Cap 4. Termodinamica Fuera Del Equilibrio

8/4/2019 Cap 4. Termodinamica Fuera Del Equilibrio

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CAPITULO 4. TERMODINAMICA FUERADEL EQUILIBRIO.


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CAPITULO 4. TERMODINAMICA FUERA DELEQUILIBRIO.

4.1 FUNDAMENTOS GENERALES.

4.2 SEGUNDA LEY PARA SISTEMAS FUERADEL EQUILIBRIO.

4.3 TERMODINAMICA FUERA DEL EQUILIBRIOEN SISTEMAS LINEALES.


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4.1 FUNDAMENTOS GENERALES.

EQUILIBRIO:

Se dice que un sistema esta en equilibrio cuando tieneuna energa libre mnima.

Se dice que un sistema aislado est en equilibrio

qumico si no suceden cambios en la composicinqumica del sistema. El criterio para el equilibrio qumicose basa en la segunda ley de la termodinmica, y paraun sistema a una temperatura y presin especificas

puede expresarse como:

0,

PTdG


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Para la reaccin:

Donde las v son los coeficientes estequiomtricos, elcriterio de equilibrio qumico puede expresarse entrminos de las funciones de Gibbs como:

que es valida para cualquier reaccin qumicaindependientemente de la fase implicada.

DvCvBvAvDCBA

0 BBAADDCC GvGvGvGv


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SOLID-LIQUID PHASEDIAGRAMS: TIN AND LEAD

Cooling curves forpure substances

Suppose you have somepure molten lead andallow it to cool down untilit has all solidified,plotting the temperatureof the lead against timeas you go. You would endup with a typical coolingcurve for a puresubstance.


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Cooling curves for tin-lead mixtures

If you add some tinto the lead, theshape of the coolingcurve changes. Thenext graph showswhat happens if youcool a liquid mixturecontaining about

67% lead and 33%tin by mass.


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If you had less tin in the mixture, the overall shapeof the curve stays much the same, but the point atwhich the lead first starts to freeze changes.

The less tin there is, the smaller the drop in the

freezing point of the lead. For a mixture containing only 20% of tin, the

freezing point of the lead is about 275C. That'swhere the graph would suddenly become lesssteep.

BUT . . . you will still get the graph going horizontal(showing the freezing of both the tin and lead) atexactly the same temperature: 183C.


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As you increase theproportion of tin, the firstsigns of solid leadappear at lower andlower temperatures, but

the final freezing of thewhole mixture stillhappens at 183C.

That continues until youhave added enough tin

that the mixture contains62% tin and 38% lead.At that point, the graphchanges.


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This particular mixture of lead and tin has a cooling curve whichlooks exactly like that of a pure substance rather than a mixture.There is just the single horizontal part of the graph whereeverything is freezing.

However, it is still a mixture. If you use a microscope to look at the

solid formed after freezing, you can see the individual crystals oftin and lead.

This particular mixture is known as a eutectic mixture. The word"eutectic" comes from Greek and means "easily melted".

The eutectic mixture has the lowest melting point (which is, of

course, the same as the freezing point) of any mixture of lead andtin. The temperature at which the eutectic mixture freezes or meltsis known as the eutectic temperature.


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What happens if there is more than 62%

of tin in the mixture?

You can trace it throughin exactly the same way,by imagining startingwith pure tin and then

adding lead to it. The cooling curve for

pure liquid tin looks likethis:

It`s just like the pure

lead cooling curveexcept that tin's freezingpoint is lower.


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What happens if there is more than 62%

of tin in the mixture?If you add small amounts of leadto the tin, so that you haveperhaps 80% tin and 20% lead,you will get a curve like this:

Notice the lowered freezing point

of the tin. Notice also the finalfreezing of the whole mixtureagain takes place at 183C.

As you increase the amount oflead (or decrease the amount oftin - same thing!) until there is

62% of tin and 38% of lead, youwill again get the eutectic mixturewith the curve we've alreadylooked at.


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Notice the lowered freezingpoint of the tin. Notice alsothe final freezing of the wholemixture again takes place at183C.

As you increase the amountof lead (or decrease theamount of tin - same thing!)until there is 62% of tin and38% of lead, you will againget the eutectic mixture with

the curve we've alreadylooked at.


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The phase diagram

Constructing the phase diagram You start from data obtained

from the cooling curves. Youdraw a graph of the temperatureat which freezing firststartsagainst the proportion of tin andlead in the mixture. The only

unusual thing is that you drawthe temperature scale at eachend of the diagram instead ofonly at the left-hand side.

Notice that at the left-hand sideand right-hand sides of thecurves you have the freezing

points (melting points) of thepure lead and tin.


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The phase diagram

To finish off thephase diagram, allyou have to do isdraw a single

horizontal line acrossat the eutectictemperature. Thenyou label each area

of the diagram withwhat you would findunder the variousdifferent conditions.


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Figura x. Gibbs energy curves to construct a binary phase diagram that

shows miscibility in both the liquid and the solid


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Figura y. Uso de las curvas de energa de Gibbs paraconstruir un diagrama de fase binario del tipo eutctico.


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Cristalizacin de un metal puro

Crystallizationis transformation of liquid phase to solidcrystalline phase.

There are two general stages of phase transformation(crystallization) processnucleation and growth:
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1. Nucleation

Nucleation is a process of formation of stable crystallization centersof the new phase.

Nucleation may occur by either homogeneous or heterogeneousmechanism, depending on the value of undercooling of the liquid

phase (cooling below the equilibrium freezing point). Presence of foreign particles or other foreign substance in the liquid

alloy (walls of the casting mold) enables to initiate crystallization atminor value of undercooling (few degrees below the freezing point).This is heterogeneous nucleation.

If there is no solid substance present, undercooling of a hundreddegrees is required in order to form stable nuclei or seeds crystals,providing following crystal growth (homogeneous nucleation)
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2. Crystal growth Number of stable nuclei per unit volume of crystallizing alloy

determines the grain size.

When a large number of stable nuclei are present in chill zone of

mold, fine equiaxed grains form. Latent crystallization heat,liberating from the crystallizing metal, decreases the undercooling ofthe melt and depresses the fast grains growth.

At this stage some of small grains, having favorable growth axis,start to grow in the direction opposite to the direction of heat flow. As

a result columnar crystals (columnar grains) form.

Contrary to the pure metals, in alloys different type of undercoolingtakes place. It is called constitutional undercooling.
http://www.substech.com/dokuwiki/doku.php?id=grain_structure&DokuWiki=43620e34d82dde46e884fe21220c958ehttp://www.substech.com/dokuwiki/doku.php?id=grain_structure&DokuWiki=43620e34d82dde46e884fe21220c958e


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Constitutional undercooling.

Since solubility of an alloying element in solid is lower, than in liquidat the same temperature, this element (solute) is rejected by thesolidifying metal to the liquid phase, enriching the region of liquidadjacent to the crystallization front.

For the most of the alloys: the higher the concentration of alloying

element in the alloy, the lower its liquidus temperature (temperatureat which crystallization of the alloy starts).

Thus crystallization temperature of the liquid, adjacent to thecrystallization front, rises with increasing the distance from the front

surface. Therefore there is a layer of the liquid, where itstemperature is lower, than its crystallization temperature. This is theregion of constitutional undercooling (see the figure below).


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Figura z. This figure represents the development of microstructure

during the equilibrium solidification of a 35 wt% Ni - 65 wt% Cu alloy.

Fig r P ti f bi h di m c t i i t h li id l lid fi ld


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Figura z. Portion of a binary phase diagram containing a two-phase liquid-plus-solid fieldillustrating (a) application of the lever rule to (b) equilibrium freezing, (c) nonequilibrium

freezing, and (d) heating of a homogenized sample.1


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Figure 1. El diagrama de equilibrio de fases Fe-C. Se muestra lamicroestructura de un acero al carbono lentamente enfriado teniendo

una composicin Co.


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Figure 1. El diagrama de equilibrio de fases Fe-C.


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Microestructuras de los aceros en equilibrio


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Microestructuras de los aceros en equilibrio

0.3 % C 0.6 % C 0.8 % C 1.1 % C


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Enfriamiento de no equilibrio.

Cuando una aleacin es enfriada rpidamente, puedenocurrir varios cambios en la microestructura:

Las fases de equilibrio pueden verse a temperaturaambiente, pero su morfologa (forma) puede serdiferente.

La microestructura de altas temperaturas puedecongelarse, y ella puede observarse a temperaturaambiente.

Puede aparecer una fase completamente nueva, la cualno esta presente en el diagrama de equilibrio de fases.


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Enfriamiento de no equilibrio.

Para velocidades de enfriamiento rpidas, los diagramas deequilibrio no pueden ser usados. En este caso, son necesarios losdiagramas TTT (transformacion tiempo-temperatura).

La figure 2 muestra un diagrama hipottico TTT. Sobre el diagramase sobreimponen varias velocidades de enfriamiento. La velocidadde enfriamiento mas lenta es enfriamiento en el horno, en el cual elmaterial es dejado en el horno y la potencia es desconectada. Asi,el material es enfriado hasta temperatura ambiente dentro del

horno. El enfriamiento en aire es algo mas rpido que el enfriamiento en

el horno. Cuando el material es sacado del horno y enfriado en airehasta temperatura ambiente, llamamos a esto enfriamiento en aire.

La velocidad de enfriamiento mas rpida es obtenida por templadoen agua. En el templado, el material es sacado del horno e

inmediatamente sumergido en agua. El medio de templado puedeser aceite o agua, pero mas rpida velocidad de enfriamiento esobtenida con agua.


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Figure 2. Curvas de enfriamiento sobre un diagrama TTThipotetico de un acero al carbono.


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En el enfriamiento al horno, la velocidad de enfriamiento es muylenta y puede considerarse que se satisfacen las condiciones deequilibrio. Por lo tanto, el material sigue los limites de fase en eldiagrama de equilibrio de fases.

En el enfriamiento en aire, la velocidad de enfriamiento es masrpida. Para aceros al carbono, el diagrama de fases es todavavalido, y se puede ver las fases predichas por el diagrama de fases.Solo cambian la morfologa y cantidad relativa de las fases. Larazn para esto es el mayor DT (T-TE), la cantidad desobreenfriamiento. Como DT es mas efectiva sobre la velocidad de

nucleacin en comparacin a la velocidad de crecimiento, seesperan granos mas finos para mayores velocidades deenfriamiento.

En el templado en agua, puede aparecer una fase completamentenueva. Por ejemplo, en aleaciones ferrosas, la austenita setransforma a martensita, si el enfriamiento es bastante rpido. Lamartensita tiene una estructura parecida a agujas y es muy dura.


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Microestructuras de los aceros fuera de equilibrio


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Effect of Alloying Elements

Figure 3.a shows a typical TTT diagram for a plaincarbon steel. The addition of carbon and alloyingelements effect several parameters in TTT diagrams,such as the shape, martensite start temperature and

relative position of the curve. In Figure 3.b, the effect of asmall amount of Cr is seen. The TTT curve is shifted toright. The higher the percentage of Cr, the largerbecomes this shift. Therefore, transformation of

austenite to martensite becomes easier in alloy steels.


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Figure 3. The schematic representation of the effect of alloying elements onthe TTT curve of a eutectoid steel.

Cap 4. Termodinamica Fuera Del Equilibrio

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