Well no, I never did during my crystallography training: it seems to be a change of definition that's occurred fairly recently, without recognition of the fact that the original definition is still in use, particularly in mineralogy of course, where, unlike often is the case with protein crystals, you can usually see the crystal faces with the naked eye! I'm thinking particularly of this site that Bernhard recently pointed out:
http://news.nationalgeographic.com/news/bigphotos/82948445.html I remember the time when we did actually measure the faces of a crystal (small molecule, not protein) and determine their Miller indices, in order to calculate the absorption correction (no doubt Shel-X still allows you to do it that way!). So it would have been a little confusing to call Miller indices and reflection/Laue indices by the same name! Cheers -- Ian On Thu, Oct 21, 2010 at 8:28 PM, Jacob Keller <j-kell...@fsm.northwestern.edu> wrote: > I like your more-accurate definition, but practically speaking, doesn't > everyone call hkl Miller indices? > > Jacob > > ----- Original Message ----- From: "Ian Tickle" <ianj...@gmail.com> > To: <CCP4BB@JISCMAIL.AC.UK> > Sent: Thursday, October 21, 2010 2:00 PM > Subject: Re: [ccp4bb] Regarding space group P1, P21 > > > Hi Clemens, > > Sorry to be picky and start the 'definition game' over again, but > 'Miller indices' are strictly not the numbers that index X-ray > reflections that everyone is familiar with (whether observed or not!). > Miller indices were introduced in 1839 by the British mineralogist > William Hallowes Miller (it says in WIkipedia) as a way of describing > the direction of the perpendicular to the plane faces that he observed > on mineral crystals. A condition is that no common denominator is > possible, since it defines only the direction of a vector; its > magnitude has no relevance in this context. So you can have Miller > indices (1,0,0), (1,2,0), (1,2,3) etc but you can't have (2,0,0), > (3,0,0), {2,4,0), (3,6,9) etc., or at least (1,0,0) means exactly the > same thing as (2,0,0) etc. You can multiply the MiIler index vector > by -1: this indicates the opposite face of the crystal. Imagine what > an electron density map would look like if you only collected > intensities at the Miller indices! > > Miller's observation of the plane faces of mineral crystals occurred > 73 years before the discovery in 1912 of X-ray diffraction by Max Laue > in Munich (he became Max von Laue in 1913 when his father was raised > to the nobility), for which Laue received the Nobel Prize in Physics > in 1914. Laue explained diffraction by means of the 'Laue equations' > which contain 3 integers corresponding exactly to the indices we are > all familiar with. I prefer to call them 'reflection indices', though > strictly I suppose we should be calling them 'Laue indices'. Almost > immediately after Laue's discovery, William Lawrence Bragg in > Cambridge devised what we now know as "Bragg's Law", wherein the > factor 'n' relates the Miller indices to the Laue indices; thus the > reflection with indices (nh,nk,nl) is the n'th order of diffraction > from the set of crystal planes with Miller indices (h,k,l). Bragg > also received the physics Nobel prize jointly with his father William > Henry Bragg in the following year, 1915, for their determination of > the crystal structures of NaCl, ZnS and diamond. > > Cheers > > -- Ian > > On Thu, Oct 21, 2010 at 4:57 PM, Clemens Vonrhein > <vonrh...@globalphasing.com> wrote: >> >> Hi Herman, >> >> On Thu, Oct 21, 2010 at 05:31:51PM +0200, >> herman.schreu...@sanofi-aventis.com wrote: >>> >>> If you process your data in a lower symmetry space group, you will have >>> more unique reflections, since reflections which are related by the >>> higher symmetry will be avaraged during scaling in a higher symmetry >>> space group (i.e. a 2fold or 3fold axis), while in lower symmetry space >>> groups they will not. So the observation to parameter ratio stays the >>> same and is only depending on resolution and solvent content. >> >> True - if you count Miller indices as observations. But if you think >> about information content than probably not (as you discuss below). >> >>> The question one has to ask of course is: are these reflections really >>> different, or are they the same only not averaged? >> >> Yes - by merging we're getting better data (better error estimate on >> the intensity due to higher multiplicity). So there isn't really >> independent information in 50% of the reflections if e.g. going from >> P21 to P1 - we've only increased the noise because the multiplicity of >> each reflection has been reduced. >> >>> In the latter case, you have more reflections, but not more >>> information. As Ed mentions, using tight "NCS" restraints would in >>> this case mimick the crystallographic symmetry. >> >> Apart from the (good) NCS argument, one could go even further: >> >> We could also just collect 36000 degree of data on a 7A Lysozyme >> crystal and refine against completely unmerged data. After all, why >> should we stop at removing only the some symmetry operators from our >> data merging ... lets get rid of all of them including th x,y,z >> operator and use unmerged data. Then we could refine Lysozyme with >> anisotropic hydrogens and no restraints against 7A data since we have >> a huge number of 'observations' ... right? >> >> But seriously: there is a difference in having reflections (H, K, L) >> and independent data (I, SIGI). Maybe we should talk more about >> (independent observations)/parameters ratio in the same way we >> look at depdencies of parameters (e.g. restraints on Bfactors etc). >> >> Cheers >> >> Clemens >> >> -- >> >> *************************************************************** >> * Clemens Vonrhein, Ph.D. vonrhein AT GlobalPhasing DOT com >> * >> * Global Phasing Ltd. >> * Sheraton House, Castle Park >> * Cambridge CB3 0AX, UK >> *-------------------------------------------------------------- >> * BUSTER Development Group (http://www.globalphasing.com) >> *************************************************************** >> > > > ******************************************* > Jacob Pearson Keller > Northwestern University > Medical Scientist Training Program > Dallos Laboratory > F. Searle 1-240 > 2240 Campus Drive > Evanston IL 60208 > lab: 847.491.2438 > cel: 773.608.9185 > email: j-kell...@northwestern.edu > ******************************************* > >
