Unit cell ntawm crystal lattice: txhais thiab hom

Cov txheej txheem:

Unit cell ntawm crystal lattice: txhais thiab hom
Unit cell ntawm crystal lattice: txhais thiab hom
Anonim

Lub tsev cell ntawm cov siv lead ua lattice ua haujlwm los piav txog cov khoom siv microstructure. Ntau lub cev thiab tshuaj lom neeg lub zog ntawm cov khoom nyob ntawm nws qhov tsis muaj: hardness, melting point, hluav taws xob thiab thermal conductivity, plasticity, thiab lwm yam. Cov hom ntawm cov txheej txheem theem pib tau piav qhia thaum ntxov li xyoo 19th. Ib tug ntawm cov ntau yam yog lub primitive cell. Txhawm rau cais cov cell hauv cov khoom siv, ntau yam yuav tsum tau ua.

Crystal lattice

Elementary cell - yog dab tsi?
Elementary cell - yog dab tsi?

Txhua cov khib nyiab raws li lawv cov qauv sab hauv tuaj yeem faib ua ob hom: amorphous thiab crystalline. Ib qho tshwj xeeb ntawm qhov tom kawg yog cov qauv tsim tshwj xeeb ntawm cov khoom.

Crystal lattice yog cov qauv yooj yim peb-dimensional ntawm cov khoom siv lead ua, uas yog siv los tshuaj xyuas lawv cov khoom hauv physics, chemistry, biology, mineralogy thiab lwm yam kev tshawb fawb. Outwardly, nws zoo li ib daim phiaj. Ntawm nws cov nodes yog cov atoms ntawm teeb meem. Qhov array ntawm cov ntsiab lus no muaj qhov tshwj xeeb, tsis tu ncua rov hais dua qhov tshwj xeeb rau txhua hom.tshuaj.

Lub cell yog dab tsi?

Chav cell ntawm cov siv lead ua lattice yog qhov tsawg tshaj plaws ntawm cov khoom uas tso cai rau peb ua tus yam ntxwv ntawm nws cov khoom. Nws ua haujlwm raws li lub hauv paus ntawm daim phiaj thiab muab luam tawm hauv nws suav tsis txheeb.

Cov qauv no yog siv los ua kom yooj yim rau qhov pom kev piav qhia ntawm cov qauv sab hauv ntawm cov muaju. Nyob rau hauv cov ntaub ntawv no, ib tug system ntawm 3 crystallographic coordinate axes yog siv, uas txawv los ntawm ib txwm orthogonal sawv daws yuav nyob rau hauv hais tias lawv yog finite segments ntawm ib tug tej yam me me. Lub kaum sab xis ntawm cov axes tuaj yeem sib npaug li 90 ° lossis tsis ncaj.

Yog tias koj densely sau ib lub ntim nrog cov qe qis, koj tuaj yeem tau txais ib qho zoo tagnrho siv lead ua. Hauv kev xyaum, polycrystals muaj ntau dua, suav nrog ntau cov qauv tsis tu ncua hauv qhov chaw.

Views

Hauv kev tshawb fawb, muaj 14 hom ntawm cov hlwb theem pib ntawm lattices nrog lub cim geometry. Lawv tau piav qhia thawj zaug los ntawm Fab Kis tus kws kho mob Auguste Bravais hauv xyoo 1848. Tus kws tshawb fawb no suav tias yog tus tsim ntawm crystallography.

Chav cell - Bravais lattices
Chav cell - Bravais lattices

Cov qauv ntawm cov qauv tsim ntawm cov siv lead ua lattice tau muab faib ua 7 pawg, hu ua syngonies, nyob ntawm qhov sib piv ntawm qhov ntev ntawm ob sab thiab qhov sib npaug ntawm cov ces kaum:

  • cub;
  • tetragonal;
  • orthorhombic;
  • rhombohedral;
  • hexagonal;
  • triclinic.
Chav tsev cell - Bravais 2 lattices
Chav tsev cell - Bravais 2 lattices

Qhov yooj yim tshaj plaws thiab feem ntau hauv qhov xwm txheej los ntawmntawm lawv yog thawj qeb, uas nyob rau hauv lem muab faib ua 3 hom lattices:

  • Cubic yooj yim. Tag nrho cov khoom (thiab lawv tuaj yeem yog cov atoms, cov khoom siv hluav taws xob lossis cov khoom siv hluav taws xob) nyob ntawm qhov vertices ntawm lub voos xwmfab. Cov khoom no zoo ib yam. Txhua lub cell muaj 1 atom (8 vertices × 1/8 atom=1).
  • Lub Cev-Centered Cubic. Nws txawv ntawm cov qauv yav dhau los nyob rau hauv uas muaj ib qho ntxiv particle nyob rau hauv nruab nrab ntawm lub voos xwmfab. Txhua lub cell muaj 2 atoms ntawm teeb meem.
  • Face-centered cubic. Particles muaj nyob rau hauv lub vertices ntawm lub elementary cell, thiab nyob rau hauv nruab nrab ntawm tag nrho cov ntsej muag. Txhua lub hlwb muaj 4 atoms.
  • Elementary cell - hom
    Elementary cell - hom

Primitive cell

Ib lub xovtooj ntawm theem pib hu ua primitive yog tias nws cov khoom nyob tsuas yog nyob ntawm lub lattice vertices thiab tsis tuaj rau lwm qhov. Nws qhov ntim yog tsawg dua piv rau lwm hom. Hauv kev xyaum, nws feem ntau hloov mus rau qhov qis-symmetrical (ib qho piv txwv yog Wigner-Seitz cell).

Rau cov hlwb uas tsis yog thawj zaug, lub atom nyob rau hauv nruab nrab ntawm lub ntim muab faib ua 2 los yog 4 qhov zoo tib yam. Nyob rau hauv lub ntsej muag-centered qauv, muaj kev faib ua 8 qhov chaw. Nyob rau hauv metallography, lub tswv yim ntawm ib tug elementary es tsis yog ib tug primitive cell yog siv, txij li thaum lub symmetry ntawm cov thawj cell tso cai rau ib tug ntau ua tiav piav qhia txog cov siv lead ua qauv ntawm cov khoom.

Signs

Tag nrho 14 hom ntawm cov qe qis muaj cov khoom sib xws:

  • lawv yog cov txheej txheem rov ua dua tshiab hauv cov siv lead ua;
  • txhua qhov chaw lattice muaj ib qhoparticles, hu ua lattice node;
  • cell nodes yog interconnected los ntawm cov kab ncaj nraim uas tsim cov geometry ntawm cov siv lead ua;
  • ntsej muag sib luag yog sib npaug;
  • qhov sib luag ntawm cov qauv theem pib sib haum rau qhov sib luag ntawm tag nrho cov siv lead ua lattice.

Thaum xaiv cov qauv ntawm lub xov tooj ntawm tes, qee cov cai tau ua raws. Nws yuav tsum muaj:

  • ntim tsawg tshaj plaws thiab thaj chaw;
  • tus lej loj tshaj plaws ntawm cov npoo thiab cov ces kaum ntawm lawv;
  • kaum sab xis (yog tias ua tau);
  • spatial symmetry, xav txog qhov sib luag ntawm tag nrho cov siv lead ua lattice.

Volume

Qhov ntim ntawm lub hauv paus ntawm tes yog txiav txim siab nyob ntawm nws cov duab geometric. Rau lub cubic syngony, nws yog xam raws li qhov ntev ntawm lub ntsej muag (center-to-center nrug ntawm atoms) tsa mus rau peb lub hwj chim. Rau lub hexagonal system, lub ntim tuaj yeem txiav txim siab siv cov qauv hauv qab no:

Unit cell - ntim
Unit cell - ntim

qhov twg a thiab c yog qhov ntsuas ntawm cov siv lead ua lattice, ntsuas hauv angstroms.

Hauv kev xyaum, qhov ntsuas ntawm cov siv lead ua lattice raug xam kom tom qab txiav txim siab cov qauv ntawm cov khoom sib xyaw, qhov loj ntawm lub atom (raws li qhov hnyav ntawm qhov muab ntim thiab tus lej Avogadro) lossis nws lub vojvoog.

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