Scienza e Tecnologia dei Materiali Ceramici Modulo 2 ...
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Scienza e Tecnologia dei Materiali Ceramici
Modulo 2: Materiali Nanostrutturati
- Lezione 2 -
Vanni Lughi
[email protected] 558 3769
Dipartimento di Ingegneria e ArchitetturaUniversità degli Studi di Trieste
Università degli Studi di TriesteDipartimento di Ingegneria e Architettura
A.A. 2021-2022
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Esame e criteri di valutazione
Modalità d’esame e criteri di valutazione• Ricerca bibliografica su argomento a scelta• Homework• Valutazione finale:
– Presentazione e discussione della ricerca bibliografica (10 punti)– Partecipazione e homework (5 punti)– Domanda a scelta dello studente (5)– Domanda a scelta del docente (10 punti)
Appelli• Ufficiali (previa conferma)• Su appuntamento (collettivo)
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Previous lectures: Review
• Course “instructions”
• Definition of objectives and overview ofcourse content
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Homework #1
Identify «hot topics» in the nanoworld. Classify themaccording to: societal challenges, key enablingtechnologies, applications
Societal Challenges:
- Health and Wellbeing
- Secure, green, efficient energy
- Food and Waste
Key Enabling Technologies
- Micro- and nanoelectronics
- Advanced Materials and Advanced Manufacturing
- Photonics
- Biotechnology (industrial)
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This lecture: Content
• Examples of what is nano and what is not
• Surfaces and interfaces (see lecture notes)
– Review of relevant thermodynamic definitions
– Fundamentals on surface energy and chemicalpotential
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When “nano” is actually “nano”?
• Example 1: Thin films
Mechanical properties (e.g. strength) Electrical properties (e.g. resistivity)
bulknano
g
inTSd
K Hall-Petch
t
KfinfTS ,, (t: film thickness)
Strength increases for thin films Resistivity increases for thin films
Bulk limit
The “nano” limit is different for different materials properties
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When “nano” is actually “nano”?
• Example 2: Spherical particles
1
1.5
2
2.5
3
3.5
4
0 2 4 6 8
Stre
ngt
h [
GP
a]
Particle size [m]
Alumina particles
Mechanical properties (e.g. strength) Optoelectronic properties (e.g. color)
Yoshida M et al., Rev. Sci. Instrum. 76, 093905 (2005) L. Cozzarini, PhD Thesis, 2012
Energy of the first absorption peak
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Importance of Surface
• Fraction of surface atoms increases rapidly when size drops
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Importance of Surface
For a compact structure with coordination 12:
Number of surface atoms, S:
S = 10n2 + 2(n is the number of shells)
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Importance of Surface
Surface energy
Forces acting on bulk and surface atoms
TPA
Gs
,
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Importance of Surface
Total surface energy increase
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Importance of Surface
Total surface energy increase
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Where are we?
2. Design di materiali nanostrutturati
– Fondamentali: stato solido, approfondimenti di fisica e chimica (anche sparsi durante il corso)
– Proprietà alla nanoscala
– Attività seminariale sulla modellazione
– Esempi in cui la nanostruttura determina le proprietà e di come queste possono essere "previste“:
• quantum wells; banda intermedia; nanocompositi; opali artificiali; modificazione dell'energia superficiale mediante nanocoatings; etc.
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• Effect of size on vapor pressure
(This is a curvature effect!)
Importance of Surface – Properties at the Nanoscale
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• Melting point vs size
Gold nanoparticles
Importance of Surface – Properties at the Nanoscale
𝑇𝑏 − 𝑇𝑚 =2𝑇𝑏
∆𝐻𝜌𝑠𝑟𝑠𝛾𝑠 − 𝛾𝑙
𝜌𝑠𝜌𝑙
23
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• Inhibition of phase transformation in zirconia
Driving force to transformation:
where
For stress-free, undoped spherical zirconia particles:
A critical particle radius exist, for which the tetragonal phase is thermodynamically stable
(5 to 10 nm for pure zirconia powders, 30 nm for solid ceramics)
Importance of Surface – Properties at the Nanoscale
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Thermodynamicsof surface-intensive systems
Surface tension(also: surface energy, surface free energy, etc.)
Chemical potential
ad-hoc term𝐺 = 𝑈 − 𝑇𝑆 + 𝑃𝑉 + 𝜇𝑁 + 𝛾𝐴
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Surface thermodynamics- Gibbs’ approach -
«excess quantities»
surface of area A
In general gs = γonly in pure single component systems
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Estimates of surface energy
Surface energy is of the same order of the surface tension FL:FL
Estimate of for a (111) surface in a compact structure leads to:
us = 0.25 Ls/Na [J/surf. atom]
Considering that = us + Pvs - Tss
we need to take into account entropy effects:
= 0.15 Ls/Na [J/surf. atom]
Ls: sublimation latent heatNa: Avogadro
ST P
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Close-packed Structures
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Corrections to surface energy estimates:Surface reconstruction
Minimization of energy - Entropy increases
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High Index Planes (Vicinal Surfaces)
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Surface Energy of High Index Planes
a
22)sin(cos
auS
E
0
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Surface Energy of High Index Planes
a
22)sin(cos
auS
us
0
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Wulff ConstructionEquilibrium shape of an isolated crystal
i
ii AMinimize
Gibb’s theorem:
Also a way to find the surface energywhen the shape of a crystal is known
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Equilibrium shape of an isolated crystal
NaCl Gold at 1000°C
Quartz
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Equilibrium shape:Roughening Temperature
• The surface energy depends on temperature :
ST P
Gold at 1000°CFacets tend to disappear upon increasing temperature
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Take-home message
• Importance of the surface
• Homegame: for a system containing a givenamount of material, calculate how the surfacearea increases when the size of the system’selement decrease
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Surface energy minimization
1. Surface mechanisms
• Surface relaxation
• Surface reconstruction
• Chemi- or physisorption ofspecies at the surface
• Surface segregation
BaTiO3/SrTiO3
Si (111), 7x7 reconstruction
Surface mechanisms ofenergy minimization are of major importance in
nanostructures
More than one dangling bond per atom
Importantconsequenceson doping ofnanostructures
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Surface energy minimization
2. Individual structure mechanisms
• Isotropic systems (liquids, amorphous solids): Total surface area minimization
• Anisotropic systems (solid crystals): Minimize
Wulff’s theorem
i
ii A
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Surface energy minimization
3. Overall system mechanisms
• Aggregation of individual structures
• Formation of new structures– Sintering
– Ostwald ripening
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Agglomeration - aggregation
• Chemical bonds
• Physical bonds (Van der Waals)
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Sintering
Mechanisms in diffusion controlled sintering:
Mechanism Source of matter
1. Surface diffusion Surface
2. Vapor transport Surface
3. Lattice diffusion Surface
4. Lattice diffusion Grain boundary
5. Boundary diffusion Grain boundary
6. Lattice diffusion Dislocations
1
23
4
56
•All mechanisms are driven by surface area reduction•All lead to neck growth•Only mechanisms 4, 5, and 6 lead to densification
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Sintering
• Stage 1:
Initial neck growth
• Stage 2:
Large necks, cylindricalinterconnected pores
• Stage 3:
Isolated, spherical pores
1
2
3
200 m100 m
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Sintering rate (time) diagrams
Rates are driven by the curvature difference
nKDAdt
dr
More to come!
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Sintering conditions
• Low porosity• Densification
• High porosity• No Densification
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Ostwald ripening- curvature and chemical potential -
Young – Laplace equation
r
2
Gibbs – Thompson equation
rS
STk c
B
2ln
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Ostwald ripening- curvature and chemical potential -
Driving force for Ostwald ripening
21
112
rr
r1
r2
1. Dissolution
3. Precipitation
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Ostwald ripening
Consequences:
• Exaggerated grain growth in sintering
• Growth of nanocrystals in solution:– Can either focus or broaden the size distribution