Talk:Coordination complex

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I'm perplexed as to why there is no mention of the importance/function of metal complexes in hemoglobin in this article whatsoever. Could someone please expand this article in that specific area? Ajaxkroon 11:02, 29 March 2006 (UTC)

I've done something about it. --Dirk Beetstra 08:40, 16 May 2006 (UTC)


Non-covalent bond? Aren't the bonds considered to be covalent since they are sharing? Olin 17:28, 31 March 2006 (UTC)

Are they not covalent once they are formed? I know they call them coordinate covalent bonds. This is what the article on CCBs has to say:

"A coordinate covalent a special type of covalent bond in which the shared electrons come from one of the atoms only." Expert needed. JohnJohn 17:16, 21 April 2006 (UTC)

I don't think the term applies to that, I'm not sure though. A coordinate covalent bond would be like the one between the extra H and N in NH4+, because both electrons come from the electron pair on N. Since complexes are often, if not mostly or always, composed of a central metal ion (which is positively charged), it'd be hard for that to donate electrons. They might come from the ligands though, although I'd still say there's a largely electrostatic attraction. I'd have to look it up to be sure. Jack the Stripper 14:57, 22 September 2007 (UTC)

Ligands (L:) in complexes use their lone pairs (if they have them) to form dative covalent bonds with the central metal atom.

Ben 15:24, 22 September 2007 (UTC)

Statements in Atomic structure of coordination compounds[edit]

I am removing some ambiguous statements in the Atomic structure of coordination compounds section of the article. Some are not untrue, but I think it is better to give real reasons (which have already been explained) instead of 'rule of thumb'-like statements. (As an example, the reason why late transition metals tend to have lower coordination numbers, is that (for a given oxidation state) late transition metal ions are smaller than the early transition metal ions (Sc3+ is much bigger than Co3+), so less ligands tend to fit around late transition metal ions. But, coordination is governed by overlap between orbitals (a thing also true for main group elements). --Dirk Beetstra 15:44, 16 May 2006 (UTC)


I just took another look at this for the Wikipedia:WikiProject_Chemistry/Worklist, and it's certainly come a long way (it was only a "Start"), thanks a lot for adding all this content Smokefoot and Beetstra! I wanted to ask a few questions:

  • I formatted a ref and noticed after doing so that it had was the same as an external link. Can you clarify which it is? (Wikipedia defines refs as actually used in the writing of the article, whereas ext links are just nice pages folks might find helpful).
No clue .. ref was there already, did not have a look .. --Dirk Beetstra 07:34, 22 May 2006 (UTC)
  • Can you make sure you add in any refs that you have used? The list seems rather short considering the amount of work.
The most I did was reorganising some pages, moving the info to the page where I thought it belonged, a lot of info is coming from Ligand (which does not contain any references as well ..). The article surely needs some references, but I must confess, most of my chemistry-books are back in NL, I (re)write info that (to me) is common knowledge or logic. I may have to have a dive into the library for some things. --Dirk Beetstra 07:34, 22 May 2006 (UTC)
  • Do you think a section on chelation, crown ethers and cryptands would be appropriate? If so, should I write it, or would one of you like to?
Chelation gets quite some space in ligand (in the section denticity, it might need some attention there). I think that it is more appropriate there, chelation is a property of a ligand, not of a complex (IMHO, it should only be noted here that complexes with chelating ligands tend to be more stable in terms of ligand dissociation).. By the way, it still lacks the thermodynamic rationale behind the concept of chelation. --Dirk Beetstra 07:34, 22 May 2006 (UTC)
  • Are there any other sections that need writing? If not, then with the above modifications we could get this article to A-Class, which would be nice! Walkerma 04:14, 22 May 2006 (UTC)
I am quite (I'd like to say: very) unhappy with the isomerism section, that needs a decent rewrite, trans-effects are completely missing, and optical isomers need to be explained here (the concept with 6-coordinate atoms is more difficult than with 4-coordinate atoms C, N (,S, P)!! Though the concepts of that should be explained in some page like chirality (chemistry) (I did not have a look on that page, yet, one moment .. OK, inorganic complexes do have a section there, but that section is a plain stub). I think important here are the effects of isomerism: cis-platin, trans-effect, orientation of reactive sites (in general cis to each other). --Dirk Beetstra 07:34, 22 May 2006 (UTC)
OK, rewrote this section to a readable and more or less correct state, still there is info missing, some linking needs to be done, and see if the concepts in this section are explained sufficiently in the pages linked to. --Dirk Beetstra 21:12, 22 May 2006 (UTC)
It is good to hear that the page is getting where it should be, after shuffling ligand and complex I already found that it was a better article, thanks for the assesment and the compliments. I think when we have these pages (ligand and complex) on a good level, they serve as a decent background for other (inorganic) chemistry concepts that need explaining. --Dirk Beetstra 07:34, 22 May 2006 (UTC)

9-coordination - help[edit]

Is what has been described as Tri-capped trigonal prismatic actually a Triaugmented triangular prism ??? --Dirk Beetstra 21:44, 22 May 2006 (UTC)

I dont think so, but I am checking with a math person. The tricapped trigonal prism is deltahedral but there are no "mu5-vertices", because the square faces are capped. --Smokefoot 23:09, 22 May 2006 (UTC) My topology friend tells me that Tri-capped trigonal prismatic and Triaugmented triangular prism are the same.--Smokefoot 18:28, 23 May 2006 (UTC)
Great, thanks. I have corrected the link in the article. Cheers! --Dirk Beetstra 18:32, 23 May 2006 (UTC)
P.S. does it make sense to your friend to make a redirect from Tri-capped trigonal prismatic to Triaugmented triangular prism as well? --Dirk Beetstra 18:32, 23 May 2006 (UTC)

Problems with this article[edit]

Reading this article I think that there are some changes required, which I think need some discussion as so many folk have contributed.For example:-

Metal complexes The definition as it stands does not include e.g Aluminium etc. Poor or post transition metals need adding to the definition for completeness.
Why is there no link to the Ligand article?
Geometry The point "the idealised descriptions of 5,7,8...etc" When a square pyramid is so distorted that it becomes an idealised tbp then it really IS a tbp. Perhaps the point to be made is that it is impossible to tell the difference sometimes between e.g a distorted sp and a distoretd tbp.
Color The reference to Tanabe-Sugano diagrams is fine but simple CFT does quite well for the less competent amongst us, and the CFT article is pretty good and deals with the colors of transition metal complexes quite well whereas the T-S article is not very helpful.
Magnetism "Metal complexes that have unpaired electrons are magnetic". This should read paramagnetic. Magnetic is misleading- as it usually understood to refer to ferromagnetism.

Axiosaurus 11:08, 27 February 2007 (UTC)


Would somebody mind to double check the nomenclature for the porphyrin complexes. It should be [5,10,15,20-tetrakisphenylporphyrinato]copper(II). Unless somebody prove me wrong. —Preceding unsigned comment added by Mandor (talkcontribs) 14:43, 15 October 2008 (UTC)

History section[edit]

The history section has no references. Also, it says Werner overthrew the theory that chirality was only for carbon compounds. Did anyone actually believe that? Crystal whacker (talk) 02:03, 16 December 2008 (UTC)

I think that there was some sort of conflation of organickiness, chirality, and vital forces that was overthrown by Werner's resolution of carbon-free complexes. Werner's work in this area does not seem particularly relevant to emergence coordination chemistry but was more of a collateral aspect. Regarding history sections, they are tricky to write objectively and they often cross the line toward original research. Russian authors favor Russian contributions, US authors favor US contributions, the French ... I for one like the idea that coordination chem began with Werner's octahedron. The areas, subheadings, of the field should mention a few sentences on the emergence of each of these themes.--Smokefoot (talk) 03:47, 16 December 2008 (UTC)

  • Linked to hexol. Unable to find a Werner reference. By the way, reference 42 in doi:10.1002/chem.200600981 has this to say: The first coordination compound H3N·BF3 was synthesized in 1809: J. L. Gay-Lussac, J. L. Thenard, Mem. Phys. Chim. Soc. d7Arcueil 1809, 2, 210. V8rik (talk) 21:49, 16 December 2008 (UTC)

Iron or platinum complex[edit]

Note to Smokefoot:

I see that you have relabeled the Fe(NH3)2F4 complex in the intro as Pt(NH3)2Cl4. I understand the point in the edit summary that you want to show a complex that really exists. However in that case the image needs to be re-drawn. At the moment readers are faced with a caption which says Pt and Cl, but the image shows Fe and F atoms! I think this is much more likely to confuse readers (especially those with little background in inorganic chemistry) than showing a correct image of a complex which doesn't really exist. Dirac66 (talk) 14:08, 20 November 2009 (UTC)

Structure of coordination complexes[edit]

The Structure of coordination complexes section currently notes: "Ligands are generally bound to said central atom by a coordinate covalent bond (donating electrons from a lone electron pair into an empty metal orbital), and are thus said to be coordinated to the atom." I believe the statement in brackets is false in the sense that it is not merely lone pairs donating, but pi bonds too. Later mentioned complexes exemplify this, and list ethene as ligand, which does not even have lone pairs. —Preceding unsigned comment added by (talk) 07:32, 17 April 2010 (UTC)

I would say the statement was "incomplete" rather than "false". I have now added a mention of pi-bond ligands with an example. Dirac66 (talk) 14:05, 17 April 2010 (UTC)


Complexation redirects to this article ... should the same be done with decomplexation? --Andersneld (talk) 19:01, 9 January 2011 (UTC)

Not until the article includes at least a word of explanation as to what decomplexation is, I think. Dan 23:30, 9 January 2011 (UTC)
Actually, a short "The term complexation refers to the process of..." wouldn't harm either: what good does a redirect do if it brings you to an article that never mentions the term you searched for? Dan 23:34, 9 January 2011 (UTC)

Virtually all compounds containing metals consist of coordination complexes???[edit]

To Smokefoot re today's edit:

1. Your edit summary reads "rvt naive edit by self-annointed expert Deng". I think it would have been more polite to write "rvt last edit and provide requested source".

2. If you have Greenwood and Earnshaw handy, could you provide the page number for the fact that "virtually all compounds containing metals consist of coordination complexes"? It is not easy to find an explicit statement of this fact - I tried without success in Miessler + Tarr, Cotton + Wilkinson, and Jolly. Dirac66 (talk) 16:33, 5 August 2011 (UTC)

Such a broad statement really needs more sources than that.Jasper Deng (talk) 16:45, 5 August 2011 (UTC)
Deng: My apologies for being offensive. On the otherhand, it is strange that an editor with no track record in this project unilaterally removes a statement. Naive, arrogant, over-reaching, or something ...
Dirac: Yours is an interesting point but it would difficult to identify a compound of a metal in solution that is not a coordination compound, you'd agree. Perhaps Deng has some insights on the subject of metal ions in solution? Or on the diversity of metal-containing compounds. Sometimes it is trickier to establish a general case vs a specific one. But again, I look forward to Deng's insights on the subject.--Smokefoot (talk) 20:21, 5 August 2011 (UTC)
Smokefoot, aqueous solutions of metal compounds are not the only ones that matter. It's pretty obvious that the magnesium chloride in the following reaction would not be considered coordination compound out of solution, even though it is one in solution. The solution state is not the only one that matters. By this argument, then this reaction Mg(s)+2HCl(aq)→H2(g)+MgCl2 would be written as 2H2O(l)+Mg(s)+2HCl(aq)→Mg(H2O)22+(aq)+H2(g)+2Cl-(aq). But more importantly, Smokefoot, please refrain from commenting on other editors and while you're at it, don't call me by my last name (I consider that a little rude). What's important here in the content, Smokefoot, is whether you have a correctly cited reliable source for such a broad statement, since a page # would help.Jasper Deng (talk) 18:14, 7 August 2011 (UTC)
Methinks a genuine apology for an offensive comment should not be followed immediately by another offensive comment ("Naive...") --Chriswaterguy talk 02:26, 20 September 2012 (UTC)

The article currently states that "Virtually all compounds containing metals consist of coordination complexes", citing Greenwood & Earnshaw. What kind of compound containing a metal doesn't consist of coordination complexes? My understanding was that complexes are independent molecules or ions like [Ti(OH2)6]3+, whereas an extended structure like titanium dioxide is not a complex. Nonetheless, you see terms like "coordination geometry" in the literature, even when referring to extended structures like TiO2.

On page 912, Greenwood & Earnshaw give a summary of Alfred Werner's original coordination theory. They state that coordination number "may be defined as the number of donor atoms associated with the central metal atom or ion. For many years a distinction was made between coordination number in this sense and in the crystallographic sense, where it is the number of nearest-neighbour ions of opposite charge in an ionic crystal. Though the former definition applies to species which can exist independently in the solid or in solution, while the latter applies to extended lattice systems, the distinction is rather artificial, particularly in view of the fact that crystal field theory (one of the theories of bonding most commonly applied to coordination compounds) assumes that the coordinate bond is entirely ionic! Indeed, the concept can be extended to all molecules. TiCl4, for instance, can be regarded as a complex of Ti4+ with 4 Cl ions in which one lone-pair of electrons on each of the latter is completely shared with the Ti4+ to give essentially covalent bonds."

What I gather from this paragraph is that the bonding in a molecular complex and in an extended structure can be pretty much the same. That doesn't mean that the names are the same, though. Would most chemists really call TiO2 a complex? We need some textbook quotes that explicitly state what defines a complex.

Ben (talk) 19:47, 7 August 2011 (UTC)

Ben, I have been thinking about this topic intermittently too. Even if we exclude solids like your TiO2, soluble titanium compounds are vastly more numerous if one considers just the many titanocene derivatives, which in turn represent one fraction of titanium complexes. But what source ever states that - its obvious to experts but nonobvious to those learning the topic. Maybe it is not important to argue about "Virtually all compounds containing metals consist of coordination complexes." I just cited Greenwood and Earnshaw because the contents of the book broadly support my geeky case, but I doubt if they come out and say such. I think I will let others deal with this topic for a while. --Smokefoot (talk) 20:38, 7 August 2011 (UTC)

I see your point, but I think it would mislead readers to use "virtually all metal compounds" when you really mean "a very high proportion of metal compounds". Probably better to say that an enormous number of molecular metal complexes exist and they are a major topic in chemistry. --Ben (talk) 21:07, 7 August 2011 (UTC)

I think a weaker statement would be less subject to criticism and not need a reference. Perhaps "Most compounds containing metals can be regarded as coordination complexes". The phrase "can be regarded" covers a case like TiCl4 which can be seen as Ti4+ + 4 Cl- (a coordination complex) OR Ti + 4 Cl (covalently bonded). Dirac66 (talk) 21:10, 7 August 2011 (UTC)
Or maybe we can say "In solution, most metal compounds are coordination complexes", which is definitely supported by Smokefoot's argument here.Jasper Deng (talk) 16:20, 9 August 2011 (UTC)

Reprise November 2011[edit]

It is definitely too broad to say that "virtually all compounds containing metals can be regarded as coordination complexes".

1) First of all, most chemists do not regard TiO2 as a coordination complex. Any atom in a crystalline ionic, metallic, or network solid can be analyzed with regard to its "coordination number". For example, the coordination number of carbon in diamond is 4. Does that make diamond a coordination complex? Of course not. Along those same lines, most chemists would not consider simple metal halides, oxides, sulfides, nitrates, carbonates, sulfates, etc. in the solid state as coordination complexes. They are simply ionic compounds (or covalent compounds, like TiCl4).

2) Secondly, most alkali and alkaline earth metals are very poor Lewis acids (with a few minor exceptions). Do potassium cations form coordination complexes as solids or in solution? Perhaps with a really good chelating ligand, but that's about it. I think it is safe to say that sodium chloride is not a coordination complex. Can we all at least agree about that? (Or are we going to throw away the concept of ionic compounds and just call everything a "coordination complex"?)

3) There are certainly similarities between different "types" of bonds, and of course all bonds boil down to electrostatic attractions. Nevertheless, there seems to still be some value in making distinctions between covalent compounds, ionic compounds, network solids, and coordination complexes, etc. This is perhaps my most important point, as Ben hinted at after his quote above. With the advent of MO theory, most chemists recognize the similarities of different bonds, but most chemists would still not call thousands of metal compounds "coordination complexes" because of the historical labels and the conceptual value of those distinctions. For example, I still teach my students about ionic compounds and covalent compounds, but I also explain that a bond is just a bond.

El Zarco 13:48, 5 November 2011 (UTC)

Most of the comments aside, I will just focus on a this one: "most alkali and alkaline earth metals are very poor Lewis acids".
of course K+ forms complexes in solution! Do you want our students deluding themselves otherwise - that that K+ is naked in solution? My guess is that K+ will outperform the usual reference Lewis acid BF3 with dozens of kcals/mol to spare! --Smokefoot (talk) 14:32, 5 November 2011 (UTC)
Interesting...many kcals/mol to spare? I wonder where you get your numbers? Just because potassium is solvated doesn't mean it is a good Lewis acid. What is the bond length of your supposed strong Lewis acid Lewis base bond between water and potassium? I assume that you have actually measured the bond length and bond strength to say you have "many kcals/mol to spare". If you think that the potassium water "bond" strength is stronger than a BF3 water bond strength, you have somehow deluded yourself. I don't delude my students and say that potassium is "naked"? It is solvated, just like H+ is solvated by more than one layer of water molecules. But does solvation imply a coordination complex? Or why don't you try to do Friedel-Crafts alkylation with your supposed powerful Lewis acid, K+? El Zarco 14:51, 5 November 2011 (UTC) — Preceding unsigned comment added by ElZarco (talkcontribs)
Feisty! Well K+ binds 6-7 water ligands (typical coordination number for K+ for most small ligands it seems), whereas BF3, which exists quite happily in unsolvated form, binds one water. That fact is some indication of the high Lewis acidity of K+. Gotta remember: it is a cation So that is some evidence that K+ is a rather good Lewis acid. Yes, the classic test for Lewis acidity, at least for sophomores in US colleges, is Friedel-Crafts catalysis. Few K+ (or Mg++) salts are soluble in the media used for this reaction (but it is a fascinating idea to use K+ salts for this application). Getting slightly less feisty, here is the view to be addressed: poor old K+ and Ca2+ just get "solvated", but transition metal dications are allowed to form a "proper complexes"? That is an incorrect and misleading view. Ligand exchange rates are high, but so are they for Mn2+ and some lanthanides. In any case good luck,--Smokefoot (talk) 15:19, 5 November 2011 (UTC)
I admit that the interaction between K+ and water involved in solvation is similar to that of a coordination complex, but very few chemists (i.e. I mean chemistry professors) would consider it as a coordination complex. Ask yourself, are the ions in tetramethyl ammonium chloride solvated? Yes. What is your coordination complex in that case? Potassium solvation is not too dissimilar to tetramethyl ammonium solvation. Remember, water can not only act as a Lewis base, but it also has a very high dipole moment. Water molecules arrange themselves around ions in multiple spheres with their dipole moments appropriately directed. In that sense, the dipole moment - ion interaction is more like strictly electrostatic attraction. In order to call something a coordination complex, you need to have coordination geometry that is not completely fluid, and you need to be able to be able to actually measure some sort of ligand-metal interaction via spectroscopy. There is some sort of Lewis acid Lewis base interaction between water and K+, but it is generally weak compared to other Lewis acids; you're biggest interaction is going to be the dipole cation interaction. El Zarco 01:56, 6 November 2011 (UTC)
This discussion is getting heated, and I note that all of today's statements (by both of you) are unsourced. Yes, we can discuss more freely on the talk page than in the article, but since the definition of what exactly is or is not a coordination complex is clearly controversial, it would be best to start checking for sources to support the eventual article text. And if reliable sources disagree with each other, we may have to quote both sides in order to maintain a neutral point of view. Dirac66 (talk) 02:04, 6 November 2011 (UTC)
Good idea about the source thing. Unfortunately I am out of the country and have no good access to anything other than online resources. I would prefer a neutral definition if someone else (other than the two of us) could think of a good neutral definition. If you actually ask several chemistry professors, I think you will find that they would agree that a number of the compounds in question (TiO2, solvated K+, etc.) are very similar in nature to coordination complexes, but they still wouldn't consider them coordination complexes, perhaps mainly for historical reasons. That really makes a good definition rather difficult. I was hinting at this earlier when I talked about ionic/covalent bonds. There is definitely some gray area where you say that a bond is somewhat "ionic" in nature and somewhat "covalent" in nature. That said, there is nothing to be gained by calling everything a "coordination complex." It seems much more reasonable to stick with the more narrow historic definition (which people still use) with the basic understanding that the distinction between ionic, covalent, and dative bonds is really quite artificial (though useful for conceptual understanding.) El Zarco 02:39, 6 November 2011 (UTC)
Oh, and with regard to the comment on the solubility of potassium salts in organic media, that is not the only problem you have with using K+ as a Lewis acid catalyst. You can make it soluble. Have you ever heard of BARF anions? I've used sodium BARF on occasion (though never potassium BARF), and it is simply a very weak Lewis acid. It can, however, be used to exchange counteranions with the precipitation of, for example, sodium chloride. El Zarco 02:39, 6 November 2011 (UTC)
Lastly, just for the record, I think the definition of a coordination complex is quite good at present and doesn't need to be revised. My only objection was with the phrase "virtually all." It seems too encompassing; there are too many exceptions.El Zarco 02:53, 6 November 2011 (UTC) — Preceding unsigned comment added by ElZarco (talkcontribs)
I agree with you on this point. As I said in August in the first part of this discussion, the quote from Greenwood and Earnshaw does not really support the use of "virtually all", unless we use their weasel words "can be regarded as". The rest of their paragraph makes clear that they do not really consider TiCl4 as a coordination complex. Dirac66 (talk) 03:24, 6 November 2011 (UTC)
Excellent. Perhaps we can agree to disagree about the whole potassium thing, esp. since it seems to be more a disagreement of semantics. As for the main page, I suggest "Many metal-containing compounds consist of coordination complexes" instead of the previous "virtually all..." Is that more acceptable, or are there some "virtually all" diehards out there that have strong objections? El Zarco 03:59, 6 November 2011 (UTC)
I am fine with "many", but Smokefoot has previously disagreed on this point, and recently about potassium. Dirac66 (talk) 12:11, 6 November 2011 (UTC)
Oh, I am fine with the decisions. Best wishes to all, --Smokefoot (talk) 12:59, 6 November 2011 (UTC)

Clarity of intro[edit]

In chemistry, a coordination complex or metal complex, is an atom or ion (usually metallic), bound to a surrounding array of molecules or anions...

On first reading, it sounds like the coordination complex is just that atom or ion, rather than the whole thing - which I'm fairly sure is wrong. --Chriswaterguy talk 02:29, 20 September 2012 (UTC)

Yes, it is the metal plus the ligands. I have reworded this sentence and included the word and. I think it is clearer now. Dirac66 (talk) 03:06, 20 September 2012 (UTC)

Shouldn't the article be called transition metal coordination complex?[edit]

The whole article currently is about transition metal complexes with short asides referring to other metals. This leads to a very misleading picture, particularly for lanthanide and actinide complexes. For example the electronic properties section is actually transition metal specific, but it reads as if it isn't. Lanthanides for example with tightly bound f orbitals are described reasonably well using LS coupling scheme unlike the spin only behavior of t metals. They are only subject to small crystal field effects - their pale colors, due to forbidden f-f transitions are virtually independant of the ligand. The magnetism section is similarly one sided. IMHO either new sections on lanthanides, early actininides and main group metals need adding with an appropriate rewrite of the whole article to remove the current "bias", OR we rename it. Axiosaurus (talk) 09:37, 18 November 2013 (UTC)

Well, I think that the most useful approach is to consider the readers, not to try to satisfy us specialists. Readers who want to know about "coordination complexes" are likely to most benefit from a single article on the topic. We should add a paragraph or two on the f-elements. Their weak colors could be mentioned in the context of Mn(II) and Fe(III). You will notice that most textbooks allocate modest space to the lanthanides and actinides, and my sense is that our allocation of emphasis might be similar. --Smokefoot (talk) 13:30, 18 November 2013 (UTC)
I have added a short section on lanthanide colors and tweaked the article where I have spotted generic references to complexes which are specific to transition metals. I have left the magnetochemistry section as is, it is generic enough on reflection. Axiosaurus (talk) 17:46, 19 November 2013 (UTC)

Assessment comment[edit]

The comment(s) below were originally left at Talk:Coordination complex/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Last edited at 15:16, 14 October 2009 (UTC).

Substituted at 12:15, 29 April 2016 (UTC)

  1. ^ Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd Ed., W. H. Freeman Company, 1980, NY. ISBN: 0-7167-1088-9; more recent editions are probably available, and Kittel introduces students to solid state physics in other publications, such as the aptly titled Introduction to Solid State Physics.
  2. ^ See for example P. A. Cox,The Electronic Structure and Chemistry of Solids, Oxford University Press, 1987, Oxford. ISBN-10: 0198552041, ISBN-13: 978-0198552048
  3. ^ See for example, Neil W. Ashcroft, N. David Mermin, Solid State Physics, 1st Ed., Brooks Cole, 1976, ISBN-10: 0030839939, ISBN-13: 978-0030839931.