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
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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
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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 $C* theory and comparison (ith experimental results Ground state
energy of superconductor 8uanti0ation of magnetic flux -osephson effects
A4C and DC and applications
( Hours
Tex" ooks
= #ntroduction to *olid *tate "hysics, C 3ittel, iley Eastern
9 4 practical approach to N)&ay diffraction analysis by
C*uryanarayana
5 *emiconductor "hysics, " * 3ireev, %#& "ublishers
8e*ere&)es
= *olid *tate "hysics, 4 - Dekkar, "rentice ;all #nc
9 #ntroduction to *uperconductivity, % inkham, %cGra();ill,
#nternational Editions
5 Elementary *olid *tate "hysics: "rinciples and applications, % 4
1mar, 4ddison)esley
1,
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NANTECHNL;G AND INDST8IAL
APPLICATINS
Sub Code : 12INT152 IA Marks : 50
Hrs/ Week : 04 Exa Hours : 0!
To"a# Hrs$ : 52 Exa Marks : 100
1$ I&dus"r- oer%e