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

t itu

tsla

t atttn

1o

in

aual

ly n

e q

Ac ol

tu

ual

ote

l

Sta

tt a

ata

t ia

ttes

t

ubds

vude

d in

s an

d

iqur

ol

otat

, A

u h

e m

atea

ual,

asc

mp

esd

a

atem

id

mo

leu

e o

Jhu

d

uid

, a

divi

ded

inte

tu

oe C

ateq

oitd

Coy

Jtal

line

n

d

) A

mop

ht.

(Cay

atalli

nee

scld

o ar

e ch

a7ac

tesi

sel

n p

aNLy

P

tet

perio

d ic

it at

smic

åt

ruct

ue.k

m

tnc

Stq

ula

t id

s Si

*he

vct2

. th

i cy

atal

lie

'atat

ehe

ado

ma x

n

clk

tuls

aA

e

tn q

uka

anel

om

tt

(oatt

ean

Aman

hou

nam

crpk

au

soli

d

thou

gh t

he

atom

o

An.ol

ecuke

c

aten

on

dal

at ha

rdly

Bhe

e ie

an

gk

eetc

al

Su

lasil 6

r p

ei

oel

city

in

th

. ut

ay

a u

htb

th

e at

om

asi

a no

kqi

d n

op

ace

n d

uck

Jc

lGd,

th

e af

om

o

cr

nele

cude

a 3

no

t u

ia

ann

l ge

smet

aI f

attes

n.

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