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Energy and Thermodynamics:
Marvelous Materials and
Phascinating Phenomena
Alexandra Navrotsky
UC Davis
Energy, Environment, Resources,
Climate
• Mineralogical, solid state chemical and thermodynamic
aspects of
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CO2 management
Nuclear energy
Water
Metals
No free lunch
Science – policy – politics
Thermodynamics wins in the long run
Materials
• Electronic, optical, multiferroic,
catalytic
• Energy storage and release- fuel
cells, batteries
• The nuclear fuel cycle
• CO2 management and
sequestration
Why I Count Calories
for a Living
• They are fascinating
– Energetics whisper secrets of the strength of chemical bonds
– Entropies sing of vibrating atoms, moving electrons, and
structural disorder
– Systematics have predictive power
• They pay
– thermodynamic data are essential to good materials processing
– Environmental science needs thermodynamics, both for issues of
stability and as a starting point for kinetics
– Mineralogy, petrology, and deep Earth geophysics need
thermodynamic data.
Thermodynamics
• Is a policeman
• Eliminates the impossible
• Identifies the improbable
• Simplifies your life
– Links what can be measured to what you really want to know
– Limits the number of independent variables
– Tells you if materials are compatible and under what conditions
they might be made
• Provides a macroscopic formalism that links to
microscopic insights
– Quantum mechanics  statistical mechanics  thermodynamics
– Links directly to structure and dynamics in solids
– “Spectroscopy without selection rules”- everything contributes
Commercial Setaram AlexSYS Calorimeter
Calorimetric Measurement of Surface
Enthalpies (Energies)
• Measure enthalpy of solution versus surface
area, slope of line will give surface energy
Complications
– Particles are hydrated and hold water strongly
– Particles may be agglomerated, twinned, etc. so
sizes estimated by Xray, TEM, BET may differ and
interfacial energies may play a role
Water Adsorption Calorimetry
Volumetric dosing system
Calvet-type twin
microcalorimeter
Micromeritics ASAP2020
Setaram DSC 111
sample
thermopiles
reference
H2O
to voltmeter
and amplifier
3
Diff. heat flow, µVx10 H2O vapor adsorbed cm /g
10
0
0.002
4
0.004
0.006
0.008
Relative Pressure P/P0
3
exo
0.3 J
5
2
1
0
0
200
400
Time, min
600
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Relaxor Ferroelectrics
B site substitution Ti4+ = 1/3Mg2+ + 2/3 Nb5+
PMNPT is lead magnesium niobate – lead
titanate
Ordering, domain structure, symmetry
changes (morphotropic transition)
Difficulties in synthesis and processing
Project with Al Migliore, Frances Hellman,
Shiv Varma, and postdoc Gustavo Costa now
at LANL
PMNPT
Enthalpies of mixing for (1-x)PMN-xPT
perovskites as a function of composition.
Enthalpies of drop solution for (1-x)PMN-xPT
perovskites as a function of composition.
Thermodynamic Constraints
on PMN Synthesis
Fluorite
Homovalent: M4+ = N4+
Heterovalent: M4+ = Ln3+ + 0.5 Vacancy
Navrotsky and Asta groups at UC Davis and Berkeley
theory and experiment
Crystal structure of defect-fluorite (Fm3m)
O
Zr+4
Gd+3
VÖ2
Energetics of doped ceria and thoria
Nanomaterials: Main Thermodynamic
Issue
• Synthetic and natural nanomaterials are often forced,
by low temperature aqueous conditions, to remain
fine grained, with particle sizes of 1-100 nm.
• How does this constraint alter thermodynamics,
phase equilibria, and the occurrence of specific crystal
structures?
• Different phases have different surface energies, thus
their stability is affected differently by grain size
diminution
• OXIDES AND OXYHYDROXIDES OF Ti, Mn, Fe, Co, Zn,
Al, Zr, Hf, Ce, U…..
SIZE EFECTS ON CHEMICAL REACTIONS
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Polymorphism
Dehydration
Redox
General principle: phase assemblage with
higher surface energy is destabilized with
respect to that with lower surface energy
• Important for ceramic, catalytic, geological,
and environmental applications
Magnitudes
• Effect on free energy of reaction:
– Surface energies range from 0.5 to 5 J/m2. Take
D(surface energy) = 2 J/m2
– Take surface area = 100 m2/g
– Take molecular weight = 150
– DG =2 x 100 x 150 = 30 kJ/mol
– General principle - small grain size
thermodynamically stabilizes phase assemblage
with lower surface energy
Calorimetric Measurement of Surface
Enthalpies (Energies)
• Measure enthalpy of solution versus surface
area, slope of line will give surface energy
Complications
– Particles are hydrated and hold water strongly
– Particles may be agglomerated, twinned, etc. so
sizes estimated by Xray, TEM, BET may differ and
interfacial energies play a role
Alumina
Enthalpy of Iron Oxides Relative to Bulk
Hematite plus Water
Goethite = Hematite + Water
Surface Energy Systematics
• Spinels (g-Al2O3, g-Fe2O3, MgAl2O4, Co3O4, Fe3O4, Mn3O4)
all have lower surface energies than rocksalt oxides (CoO,
NiO), metals, or trivalnet non-spinel oxides
• Metals (Fe, Co, Ni) have lower surface energies than rocksalt
oxides
• So phase field (in pO2-T space) of rocksalt oxides shrinks at
nanoscale and that of spinel expands.
• This appears general
Co-O Phase Diagram
0 bulk
-20
-40
2b
Co3O4
log[P (O2 /1 atm)]
log[P (O2 /1 atm)]
2a
CoO
Co
-60
0
10 nm
-20
-40
-60
300
-1
Temperature (K)
600
Co3O4
CoO
Co
900
300
600
-1
Temperature (K)
900
Oxidation-Reduction Equilibria among Transition Metal Oxides Change
Dramatically at the Nanoscale Because of Differences in Surface Energies
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Relevant to materials processing, environmental science, geology, and even biology
For example, for10 nm iron oxides, wustite FeO has no stability field at all, with iron
coexisting with magnetite
Spinels, M3O4 have lower surface energies than divalent oxides MO and trivalent oxides
M3O4, expanding the spinel stability field.
Navrotsky et al. Science 330, 199-201 (2010)
MANGANESE OXIDES
Mn – O
Birkner and Navrotsky (2012) Am. Min.
The Path Forward
• Rigorous - include surface energy as a
variable for all phases and calculate equilibria
for given particle sizes
• Practical – Choose particle size of 10 and 100
nm and add constant free energy terms to
each phase (estimating when necessary) and
calculate phase diagrams for “small” and
“very small” particle systems
Implications of Redox Shifts
• Catalysis, hydrogen production, water
splitting, batteries,sensors
• Environmental redox of Fe, Cr, U….
• Biology, origin of life, interpretation of data
from Mars
• THERMODYNAMICS AS WELL AS KINETICS
Catalysis, sensors, batteries:
some recent studies
• “CoO” catalysts for CO oxidation probably are
Co3O4, low surface energy may be important
both thermodynamically and catalytically
• SnO2 a better gas sensor than TiO2
• “CaMnO” catalyst for water splitting, a
biomimetic of Photosystem II in
photosynthesis
• Li battery materials – nanoscale and surface
effects
Why is SnO2 such a good gas sensor?
SnO2
TiO2
• Energy of anhydrous surface (J/m2)
1.72
2.22
• Energy of hydrous surface (J/m2)
1.49
1.89
• Coverage below which differential heat of adsorption <-125 kJ/mol
(molecules/nm2)
0.2
0.5
• So SnO2 holds on to water less strongly and
gases to be sensed can compete better for
surface sites
CaMnO water splitting catalysts
• Nominally CaMn2O4.nH2O and
CaMn3O6.nH2O but actually more oxidaized
so there is Mn3+ and Mn4+
• Nanophase layered structure
• Relatively low surface energy (higher than
Mn3O4 spinel but lower than Mn2O3 and
MnO2
Battery materials
• LixMO2 rocksalt type vs. LixM2O4 spinel
type- predict spinel has lower surface energy
• Redox equilibria and therefore
electrochemical potential may depend on
particle size
• Thermodynamics of other materials, e.g.
triplite-tavorite
LiCoO2 : Layered rocksaltderived structure
Hexagonal, R-3m
a = 2.82 Å ; c = 14.08 Å
Cubic close packing of oxide ions – octahedral
sites of alternate layers are occupied by Li &
Co respectively
LiCoO2 / Li battery: Li+ ions
intercalate/deintercalate
Co formal oxidation state goes from 3+ to 4+
Cell voltage is 4 V, related to free energy of
reaction. Does it change with particle size?
c
a
b
Surface energy
Energy of hydrous surface –
2.10 ± 0.35 J m-2
Energy of anhydrous surface 2.29 ± 0.35 J m-2
almost no stabilization by hydration
Compare to CoO
Energy of hydrous surface –
2.82 ± 0.20 J m-2
Energy of anhydrous surface 3.57 ± 0.30 J m-2
DFT calculations, Shirley Meng
group (2012), give 2.1 J/m2 for
anhydours surface, influenced
by coordination geometry and
spin state of Co3+
Transformation and Crystallization Energetics of
Synthetic and Biogenic Amorphous
Calcium Carbonate (ACC)
The transformation/crystallization enthalpies were measured using isothermal acid solution
calorimetry and differential scanning calorimetry (DSC)
Synthetic ACC – chemical precipitation and Biogenic ACC - extraction from California purple sea urchin
20
10
0
Phase
•ACC is a highly metastable phase compared to all
crystalline CaCO3 polymorphs
•Dehydrated synthetic ACC produced by heating is
energetically similar to biogenic ACC
•The formation of anhydrous ACC from hydrated
ACC is exothermic
• ACC crystallization is energetically downhill
through stepwise evolution of series of phases as:
Calcite
30
Aragonite
40
Vaterite
50
ACC biogenic
anhydrous
60
ACC synthetic
anhydrous
70
ACC synthetic hydrated
less disordered
80
ACC synthetic hydrated
more disordered
Enthalpy relative to calcite (kJ/mol)
Major findings
More metastable hydrated ACC → Less metastable
hydrated ACC ⇒ Anhydrous ACC ~ Biogenic anhydrous ACC
⇒ Vaterite → Aragonite→ Calcite
PNAS, (2010) 107, 16438–16443
Center for Nanoscale
Control of Geologic CO2
Energetics of Amorphous
Ca1-xMgxCO3·nH2O
AMC is more metastable than ACC but more persistent
Two distinct regions of amorphous Ca1-xMgxCO3·nH2O (0<x<1) phases
Homogeneous single phase (x < 0.47) and heterogeneous two phases (x > 0.47)
Two distinct amorphous precursors
x = 0-0.2 - less metastable single phase is frequently found in biogenic carbonates
x ~ 0.5 - least metastable phase could possibly be dolomite precursor
NSF and DOE and UC

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