Post on 25-Jun-2022
Cvyatal knolatiom Vectors Jn Ovdert to repent Jattice poitto n pa
a co-ovdinale dytem io vqulsed.
Dnto un pace. can e 9eneafeol y tyanalatug
the nen-coplanan. Unlt vectors. "Uhe thiz
n-Coplanas divetions conotitub a co-ordinau:
dtem
dl dhe laktice
Linta Lattice
D
point. Fisl).
T ,a + 2lb+
WKnovo that a. thonalafion &pcsa:tDs Can loe
"te fouald an clject ingintt tinmto 't'n one diyer.
Cuncl Cwaqontl
Hiault, in a lincas
pcth. o Li shon n ig ti) *ohich i iapecto abjet. d red opoirts siapat.
aS1guias intea
Callel a uncar
Lattice.. Nou if -the pottern tn ig0
T
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o o
atta Brnvais attice. and Gyatal ya7
Cyatal Syati ravaio lattia Sjmesla
Simt Bady-Cantul Face-Cont ved
Cuic
Simta 3 ody-centyl Sia
TeAvagenal
O»thoxhondaic Bodd-Cat sd Fata-cet red Sipk Monocliaie aae-Centhe d
Jiline Siomp
Sinpt R
Simpa HexagenA
pata Latice ubic. yadrwa
hene oase thut Biavaio Lattica o Cubic yattn
1) Simmple. cubi. (Or fimiive Cakic)o
Cbic P-Aype
lattice.. Simple cubic. (s) Lattia, there. a
ig Rattice peiRto ot fha. CoTna te utatt.
aa lows
Exape kce, aned Po t
centan ctenp'.
(2) Fo.ce. Centred Culoi or Cubit F-Ratttea i- 9n add
c he attica poirito af the. cught coao f
t Lottice peT al thc Caiiae Contaiw latie point at xhi otve oach 1
L the tace- coctt Culoic CFCC) Lattta
fem Or an identia qreup o atoms io attachek c evlattica poid, we ohtau a Crystal abuctue fig w. ie, hattia i a gesmetrical Concopt ohr ca Cryatall a rial thing
kattita,+ Baaio= Cryatal tsuctuxe. . hu Cyatal i aot a lattice lot it a
Lattice d anay o OcTem
ena loctwcen Uait Cell nol rimi tive ell
4 Umt cell, in addition do an alom at o 2ach
Cog ne may or may net centain additon oten Sr atsm d a pvnetive unid coll contauim on Gne atem at ito ach C0ra
aUdt Cell ) imichive Unit Cttl
Tem Ove coe may Concluke that al primitive. Colto are Uut ceN loct all uut cul may or may
snct aa primitive Clla.
attbce Conatant Uhe ksngth a ,ls anel c pecitg cth: siz of a
uct Cll are Callual Aatice cenatanta. Fos Cubi
Cxyatl a = b =c arcl a to calla laktia conatat.
ovaio Lattico 01avt 1884 proposed hecencept o th ac Lattie. Spaco. lattice to oa mathe mafal
Ceept which eptoLnt, in-in numlaus P paco. uch hat ethe arsangemit o peirtt
CAUT a. qivon pett do Sinilan te -fhoct odi CuL
ny then it
Jhese. ate 4.olistingui Shalile mys in ohuck Potlo Can lea. A3angecl in.' 3- D spate Uhe1
Bravaio attie. aEe number anel be fong to t ytal YKtem Uhe 14 1Baavato attice. anc thur
Name CLBe iSecd in. ecloo clngon
oJ-r
Ltgond Body andrd implk on 4k i Tata onal (BC7) sDR)
the Th ta
Jurc example faka a plane having tha
vTevcept a length 2a,b ancl 2e wi th Ha three Cyatal åxes. 9n crder fs ind t Miler
4Dcdites et tak He Tectprctala of2,1and 2
ttinga 1, ane then ind he inttegev that ane. in -he dame. "ratio as 1, Ohio
givss-the Miller. indite (1 2 1).
do sepeatl at an tndeval ls an a directo
than han Hhat orepidion tn g O, the t6
oumandenal aray op0 int, is olclauneel 2 shodr
Finall,i the plane pattnn o 17 iavingiepetiton intvals a, anel b, Lo Tp eae
y a Haol non- cophnas translahen cd ahe
AndnsOnal ate latice. ds 9eneratecl.
Ah6usn
Rhe tanalatiena ,t ondl 2 Ge, *gaa dac
a veLtors and he hree. tyaroatien diveuten an
delected, a cryztalkogaohic. aXLD an
opectve Cit. any lattice, peithestra
OY9tu , the ha tocactio any ather lattiee po int
P) Can ee deline cl ot his orig in
T, n+ aC
che , and 3 Qse asbitrart inTegv
a anol C are Called. unolamantal vechrs
Lakle TL called. Cryclal Jhanalation. Vector.
poper clinipten ohe. ukjet may ec
Cavied. Cut y 7eferving de the -hre. dimeroicnnl
Spaca. lattias."Dyad avetov T Conneting o
LVI. pcint P anol P a ahovn igu Pnrol
Wa he pooituen vectns i anol 2
opectivtlyp. Shen he vecfo T io qiu lay the Telaten
T n,a+ , +
'2= +,a+32 + 3
Cxpola Cau, Ni, A, Ag Captals.
3)Beoy-atel cueic. orc uic I la tice -
ols Cehed cubic CBCC lattia. fhare to O addiekienl Ratlice. pcint aiuates ot e lod Ctve eaide Cigke latticn.paid, aituated at Ahe
Cught c0na.uo theu is ar efa lattite
po t the loody Cotu a the unit cell.
Cxanple Li, Na., k, cr CTya
Calealatio Numc atom per unit cce
)Simgele Cabic CS) latkita Eve lattice peuit
in Se lattice Atuatl at khe cotnE dhe unt ceuL is share ol. Duy ciqist uict uls anel hunt d Centrilbwten e ach cau i
Total cedrileuctien k co uv o-the se
attica io 4
h,Tt an Sc loctlico. there te bne Cattitepeint
P ndt colt.
f-
aa-Catved Cauloic (FC) latia Jhene are
eight lattite pot, at the eigkt couso o{ tha
FCC lotfita. andl Cetilwtien o{haae ight Lattua
pout, te the unit cella io x
tt.
addto Mecsuer, fAhera coe aix ace the unt ct cac
atem a ahich ilengo te tue un i Se, fhe Cerctnfaatien theac Aix Kattica. peint ts tu undt
Cell to 6= 3. attta
6sAal inlher o att ca poit. pes Fcc Ccell is -+3=4
Sed-Candvd Culie Cec)-Ae these ane CAgit Rattice peit, af -fhe. igkt cevne
the undt Lttt dhd iach oa numet o t A CRt n adAitien hare is one lattca pot od Cody cent So, the =tetel nuiluer.
Cattice pout. p' Bcc unid ceu
+I=2
CO-03cinoctie w (CN) o proticulas lattiee Co-cidinactuo 37umdees
eat LgloDus te a posctiulas atem h yatal atice .
Nuut nughloeuss olisianue () io daincd ao tha odi'stance. loctocc tke
Countrea toe ntartot igheusing cetem Cryatal
Ah nenast neiqhsu
distanais 2.
toc zacliu ):
temc adus io do a halt sthe dita Csehwun neaut neigbe actem in te apola
phoual n te and ap tos ncighieeuving CvTtituch tach a-thr.
) Sc lattika
d honn t h -i. AB ropratnt -the yaeli
Can aitemm ono x nat naleun olislaa
xa /2. Jhe neanist neighle ous diaBante. d - 21 2xV2-a
()BC.c Rattice
uemiy t a Rcc ul cal
d a Bcc unit call to sheun o luxe Aeaa
ABEa ane AC=(JEa+ a= a.
AC actemic Trelius = a" 4r = 3
4 Sih atot saoliue of a'Bcc cyttal is r-
Ta and uiqheous. datance d =27= 2
Mile olis cavevcel a methiod te derighik a plane. in a Crytal using cthec. munee,
h,k and kneon aa Milict iolia.
Mer inolices ane he 3 Amalhct pesihe ATegea vohich have. cthe aama. actio as t Teiprocalo the. intty capt ofhe plaa CSnceTmed. 6 the. 3 a Ke.
Jnelice aattie Diechion ancl Lattice Plant- The exertciae o deacribig a Cyatal
Strutwa tidentially amourts or ocating poaisten of diferuct ateis zn athe."
unit cell But the Ahuelp 3may Phyo ital
prepaotu a cyafala oëcomt meic meaningtul avd comptste cwith Bhe Knpuolesdge of di'se tionand vavieus atemie plaune viualizd icthun heir Cryatalline meclium hae ane ideudiiael
aywaing the ineex ystem dis cusa e blow
9nelie oa lattice. directiondvcor L draon. aleng (orc payallel to)
the deoired directher em u originixdox the axes Dyatm. . Uhe cempeneit hiae
vectors aong the Cyaia an dctrrnune.d and vecduced. to omallect nteger. Dhi intege -hen ritt icthin. aquasè. orackit, roprserts
h inditt o+he curection. A kar on the inds x
nhat he. mopectuu Cempenuct thi
Ve ctor 3egative 257
neio aa Locttice Plane Eve Cyatal plane is icdoneti jied y
Oitntatien which is charate rized ky plane
ATte rccat with thi cryatal a he Rq a pkone having inft7 Copto p, nd 7
Coith a,y and z axes la given ur
1
Jhe tovm oth cq hao loecn exploi sd y Mir to develep an index yt t hem the inclia arce amid Miller indiwa. he Milur DnelicB Sa lan are defrnind
the tollowtng proteclura )Fnol he inctrce en the tha Cxyatallogophie axt Ox, Oy anol OZ.
(n) Na thiir repoal
(00) Clear the raction
Lect he. incterapto oaplane oith aunel C meaaune a pa,jo anol C
1Lapketivel.Jake Hhin rêcipotal At
to tu hrec. ntageno h,k,
having te Samc 3ate a Jhis St
inclites hcken oyiKt 1 parruai
(hk) the miLles. ivdito a thr plane .
)FCC lattice
N t On FCc uuit cell whoseace diagenal
Ac
ace diagenal, AC= Da = 43
NTEmaC Tadu ,
2
The neaat nuighloen
dictance d-2 =
Lattice Plant anel Mre 9nelice
)
V)
FigSct alattice plavta
A cnyatal Lottice may e cono ider as an
aggrcgata aa act a pavalel equidizlauue
plana pasoing th3ugh he lattite point,hat
P
Aecto pasallet planto a Callsd Lattice pla.
tehich Can lae Choat in a umlegs. o ay
ike ), ), u) and Uy a2 Ahton in Hhe higu
(*o Cantve 4 monnchdc
icdenie
K)He*ag oaA
Jalta C7yatal&yat
Ex apla Lattca Cy Conalae , 3,Y
Culeic a ==c Y-9 Nack, Cafz , Na C02 Tetaagena a=k#C K= -90 NiSe, SnO
Ov hov homlit a # l+c K=B-9=Y KNO3, Baso,, Mgso Manoclinie atAtc Kl-+40 Na2S04, FESO4 Tic finc
Tga abec K=l-1 CasO4 Hexagenal ab#c K=B-1012e Si Oa , hq
2o{sfa1