Baker-Lesson-2

# Baker-Lesson-2 - l ® thwmm 1 ‘ [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ﬁgltk 6...

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Unformatted text preview: l ® thwmm- 1 .. .. . , ‘ L7 @JchLEﬁgltk 6% M10466“ 9." _ 1 ea w M : Mm Man“ «WU Mme, 6‘ app/Mu [owhwf’ va0*«$__ . 7 g . .. 7 *9 “Clam? EWLW M»: WWW/1A7 Maid“ was , WW a4 WWW M, QMWM " .. 5"? 9§W$LCMQL$,th .9??? = . . v (Wﬁkfééwry [W M: m in ,chéw I —,,--:i~,,.:::i__._:‘ :__ __:_:__:,.::..; -_._______ ._. _, W , a ,, e W. _ _. ‘ q . ___._W.K. ":33". ML m Mm ..W_w:_mﬁ}gg__arédalgm“qmjpimai. . _s_~_0r'2fM _ . . . _ .!_______.+V;UHAmde-MWJJQMMJ ( MELM) I , f - T} Hie f Xitj. H ' _ MW EM aa.._....d~x/xw ,6 é W _ 0:0? Eaﬁkytjﬂﬂaﬁmmﬁmﬁﬂegw[’QLZMEﬂHwWw : Z; :23:iﬁ:§é&§é§ﬁ£ﬁ£ﬁiﬁ,:_:m _AW(@;LE@~£%M$¢7.%;2M$0L1B ®ﬂ¥wo.ggw_‘gmw,&7_ ML MMﬂ; MW““meﬁ93:-..§aﬂ._[<L.e<yL_;S%y..£AW.w-_.._..WWM__u __WW_ MWMW—kw - r wakinmw~W~ﬂmmmnm “WW—h C93 " W: dicrcamN/u‘uﬁng M W UGFWJ W (try. Carr (acawrmﬁr'M-Jy w“ " . ‘ *9 A— MEAN—st CM- jut/'17! swam—$7 , My war/1L9 ‘ _ _ _ ‘ Ch. 1, §3 .e IUPAC 1988, the columns are ssed in this chapter are shadowed. Hanna nber of atoms in the unit cell lumber of atoms in the corre- uld be three times as much. mbol. )3 red ttered ie-face centered ral (b) Fig. 9. Histograms of distances and coordination polyhedra of (a) hexagonal and (b) cubic closest packing (from Dams er al. [1991]). 3.2. Group 1 and 2, alkali and alkaline earth metals The alkali and alkaline earth metals (table 5) belong to the typical metals. The outer electrons occupy the _ns-orbitals, ionization removes the electrons of a whole shell, thus drastically reducing the atomic radius (Li: atomic radius 156 A, ionic radius 0.60 A, for instance). The absence of directional bonds forces close atomic (sphere) packings; the alkali metals conform most closely to the free electron gas model of metals. Under ambient conditions the alkali metals all crystallize in the simple body-centered cubic Choc) structure cIZ—W (ﬁg. 12). The bcc structure is assumed to be more stable at higher temperature than the cop or hop one owing to its higher vibrational entropy. At lower temperature or higher pressure. the bee structure is transformed martensitically to the closest-packed lattice types, hRS—Sm or cF4—Cu, respectively. Contrary to earlier studies, the hexagonal closest—packed phases are not of the hP2—Mg but of the hRB—Sm type (ﬁg. 10) with stacking sequence ...ABABCBCAC.. (YOUNG [1991]). The extremely strong dependence of the atomic volume on pressure, which increases with increasing atomic number due to the shielding of the outer electrons by the References: )7. 45. 16 F W. Steurer (d) Ch. 1, §3‘ Fig‘ 10. Schematical representation of the stacking sequences of the closest-packed structures (a) hP2—Mg, (b) cF4—Cn, (c) hP4—La and (d) hR3—Sm. Ch. 1, §3 Structure information ﬁrst line of each box conditions is listed. In is tabulated: limiting t1 T[K] P[GP:L Li 3 Var=2l.6( 151251 a <70 3 7 >63 Na 11 Vm=39.5( 15227132196135i a <40 :3 K 19 Vm=75.33 152252p6352p5451 CE ,3 >12 Rh 37 Vm=92.59 152252p5351p5dw4szp55 a ,8 >10 7 > 14 5 > 17 .9 > 20 Cs 55 Vm=117.7‘ 153232p6353pﬁdw453p5d a! B > 2.37 [3' >422 7 >427 'o‘ > 10 a > 72 Fr 8'? 132253p63 szp‘sd 1°4slp6d M increasing number ‘ increasing pressure large number of pre: 237 GP Chi-CS <2} Cll- 1. §3 Ch, 11 § 3 Crystal SH‘HL‘t‘HJ't' oj’thz' nwt‘alh‘c elements 17 Table 5 Structure information for the elements of group 1, alkali metals, and of group 2, alkaline earth metals. In the ﬁrst line of each box the chemical symbol, atomic number Z, and the atomic volume Vm under ambient conditions is listed. in the second line the electronic ground state conﬁguration is given. For each phBSE there is tabulated: limiting temperature TEK] and pressure PIGPa]. Pearson symbol PS. prototype structure PT, and. if applicable. the lattice parameter ratio c/a. T[l(] PEGPa] PS PT cla THC] P[GPa] PS PT Li 3 val =21.so A} Be 4 Val: 3.11113 1s2251 1522512 cc < 70 hR3 Srn a' 11132 Mg 1.568 ,8 e12 w a >1543 cl'l w 7. >63 cF4 Cu 3! >233 11P8? 0.739 Na 11 \rm=39.50ﬁta Mg 12 vm=2324£13 szlszrn"3s1 1 152252136352 .1 <40 I1R3 sm (1 _ . hPZ Mg 1.624 .8 on W 13 >50 c12 w K 19 Vm=75.33,3_3 Ca 20 Vm=43.62.5x.a 15225213635211‘5451 _ 152252336352116452 Ct' 1:12 W 0.‘ CM Cu 5 >12 eF4 Cu [3 > 728 or > 19.5 (:12 w 1.! >32 cPl ct-Po Rb 37 vm=9259 A3 Sr 38 v =56.35 A3 '1 -1 ' a m lsZQS”p635'p"d 1045116531 1522s2p5352pﬁdm452p65 s2 o: (:12 W a c114 Cu 13 >7.0 cF4 Cu ,3 > 504 11P2 Mg 1.636 31 > i4 7 > 396 or > 3.5 (:12 W 5 >17 5 >26 .5- > 20 t14 a > 35 Ba 55' V1263.36A3 Ll tszzszpﬁsszpﬁd‘ﬂttszpmmsﬁaéesﬂ Cs 55 $5117.79? 152252p6332p6d104sﬂpﬁd1055296651 at 1:12 W o' (:12 W ,3 >237 cF4 Cu ,3 >533 hP2 Mg 1.531 5' >422 , cF4 Cu 1' >75 7 >427 n4 5 >115 5 >10 .5- >72 eF4? Fr 37 R3 88 szss.22il3 1$2252 a3szpsdm452 admin-1552 admészpaht 15225') 5352 6.310432 sd1of14552ped10652 6751 P P P “P P P P 51' CIZ W increasing number of inner electron shells, is shown by the example of Cs (ﬁg. 13). With increasing pressure, the valence electrons change from s to d character, giving rise to a large number of pressure-induced phase transitions at ambient temperature (YOUNG [1991]): mmmcms (ﬁlm-Mam 2.3? GPa 4.22 GPa 4.27 GPa 10 GPa 72 GPa a-Cs <2: B-Cs <=> B’rCs <:>, y—Cs <:> 5-Cs <=> a-Cs References: [2. 45. 18 W: Steurer Ch. 1, §3 Fig. 11. Relationship between body—centered cubic (bcc) a-Fe, c12—W type, space group Im3_m, No. 229, 1a: 0 O 0, and face-centered cubic (fcc) y—Fe, cF4—Cu type, space group Fmgm, No. 225, 4a: 0 O O. The face- centered tetragonal unit cell drawn into an array of four bcc unit cells transforms by shrinking its faces to fee. The alkaline earth metals behave quite similarly to the alkali metals. They crystallize under ambient conditions in one of the two closest—packed structures (ccp or hcp) or in the body—centered cubic Cbcc) structure type and also show several allotropic forms (ﬁg. 14). The large deviation cla=1;56 from the ideal value of 1.633 for beryllium indicates covalent bonding contributions. For alkali and alkaline earth metals, the pressure—induced phase transitions from ch—W to cF4—Cu occur with increasing atomic number at decreasing pressures. 3.3. Groups 3 to 10, transition metals The elements of groups 3 to 10 are typical metals which have in common that their d—orbitals are partially occupied. These orbitals are only slightly screened by the outer s-electrons, leading to signiﬁcantly different chemical properties of the transition eiements going from- left to right in the periodic system. The atomic volumes deerease rapidly with increasing number of electrons in bonding d—orbitals, because of cohesion, and increase as the anti—bonding d—orbitals become ﬁlled (fig. 15). The anomalous behavior of the 3d—transition metals, Mn, Fe and Co, may be explained by the existence of non-bonding d-electrons (PEARSON [1972]). Scandium, yttrium, lanthanum and actiniurn (table 6) are expected to behave quite Fig. 12. Unit cell of the body-centered cubic structure type ch—«W, space group im'E‘rn, No. 229, 1a: 0 0 0. Ch. 1, {$3 120 100 ATOMIC VOLUME, R3 03 O .60 0 LC Fig. 13. The variation of l similarly. Indeed the elements occur as the of lanthanum, with th structures common ft lanthanides is the hRI and ﬁg. 10). Titanium, zirconi‘ structure type and tra phase is obtained (ﬁ; slightly larger than th than for bcc (~0.68) c the w-Ti phase is st transfer. At even higl while titanium rema considerations it is a1: high pressures (AHUJ Hf is shown in ﬁg. 1 Vanadium, niobil Ch. 3, §3 race group knit-n, No. 229, in: No. 225, 4a: 0 0 0. The face- ns by shrinking its faces to ice. metals. They crystallize tctures (cop or hcp) or in eral allotropic forms (ﬁg.$3 for beryllium indicates d phase transitions from :reasing pressures. ave in common that their ntly screened by the outer perties of the transition atomic volumes decrease tals, because of cohesion, :ﬁg. 15). The anomalous ixplained by the existence expected to behave quite mp Inﬁm, No. 229, 1a: 0 U 0. '5 ATO Mic VOLUME, A Ch. 1, §3 Crystal structure of the metallic elements 19 120 100 OJ O ’50 o to 2.0 so 4.0 so masseuse, GPa Fig. 13. The variation of The atomic volume of cesium with pressure (after DDNOHUE [1974]). similarly. Indeed they show similar phase sequences: the high-pressure phases of light elements occur as the ambient-pressure phases of the heavy homologous. The hP4 phase of lanthanum, with the sequence ..ACAB.., is one of the simpler closest-packed polytypic structures common for the lanthanides (ﬁg. 16 and ﬁg. 10). Another typical polytype for ianthanides is the hRS phase of yttrium with stacking sequence ..ABABCBCAC.. (ﬁg. 17 and ﬁg. 10). Titanium, zirconium and hafnium (table 6) crystallize in a slightly compressed hcp structure type and transform to bcc at higher temperatures. At higher pressures the m-Ti phase is obtained (fig. 18). The packing density'of the hP3—Ti structure with ~0.57 is slightly larger than that of the simple cubic (tr—PO structure (-0.52) but substantially lower than for bcc (~O.68) or cup and hop (-0.74) type structures. Calculations have shown that the w—Ti phase is stable owing to covalent bonding contributions from s—d electron transfer. At even higher pressures. zirconium and hafnium transform to the ch—W type, while titanium remains in the hp3~Ti phase up to at least 87 GPa. By theoretical considerations it is also expected that titanium performs this transformation at sufﬁciently high pressures (AHUJA er a1. [1993]). A general theoretical phase diagram for Ti, Zr and Hf is shown in ﬁg. 19. Vanadium, niobium, tantalum, molybdenum and tungsten have only simple bcc References: 19. 45. 20 W. Stcurer Ch. 1, §3 (b) ‘ Fig. 14. Illustration of the bcc-to-hcp phase transition of Ba. (a) bee unit cell with (110) plane marked. (b) Projection of the bee structure upon the (110) plane. Atomic displacements necessary for the transformation are indicated by arrows. structures (table 7). Up to pressures of 170 to 364 GPa no further allotropes could be found, in agreement with theoretical calculations. Chromium shows two antiferro- magnetic phase transitions, which modify the structure only very slightly (YOUNG [1991]). The high—temperature phases of manganese (table 8), 'y—Mn, cF4—Cu type, and 6-Mn, cIZ—W type, are typical metal structures, whereas a—Mn and ,B—Mn form very compli— cated structures, possibly caused by their antiferromagnetism. Thus, the cr—Mn structure can be described as a 3 ><3><3 superstructure of bee unit cells, with 20 atoms slightly shifted and 4 atoms added resulting in 58 atoms over all (ﬁg. 20). The structure ofB—Mn (ﬁg. 21) is also governed by the valence electron concentration (“electron compound” or Hume—Rothery-type phase). The variation of the atomic volume of manganese with temperature is illustrated in ﬁg. 22. For technetium, rhenium, ruthenium and osmium, only simple hep structures are known. The technically most important element and the main constituent of the Earth’s core, iron (table 8) shows ﬁve allotropic forms (ﬁg. 23): ferromagnetic bcc vac-Fe transforms to paramagnetic isostructural B-Fe with a Curie temperature of 1043 K; at 1185 K fee y-Fe forms while at 1667 K a bee phase, now called 6—Fe, appears again. For the variation of Ch. 1, §3 Fig. 15. Atomic volumes (after PEARSON [1972]). the atomic volume existing above 13 G Cobalt (table 9) . tures. By annealing sequence ..ABAB.. ..ABABABABCBC1 Rhodium, iridium, n packed structures. 3.4. Groups 11 The “mint metal structure type (ﬁg. 2 than the as electron I contribute to the II Ch. 1, {\$3 . with (110) plane marked. (h) ssary for the transformaﬁon are rther allotropes could be 11 shows two antiferro— a very slightly (YOUNG cF4~Cu type, and d-Mn, B-Mn form very compli- Thus, the 01~Mn structure s, with 20 atoms slightly 1). The structure of ,B-Mn (“electron compound” or ume of manganese with ruthenium and osmium, ituent of the Earth‘s core, .ic bcc cu-Fe transforms to )43 K; at 1185 K fcc y—Fe [gain For the variation of C11. 1, § 3 CD‘SIGI Structure qfﬁre metallic elements 21 34 V 32 so - V as / I n 26 ,m/ I 24 V 22 20 ATOMIC VOLUME (33) IS 15 £4 ScTi V Cr Mn Fe Co Ni Cu Zn Go Ge Y -Zr NbMo Tc Ru Rh Pd Ag Cd In Sn Hf Tu W Re 05 Ir P1 Au Hng Fig. 15. Atomic volumes of the transition metals. a means cF4—‘Cn type, V hPE—Mg. O sill—W, 1:! other types (after PEARSON [1972]). the atomic volume with temperature see ﬁg. 24. High-pressure nonmagnetic e-Fe, existing above 13 G‘Pa, has a slightly compressed hcp structure. Cobalt (table 9) is dimorphons, hcp at ambient conditions and ccp at higher tempera- tures. By annealing it in a special way= stacking disorder can be generated: the hop sequence is statistically disturbed by a cop sequence ..ABCABC.. like ..ABABABABCBCBCBC.. with a frequency of about one ..ABC.. among ten ..AB... Rhodium, iridium, nickel, palladium and platinum all crystallize in simple cubic closest— packed structures. 3.4. Groups 11 and 12, copper and zinc group metals The “mint metals”, copper. silver and gold (table 10) are typical metals with cop s11'uctnre type (ﬁg. 25). Their single ns electron is less shielded by the ﬁlled d—orbitals than the ns electron of the alkali metals by the ﬁlled noble gas shell. The d-electrons also contribute to the metallic bond. These factors are responsible for the more noble Refemnces: p. 45. 22 W Srenrer Ch. 1, §3 Fig. 16. One unit cell of the hP4—La structure type, space group P63Immc, No. 194, 2a: 0 0 0, 2c: 1/: 2/3 ‘A. character of these metals than of the alkali'metals and that these elements sometimes are grouped to the transition elements. For zinc, cadmium and mercury (table 10) covalent bondng contributions (ﬁlled d- band) lead to deviations from hexagonal closest packing (hop), with its ideal axial ratio cla: 1.633, to values of 1.856 (Zn) and 1.886 (Cd), respectively. The bonds in the hop layers are shorter and stronger, consequently, than between the layers. With increasing pressure, c/a approximates the ideal value. 1.633: for Cd cla: 1.68 was obServed at 30 GPa (DONOHUE [1974]), and for Hg, cfa: 1.76 at 46.8 GPa (SCI-IULTE and HOLZAPFEL [1993]). The rhombohedral structure of cr-I-Ig may be derived from a cop structure by compression along the threefold axis (ﬁg. 26). In contrast to zinc and cadmium, the ratio dc: 1.457 for a hypothetical distorted hcp structure is smaller than the ideal value. There also exist several high-pressure allotropes (ﬁg. 27). 3.5. Groups 13 to 16, metallic and semi-metallic elements Only aluminum, thallium and lead crystallize in the closest-packed structures characteristic for typical metals (table 11). The s—d transfer effects, important for alkali- ' and alkaline—earth metals, do not appear for the heavier group 13 elements owing to their ﬁlled d—bands. Orthorhombic gallium forms a 63 network of distorted hexagons parallel to (100) at heights x=0 and 1/2 (ﬁg. 28). The bonds between the layers are considerably Ch. 1, §3 Fig. 17. One unit cell of Ch. ], §3 Ch I, §3 C’ijsml sn‘ucmm afﬂm metallic elements 23 .194, 221:0 O 0, 20: V: 2/3 ‘A. 5 elements sometimes are .g contributions (ﬁlled d— Wlﬂl its ideal axial ratio 131‘ The bonds in the licp e layers. \Vith increasing 1.68 was observed at 30 Emma and HOLZAPFEL tom a cop structure by u: and cadmium, the ratio nan the ideal value. There ts closest-packed structures 'ects, important for alkali- 3 elements owing to their istorted hexagons parallel 1e layers are considerably Fig. 17. One unit cell of the hRB—Sm structure type, space group Rim, No. 166, 3a: 0 0 0, 6e: 0 0 0.22. References: p. 45. ...
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## This note was uploaded on 12/05/2011 for the course MSE 4100 taught by Professor Hennig during the Fall '11 term at Cornell.

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Baker-Lesson-2 - l ® thwmm 1 ‘ [email protected]ﬁgltk 6...

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