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ENCYCLOPEDIA
OF

MATERIALS SCIENCE
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ENGINEERING

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MichaelB. Bever
Massachusetts Institute of Technology

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Sisal
Becauseof higher production costs,tighter loan policy and curtaileddemandbecause competition of from synthetics,land producing henequen- the in Yucatan peninsulaof Mexico has been shifted to other crops. Virtually all of Mexico's henequenis consumedby a cordageindustry which producesagricultural twines and rugs. See also:NaturalFibersin the World Economvi Materials of Biological Origin: Overvieu' An Bibliography Commonwealth Economic Committee 1954 Industrial Flbres. HMSO. London DeweyL H 1943FiberProduction the Western in Hemisphere. Miscellaneous Publication 518.US DepartNo. mentof Agriculture. Washington, DC Lock G W 1962 Slsa/. Wiley, New York Ochse J, Soule DijkmanM J. Wehlburg 196L J J. C Tropical and Subtropical Agriculture. Macmillan, New York P. Ross The magnitude/ measured this manneris averaqed in over all electronsparticipatingin the conductiriir. More information on electronsin metals can be obtained from size effects in a maqnetic field as the magnetic field changes shapean? sizes electron the of trajectories. The best known of these effects is the Sondheimer effect-oscillations of the magneroresistance a plate in a magneticfield. Electrons of which pursuehelicalpathsabout the directionof the magnetic field contribute differently to the current. dependingon whether they compl6tea w,holeor a fractional number of revolutionson the path from one side of the plate to the other. This sives ri:c to oscillations when the magneticfield varies.The periodsobservedin the expe-riment due to those are trajectories alongwhich the majority of electrons are travelling. 2. Radio-Frequency Size Effects Radio-frequency effects(RFSEs)form a specific size group. When an extremal dimensionof an el-ectron orbit becomesequal to the metal plate thickness. anomaliesof the surface impedanceof the plate occur. They are rather small. but observable.For example,the diameter D of the orbit shorvnin Fie. 1 decreases proportionallv to an increasein the lleicl H. An RFSE takes place at that 11value at rvhich l) becomes equal to d.
dX dH

SizeEffectsin Electrical Conductors
In highlv perfectmetal singlecrystals, mean free the path of electronsat liquid helium temperatures may be as great as severalmillimeters.This enables electron beamsto be formed and transmittedinsidethe metal as occursunder vacuumin numerouselectron devices.However, the dispersion law-the relation between the momentum of an electron and its energy-differs for an electron in a metal and in a vacuum, so methods are needed to study electron orbits insidethe metal and to measureth6ir dimensions. For this purpose the effects determined by the relations between the dimensionsof electron trajectories and thoseof the sample(sizeeffects)are most suitable. l. Direct-Current Size Effects The simplest of size effects is the dc size effect. It is manifested a decrease electricalconductivitvo as in of thin plates and wires compared with that oi a massive metal o0. This decrease due to additional is electronscattering the surfaceof the specimen. by If this scatteringis diffusive,that is, if the electronrs reflected at random from the surface, completely losing its drift velocitv, the conductivityof a plate with thickness is described the exoressions d bv

D

-1lh^*ru
;
H(kA m

it il

t

I

I

:
)

Figure I Observation RFSEs: different of (a) possible relarions between platethicknessandorbitdiameter (b) the d Dl a sample the coil;(c) an example RFSErecords in of

olor: 1 - : ,
jd

JI

(l I

6A

:; oior:t

tn +J ; /a

(t > d)

(1)

Theseexpressions permit the mean free path / to be determinedby measuring dependence o on d. the of ,1458

To observeRFSEs, a metallicplate is exposed to an electromagnetic field in the radio-frequency range l-100 MHz. For this purposeit is commonto plaie the plate inside a tuned circuit inductancecoil. ln this caseeither the Q-factor or the self-inductance of the coil, that is, the real or the imaginarypart of the plate impedance, can be measured. With the aim of increasingthe sensitivity.the derivativesof these quantities often measured. are Electronicequipment


SizeEffects in Electrical Conductors
for these experimentsis usually completely identical io that usedfor nuclear magnetic resonancestudies. Impedanceanomaliesappearin the form of narrow linesiesemblingresonanielines.That is why RFSE lines are sometimes called spatial resonances.The fractionaf width of these lines is given by -LHIH 6/D (where6 is the skin depth,which is 10-r-10-ucm for the frequencies mentioned). This restricts the the plate thicknessd. Fairly possibility of decreasing nu.to* liiresmay be prdducedwhen usingplateswith d > 0.7 mm. Sincethe mean free path / shouldbe at least of the order of d, this dictatesrequirementsfor the metal purity (a total impurity content of no more 'do) and crystal quality (an averagedisthan l0 cm 21.In locationdensityno ft.atef thai 105-100 sDite of such stringent requirements,RFSEs have been observedin alkali and noble metals (K, Cu, metals(Mg.Zn. polyvalent Ag, Au), non-transition (Bi. Cd'.Hg. Al. In. Ga. Sn. Pb) and semimetals Sb) as in sometransitionmetals(W, Mo, Re)' At aswell present,the fact of observingRFSEs alone certifies h high purity level for a given element. 3. Radio-Frequency Size Effects in Multiple Fields A large mean free path drastically alters the electrodynamic properties of the metal. Under ordinary conditions, an electromagneticfield does not penetrate the bulk but becomeslocalized in a thin skin of layer. In the presence an externalmagneticfield, a metal with a large electron mean free path may cease to be a screen for electromagneticradiation and become transparent to radio waves' RFSEs are intimately connected with one kind of field penetration into the metal, called ballisticpenetration. The ac field is transmitted inside the metal by separate groups of electrons bunched together by the external field. Ballistic penetrationresultsin a multilayered structure of the ac field: images of the surfacecurrent layer arisein the bulk. Thesecurrent sheetsare locatedperiodically,deep into the metal. The distancesbetween the sheetsare determined by of the dimensions the orbits. RFSEs offer the main experimentaltechnique for the observation of ballistic penetration' Consider a plate excited on one face by an incident radiofrequencyradiation with a magneticfield H parallel and circularelectronorbitsof diameter to the surface D. Travelling along those orbits which passthrough the skin layer but do not intersectthe surface,electrons increasetheir velocity by a small amount Au. Each of these electrons thus becomes a carrier of part of the skin current Li : eLu. At the deepest boint -ellingof its circular orbit, the electron, again travparallel to the surface,reproducesthe velocity change-Au and the current -Al. This givesrise to the current sheet at the dePth z : D. The thicknessof this current sheet is of the same order as that of the initial skin layer Az: 6. This current sheet plays the role of the starting skin layer for the next skin image to occur at the depth z = 2D, along and so on. As a resulta chainof orbits appears, which the electromagneticfield finds its way into the bulk. The distancebetween the sheetsin a certain magnetic field is defined by the shape and dimensions of the metal Fermi surface. It is always inversely proportional to 11. By changing the field, the scale of the entire ac current distribution can easily be altered. The width of the current layers, however, remainsof the order of 6, so that in very large always fields the layers merge the As the field 11varies. relationd : nD becomes for valid in succession n : 7, 2, 3, . . .. This implies that the correspondingcurrent sheethas reachedthe far side of the plate. When this occurs, the surface impedance of the plate alters and it is this that is registeredas RFSE lines. The lines appear periodically in the magnetic field scale : (2) Hn: nH1: nPpfed (.n 1,2,3,. . .) where pp is the diameterof the Fermi surface. RFSEs may be related to orbits of different shape. In particular, infinite periodic trajectorieswith some portions in which the electron travels parallel to the surface come into play when the magnetic field is inclinedto the metal surface.An exampleof sucha in trajectoryis presented Fig. 2. The meaningof the magnitudeu is clear from the diagram.It servesin the sameway as the diameterD in Fig. 1. Now it is the condition d: nu that leads to a sequenceof RFSE lines periodic in the 11 scale.

H (kari ) Figure2 RFSEs the inclinedfield arransement in The distancetravelled by an electron in passing from one side of the plate to the other is equal to may be much dsin E. When q is small, the distance it greaterthan d. Experimentally hasprovedpossible io observeRFSE lines in a tin sample0.4 mm thick with an angle g : 1'30' when the length of the

4459


SizeEffects in Electrical Conductors
electronpath betweenthe facesof the plate exceeds 1) mm. 4. Applications The shape of electron orbits is determined by the Fermi surface of the metal (see Fermi Surfaces).In k-space, an electron travels along the line of intersection of the Fermi surface with a plane perpendicular to the field 11. The resultant curve in k-space similarto the projectionof the orbit in the is crystal on the plane perpendicular to 11. Therefore the information derived from RFSEs on electron orbit dimensions allows those of the Fermi surface to be determined. Thus RFSEsvield imoortantinformation about the Fermi-surfac'e geom6try. The srrengthA of the RFSE signal (the height of lines above the background)is proportionalto the number of electronswhich survive without collisions for the distancefrom one side of the olate to the other: A x exp(- udll). Here the factor a takesinto accountthe orbit shape.Thus measurements line of amplitudedependences differentfactors,suchas on temperature.impuritv or dislocationdensity,mpke it possibleto obtain information on the interaction of electronswith different scatterers.Moreover. since each RFSE, line is related to a cerrain orbit, bv comparing thesedependences differentlines,dati for can be obtainedon the anisotropy scattering of probability at the Fermi surface. In this lies another important applicationof RFSEs. See al.ro: Electrical Conductivity Metalsand Alloys of Bibliography" Gantmakher F 1967Radiofrequencv effects V size in rnetals. Prngr.Low Temp.Phys.'5:l8j-234 WalshW M Jr 1968 Resonances temporal spatial. both and solidstatePhvs' 1:127-252 v. F. Gantmakher L lron Blast-Furnace Slag Iron blast-furnace slag is produced in larger quantities and is usedto a greaterdegreethan any other type. Produced simultaneouslywith molten iion in a blast furnace, it consistsprimarilv of silica and alumina from the iron ore combinedwith calciumand magnesium oxidesfrom the flux stone.It leavesthe furnacesas a liquid at about 1500"C. Three different types of product can be produced by varying the cooling method. Air-cooled blast-furnace slagis producedby allowing the- molten glag to solidify under prevailing atmosphericconditions. It is predominantlv crvstalline with a cellularor vesicular structureresultine from bubbles of gases that were dissolved in thE molten material. After crushing and screeninsto desiredsizesthe slag is used in- the same rnuin.. as gravels and crushed stones in a great varietv of applications.Principal usesare in the construciion as -iement Sggregate.category road basesand fills, aggregate in bituminous mixtures and Portland concrete, railroadballast,roofingaggregate sewand age-plant filter media.Other applications includeuse as a raw material for manufactureof mineral wool. Portland cement and glassand as a soil conditioner to counteract acidity and furnish trace elementsfor plant growth. Granulated blast-furnace slag is produced b_v quickly quenchingthe molten slag so-asto form a glassy material with very little mineral crystallization. The most common process quenching is with water, but air or a combinationof air and water may be used.The slagglasscontainsthe samemajor oiides as Portland cement. but with different proportions of limeandsilica. hasexcellent properries It hydraulic and setsin a mannersimilarto Porilandcemeniwhen combinedwith a suitableactivator such as calcium hydroxide.The principal use for granulatedslagsis as a cementltrous material. Finely ground slagsare used in a variety of cements.most commonly combined with Portland cement. Such cements have improved resistance to seawater and sulfate exposure.Other applications include soil and basecoursestabilization,glassmanufacture" asricultural liming material and production of Portlaid cement clinker. Expandedor foamed slagis producedby treating the molten blast-furnace slas with limited quantities of water, lessthan that requiied for granulaiion. The resulting product is more cellular or vesicularin naturethan the air-cooled slagand is much lighterin weight. Variations in the amount of water and the particularprocess usedcontrol the coolingrate, and can produce materialsrangingfrom highly crystalline vesicular slags glassy to materials similarto the granuIated slags.Various pit and machinemethodshave been developed to combine the molten slag and water, including a pelletizing processthat makes

Slag Utilization
Extraction of a metal from an ore bv heat oroduces both a molten metal and a slag. The lattei is composedof the nonmetallicmineial material from the ores. fluxesand fuels used. Slagsare also formed in refiningand alloyingoperations the basicmetals. on When producedin largequantities, slagmay present a major disposalprobtem unless it ian 6itirer Ue utilizedas a raw materialfor other industries. find or direct use in construction and agricultural applicaticlns. Such usesdate back some2000yearsto ihe Roman use of broken slag. from the iron-making Catalanforges. in road construction.Utilization oT slag conserves natural resourcesof raw materials, avoidsenvironmentalproblemsin disposalof large quantities wastematerials of and is of gieat economic ralue bv eliminating disposal costs. 4460