VTU Nanotechnology Syllabus

7/22/2019 VTU Nanotechnology Syllabus

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APPLIED MATHEMATICS

Sub Code : 12INT11 IA Marks : 50

Hrs/ Week : 04 Exa Hours : 0!

To"a# Hrs$ : 52 Exa Marks : 100

1$ L%&ear A#'ebra: Definition of a matrix, types of matrices, matrix

operations such as addition, subtraction, scalar and vector multiplication,

matrix characteristics like rank, transpose, trace, determinant, inverse of a

matrix: identity matrix method and cofactor method of finding the inverse of

a matrix, rules for binary operations, unary operation, Eigen values and Eigen

vectors, linear systems of equations, solutions of linear equations by Gauss

elimination and Cramers rule

( Hours

2$ Nuer%)a# So#u"%o&s o* A#'ebra%) a&d Tra&s)e&de&"a# E+ua"%o&s:

!ixed "oint #teration, $isection %ethod, !alse "osition or &egular !alsi

%ethod, 'e(ton)&aphson %ethod, *ecant %ethod, %uller+s %ethod,

improved 'e(ton %ethod

, Hours

!$ S-s"e o* E+ua"%o&s: *imultaneous equations in matrix form,

consistency of equations, types of solutions, methods of solving

simultaneous equations: Gauss elimination method, Gauss)*iedel method,

#nverse matrix method, Giraff* root square method, determinant method,

riangular *ystems and $ack *ubstitution, Gauss)-ordan Elimination and

"ivoting, ri)Diagonal %atrices, #nverse %atrix, ./ !actori0ation,

Cholesky, -acobi, "ivoting %ethods, #terative &efinement, .inear

"rogramming)*implex %ethod

( Hours

4$ E%'e& .a#ue Prob#es: Definition, Eigen values and Eigen vectors,

heorems of Eigen values and Eigen vectors, methods of solving Eigen

value problems: Characteristic equation method, #terative method *ome

applications of Eigen value problem

( Hours

5$ r"o'o&a#%"- a&d Leas" S+uares: #nner product, length and

orthogonality, orthogonal sets, 1rthogonal pro2ections, he Gram)schmidt

process, .east *quare problems, #nner product spaces

, Hours

5


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,$ Cure %""%&': .east *quares .ines, .east *quares "olynomials,

'onlinear Curve !itting, .ogistic Curve, !! and rigonometric

"olynomials, Conic !it, Circle of Curvature

, Hours

($ So#u"%o& o* rd%&ar- D%**ere&"%a# E+ua"%o&s: Euler+s %ethod, aylor

*eries %ethod, &unge)3utta %ethod, &unge)3utta)!ehlberg %ethod,

4dams)$ashforth)%oulton %ethod, %ilne)*impson+s %ethod, "redictor)

Corrector %ethods, Galerkin+s %ethod

, Hours

3$ Nuer%)a# I&"e'ra"%o&: %idpoint &ule, 'e(ton)Cotes #ntegration,

rape0oidal &ule for 'umerical #ntegration, *impson+s &ule for 'umerical

#ntegration, *impson+s 567 &ule for 'umerical #ntegration, 4daptive*impson+s &ule, Gauss).egendre 8uadrature, Cubic *pline 8uadrature,

%onte Carlo "i, %onte Carlo #ntegration, 9D rape0oidal and *impson

&ules

( Hours

Tex" ooks:

1 S"ee& C$Co6ra7 8a-o&d P$Ca&a#e9Nuer%)a# Me"ods *or

E&'%&eers7 4" Ed%"%o&7 Ta"a M);ra< H%##$

2 Pere= Mo%& 9A66#%)a"%o& o* Nuer%)a# e"ods "oE&'%&eer%&'$

! Da%d$ C$ La-7 9L%&ear A#'ebra a&d %"s A66#%)a"%o&s >!rd

Ed%"%o&7 Pearso& Edu)a"%o&$

8e*ere&)e ooks:

1 M ?$ @a%&7 S$8$? I-e&'ar7 8 ?$ @a%& Nuer%)a# Me"ods *or

S)%e&"%*%) a&d E&'%&eer%&'7 Co6u"a"%o&$ NEW A;E

INTE8NATINAL Pub#%sers$

2 S$S$Sas"r- 9Nuer%)a# A&a#-s%s *or E&'%&eers>Ta"a M)'ra and ;9) Excited states

of ;9, ?$ theory, Comparison of ?$ vs %1 methods, 'on crossing rule,

correlation of homo)nuclear diatomic, %1 configuration, Electronic states

and erm symbols

( Hours

($ A66rox%a"%o& e"ods: ime independent and time dependent

perturbation theory for non)degenerate and degenerate energy levels, thevariational method, 3$ approximation, adiabatic approximation, sudden

approximation

, Hours

3$ Bua&"u )o6u"%&' o- +ua#%"a"%e a66roa)

uring machines, logic gates, and computers @ reversible vs irreversible

computation @ .andauers principle and the %ax(ell demon @ natural

phenomena as computing processes @ physical limits of computation @

%oores la( @ quantum computation @ historical development of quantumcomputation @ quantum bits @ quantum logic

( Hours

Tex" ooks:

= ext book of 8uantum %echanics: " % %athe(s and 3

?enkateshan A%;, =BB

9 8uantum "hysics of 4toms, molecules, solids 'uclei and particles9ndEd by Eisberg, &obert, &esnick &obert

3


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5 $ &ogers, * "ennathur and - 4dams, 'anotechnology:

/nderstanding small systems C&C press 97

" 4tkins and &* !riedman: %olecular quantum mechanics,

oxford 9F

8e*ere&)es:

= 8uantum %echanics: ? 3 hankappan Ailey Eastern, =B7

9 8uantum %echanics: $ 3 4gar(al and ;ari "rakash A"rentice)

;all, =BB

5 "hilip 3aye, &aymond .aflamme, and %ichele %osca, 4n

introduction to quantum computing, 1xford /niversity "ress,

9

NANSCIENCE AND NANMATE8IALS

Sub Code : 12INT1! IA Marks : 50

Hrs/ Week : 04 Exa Hours : 0!To"a# Hrs$ : 52 Exa Marks : 100

= #ntroduction to nanoscience and nanotechnology, history, background

scope and interdisciplinary nature of nanoscience and nanotechnology,

scientific revolutions, nanosi0ed effects surface to volume ratio, atomic

structure, molecules and phases, energy at the nanoscale molecular and

atomic si0e, quantum effects, types of nanotechnology and nano machines

, Hours

9 Classification of nanostructures ) Hero dimensional, one)dimensional and

t(o dimensional nanostructure materials ) clusters of metals, semiconductors,

ceramics and nanocomposites, si0e dependent phenomena, quantum dots,

nano(ires, nanotubes, nanosheets, nano and mesopores, top do(n and

bottom up approach, misnomers and misconception of nanotechnology,

importance of nanoscale materials and their devices

, Hours

!$ Pro6er"%es o* Na&oa"er%a#s:) %echanical properties ) hermo physical

properties ) Electric properties ) Electrochemical properties ) %agnetic

properties ) 1ptical properties @ Catalytic property ) "roperties of gas

permeation and separation membranes

F


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( Hours

4$ Na&os"ru)"ure des%'&: !unctionality of nanostructures and their

characteristic evaluation, *i0e effect in semiconductor nanoparticles) "article

si0e, shape density ) %elting point, surface tension, (ettability ) *pecific

surface area and pore ) 4ssembly of nanoparticles and functionali0ation )

'anoparticles arranged structures as 'anopores and 'anocomposites )

*tructure control of nanoparticle collectives by sintering and bonding ) *elf)

assembly 'anoparticle dispersion and aggregation behavior ) *ingle

nanoparticle motion in fluid @ $ro(nian diffusion ) 4dsorption properties )

#nteractions bet(een particles ) 4ggregation and dispersion, characteri0ation

and control ) &heology of slurry ) *imulation of colloidal dispersion system

3 Hours

5$ Me#"%&' 6o%&" a&d 6ase "ra&s%"%o& 6ro)esses: quantum)si0e)effectA8*E *i0e)induced metal)insulator)transition A*#%# ) nano)scale

magnets, transparent magnetic materials, and ultrahigh)density magnetic

recording materials ) chemical physics of atomic and molecular clusters

*urface energy @ chemical potential as a function of surface curvature)

Electrostatic stabili0ation) surface charge density)electric potential at the

proximity of solid surface)?an der aals attraction potential

"hotochemistry< "hotoconductivity< Electrochemistry of 'anomaterials )

Diffusion in 'anomaterials< 'anoscale ;eat ransfer< Catalysis by Gold

'anoparticles< ransport in *emiconductor 'anostructures< ransition %etal4toms on 'anocarbon *urfaces< 'anodeposition of *oft %aterialsra- d%**ra)"%o&:N)ray diffraction, $ragg la( .aue equations 4tomic

form factor and *tructure factor Concept of reciprocal lattice and E(alds

construction Experimental diffraction methods: .aue, &otating crystal

method and "o(der method

, Hours

2$ Cr-s"a# b%&d%&': ypes of binding ?an der aals).ondon interaction,

&epulsive interaction %odelung constant $orns theory for lattice energy inionic crystals and comparison (ith experimental results #deas of metallic

binding, ;ydrogen bonded crystals

La""%)e %bra"%o&s: ?ibrations of monoatomic lattices !irst $rillouin 0one

8uanti0ation of lattice vibrations ) Concept of "honon, "honon momentum

*pecific heat of lattice Aqualitative

K ;ours

!$ E&er'- ba&ds %& so#%ds:!ormation of energy bands !ree electron model:

free electrons in one and three dimensional potential (ells, electrical

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conductivity, heat capacity, paramagnetism, !ermi)Dirac distribution, density

of states, concept of !ermi energy 3ronig)"enny model 'early !ree

Electron %odel Aqualitative ight $inding model Aqualitative

De*e)"s %& so#%ds: "oint defects: *chottky and !renkel defects and their

equilibrium concentrations .ine defects: Dislocations, multiplication of

dislocations A!rank)&ead mechanism "lane defects: grain boundary and

stacking faults

( Hours

4 Se%)o&du)"ors: #ntrinsic and extrinsic semiconductors, concept of

ma2ority and minority carriers *tatistics of electrons and holes, electrical

conductivity ;all effect Experimental determinations of resistivity of

semiconductor by four probe method, Hours

5$ Tra&s6or" 6ro6er"%es o* e"a#s: $olt0man equation, Electrical

conductivity, Calculation of relaxation time #mpurity scattering, #deal

resistance General transport coefficients, hermal conductivity,

hermoelectric effects, .attice conduction, "honon drag

Tra&s6or" 6ro6er"%es o* se%)o&du)"ors: hermal conductivity

hermoelectric and magnetic effects ;ot electron and energy relaxation

times ;igh frequency conductivity 4coustic Adeformation and pie0oelectric

and optical Apolar and non polar scattering by electrons

( Hours

,$ D%e#e)"r%) 6ro6er"%es o* so#%ds: %acroscopic description of static

dielectric constant, Electronic, ionic and orientational polarisation, .orent0

field, Dielectric constant of solids, complex dielectric constant and dielectriclosses heory of electronic polarisation and optical absorption

erroe#e)"r%)%"-: General properties, Classification, Dipole theory and its

dra(backs, hermodynamics of ferroelectric transitions, !erroelectric

domains

, Hours

($ Ma'&e"%) 6ro6er"%es o* so#%ds: Classification, .angevin theory ofdiamagnetism, 8uantum theory of paramagnetism !erromagnetism: Concept

of domains, thermodynamics, thickness of $loch (all, %olecular field

concept, eiss theory, ;eisenberg exchange interaction, #sing model, *pin

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(aves ) dispersion relation Aone dimensional case, quanti0ation of spin

(aves, Concept of magnons and thermal excitation of magnons, $loch 569

la( for magneti0ation 4ntiferromagnetism: (o sublattice model

!errimagnetism in the context of #ron garnets

( Hours

3$ Su6er)o&du)"%%"-: &evie( of basic properties, classification into type #

and type ## Energy gap and its temperature dependence *uper currents and

Critical currents .ondons phenomenological equations, "enetration depth

Cooper pairs, Coherence length #nstability of !ermi surface and cooper

pairs $C* theory and comparison (ith experimental results Ground state

energy of superconductor 8uanti0ation of magnetic flux -osephson effects

A4C and DC and applications

( Hours

Tex" ooks

= #ntroduction to *olid *tate "hysics, C 3ittel, iley Eastern

9 4 practical approach to N)&ay diffraction analysis by

C*uryanarayana

5 *emiconductor "hysics, " * 3ireev, %#& "ublishers

8e*ere&)es

= *olid *tate "hysics, 4 - Dekkar, "rentice ;all #nc

9 #ntroduction to *uperconductivity, % inkham, %cGra();ill,

#nternational Editions

5 Elementary *olid *tate "hysics: "rinciples and applications, % 4

1mar, 4ddison)esley

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NANTECHNL;G AND INDST8IAL

APPLICATINS

Sub Code : 12INT152 IA Marks : 50

Hrs/ Week : 04 Exa Hours : 0!

To"a# Hrs$ : 52 Exa Marks : 100

1$ I&dus"r- oer%e

VTU Nanotechnology Syllabus

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