# Curious phase transition

1. Nov 13, 2012

### flicflex

Hello, I ask for your help because I can't find any information about earth crust-atmosphere phase transition. I noticed indeed that our feet tread upon a solid surface, while our nostrils breath a gazeous compound !

This remark seems so obvious that I can't find any description neither analysis about this phase transition. If we look under our feet, there is no problem, we can find the moho' discontinuity at 35km, the gutenberg discontinuity at 2885km, etc...

Same if we look over us, there is the tropopause at 11km, then the stratopause, etc...

But it is impossible for me to find any schema or study including earth mantel AND atmosphere. Why the hell is the 0 km discontinuity located at 0 km? Which statistic model let us understand it? This lack of back standing about our self-environnement make me feel like the human being is still the center of the universe like 500 years ago...

(I mean if the human being was born in a solid/ductile part of the earth mantle like termites or whatever the "surface" of our world would had been at -10 km or any other value)

I am mostly looking for the mathematic explanation of the phenomenon (explanation of the localization (height) and cause of earth crust-atmosphere phase transition)

PS . I am not physician.

Last edited: Nov 13, 2012
2. Nov 13, 2012

### flicflex

Why 2 draws when we could have a beautiful unique draw?

3. Nov 13, 2012

### Staff: Mentor

There is no phase transition between Earth crust and atmosphere. Phase transition means the same substance changing state of matter (like ice melting), not different substances being in contact (like nail in the water).

And the Earth surface is at zero, because we decided the surface is at zero and we measure everything from the surface. It is like asking why all distances from home are measured from home, as if the home was the center of the world. Well - if you ask what is the distance from the home to the gas station, don't be surprised the distance is measured from home.

4. Nov 14, 2012

### flicflex

OK thank you, that means that we assume to be the center of our environnement . Why not (but it's a rather old school style)

I appreciate your answer Borek, but I'm sorry to say that according to wikipedia you are wrong.

That's why I ask for your help again : what is the mathematic characterization of the crust-atmosphere phase transition?

Thank you, Thibault.

5. Nov 14, 2012

### flicflex

The phase transition is also obvious trough the temperature point of view
On the attachment I draw earth temperature gradient (0 km = earth center on the graphic ; 6400 km = earth radius).

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6. Nov 14, 2012

### Staff: Mentor

As much as I like wikipedia its reliability is questionable. Now you know why. In this case perhaps it is just a matter of inconsistency between two different articles.

There is no phase transition here as the composition changes.

7. Nov 14, 2012

### Andre

A question of definition. What wiki describes is the phase transition of one particular compound. Water for instance, phase transition solid - liquid - gas is via melting, evaporization etc etc.

That's not the same as the boundary layers between the different shells in and around the Earth

8. Nov 22, 2012

### Darwin123

The earth atmosphere interface is not associated with a change in phase, only with a change in composition. As you pointed out, this is a discontinuity associated with compositional transition, not phase transition. The proportions of different elements are different between atmosphere and crust.

There are phase transitions associated with the different shells within the earth. The composition of the mantle does not change that much from surface to core. In other words, the ratio of elements varies continuously throughout the mantle. However, the precise phase of the material does vary due to changes in pressure and temperature. These changes in phase, without a sudden change in composition, are associated with phase changes.

Although a discontinuity in the earth’s structure can’t be a phase transition, a discontinuity is often associated with a phase transition. The pressure on the materials of the earth increases continuously with depth. Even though the stochiometry of the mantle may vary continuously, different mineral forms are more stable at different pressures. Thus, other are regions of depth where different minerals are stable regardless of the proportions of the different elements.

Phase transitions occur when the pressure or temperature exceed certain thresholds. Discontinuities can occur at certain times if the pressure and temperature are changing with time. However, the pressure and temperature vary more with depth instead of time. There are discontinuities in depth associated with temperature and pressure changes.

Variation in pressure is more important than variation in temperature for most of these discontinuities. Temperature evens out eventually due to the flow of heat. Eventually, the temperature profile reaches a steady-state condition where the temperature varies slowly. However, the variation in pressure does not change in time. There will always be a gradient of pressure within the earth even in the far, far future where the temperature is the same throughout the earth.

Here are some links on phase transitions in the mantle.

http://en.wikipedia.org/wiki/Transition_zone_(Earth)
“The transition zone is part of the Earth’s mantle, and is located between the lower mantle and the upper mantle, between a depth of 410 and 660 km. The Earth’s mantle, including the transition zone, consists primarily of peridotite, an ultramafic igneous rock.
The mantle was divided into the upper mantle, transition zone, and lower mantle as a result of sudden seismic-velocity discontinuities at depths of 410 and 660 km. This is thought to occur as a result of rearrangement of atoms in olivine (which constitutes a large portion of peridotite) at a depth of 410 km, to form a denser crystal structure as a result of the increase in pressure with increasing depth. Below a depth of 660 km, evidence suggests that atoms rearrange yet again to form an even denser crystal structure. This can be seen using body waves from earthquakes, which are converted, reflected or refracted at the boundary, and predicted from mineral physics, as the phase changes are temperature and density-dependent and hence depth dependent.”

http://www.ucl.ac.uk/EarthSci/people/stixrude/stixrude_97.pdf
“Structure and sharpness of phase transitions and mantle discontinuities
Abstract: The structure of phase transitions from the standpoint of equilibrium thermodynamics is examined…We predict that the olivine to wadsleyite transition in the presence of pyroxene and garnet is approximately half the binary loop at typical transition zone temperatures. The estimated effective width of this transition (4-8 km) is marginally consistent with observations of high frequency (0.5-1.0 Hz) P-waves from the 410 km discontinuity….this transition can account for the properties of the 710 km discontinuity.”

http://www.eos.ubc.ca/~mjelline/453website/eosc453/E_prints/newfer06/2005RG000186.pdf
“The stability of (Mg,Fe)SiO3 perovskite in the deep lower mantle has long been uncertain. Recently, a phase transition from perovskite to postperovskite was discovered
through a significant change in the X-ray diffraction pattern at high-pressure and high-temperature conditions corresponding to the core-mantle boundary region. This
phase transition was also confirmed by first-principles calculations.”

9. Nov 22, 2012

### Staff: Mentor

Right. There is no flaw in the Wiki articles there, only in the OP's comprehension of them: The Earth/atmosphere boundary is not a thermodynamic system.

10. Nov 23, 2012

### Staff: Mentor

Perhaps my English fails me, but I have a feeling boundary fits the definition of the thermodynamic system as quoted earlier by OP. You can select a volume that contains the boundary and describe processes inside it using thermodynamics.

It will still not make these processes phase transition, no doubt about it.

11. Nov 23, 2012

### Ophiolite

flicflex, where do you wish to measure things from? There are really only two viable options: the surface of the Earth, or its centre. No other points or surfaces are well defined. It is convenient, in many instances, to continue using the Earth's surface (however now defined) as the reference surface. That's not old school, as you suggest; that's just solidly practical.

12. Nov 26, 2012

### flicflex

Yes of course.
Definition of the french wikipedia

id est

Since (darwin123) that we have a drastic change of the composition at the earth surface, we can indeed consider it as an abscissa. But I guess that overall we should consider altitude 0 of our earth system the same way we consider the altitude 0 of another planet. Anyway this is a detail :)

13. Nov 26, 2012

### flicflex

As a phase transition is defined in math-phys as non-analyticity of certain parameterized functions on a configuration space IN the parameter variable, we can consider the non analicity of internal energy (or pressure if you prefer) depending of the earth radius parameter, at any point of the radius, including earth surface, right?

But I guess that building such a function in a such heterogenous space would be really difficult.

Then can you give me an example of a similar function which could describe surface's radius (distance surface-center) of another planet (with a homogenous materia system)? Or even of earth but during its very early history (when it turned to be a gaz planet to magma/gaz planet)?

Last edited: Nov 26, 2012
14. Nov 26, 2012

### Staff: Mentor

No. A thermodynamic cycle contains a working fluid (or two or three) that move and typically change state in order to carry energy from one place to another and/or transform it between electrical/mechanical/thermal forms. Let me explain, with an example:

Draw a cylindrical boundary of 1 km diameter and 15 km height, with its bottom on the surface of the earth, on an externally calm day (so no significant mass flow in and out of the cylinder) that is warm, sunny, and humid. This is the boundary of a thermodynamic system, with two working fluids: water and air. On a day like this, a thunderstorm is likely: The external heat source is the sun, it warms the ground, evaporating liquid water (changing its state/phase, causing air to heat and rise, carrying water vapor up. The mixture of water and air cools as it rises and the water vapor condenses, (changes state/phase to liquid), then precipitates out, falling back to the ground. The cycle repeats the next day.

Notice:
1. Nothing but heat is moving across the boundary.
2. The changes in state happen to one of the working fluids, which is conserved and is singular in its composition (it is just water).

Try the same with drawing a 1m cube, half of which is underground. It is just a box of dirt and air. Though there may be heat transfer initially, eventually there will be an equilibrium in this box, where nothing is happening.

So, to be clear:

In thermodynamics, a "phase transition" is referrring to a working fluid that changes its phase while performing some thermodynamic task (carrying energy, performing work).

One can call the boundary of the ground and air by any name you want, but calling it a "phase transition" is going to have a different definition than the thermodynamic one. Similarly, I can say "when I jumped in a pool, I 'transitioned' from being in one phase of matter to being in another", but that has nothing whatsoever to do with thermodynamics.

Now. I'm sure you aren't here to argue about the definition of "phase transition" whether pertaining to thermodynamics or not. So please rephrase your question. To be perfectly honest, it mostly sounds like gibberish to me (being born underground?), though some may be a language barrier.

The specific question you asked at the end of the first post has an easy answer: When the earth was formed, it was formed out of a mixed-cloud of gas and dust/rock. The dust/rock is heavier than the gas, so it sank and formed a clump on the inside (the earth) while the gas is light and so it stayed on the outside. That really is all there is to it. Besides the initial formation, there really isn't anything about this to study - it is too simple. Unlike what is going on inside Jupiter, for example, where there is no well defined transition plane between gas and liquid.

15. Nov 26, 2012

### flicflex

Well, the french (again) wikipedia has two different articles : one for "phase transition" (transition de phase) which I quoted, and one for "state transition" (changement d'état) which seems to be a subcategory of phase transition. But let stick to you definition (you have 20345/7= 2907 times more messages than me!).

My question could be reformulated like this :

trough a mathematical point of view, why does the solid part of earth has a precise radius of 6400km?

If the question is too difficult, can you give the answer for the similar question to any planet easier to study?

16. Nov 26, 2012

### Staff: Mentor

1. It doesn't.

2. Looking for a logic behind the Earth radius is a pure numerology. IOW: there is no scientific meaning behind.

17. Nov 26, 2012

### AlephZero

As Borek said, it doesn't. But the reason the radius is approximately 20,000/∏ km is because of the way the meter was first defined. http://en.wikipedia.org/wiki/History_of_the_metre

18. Nov 27, 2012

### Ophiolite

Hmm. Questionable. The gasesous components of the Earth are almost entirely (perhaps entirely) derived from degassing of the interior once formed from solid planetesimals and from volatiles provided by cometary and asteroidal impact. There is no evidence I am aware of that would involve a meaningful contribution of nebular gases to the proto-Earth. I stand ready to be corrected on provision of relevant citations.

19. Nov 27, 2012

### Staff: Mentor

Sigh. Yes, it is a simplification. Yes, we did have nebular gasses, but it was mostly hydrogen and most blew away during Earth's formation and the start-up of the sun. But whether we call the "degassing" process that created our current atmosphere part of the formation of earth or not is yet another hair I don't care to split. It still follows the description I laid out: Heavier substances sink and lighter ones rise. That's why all of the gases are now in Earth's atmosphere instead of its core.

http://en.wikipedia.org/wiki/History_of_the_Earth#Solar_System_formation

20. Nov 27, 2012

### Staff: Mentor

The reason the Earth's radius is what it is is because that's how much solid matter there was floating around our proto-solar system, in range of Earth's gravity when it formed. There really is nothing more complicated about it than that.