Qhov Tseem Ceeb Qhov Sib txawv – Point Group vs Space Group
Cov ntsiab lus pab pawg thiab pawg chaw yog siv hauv crystallography. Crystallography yog txoj kev tshawb fawb txog kev npaj ntawm atoms hauv cov khoom siv crystalline. Cov pab pawg crystallographic point yog ib txheej ntawm symmetry ua haujlwm uas tawm tsawg kawg ib qho taw tes tsis txav. Kev ua haujlwm symmetry yog ib qho kev ua kom tau txais cov duab qub ntawm ib qho khoom txawm tias tom qab txav nws. Cov kev ua haujlwm symmetry siv nyob rau hauv cov pab pawg taw tes yog kev sib hloov thiab kev xav. Ib pawg chaw yog pawg 3D symmetry ntawm kev teeb tsa hauv qhov chaw. Ib pawg symmetry yog pab pawg ntawm txhua qhov kev hloov pauv tau txais yam tsis muaj qhov sib txawv ntawm qhov sib txawv thaum lub sijhawm ua haujlwm pab pawg. Qhov sib txawv tseem ceeb ntawm pawg taw tes thiab pawg chaw yog tias muaj 32 pawg taw tes crystallographic thaum muaj 230 pawg chaw uas tau tsim los ntawm kev sib xyaw ntawm 32 pawg taw tes thiab 14 Bravais lattices.
Point Group yog dab tsi?
Cov pab pawg crystallographic yog ib txheej ntawm kev ua haujlwm sib luag uas tawm tsawg kawg ib qho tsis txav mus. Cov kev ua haujlwm symmetry tau piav qhia hauv pawg pawg yog kev sib hloov thiab kev xav. Hauv kev ua haujlwm ntawm pab pawg symmetry, ib qho tseem ceeb hauv cov khoom yog khaws cia tsis txav (tso) thaum txav lwm lub ntsej muag ntawm cov khoom mus rau txoj haujlwm ntawm cov yam ntxwv ntawm tib yam. Nyob ntawd, cov yam ntxwv macroscopic ntawm cov khoom yuav tsum nyob twj ywm tib yam ua ntej thiab tom qab kev ua haujlwm symmetry.
Rau txhua yam khoom, muaj qee qhov kev ua haujlwm symmetry ua tau (nrog cov kev sib raug zoo geometrical ntawm kev ua haujlwm symmetry). Cov khoom tau hais tias muaj qhov sib luag piav qhia los ntawm pawg taw tes. Yog li ntawd, cov khoom sib txawv uas muaj qhov sib txawv ntawm qhov sib txawv tau piav qhia los ntawm cov pab pawg sib txawv.
Nyob rau hauv lub cim ntawm pawg taw tes, muaj ob lub tshuab siv;
Schoenflies Notation
In Schoenflies notation system, point group are named as Cnv, Cnh, Dnh, Td, Oh, thiab lwm yam. Cov cim sib txawv siv hauv qhov kev sau ntawv no tau muab hauv qab no.
- n yog tus lej ntau tshaj ntawm kev sib hloov axes
- v yog daim iav dav dav (hais tsuas yog thaum tsis muaj daim iav kab rov tav)
- h is the horizontal mirror planes
- T is a tetrahedral point group
- yog pawg octahedral point
Piv txwv li, Cn yog siv qhia tias pawg taw tes muaj n-fold axis. Thaum nws muab raws li Cnh, nws txhais tau hais tias muaj Cn nrog rau daim iav dav hlau (reflection plane) perpendicular mus rau axis ntawm kev sib hloov. Nyob rau hauv sib piv, Cnv yog Cn nrog ib daim iav dav hlau mus rau lub axis ntawm kev sib hloov. Yog hais tias pawg taw tes muab raws li S2n, nws qhia tias pawg taw tes tsuas muaj 2n-fold rotation-reflection axis.
Hermann-Mauguin Notation
Hermann-mauguin sau ntawv feem ntau yog siv rau pawg chaw. Tab sis, nws kuj yog siv rau crystallographic point pawg. Nws muab qhov siab tshaj plaws kev sib hloov axis. Piv txwv li, pawg taw tes tsuas muaj 2-fold tig axis yog suav tias yog 2. Cov pab pawg taw tes muab raws li C2h los ntawm Schoenflies sau yog muab raws li 2 / m hauv Hermann-mauguin notation system hauv uas lub cim 'm' qhia txog daim iav dav hlau thiab lub cim slash qhia tias daim iav dav hlau yog perpendicular mus rau ob-fold axis. Cov lus hauv qab no qhia cov cim sib txawv ntawm pawg taw tes rau cov tshuab lattice sib txawv.
Daim duab 01: Daim iav dav hlau thiab cov dav hlau glide ntawm cov dej khov hexagonal qhia tias pawg chaw dej khov yog P63 / mmc
Muaj 32 pab pawg. Cov pawg ntsiab lus yooj yim tshaj plaws yog 1, 2, 3, 4, 5 thiab 6. Tag nrho cov ntsiab lus no tsuas yog ib qho kev sib hloov axis. Rau rotary-inversions, muaj axes npe -1, m, -3, -4 thiab -6. Lwm pawg 22 cov ntsiab lus yog kev sib txuas ntawm cov pab pawg no.
Space Group yog dab tsi?
Ib pawg chaw yog pawg 3D symmetry ntawm kev teeb tsa hauv qhov chaw. Muaj 230 pawg chaw. Cov 230 pawg no yog kev sib koom ua ke ntawm 32 pawg ntseeg cov ntsiab lus (hais saum toj no) thiab 14 Bravais lattices. Lub Bravais lattices tau muab rau hauv cov lus hauv qab no.
Ib pawg chaw muab cov lus piav qhia ntawm symmetry ntawm lub ntsej muag. Cov pab pawg chaw yog kev sib txuas ntawm kev txhais lus sib luag ntawm chav tsev cell thiab symmetry kev ua haujlwm xws li kev sib hloov, rotary-inversion, kev xav, ntsia hlau axis thiab glide dav hlau symmetry ua haujlwm.
Qhov txawv ntawm Point Group thiab Space Group yog dab tsi?
Point Group vs Space Group |
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| Cov pab pawg crystallographic point yog ib txheej ntawm kev ua haujlwm sib luag uas tawm yam tsawg kawg ib qho tsis txav. | Ib pawg chaw yog pawg 3D symmetry ntawm kev teeb tsa hauv qhov chaw. |
| khoom | |
| Muaj 32 pawg taw qhia crystallographic. | Muaj 230 pawg chaw (tsim los ntawm kev sib xyaw ntawm 32 pawg taw tes thiab 14 Bravais lattices). |
| Kev ua haujlwm sib luag | |
| Cov kev ua haujlwm sib luag uas siv rau hauv kev tshawb nrhiav pab pawg yog kev sib hloov thiab kev xav. | Kev ua haujlwm sib luag siv nyob rau hauv qhov chaw tshawb nrhiav yog kev sib hloov, tig-inversion, kev xav, ntsia hlau axis thiab glide dav hlau symmetry kev ua haujlwm. |
Summary – Point Group vs Space Group
Cov pab pawg thiab pawg chaw yog cov lus piav qhia hauv crystallography. Cov pab pawg crystallographic point yog ib txheej ntawm symmetry ua haujlwm tag nrho cov uas tawm tsawg kawg yog ib qho taw tes tsis txav. Ib pawg chaw yog pawg 3D symmetry ntawm kev teeb tsa hauv qhov chaw. Qhov sib txawv ntawm pawg taw tes thiab pawg chaw yog tias muaj 32 pawg taw tes crystallographic thaum muaj 230 pawg chaw (tsim los ntawm kev sib xyaw ntawm 32 pawg taw tes thiab 14 Bravais lattices).
