1. The document discusses phase diagrams and thermodynamics of mixing.
2. It explains how phase diagrams can be used to determine the number and types of phases present, the composition of each phase, and the amount of each phase at a given temperature and composition.
3. Binary eutectic and eutectoid systems allow for a range of microstructures depending on the cooling rate, and alloying generally increases strength but decreases ductility due to solid solution strengthening.
THE PHASE RULE
phase rule
degree of freedom in mixture
one component system
two component system
pressure temperature diagram sulfur hydrogen
eutectic eutectoid mixture
Development of Microstructure in eutectic Alloys and Practice problems on Binary Eutectic system
Reference: Material Science and Engineering, William Callister
Postsecondary lesson for pre-u students or form 6th students on mole concept, stoichiometry, limiting reagent, spectrometry and percent yield and percent purity.
A 2 hour fun and interactive workshop for students at the University of Liverpool that introduces the use of Microsoft Teams as a professional tool for collaborative working.
Briefing for the RSA International Solar Challenge. Delivered by Rob Treharne on Thurs 25 Feb 2016 @ 11am, Stephenson Institute for Renewable Energy, University of Liverpool
An introduction to the fundamental physics of transparent conducting oxides including a review of the electrical and optical properties of common materials.
A Combinatorial Approach to the Optimisation of Cd (1−x) Zn x S Layers for Cd...University of Liverpool
A combinatorial methodology has been adopted to determine the optimum composition of a Cd ( 1 − x)Zn x S window
layer for CdTe solar cells. The methodology generated a large, self
consistent dataset which permitted an unambiguous relationship
between x, conversion efficiency and related cell parameters to
be determined. An optimum composition of x = 0.57 was shown
to maximise cell efficiency. Analysis of J − V curves, measured
over 72 separate cells show that both short circuit current, J SC ,
and fill factor, F F , values increase with respect to x over the
range 0.1−0.57. EQE measurements show that further increases
in J SC value are limited by the band gap of the highly resistive
transparent (HRT) ZnO layer. The methodology demonstrates a
rapid route, compared to conventional experiments, to the further
optimisation of CdTe solar cells.
A low-cost non-toxic post-growth activation step for CdTe solar cellsUniversity of Liverpool
Cadmium telluride, CdTe, is now firmly established as the basis for the market-leading thin-film solar-cell technology. With laboratory efficiencies approaching 20 per cent1, the research and development targets for CdTe are to reduce the cost of power generation further to less than half a US dollar per watt (ref. 2) and to minimize the environmental impact. A central part of the manufacturing process involves doping the polycrystalline thin-film CdTe with CdCl2. This acts to form the photovoltaic junction at the CdTe/CdS interface3, 4 and to passivate the grain boundaries5, making it essential in achieving high device efficiencies. However, although such doping has been almost ubiquitous since the development of this processing route over 25 years ago6, CdCl2 has two severe disadvantages; it is both expensive (about 30 cents per gram) and a water-soluble source of toxic cadmium ions, presenting a risk to both operators and the environment during manufacture. Here we demonstrate that solar cells prepared using MgCl2, which is non-toxic and costs less than a cent per gram, have efficiencies (around 13%) identical to those of a CdCl2-processed control group. They have similar hole densities in the active layer (9 × 1014 cm−3) and comparable impurity profiles for Cl and O, these elements being important p-type dopants for CdTe thin films. Contrary to expectation, CdCl2-processed and MgCl2-processed solar cells contain similar concentrations of Mg; this is because of Mg out-diffusion from the soda-lime glass substrates and is not disadvantageous to device performance. However, treatment with other low-cost chlorides such as NaCl, KCl and MnCl2 leads to the introduction of electrically active impurities that do compromise device performance. Our results demonstrate that CdCl2 may simply be replaced directly with MgCl2 in the existing fabrication process, thus both minimizing the environmental risk and reducing the cost of CdTe solar-cell production.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
What is greenhouse gasses and how many gasses are there to affect the Earth.
Lecture 8: Phase Diagrams
1.
2. Learning objectives
2 Phase diagrams
Be able to read a phase
diagram
Be able to identify the phases
present at a given point
Be able to calculate how much
of those phases there are
Be able to predict the
microstructures from the phase
diagram
3 Mixing
Understand the thermodynamic
basis of mixing
Understand the origin of the
miscibility gap
Be able to use the phase
diagram to predict miscibility
phenomena
1.Solid state reactions
Recap: how Gibbs Free Energy
can be used to predict reactions
There will be worked
examples on this bit
for you to practice ….
3. 1. Prediction of reactions
e.g. solar cell contact – metal M to semiconductor AB
AB
M
AB
M
MB + A
AB
M
or
stable
unstable
M + AB MB + A Will it happen at equilibrium?
keqm = [MB]*[A] /[M]*[AB] If keqm is large, the reaction goes from l to r
)ln( eqmkRTG Find the Gibb’s free energy for the reaction.
If ∆G is large and negative, keqm is large and the reaction goes from l to r
4. 1. Prediction of reactions
initialfinalreaction
initialfinalreaction
initialfinalreaction
reactionreactionreaction
SSS
HHH
GGG
STHG
M + AB MB + A
etc
GGGGG ABMAMBreaction )()(
If ∆G is large and negative, keqm is large and the reaction goes f
In this case the contact would be unstable to reaction with the solar cell
materials. The contact could become non-Ohmic, the series resistance
could increase, and the performance could become unstable.
5. ISSUES TO ADDRESS...
• When we combine two elements...
what equilibrium state do we get?
• In particular, if we specify...
--a composition (e.g., wt% Cu - wt% Ni), and
--a temperature (T)
then...
How many phases do we get?
What is the composition of each phase?
How much of each phase do we get?
2. Equilibrium phase diagrams
Phase BPhase A
Nickel atom
Copper atom
6. • Components:
The elements or compounds which are present in the mixture
(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regions
that result (e.g., and ).
Aluminum-
Copper
Alloy
Components and Phases
(darker
phase)
(lighter
phase)
Adapted from
chapter-opening
photograph,
Chapter 9,
Callister 3e.
7. Phase Equilibria
Crystal
Structure
electroneg r (nm)
Ni FCC 1.9 0.1246
Cu FCC 1.8 0.1278
• Both have the same crystal structure (FCC) and have
similar electronegativities and atomic radii (W. Hume –
Rothery rules) suggesting high mutual solubility.
Simple solution system (e.g., Ni-Cu solution)
• Ni and Cu are totally miscible in all proportions.
8. Phase Diagrams
• Indicate phases as function of T, Co, and P.
• For this course:
-binary systems: just 2 components.
-independent variables: T and Co (P = 1 atm is almost always used).
• Phase
Diagram
for Cu-Ni
system
Adapted from Fig. 9.3(a), Callister 7e.
(Fig. 9.3(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P. Nash
(Ed.), ASM International, Materials Park,
OH (1991).
• 2 phases:
L (liquid)
(FCC solid solution)
• 3 phase fields:
L
L +
wt% Ni20 40 60 80 1000
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid)
(FCC solid
solution)
L +liquidus
solidus
9. wt% Ni20 40 60 80 1000
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid)
(FCC solid
solution)
L
+
liquidus
solidus
Cu-Ni
phase
diagram
Phase Diagrams:
number and types of phases
• Rule 1: If we know T and Co, then we know:
--the number and types of phases present.
• Examples:
A(1100°C, 60):
1 phase:
B(1250°C, 35):
2 phases: L +
Adapted from Fig. 9.3(a), Callister 7e.
(Fig. 9.3(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P. Nash
(Ed.), ASM International, Materials Park,
OH, 1991).
B(1250°C,35) A(1100°C,60)
10. wt% Ni
20
1200
1300
T(°C)
L (liquid)
(solid)L +
liquidus
solidus
30 40 50
L +
Cu-Ni
system
Phase Diagrams:
composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
• Examples:
TA
A
35
Co
32
CL
At TA = 1320°C:
Only Liquid (L)
CL = Co ( = 35 wt% Ni)
At TB = 1250°C:
Both and L
CL = Cliquidus ( = 32 wt% Ni here)
C = Csolidus ( = 43 wt% Ni here)
At TD = 1190°C:
Only Solid ( )
C = Co ( = 35 wt% Ni)
Co = 35 wt% Ni
Adapted from Fig. 9.3(b), Callister 7e.
(Fig. 9.3(b) is adapted from Phase Diagrams
of Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
B
TB
D
TD
tie line
4
C
3
11. • Rule 3: If we know T and Co, then we know:
--the amount of each phase (given in wt%).
• Examples:
At TA: Only Liquid (L)
WL = 100 wt%, W = 0
At TD: Only Solid ( )
WL = 0, W = 100 wt%
Co = 35 wt% Ni
Adapted from Fig. 9.3(b), Callister 7e.
(Fig. 9.3(b) is adapted from Phase Diagrams of
Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
Phase Diagrams:
weight fractions of phases – ‘lever rule’
wt% Ni
20
1200
1300
T(°C)
L (liquid)
(solid)L +
liquidus
solidus
30 40 50
L +
Cu-Ni
system
TA
A
35
Co
32
CL
B
TB
D
TD
tie line
4
C
3
R S
At TB: Both and L
%73
3243
3543
wt
= 27 wt%
WL
S
R +S
W
R
R +S
12. wt% Ni
20
1200
1300
30 40 50
1100
L (liquid)
(solid)
L +
L +
T(°C)
A
35
Co
L: 35wt%Ni
Cu-Ni
system
• Phase diagram:
Cu-Ni system.
• System is:
--binary
i.e., 2 components:
Cu and Ni.
--isomorphous
i.e., complete
solubility of one
component in
another; phase
field extends from
0 to 100 wt% Ni.
Adapted from Fig. 9.4,
Callister 7e.
• Consider
Co = 35 wt%Ni.
e.g.: Cooling in a Cu-Ni Binary
4635
43
32
: 43 wt% Ni
L: 32 wt% Ni
L: 24 wt% Ni
: 36 wt% Ni
B: 46 wt% Ni
L: 35 wt% Ni
C
D
E
24 36
13. Equilibrium cooling
• The compositions that freeze are a
function of the temperature
• At equilibrium, the ‘first to freeze’
composition must adjust on further cooling
by solid state diffusion
• We now examine diffusion processes –
how fast does diffusion happen in the solid
state?
14. Diffusion
Fick’s law – for
steady state
diffusion
J = flux – amount
of material per
unit area per unit
time
C = conc
dx
dC
DJ
C
x
Co
C
x
Co/4
Co/2
3Co/4
x2
t = 0
t = 0
t = t
Dtx
2
15. Diffusion cont….
• Diffusion coefficient D (cm2s-1)
• Non-steady state diffusion
Fick’s second law
• Diffusion is thermally activated
RT
Q
DD d
exp0
2
2
x
C
D
t
C
17. • C changes as we solidify.
• Cu-Ni case:
• Fast rate of cooling:
Cored structure
• Slow rate of cooling:
Equilibrium structure
First to solidify has C = 46 wt% Ni.
Last to solidify has C = 35 wt% Ni.
Cored vs Equilibrium Phases
First to solidify:
46 wt% Ni
Uniform C:
35 wt% Ni
Last to solidify:
< 35 wt% Ni
18. Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
--Tensile strength (TS) --Ductility (%EL,%AR)
--Peak as a function of Co --Min. as a function of Co
Adapted from Fig. 9.6(a), Callister 7e. Adapted from Fig. 9.6(b), Callister 7e.
TensileStrength(MPa)
Composition, wt% Ni
Cu Ni
0 20 40 60 80 100
200
300
400
TS for
pure Ni
TS for pure Cu
Elongation(%EL) Composition, wt% Ni
Cu Ni
0 20 40 60 80 100
20
30
40
50
60
%EL for
pure Ni
%EL for pure Cu
19. : Min. melting TE
2 components
has a special composition
with a min. melting T.
Adapted from Fig. 9.7,
Callister 7e.
Binary-Eutectic Systems
• Eutectic transition
L(CE) (CE) + (CE)
• 3 single phase regions
(L,)
• Limited solubility:
: mostly Cu
: mostly Ag
• TE : No liquid below TE
• CE
composition
Ex.: Cu-Ag system
Cu-Ag
system
L (liquid)
L +
L+
Co wt% Ag in Cu/Ag alloy
20 40 60 80 1000
200
1200
T(°C)
400
600
800
1000
CE
TE 8.0 71.9 91.2
779°C
20. L+
L+
+
200
T(°C)
18.3
C, wt% Sn
20 60 80 1000
300
100
L (liquid)
183°C
61.9 97.8
• For a 40 wt% Sn-60 wt% Pb alloy at 150°C, find...
--the phases present: Pb-Sn
system
e.g. Pb-Sn Eutectic System (1)
+
--compositions of phases:
CO = 40 wt% Sn
--the relative amount
of each phase:
150
40
Co
11
C
99
C
SR
C = 11 wt% Sn
C = 99 wt% Sn
W=
C - CO
C - C
=
99 - 40
99 - 11
=
59
88
= 67 wt%
S
R+S
=
W =
CO - C
C - C
=
R
R+S
=
29
88
= 33 wt%=
40 - 11
99 - 11
Adapted from Fig. 9.8,
Callister 7e.
21. • 2 wt% Sn < Co < 18.3 wt% Sn
• Result:
Initially liquid +
then alone
finally two phases
poly-crystal
fine -phase inclusions
Adapted from Fig. 9.12,
Callister 7e.
Microstructures
in Eutectic Systems: II
Pb-Sn
system
L +
200
T(°C)
Co , wt% Sn
10
18.3
200
Co
300
100
L
30
+
400
(sol. limit at TE)
TE
2
(sol. limit at Troom)
L
L: Co wt% Sn
: Co wt% Sn
26. • Phase diagrams are useful tools to determine:
--the number and types of phases,
--the wt% of each phase,
--and the composition of each phase
for a given T and composition of the system.
• Alloying to produce a solid solution usually
--increases the tensile strength (TS)
--decreases the ductility.
• Binary eutectics and binary eutectoids allow for
a range of microstructures.
Summary
27. 3)Thermodynamics of mixing
• Why do some things mix and others
not?
• Why does heating promote mixing?
• Is an alloy of two semiconductors a
random solid solution, or is it just a
mixture of two phases?
Solid solution Mixture of phases ?OR
28. Free energy of mixing
• Enthalpy term – bond energies
• Entropy term – stats of mixing
behaviour of mixtures
consider the case: Pure A + Pure B
mixture AxB1-x
mixmixmix STHG
29. Enthalpy term: Compare the energy
in bonds (VAB etc) before and after
mixing
Heat of mixing Binding energy
in mixture
compared to
average in
components
Binding
energy
change on
mixing
ΔHmix
Exothermic VAB
> 1/2(VAA
+ VBB
) Stronger -ve
Ideal VAB
= 1/2(VAA
+ VBB
) Same 0
endothermic VAB
< 1/2(VAA
+ VBB
) Weaker +ve
30. ΔHmix derived
ΔHmix = (H for mixture AB) – (H for pure A + H for pure B)
• ΔHmix = zNxA xB {1/2(VAA + VBB) – VAB}
NAA etc = number of bonds of type
AA, AB etc
NA, NB, number of atoms of A, B. NA
+ NB = N
VAA, VBB, VAB, = binding energies of
pairs A-A,
xA etc = NA/N = mole fraction of A
For reference only
31. ΔSmix derived
ΔS = (Sfinal – Sinitial)
Sfinal from the statistical definition S = kBlnw
ΔSmix = kBln
Using Stirling’s approximation lnn! = nlnn-n gives
• ΔSmix = -NkB[ xAlnxA + xBlnxB]
)!()!(
!
BA NxNx
N
For reference only
32. ΔGmix - the formula
• ΔGmix = zNxA xB {1/2(VAA + VBB) – VAB}
+ NkBT[ xAlnxA + xBlnxB]
Binding energy term {...} may be +ve or –ve
Entropy term [...] is negative
mixmixmix STHG
For reference only
33.
34.
35. changing ΔHmix e.g. #3
iv) ΔHmix large
and positive
• Enthalpy
dominates
• miscibility
gap exists
• In gap, solid
segregates
into xA’ and
xA’’
0 0.5
1
Energy
ΔS
ΔH
ΔG
x’ x’
’
Miscibility
gap
x
T