2. One hour annealing temperature above which . 15 pm thick glassy ribbons show a loss in ductility on hcntfing und ratio of one hour embrittlement tem~rature fq)r the h;~sc;tllny to that of the embritt~er-containing alloy T,/T,. Composition
F‘o8, 5B1dL Fcal.JB,*.ISi3.9Sbo., Fcsi.~Bil.,Si3.9Seo.1
Fe~i.AG%.9Teo.t Fer&.J& ~e~oNi~oB,9,9Sb~., Fel&iloBI&k~ Fe&Ji.&9.9Teo.t Ni~l.A4.& Nisl.IB,4.1Si).9SbO.l Nisl.,Bl~.sSi3.9Seo., Nis,.AG&Teo.~
1h Tmt.,(K) 600 510 CRT
TdTe 1.18
> 2.01 > 2.01 1.09 1.50 > 2.01
p
0.6 -
d
l "'61.6~14.6%.~t
0.2 -
1G 1.47 1.67
shown are not believed to be very much affected by the slight variations in transition metal: metalloid ratio or Si:B ratio in the three base alIoy compositions and show apparently increased embrittlement as Ni is replaced by Fe. Stress relaxation Stress relaxation of ribbon samples was conducted as described by Luborsky et al. [15]. The results are an indication of the extent to which atomic rearrangement occurs during a given annealing treatment. A stress relief fraction of 1.0 corresponds to complete relaxation of the ribbon. As an example, the data taken for the Nisl.sB1,&G, alloy series as a function of average ribbon thickness is shown in Fig. 4. The decrease in stress relief with increased ribbon thick-
3’w Itlf__// 3.50 -
1.00
Fig. 3. Relative embrittlement (T&/T.) as a function of base alloy composition and 0.1 at.% tmbrittlcr species.
Fig. 4. Stress relaxationdata for the NisI.sBI,.sSi+ giassy alIoy series is a function of aveqe ribbon thickness. Sampleswere annealed 2 h at 498K for relaxation.
ness is presumably the result of self-annealing of the ribbon during casting, as discussed earlier. By determining the stress relaxations for a given sample thickness on the data curves shown in Fig. 4, the dependence of ribbon stress relaxation on embrittler ~on~ntration for various ribbon thicknesses may be plotted, as shown in Fig. 5. Note that these plots are linear because only two data points arc available per ribbon composition and thickness. Table 3 lists the Table 3. Linearized dependence of stress relaxation on embrittler content as a function of embrittler spccics and average sample thickness. Base alloy
Embrittler
TC Sb Se TC Sb se Te Sb se Te Sb Se Te Sb Se Te Sb Se Te Sb se :; Se Te
S,pm
-d(oR)/dC
20 20 20
0.0 0.0 0.0
:
1.5
1.5
: 35 35 $ 20 30 30 :: 35 35 IO 10 10 20 :: 30 :
iI; 2.1 >5 0.8 0.8 3.4 3.1 1.9 >5 >5 3.5 .“>5 0.0 0.0 0.8 0.0 0.0 3.3 1.5 3.2 5.7
LIBBERMANN AM) LUBORSKY:
EMBRITTLEMENT
1.0
1
OF METALLIC GLASSES
-
%s4
0.04 AlMCF%fkXNTE~E~
0.00
Fig.5. Stressrelaxation
ments occur on annealing with the addition of the three embrittlers to the base alloys. For a given ribbon thickness, a large negative value of du/dC indicates a system for which the stress relaxation depends greatly on embrittler content.
Differential ~g’calorimetry (DSC) has been used to obtain start-of-crystallixation temperatures, T:, and crystallization peak temperatures, I’:, for sample compositions as &ted in Table ‘4.The results show a slight decrease ,in ‘crysta&ation temperature of the Fesr.sBr&~ alloy when replacing 0.1 at% Si with Te. The scatter in the Fe,,Ni&, base alloy data shows no systematic trend. The Nisr.sBr&~ metallic glass temperatures are given for comparison with those of the other two base alloys. As-cast ductile glassy alloy ribbons having nominal compositions Fe4eNi4,,Bse, FeMN&Br9.sSb0.s, and Fe40Ni19$e0.r with similar cross-sections (- 12p x 0.9 mm) all were measured to have a magnetic coercivity of - 1.3Am-’ (160mOe) in a longitudinal drive field of 800 Am" (IOOe). A subsequent 1.5 hour anneal of these samples at 623 K reduced the magnetic coercivity to - 0.6 Am- ’ (70 mOe). After Table 4. Crystallization start, T: and peak temperatures, T,P, as obtained by DSC at 40 K/min. 7% (K) T,c, (K) 7% (K) Z,(K)
ii 108 loo 703
0.12
799 793 121 134 132 720
this annealing treatment, only the Sb and Se-bearing samples showed embrittlement. tonger annealing times resulted in substantial embrittlement due to crystallization and a corresponding coercive field increase.
CONCLUDING
Thermal and magntftic’measuments
Fe~l.,Bt&& Fesl.sB14,~Si~.9Teo.l Fe,oNi4oBzo Fe,oNi40Bt9.9Sbo.l Fe,ONi4OB,9,9Seo., Ni 81.~B&ji4
0.06
as a function of glassy alloy embrittler content and average ribbon thickness for the Ni SI.sB,4,5Si, alloy series.
slopes of the lines geuerated in such a fashion and thereby gives the extent to which atomic rearrange-
Composition
1417
820 813 -
833 821 -
REMARKS
Enhanced temper embrittlement in Fe and/or Nibased metallic glasses by small additions of Sb, Se and Te has been found in the present investigation. The precise embrittlement mechanism remains to be defined. From the present work, it appears that the embrittling strength of the elements investigated scales as Te > Se $=Sb, which is the same sequence found in steels [l]. Furthermore, the embrittling strength of P is feeble by comparison. For all of these embrittling elements, loss of metallic glass ductility is accelerated with increased embrittler content, as is exemplified in Table 1 for the case of Sb in FetiN&Blo base metallic glass. Walter et al. [6] have proposed an embrittlement model based on fast diffusion of the smaller metalloid atoms to form highly localized clusters which embrittle the sample. While such a concept perhaps seems feasible for explaining the temper embrittlement of metallic glasses containing P and smaller metalloids, it seems unlikely that atoms as large as the embrittlers studied in the present investigation would be capable of extensive diffusion at the annealing temperatures and times used. Furthermore, it is remarkable that the embrittling strength of these elements is as strong as has been shown in view of the relatively low atomic mobility anticipated. Unlike the contention by Chen (163 that glassy alloy embrittlement comes about through incomplete filling of transition metal 3d electron shells, and the
1418
LIEBERMANN
AND
LUBORSKY:
EMBRITTLE‘MENT OF METALLIC GLASSES
Walter et ul. concept of long ,range metalloid diffusion, it seems that embrittlement by an individual species of atom in a metallic glass depends on a combination of aspects such as embrittler electronegativity and ionic size. The embrittler strength scales with neither electronegativity nor size alone. Figure 1 shows that similar embrittlement behaviors may be exhibited by Sb-bearing and Se and Te-bearing glassy alloys by simply increasing the content of the weaker embrittling element. Thus, embrittlement in metallic glasses most likely is based on the ability of embrittler atoms to localize electrons from the matrix. Embrittlement of metallic glasses occurs as the result of annealing, whether intentionally by heat treatment or unintentionally by fabricating ribbon samples which are very thick and/or departing prematurely from the substrate surface on which they are cast. Nevertheless, the ribbons used in the present investigation may be viewed as having undergone varied degrees of heat treatment during casting, depending on the particular process conditions and sample composition used. Evidence for this appears in
stress relaxation is the densification (reduction in free volume) found when metallic glasses are annealed. Thus, the contribution to stress relaxation due to embrittler atoms is rather small when the prominent contribution due to densification is subtracted out. The DSC and magnetic measurements show that although glassy alloy embrittlement may occur as a result of low temperature annealing, the crystallization characteristics and structure-sensitive magnetic coercivity are relatively unaffected by small additions of embrittling elements. Finally, since the samples
annealed to embrittlement show no detectable coercivity changes, the embrittler-induced atom localization is probably on a very fine scale. Acknowledgements-The authors are grateful to
N. A. Marotta for the DSC runs, S. J. Kelly for the magnetic measurements, and to C. L. Briant for helpful discussions and critical reading of the manuscript.
REFERENCES
1. C. J. McMahon, Grain Boundarks in Engineering Table 1, in which the c of only the Nisl.sBt,.sSi, Materials (Edited by J. L. Walter et al) p. 525, Claitor’s metallic glasses are independent of embrittler adPublishing (1975). ditions. Both the FesI.sB,,,sSi4 and the Fe40Ni40B2,, 2. C. L. Briant and S. K. Bane@, Int. Metal/. Rev. 23, 164 (1978). base glassy alloys show a variation in maximum as3. D. G. Ast and D. Krenitsky, Mater. Sci. Engng. 23,246 cast ductile ribbon thickness which depends on the (1976). embrittler and its concentration. Thus, the anneal to 4. F. E. Luborsky and J. L. Walter, J. appl. Phys. 47, 3648 which the ribbon is subjected during casting is suf(19763. ficient to cause some ductility loss in FetiN&,BZO 5. R. S. Williams and T. Egami, IEEE km. Msg. MAGl2,927 (1976). and Fesl.sB14.sSi4ribbons having thickness >$. The 6. J. L Walter, F. Bacon and F. E. Luborsky, Mater. Sci. ribbons selected for the 1 h annealing embrittlement Engng. 24,239 (1976). treatments have therefore intentionally been selected 7. J. L. Walter and F. E. Luborsky, Mater. Scf. Engng. 33, to have a maximum thickness of less than Q in order 91 (1978). 8. R. S. Williams and T. Egami, Rapidly Quenched Metals to have a fully ductile starting sample. However, the III Vol. I, p. 214, The Met& Society, London (1978). varying susceptibility of the various metallic glasses to 9. M. Guttmann and D. McLean, Intcrfcrcrrr~Segregation embrittlement during casting should be considered in (Edited by W. C. Johnson and J. M. Blakely) p. 261 the interpretation of the results. ASM (1979). The trends in the stress relaxation data mirror 10. G. C Chi, H. S. Chen and C. E. Miller, J. appl. Phys. 49.1715 (1978). those of the embrittlement data, although fractional 11. H. H. Liebcrmana, J. Mater. Sci. liZi (1980). change in stress relaxation is not as great as fractional change in bend ductility after a given anneal. This correspondence between stress relaxation and embrittlement data exists because the reduced stress relaxation observed during embrittlement indicates reduced atomic motion and presumably results from reducedatomicmobilitycaused by theembrittleratoms. A concurrent atomic mechanism resulting in redbced
12. F. E. Luborsky, H. H. Li&rmann and J. L. Walter. Pm. Con/. Merallic Gkuses, Budapest (1980). 13. H. H. Liebcrmann, Mater. Scl. Engng 43,203 (1980). 14. P. Kozakeviteh, Su&ee Pherwmenaof Metals, p. 223.
S.C.I. Monograph No. 28, Society of Chemical Industry, London (1968). 15. F. E. Luborsky, J. J. Becker and R. 0. MeCary, IEEE 7h1~. Mug. MAGll, 1644 (1975). 16. H. S. Chen, Mater. Sci. Engng. 26, 79 (1976).