Topics in.
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Edited by GALEN W . EWING, Seton Hall University, So. Orange, N. J. 0 7 0 7 9
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hese articles, most of which are to be contdmted by guest authws, are intended to serve the readers of this JOURNAL by calling attation lo new developments i n the t h w , design, OT availability of chemisal labomtoly instrumentation, or by presenting useful insights and i planations of topics that are of practical im&rtance to those who use, w teach the use of,-modem instrumentation and inslrumenlal techniques.
XXXk X-Ray Diffraction Analysis Part Five-Single
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ccontinuec~,*
Crystal Methods
REUBEN RUDMAN, Department of Chemistry Brookhaven National Laboratory, Upton, N.Y. 7 7 9 7 3 SINGLE-CRYSTAL TECHNIQUES' Single-cryshl techniques are used for orienting crystals, obtaining unit cell dimensions and space group information, and for the collection of intensity data suitable for crystal structure analysis; they are too complex to he used for routine identification problems. The experimental data usually consist of several hundred to several thousand independent reflection intensities. The arrangement of scatterem (i.e., atoms) in a given crystal is responsible for the observed intensities; it is tho crystdographer's job to start from these intensities and to detelmine the atomic amaneement,. Most crystals used in X-ray diffractio~i investigations have a number of disloca, tions and consist of mosaic blocks tilted a t small angles (of the order of 3') to each other. (The techniques used for investigating the degree of perfection of a crystal and for measuring the number of dislocations present will not be discussed.) In order to properly understand the basis of single-c~ystalmethods, use must be made of the "Reciprocal Lattice" concept. The reciprocal lattice is a representation of the crystal in which each family of parallel planes with indices, hkl, and interplanar spacing, d, is represented by a single point Located a t the end of s. vector whose magnitude is a reciprocal function of the interplanar ~~
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angle thela eorrcsponds t,o the rot,ation of the crystal through the same angle. When the reeiproca.-lattice point lies on the sphere of reflection, the Bragg conditions are fnlfillcd and theta is the Bragg angle. Thus., bv " examinine t,he orientation of the reciprocal lattice about its origin, one can determine which family of planes is irl diffractingpasition. From this diagram we can also see that the mazimun~ d* value is 2; i.e., the mznimum d value is X/2. (The same inform,,,,, O, co,,e, is obtained directly from the Braee Law for 0 = go".) I n order to increase the number of observable reflections, one must go to shorter wavelengths.
Mounting of Single-Crystal Specimens
spacing ( k / d , where k is usunlly h or 1) and whoso dit.eet.ion is determined by the ~ m m a lto the planes from the nnit cell origin. The origin nf the ~ . e e i p n dlattice is plated ILL the intersection of t,he direct hcam with thc surface of an imaginary ;iphcre (of radius equal to 1 when d y = hid) which s n ~ m x ~ n dthe s crystal. This sphere is called tho "Sphere of Itefleetion." Whenever a recipmcal-lattice point lies on the surface of thesphere of reflection the family of planes represented by that reeiprocal-lattice point is in reflecting position. Figure 75 shows that the ~.ots, tion of the recipnd-lat,tice point through
.4side from the large crystals which are nligned u i n g back-reflection Laue techniqnes, single cryst.als used in X-ray diffraction investigations are generally no larger than 0.4 mm in crasssection. During these investigations (and this is particularly true when counter methods are employed) the crystal must be held firmly in the desired orientation. For (his reason mounting adhesives and goniometer heads (devices for orienting and eeutering the specimen) are of primary imoortance. Mounting -4dhesiues. A discussion of specimen preparation and mounting is (Continued on page d4W)
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*Prepared under the auspices of the Atomic Energy Commission. ' T h e List of hlanufaeturers is in the first installment, THIS JOURNAL, 44, A42 (1967). Price Range: A = under $10; B = $10-50; C = $5&100; D = $100-300; E = 5500-1000; F = 51000-3000; G = 53000-7000; H = $7000-12,000; I = $12,000-25,000; J = above $25,000.
RECl PROCAL LATTICE
RECIPROCAL LATTICE
Figure 75. W h e n a ref of parollel planer of interplonor spacing d is in reflecting position the reciprocal lottice point representing there planes i 9 lacoted on the svrfoce of the sphere of reflection.
Volume 44, Number 5, May 7 967
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A399
Chemical Instrumentation fo~lndit) Itel. (I&), pp. 21-34. Included in this dis,:~~ssion is a table in which the pvopwl,iea of a number of adhesives are disctrssnl. Ncw adhesives have hecome nvnilnlde i l l recent years and one of these, lhslmul~l 010 Adhesive (distributed hy A~.msft.rmgCork Co.), has been used quite s~teerssf~~lly in a inmber of laboratories. Goniomrlw Ilmds. Commerrially availahlc goniometn. heads u s r d l y eontsin two nws ( p e r p e ~ d c d n rto each ntber) and two trm-.lat.iom (perpendicular to each ~llhcra d pnrallel to the ares). A numher uf models ilw also equipped with an elevator (~tp-dowl ur 2-translation). These devisrs sho~llrl be equipped with ACAtlrren,la (1.7) so as to be interchangeable lretweel~val.iot~sgoniometem. The goniomriel. heads sllonld be designed so as not. to weep or slide once the cr,ystd ha.? been arlimt,ed. Ovemized gears, dovetails, and spl.iug-loading have been used in attempts t,o irnprovr tireslability of theseobjeets. Thwe are t,wo common classes oi goniomelel. heads: s t a n d a d and eucentric. Stanrlavd gwiometer heads are generally apptmirnat,cly 65 mm in height from the base lo the lop of the mounted specimen. The a w s are mounted ahave the transls, lions; most models have no elevator. Euaentria goniometer heads have a fixed common inter;ect,ion of the principal axis and the veu1el.s of both arcs and provide I,r:~~~sl:lli,ms w d elevation only ahove the
goniomeier heads which are availahle. The Stoe eucent,rie gnniomet,er head has arcs that e m be xljusled up to &15' rather than the 1 2 5 ' that are spxilxble on most other models, wilh a corresponding reduction of the mne of o b struction to thediRracted b e a m . Stoe RISO m m u f a ~ t , ~ r eas micro goniometer head (GI1 l l ) , whirh can he adjusted to 1 2 0 " , t,he t.ranslation movements being zt2.5 mm. This head oan he used wil,h Stoe and Siemens Eulerim cradles. (Their stmdnni goniometer hcad (GH 12) can be adjurtod to 1 3 0 ° , the translational movements beine 1 2 0 mm.) All Stoe goniometer heads are in price Range D.
Figure 79.
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Stntdnld got~imneterheads are avail:thle from S ~ p p e r(Cat. No G20F, 818.5) (over 5000 are i n we, Fig. 76), Nonizrs, Jawel& Ash (Cat. N o 80-024 $185, Fig. 77), Sloe m d Philips (Cat. No. 52319). Sloe ~ W I I I I I ' R C ~ ~ ~ I 'an ' ? ~ eueentric ganiomelw lwnd ((:IT 13) with a center 6'3.96 mm atwve the base and a &translation. This is nppl.oaimately the same height a3 the al.x~c
