材料科學(xué)基礎(chǔ)輔導(dǎo)與習(xí)題-上交課件 06ch2-2

§2-2參考書盧光熙等，金屬學(xué)教程，上?？茖W(xué)技術(shù)出版社，1985

胡賡祥等，金屬學(xué)，上?？茖W(xué)技術(shù)出版社，1980

[美]約翰.D.費豪文，物理冶金學(xué)基礎(chǔ)，上海科學(xué)技術(shù)出版社，1980

石德珂等，材料科學(xué)基礎(chǔ)，機械工業(yè)出版社，1999潘金生等，材料科學(xué)基礎(chǔ)，清華大學(xué)出版社，1995

1§2-2元素的晶體結(jié)構(gòu)1.周期表中的元素分類2.典型金屬的晶體結(jié)構(gòu)3.晶體中原子的堆垛方式4.晶體結(jié)構(gòu)中的間隙5.金屬原子半徑6.亞金屬的晶體結(jié)構(gòu)21.周期表中的元素分類ⅠBⅡBⅢAⅣAⅤA

BCN

Al

SiP

CuZnGaO

GeAs

Ag

CdInA6SnA4A5

Sb

Au

HgRTTlA2A3PbA1

BiA7

Zn、Cd雖為A3結(jié)構(gòu)，但其c/a較大;Tl和Pb的結(jié)構(gòu)和第一類相同，但原子的離子化不完全，原子間距也比典型金屬大;Hg和Sn的結(jié)構(gòu)比較復(fù)雜;而Ga則具有復(fù)雜的正交結(jié)構(gòu)。

31.1第一類為真正的金屬包括ⅠB族及其以左元素,另外還有ⅢA族的Al元素。它們絕大多數(shù)都具有高對稱性的簡單結(jié)構(gòu)，其典型結(jié)構(gòu)為:面心立方結(jié)構(gòu)(代號為A1)；體心立方結(jié)構(gòu)(A2)；密排六方結(jié)構(gòu)(A3)。1.2第二類為八個金屬元素1.3第三類多數(shù)為非金屬元素如硅、鍺、銻、鉍等，這類元素多數(shù)具有復(fù)雜的晶體結(jié)構(gòu),每個原子具有(8-N)個近鄰原子，N為該原子的族數(shù)。4/periodic/periodic.html52.典型金屬的晶體結(jié)構(gòu)

金屬晶體中的結(jié)合鍵是金屬鍵，由于金屬鍵沒有方向性和飽和性，使大多數(shù)金屬晶體都具有排列緊密、對稱性高的簡單晶體結(jié)構(gòu)，即A1(FCC)、A2(BCC)、

A3(HCP)晶體結(jié)構(gòu)。62.1FaceCenteredCubic(FCC)Atomsarearrangedatthecornersandcenterofeachcubefaceofthecell.Atomsareassumedtotouchalongfacediagonals72.1FaceCenteredCubic(FCC)Thelatticeparameter,a,isrelatedtotheradiusoftheatominthecellthrough:Coordinationnumber:thenumberofnearestneighborstoanyatom.ForFCCsystems,thecoordinationnumberis12.82.1FaceCenteredCubic(FCC)AtomicPackingFactor:theratioofatomicspherevolumetounitcellvolume,assumingahardspheremodel.FCCsystemshaveanAPFof0.74,themaximumpackingforasysteminwhichallsphereshaveequaldiameter.9

2.1FaceCenteredCubic(FCC)

1、Numberofatomsinunitcell

2、Theradiusoftheatom

3、Coordinationnumberandefficiencyofspacefilling

10ThecoordinationnumberforFCCsystems11DensityCalculations

Inthefcccelltheatomstouchalongthefacediagonals,butnotalongthecelledge:Lengthfacediagonal=a(2)1/2=4r

Usethisinformationtocalculatethedensityofan

fccmetal.12Examplecalculation.

Alhasaccparrangementofatoms.

TheradiusofAl=1.423?(=143.2pm).

CalculatethelatticeparameteroftheunitcellandthedensityofsolidAl(atomicweight=26.98).Solution:

BecauseAlisccpwehaveanfccunitcell.

Cellcontents:4atoms/cell

[8atcorners(each1/8),6infaces(each1/2)]Latticeparameter:

atomsincontactalongfacediagonal,therefore4rAl=a(2)1/2,a=4(1.432?)/(2)1/2=4.050?.Density(=rAl)=Mass/Volume=Massperunitcell/Volumeperunitcell

g/cm3

Massofunitcell=mass4Alatoms=(26.98)(g/mol)(1mol/6.022x1023atoms)(4atoms/unitcell)=1.792x10-22g/unitcellVolumeunitcell=a3=(4.05x10-8cm)3=66.43x10-24cm3/unitcellTherefore

rAl

={1.792x10-22g/unitcell}/{66.43x10-24cm3/unitcell}=2.698g/cm3

132.2BodyCenteredCubic

Atomsarearrangedatthecornersofthecubewithanotheratomatthecubecenter.142.2BodyCenteredCubicSinceatomsareassumedtotouchalongthecubediagonalinBCC,thelatticeparameterisrelatedtoatomicradiusthrough:152.2BodyCenteredCubicCoordinationnumberforBCCis8.Eachcenteratomissurroundedbytheeightcorneratoms.ThelowercoordinationnumberalsoresultsinaslightlylowerAPFforBCCstructures.BCChasanAPFof0.68,ratherthan0.74inFCC16

2.2BodyCenteredCubic

1、Numberofatomsinunitcell

2、Theradiusoftheatom

3、Coordinationnumberandefficiencyofspacefilling

172.3HexagonalClosePackedCellofanHCPlatticeisvisualizedasatopandbottomplaneof7atoms,formingaregularhexagonaroundacentralatom.Inbetweentheseplanesisahalf-hexagonof3atoms.HCPisaverycommontypeofstructureforelementalmetals.

ExamplesincludeBe,Mg,Ti,Zr,etc.182.3HexagonalClosePackedTherearetwolatticeparametersinHCP,aandc,representingthebasalandheightparametersrespectively.Intheidealcase,thec/aratiois1.633,however,deviationsdooccur.Thecoordinationnumberoftheatomsinthisstructureis12.

Theyhave6nearestneighborsinthesameclosepackedlayer,3inthelayeraboveand3inthelayerbelow.Thisisoneofthemostefficientmethodsofpackingspheres(theotherthatisequallyefficientiscubicclosepacking,seebelow).

Inbothcasesthespheresfill74%oftheavailablespace.19Hexagonalclose-packedcrystals:theaxialratio

Theidealaxialratio(c/a)forahexagonalclose-packedcrystalstructurecanbecalculatedbyconsideringnon-interactinghardspherespackedinanh.c.p.lattice.Ifthesphereradiusisr,thenthelatticeparametersa(=b)andccanbewrittenintermsofr:2021Thesetworelationshipscanbesolvedfortheidealaxialratioc/a:2r

=

a

={(a/2cos30°)2+(c/2)2}?a2

=

a2/3+c2/44=4/3+c2/a2c/a

=1.633ManymaterialshavethehexagonalPcrystalsystem,buttheaxialratioisrarelyideal.Cadmium,forexample,hasanaxialratioofc/a=1.886.Thisnon-idealstructurehasimplicationsforthebehaviourofthematerial,forexampleinslip.22

2.3HexagonalClosePacked

1、Numberofatomsinunitcell

2、Theradiusoftheatom

3、Coordinationnumberandefficiencyofspacefilling23

ThespacelatticeofHCP

把A、B兩個陣點作為一個陣點看待，就可看出密排六方晶體點陣實質(zhì)上就是一個復(fù)式簡單六方空間點陣。

242.4多晶型性

在周期表中,大約有40多種元素具有兩種或兩種以上的晶體結(jié)構(gòu)，即具有同素異晶性，或稱多晶型性。它們在不同的溫度或壓力范圍內(nèi)具有不同的晶體構(gòu)，故當(dāng)條件變化時，會由一種結(jié)構(gòu)轉(zhuǎn)變?yōu)榱硪环N結(jié)構(gòu)稱為多晶型性轉(zhuǎn)變或同素異構(gòu)轉(zhuǎn)變。25PolymorphismandAllotropyPolymorphismisaphysicalphenomenonwhereamaterialmayhavemorethanonecrystalstructure.Amaterialthatshowspolymorphismexistsinmorethanonetypeofspacelatticeinthesolidstate.Ifthechangeinstructureisreversible,thenthepolymorphicchangeisknownasallotropy.Theprevailingcrystalstructuredependsonboththetemperatureandtheexternalpressure.Onefamiliarexampleisfoundincarbon:graphiteisthestablepolymorphatambientconditions,whereasdiamondisformedatextremelyhighpressures.26Thebestknownexampleforallotropyisiron.Whenironcrystallizesat2800oFitisB.C.C.(d-iron),at2554oFthestructurechangestoF.C.C.(g-ironoraustenite),andat1670oFitagainbecomesB.C.C.(a-ironorferrite).Figure1.Coolingcurveforpureiron.(Allotropicbehaviorofpureiron)2728a-iron(alpha)Theothernamefora-ironisferrite.Thiscrystalhasbodycenteredcubicstructure.TheunitcellandthemicrographofthecrystalareshowninFigures(2)and(3).Figure2.Alphairon(B.C.C)unitcellFigure3.Ferritecrystals29g-iron(Gamma)Theothernameforg-ironisaustenite.Thiscrystalhasfacecenteredcubic(F.C.C)structure.TheunitcellandthemicrographofthecrystalareshowninFigures(4)and(5).Figure4.FacecenteredcubiccrystalunitcellFigure5.Austenitecrystals303.晶體中原子的堆垛方式晶體結(jié)構(gòu)配位數(shù)致密度是否密排間隙大小Fcc120.74是小Bcc80.68否大Hcp120.74是小313.晶體中原子的堆垛方式3.1晶體中原子的二維排列方式3.2晶體中密排面原子排列方式3.3空隙位置和密排面的堆積方式3.4面心立方結(jié)構(gòu)中原子的堆垛方式3.5密排六方結(jié)構(gòu)中原子的堆垛方式32ClosepackedlayersofatomsIfwetreattheatomsasspheresandconsideralltheatomsinthesolidtobeofequalsize(asisthecaseforelementalmetals),themostefficientformofpackingistheclosepackedlayer.

Thisisillustratedbelowwhereitisclearthatclose-packingofspheresismoreefficientthan,forexample,squarepacking.

333.1晶體中原子的二維排列方式Belowontheleftisasquarepackedarraycomparedtothemoredenselypackedclosepackedarray.

Withinthesquarepackedlayerthecoordination#ofeachatomis4,

intheclosepackedlayeritis6.

343.2晶體中密排面原子排列方式353.3空隙位置和密排面的堆積方式Tobuildour3-dimensionalmetalstructureswenowneedtostacktheclosepackedlayersontopofeachother.

Thereareseveralwaysofdoingthis.

Themostefficientspacesavingwayistohavethespheresinonelayerfitintothe"holes"ofthelayerbelow.

36ClosePackedStructures

EventhoughFCCandHCPareclosepackedstructures,theyarequitedifferentinthemannerofstackingtheirclosepackedplanes.ClosepackedstackinginHCPtakesplacealongthecdirection(the(0001)plane).FCCclosepackedplanesarealongthe(111).Firstplaneisvisualizedasanatomsurroundedby6nearestneighborsinbothHCPandFCC.37ClosePackedStructuresThesecondplaneinbothHCPandFCCissituatedinthe“holes”abovethefirstplaneofatoms.TwopossibleplacementsforthethirdplaneofatomsThirdplaneisplaceddirectlyabovethefirstplaneofatomsABAstacking--HCPstructureThirdplaneisplacedabovethe“holes”ofthefirstplanenotcoveredbythesecondplaneABCstacking--FCCstructure38ClosePackedStructures39SimilaritiesandDifferenceBetweenthe

FCCandHCPStructureThefacecenteredcubicandhexagonalclosepackedstructuresbothhaveapackingfactorof0.74,consistofcloselypackedplanesofatoms,andhaveacoordinationnumberof12.Thedifferencebetweenthefccandhcpisthestackingsequence.Thehcplayerscycleamongthetwoequivalentshiftedpositionswhereasthefcclayerscyclebetweenthreepositions.Ascanbeseenintheimage,thehcpstructurecontainsonlytwotypesofplaneswithanalternatingABABarrangement.Noticehowtheatomsofthethirdplaneareinexactlythesamepositionastheatomsinthefirstplane.However,thefccstructurecontainsthreetypesofplaneswithaABCABCarrangement.NoticehowtheatomsinrowsAandCarenolongeraligned.Rememberthatcubiclatticestructuresallowslippagetooccurmoreeasilythannon-cubiclattices,sohcpmetalsarenotasductileasthefccmetals.40

41Thetablebelowshowsthestableroomtemperaturecrystalstructuresforseveralelementalmetals

Ananometer(nm)equals10-9meteror10Angstromunits.42MetalCrystalStructureAtomicRadius(nm)AluminumFCC0.1431CadmiumHCP0.1490ChromiumBCC0.1249CobaltHCP0.1253CopperFCC0.1278GoldFCC0.1442Iron(Alpha)BCC0.1241LeadFCC0.1750MagnesiumHCP0.1599MolybdenumBCC0.1363NickelFCC0.1246PlatinumFCC0.1387SilverFCC0.1445TantalumBCC0.1430TitaniumAlphaHCP0.1445TungstenBCC0.1371ZincHCP0.1332433.4CubicClosePacking(CCP)WhilefortheHCPstructurethethirdclosepackedlayerwaspositionedabovethefirst,analternatemethodofstackingistoplacethethirdlayersuchthatitliesinanuniqueposition,inthiswayan"ABCABC..."

closepackedlayersequencecanbecreated,seebelow.

ThismethodofstackingiscallCubicClosePacking(ccp)44453.4CubicClosePacking(CCP)463.5HexagonalclosepackingIfwecallthefirstlayer"A",thenthesecondlayer("B")ispositionedasshownontheleftofthediagrambelow.

Thethirdlayercanthenbeaddedintwoways.

InthefirstwaythethirdlayerfitsintotheholesoftheBlayersuchthattheatomslieabovethoseinlayerA.

ByrepeatingthisarrangementoneobtainsABABAB...stackingorhexagonalclosepacking.

4748Top:Anotherlayercanbeplacedontopinoneoftwoways:overtheupward-pointinggaps(blue)orthedownward-pointinggaps(yellow).LayersBandCshowlayersinthesepositions.

Bottom:Iflayersalternate(left)orarerandomlystacked(right)theoverallstructurehasonlythehexagonalsymmetryofthe

individualsheets.ThealternatingpatterniscalledHexagonalclosepacking.Theoxygenatomsincorundumandhematitehavethispacking.494.晶體結(jié)構(gòu)中的間隙4.1面心立方結(jié)構(gòu)中的間隙4.2體心立方結(jié)構(gòu)中的間隙4.3密排六方結(jié)構(gòu)中的間隙4.4晶體結(jié)構(gòu)中各種間隙匯總504.1面心立方結(jié)構(gòu)中的間隙4.1.1FCC結(jié)構(gòu)中間隙的位置4.1.2FCC結(jié)構(gòu)中間隙的大小4.1.3FCC四面體間隙的位置與個數(shù)4.1.4FCC八面體間隙的位置與個數(shù)514.1.1FCC結(jié)構(gòu)中間隙的位置524.1.2FCC結(jié)構(gòu)中間隙的大小534.1.3FCC四面體間隙的位置與個數(shù)4+4544.1.4FCC八面體間隙的位置與個數(shù)1+3554.2體心立方結(jié)構(gòu)中的間隙6×1/2＋12×1/4=66×4×1/2=1256體心立方結(jié)構(gòu)中間隙的位置▲四面體空隙是否為八面體空隙的一部？574.3密排六方結(jié)構(gòu)中的間隙四面體：C軸2

＋

豎直棱6×2×1/3＋中心3×2=12584.4晶體結(jié)構(gòu)中各種間隙匯總晶體結(jié)構(gòu)八面體間隙四面體間隙間隙數(shù)rB/rA

間隙數(shù)rB/rA

Bcc60.155120.291Fcc40.41480.225Hcp60.414120.225595.Atomicandionicradii根據(jù)X射線測定的晶體結(jié)構(gòu)類型和點陣常數(shù)大小，可計算出元素的原子半徑R。實際上任何元素的R都不是固定不變的，而是受外界條件、原子間結(jié)合力、結(jié)合鍵類型、配位數(shù)等多種因素的影響而變化。605.1外界溫度和壓力的影響溫度改變，原子熱振動及晶體內(nèi)點陣缺陷平衡濃