PHYSICS MATERIAL FUNCTION,PROPERTY,DEVICES.pdf

PHYSICS MATERIAL FUNCTION PROPERTY DIFFERENT DEVICES

1. Physics of Functional M aterialsand Devices
Prof. Amreesh Chandra
Department of Physics, IIT KHARAGPUR
Module 05: Thermal properties of solids
Lecture 22: Thermal Properties of SolidsNPTEL

2. Introduction
DifferentT
hermalPropertiesofSolids
ThermalExpa
nsion
ThermalSt
ress
ThermalC
NPTEL

3. Int of usaresurroundedbymatter.Matteris differentfromeach other
accordingtosomeoftheirintrinsicproperties.
Differentintrinsicpropertiesofmatter,are:
Mechanical p
roperties
Chemical p

Physical p

Dimensionalp
roperties
Thermal p
NPTEL

4. What are the thermal propertiesofmatter?
Itisoneofthe main propertiesofmatter,whichdealswiththe heatconductivityand thermal
capacity ofmatter.Itdealswithheatfluctuation.
4 major components of thermal properties of matter:
Heat C

ThermalEx
pansion
Thermalst
ress
Thermalcon
ductivityNPTEL

5. Heat capacity and specific heat of matter
Heat C
:Itistheamount ofheatrequiredtochangethetemperatureofabodyby 1
degree.
TheS
heatcapacity is Joule/Kelvin.Mathematically,itcanbeexpressed as,????????????=
????????????????????????
????????????????????????
.
Heatca
arisesduetothe fewsources.Some ofthem are:
Vibration of the atoms.
Ordering of t
he atoms(defect).
Conduction of elect
rons.
Specifich :Itisrelatedtotheheatcapacity of solids.Itis
definedastheamountof heatrequiredtoenhancethe
temperatureoftheunitmassofasubstanceby aunitdegreeof
temperature.NPTEL

6. Thermal energyisthecombinationofthekineticenergyofatomicmotionsand the potential
energyduetothedistortion of interatomicbonds.
Vibrations ofa
tomsisoneofthe mainsources ofthermal energy.
Notable points about thermal energy
Vibrations of individualatomsin solidsarenotindependentfrom
each other.
Theco
of atomicvibrations ofadjacentatoms resultsin
wavesof atomicdisplacements.
Eachwa
ischaracterizedbyitswavelengthandfrequency.For
awaveofagivenfrequencyν,thereisthesmallest “quantum”of
vibrationalenergy,hν,called asphonon.
Thus, t
energyisthe energyofallphonons(orall
vibrationalwaves)presentinthe crystal atagiven temperature.
Figure: Vibration of atomsNPTEL

7. Temperature dependence of specific heat
Figure: Temperature dependence of specific heat
Heat c
at high temperature.
Atl
temperature,specificheatobeysEinstein’s
quantumtheory.Hence,C
vvarieswithT
3
.
Atro
temperature,C
vattainsaconstantvalue,
i.e.,nearly3Rfor1mole.This lawis famousas
Dulong-Petit’Slaw.
The l
inventedin1819.The law was basedon
theclassical equipartitiontheory.
Thec
illustratesthevariationofspecificheatwithtemperature
for differentsynthesized materials.
When t
specificheat approachesacertain
constantvalue.NPTEL

8. Thermal Expansion of Matter
Thermale
is one ofthe thermal propertiesofmatter,duetowhichmatterchanges
itslength,shape,volume,anddensityinresponsetothevariation intemperature.
Ing
transition isnotincluded inthe thermalexpansion.
????????????
∆????????????
Linear expansion
A
∆????????????
Areal expansion
V
∆????????????
Volume expansion
The ad figureillustratesthreetypesofthermal expansion,
linear, areal, andvolumeexpansion.NPTEL

9. Linear expansion co-efficient
????????????
∆????????????
Linear expansion
Ifthesubstance isaformofarodoflength????????????????????????????????????????????????????????????uetoth e
increaseintemperaturefromTtoT+∆????????????,t lengthchanges
to????????????+∆????????????.
Int case,
∆????????????
????????????
=????????????
????????????∆????????????,wh ????????????
????????????isthecoefficientoflinear
expansion.
Linear ex coefficient is anintrinsic propertyofmatter.
Materials ????????????
????????????(10
-5
K
-1
)
Alumiminium 2.5
Brass 1.8
Copper 1.7
Iron 1.2
Silver 1.9
Glass (pyrex ) 0.32
Lead 0.29
Thea tablegivesthe
averagevaluesofthelinear
expansioncoefficientofthe
materialsinthetemperature range
0to100 °C.
Fromt
table,itis obviousthat
thecopper expandsfivetimesmore
comparedtoglassforsame risein
temperature.NPTEL

10. Relation between linear expansion co-efficient and volume expansion co- efficient
Consideracubeoflength????????????.Suppose,duetotheincreasein
temperature∆????????????,thelengthin eachdimension enhancesequally.
One side,theincreaseinlengthis∆????????????.
Wehave,∆????????????=????????????????????????
????????????∆????????????.
Int case,change of volume,∆????????????=(????????????+∆????????????)
????????????
−????????????
????????????
=????????????????????????
????????????
∆????????????.
Thete
∆????????????
????????????
and∆????????????
????????????
areneglected.
Hence,
∆????????????
????????????
=????????????.
∆????????????
????????????
=????????????????????????
????????????∆
????????????=????????????
????????????∆????????????.
So,t relationbetween linear and
volumeexpansioncoefficient, is:????????????
????????????=????????????????????????
????????????.
∆???????????? ????????????
Volume expansionNPTEL

11. Considerar ectangularsheetoflengthaand
widthb.
When thetemperatureincreasesby∆????????????,then,
changeoflength,∆????????????=????????????????????????
????????????∆
????????????a change of
width,∆????????????=????????????????????????
????????????∆
????????????.
Accordingtot headjacentfigure, changein
area,∆????????????=????????????∆????????????+????????????∆????????????+∆????????????∆????????????.
Hence,∆????????????=????????????????????????????????????
????????????∆????????????+????????????????????????????????????
????????????∆????????????+????????????????????????(????????????
????????????∆????????????)
????????????
.
Thel isneglected,as it isverysmall.
Hence,
∆????????????
????????????
= 2.????????????
????????????∆
????????????=????????????
????????????∆????????????⇒ ????????????
????????????=2.????????????
????????????
Relation between linear expansion co-efficient and areal expansion co- efficient
????????????+∆????????????
????????????
????????????
????????????+∆????????????
????????????∆???????????? ∆????????????∆????????????
∆????????????.????????????
So,there lationbetweenlinear,areal, andvolumeexpansioncoefficient,
is:????????????
????????????=
????????????????????????
????????????
=
????????????????????????
????????????
.NPTEL

12. Thermal Stress
Thermalst ress isthestress caused byanyvariation in amaterial'stemperature.Thermalstress is
induced in a solidmaterialwhenthetemperatureofthematerialis increasedordecreased butthe
materialisnotallowedtoexpandorcontract.
Thet
thermalstress includes bothheat andcoldstress.
Stress isth
eforce actingperunitarea. Theforcecanbeofanyform.Whentheappliedforceis
intheformoftemperaturetheresultant stress iscalledThermalstress.
????????????
∆????????????
Assh
Figure,when thetemperature is raisedby∆
????????????,thenlengthof
therod increases by∆????????????. Iftheexpansionisstoppedforcefully,then
thermalstress arises.
Forthec
theexpressionforthe thermalstress is,
????????????
????????????=????????????????????????∆????????????.
Thermostatis a v erygoodexampleoftheapplicationofthermalstress.NPTEL

13. Thermal Conduction
Thermalc theabilitytotransferheatfromonesideofthemediumto theotherside,
owingto thedifference in temperature.
Fourier’slawofthermalconduction:Thislawisalsoknownasthelawofheatconduction. According
to thatlaw,therateoftransferofheatthroughamaterialisproportionalto thenegativeofthe
temperature gradientandisalsoproportionalto theareathrough whichtheheat flows.
The d
ofthislaw canbe expressed throughthefollowingequation:
q = -κ
.∆????????????
where∆????????????referstothetemperature gradient, qdenotesthethermalfluxorheatflux,andkrefersto
the thermalconductivityofthematerial.
Metalsa rich conductorsofheat.Whereas, wood,plastic,andrubberare
thebadconductorsofheat.NPTEL

14. Steady- state heat transfer
Consideram
etallicbaroflengthLanduniformcross sectionA
withitstwoendsmaintained atdifferent temperatures,T
CandT
D.
Thiscanbed
one,forexample, byputtingtheendsinthermal
contactwithlargereservoirsattemperatures,asshowninadjacent
Figure.
Assumingt
heideal conditionthatthesidesofthebararefully
insulated sothatnoheatisexchangedbetweenthesidesandthe
surroundings.
????????????
????????????
????????????????????????
????????????????????????
Steady state heat transfer
Afters asteadystatewillbe reached;
thetemperatureofthebardecreasesuniformly
with distancefromT
CtoT
D;(T
C>T
D).NPTEL

15. Steady- state heat transfer
????????????
????????????
????????????????????????
????????????????????????
Steady state heat transfer
Ther offlowofheat(orheatcurrent) H is proportionaltothe
temperature difference(T
C– T
D)andtheareaofcross-section Aandis
inversely proportionalto thelengthL.

Thisis equalto,????????????=????????????????????????.
????????????????????????−????????????????????????
????????????
, where K is calledthethermal
conductivity.
TheSI un
ofthermalconductivity K is J S
-1
m
-1
K
-1
orW m
-1
K
-1
.Materials Thermal conductivity
(J s
-1
m
-1
K
-1
)
MaterialsThermal conductivity
(J s
-1
m
-1
K
-1
)
Silver 406 Insulating
brick
0.15
Copper 385 Concrete 0.8
Aluminium 205 Body fat 0.20
Brass 109 Felt 0.04
Steel 50.2 Glass 0.80
List of thermal conductivities of some materialsNPTEL

16. Thermal p ofmatterareintrinsic properties,whichare material dependent.
Atr
temperature, themolarheatcapacity ofall thesolids isattainedaconstantvalue,which
isknownasDulong-Petit’slaw.
Ats
temperature,specific capacityvarieswithtemperature,obeyingtheT
3
rule.
Thev
expansion,arealexpansionand linearexpansioncoefficientsgenerally obeyacertain
relationship among them,i.e.:????????????
????????????=
????????????
????????????
????????????
=
????????????
????????????
????????????
.
Heatcon
dependsuponthe free electrons.That’swhygoodthermalconductors in
general,possessgoodelectricalconductivity.NPTEL

17. •Physicsof F unctional MaterialsbyHasse Fredriksson&UllaAkerlind.
•ThermalP
ofMatterby JoeKhachan.
•AT
onHeatbyMeghnadSaha,B. N.Srivastava.NPTEL

18. Thank you…NPTEL

19. Physics of Functional Materials and Devices
Prof. Amreesh Chandra
Department of Physics, IIT KHARAGPUR
Module 05: Thermal properties of solids
Lecture 23: Negative and Zero E xpansion CeramicsNPTEL

20. Thermale inceramics
Negativea
ndzerothermalexpansionceramics
ExamplesofN
egativeandzerothermalexpansionceramics
Applicationsofnega
tiveandzerothermalexpansionceramicsNPTEL

21. Thermal expansion
Whatisthermal expansion?
Thermalexpansionreferstothephenomenonwhereamaterialundergoes
dimensionalchangesinresponsetochangesin temperature.Whenasubstance
isheated,itsparticlesgainenergyandbecome moreactive,causingthemto
moveandvibratemorerapidly.Thisincreasedmolecularmotionleadstoan
increaseintheaverageseparationbetweenparticles(interatomicdistance),
resultingin expansionoranincreaseinvolume.NPTEL

22. Thermal expansion
Expansion behavior of materials is
governed by lattice constant
Whatislattice constant?
Theexpansionbehaviorofmaterialscanbedescribedbythecoefficient ofthermalexpansion(CTE),which
measureshowmuchamaterial'sdimensionschangeper unit temperaturechange.The CTEistypically
expressedinunitsoflengthper temperature(e.g.,millimeters per degree Celsiusorinchesper degree
Fahrenheit).NPTEL

23. Thermal expansion in ceramics
Ceramicsa regenerallycomposed ofathree-dimensionalnetworkofatomsorionsheldtogetherbystrong
chemicalbonds.
Whenac
materialisheated, theincrease intemperatureprovidesenergyto the atomsor ions,leading to
greater vibrationalmotion.Thisincreasedmotioncausesthe atomsorionstomoveslightlyfurtherapartfrom
eachother,resultingin expansion.
However,w
henthetemperature decreases,thereduced energy causesthe atomsorionstovibrateless
vigorously,leading toacontraction or compression ofthe material.
Temperature decreased
Contraction
ExpansionNPTEL

24. Thermal expansion in ceramics
General trendsofexpansioninceramics:
Dueto str ofthe atomic bondsceramicsoftenhavealowercoefficient ofthermalexpansion(CTE)
thanmetals,whichmeansthey expandorcontractlessforagivenchangeintemperature.
Ceramic ma
terialsexhibitanisotropicthermal expansion, meaning that theirexpansionorcontraction rates can
varydependingonthedirection orcrystallographic orientation. Thisanisotropyarisesfromthe preferential
alignmentofatomsorionsalong certain crystallographicplanesor directions,resultingindifferentexpansion
coefficientsalongdifferent axes.
Low coe
thermalexpansionexhibitedbysomeceramics makesthemdesirableforcertain applications
wheredimensional stabilityis crucial suchasin electronics,refractorymaterials,and high- precisionengineering.
Why negative and zero thermal
expansion ceramics??NPTEL

25. Negative thermal expansion ceramics
Ceramicsa retend to expandwhenheated and contractwhencooled.
Butthe
areanotherclass ofinterestingceramicsviz.,’negative thermalexpansion ceramic’.
What arenegativeand zeroexpansionceramics?
Negative andzeroexpansionceramics,alsoknownaszerothermalexpansion(ZTE)ceramics ornegativethermal
expansion(NTE)ceramics,are aclass ofmaterialsthatexhibitminimalorevennegative thermal expansion
coefficients. Thismeansthat theyeither minimallyexpandorgetcontractwhen subjectedtotemperaturechanges.
Zeroe
ceramicshaveacoefficient ofthermalexpansion(CTE)closetozero,meaning they undergo
negligibledimensional changeswhen subjectedtotemperaturevariations.
Negative e
ceramics,onthe other hand, haveanegativeCTE,implyingthatthey contractorshrinkin
volumeastemperatureincreases.
Distortion or stress caused by thermal expansion CAN BE
AVOIDED USING NEGATIVE AND ZERO EXPANSION
CERAMICSNPTEL

26. Let us take an example of
a functional ceramicNPTEL

27. Aninterestingfeaturewhichhasbeen observed
inmostofthecommonand usefulferroelectric
materials isthattheyhavecrystalunitcell
which isofperovskiteABO
3
-type.NPTEL

28. SAMPLE REPARATION



Mixing of PbCO3, CaCO3 and TiO2 in mortar pestle for 2h in acetone.












Ball milling for 6 h using acetone as mixing media
First calcination in air at 750
o
C for 6 h























Second calcination in closed PbO atmosphere at 900
o
C for 6h.
Ball milling for 1h using acetone as mixing media to break the
agglomerates
Pelletization at an optimized pressure














Sintering in closed PbO atmosphere at 1200
o
C for 6h to get dense
ceramic pellets having density >94%. NPTEL

29. Room Temperature powder XRD Pattern of sintered PbTiO
3and CaTiO
3
20 40 60
220
202
211
112
201
102
200
002
111
110
101
100
001
X-ray diffraction pattern for pure PbTiO
3
.
All the peaks are indexed using a tetragonal P4mm unit cell
Intensity (a.u.)
2θ (degrees)
20 40 60
404
223
313
421
224
400
312
222
311
310
221
202
201
200
X-ray diffraction pattern for pure CaTiO
3
.
All the peaks have been indexed using a orthorhombic Pbnm cell.
Intensity (a.u.)
2θ(degrees)NPTEL

30. Compositional Dependent Structural Changes in Pb
1-xCa
xTiO
3at room temperature
46 48
35 38
35 38
47 4935 38
120
021
012
200
002
111
(a)
(e)
203
312
421
402
313
222
004
310
311
322
(f)
(b)
(c) (g)
35 39 43 47 51 55
(d)
Two-theta (deg.)
37 41 45 49 53
x=0.20
x=0.30
x=0.40
x=0.50
(h)
322


310
311

311
310


x=0.60

322
x=1.00
x=0.80
x=0.70

311
310
Note: There is sudden change
in XRD pattern at x=0.40 with
appearance of weak
superlatticepeaks (shown in
Inset). These superlattice peaks
have significant intensity at
x>0.60.NPTEL

31. Theoriginofthermal expansioncanbeunderstoodbyconsideringtheeffect
ofanharmonictermsinthepotentialenergywellbetweenapairofatomsina
solid. Atypical anharmonic potentialenergycurveis schematicallyshownin in
thisviewgraph.
Thermal expansionisadirectconsequenceofthedeviationfromsymmetry
(thatis,asymmetry)ofthepotentialenergycurvecharacteristicofsolids.
UNDERSTANDING ORIGIN OF EXPANSION IN SOLIDSNPTEL

32. EXPERIMENTAL SET-UP FOR DILATOMETRY
A LKB fused quartz
thermodilatometerNPTEL

33. 275 475 675 875 1075
0
20
40
60
80
(d)PCT45
Temperature (K)
% Linear thermal expansion (10
6)
275 475 675 875 1075
0
20
40
60
275 350 425 500
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
(c)PCT40
% Linear thermal expansion (10
6)
Temperature (K)
% linear thermal Expansion
Temperature (K)
275 475 675 875 1075
-15
-5
5
15
25
35
(b) PCT35
% Linear thermal expansion (10
6)
Temperature (K)
275 475 675 875 1075
-20
-10
0
10
(a) PCT30
Temperature(K)
% Linear thermal expansion(10
-6
)
DILATOMETRIC RESULTSNPTEL

34. Sample
Composition
Temperature
range in
(K)
Coefficient of Thermal
Expansion x 10
6
(K
-1
)
PCT30 I (300-520)
II (520-652)
III (652-1023)
-8.541
-1.735
9.662
PCT35 I (300-491)
II (491-820)
III (820-1023)
-5.688
12.35
2.863
PCT40 I (300-410)
II (410-470)
III (470-850)
IV (850-1023)
-0.6673
3.569
14.24
7.756
PCT45 I (300-345)
II (345-1023)
0.6568
12.59
VARIATION OF LINEAR THERMAL EXPANSION COEFFICIENTS FOR PCT COMPOSITIONSNPTEL

35. 275 475 675 875 1075
0
1000
2000
3000
4000
0
1000
2000
3000
275 475 675 875 1075
-20
-10
0
10
(a)
For Pb
0.70
Ca
0.30
TiO
3
(a) Variation of percent linear thermal expansion
(b) Variation of real (ε
/
) and imaginary (ε
//
)
parts of dielectric constant
Temperature(K)
% L.T.E. (10
-6
)
(b)
ε
/
Temperature(K)
ε
/
ε
//
ε
//


CROSS OVER FROM NTE TO PTE IS RELATED
TO A PHASE TRANSTIONNPTEL

36. Thermal expansion behaviour of
PCT using X-ray diffraction studiesNPTEL

37. 0 200 400 600 800
3.940
3.944
3.948
3.952
3.956
0 200 400 600 800
3.86
3.91
3.96
4.01
4.06
4.11
050 100
3.950
3.952
3.954
3.956
3.958
For Pb
0.70
Ca
0.30
TiO
3
.
a) Variation of the unit cell a,c parameters
b) Variation of the unit cell volume
The inset shows the sudden change in
volume expansion at around 70K
b)
cell volume
cell-volume
1/3
(A)
Temperature (K)
o
o
a)
cell-parameter (a,c) (A)
Temperature (K)
a parameter
c parameter
cell volume (a
2c)
1/ 3
(A)
Temperature (K)NPTEL

38. VariationofBonds LengthsandDeterminationofMajor bond lengths,whichplaythedominantrolein introducingNTE
behaviourin PCT
Displacement Directions in
Tetragonal cell with P4mm
space group
2.33
2.36
2.39

Ti-O
I (-)
1.74
1.78

Ti-O
I (+)
1.97
2.00

Ti-O
II
Bond Length (A)
2.761
2.786
2.811

Pb-O
(I)
2.487
2.512

Pb
(-)
O
(II)
3.17
3.21

Pb
(+)
O
( II )
0100 200 300
2.003
2.007
Average Ti-O
0100 200 300
2.831
2.839
2.847
Average Pb-O
Variation of various
bond length in PCT10
Temperature (K)NPTEL

39. 1)PCT ceramics withx=0.30, 0.35and0.40revealpresenceofnegativethermal expansion behaviour above.Forx=0.45,the
expansioncoefficientbecomespositive.
2)Forx=0.30isquitelargeNTEcoeeficient is(–8.541 x 10
-6
K
-1
)inthetemperature range300to520K.
3)NTEbehaviour hasalsobeen confirmedintheXRDstudies.
4)The NTEbehaviouris closelyrelatedwith ferroelectricphasetransition
5)The NTEbehaviourispresentonly inthetetragonalcompositions ofPCT
6)TheexpansioncoefficientofPCT ceramicscanbetailored fromnegativetopositivevaluesbyvaryingtheCa2+content.NPTEL

40. Examples of negative and zero expansion ceramics
ZirconiumT ungstate(ZrW
2O
8):
Zirconiumtu
ngstateisawell-knownnegative expansionceramicwitha verylow
CTE(averageCTEof-7.2x10
−6
K
−1
)
Ite
acontractioninvolumecontinuouslyastemperatureincreasesover
the rangeof0.3to1050K.
Ite
in cubicstructuresothe thermal contractionis isotropic-equalinall
directions.
SiliconCar
(SiC):
CertainS
-basedcompositescanexhibitnear-zeroorevennegative thermal
expansionbehaviorwithCTEofSiCtypicallyrangesfrom 4-6 x10
-6
perdegree
Celsius(μm/°C)inthetemperaturerangeof25-1000°C.
SiC'slo
thermalexpansionhelpstominimizethe potentialforthermalstress
and deformationincomponentssubjectedto thermalcyclingorhigh-temperature
conditions
Alumina-M (Al
2O
3-SiO
2):
Alumina-mul
liteceramicscanbetailoredto haveloworevennegative
expansioncoefficients,making themsuitableforapplicationswherethermal
stabilityiscrucial,suchasinrefractoryliningsorhigh-temperature
environments.NPTEL

41. Applications of negative and zero expansion ceramics
AerospaceI ndustries: Negative andzerothermalexpansionceramicsfind applicationsintheaerospace
industrywheretheyareusedin componentsthatrequirehigh thermal stability.
These materialscanbeusedinthe fabricationofsatellitecomponents, rocketnozzles,and thermalprotection
systemsforre-entryvehicles.
Satellite Co
mponents: Satellites operateinextreme temperaturevariationsas they transitbetweensunlight
and shadowed areas.
Negative andzerothermalexpansionceramicscanbeusedintheconstruction ofsatellitecomponents, suchas
reflectors,antennasupports,and structuralelements.
These ceramics helpmaintain the structural integrity and dimensional stabilityofthe components as they
experience temperaturefluctuations.NPTEL

42. Applications of negative and zero expansion ceramics
RocketN :Rocketengines generate intense heat during operation,causingthenozzleto expand.
Theuseofnegative andzerothermalexpansionceramicsintheconstruction of rocketnozzles helpsto
counteract theexpansionand maintain thenozzle'sshape andperformance.
These ceramicscan withstand hightemperaturesandminimizethermalstresses,ensuring thereliabilityand
efficiency ofthepropulsionsystem.
HypersonicV
ehicles:Negative andzerothermalexpansionceramicsareusedinhypersonic vehicles, such
vehiclestravelatextremelyhighspeeds,generating intense heatdueto aircompression.
Negative andzerothermalexpansionceramicscanhelpmitigate thermalexpansioneffectsand maintainthe
structural integrityof critical components, suchas leadingedges,control surfaces,and thermalshields.NPTEL

43. Applications of negative and zero expansion ceramics
Electronicsan dSemiconductors: Theelectronicsandsemiconductorindustriesrequire materialswithprecise
dimensional stability toensure reliable performance.
Negative andzerothermalexpansionceramicscanbecan counteract the expansionmismatchbetween different
materials.
OpticalDev
icesandLasers:
Negative andzerothermalexpansionceramicsareemployedinthe
manufacturingofopticaldevices, suchaslenses,mirrors,andlaser
components.
Theseceramicsofferexcellentthermal stability,allowingprecise
alignment and maintaining opticalperformance undervaryingtemperature
conditions.
They helpminimizedistortions andensure reliableoperationofoptical
systems.NPTEL

44. Applications of negative and zero expansion ceramics
Micro- elec :Microelectromechanicalsystems(MEMS)
often require materialswithcontrolledthermalexpansionproperties.
Negative andzerothermalexpansionceramicscanbeutilizedinthe fabricationofMEMS
devicestominimizethermalstressesandensureaccurateoperation.
They helpmaintain the structural integrity and functionalityofMEMS componentsunder
varyingtemperatureconditions
Substrates and PCBs: : Aprintedcircuitboard,orPCB,incorporatestoprovide
electricalconnectionsinelectroniccomponentsusing conductivepathways
suchascoppersheets.
Negative andzerothermalexpansionceramicshelpcontrol thecoefficient of
thermalexpansion(CTE)ofthe substratematerial,enablingbettermatchingwith
semiconductorcomponents andreducingtherisk ofsolderjointfailuresdue to
thermalcycling.
They alsoprovideimproveddimensional stability,ensuring reliable performance
ofelectronic assemblies.NPTEL

45. Applications of negative and zero expansion ceramics
Energyan Nuclear Applications: Negativeandzerothermalexpansionceramicsarealso utilizedinthe
energysectorespeciallyinthefieldofnuclear,solar,andenergyconversionsystems.
Fuel E
and Cladding:
Negative andzerothermalexpansionceramicscanbeemployedasfuel elementsorcladding materialsinnuclear
reactors.
Theseceramicscan maintain their dimensional stabilityevenathightemperatures, reducingtherisk of
deformationorfailure.
Theycanhelp prevent fuel swellingand maintain the integrityofthefuel assembly,enhancing thesafetyand
efficiency ofthe reactor.
In nuclear reactorsNPTEL

46. Applications of negative and zero expansion ceramics
Neutrons Absorbers:
Inn
uclearreactors,neutronabsorbers areusedtocontroltheneutron fluxand maintain thedesired power
level.
Negative andzerothermalexpansionceramicscanbeincorporatedintoneutronabsorbermaterialstoprovide
stabledimensionsand enhance theireffectiveness.
Theprecise control ofthermalexpansionpropertiescanhelpoptimizetheperformanceandefficiency of
neutronabsorbers.
Coatings and Insulation:
N
TEandZTEceramicscanbeusedas coatingsorinsulationmaterialsinnuclear
reactors.
These ceramicscanprovidethermalexpansionmatchingwithothercomponents,
reducingstressand preventing the degradationofcoatings.
Additionally,they canoffereffectivethermal insulation,reducingheat transfer and
improvingenergyefficiency inthe reactorsystem.NPTEL

47. Applications of negative and zero expansion ceramics
In solar cells
ConcentratedSo lar Power(CSP)Systems:CSPsystems usemirrorsorlenses
to concentrate sunlight ontoasolarreceiverto generate heator electricity.
NTEandZTEceramicscanbeusedintheconstruction ofthese concentrator
systemsto maintain dimensional stability andminimizetheeffectsofthermal
expansionandcontraction.
Byutilizing ceramicswithtailoredthermalexpansionproperties,the concentrators
can maintaintheirshape and alignmentoverarangeoftemperatures,optimizing
theefficiency oftheCSPsystem.
Solar T
Collectors:NTEandZTEceramics canbeutilizedinthe
constructionofsolarthermalcollectors, whichabsorbsunlight andconvertit
into heatenergy.
By incorporating theseceramicsinto thecollectormaterials,it is possibleto
minimizetheeffectsofthermalexpansionand contraction,ensuringthe
structural integrityofthecollectorandmaximizingthe heatabsorption efficiency.NPTEL

48. Applications of negative and zero expansion ceramics
In energy conversion systems
Heat E ThermoelectricDevi ces:Thermal E Storage
Theseceramicscanhelpcounteract
thermal expansion mismatches
between differentcomponents, such
astubes,fins,and headers,reducing
stressandimprovingheat transfer
efficiency.
NTEandZTEceramicscanbe
utilizedinthermoelectric
devices,which convert
temperature differencesinto
electricity.
Ceramicsmitigate thermalstresses
andensurethe dimensional stability
ofthermalenergystorage materials,
improvingtheir reliabilityand
efficiency.NPTEL

49. Thermal e xpansion brings dimensional changes inresponse to changes intemperaturein
materials.
Duet
ceramicsoftenhavealowercoefficientof thermal
expansion(CTE)than metals.
Negativea
ndzeroexpansion ceramics, either minimallyexpandor get contracted when
subjected to temperature changes.
Negativea
ndzeroexpansionceramicsfind applications inalargenumber ofapplications
rangingfromaerospace,energy conversion systems, electronics to semiconductors industry.NPTEL

50. ⮚Physics of Functional Materials by HasseFredriksson & Ulla Akerlind
⮚Introduction to Solid State Physics by Charles Kittle
⮚Atkins’s Physical Chemistry by Peter Atkins, and Julio de Paula.
⮚A Textbook of Nanoscience and Nanotechnology, P. I. Varghese and Thalappil, McGraw Hill
Education, 2017.
⮚PhD Thesis –AmreeshChandra (2004), SMST, IT BHU.
⮚Research Publications of Prof. AmreeshChandra.NPTEL

51. Thank you…NPTEL

52. Physics of Functional Materials and Devices
Prof. Amreesh Chandra
Department of Physics, IIT KHARAGPUR
Module 05: Thermal properties of solids
Lecture 24: Heat CapacityNPTEL

53. Heat Transfer
Specific H
Heat
Specific H
Pressure
Enthalpy
Re
between C
Pand C
Vfor an Ideal Gas
Heat Capacity of Solid-i) D
ulong– Petit law
ii) Einstein model
Einstein m
NPTEL

54. Heat Transfer
Heat is defined as the kind of energy that is transmitted over a boundary as a result of a temperature differential.
In the process of reaching thermodynamic equilibrium, heat is transferred
from the warmer object to the cooler object.
At the thermodynamic equilibrium heat transfer is zero
How heat will transfer??NPTEL

55. Process involve in heat transfer
Heat transfer is classified into t hree types: -
•Heat c
or thermal conduction: -
The transfer ofenergyfrom one medium particletoanotherwiththeparticlesindirect
contactwithone other.
•Convection o r thermal convection: -
The movement of fluid thatcauses heattobe transferred from onelocation toanother.
•Radiation or thermal r adiation: -
The energyemittedbymatter inthe form of photons orelectromagnetic waves.
Conduction of heat
Convection of heat
Radiation NPTEL

56. Example
Con
duction, convection and radiation of heatNPTEL

57. Specific Heat and Latent Heat
Specific H
The quantity of heat that must be added to a substance's mass in order to raise its temperature by one degree.
Q = C m ∆t (S.I unit of specific heat is J kg
-1
K
-1
)
Where,
Q = quantity of heat absorbed by a body
m = mass of the body
∆t = Rise in temperature
C = Specific heat capacity of a substance depends on the nature of the material of the substance.NPTEL

58. Latent H
Latentheatisenergyabsorbedorreleasedbyasubstanceduringachangein itsphysicalstate(phase)
thatoccurswithoutchangingitstemperature.
Thelatentheatproducedbymeltingasolidorfreezingaliquid.
2) Heat of vaporization1) Heat of fusion
Two types of latent heatNPTEL

59. Specific Heat at Constant Volume and Pressure
Specific Heat at Constant Vo lume
Therateof change ofspecificinternalenergywithrespectto
temperaturewhenthe volumeisheld constant.
Specific Heat at Constant Pr essure
The rate of change of enthalpy with respect to temperature when
the pressure is held constant
????????????
????????????=
????????????????????????
????????????????????????
????????????
????????????
????????????=
????????????ℎ
????????????????????????
????????????
Where, ????????????= internal energy, ????????????= temperature, ????????????= volume
Where, ℎ= enthalpy, ????????????= temperature, ???????????? = volume
The heat capacity at constant pressure CP is greater than the heat capacity at constant volume
CV , because when heat is added at constant pressure, the substance expands and workNPTEL

60. •The s
system.
•Enthalpy is a property or state function that resembles energy; i
t has the same dimensions as
energy and derives all of its value from the system's composition, temperature, and pressure.
•The enthalpy change is exactly equal to the heat imparted to the syste wh
enthe only work
involved is a change in volume at constant pressure.
Enthalpy
Where, H = enthalpy,
E= internal energy of thermodynamic system,
P = pressure of thermodynamic system,
V = volume of thermodynamic system
H = E + PVNPTEL

61. Relationship between C
Pand C
Vfor an Ideal Gas
From the equation,
Q = n C∆T
Atconstant pressureP,
Q
P= n C
P∆T
This valueisequaltothe changeinenthalpy,
Q
P= n C
P∆T=∆H
Similarly,atconstant volumeV,wehave
Q
V= n C
V∆T
This valueisequaltothe changeininternal energy,
Q
V= n C
V∆T=∆U
Weknow that for onemole(n=1) ofan idealgas,
∆H =∆U+∆(PV )=∆U+∆(RT)=∆U+ R∆T
Therefore,
∆H =∆U+ R∆T
Substituting the values of ∆H and ∆U from above in the
former equation,
C
P∆T = C
V∆T + R ∆T
C
P= C
V+ R
C
P– C
V= R
Where, C
p= Specific heat at constant pressure
C
V= Specific heat at constant volume
R = gas constant
Q = heat
T = temperature
U = internal energyNPTEL

62. Heat capacity ratio
•The h
•The r
constant pressure (C
P) to heat capacity at constant volume
(C
V).
•It i
factor.
•It re
the γfor an ideal gas and κ isentropic exponent for a real gas.
•Heat capacity ratio-
????????????=
????????????????????????
????????????????????????
The heat capacity ratio is important for its applications inthermodynamicalreversible processes.
where, C
p= Specific heat at constant pressure
C
V= Specific heat at constant volume
R = gas constant
????????????
????????????=
???????????? ????????????
???????????? −1
????????????
????????????=
????????????
???????????? −1NPTEi

63. Dulong–Petit Law
DulongPwhich states the classical expression of molar specific heat capacity.
•According t
Dulong and Petit law, the gram-atomic heat capacity i.e. the product of the specific heat capacity and the
atomic mass of an element remains constant.
•The D
and Petit law offers a good prediction for the heat capacity of many elementary solids at higher temperatures .
DulongP
Equation
c×M=k
c×M=3R
For a mass m of the sample divided by its molar mass M, gives us the number of moles.
C×(M/m)=3R
C/n=3R
C = 3nR = 3nK
B
here, c = specific heat capacity, M = molar mass, k = constant, n = number of moles, R = gas constant,
K
B= Boltzmann constant
The law is invalid for
compounds found in the
cryogenic range.NPTEL

64. Einstein model
Thee theoremassumedthateachatomcanbemodeledasaclassicharmonicoscillator.However,atlow
temperaturesthisled toa discrepancyintheheatcapacity betweenthelawof Dulong–Petit andtheobservedheatcapacity. the
quantummechanicalbehavior of harmonicoscillators isdifferent,especially atlowenergies.
Einsteinc
-
i) Theatomsare independent quantum harmonicoscillators
ii)Eachatom has thesamefrequency
Heat cap
per harmonicoscillator-
C(T) =????????????
????????????
????????????????????????
????????????
????????????
????????????
????????????
????????????
(????????????
????????????
????????????
????????????
− ????????????)
????????????
where, theEinstein temperature T
E =
ℏω
0
????????????
????????????
, T = temperature, K
b=constantNPTEL

65. NPTEL

66. •Heat t fromahighertemperature toalowertemperature. Therefore,at
equilibrium,heattransferiszero.
•Specifiche
atisneededtoincreasethetemperaturebyone degree.
•Latenthe
changesthephysicalstateofamaterial.
•Dulong-Pe
titlaw givesus an appropriate relationship ofspecificheatcapacityand
atomicmassesof solids.
•TheEi
correctlypredictsthat the heatcapacitydropsto0asT→0.NPTEL

67. •Physicsof F unctional MaterialsbyHasse Fredriksson&UllaAkerlind.
•ThermalP
ofMatterby JoeKhachan.
•AT
onHeatbyMeghnadSaha,B. N.Srivastava.NPTEL

68. Thank you…NPTEL

69. Physics of Functional Materials & Devices
Prof. Amreesh Chandra
Department of Physics, IIT KHARAGPUR
Module05:Thermalpropertiesofsolids
Lecture25:Thermogravimetric(TGA)analysisNPTEL

70. IntroductionToT hermalAnalysis
Processeso
masschange
Workingm
ofTGA
TGAt
analysis
Exampleo

Applicationso
fTGANPTEL

71. 3
Thermalanalysis isatechniquetostudythebehaviorandpropertiesofmaterialsas
theirresponsetochangesintemperature.
Itinvolves measuring andanalyzing variousthermalproperties
Introduction To Thermal Analysis
What is Thermal Analysis
Property Technique
Change in weight of a sample Thermogravimetric Analysis (TGA)
Change in heat of Transitions Differential Thermal Analysis (DTA)
Thermal Expansion Thermal Mechanical Analysis (TMA)
Heat flow during Transitions Differential Scanning Calorimetric (DSC)
Temperature at which gas is desorbed from
(catalyst) surface
Temperature Programmed Desorption (TPD)
Types of thermal analysis:NPTEL

72. 4
Introduction
Thermal Gravimetric Analysis
Temperature
variation
Mass change Microbalance
causing detected by
•Thermogravimetryorth ermogravimetricanalysisis an analytical
methodthatrecordsthemasschangebytemperatureofa
samplethatis facingacontrolledtemperatureprofile.
•Thesample undergo heating,cooling or isothermalsteps.
•Theresulting measurement signal gives theabsolutemass
change in[mg]andrelativemasschange in[%].
What is thermogravimetric analysis?
Fig. : TGA Sensor setup in a typical
thermogravimetric analyzerNPTEL

73. 5
Processesofmasschange
Weight loss processes:
oDecomposition: The breaking apart of chemical bonds.
oEvaporation: The loss of volatiles with elevated temperature.
oReduction: Interaction of sample to a reducing atmosphere (hydrogen, ammonia, etc).
oDesorption
Weight gain processes:
oOxidation: Interaction of the sample with an oxidizing atmosphere.
oAbsorption
oAdsorption
oNitrideformation
All of these are kinetic processes
(i.e. there is a rate at which they occur)NPTEL

74. 6
WorkingmechanismofTGA
Weight change
Null detector
Restoring force
•The balanceoperates onanull-balance principle.At thezero,
or“null”position equalamountsoflight shineontwo
photodiodes.
•Ifthebalancemovesoutofthenullpositionanunequal
amountoflightshinesontwophotodiodes. Current isthen
appliedto themeter movementtoreturnthebalanceto the
nullposition.
•Theamountofcurrentappliedis
proportionalto theweightlossor
gain.
Fig. : TGA Instrument Scheme
Fig. : Null point balance
https://sites.google.com/a/iastate.edu/laboratory-10-thermogravimetric-
analysis/experimental-methodsNPTEL

75. 7
Workingmechanism
TGA thermogram analysis:
https://psiberg.com/thermogravimetric-analysis/
where,
•????????????m ischangeinmass
•T
iis initial temperature
•T
fisfinaltemperature
•Onset:Thetemperaturepointonthe
thermogram where thethermaldecomposition
orreactionofthesamplebegins.
•Endpoint:Thetemperaturepointonthe
thermogram where thethermaldecomposition
orreactionofthesampleiscompleteNPTEL

76. 8
TypesofTGAcurves
WEIGHT PERCENT
(%)
TEMPERATURE (
o
C)
0
20
40
60
80
No significant
weight change
200 400 600 1000800
WEIGHT PERCENT
(%)
TEMPERATURE (
o
C)
0
20
40
60
80
200 400 600 1000800
Drying of solvents and
no further change
WEIGHT PERCENT
(%)
TEMPERATURE (
o
C)
0
20
40
60
80
200 400 600 1000800
Signature curv e of TGA
Multi step weight loss
WEIGHT PERCENT
(%)
TEMPERATURE (
o
C)
0
20
40
60
80
200 400 600 1000800
Oxidation curve
1. No significant change in mass 2. Drying or desorption occurs 3. Single-step decomposition
4. Multistep decomposition 5. Oxidation
https://psiberg.com/thermogravimetric-analysis/NPTEL

77. 9
Factors affecting TGA curves:
1. Heating rate
2. Sample size
3. The particle size of the sample
4. Crucible shape and type
5. Gas flow rate
6. Gas type Fig. : Effect of heating rate on TGA curve of Teflon
https://psiberg.com/thermogravimetric-analysis/NPTEL

78. 10
Applications of TGA:
Activation energy
T
hermal stability
Determination of accurate drying temperature
Analysis of the burning point and ash content
Material identification and purity assessment
Deduction of the composition of materials and their characterization
Corrosion studies of chemical substances
Aging studiesNPTEL

79. NPTEL

80. The t analysis (TGA)methodhasbeendiscussedbriefly.
Differentt
ypesof TGAcurvehasbeenhighlighted.
Heating r
samplesize, particle size,andother factorsaffectthe TGAanalysis.
Different ap
plicationsof TGAhavebeenhighlighted.NPTEL

81. ⮚Physics of Functional Materials by HasseFredriksson & Ulla Akerlind
⮚Introduction to Solid State Physics by Charles Kittle
⮚Atkins’s Physical Chemistry by Peter Atkins, and Julio de Paula.
⮚A Textbook of Nanoscience and Nanotechnology, P. I. Varghese and Thalappil, McGraw Hill Education, 2017.NPTEL

82. Thank you…NPTEL