Prediction of temperature of phase change
Is there no literature on whether the temperature of a phase change for a particular element or compound can be predicted from current physics (i.e. quantuum mechanics)?
Does current physics explain why mercury is a liquid in its "normal" state but Oxygen is a gas in its "normal" state?
From the article: "This means, for example, that it is impossible for the solid-liquid phase boundary to end in a critical point like the liquid-gas boundary. However, symmetry-breaking transitions can still be either first or second order."
- [Question from J]: Could you give an example of a symmetry-breaking transition which is second order? Thanks. 126.96.36.199 14:24, 5 November 2005 (UTC)J
- Ferromagnetic to paramagnetic transition. -- CYD
From the article:
- The ferromagnetic transition is another example of a symmetry-breaking transition, in this case time-reversal symmetry. The magnetization of a system switches sign under time-reversal (one may think of magnetization as produced by tiny loops of electrical current, which reverse direction when time is reversed.) In the absence of an applied magnetic field, the paramagnetic phase contains no net magnetization, and is symmetrical under time-reversal; whereas the ferromagnetic phase has a net magnetization and is not symmetrical under time-reversal.
This isn't my area of expertise, but I'm pretty sure this is wrong. The direction of the magnetic field always reverses under time reversal, but that's because of the way the field is represented mathematically; it isn't a T violation. -- BenRG 05:51, 24 Sep 2003 (UTC)
- I'm note sure what you mean by "that's because of the way the field is represented mathematically". Note that "symmetry breaking" has a narrow meaning in the context of the article. It refers to a symmetry that is unbroken by the underlying physical laws, being broken by a particular configuration of the system. In this case, the laws of electromagnetism are T-invariant, but magnetic systems break T invariance. To give another example, crystals break continuous translational symmetry, even though the physics of spacetime are symmetric under arbitrary spatial translations.
- Is this what you're worried about? -- CYD
What I meant is just that the magnetic field is an axial vector field. I agree that symmetry breaking takes place in the ferromagnetic transition, but it's not time reversal symmetry that's broken. Time reversal symmetry is only broken by the second law of thermodynamics and (in a different sense) by weak interactions. The formation of ferromagnetic domains resembles crystallization and has the same symmetry-breaking properties (i.e. it breaks isotropy).
I've never heard time-reversal symmetry mentioned in the context of thermodynamic phase transitions, but if you can find a textbook that disagrees with me I'll reconsider my position. -- BenRG 08:48, 25 Sep 2003 (UTC)
- It is fairly uncontroversial, at least in condensed matter physics, to say that magnetic systems break T. See, for example, p.18 of Basic Notions of Condensed Matter Physics by P.W. Anderson, and p.40-54 of Lectures on Phase Transitions and the Renormalization Group by N. Goldenfeld. (Both books have many profound things to say about the subject of phase transitions, by the way.)
- Anyhow, your argument does not compute. You claim that magnetic systems cannot break T because T is only broken by the second law of thermodynamics and weak interactions. By the same token, no systems can break continuous translational symmetry, because that symmetry is unbroken by all known laws of physics; but this assertion is false, as demonstrated by the existence of crystalline solids (or, for that matter, by the inhomogenous distribution of matter in the universe.) -- CYD
Goldenfeld answered my objection in his very first sentence when he wrote: "The first symmetry which we discuss is up-down symmetry, sometimes called time-reversal symmetry or Z2 symmetry." In other words, it's really about reversing the magnetic field, and time reversal is just one (theoretical) way to describe that. I interpreted "time reversal" to mean reversing the evolution of a dynamic system, and in that sense it's a little weird to say that any static system (like a ferromagnet in thermal equilibrium) violates time reversal symmetry.
I propose that the paragraph be changed to something like this:
- Another symmetry which can be broken by a phase transition is "up-down symmetry" or "time-reversal symmetry", which is symmetry under the reversal of the direction of electric currents and magnetic field lines. This symmetry is broken by the appearance of magnetized domains in the ferromagnetic transition. The name "time-reversal symmetry" derives from the fact that electric currents reverse direction under negation of the time coordinate.
I'm not sure that I phrased it too well, but the three main changes are: 1. Makes the symmetry, rather than the phase transition, the topic of the paragraph (otherwise it's unclear why the paragraph doesn't mention that the ferromagnetic transition also breaks isotropy); 2. Removes the link to the T-symmetry article, which is about a different symmetry entirely; 3. Clarifies that time reversal is just one way of looking at the symmetry in question. Is this acceptable?
By the way, I agree that what I wrote above beginning "Time reversal symmetry is only broken by..." is nonsense. What I was trying to articulate is that physicists don't normally talk about time-asymmetry in actual physical systems because it's ubiquitous. To say that a physical law violates time-reversal symmetry is to say something interesting and meaningful because there are so few that do; but to say that a particular system violates it is to say very little. I agree, though, that it does make sense to talk about it in this context. Sorry. -- BenRG
- Your paragraph looks okay. I'd make a few modifications, like this:
- Another example of a symmetry that can be broken by a phase transition is "up-down symmetry", also called "time-reversal symmetry", meaning symmetry under the reversal of the direction of electric currents and magnetic field lines. This symmetry is broken during the transition to a ferromagnetic phase, due to the formation of magnetic domains in which individual magnetic moments are aligned with one another. Within each domain, the magnetic field points in a fixed direction chosen during the phase transition. The name "time-reversal symmetry" comes from the fact that electric currents reverse direction when the time coordinate is reversed.
- I seem to be having some sort of technical problem with editing the article, so why don't you go ahead and make whatever change you like. -- CYD
--- Shouldn't the various terms for the various phase transitions be noted and defined or at least linked-to in this article? ie. condensation, melting, boiling, sublimation etc?? I was trying to find the term for solid -> gas transition (sublimation) and had to resort to google because the obvious place for it to me (this article) had no mention of the term...
--- The wikipedia term order parameter gets redirected to this page. Perhaps another page should be created for it? The order parameter is a relatively new concept that can be a rich source of future work. For instance, in systems with quenched disorder, such as a glass, below T_c, the system is split into multiple ergodically-separated phase regions. A single-valued order parameter would be meaningless in this case. In replica techniques, the order parameter of this glass would be described by an N x N matrix where N is the number of replicas. (Also, , but that's another story.) Wilgamesh 22:51, 18 Sep 2004 (UTC)
- That would be great. Would you like to do it? Btw, it is not a true statement that the order parameter is a new concept. Landau introduced it way back in 1936. -- CYD
- Right, I only mean that it's a relatively new term, and that it's by no means something that's fixed in stone. cf partition function. I guess I'm stuck in Landau's age. Oh, I thought of another thing, like in liquid crystals, there's a nematic phase: picture rods aligned, but not all in plane. Since rods are the same under inversion, a vector is inappropriate as an order parameter. Instead we must use a matrix. Wilgamesh 19:22, 21 Sep 2004 (UTC)
- Depends on what you mean by "relatively new", I suppose. The venerable statistical mechanics text of Landau and Lifshitz talks about the "order parameter". Even the idea that the order parameter can be something other than a simple real number is not that new: AFAIK the first non-trivial order parameter was the superconducting order parameter, a complex scalar. That was introduced in 1950 by the Ginzburg-Landau theory, though it was only explicitly identified as an order parameter by Gor'kov around 1955, I think. By the way, I believe the order parameter for nematics is more succinctly described as a line element (a vector without an arrow.) -- CYD
- The term 'phase change' is used for changes in small (nanometric) systems as
clusters of atoms and molecules or small proteins. Many articles devoted to the subject discuss usefulness of concepts like 'phase'/'phase change' in systems that are so small that thermodynamics equilibrium (N-> \infty) is far away. In fact the notion in the textbooks (N-> \infty) should be considered as a mathematical limit rather than a meaningful physical limit. Because cluster physics is more and more developed, I'd suggest to keep both: 'phase change' for strictly small systems, and 'phase transition' for bulk.See for example 'Theory of Atomic and molecular clsters' (J.Jellinek,ed.) Springer 1999[User:AIP] October, 22, 2005
It would be nice to include sample (possibly schematic) phase diagrams for a few typical systems, e.g. water (P vs. T), a ferromagnet (H vs. T), and superconductivity (H vs. T). The same diagrams should be included on the respective pages, and perhaps discussed in more detail there. Steven G. Johnson 21:28, 24 Mar 2004 (UTC)
Higher-order phase transitions
The article represents third and higher order phase transitions as a theoretical possibility. Have they actually been observed in practice? --188.8.131.52 22:47, 14 Oct 2004 (UTC)
It may have been. It seems that the signature of a higher order phase transition is sometimes easy to overlook. There is some indication (Physical Review Letters, 1999) that the appearance of superconductivity in BaKBiO3 is a fourth order phase transition.
liquid/gas possible confusion
Most people probably think of the liquid/gas system as having a first order phase transition. I think a couple of extra sentences could help explain what is continuous in this system. Ie the change in density across the phase coexistance line as a function of (T-Tc). Although I'm not confident enough that I won't make it worse to clarify this myself.
- Er, it is a first-order transition (except at the critical point). -- CYD
Ehrenfest's classification of Phase Transitions does not have anything to do with mean field theory (or any other approximation method), contrary to what the author says. It's based on analytic properties of the EXACT free energy.
Why were the references and some of the interwiki links removed? I'm restoring them, but if there is a good reason to remove them, let me know. Salsb 17:56, 22 September 2005 (UTC)
Removal of table of phase transition "names"
The table of "names" for phase transitions -- "boiling = liquid -> gas", "freezing = liquid -> solid", etc -- is not meaningful. As the article explains, solids/liquids/gases are only three examples for phases. It is generally not scientific practice to give names to the transitions, only the phases. The terms "boiling", "freezing" etc. are colloquial terms, so it is sufficient to mention them in the introductory text (as is already done in the article). It's not necessary to insert an important-looking table that in fact has no scientific merit. -- CYD
- I agree with your removal of the table as it gives only a few examples without details, and doesn't add much to the article. However, while this might be picky, I object to some of your reasoning. The naming of phase transitions is a standard practice as is the use of names for phase transitions. For example, both the Landau and Anderson references given in the article do so, using boiling, melting, condensation, freezing etc. So to say that they are colloquial is incorrect; see Landau's Statistical Physics for a nice intro to phase transitions. Salsb 13:29, 28 September 2005 (UTC)
- Although I'm not a physicist I have taken two years of physics in college (and one of chemistry) so I have more than a passing understanding of physics (although I admittedly have never heard the term "first-order phase transition" in school).
- Firstly I agree that my placement of the table was poor, it doesn't belong as an overview of the article but rather part of a subsection. Secondly, I realize that the terms are not perfect however they deserve more then a passing note in parentheses. Although the first-order phase transitions are by no means the only kind they are to a huge extent the most common, both in how often they occur and what people understand. Superconductors are nifty but they aren't every day (not until we find a room temperature one that is). You'd be hard pressed to find an example of a single second or third order phase transition in an average day. As for first-order, you don't even have to be at your stove, how about with you see your breath (condensation), or when your winshield is frosted (deposition), or when you get freezer burn (sublimation), or your after you wipe off your counter it dries (evaporation). Not only do people know most of these terms but they deal with these things all the time.
- I imagine at this point you're thinking something to the effect of, "when water is in an intermediate stage at 100° boiling, evaporation and condensation are all happening to different extents and just because water is going into the air doesn't mean you can call it a phase transition with a pretty label." Yeah I get what you're saying but are you telling me you expect people to not say "is the water boiling yet?" and instead say, "is the water undergoing a phase change from liquid to gas" which I might add is even less descriptive because it doesn't distinguish between boiling and evaporation (as a majority of the method).
- The main reason I think the table should be here is I think a decent amount of people would be interested to see what the other names for phase transitions are. If they show up thinking, "I know boiling and condensation and etc. but what is it called when it goes to straight from solid to gas?" and they find this article and start reading about Ehrenfest classification and Curie point, their eyes will gloss over. I'm not saying we need to dumb down the article, but a stepping stone between the real world and the scientific jargon seems appropriate. Vicarious 01:25, 29 September 2005 (UTC)
Propose to merge Phase change into the present article
The article on phase change should be merged into this one since it addresses a small subset of phase transitions — those between solid, liquid and gas. Those issues can be perfectly well discussed in the introductory material to the present article.
Thoughts? — WebDrake 00:43, 19 October 2005 (UTC)
- Category:Phase transitions probably? Agree with all the rest. --ACrush ?!/© 10:49, 19 October 2005 (UTC)
Abruptness of Chage
Can anyone explain why phase changes tend to be abrupt with respect to temperature? For example, some materials exhibit creep in the "solid" state, but even so, most materials have a defined melting temperature rather than having a yield stress that slowly approaches zero as Tm is reached. Since abrupt phase transitions are the norm, there must be a general explanation. Why? —BenFrantzDale 21:20, 19 December 2005 (UTC)
- They aren't always abrupt. Many materials are known for having rather vague melting points. That's often taken as a sign of chemical impurity, but it's also not unusual for amorphous materials or materials with lots of long molecular chains (polymers, for instance, or some catenating elemental allotropes). If you have a chemically pure substance with a very regular structure, every local set of molecules is identical, so naturally the conditions for making the phase change thermodynamically favorable is the same for all of them. Even so, it is also not unusual for a crystal to be thermodynamically "ready" to undergo a phase transformation but still sit around in the old phase for a while before it takes place - this is very similar to supersaturation in solutions. In such cases, the phase change when it happens tends to be widespread and rapid, much like precipitation from a supersaturated solution. In most such cases, the phenomenon is due to the requirement of a small amount of activation energy to make the transition happen. Once that's delivered, perhaps in the form of some local disturbance, the energy released by the phase transition in the disturbed area creates a sort of chain reaction that propagates through the whole material. Tarchon 21:37, 5 June 2006 (UTC)
- Thanks for the reply. Let me try to elaborate. If I have a crystal of lead, the speeds of the atoms should follow a Maxwell–Boltzmann distribution, thus some atoms should be above melting temperature (in as much as a single atom has its own temperature) even when the bulk temperature is well below the melting temperature. (As I understand it, this is what allows crystalline metals to creep and what allows ice to sublimate.) In my experience, though, lead always melts suddenly when heated, just like ice.
- On the other hand, glass (silicon dioxide) always seems to soften gently as it is heated. Perhaps this has to do with the difference between crystalline solids and amorphous solids? Perhaps liquid glass just has a high viscosity and so its transition isn't as abrupt? —Ben FrantzDale 19:28, 2 March 2007 (UTC)
- Your understanding of creep is incomplete. There are many kinds of creep, named according to mechanism and rate-temperature dependence. Mechanistically, some have to do with 1D defects (dislocations) moving through a material, carrying deformation, while others have to do with 0D defects (missing atoms) that allow single atoms to diffuse preferentially in the direction of applied stain. Neither of those has to do with melting.
- Glasses, by nature, do not have a long range order, and therefore do not have dislocations, so are not subject to those kinds of creep. Glasses, by nature are supercooled liquids, not proper solids. During the melting of a solid, you're pumping a lot of energy into a phase transformation that glasses do not have. —Preceding unsigned comment added by 184.108.40.206 (talk) 20:14, 19 June 2009 (UTC)
i have no idea what to do and my teacher made me do an assignment
The following paragraph appears:
"The presence of symmetry-breaking (or nonbreaking) is important to the behavior of phase transitions. It was pointed out by Landau that, given any state of a system, one may unequivocally say whether or not it possesses a given symmetry. Therefore, it cannot be possible to analytically deform a state in one phase into a phase possessing a different symmetry. This means, for example, that it is impossible for the solid-liquid phase boundary to end in a critical point like the liquid-gas boundary. However, symmetry-breaking transitions can still be either first- or second-order."
I can't make sense of it. While this could certainly be my mistake, I think it could be made clearer. Could someone look it over and make sure the wording is as clear as possible? Thanks. 220.127.116.11 14:06, 18 July 2006 (UTC). Adding my real sig: PitOfBabel 14:07, 18 July 2006 (UTC)
I've got a question. In the article, there is "... including the solid/liquid/gas transitions and Bose-Einstein condensation." - for first-order phase transition.
But in the paragraph named Critical points, there is "..at which the transition between liquid and gas becomes a second-order transition".
Is there something I didn't catch or it's typing error?
Hello physicists, I was trying to learn about order parameters, which i get the vague notion sort of describe something about how something changes during a phase transition. great!! but -- the page for Order Parameters redirects to this page, and this page says "... order parameters, which we will describe later ..." lies! there are no later descriptions! silly physicists... now i still don't understand order parameters.
- Have you read Landau theory on second order phase transitions? TomyDuby (talk) 01:57, 14 July 2008 (UTC)
The article lists the change from liquid to gas as boiling/evaporation. Surely evaporation is the change from liquid to vapour, not gas. That's why it is called eVAPORation. 18.104.22.168 20:53, 12 May 2007 (UTC)
- I assumed vapor and gas were interchangeable, apparently not. After a quick skim of their articles, it seems like the term is used correctly, although it could perhaps have been named more sensibly in the first place.Bistromathic 15:27, 20 May 2007 (UTC)
- boiling is the phenomena where a gas phase forms within the bulk liquid phase. It takes a little more energy to nucleate (start) a bubble than it does to evaporate an equal amount of liquid at an existing gas-liquid interface. Boiling requires that the liquid be superheated. —Preceding unsigned comment added by Pvkeller (talk • contribs) 15:58, 4 December 2008 (UTC)
Ehrenfest classification system
Could anyone explain in more detail the difference between the two classification systems? I assume they are equivalent in most cases, is this true? Is the Ehrenfest system actually disused? This system was taught to me in a recent lecture, albeit by a rather hopeless lecturer... He also kept going on about Lambda Transitions, which do not seem to be as important as the impression he gave, as they are not mentioned in this article (please ignore me if I have had a bout of stupidity and / or blindness and missed it).Bistromathic 15:32, 20 May 2007 (UTC)
Diagram Labeling Error
The first diagram showing the phase changes indicates that "Sublimination" is a phase change. The term is in fact--as the table later shows--"sublimation." "Sublimination" isn't related to physics--it might be a paranormal term but it's definitely wrong here.22.214.171.124 04:06, 25 July 2007 (UTC)
- You are correct, I made a mistake when making that image. The correct word is Sublimation. The Image is now fixed-- Penubag 05:15, 25 July 2007 (UTC)
The phase diagram shown in the article has a small error, but I am no good at editing images so I was hoping I could raise the awareness and someone might fix it up. The dotted line showing the phase transition from solid to liquid for water is drawn in as a very curvy line. In every phase diagram of water I have ever seen it looks more like a straight line with more of an obviouse 'negative' slope. The line stays straight at least until 200+ atmospheres of pressure. Also, where the dotted line first branches out from the solid line at first it appears to have a slightly positive slope, and this is definately incorrect...Thanks, and comments much appreciated. CoolMike 00:51, 2 August 2007 (UTC)
Discontinous phase transitions
This article seems to deal primarily with discontinous/first order phase transitions. E.g. "The order parameter is the quantity which is indeterminate at the critical point" this is true for a discontinous phase transition but not for a continous/second order phase transition. /Lokal_Profil 12:43, 3 March 2008 (UTC)
Second class of phase transitions -- there is some confusion
The article says: "The second class of phase transitions are the continuous phase transitions, also called second-order phase transitions." Two paragraphs later: "Several transitions are known as the infinite-order phase transitions". Can I from this deduce that infinite order phase transitions are second order phase transitions?
I think that this needs clarification.
Melting and fusion are synonymous
I made an edit earlier that was promptly reversed by adding /Fusion next to Melting in the phase change table. I believe these terms are synonymous and it should be reflected in the article.
Reference: Chang, R., Chemistry, 7th Ed, McGraw-Hill (2002)
I've also seen this my physics and physical chemistry text books as well as online dictionaries.
- Thanks for citing a reference; I will unrevert the change. Here on Wikipedia, we are really sensitive to information that seems like it is just randomly entered. -- penubag (talk) 22:57, 9 November 2008 (UTC)
- As a linguistic activist, I must say that I think a more proper use of the word fusion (with respect to melting) comes from the Oxford English Dictionary: "fusion, n. 3.a. The union or blending together of different things (whether material or immaterial) as if by melting, so as to form one whole; the result or state of being so blended." This use the term "fusion" is related to but distinct from the term "melting". This definition expresses the idea "fusing-by-melting" or "melt-fusion". Using the word "fusion" as a synonym for "melting" itself is potentially confusing because fusion seems to relate more to the process of freezing, where molecules fuse together to form rigid structures. --Zeroparallax (talk) 05:41, 10 August 2012 (UTC)
This is a minor but common point: phase transition or phase-transition; phase change or phase-change ? I see that both forms are used in the article at the moment; maybe one should fix one form according to the style of wikipedia. --PMajer (talk) 12:39, 4 December 2008 (UTC)
solid to plasma transition
In the table of transitions plasma is reached only from gas/fluid. But this is not so obvious from the P-T diagram - there it seems that if P is high enough maybe solid-to-plasma transition can occur. It is not very clear, because plasma is not shown on the P-T diagram. So, we should eighter mention solid-to-plasma or change the P-T diagram so that it shows a negative slope on the solid/liquid line after some point so that there is no solid-to-plasma. In eighter case the plasma phase should be added to the P-T diagram. Alinor (talk) 17:49, 4 October 2009 (UTC)
Where does Engels come into this???
I found a line saying one of the earlier attempts to formulate a scientific law of phase transitions was by Engels. I thought it was irrelevant and deleted it promptly. —Preceding unsigned comment added by Pteradactyle (talk • contribs) 22:50, 4 December 2009 (UTC)
About "Mistake" - order of liquid/gas transition
about Mistake - is liquid/gas first or second order?
The article says the liquid/gas transition is first order, but then later says it has the same critical exponents as the uniaxial (a term which is not explained) ferromagnet, which is second order. The comment "Mistake" above makes a related point. Paulhummerman (talk) 10:59, 23 September 2010 (UTC)
- The ferromagnetic phase transition between magnetic moment up and magnetic moment down is a first order transition. The transition line lies at external field h=0. But for increasing temperatures, this transition line ends in a critical point, beyond which only one phase, the paramagnetic phase, exists. The same is true for liquid-gas transition. At lower temperatures, the phase transition is first order, but for increasing temperatures it ends in a critical point, above which neither gas not liquid exists, but just single homogeneous phase (you may want to have a look at the phase diagram of water to better understand what I am saying). This brings with it the interesting consequence that liquid and gas are only distinguishable in pactice, not in principle. Alas, this is a source of a lot of problems in describing what seems to be an everyday phenomenon; and I've not seen a good physical explanation, yet. Most things I've seen mix up the transition between liquid and gas and the transition between "liquid and gas can exist" and "only one phase can exist" in an erroneous manner (for instance, this very article says that "The order parameter is normally a quantity which is 0 in one phase (usually above the critical point), and non-zero in the other. [...] For liquid/gas transitions, the order parameter is the density.", which is clearly self-contradictory). --timo (talk) 21:50, 26 May 2011 (UTC)
Lack of Generality of the Article
Hello, I'm not well versed on the propper form of Wikipedia editing so if I'm doing something wrong I apologize in advance.
What I wanted to discuss is that this article on phase transitions isn't general enough to describe what phase transitions actually are. It states in the opening statement that "A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another." and this is merely one of the many kinds of phase transitions there are. A phase transition is the physical process through which a system (thermodynamical, classical, quantum...) undergoes a discontinuous behavioral shift. Condensed Matter physics is ripe with examples of this: not only the thermodynamical "matter phase transitions" but Bose-Einstein condensation (fluid-superfluid transition) or Superconductivity which can actually be seen as a change in the nature of matter (from fermionic to bosonic!) and other fields of Physics deal with phase transitions. As another example, the Higgs mechanism implies a phase transition on the Standard Model, and most inflationary processes in Cosmology are models that create a phase transition in the early Universe.
It is my belief that presenting phase transitions as a purely thermodynamical mechanism is misleading and detracts from their position as one of the most important mechanisms to understanding the natural world. The Wikipedia article on Landau Theory is a great place to start for those whose interest is picked. My suggestion is that a tag is added to the article saying it needs to be generalized so it will hopefully garner the attention of an expert (the current incarnation of the article could be the "Thermodynamical Phase Transitions" Section). I might even help out if needed (the field is so incredibly vast that rewriting this article in those lines is a very, very daunting task).
And in case you're wondering, no, I'm not a phase transition academic that wants to see my field of work get more recognition :) I'm just a Physics grad student that has been marvelled by the subject ^^
P.S.: My apologies to whoever editted above me as I accidentaly added this comment to his topic despite them being absolutely decorrelated. I edited it out again and started this new topic, I hope I didn't do anything wrong :/
The article (or someone here) should answer these questions: In the modern classification scheme, are there solid rules for defining the transition categories, or is it more like a loose collection of similar phenomena (like classification in biology)? Is there an easy way to define infinite-order phase transitions other than saying "They are continuous but break no symmetries."? (And do the other continuous transitions always break symmetries?) Also, if the second-order transitions are characterized by divergences, do infinite-order transitions lack such divergences? --Zeroparallax (talk) 06:02, 10 August 2012 (UTC)
I presume you referring to infinite-order PHASE transitions. Well the free energy has an essential singularity and any order derivative of the free energy does not diverge.
plasma phase transition on phase diagram
Right now we just have a gas/liquid/solid phase phase diagram in pressure temperature. Since plasma seems to be singled out as "the fourth phase", it would be nice to also add on the plasma phase to the P-T diagram, although I'm not sure what the generic form of this is. For example, I suppose that upon heating a molecular substance it first decomposes into a polyatomic gas, and then finally begins to ionize. To avoid that extra intermediate phase we could consider a more simple specie, perhaps cesium.
It sounds like some such experiments have been done with cesium. This paper offers some insights however the diagram is not quite what we want (pressure-volume or axes instead of pressure-temperature). A few key things we can note:
- The transition to plasma seems to be gradual as temperature is increased. The parameter alpha only varies gradually. This seems to indicate that it is not really a proper phase transition, but rather more resembles the gradual transition from liquid to supercritical fluid. Possibly it could also be a second order phase transition. If so, it is not clear to me where the critical point of the gas-plasma transition is.