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Diagramas de equilibrio
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DIAGRAMAS DE EQUILIBRIO
Son representaciones de temperatura (en algunas
ocasiones presión) frente a composición
Gráficamente se resumen los intervalos de temperatura (o
presión) en los que ciertas fases, o mezclas de fases, existen
en condiciones de equilibrio termodinámico
Se puede deducir el efecto de la temperatura sobre los
sólidos y las reacciones que pueden producirse entre sólidos
Se aplican en condiciones de equilibrio termodinámico, en
la práctica son muy útiles en condiciones de no equilibrio
History
In 1876 and 1878 J.Willard Gibbs published work that provides
the thermodynamic basis for understanding the equilibrium
state of any arbitrary combination of substances under
specified conditions.
However, Gibbs had been in communication with James
Clerk Maxwell, and Maxwell knew of and understood Gibbs’
work.
Though Maxwell died only a very few years after the
publication of Gibbs’work, Maxwell had made known the
work to Van der Waals who in turn made it known to H.W.
Bakhuis Roozeboom.
Bakhuis Roozeboom successfully incorporated Gibbs’
concepts into his own work.
What is believed to be the first temperature-
composition plot was made by Roberts-Austen and
was published in 1875, the Ag–Cu system.
The system needs a thermocouple instead of ordinary
thermometer. Improvement awaited the
development of a stable thermocouple, and a
reliable Pt–Pt10%Rh thermocouple was developed by
Le Chatelier in 1877.
Sorby was contemporaneous with Roberts-Austen
and he named the phases which he observed in
his metallographic studies of iron–carbon alloys
as follows:
Ferrite for the terminal BCC-Fe solution;
austenite for the FCC-Fe solution;
pearlite for the Fe–Fe3C eutectic;
cementite for the Fe3C phase;
and martensite for the hardening precipitate
phase.
Sorby chose the name austenite in honor of
Roberts-Austen
1897 Roberts-Austen diagram has been called
“the first phase diagram”.
The temperature-composition diagrams of that
period were plotted from dynamic
measurements and the Roberts-Austen diagram
was not an “equilibrium” diagram since it lacked
compatibility with the equilibrium reversibility
inherent in the thermodynamic constraints
codified by Gibbs.
Roberts Austen invited Bakhuis Roozeboom to modify
the 1899 temperature composition diagram for
compatibility with the Gibbs phase rule. The result was
a thermodynamically valid equilibrium Fe–Fe3C
diagram in 1900
Many materials are used in “frozen in” non-equilibrium
states and phase diagrams provide a means of
showing where the material started and where
equilibrium will be reached, the path that the
material should follow in transforming from initial state
to equilibrium is cogent to understanding the state
where it might be in a non-equilibrium “freeze”
The Fe–C diagram without the metastable Fe3C has also
been proven useful in cast iron technology.
Sorby became aware of the Widmanstätten prints and
used an optical microscope with polished and etched
specimens to make the aforementioned study of the
microstructures of iron–carbon alloys.
Metallography, X-ray diffraction, electron and neutrón
diffraction
Internal energy. The sum of the kinetic energy (energy of
motion) and potential energy(store energy). Its
characterized solely by the state of the system
Closed system. A thermodynamic system that undergoes
no interchange of mass (material) with its surroundings,
but can interchange energy with its surroundings.
First law. (Mayer, Joule, Helmholtz)energy can be neither
created nor destroyed.
𝑑𝐸 = 𝛿𝑄 − 𝛿𝑊 or 𝑑𝐸 = 𝛿𝑄 − 𝑝𝑑𝑉
Thermodynamics
Enthalpy. Thermal energy changes
under constant pressure (again
neglecting any field effects)are most
conveniently expressed in terms of
the enthalpy
Its a function of the state of the
system, as is the PV
ThermodynamicsThe present treatment is meant only to highlight the factors
that need to be taken into account when constructing or
examining a phase diagram.
For any system the number of arbitrarily alterable variables
constitute the degrees of freedom, f.
For a system in which P dV work is the sole work
contribution, the first law of thermodynamics in differential
form is
dE = T dS - P dV
and T and P are system intensive variables
These two plus the number of components, c, yield the
total number of variables, n.
The number of phases, p, represent the number of ways
in which the variables are related, m. Thus the number of
degrees of freedom can be represented as
F= n – m = c – p + 2
This is the phase rule, and this in combination with
thermodynamic considerations determines the
constraints that are placed upon a phase diagram.
Along the line defining the liquid–gas equilibrium, the Gibbs
energies of the two phases must be equal, so:
ΔtG = ΔtH - TΔtS = 0
which leads to
ΔtH/T = ΔtS
At any given pressure at all temperatures below the
transition temperature, T <Tt, the liquid is the stable phase so
the Gibbs energy of the liquid must be lower than the Gibbs
energy of the gas, Gl < Gg.
Phase
Phase. Region of space occupied by a physically
homogeneous material. However, there are two uses of
the term: the strict sense normally used by physical
scientists an the somewhat looser sense normally used
by materials engineers.
In the strictest sense, homogeneous means that the
physica properties throughout the región of space
occupied by the phase are absolutely identical, and
any change in condition of state, no matter how small,
will result in a different phase.
Equilibrium
There are three types of equilibria: stable, metastable,
and unstable.
Stable equilibrium exists when the object is in its lowest
energy condition
Metastable equilibrium exists when additional energy
must be introduced before the object can reach true
stability
Unstable equilibrium exist when no additional energy is
needed before reaching metastability or stability
Polymorphism
The structure of solid elements and compounds under
stable equilibrium condiction is crystalline, and the cristal
structure of each is unique.
Some elements and compounds are polumorphic
(multishaped); their structure transforms from one cristal
structure to another with changes in temperatura and
pressure, each unique structure consisting a distinctively
separate phase.
Allotrpy is usually used to describe polymorphic changes
in chemical elements
Metastable phases
Under some conditions, metastable cristal
structures can form instead of stable
structures. Rapid freezing is a common
method of producing metastable
structures, but some (cementite) are
produced at moderately slow cooling
rates.
Systems
A physical system consists of a substance (or a
group of substances) that is isolated from itssurrounding (isolatedthere is no interchange of
mass between the substance and its surroundings)
Diagrama PVT
Es la representación en el espacio tridimensional
Presión-Volumen específico-Temperatura de los
estados posibles de un compuesto químico.
Estos estados configuran en el espacio PVT una
superficie discontinua, las discontinuidades a los
cambios de estado que sufre el compuesto al
variarse las condiciones de presión y temperatura
Las superficies delimitan las zonas de existencia de
a fase sólida, la fase líquida y la fase gaseosa
Diagrama de fases de un componente
Se debe especificar el estado termodinámico
de un sistema formado por una sustancia pura,
dado por el número de variables intensivas
independientes (grados de libertad)
Se representa por el diagrama P-T conocido
como diagrama de fases