O^Wv'-vvvvt^x)JLfo.INTRODUCTION TO METALLOGRAPHYLISTofBOOKSonMETALLURGY,MINERALOGY,and MINING.TheAnalysisof Steel=works Materials.ByHARRYBREARLEY and FREDIBHOTSON,B.Sc.(LoND.).With85Illustrations.8vo, 14^.net.Metals: theirPropertiesandTreatment.ByA. K.HUNTINGDON and W. G. M'MiLLAN. With 122 Illustra-tions. Crown8vo, 7.5-.6d.ElementaryPracticalMetallurgy: Iron andSteel.ByPERCY LONGMUIR. With64Illustrations. Crown8vo,5-r.net.LaboratoryNoteson PracticalMetallurgy:beingaGraduated Series of Exercises.ByWALTERMACFARLANE,F.I.C. Crown8vo,2s.6d.ThePrinciplesand Practice of Iron and SteelManufacture.ByWALTERMACFARLANE,F.I.C.Crown8vo, 3.?.6J. net.Metallurgy.AnElementaryText-book.ByE. L.RHEAD.With94Illustrations.Fcp.8vo, 3.5-. 6d.AssayingandMetallurgical Analysisfor the useofStudents, Chemists,andAssayers. ByE. L.RHEAD and A. HUMBOLDTSEXTON,F.IC.,F.C.S.8vo,io.r. 6d. net.TheCrystallisationof Iron andSteel: anIntroduc=tion to theStudyofMetallography. By J.W.MELLOR,D.Sc. With65Illustrations. Crown8vo, 5^.net.SystematicMineralogy. ByHILARYBAUERMAN,F.G.S.WTith373Illustrations. Crown8vo,6s.DescriptiveMineralogy. ByHILARYBAUERMAN,F.G.S.With236Illustrations. Crown8vo,6s.Mining.AnElementaryTreatiseontheGettingofMinerals.ByARNOLDLUPTON, M.P.,M.I.C.E.,F.G.S. Witha Geo-logical Mapof the British Isles and596 DiagramsandIllustrations. Crown8vo, ys.net.A PracticalTreatiseonMineSurveying. ByARNOLDLUPTON, M.P.,M.I.C.E.,F.G.S. With 216Diagrams.Medium8vo,I2s. net.Electric Furnaces: the Production of Heat fromElectricalEnergyand the Construction of EIec=trie Furnaces,byWILHELMBORCHERS,Professor ofMetallurgyat theRoyalTechnicalCollege,Aachen. Trans-latedbyHENRYG.SOLOMON,A.M.I.E.E. 8vo.LONGMANS,GREENANDCO.,LONDON,NEWYORK, BOMBAY,AND CALCUTTA.INTRODUCTIONTOMETALLOGRAPHYBYPAULGOERENS,DR.-!NG.[DOCENTIN PHYSICAL METALLURGY AT THE ROYAL TECHNICALHIGHSCHOOL, AACHEN)TRANSLATED BYFREDIBBOTSON,B.Sc,(LoND.),A.R.C.Sc.I(LECTURERINMETALLURGY,THEUNIVERSITY,SHEFFIELD)LONGMANS, GREEN,AND CO.39PATERNOSTERROW,LONDONNEWYORK, BOMBAY,ANDCALCUTTA1908T/V4 tAUTHOR'S PREFACEALTHOUGHMetallographyis avery youngscience,itsstudyisbynomeansaneasytask,partlyduetothe fact that inGermanythe numerouspaperson thesubjecthave notyet undergonesystematiccollection.Moreover,thenomenclatureof the micro-constituents,particularlythat of the iron-carbonsystem,is notuniversallythesame,andconflicting opinionsstillexist,so thatthebeginneriseasilyliabletobemisled.This little workproposesto introduce the learner to thesomewhat unfamiliarphenomenaofPhysical Chemistry,so farastheyneedconsideration formetallographical purposes,andtomakeitpossiblefor him to obtainaglimpseof the methods ofinvestigatingmetalsandalloys.The author is well aware that his work cannot claim to becomplete,and solicits kind consideration at the hands of hisconfreresinpronouncingjudgmenton it.The author is indebted to his esteemed teacher andchief,Prof.Wust,forincitinghimto thecompilationof thework,andhehereby expresseshis heartiest thanks for the advice andassistancerenderedtohim.P. GOERENS.AACHEN,June, 1906.30527OTRANSLATOR'S PREFACETHEpleasurederived from aperusalof Herr Goerens'"Einfuhrungin dieMetallographie"is theprimarycause oftheappearanceofthisEnglisheditionofthework.Thesection on Iron and itsAlloysdiffers from theoriginalGerman in that it has beenpracticallyrewritten and thusbrought upto datebytheauthor,to whom the translatortakesthisopportunityofexpressinghiswarmestthanks.Thqtranslator's task wasverymuchlightened bytheassistance and advicegenerouslytenderedbyhis friend andcolleagueMr.J.H.Wreaks,Demonstrator ofMetallographyat theUniversityofSheffield,without whoseco-operationtheappearanceof this edition would have beenvery considerablydelayed.THEUNIVERSITY, SHEFFIELD,February, 1908.SUMMARY OF CONTENTSTHE PHYSICAL PROPERTIES OF MATTERPAGEALLOTROPYiProofoftheexistenceofAllotropicFormsbyThermalMethods .3COOLING CURVES 4Meaningandexperimentaldetermination of them4MeasurementofTemperature6Graphicrepresentation 13THE PHYSICAL MIXTUREAQUEOUSSOLUTIONS29FreezingPhenomena ....29Graphicrepresentation 30DiscussionofFreezing-pointCurves31FUSED SALTS36AnalogybetweenFusedSaltsandAqueousSolutions.....36TheSolid Solution36ALLOYS45AnalogybetweenAqueousSolutionsandMoltenMetals ....46Applicationofthe PhaseRule '.47Freezing-point DiagramsofBinaryandTernaryAlloys....54PRACTICAL MICROSCOPY OF METALSPREPARATION OF THE SECTION 121GrindingandPolishing(MartensandLeChatelier)122DEVELOPMENTOF THE STRUCTURE131DescriptionofvariousMethodsofEtching 134PreparationofEtchingMedia . .134CONTENTSTHEMICROSCOPEDescriptionof and Directionsforusingthe Martensand LeChatelier MicroscopesPAGE138PHOTOGRAPHY. .SPECIALMETALLOGRAPHYOF IRON-CARBONALLOYSTHE FREEZING-POINTDIAGRAMOF IRON CARBON ALLOYS. . 166THE CONSTITUENTSOF IRON-CARBONALLOYS. .180INDEXOF AUTHORS.INDEXTOSUBJECTS2I2THE PHYSICAL PROPERTIESOF MATTERAllotropy.The heat administered to abodyisexpendedintheperformanceofexternalwork,the elevation oftemperature,and the increase of thepotential energyof thebody.Theamountofheatavailable fordoingexternalwork,in the casesof solid andliquid substances,is so small incomparisonwiththeothertwo,that itmaybeneglected.The rise intempera-ture of abodyis an indication that its heat-contents haveincreased. If t denote thetemperatureindegreesCentigradebeforeheating,and -T thetemperatureafterheating,P theweightofthebodyingrams,c itsspecificheat,thentheamountofheattakenupisW=P.c(T-t)heatunits . . , .(i)Thetotal internalenergyof abodyconsists of twoparts ;the heat-contentsexpressedbyformula(i)and thatwhichmaybecalled here"latentenergy."The latter does not lend itselfto directmeasurement, althoughinmanycases itappearsasheat: inconsequenceit isspokenof as latent heat. If onegramofsteam is cooledfrom about 150C. underapressureofoneatmosphere,itbeginsto condenseat 100 C.anddisengageits latent heatofvaporization.Whenthishastakenplace,and600 units of heat have been evolved into thesurroundingmedium,thesteam at 100 C. haschangedinto water at 100 C.Tochangethewaterintosteamagain,600unitsofheatmustbesupplied ;duringthe whole of this time thetemperatureremains constant at 1 00C.,althoughheat isbeingadded.Assoon asthecondensationofthesteam isended,thetempera-ture sinksregularlytoo C. Another sudden decrease of theinternalenergytakesplaceatthispointwhilstthewaterchangesto ice. In the converseoccurrence,thechangeof ice intowater,80units ofheatmustbesuppliedto onekilogramoficeato C. in ordertoconvert it intowaterato C.B2 THE*!>HY&ldA "PROPERTIES OFMA TTERThepointso and 100 aregenerally designatedtransitionpoints.In theexamplechosen ofice, water,andsteam,achangein the state ofaggregationoccurred at thesepoints.Suchchangesweare able toperceiveat oncewith our senses.Accordingto thekinetictheory,thedifferent states ofaggrega-tion aredistinguishedfrom one anotherbythe difference inmobilityand thecorresponding arrangementof the molecules.In thesolid statethemoleculesoccupya definitepositionat adefinite distancefromeach other. If the distance isincreased,orthepositionaltered(extension, twisting),force is called intoplay,the force ofcohesion,whichopposesthesechanges.In theliquidstate,the molecules arepositedat a definitedistancefromoneanotherbutnotin adefiniteposition. Lastly,themolecules,in thegaseousstate,areindependentof oneanotherinpointofdistanceandposition.A directconsequenceofthesepropertiesofthe different states ofaggregationis thata solidbodyretains theshapeonceimpartedtoit,aliquidconformstotheshapeofthe vesselin which it is contained sofaras itsvolumepermits,whereasgasesfillanyspaceoffered tothem.Thespecifieddifferences in the internalenergyofbodies,due tochangesin the state ofaggregation,are not theonlyones, however,to which it issubject.Anexamplewill makethispointclear. If 12gramsofdiamond are burnt to carbonmonoxide,26*1 unitsofheatareliberated,whilstbyusing purecarbonobtained fromsugar charcoal, 29-0units aredeveloped.Inbothcases 28gramsofcarbon monoxide result.Althoughthechemicalcompositionofthe initial substance is thesame,12gramsofcarbon,the amount of heatdevelopedis different.Thesamebody, carbon,hastherefore at the sametemperaturedifferentproperties accordingto whether it is existent asdiamondor assugarcharcoal. These two forms are describedasallotropicmodificationsof carbon. The differences betweentheallotropicformsofabodyareingeneralnot sopronouncedasthose of the different states ofaggregation,andcertainly,afundamentaldifferencebetweenthesinglestates ofaggregationand theallotropicmodifications is not so obvious. On thispointLotharMeyerlexpresseshimselfas follows :1LotharMeyerin Watts'Dictionary of Chemistry,2ndEd.,1888,p.128.POLYMORPHISM3"Thechangeofoneallotropicmodification is so similar tothechangeofonestate ofaggregationintoanother,that,strictlyspeaking,thethree states ofaggregationofanysubstance at allmust be described as threeallotropicmodifications of it. ...Themeltingofice,forexample,is the conversion of thelightintotheheavymodification(ofwater)."Justasbythe conversion ofone state ofaggregationintoanother,heatmanifestationsoccur,soalso is this thecase in thechangefrom oneallotropicforminto another;and that whichisdesignatedin theformerphenomenonlatent heatoffusion orlatent heat ofvaporization,is called in the latter case heat oftransformation(Umwandlungswarme).Thefollowingelementsoccurin differentallotropicmodifica-tions,and are thereforepolymorphic1:antimony,arsenic, lead,iron, iridium, carbon,phosphorus, sulphur, selenium, silver,tellurium, zinc,tin.Asin thechangefromonestateofaggregationintoanother,so alsothechangefrom onemodification toanother takesplaceat a definitetemperature.In thisrespectthe twochangesareagainverysimilar. It is wellknownthat it ispossibleto coolwater below o C. withoutfreezingit;this isspokenofas anunder-cooling. Frequentlyaslightdisturbance(e.g.the intro-duction of a smallparticleofice)suffices todestroythis con-dition. The water thensuddenlyfreezes to ice and the heattherebyliberatedraisesthetemperaturealmosttoo C.Further,thepositionof thefreezing-pointis influencedbythepresenceofathirdbody. Similarly,inallotropic transformations,under-coolings,as well as the effect of a thirdbody,have beenobserved. Thelattermaybe solargeas todepressthe trans-formation-pointmorethan 100degreesoftemperature.Thepositionofthetransformationpointsisclearlyshownbygraphic representation. Correspondingly,when a heatedbodyissubjectedto a slowcooling,a retardation in the fall oftemperaturetakesplaceat thosepointsat which heat wasliberated. Time andtemperaturebeingselected asco-ordinates,the former as abscissae and the latter asordinates,thecoolingcurveof thebodyunder observation is obtainedbyjoiningtheseparatepointsbya line.1Landoldt-Bornstein'sPhysikalisch-chemischeTabellen. Berlin. G.Springer. 1905.THEPHYSICAL PROPERTIES OFMATTERFig.i showsin thiswaythe curve forpure platinumcooledfrom 1000 C. Thebehaviourofsteam cooled from150C. isdepictedinFig.2. Thecoolingis at firstregulardown to1 00 C.;at thispointcondensationoccurs,and for aperiodLof abminutes,duringwhichthephenomenonlasts,thetemperatureremains constant at100 C. When con-densation iscomplete,thetemperature againsinksregularly to oC.,whenwater freezes toice. Heat isagainliberatedbythisoccur-rence,and the tem-peratureremains con-stant at C. untiltheTemperatureC.ofO>

FIG. 20.Compensa-tionarrangementfor determinationofcoolingcurves(Heyn).of thecoolingcurvewith timeandtemperatureas co-ordinateswasintroducedbyCharpy.1Roberts-Austen,"FiveReportstotheInstitutionofMechanicalEngi-neers."Proceedings, 1891, p. 543 ; 1895, p. 238 ; 1893. p.102; 1897,p. 31 ;1899, February.2E.Heyn,/. Bericht uber diemikroskopische Untersuchung der,etc.Verh.des Ver.zurBef.d.Gewerbefleisses. November, 1904,Berlin.24THE PHYSICAL PROPERTIES OFMATTERFortheproductionofaregularmovementheemploysclock-worksimilartothechronographpreviouslydescribed,whichsetsinregularmotionacylindercovered with sensitivepaperandcontained in alight-tightbox. The axis of thiscylinderishorizontal. Twopencilsoflightfalluponthe mirror of thegalvanometer;one is so directeduponthecylinderthat itentersthrougha narrow slit and can trace acontinuous lineonthe surface of theregularly rotating cylinder.Therays pro-ceedingfrom the second source oflightare reflecteduponascreen,and are in thiswaymade accessible to individualobservation.Averyneatexperimental arrangement" was constructedbySaladin,theengineerattheCreuzotworks,and LeChatelier.1Themethodshitherto described make itpossibleto indicatethe difference oftemperaturebetweenthebodyunderexamina-tionandthecomparisonbodyas afunctionoftimeonly.If itis desired toexpressit as a function of thetemperature,thentwo records areneeded,viz. the curve of the difference oftemperatureas afunctionofthetime,andthecoolingcurve,i.e.the actualtemperatureas afunctionof the time. From thesetwo there canthen be constructedpoint bypointthecurve ofthedifferenceoftemperatureas afunctionofthetemperature.The directrecordingof a curve of which the abscissaerepresenttemperatures,theordinates,thedifferencesoftempera-turebetweenthetestpiece andthecomparisonbody, washithertoimpossible,because theverysensitivegalvanometersnecessarilyemployedwerefurnishedwith verticalsuspension,andthereforecouldonlybedeflectedin ahorizontalplane,whereasoneofthedeflections mustbevertical.NowSaladin makes use of thepropertyofa45mirrortogivea verticalimageof a horizontalstraightline.If,forinstance,s is thereflectingsurface inFig.21,d =45,thentheimageof ab must lie ata'b',and it is vertical if ab lieshorizontally.InsteadofamirrorSaladin usesaprismarrangedfor total reflection.Fig.22 shows the scheme of the entirecontrivance;s is the mirror of thegalvanometerwhich isdeflectedbythethermo-electriccurrent whichservesto measure1H. LeChatelier,"Nouveaudispositifexperimentalde la me'thodedeM.SaladinpourTenrdgistrementdespointscritiques."Revuedemetallurgie,1904. Paris,Dunod49, quaidesGrands-Augustins.SALADHPS APPARATUSthetemperature.Ascreen,havinga hole of 0*1 to 0*2 mm.diameter,isplacedat the focus F oftheachromatic lensAandimmediatelybefore the sourceoflightLwhichmaybe,eg.aNernstlamp.Thedivergent penciloflight issuingfrom theFIG.21. Actionof theobliqueprismin the Saladin-LeChatelierapparatus.FiG. 22. Path of thelight raysin theSaladin-LeChatelierapparatus.openingin the screen ischanged bythe lens A into oneofparallel rayswhich falluponthe first mirrors. This reflectsthem into theobliquelyplaced prismP.Bythe deflection ofthe mirrors,theraysBaredisplacedin a horizontalplane,afterpassing throughPtheymove in a verticalplane.Themirror/ofthesecondsensitivegalvanometer,whichis deflectedbythe current due to the differenceoftemperatureof thetwobodies,must besufficientlyhighto catch theraysdisplacedintheverticalplanewhichmaystill falluponit.BythedeflectionFiG.23.Schemeforaregisteringapparatusforcoolingcurves(Dejean).ofthelattergalvanometerthelightisagaindisplacedhorizontallyandfinallyconcentrated to apoint bymeansofthe lens A'atits focus. Atthispointaphotographic plateisplacedwhichrecords the movementof thepointoflight.Since thismove-mentregisterstheresultant ofthedeflections ofthetwogalvano-metersthere is acurveupontheplateshowingthe differenceintemperatureofthetwobodiesas afunctionofthetemperature.26 THE PHYSICAL PROPERTIES OFMATTERThearrangementdescribedabovepossessesthedisadvantagethat thesizeofthebodiesunderresearch isverylimited. More-over it isextremelydifficult and inmanycasesimpossibletocarryoutamelting-pointdeterminationbecauseofthedifficultiescreatedbythearrangementofthecomparison body. Dejean,1therefore,proposesanarrangementbywhich,ontheonehand,thecomparison bodymaybedispensed with,and on theother,the dimensions of the material under examinationmaybe asgreatas desired. TheprincipleofDejean's apparatusis asfollows: instead ofmeasuringthe times which arerequiredtocoolthroughadefinite intervaloftemperatureas in Osmond'smethod,theapparatusgivesthereciprocal value,i.e. thechangeoftemperature perunittime,or thevelocity,thediagramofwhichwehave learntalready (p. 15andFig.nonp.16).TheapparatusconsistsofakindofDesprez-d'ArsonvalgalvanometerA,theactuatingcoil of which carries twowindings,insulatedfromoneanother,whichare connectedtothefourbindingscrewsI, 2, 3, 4.Thebindingscrews I and 2 ofthe first(inducting)windingare connecteduptoaLeChatelierthermo-couple,thehotjunctionofwhich is inserted in thesampleforexamination,B.Duringtheheatingandcoolingthe coil is twisted in themagneticfield aboutitspointofsuspension ;this motioninducesacurrent in the secondwinding,thestrengthof which ispro-portionalto thevelpcityof the coil'smovement,and conse-quentlyto thevelocityofheatingorcoolingof thesample.Thiscurrent is conductedtothesensitive mirrorgalvanometerCoftheSaladin-Le Chatelierapparatus.The deflections of thisgalvanometerare at a minimumorbecome zero if thevelocityofcoolingorheatingdecreases or becomeszero,that is tosay,whena criticalpointoccurs. Thetemperaturesat which thisappearsareyieldedbyasecondgalvanometerin connectionwitha secondthermo-couple.Itfollows, therefore,that the curvedescribedonp.16Fig.nisautomatically obtained,and showsthevelocityof thechangeoftemperatureas a function ofthetemperature.1M.Dejean,"Galvanometred'inductionpour1'etudedespoints desolidi-ficationetpoints critiques."RevuedemetallurgieMemoires, 1905.THE PHYSICAL MIXTURE.1Between theelements,the molecules of which consistofatomsofthesamekind,andcompounds, whosemoleculesconsistofatomscombinedaccordingtotheirvalencyvalues,ontheonehand,and mechanicalmixtures,the individualcomponentsofwhich can beseparated bymechanical means on the otherhand,there stands aclass ofsubstanceswhich wegroupunderthename"physicalmixtures." With elements andcompoundstheysharethepropertyofperfectlyuniformcompositionthrough-outtheirmass; theydifferfrom them in that thiscompositionis notgoverned bythelawsofvalency.Thephysicalmixtureis to be metwith in thesolid,liquid,andgaseousstates ofaggregation.Ingeneral,thepropertiesof the mixture are notstrictlyadditive,that is tosay,aparticular propertyof the mixture isnotexactlythe meanof the samepropertyof itscomponents;theychangewiththecomposition.As one wouldexpectfrom the constitution ofgases,therelations are of thesimplestkind in mixturesofgasesinwhichno chemicalchangeoccurs. Since in such mixtures eachgasbehaves,as is wellknown,asthoughit alone werepresent,thepropertiescaneasilybe deducedbyasimple"partnership"calculation. Therelations are different inliquidmixtures. Toconvinceourselvesoftheimportanceofthese differenceswewillconsiderbrieflyhowtheregulardistribution of thesinglecom-ponentsis conditioned.Inagas,as wehaveseenpreviously,theindividualmoleculesare not heldtogetherat a definitedistance,but endeavourtooccupythegreatestavailablespace. Consequently,as soonastwo or moregasesmeettogetherin adefinedspace,each one1W.Nernst,Theoretische Chemie. TranslatedbyC. S. Palmer.(Macmillan.)28THEPHYSICAL MIXTUREstrives to fill itcompletely, independentlyof the othergasespresent.Fromthis it followsthat allgasesmixtogetherin allproportions, supposingthatnochemicalchangetakesplace.In theliquidstate,on thecontrary, perfectmiscibility,fromwhat has been saidpreviously,cannot beexpected.If twosuitableliquids, saya litre ofeach,bepoured togetherinto avessel,thespecificallyheavieronewilloccupythelowerpartandthelighteronetheupper partof thevessel,and thesumof thevolumeswill amount to twolitres,as beforemixing.Oil andwater,forinstance,conductthemselves in thisway.Nowphysicsteaches that forcesoperatebetween theindividualmoleculesof thesamebodyaswell as betweenthoseof differentbodies,cohesion in the formercaseand adhesioninthe latter. Itis thereforeclearthat ifoilandwaterarestratified,thecohesionwhichholdstheindividualmoleculesofoiltogetheras wellas thatwhichbindsthewatermolecules,mustbegreaterthantheadhesionbetween thewaterandoil molecules.If,ontheotherhand,weselectsulphuricacidandwater,thefollowingtakesplace.Thewater molecule issubjectedto theinfluenceoftwoforces,the cohesion of thenearest water mole-culesandthe attraction(adhesion)of the nearestsulphuricacidmolecules. Nowtheadhesion betweensulphuricacidandwaterisgreaterthanthecohesion ofwatermoleculesaswellasthat ofsulphuricacid molecules.Consequentlythe water moleculeunderconsiderationyieldsto theadhesion,is severedfrom thesurroundingwatermolecules,andpassesinto thesulphuricacid.Thismovement willrepeatitself until the force of adhesion isneutralized,i.e. untilone substance is saturated withrespecttotheother.Quitethesamereasoning appliesto the caseofsolid-liquidas well as to solid-solid bodies. Thedegreeof mutual inter-penetrationdepends uponhowmuch adhesionexceedscohesion,and this isnothingelse but anexpressionfor thesolubilityofonebodyintheother.From thepointof view thus stated itdirectlyfollows thatwecannotingeneral speakofthedissolvedbodyandthesolvent,butof the mutualsolution of the two bodies. In thosecases,where one of thecomponentsispresentinlargeexcess,it isfrequentlydesignatedthe solvent.Inoppositiontogasmixtures,inwhichthesolubility (if oneAQUEOUSSOLUTIONS29mayso describe thecompletemutualinterpenetration)isindependentoftemperature, pressure,and the nature of thecomponents,inliquidand solid mixtures this islargelyinfluencedbythe factors mentioned. Thechanges resultingfrom thebuilding upof the mixture will be considered morecloselyin whatfollows.In order toarrangethesubject clearly,mixturesmaybedividedupas follows :I.Aqueoussolutions;II. Fused saltmixtures;III. Fusedalloys.We shall see that these three classes exhibit sogreatasimilarityin allrespectsthat this divisionappearssomewhatarbitrary.It must howeverbenoted,on the otherhand,thatthissimilarityor ratheridentity onlybecame known later;itisalways interestingto trace the evolution of alaw,for onetherebybecomes morethoroughlyconversantwith itsmeaning.Inconsequencetheidentityof thegroupswill bededuced herefromtheircommonproperties.AqueousSolutions. The coolingcurveofpure waterexhibits,aswe have seenearlier,apointof arrest at o C. which corre-spondstotheformationofice. ThiscurveinFig24.is o. Ifa10percent, solution of salt ismade,in addition to thepointofarrest e at4 C.,another one kcan be observed at 22 C.(curve i) ; 15 percent, of salt lowers thepositionof the firstpointe stillfurther,whilst the second occurs at the sametemperature-22 C.(curve 2).With23 percent, of salt thefirstpointhas fallen also to 22C.,so that this mixturepossesses onlyone suchpointof arrest. Solutions with morethan23 percent, of salt show twopoints again,the first ofwhichs riseswithincreasingamounts ofsalt,whilst the secondremainsconstantat 22 C.Tomakethesignificanceofthesearrest-pointsclear,observa-tionsofthechangeswhichthemixtureundergoesatthemcanbemade. Ato C.waterfreezestoice;fromasolutionconsistingoflopercent.NaCland90percent.H2 O,crystalsseparateoutat the firstpointwhichproveonanalysistoconsistofpureice.This fact leads to thegeneralizationthat thefreezing-pointofwater isdepressed bythepresenceofsalt;the amountof thisTHEPHYSICAL MIXTURE2030Vs*10 15 20 25 30Percentagesof salt.FlG.24.depressionincreasesatfirst withthe amountofsalt. Ifthesmallcrystalsof icewhich have formed becarefullyremoved,thereremains a solution(mother-liquor)whichpossessesa corre-spondinglyhigher percentageof salt.Consequentlythe freez-ing-pointofthis solution is lowerthan thatofthe first andmorecrystals, whichprovetoconsistofpureice free fromsalt,separateoutonly bycoolingfurther.Byremovingthesecrystalsalso,thesolution becomesricher and richer insalt,thetemperatureat whichcrystallizationtakesplacefalls further andfurther,untilfinallyat 22 C. the whole masssuddenlysolidifies. Whenthis solid isanalyzed,itprovesto consist of23*5 percent, salt and76^5percent,water. Ifanotherconcentrationisselected fortheoriginalsolution, say1 8percent.NaCland 82percent.H2 O,theprocessisstrictlyanalogous,onlythatthefirsticecrystalsoccurlater,at about10 C. Themixtureremainingliquiduntilthelast, whichsolidifiessuddenlyat 22 C.possessesagainthesamecomposition 23^5 NaCl,76*5H2O.If the solutionpossessesthiscompositiontobeginwith,ithasonlythe onefreezing-pointat 22 C. In solutions whichcontain more than23*5 percent, ofsalt,anotherpointof arrestagainappearsabovethistemperature.Amixture,forinstance,containing 25 percent.NaCl, 75 percent, waterbeginstodepositatits first arrestpointscrystalswhichanalysisshows toconsistofpuresalt. Theremainingmother-liquorconsequentlybecomespoorerin salt untiltheamount23*5NaCl, 76*5H2Oisreached,solidifyingat 22 C.Thismixture,whichalwayshas the samecomposition,possessesa constantfreezing-point,and remainsliquid longestfrom the wholeseries of salt-watermixtures is called"eutecticmixture"or"eutectic."Thepropertiesof theeutectic,viz. itspossessionofconstantcompositionandmelting-pointledformerlyto itsbeingregarded35 toTHE ICE-SALTSYSTEM31asachemicalcompound.Frommoreexactinvestigations,how-ever,it resulted that thecomponentswere not in molecularproportions,and therefore the chiefrequirementfora chemicalcombinationwasnotfulfilled.Further,themicroscopeestablishedthe fact thatthe eutectic consistsofinnumerableplatesofwaterandiceplacedin mechanicaljustaposition.Inordertodepictthesolidification andcoolingrelationsofthe whole series of salt solutionscomprehensively,thegraphicrepresentationis alsomadeuseof. InFig. 24thecoolingcurvesof solutionsof different salt contents are set out sidebyside.Thepointsecollectivelydenote thetemperatureat which iceseparatesout,thepointsk the solidification of the eutecticmixture,whilst thepointsscorrespondtotheseparationof saltfrom the solution. If now all thepoints, e, k, s,arejoinedtogether bya continuousline(thedotted line ofFig. 24),thediagram Fig. 25is obtained.Following Heyn'slprecedent,itis called thefreezing-pointdiagram,and it is thereforenothingbutthelocusof all the criticalpointsof a series ofsolutions ofincreasingsalt contents. In thefreezing curve,Fig 25,ABthereforecorrespondsto theseparationofpureice,BC to theseparationofsalt,and DDto theseparationof eutectic water-salt. From thediagramthe condition ofanyselected saltmixturecan bereadoff,as soon as the concentration and thetemperaturearegiven.Asolutionconsistingof 10percentNaCl and90 percent, ofwater,as is seen from thediagram,beginstodepositicecrystalsat thetemperaturea. When thesurrounding temperaturehas fallen to about 10C.,so muchwater hasalreadyseparatedas ice that theremainingmother-liquorcontainsdepercent,ofsalt.Proceedingfrom thefollowingconsideration,the relativeamounts(ofthe twosubstances) maybeclearlydeduced.Supposethat the flakelets of icepresentatanyinstant areseparatedfromthemass,so thatthesolutiononlyis left. Thenif thetemperaturefallsonlyto the extentof aninfinitesimallysmallamount,asmallfreshquantityofice willfreeze out. Hencethe solution at-10 C. is a saturatedone,andwe obtain itscompositionbydrawingahorizontallinethroughtheordinateat-10C.,cuttingABin e. The abscissadeof thispoint gives1Heyn,DieMetflllographieim Dienste der Hiittenkunde.Freiberg,Craz. u. Gerlach.THE PHYSICAL MIXTUREustheamountof salt in themother-liquor,for this is theonlyoneof thewholeseriesof salt solutionswhichbeginstodepositice at 10 C. It ispossiblenow to calculate howmuch icehasseparatedat thispoint.Mbeingthe totalweightof the2010Q.I-10-20-3010 30 20Percentagesofsalt.FIG.25. Freezingdiagramoficeandsalt solutions.solution,its salt content d2=10percent,thenthe amountofsalt in thesolution isM.d2 xxgrams(i)100If x be therequiredamount ofice,the mass of the mother-liquoris M-x. Thiscontains,aswesawabovedepercent, ofsalt. Thetotalamountofsaltcontained in it is therefore(M-x]de100grams(2)FERRIC CHLORIDE-WATERSYSTEM33Asthecrystalsofice are free fromsalt,the fractions(i)and(2)mustbeequal,henceMd2=(M-x)de100 100Md2-Mde-xdexde=M(de-d2)M. 2ex^ __2eM~~deThatis,theamountof iceseparatedat aparticular temperaturebearstothetotalamount ofthemixturetheproportionexpressedbythelengths2e : deintowhich thevertical linedrawnthroughthepercentageof salt divides the horizontal linethroughthetemperatureordinate.Thephenomenaoffreezingarenotalwayssosimpleastheyhavebeen described herein theexampleof salt andwater. Ithas beensupposedthatpuresaltseparated alongthe lineBC,and that the eutectic consisted of lamellae of ice and saltdepositedsidebyside. This is notalwaysthe case. Muchmorefrequentlychemicalcompoundswith the waterseparateoutinsteadof thepure salt,andto eachparticular hydratetherecorrespondsaparticularbranchofthelineBC.Asanexampleofthiskindoffreezing,thesolutionsofferricchloride,which were firstsystematicallyinvestigatedbyRooze-boom*will bediscussed. Ferricchloride formswithwater thefollowinghydrates:Fe2Gl6.4H2O;Fe2Cl6.5H2O;Fe2Cl6.;H2O;Fe2Cl6. I2H2O.Imaginenoweach oneofthese salts tobein theliquidcondi-tion,thenoncoolingtherewill beapointat whichitswhole masssolidifies,viz. themeltingorfreezing-pointof the salt. Themelting-pointof thehydrateFe2Cl6 .4H2Olies at73-5C.Byaddinganhydrousferric chloride to theliquid hydrate,the melt-ing-pointisdepresseduntil at66 C. theeutectic ferric chloride-hydrate^ appears. (Forthe sake ofbrevitythehydrateisrepresentedbytheindex numbercorrespondingto the numberofmoleculesof waterpermoleculeofferric chloride.Hydrate*1BakhuisRoozeboom,"Uber dieHydratedes Eisenchlorids." Zeit-schriftfiir physikalischeChemie, 10,s.477 (1892).D34THE PHYSICAL MIXTUREthereforemeansFe2 Cl6.4H2O)Thediagramof freezing,Fig.26,is identicalwiththatofsalt-water. ThereforewehaveAlong JKseparationofthepurehydrate*,KLseparationofpureferricchloride,,,KKfreezingof the eutectic mixturehydrates-ferricchloride.Fig27representsthefreezingcurveofhydrate*andhydrate5andneedsnofurtherexplanation.i2!f-8.jVhK805 60GMKM25 30Molecules ofFe.,CI,100 mols. H2O.FIG. 26.in20Z5Molecules of Fe2CI6in100 mols. H2O.FIG.27.Torepresentclearlythewholediagramforthesystemwater-ferricchloride,the collectedseparate portionsareput together.Fig.28,in which each cross-hatched arearepresentsadivision,showsthewholearrangement.Withrespecttotheco-ordinatesit shouldbenoted, however,thattheordinatesrepresenttempera-tures asusualandtheabscissae,insteadofthepercentage amountofferricchloride,givethenumberofmoleculesofferric chloridein 100 molecules of water. Thisrepresentationfurnishes inmanycases amoreluciddiagramthantheformer.Theadvantageof sucharepresentationis at onceprovedifthe occurrencesareto betracedwhenoneofthecomponentsisgraduallyremoved;forexample,when thewater isevaporated.Forthesakeofsimplicity,it willbesupposedthatthetempera-ture remainsconstant at about30C. Thechanging composi-tion will then begiven byahorizontal line drawnthroughtheordinate30.Atfirst thewholesystemisliquiduntil so muchwaterhasevaporatedthatthere is onemoleculeofferric chlorideFERRIC CHLORIDE WATERSYSTEM35to twelve moleculesofwater;this is thecompositionof thehydrate^and as itsmelting-pointishigher,viz.37C,the whole mass so-lidifies to a con-glomerateofcrystalsofthehydrate^; byfurtherevaporationof water theregionin which aliquidmixtureofwaterandhydrate?exists isreached;atthepointdthehydrate?be-ginstosolidify,becomingunder in-creasing tempera-ture aliquidmixturehydrate5-water andthen solidhydrate5.From the com-plete freezingdia-gramit can beseenthat each definitecompoundcorre-spondsto a maxi-mum in the curve.CertainlyRooze-boomproceededconversely;he firstestablished the curvefor the water- ferricchloridesystemandarguedthe exist-ence of the variouscompoundsfromthe occurrence of1005 10 IS 2025Mols. ofFe2CI6in 100 mols. H2O.30FlG. 28.Solubilitycurveofferricchloridein water(Bakhuis Roozeboom).36THE PHYSICAL MIXTUREmaximain theseparatebranches ofthe curve. These investi-gationsareveryvaluable from asystematic pointofview. Asimilarmethod,forinstance,serves for mixtures of metals todeterminewhetherdefinite chemicalcompoundsof theseparatecomponentsofanalloyexist.FusedSalts.Ifa moltenmixtureoftwo salts is allowed tosolidify,theperfect miscibilityof thetwocomponentsobtainingatthe timemayremain after solidification or itmaybewhollyorpartially destroyed.Supposingthatthewholeofthemoleculesoftheliquidmassoccurringat agivenmoment wereto remain in thepositionwhichtheypossessedat themoment,a solidbodywould-beformedcharacterizedbythis,that its moleculesoccupyadefinitefixedpositionand distance from each other(see p. 2).Theconfigurationofthis solidbodywouldthen be thesameas thatoftheliquidmass fromwhich it resulted;the individual com-ponentswould not beseparable bymechanical means; theywouldbedissolved. Thesolidcomplexwouldpossessthecon-stitution ofasolid solution.Bymeltingtogetherlime, silica,andalkali,aglassis formed.Now thepropertiesof theglass change accordingtothepro-portionsin which the constituents named entertogether,andcontinuouslywiththecomposition.Thepossibilityofchangingthecompositionwithout anaccompanyingsuddenchangeofpropertiesconstitutesaleadingcharacteristicofsolid solutions.When a solid solutionpossessesthepropertyofformingcrystals,the latter aredescribed asmixedcrystalsof bothcom-ponents.Inthemain,isomorphousbodiesform mixedcrystals,butisomorphismis notnecessarilya sinequdnon for theformationofsolid solutions.Inoppositiontothesaltmixtures, whichformahomogeneousmassaftersolidification,thecomponentsofwhich thereforeenterintosolidsolutions,there stand those thecomponentsof whichafter solidificationpossessno furthersolubilityfor each other.Inaqueoussolutions thiscorrespondsto thesystemsodiumchloride-water,which aftercompletesolidification consists ofspacially separated particlesof salt and ice. Such salt-meltssimilarlybreakup quantitativelyon solidification into theircomponents.Between these two extremecases,thecomplete solubilityFUSED SALTS37andthecompleteinsolubilityof thecomponentsaftersolidifica-tion,a series of intermediate substances ispossible.In thesecases thesolubility suddenlydecreasesconsiderablyat themoment ofsolidification,without howeverbecomingnil. Inmanycases, also,thesolubilitydecreases still further in theprocessofcooling,whichgivesrise totheseparationof acorre-spondingamountof oneof thepurecomponentsin the interiorofthesolid mass.Further,it ispossiblefor definite chemicalcompoundstoform between the twocomponents,the so-called doublesalts,correspondingtothehydratesin thesystemferricchloride-water(p- 33) 5 then,justas inthose,these double salts can be con-sidered as newcomponentswhichgiverise to the samephenomenaashavebeenalreadydiscussed forthesinglesalts.Nowaccordingto thetypeofsolidification,there are dis-tinguished,in solidified salt mixtures:I.Systems,whichdonotformdoublesalts.(a)The twocomponentsform a continuous series ofmixedcrystalsofthesamekind.(b)Thetwocomponentsdonotform a continuousseriesofmixedcrystalsofthesamekind.(c)The twocomponentsform a discontinuous series ofmixedcrystalsofdifferent kinds.II.Systems,whichform"*doublesalts.I. SYSTEMSWHICH DO NOT FORM DOUBLE SALTS.(a)Thetwocomponentsformacontinuousseriesof mixedcrystalsofthesamekind.ImaginetwosubstancesAandBwhichareperfectlysolublein one another in theliquidas well as in the solid condition.AccordingtotheresearchesofB. Roozeboom1thephenomenonofsolidificationofsuchasolution isnotsosimpleas wasformerlysupposedfor such bodies. Ingeneralthesolidification doesnottakeplaceat a definitetemperaturebutduringan interval of1B.Roozeboom,"ErstarrungspunktederMischkristallezweier Stoffe."Zeitschriftf.physikalischeChemie, 1899,Bd.30, 5.385.THEPHYSICAL MIXTUREtemperature.Thisdependsuponthe fact that thecrystalsfirstformed have notthesamecompositionastheliquidsolution outofwhichtheyseparate.Inbyfarthe mostcases,theliquid,incomparisonwith themixedcrystals, possessesagreateramountof thatcomponentbywhosepresencethefreezing temperatureis lowered.Roozeboomemploysthefollowing graphicrepresentationforillustratingthis(Fig. 29).Let ACand BD be themelting-pointsof the twocomponentsA and B. In the co-ordinatesystem,the abscissse denote thepercentagecontents of the Bconstituent,and the ordinatestemperatures.There is nowfor each melt atemperatureatwhichmixedcrystals begintoseparateout. Thelocusofthesepointsis markedCL(liquidus) ;inFig. 29this isthelineCpnD.Furtherthereexistsasecondpointat whichfreezingis at an end;thesepointsjoinedbyalinegiveCs(solidus) ;inFig. 29 CgoD.Acertain solutionmsolidifiesas follows i at thetemperature;/ mixedcrystals begintoseparate,the A content ofwhich, accordingto the state-0.ErV \~>composition.BFIG.29.Solidificationdiagramof asystem,thecomponentsofwhichforma continuous series of mixedcrystalsofthesamekind.mentexpressedabove,issmallerthanthatof theliquid.Accordingto Roozeboom thiscontent is foundby drawinga horizontal linethroughn whichcuts Csin thepointo. The abscissa of thispoint givestheBcontentofthemixedcrystals.Bytheseparationofthecrystalsrich inBfromthesolution,this has become richer inA and hence its solidificationpointfalls. Atagiveninstant letthis, e.g.be t;thecrystals separ-atingoutat this moment havethecompositionu. Themassofthemother-liquordecreases inproportionto theseparationofthe mixedcrystalsuntilfinallyat thetemperature qit hasbecomezero. Thecrystalsseparatinglast ofall of thecomposi-tionqwerecrystallizedfromamother-liquor of thecomposition/.FREEZING TYPE I39Theoriginally separated crystalswhich werepoorerin Aequalizetheircompositionlittlebylittle astheyabsorb fromthemother-liquoracorrespondingamountofA,so thatfinallythe wholemassconsists ofhomogeneousmixedcrystalsof thecompositionm. Tothis end it is of coursenecessarythat thecooling proceedssoslowlythatthis enrichment of thealreadysolid massbydiffusion of theconstituent Aispossible.Ifthisdoesnottakeplace,theensuing aggregateofmixedcrystalsisheterogeneousand thefreezing temperatureof the latter fallslowerthanexpectedfromtheconcentration.Therepresentationallowsoneto establishtheamountofthemixedcrystalsatanyinstant,whichhavealreadyseparatedout.Letthetotal amountofthe melt be100,thecompositionin theliquidstatem,andthetemperatureat themomentbet. Accord-ingto the above statements thecompositionof theseparatedmixedcrystals=,thatoftheremainingliquid=t. Letnowmassofcrystals=xthenmassofmelt=100 x/2 -contentofthecrystals=xuw^-contentofthemelt=(100 x)twButtotalAcontentofthemass=100vwHencex .nw+(100 x)tw=100vw.xtv massofmixedcrystals.Whence-=-----=-. . ...-_.100 x vu massofremainingliquid.Roozeboomhasdenotedthis kindoffreezingasTypeI. InthegroupofhomogeneousmixedcrystalsRoozeboomdistinguishestwo furthertypesinwhich,between thefreezing-pointsof thecomponentsthe curves CsandCLshow a maximum or aminimum. Wecan, however,leave both these cases out ofconsiderationhere,sinceupto now noexampleshave beenestablished withcertainty.(&)Theliquidsolidifiesto a discontinuous seriesofmixedcrystals ofthe samekind.The casemayoccur in which onecomponentApossessesonlya limitedsolubilityfor B and vice versa.Fig. 30showsthefreezingdiagramforthiscase, whichwasdesignatedTypeIV.byRoozeboom. At thetemperaturet of the transitionpoint,THEPHYSICAL MIXTUREthemeaningofwhich willbediscussed furtherin thesequel,thesolubilityofBin Amaybetakenequalto the abscissa of thepointF,thatof AinBequalto G. At thetemperatureo,letthesesolubility capacitiesbe smaller still andequalto AHandKB.MeltsbetweeneDsolidifyasfollows: Assoonastheline EDis reachedduringthecooling,mixedcrystals separateout,thecompositionof which as described under(a),isyielded bytheabscissa of thepointof intersection of GDwith the horizontaldrawnthroughthepointinED.Byfurthercoolingnootherchangeoccurs,as atthetemperatureo thesolu-bilityofB for A isequaltoKB.Aliquidof the com-positioncseparatesoncool-ingat first mixedcrystalsd;liquidandcrystalsaltertheircompositionfrom cto Eand from dto G re-spectively.Now in orderthatbyfurthercooling,thecompositionof theliquidcanbealtered furtheralongFIG.30. Freezing diagramof asystem,thecomponentsof which form a discontinuousseries ofmixedcrystalsofthesamekind.ECand that of thesepa-rated mixedcrystals alongFC,the wholecomplexofthe Gmixedcrystals presentmust be converted intoFmixedcrystals.This takesplaceat constanttemperature^bythereaction :LiquidE-f-mixedcrystalsG=mixedcrystals F .(i)Ifmother-liquorremains afterthisreaction,it freezesalong ECwithseparationofmixedcrystals along FC;this is the case forall melts from Eto c. If more mixedcrystalsthan mother-liquorarepresentin ordertocompletethereaction(i),the latterwill bequite saturated,and the mass consists later of mixedcrystalsGandF. This is the case for melts between c and a.ItwassupposedabovethatthesolubilitygapFCincreaseswithFREEZING TYPE IV41fallingtemperatureand isequalto HK ato C. Inconsequenceofthis,all thosecomplexeswhich at thetemperaturet containmixedcrystalswith morethan AHpercent.Bor KBpercent.AintersecttheVmes FH andGKduringthecooling,andfurtherseparationoccurs.For the readierunderstandingof these rathercomplicatedphenomena,anumber ofcoolingcurves(see p. 4)areschemati-callyshowninFig. 31.Thethick linesshowthosepartsof thecurveduringwhichanychangetakesplace,whilst the thin linescorrespondtonormalcooling.A H K bFIG.31.InFig. 31thereforea=thetemperatureintervalduringwhich mixedcrystalsseparatealong DG;b =.thepointatwhichthechangemixedcrystalsG4-liquidE=mixedcrystals F takesplace ;c thetemperatureintervalduringwhich"limit-crystals"GKand FHrespectively separate ;d=the intervalduringwhichmixedcrystalsCFseparate;e=thefreezingofthepuresubstanceB.Ifthegapofsolubilityisverylarge, TypeV. occurswhich isrepresentedinFig. 32.The course of thefreezingdoes not differessentiallyfromthat ofTypeIV. Whilst theliquidmeltspass throughthecompositions DEorCE,theseparatedmixedcrystalssimulta-neously change accordingto DGand CFrespectively.Meltslyingbetween F andGsolidify simultaneouslyattemperaturetTHE PHYSICAL MIXTUREtoanintimatemixtureofcrystalsGandcrystalsF. Eis,how-ever,a eutecticpoint.In this case alsowhathasbeensaid forTypeIV.applies.ThegapFG can increase withfallingtemperatureso that in thecourseofthecoolingafurtherseparationcan takeplace.Examplesof thistypearefound in thesystemsiron-carbon,andpotassiumnitrate-thallium nitrate.AHFIG.32.K B(c]Theliquids solidifyto twodifferentkindsof crystals.Thiscasecarriesonebackto theforegoing. Imaginethat inFig. 32thecrystalsseparating alongDG areregular,thosealongCFhexagonal,then thefreezingisexactlyof thistype./ is then the eutectictemperatureat which anintimate mixture of hexa-gonalandregular crystalssimultaneouslyfalls out. Inthiscategoryall thosesystemsfall whosecomponentsarecompletelyinsoluble in eachother andof whichthesystemKC1^.presentsanexample.If inFig. 32thepointFmoves back to the ordinateBFIG.33. A,Gto the ordinateB,thetype reproducedinFig. 33,whichmaybedesignatedTypeVa,ensues.Asisevident,this isabsolutelyidenticalwith the salt watertypeoffreezing.Thephenomenawhichthediagramillustratesareexactlylike those in thefreezingof the salt-watersystem.HenceinFig. 33DOUBLESALTS43CErepresentstheseparationofthepurecomponent AEDrepresentstheseparationofthepurecomponentBE'E"representsthefreezingoftheeutecticmixtureAB.II. SYSTEMS WHICH FORM DOUBLE SALTS.Thesystemsfallingunderthis head form ananalogueto theferric chloride-watersystempreviouslydescribed. Theseparateddouble salts can form further one or several kinds ofcrystalsamongstthemselves and with thecomponents,and can mixpartiallyorcompletely,so that of thepreviouslymentionedtypesseveralmayoccurtogetheror berepeated.On thisaccount theinterpretationofthefreezingcurves can become averydifficult matter under somecircumstances,particularlywhen the results cannot be testedchemically, optically,or insomeothermanner.It wassupposedearlier,thatneither thecomponentsnor themixedcrystalsunderwentfurtherchangesafterfreezing.These(changes)are, however,very frequent,as has been described inanearlierchapter.Fromthegreat similarityexistingbetweenallotropictransformations andfreezing phenomena,itmaybeconcludedthat thesamephenomena,whichhavebeendescribedforfreezingin theforegoing,can berepeated.Inpointoffact,Roozeboom hasdeveloped theoreticallyallpossiblecases ofthesetransformations,and has demonstrated them for varioussystems.1It would leadustoofartodiscuss Roozeboom'sveryinterestingresearches at thispoint ; onlyone characteristicexample,thesystem potassiumnitrate-thallium nitrate2will beselected.Potassiumnitrate and thallium nitratewhenchemicallypurebothpossesstransformationpoints, potassiumnitrate at 126 C.andthalliumnitrateat142C. Above126 C.potassiumnitrateexists in thea-conditionand formsrhombohedralcrystals ;belowthistemperatureit exists in the/3-conditionandthecrystalsare1B.Roozeboom,"Umwandlungspunktebei Mischkristallen." Zeit.f.physik.Chem.1899,Bd.30s.414.2C.vanEyk,"Uber dieBildungundUmwandlungderMischkristallevon KaluimnitratundThalliumnitrat."Ztsch.f.physik.Chem.1899,Bd.30s.430.44THE PHYSICAL MIXTURE.lift32C3062Sf2602 W2? 2003160rhombic. For thallium nitrate the a-condition alsocorrespondsto the rhombohedralandthe/3-conditiontotherhombiccrystals.Fig. 34shows thefreezing diagramfor the whole series ofmixtures. Itcorrespondsto thefreezing-typeIV,that is tosay,theseries of mixedcrystalswhichseparateinfreezingisdiscontinuous,and has agapbetweenDandE(20and50 percent, ofpotassiumnitrate).Themeltslyingbetweenthese limits freeze therefore to aconglomerateofmixedcrystals, onecontaining20 andtheother50percent, ofpotassiumnitrate. At themoment of their formation themixedcrystalsare rhombohedral :they change,however,at a definitetemperatureinto therhombic form.Thetemperatureof the mixedcrystalssinkscontinuouslybetweenFand Hfrom the transformationpointofthepurethalliumnitrate tothatofthe finalcrystals.Asin thefreezing,thisre-crystallizationisspreadover a definiteinterval,aswould be indicatedbythe lineFH%(correspondingto ADin thefreezing.From thepointHwehave aconglomerateof mixedcrystalscontaining20percent, andasimilaronecontaining50 percent.I2C60PercentagesofKNO,,ofpotassiumnitrate. Asthetrans-FiG.34. Diagramoffreezingandrallotropictransformation of the formation of the rhombohedralto the 20percent,crystals,thetransformationtemperaturemustremain constant andexpressedbythestraighthorizontal lineHH\.Whilstbyfurthercoolingon the thallium nitrateside,thelimitcrystalsretain their concentration of 20percent.,thoseabove50 percent,potassiumnitrateseparate accordingto theALLOYS45lineEHiJ'. Thetransformation ofthe rhombohedralcrystalsa'begins alongthe lineGJand iscompleted along GJ\: in thepoint/thelimitingorsaturationpointis reached.Consequentlythetransformation of furthercrystalsmust follow at a constanttemperature. AlongthehorizontalstraightlineJJ2theremainingrhombohedralcrystalsaretransformed,and belowJzjithe massconsists ofaconglomerateofrhombiccrystals only,with J%and J\percent, ofpotassiumnitrate. These limitsare,asbefore,dis-placedat a lowertemperatureso that after the end of all thetransformations,aconglomerateofcrystalsKand K' exists.Collectingtogetherall theresultsagain,wehaveexisting1. Above ACB\liquid.2. Inside A CD: rhombohedralmixedcrystals ADandliquidAC.3.InsideCBE: rhombohedral mixedcrystals BEandliquidBC.4.Inside ADHF\rhombohedralmixedcrystalsa.5.InsideBEH\JG: rhombohedralmixedcrystalsa'.6. Inside HDEH\: rhombohedralmixedcrystalsaandrhom-bohedralmixedcrystalsa.7.InsideFHHz: rhombohedral mixedcrystalsFHandcorrespondingrhombiccrystalsFH%.8. InsideGJJ\: rhombohedralmixedcrystals GJandcorre-spondingrhombiccrystals GJ\.9.InsideH^HH^JJ^: rhombic mixedcrystals |3and rhom-bohedralmixedcrystalsa.10. InsideFH^J^KL: rhombicmixedcrystals /3.11. InsideJ^J^K'K: rhombicmixedcrystals )3andrhombicmixedcrystals )3'.12. InsideGJ\K': rhombicmixedcrystals ]3'.Alloys.It isonlyof lateyearsthat thealloysof so muchtechnicalimportancefell into thesphereofsystematicscientificresearch. Thankstotheworkofcommissions formed in severalindustrialstates,whosebusiness it wastoinvestigatethegenesisas well as thepropertiesof metals and theiralloys,there areto-daysufficientpaths opento us toexplorewith success adomainwhich wasformerlyof anextraordinarily problematicalcharacter.Onecansaythat thestudyofmetallicalloysfirst received aTHE PHYSICAL MIXTUREremarkableimpetusatthetime whenGrahamfurnishedtheproofthatthelawsvalidingeneralforaqueous solutions,can be em-ployedunalteredformoltenmetallicsolutions,as wehavealreadylearnt.The closerstudyof thephenomenaoffreezingand trans-formation ofalloyshas shown that Roozeboom's views on theformationandtransformationof mixedcrystalsmust be invokedinexplanation.Tothisinvestigatorweoweasystemwhich firstmadeitpossibleforustoperceiveandinterpretthe transforma-tionphenomenaof thehighly importanttechnicalalloys (iron-carbon, brass, bronze).In the theoreticaldevelopment,he setoutfromthestand-pointofGibbs'PhaseRule,withwhichso farasconcernsourpurpose,wewill first ofalloccupyourselves.ImagineinFig.35wehavetwomoltenmetals,oneabovetheBAd-x)tyBu.FIG.35.FIG.36.otheraccordingtotheirspecific gravities.If,as anexample,Ais leadand Biron,nochangetakesplacein thesystem,as bothmetals arecompletelyinsoluble in one another.If,on thecontrary,bothmetalspossessa certainsolubilitythe one for theother,thephenomenonof diffusionbegins^asforexampleinthesystemlead-bismuth. Adiffuses intothemetal,inspiteofitsdensity,whilstaportionofBpassesinto A. If thispheno-menonlastslong enoughfor both metals to berdissolvedcom-pletelyin eachother,sothat ateverypointof the volume abedthecompositionisequal,the metals are said topossess perfectsolubilityforeachother.Frequentlyhowevertheprocessis suchthatonlya certain amount ofBpassesinto A and ofA intoB. Inthiscasebothmetalspossessa limitedsolubilityfor oneanother.SupposethatfromA, xparts passintoB,andfromB,ypartsinto A;afurtheralterationofthe contents does not takeplacesolongas bothresultingmixtures are in contact. TheTHEPHASERULE47compositionof the twosolutions is nowA(ix)4-yBand B(i-y)+*A(Fig. 36).Inthelanguageofthephaserule the variouscomplexesaredesignatedas follows :Themetals Aand Bare thecomponentsofthesystemabed,that is tosay,those constituents of thesystemwhich remainchemicallyunaltered- underthegivencircumstances.The solutionsA(Ix)+yBandB(iy)+ xA are calledphasesythat is tosay,those constituents ofthesystemwhich canbeseparatedfrom each otherby physicalmeans. In the caseunderconsiderationbothphasesareliquid ;theycould thus beseparatedbyskimmingoffthespecificallylighterone. Wehavesupposedthatassoonasthegivencompositionofthe twophasesisreached,furtherchangesare excluded;this isexpressed bysayingthatphaseI is inequilibriumwithphaseII. Thisequi-libriumcanbedestroyedbyvarious means.If,forexample,thesystemis heated to anothertemperature /,thecompositionofbothphasesalters untilequilibriumcorrespondingtothetempera-ture/is reached. Thenewconcentrationsmaybe called I' andII'.GenerallythesolubilityofthecomponentsAand Bforeachotherincreaseswiththetemperature,untilfinallyat somegivenmoment thecompositionof bothphasesis thesame,and thesystemthereforeconsistsof onephaseonly.A further factor which influences thecompositionof thephaseswhich are inequilibriumis thepressureon thesystem.Asthishoweveris constantin allphenomenato beconsideredinthesequelandequalto oneatmosphere,itmaybe left out ofconsideration.Nowtherearecertain relations between the number ofcom-ponentsandphases,thetemperatureand thepressure,whichmustbesatisfied inorderthatthesystemmaybe inequilibrium.Thephaseruleexplainstheserelations. Atthispointit mustbeclearlysetdownthatthephaseruleonlyexplainsthequalitativeandnotthequantitativeconditions. It is thereforeonlyofvaluewhenperfectequilibriumis reached;thephaserule hasnothingtosayaboutuncompletedreactions and theproducts resultingtherefrom. Nowthe materialsemployedfor technicalpurposesare for the mostpart productswhichcorrespondto such in-completedreactions. The soleapplicabilityof thephaseruletopracticeconsists therefore indeterminingwhetherperfect48THE PHYSICAL MIXTUREequilibriumis reached ornot,and thisis,atanyrate,importantinmanycases.Leaving pressureout ofconsideration,thephaserule statesthatF =n+i-(j>, . . . ."..... (i)where F denotesthenumber ofdegreesoffreedom,i.e."possi-bilities ofchange,"n the number ofcomponents,and thenumberofphases.Afewexampleswill makethisequationclear.1.Supposethat asystemconsists of onecomponent, pureiron,then n=r. Let the number ofphasesbe also=I,e.g.supposethe iron to becompletely liquefied,a condition whichobtainsat1700C. Thenthephaserule states^=#+1-0=1+1-1=1. .(i')Thesystemhasonedegreeoffreedom. Thatistosay,ofthefactorswhichcaninfluencethesystem, onecanbealteredwithoutproducingachangein thesystem.As it is assumed that thepressureis left outofconsideration,thetemperature onlycanexercise an influence. It is seen fromequation (i')that thetemperaturecan bechangedwithoutproducing changein thesystem.2. Let anothersystemconsistof onecomponent,pureiron,andtwophases, liquidandsolid iron. Thenequation (i) givesF=i+i-2=o,thatis,thenumberofdegreesof freedom is o. There is there-foreonlyonesingle temperatureat whichsolidandliquidironcanco-existinequilibriumthemelting-pointofiron.3.Asystemof twocomponents,tin andlead,consistsof onephase,theliquidmelt. Then/7=72+I_0=2+I-1=2.Thesystemcan therefore be altered in twowayswithoutdestroyingtheequilibrium. Temperatureand concentrationcantherefore have different values and thesystemwill consist asbeforeofonephase.4.The samesystemconsists of twophases, liquidmeltandseparatedleadcrystals.Then F=I. Thatis tosay,eitherthetemperatureortheconcentrationcan besuitablychosen. If thetemperature,forinstance,is chosen=250 C.,the onedegreeofAPPLICATIONS OF THE PHASE RULE49freedomhasbeenmadeuseof,andthecorrespondingconcentra-tion is therefore determined. Inpointoffact,onlythesystem65 percent, leadand35 percent, tin can consist at250C. ofsolid lead and molten solution.Everyothersystemat thatparticulartemperatureis eitherperfectlysolidorperfectly liquid.5.Thesamesystemconsists ofthreephases,solidlead,solidtin,andliquidmelt. Here F=o. Thereis thereforeonlyonedefinitetemperatureand concentration atwhich thissystemispossible. Experienceshows thatonlythe eutectic mixture(32percent, leadand68percent,tin)canexistalongwiththeliquidmeltat 180 C.6.Supposethatthemetallographic investigationof asectionshows thephases, pureiron,pure carbon,and iron carbide atvarioustemperatures.Thephaserule teaches that thissystemisonlypossibleatoneparticular temperature.But asexperienceshows that thesystem (grey iron)iscapableof existence atverydifferenttemperatures,adisagreementbetween law and actual factapparentlyoccurs in this case. Thedifficultyiseasilyremoved,since thephaseruledoes notapplyto thesystemunder con-sideration for it is notin astateof(stable)equilibrium ;that is tosay,all thechangeswhich should have takenplacehave eithernotdonesoorhavenotproceededtocompletion.Theselawsapplyequallyto solid as toliquidmixtures. Ashas beenexperimentallydemonstratedbyRoberts-Austen1forthesystemgold,lead, etc.,solid metalsandmetalloidscan diffuseinto one another. The diffusion of carbon into solid iron isturnedtoaccounttechnicallyin thecementationprocess.Forasurveyofthesolubility relationshipsof twocomponentsat differenttemperatures, graphic representation maywithadvantagebeemployed.LetAB,Fig. 37,denote thesystemoftwo metals A and B. Eachpointon this linerepresentsadefinitealloyof the twocomponents; thus,forexample,Crepresentsamixtureof A Cpercent, of the metal Band CBpercent, of thebodyA. If nowthe twoliquid layerssketched inFig. 36areanalyzedfor eachtemperature,it results forinstance,that at thetemperaturet=AH,onelayerconsists ofHFper1Roberts-Austen,Phil. Trans.RoyalSoc.,1896, CLXXXVII,p. 383.ETHE PHYSICAL MIXTUREHcent, of BandFIpercent, of A,theotherof HGpercent, ofBand GIpercent, of A.EmployinginFig. 37ordinates fortemperaturesandabscissae for thecompositionsof thephases,acurveCFDGEisobtained,thesolubiltycurveofthesystemAB.To learn thecompositionof the differentliquid phasesof thesystemat agiven temperature,it isonly necessaryto draw ahorizontal line ataheight^/^correspondingto thetemperaturet. Thepointsofintersection, FandG,of the latter with thesolubilitycurvegivethe desiredcompositions.It follows fromthis thatonlythesystemswhosetemperaturesandconcentrationscorrespondto the un-sectionedpartCFDGE consist of twophases,,whilst thesystems lyingin thesectionedportionconsist ofonephaseonly.Thegraphicmethod employedinFig. 37isonlysuit-able forbinarysystems,thatis,forsystemsinwhich thenumber of com-ponentsis two. Ifathird isintroduced,thesystemof tri-angularco-ordinates described in thefollowingisemployedforrepresentation.Ifany pointPbe taken in theequilateral triangleABC(Fig. 38),thesumofits distancesfromthethreesides is constantandequaltotheheightofthetriangle.ThatisPb+ pa +PC=Be[Proof:Drawthrough Pa line A'B'paralleltoAB,B'b'per-pendicularto AC\ Pdparallelto A C. From theequalityof thetrianglesPB'd and PB'a it follows that Pa=B'd. Fromtheequalityof thetriangles BB'f andcPgit follows thatPC =Bf.AlsoPb=db'. Hence-Concentration.FIG.37.BPb+Pa+ pc=db'+dB'+JB =Be.]Thuseveryalloycan berepresented byapointinside theTERNARYMIXTURESequilateral triangleABC. Thecornersof thetriangle representthepuremetalswhilst thestraightlineperpendiculartoa sidegivesthepercentageamountofthe individual metals. HencePa=amountof Apercent.Pb= BPc= CIn ordertorepresenttheequilibriumrelations of such aternarysystem graphically,supposethatthroughthe linesAB,BC andCAplanesABWU,BCWVandA CUV are drawnperpendicularto theplaneof thetriangle,whichwouldgivethe direction of thetemperatureaxes.FIG.38. Triangularco-ordinates forrepre-sentingternaryalloys.ThesolubilitycurvesDMSNE,FKTLG,and IPROHoftheseparate pairsofcomponentscan betraced out in thenewlyobtainedplanesexactlyin thesamewayasthatofFig. 37.Inside theprism ABCVWU there is now a surface whichgivesthesolubilityrelationsofthedifferentalloys,andis boundedbythe threesolubilitycurves. To determine the form of this"solubilitysurface"inside theprism, imaginethis to be cutbyhorizontalplanes.Suchasectiontakenataheight/ is showninFig.40;the shadedpartof this denotes theprovinceof thosealloyswhichat thetemperaturefconsistof onephaseonly.Ifthesolubilityrelations of suchsystemsbe determined atTHEPHYSICAL MIXTUREvarioustemperatures,thesolubility surface canbe determined withsufficientaccuracybyplacingthefiguresobtainedononeanother.Accordingtotherelativepositionsof apointwithrespectto thissurface,thecorresponding alloywill consistofoneormorephases.Thealloy A(Fig.40)forinstance,consists of thetwophasesA'andA",which are obtainedbydraw-ingalineparalleltoac;thepointsofintersectionA'and A"withtheboundinglinesgivethecomposi-L tions ofthetwophases.a PCLead-Zinc.FIG.40.The lead-zincalloys presentaninteresting exampleof metallic mixtures whosesolubilityinthe molten condition ismarkedlyvariable.Accordingto the000900CLASSIFICATION OFALLOYS53whilst it decreases withfalling temperature.The conditionsgoverningthis aregraphicallyshown inFig. 41.After theexplanationonp. 50thisdiagramis clear without furtherdescription ;allalloysabove the line ABCconsist of a homo-geneous liquidmass whichseparates,however,into twolayersas soon as thetemperaturefalls belowABC. Amelt with30percent, of lead and70 percent, ofzinc,shown at700C.bythepointJ/,consists of twolayers,one of which contains8percent, of lead and92 percent, ofzinc,the other 81percent, lead and19 percent. zinc. If the two metalsseparateentirelyfromoneanother above thefreezing-point,thefreezing-pointcurveof the lead-zincalloyswill consistof two horizontalstraightlinesonly,whichbeginat themelting-pointsof the twometals.It ispossiblenowto divide thelargenumberofalloysintogroupsaccordingtotheconditionsdeterminingtheir existence inthesolidcondition.Binaryandternaryalloysonlywill becon-sideredhere. Thesystemswithmorethanthreecomponents,onaccount of theirpossible complications,areverydifficult,andhave still beeninvestigatedlittle or not at all. Thefollowingclassification will betaken.I.Binary Alloys.A. Nochemicalcompoundsofthetwocomponentsexist.1. Thetwocomponentsformacontinuous series ofsolidsolutions.(Theyarecompletelysoluble in eachother.)2. Thetwocomponentsformamechanical mixtureaftersolidification.(Theyareperfectlyinsoluble in eachother.)3. Thetwocomponentsarepartlysoluble in eachother;thealloyafter solidification consistsofsolid solutionsormechanicalmixturesofsolid solutions.B. Thetwocomponentsformone or severalcompoundswitheachother.1. Thecompoundsarewhollyorpartlysoluble in thecomponentsorin oneanother.2. Thecompoundsarecompletelyinsoluble,reciprocallyas well as in thecomponents.54THE PHYSICAL MIXTUREII.Ternary Alloys.Thepossibilitiesof the differentgroupsis indicatedbythesubdivisiongivenunder I. without furtherdescription.It canbeseenthatthenumberofgroupsthusobtainable isverylarge,sinceherealsothere is thepossibilityofdefinitecompounds,andtheperfectorimperfectsolubilityof all thecomponentsin eachother and in theircompounds.Indeed the case in which aternary alloyabc can containonlythreecompoundsab, ac, be,givesanimmeasurablenumberofdifferentpossiblecombinations.On this accountonlyaveryfewsimplecases have beenstudieduptonow,in which the threecomponentsform no chemicalcompoundamongstthemselvesandareperfectlyinsoluble in oneanother.I. THEBINARY ALLOYS.A. Thecomponents formnochemicalcompoundivith each other.i. The twocomponentsform a continuous series of solidsolutions.Thephenomenaoffreezingof thesystems comprisedunderthisheadingcorrespondto thetypeI. of Roozeboomexplainedonp. 37.Thefollowingonlyneedbeadded.AccordingtotheviewofRoozeboom,mixedcrystals separateat the commencementoffreezing,containingasmall amountofthatconstituentbywhichthemelting-pointis lowered. In con-sequencethecompletesolidification does not takeplaceat adefinitetemperaturebut extendsover alongerinterval. Nowthis is notalwaysthe case withalloys. Accordingto Roberts-Austen'sexperiments,crystals separatefrom certainalloysofthenoblemetalswhichpossess exactlythesamecompositionas thatof themother-liquoroutof whichtheyoriginate.Thisobserva-tion canperhapsbe madeto harmonizewith Roozeboom'sviewbysupposingthetemperatureinterval tobeso smallthatiteasilyescapesdirectdetermination.The structure of this class ofalloysisquite homogeneous,sinceeverypartof it has the samecomposition.If,notwith-standing,aheterogeneousstructure occurs inmanycases underthemicroscope,this is because thecrystalsfirstseparatedcannotattain aregular composition sufficiently quickly,and thus afterthefreezinghave acomposition differingfrom that of theANTIMONY-BISMUTHremainderof the mixedcrystals,avoidedbyprotractedcooling.Such occurrences arelargely622Antimony-Bismuth.The curve of -thebeginningoffreezingBiASb(Fig. 42),published byGautierlslopes continuouslybetween themelting-pointsBi,Sb of thepuremetals. Thepropertiesalso of thevariousalloysvarycontinuouslywiththecomposition.Themicroscopic investigationof theseries,pursued byCharpy2andbyHiittner and Tammann3confirmtheprogressof thefreezingof mixedcrystalsas contendedbyRoozeboom. Thatis tosay, accordingtothe rule mentionedonp.38themixedcrystalswhichseparateat firstarealways poorerinthatbodyon accountofwhosepresencethefreezing-pointislowered;in thiscase,bismuth. Torepresentthecomplete progressof thefreezingit isnecessaryto add asecond curve(showndotted inFig. 42) showingtheendofthesolidification. Ameltcontaining 50percent, ofantimonywouldbegintodepositatthepoint A, 500 C.,mixedcrystalswith Bpercent, ofantimony.Theremainingmass,poorerinantimony,wouldcool furtherwitha continualseparationofever-increasingbismuthcontents,untilfinallyatC solidification is ended. The frozenmass, however,consists ofhomogeneousmixedcrystals containing 50percent.1Gautier,"Recherchessurla fusibilitd desalliages me'talliques/'Bulle-tindelaSoc.d^Enc.p.Find,nationale, 1896.Alsoin ContributiondPetudedesalliages.Paris,ChamerotetRenouard, 1901, p. 133.2Charpy,"Etudemicroscopiquedesalliages me'talliques."Bull.Soc.(PEnc., 1897.Alsoin Contrib.dVetd.all., p.121.3Huttner undTammann,"Uber dieLegierungendesAntimons undWistnuts."Ztschr.f. anorgan. Chem., Bd., 44,s.131.TemperaturesC.sa10a,.pOi2-Da*ooooc500CTHE PHYSICAL MIXTUREofantimony,onlyin case the earliestcrystals, poorinbismuth,canenrich themselves with this metalsufficiently quicklyduringtheprocessoffreezing.This is notthecase, however,accordingto what is foundbythemicroscope. Bypolishingthesamplepartsareshownin relief whichexhibitnosharp edges;itappearsthereforethatthehardnessofthecrystalsvariescontinuouslyjustlike theircomposition.Thecrystalsstandingin reliefcorrespondtothemixedcrystals, precipitatedfirst whicharehardandrich inantimony ;to these are attached softercrystalsofgraduallyincreasingbismuth contents.By heat-tinting, brighteranddarkerparts maybe seen on such apolishedsurtace,whichgraduallyfade into one another. It isimpossible. to obtain auniformbismuthcontentbysubsequent prolonged heating,sincethevelocityofdiffusionappearstobeextraordinarilylow. How-ever,it is observed that at ahigher temperature,the softerportionsmelt and runtogetherintosmallglo-bules,whilst the hardedgesretaintheirshape.Gold-Silver.The curve of thecommencementof freez-ingofgold-silver alloysrunscontinuouslybe-tweenthemelting-pointsof the two metals.Fig. 43shows thefreezing-pointcurvepublishedbyRoberts-Austenand Kirke-Rose.1It can be seenfrom it that small amounts of silver lower thefreezing-pointofgold only slightlyor not atall,and that themelting-pointof analloy containing 50atomspercent, of silver liesonly3C. lowerthanthatofgold.Gold-Platinum.Accordingto theresearches ofErhard andSchertel2thecurveof the initialfreezingofgold-platinum alloysrunscontinuously1Roberts-AustenandKirke-Rose;"Oncertainpropertiesofthealloysofthegold-silverseries." Chemical News87, 1903, p.2.2ErhardandSchertel,"JahrbuchfurBerg-undHiittenwesenSachsen,"s.17-10 20 30 f-0 SO 60 70 80 90Percentagesof silverbyweight.tooFIG.43. Freezingcurveofgold-silveralloys.(Roberts-AustenandKirke-Rose.)IRON-MANGANESE57and almostin astraightline between thefreezing-pointsof thepuremetals,asshowninFig. 44.1800177517001600d1500

3 JVOO1300Q,I 1200h11001000X5oTHE PHYSICAL MIXTUREthecommencementoffreezing (Fig. 45) however,hasbeendeter-minedwithcertaihty ;thatofthecompletionoffreezingcannotbe established withcertaintyfrom thecoolingcurves. In thiscaseagain,therate atwhichthe firstprecipitatedmixedcrystals,poorerinmanganese,absorbmanganesefrom the fluid mother-liquorricher inmanganese,is so slow that thetemperaturefallstooquicklyand acomplete equilibriumcannot be established.Correspondingly,the frozenalloysdonotexhibitahomogeneousstructure,butanaggregationofmixedcrystalsofdifferingcom-positions.Alongerannealingof theheterogeneousmass,how-ever,bringsaboutanequalizationofthecomposition.2. The twocomponentsform a mechanical mixture aftersolidification.Thefreezingcurveofthisgroupofalloys correspondsto theFIG.47.typeVaofRoozeboom'sclassification. InFig. 46, therefore,accorrespondsto theseparationof onepureconstituentA,be tothatoftheotherB,anddeto theeutecticAB.The structure of thesealloysshows eithercrystalsofA-feutectic,eutecticonly,orcrystalsof B4-eutectic. In thedescriptionof themicro-photographs,care is taken to estimatetheareasoccupiedbythedifferentconstituentsaspercentagesofthetotal surface. This is doneas follows. InFig.46letA C =mrepresentthepercentageamount ofB in the eutectic. Theareasoccupiedby Aandtheeutectic in aplanesectionthroughanalloycontainingnpercent, of Barecalculatedas follows.Letxbe the surfaceoccupied bythe constituentA,ythatoccupiedbytheeutectic,bothbeing expressedinpercentagesofthetotal sectional area. Thenwehave first :x +y=100(i)AMOUNTOFCOMPONENTS OFBINARYALLOYS59Further,the Z?-contentsofthe eutectic must beequalto thetotal ^-contents of thealloy,since the constituent Aalreadyseparatedisentirelyfree fromB;thus :y.mIOO~From(i)and(2)wehave=n .(2)IOOIOO,=(m n)mloonIf wesuppose,as is thecase inFigs.46and47that thealloycontains20percent, ofB,theeutectic40percent, of B,thenwillx=50y=sothatis,theareasoccupiedbythetwoconstituentsareequal.Inorder toperceiveat aglancethe areaoccupied byeachconstituent in awholeseries,thegraphicrepresentationintroducedbySauveur1isadvantageouslyemployed.InFig. 47uponthe line ab the ^-contents of thealloyareplottedandupontheabscissaad thecompositionofthestructureinpercentagesof the total area. At the eutecticpointCthemass consistsentirelyofeutectic,thatis,100percent, of thesurface isoccupiedbytheeutectic mixture;atthepointsaandbthe structure showspuremetalsonly,thatis,the mass of theeutectic=opercent. The course of the line aCb indicatestherefore thatpartoftherectangleabed in which the eutecticappears.Theamountofthelatter is foundbydrawingaverticallinethroughthepointin theabscissacorrespondingto thealloy.(Thedottedline ofFig. 47).Thepartsinto which this line isdividedgivethepercentagesof the surfaceoccupied byeutecticand Arespectively.It is seen that in the case of theexamplechosen,i.e. analloywith20percent, ofB,theintercepted partsonthe vertical line areequal ;thatis,thealloyconsists of50percent, of Aand50percent, ofeutectic.Ontheotherhand,if theproportionof the surfaceoccupiedbyasingleconstituent isknown,thecompositionof thealloymaybe deduced therefrom. Theequations (i)and(2)would1A.Sauveur,TheMetaUographist,vol. i.60 THE PHYSICAL MIXTUREserve for this calculation withthe differenceonlythat xandyareknown,andn is unknown.Fortheexperimentaldetermination of theportion occupiedby asingleconstituentaplanimeterisused,as differentinvestigators,viz.Sauveur,Heynand Benedicks havesuggested.To reduce the errors ofreadingto assmall an amount aspossible,it is advis-able totrace round theseparatefields inonejourney,and inpassingfrom one toanother,to follow the same linegoingandreturning.InFig. 48the coursewhichthetracing pointof theplanimetershould follow is indicatedbyarrows,AFIG.48.beingthesupposedstarting point.Antimony-Lead.Thefreezing-pointcurveofantimonyleadalloys reproducedinFig.49waspublished byRoland-Gosselin.1It follows fromTemperatureC.fvjCwLEAD-TIN 61investigation,pursued byCharpy,1isinagreement withthethermalresearch.Alloyswith less than 13 percent, ofantimonyconsistofleadcrystalsembeddedin eutectic;if theantimonycontentsexceed the eutecticcomposition,freeantimony crystals appear,surroundedbyeutectic. Nitricandhydrochloricacids are to berecommended asetchingmedia,the lattercolouringthe leadwhite.Lead-Tin.AccordingtotheinvestigationsofGuthrie,2Roberts-Austen,3andothers,thelead-tinalloysyieldthefreezingcurve(Roberts-Austen)reproducedinFig. 50.The eutectic consists of70 percent, oftin and30percent,oflead. Itsfreez-ing-pointis 1 80 C.Hypo-eutectic alloys,thatis,those contain-ingless than70 percent, oftin,are com-posedof leadcrystals330. 326300250200Pb10 20 30 tO 50 60 70 80 90 100Percentagesoftinby weight.FIG.50.- -Freezingpointcurveoflead-tinalloys.(Guthrie.)surroundedbyeutec-tic; hyper-eutecticalloysconsist of tincrystalswhich lie in theeutectic.Microscopic investigationisbyno meanseasy,asthealloysare difficult topolishonaccount of their softness. Assistance isaffordedbypouringthemoltenalloyuponapolishedsteelplate(oritsequivalent)andetchingtheplanesurface so obtaineddirectly. AccordingtoCharpy's4experiments,hydrochloricandnitric acidsaretoberecommended for thispurpose.The sameobserver found that the structuresagreed perfectlywith therequirementsofthefreezing-pointcurve.temperaturesgivenbytheauthorsarereproducedunchanged.Itappearedunnecessaryto correct the numbersbytheair-thermometer,since noassurance of thepurityof theoriginalmaterials wasgivenin the olderexperiments.1G.Charpy,"Etudemicroscopiquedesalliages me'talliques."Contri-bution aPetudedesalliages 1901, p. 107. Paris,Chamerotet Renouard.2Guthrie,"On Eutexia."Philosophical Magazine,vol. XVII.1884,p. 462.3Roberts-Austen, Engineering, 1897, 63, p. 223.4Charpy,"Etudemicroscopiquedesalliages me'talliques."Bull. Soc.(PEnc,, 1897.Contribution aVetudedesalliages, 1901, p.121.62 THE PHYSICAL MIXTURECadmium-ZincThetwometalscrystallizeoutpure,sidebyside,asFig. 51,thefreezingcurveplotted accordingto the researches of H.Gautier,1shows. Thephysical propertiesofthealloyslie betweenthoseofthecomponents.The horizontal eutectic line is drawninFig. 51fromoto 100percent. zinc.HeycockandNeville,250020010 20 30 40 50 60 70Percentagesofzincbyweight.FIG.51. Freezingcurveofcadmium-zincalloys. (G90Gautier.)100however,who also made thermalinvestigationsof thissystem,wereableto tracetheeutectic line between about24and50percent, zinconly,sothat it isquitepossiblethat zinc andcadmiummightformacontinuousseries of mixedcrystals.Ofthispointfurthersupplementaryinvestigationsmustbemade.Lead-Silver.Thefreezing-pointcurveof lead-silveralloys,determinedbyHeycockandNeville,3isreproducedinFig. 52.This shows aeutecticpoint Bat aweight percentageof96lead and4silver.The branchAgB,whichcorrespondsto theseparationofpuresilverfromthemelt,bendsmarkedly.This isexplainedon thesuppositionthatthemolecularvolumeofthedissolvedleadvarieswiththeconcentration. Itispossiblehoweverthatthe lead-silveralloysstanduponthedividingline between thealloyswhichareperfectlymiscibleandthosewhichareimperfectlymiscible in theliquidstate. In fact the latteralwaysshow a more or less1H.Gautier,"Recherches sur la fusibilite* desalliages me'talliques."ContributionaVetudedesalliages, 1901, p. 93.2T.HeycockandH.Neville,"Thefreezing-pointsofalloyscontainingzincandanothermetal."Journalofthe ChemicalSociety, 1897, I., p. 383.3HeycockandNeville,"Complete freezing-pointcurves ofbinaryalloys." PhilosophicalTransactions, 1897, iSgA., p. 137.SILVER-TIN63extendedhorizontalpartin oneof thebranches. Adiptowardsthe horizontal which is seen onAgBinFig. 52would thusindicateaslightseparationalreadyin the fluidcondition. Whichofthetwoexplanationsholdsgoodforthis case is still undecidedSilver- Tin.Thefreezing-pointcurves,Figs. 53and54,drawnup byGautier1andHeycockand Neville2showthat the branchlyingon the side of the silver is notstraight,but runs in a curve.959900800700600500too30064PHYSICAL MIXTUREwithcertaintyfrom thefreezing-pointcurve.Behrens,1from ametallographicexaminationof aseries of silver-tinalloys,comesto theconclusionthat silverandtin enterinto thefollowingcom-binationswitheachother :Ag6Sn,Ag4Sn,Ag3Sn,Ag2Sn, AgSn, Ag2Sn3,AgSn2.Behrensbases hisconclusion on the fact that all these meltsconsist ofhomogeneous crystal conglomerates,but it must beTemperatureC.sss.8saB8BISMUTH-TIN65silver. From themicroscopicresearches ofCharpy,it followsthat allalloys upto65 percent, of silver show eutectic.Thiswouldcorrespondto thecompound Ag2Sn,which can there-TemperatureC.IS111166 THE PHYSICAL MIXTUREZinc- Tin.Fig. 56shows thefreezing-point diagramof zinc-tinalloys,accordingto the determinations ofHeycockand Neville.1' 2Compositionof theMB400300232200100FIGCOPPER-SILVER67Kirke-Rose.1The eutecticpointlies at 82percent,goldand905C.IKUU0080060040030068 THE PHYSICAL MIXTUREFIG.59. Freezing-pointcurveoftypeV. offreezing. (Roozeboom.)3.Thetwocomponentsarepartiallysoluble in eachother;thealloyconsists,afterfreezing,of solid solutions ormechanicalmixturesofsolid solutions.Accordingto the theoreticaldevelopment by Roozeboom,thesealloys correspondtotypeV. offreezing.In thediagramFig. 59 therefore,ACBf(Bcorrespondstothebegin-ningoffreezing,whenmixedcrystalsof thecompositions AD, BE,separatefrom solutionsof thecomposition AC,CB.Alloyslying betweenDand Edepositat fC.a eutecticconsistingofmixedcrystalsDandE.DFandEGcorrespondto thechangesin concentrationduringfurthercooling,fromwhichfinallythe mixedcrystalsFandGresult. In a mannerquite analogousto what was seen in the case of thealloysofgroup2(see p. 58),thecompositionof the structuremaybedetermined. InFig.60afihrepresentsthe domain of existenceofhomogeneousmixedcrystalsofchangingcomposition. Alloyslyingbetweenfandgare amixture of"limit-crystals"F and Gand eutectic. Analloyforexamplecontain-ing 40 percent, ofBcon-sists of70 partsof eutecticand30 partsof"limit-crystals"F.Theexperimentaldeter-minationoftheareasoccupiedbythedifferent constituentscanbemadebymeansofaplanimeterin themannerdescribedonp.60.Aluminum-Zinc.The curve of the commencement of thefreezingof thealuminium-zincalloys,establishedby Roland-Gosselin,1showed1H.Gautier,"Recherches sur la fusibilite desalliages mdtalliques."Bull. Soc. d'Enc. pourI Ind. nat, 1896Also in ContributiondVetudedesalliages, 1501, p. 133.FIG. 60.ALUMINIUM-ZINC 69that it consistedoftwobranchesintersectingat anangle.LaterresearchesbyHeycockandNeville,1andparticularly Shepherd,2provedthat on the one hand the eutectic line vanished at acertainaluminiumcontent,butalsoontheother,thatthestructureofmanyaluminium-zincalloyswasentirelyhomogeneous. Fig.61 shows thefreezing-point diagram (Zustandsdiagram) repro-duced from the researches ofShepherd.From this it followsthatabovetheoutlineZnAAl,thealloysarehomogeneousfluids.IntheregionZnAamixedcrystalsofthecompositionZnaexistinequilibriumwithmoltenalloyZnA. In like mannerprimaryaluminiumcrystalsco-exist in theregionAAlb with moltenalloy A/A. At the tem-peratureofthestraightline aAb the eutecticmixture of mixedcrystalsof the com-positiona with those700coo5003rt t25tooE9I-30020065010020 to 60 80Percentagesofaluminium.FIG. 61.Freezing-pointcurveof aluminium-zincalloys. (Shepherd.)ofcompositionbsepa-rates out. Themutualsolubilityof the twometalschangesto someextent withfallingtemperature,corre-spondingto the linesadand be.AccordingtoFig6 1therefore,thefollowing phasesexist in the differentdomainsZnade: mixedcrystals Zn(Al),aAbed: mixedcrystals Zn(Al)+Al(Zn),cbAlf:mixedcrystals Al(Zn).Themicroscopic investigationof the aluminium-zincalloysby Charpy3andShepherdshowscomplete agreementwith the1HeycockandNeville,"Thefreezing-pointsofalloys containingzincandanothermetal."JournaloftheChemicalSociety, 71, 1897, p. 383.2E. S.Shepherd,"Aluminium-ZincAlloys." Journal ofPhysicalChemistry, 1905, 9, p. 504;alsoMetallurgie, 1905, p.86.3Charpy,"Etudemicroscopiquedesalliages me'talliques."Bull. Soc.897.Alsoin Contr.dFettided.AIL,p. 13.70THE PHYSICAL MIXTUREindications of thediagram,sinceonlythealloysbetween4 percent, and45 percent, ofaluminium consist of two constituents.Fordevelopingthe structurepotashsolution isrecommended,whichtints thealuminiumdark.Gold-Nickel.Thediagramofthegold-nickel alloys, reproducedinFig.62fromtheresearches ofLevin,1shows that the two metals formmixedcrystals,theseries of which isinterrupted byagap. Accordingtothe views of Rooze-boom,thefreezingwould therefore runas follows.At thetempera-tureofthe lineAuAmixedcrystalsbegintoseparate,thecom-positionof whichwould begiven bythe line(showndotted) runningsomewhat likeAuB.The latter like NICcould not and hasnotyetbeen deter-minedwithcertainty.This is becausethemixedcrystalsfirstseparatedreactwith theremainingmasstooslowly. Equilibriuminconsequenceis notattained.Correspondingly,it is found that the micro-structureof the mixedcrystalsis nothomogeneous,butcontinuouslyvariable.Byaprolonged exposureto ahigh temperature,anequalizationof thecompositionof the frozen mass takesplace.160015001fOOd1300o\1120011001064-1000annCOMPOUNDS OF TWOMETALSB. The twocomponents formone orseveral chemicalcompoundswitheachother.I. Thecompoundsare ascompletelyinsoluble in the com-ponentsas in eachother.Inorderthatanalloyof twocomponents maybe referred toas a chemicalcompoundthefollowing stipulations,with theexceptionofacasetobediscussedlater,mustbefulfilled :(a)Thealloymustfreezecompletelyat a definitetempera-ture which remains constantduringthe interval ofcrystallization.(b)Theproportionsin which thecomponentsoccur must beconstant andstochiometric,i.e. wholemultiplesof theatomicweights.(c)The structure of thefrozenalloycanshowonlyoneconstituent.The theoretical deduc-tions from the differentpossiblekindsoffreezingofRoozeboom show that thesystemsoftwocomponentspossesstwofreezing-points,FIG.63.theupper onecorrespondingtotheseparationofonepurecomponentand the second to thatofthe eutectic. Butthe eutectic mixture is theonlyonewhichpossessesa constantfreezing-pointand constantcomposition.Thusofthethreeconditionsspecifiedabove,the eutectic solutionfulfilsonlythefirst,but not those of stochiometric ratio and ofhomogeneousstructure;for this reason the eutecticalloysmustnotbeconsideredascompounds,asfrequentlyoccurred earlier.The existence of a definitecompoundwill nevertheless beexhibitedonthefreezing-pointcurve.ImaginetwocomponentsA andBwhich form a definite chemicalcompoundA^B^witheachother. Theseries ofall thepossible alloyscan be dividedinto twogroups;thosealloyswhich contain more and thosewhichcontain le'ss ofthe constituent Bthancorrespondsto thepurecompound.Let us first consider the first of these twogroups.ItsTHEPHYSICAL MIXTUREfreezing-pointcurve canhave,forexample,the form shown inFig. 63: Acorrespondsto themelting-pointof one of thepurecomponents Aandbytheadditionof A%B3willbedepressed downQto the eutectictemperatureE.A2B3is themelting-pointof AzB3,which on itspartis likewisedepressedtowards Ebythepresencee'e't'of A.FinallyeEe is thelineoftheeutecticA,A^B3.In a similarmanner,thefreezing-pointcurve of thesecond class can bedrawn(Fig. 64).In this case aeutecticB^A^B^appearswhichfreezes at thetemperaturet'. Ifnow,thesetwofreezingcurves,Figs. 63and64,be combined inFIG.64.one,acomplete freezing-pointcurve of thesystemis obtained(Fig. 65).Inthis,thereforeAEcorrespondstotheseparationof thepure component A;EA^BzE'compound A2B3 ;E'Bpure componentB;COMPOUNDS OF TWOMETALS73eecorrespondstotheseparationoftheeutecticA,A2B3 ;e'e' eutecticB,A2B3.Fig.66showstheproportionsofthe different constituents ofthestructure. Fromthis it follows thatalloysbetweenaandb consistofpure component^andeutecticyi,A^B3 ;b ccompoundA^B3andeutecticA,A2B3 ;c dcompoundA^B3andeutecticdcomponent.5andeutectica c dFIG. 66.In theexperimentalestablishment of such afreezing-pointcurve,difficulties arefrequentlyencountered which militateagainsttheexactdeterminationofthesingle points.Tammann1is to be thanked for the introduction of certain methods ofinvestigationto over-come these diffi-culties.AccordingtoFig.66,thealloys betweena and b contain anincreasingamountofeutectic. Asit mustbe assumed that theamounts of heatdevelopedonfreezingareproportionalto theweightsof theseparated eutectic,so also thetime, duringwhichthetempera-ture remains constant on the formation of theeutectic,willalso beproportionalto theseweights.At thecompositions#, c,and e the amount of theseparatedeutectic is nil. Thecoolingcurves of thesealloyswill therefore exhibit no eutecticpoint.Atthecompositionsband''/?Theproportion-=-=-/..=concentration=C.x-\-ytotal massofalloyThisgivesforequation (i)z;=fi+(z;a-Vl)C1. .. . .(i')Thatis tosay,thespecificvolume ofthealloyis alinearfunctionoftheconcentration.If thealloyconsiststhereforeof thetwo constituents AandA%B&then thespecificvolume isrepresented byastraightlinehg;this is thecasewith allalloysbetweenaand/.Between/and b thealloysconsistof thecomponentsA2B3and B;thespecificvolumesof these are alsorepresented byastraightlinegi.Theinclinationsof the two lineshgandgito the horizontal aredifferent,sincetheyaredependentuponz/2, z/i,and v.Quitethesame considerations are involved when insteadoftheonemaximum, A2I>3,severalsuchoccur,thatis,whenseveralcompoundsof thetwocomponentsexist. Thetin-sodiumalloys2presentacase inpoint.Toobtainarapidsurveyofthestructureofthedifferentalloysof agiven system,adiagramshowingtheprevailingconditions(Zustandsdiagram)shouldbeconstructed.Bythis is understoodafiguredividedbylines intoseparatedomainsof which eachcontainsadefinitegroupofphases.Theupper limitingline ofsuchadiagramwill be in all cases the curveof the commence-mentoffreezing,since for the onephase,fluidmelt,asecond,solidcrystals, beginstomakeitsappearance (forinstanceFig.61,P.69).'Seep. 73."Seep.'8i.LEAD-MA GNESIUM75Lead-Magnesium.Thediagramof thelead-magnesium alloys,constructedbyGrube,1isreproducedinFig. 67.It follows from this that thetwo metals enter into chemical combination with one anotheraccordingtotheformulaPbMg2correspondingto the maximum700 r650-9Pb326.9Pb+LiquidPb+EutechcPbPbMg21501020 IQO 30 40 50 60 70 80Percentagesof leadby weight.FIG.67. Diagram(Zustandsdiagram)ofthe lead-magnesiumalloys (Grube).C. Thephasescorrespondingtotheseparatefields areindicatedin thediagram.Themetallographicresearch,alsoconductedbyGrube,of thelead-magnesium alloys, yielded perfect agreementwith thediagramofFig. 67.Asimple exposureto moistair,which atonce attacks the cutsurface,suffices to render the structurediscernible.1G.Grube,"UberMagnesium-Bleilegierungen."Zeitschriftf. anorgChemie, 1905,Bd.44,s.117.THE PHYSICAL MIXTUREMagnesium-Tin.Acomplete diagramfor themagnesium-tin alloyswaspro-ducedbyG. Grube.1InFig. 6/A, MgABCSnis the curveof the commencementoffreezing,whichhasat AandC two eutecticpointsandat Baroo650,9600500400300200100NICKEL-TIN77I. Theregionabove MgABCSn homogeneousliquidalloy.II.MgAd primarymagnesiumcrystals-f-fluid;ABejBCprimarySnMg2crystals+fluid;CSnkprimarytincrystals-ffluid.140013001200tlOO1000900aoa700600500too3002322001450Ni20 30 40 50 6070 60Percentagesofcopper by weight.100FIG. 68.Freezing-pointdiagramofthe nickel-tinalloys (Gautier). ]III.dAgf primarymagnesium crystals+eutectic A(61percent.Al,39percent.Sn) ;gAeh primary Mg2Sncrystals-feutectic AiClhprimaryMg2Sncrystals +eutecticCCkmlprimarytincrystals+eutectic C.Nickel- Tin.TinandnickelformthecompoundNi3Sn2,as is seenfromthefreezing-pointcurveofFig.68,plottedfromthedeterminationsofGautier.1Thetwoeutecticmixturesfreezeat231C. and 1160 C.1Seep. 60,footnote i.78THE PHYSICAL MIXTURETheycontain O'Oipercent, and70 percent, of nickel. Thealloyswith smallquantitiesof tin areconsiderablyharder thanpurenickel.Charpy1hasprosecutedthemicroscopic investiga-tionoftheseries andhasestablishedthe fact thatuptoabout3 5percent, ofnickel,increasingamountsof ahardcrystallinecon-stituentofthecompositionNi3Sn2appear.Antimony-Zinc.Thealloysofantimonyand zinc afford anexampleof theappearanceof severalcompoundsbetween twometals,and theTemperatureC.a09>0.Ul0)o(_rO03OJOOlOCjoocSoooocANTIMONY-ZINC79ZnA showstheseparationofzinc.ABCseparationofZn3Sb2.CDEseparationofZnSb.ESbseparationofantimony.AtthetemperaturesA, C, Etheeutectic mixturesZn3Sb2,ZnSbandSb,ZnSb650600Temperatu*msgCA) sB\>tfs630100 10 20. 30 fO SO 60 70 80 90Percentagesofantimonybylweight.FlG.70. Diagramfor theantimony-zincalloys(Monkemeyer).freeze,andcorrespondinglythedifferentantimony-zinc alloysarecompoundedas follows :Betweennand ;;/ zinc-feutecticA.Betweenmando-Zn3Sb2 -heutecticA.Betweenoand/Zn3Sb2+eutectic C.Between pandqZnSb+eutectic C.Betweenqandr ZnSb+eutectic E.Betweenrandsantimony+eutecticE.8o THE PHYSICAL MIXTURETellurium-Bismuth.Thediagramof the tellurium-bismuthalloys,drawnup byMonkemeyer,1isreproducedinFig 71.It shows thetypeoffreezingofFig. 65in itssimplestform.Thefollowingtablegivesthephases corresponding|to thedifferent fields.600560520ONa4Sn . . . .(i)Asit wasassumed that theoriginalmeltpossessesthecom-positionNa4Sn,the wholeof themother-liquorwill be usedupbythis reaction. If the melt contains less than thecompoundNa4Sndemands,mother-liquorremains after reaction(i),andfreezesthentothe eutectic atNaa. On the otherhand,withahighertin content thecompoundNa2Snis in excess in reaction(i),andinconsequencethemother-liquorisentirelyusedup,sothat below Bbb' the mass consists of a mixtureof Na2Sn andNa4Sncrystals.Thealloyof thecompositionNa2Sn freezescompletelyatthetemperatureC tohomogeneouscrystals,sothaton thecoolingcurve alongerhorizontalportionoccurs at thistemperature.Thearrest-points correspondingto the line Bbb'andNaahaveentirelydisappeared.Iftheamount oftinpresentisgreaterthancorrespondstothecompoundC and smallerthancorrespondsto thealloyD,primary crystalsof Na2SnseparatealongCD,whilstanintimatemixtureof Na2Sn and Na4Sn3pro-ceedstofreezeontheeutecticlinedDdf. DEcorrespondsto theprimary crystallizationof Na4Sn3. Now this lattercompoundpossessesatransitionpointatthetemperature y.Thecrystalsof/3-Na4Sn3changeinto a-Na4Sn3crystalswith an increase involume; indeed,the increase is soconsiderable in thecase ofthealloysricher intin,that theglassvesselwhich contains themisburst. Allalloyswhich contain thecompoundNa4Sn3musttherefore show the transitionpointin theneighbourhoodofj,whichfact is indicatedbythe line e"e"'. Theslopingdirection ofthismaypossiblybeaccountedforbyinternal stresses and con-sequentdepressionofthetransformationpoint.As alsothecompoundNa4Sn3decomposesbelowitsmelting-pointintoliquidand a kindofcrystaloftheformulaNaSn,thesamephenomenaarerepeatedas intheformationof Na4Sn;thatSODIUM-TIN83is tosay,at thetemperatureofthehorizontalEee1thefollowingreaction takesplace:NaSn+liquid -> Na4Sn3....(2)Analloylyingbetween Eand F wouldthereforefreezeasfollows.Onthebranch EFprimarycrystalsofj3-NaSnseparate.Thesehave a transitionpointatfff\at whichtheyare transformedintothea-modification.Finally these aNaSncrystalsarechangedat Eeeaccordingtoequation(2).Theresulting compound jS-Na^Snachangesate"e"intothe a-modification.Further,thecompoundNaSn2separates primarilyonlyalongGH.GG'ggivesthetemperatureatwhichthecompoundNaSn2resultsfromNaSncrystalsandliquid,andaccordingtothefollow-ingequation:NaSn-fliquid -> NaSn2(3)NaSn2is transformed atg'"g"g'into anallotropicmodification.HSnfinallycorrespondsto theprimaryseparationoftin,h'h tothatofthe eutecticNaSn2,Sn.It is notalways possible,however,to deduce the existenceof a chemicalcompoundfromthecollectivearrangementof thecriticalpointsof anumber ofalloys.This isespeciallydifficultwhenthecompound decomposesbefore it melts. Inmostcases,nevertheless,theformulaofthecompoundis arrivedatbyasuit-ableinterpretationof thecooling phenomena,andby metallographicinvestigation,asTammann1hasshownin aningeniousmanner.Fig. 73showsthefreezing-pointcurveofthesystemA,B.acirepresentstheseparationof thecomponentA,compound Am Bn,componenteutecticA,AmBformeutectic AmBn,B.eutectc, mn,formationofAmBnandseparationof theThe two bodies A and Bmayform thecompoundAmBnwithone another. Thismay,however,onlybe stablebelowthetemperature/2 ,itsmelting-point,thatis, whenthepurecompound1G.Tammann,"UberdieAnwendungderthermischenAnalyseinabnor-menFallen."Zeitschriftf. anorg. Chemie, 1905,Bd.45,s.24.84THEPHYSICAL MIXTUREisheated,it will notmelttoahomogeneousliquidbutdecomposeatthetemperature/2accordingtotheequation-a)B +mA] (i)intocrystalsofthebody Band aliquid (^ a) B+mA. Con-versely,ifthesystemaB-f- \(n a) B +w^4