
 ô"All parts CGA2.1 29 Nov89 ô last mod 16.3.90 ô + ô Authors K.M.Crennell L.S.Dent Glasser" ô program subject to copyright( î … å t`O * ÞX(2,7),q%(8),c%(131)+ :, ë1:òINTRO:òINIT¥4 ñ'I$;"Do you want to start at the beginning(B)or jump to the revision examples (R)    for this module?   Press B or R ";N$;:òg("BbRr"):ç A$="R" „ A$="r" Œ å d\@< òS1: ç A$<>" "å T|@F òS5: ç A$<>" "å DF@P òS7: ç A$<>" "å DF@Z òS14:ç A$<>" "å DP@d òS17:ç A$<>" "å DZ@n òS22:ç A$<>" "å Dd@x òS25:ç A$<>" "å Dn@‚ òS32:ç A$<>" "å Dx@Œ òS34:ç A$<>" "å tB@– òS36:ç A$<>" "å tL@  òS39:ç A$<>" "å tV@ª òS43:ç A$<>" "å t`@´ òS50:ç A$<>" "å tj@¾ òS52:ç A$<>" "å tt@È òS53:ç A$<>" "å t~@Ò òS54:ç A$<>" "å dH@Ü òIntroræ òS59:ç A$<>" "å df@®ð òtxt:Û:ñ''I$"Cubic closest pack-ing"+N$+" is also looked  at in the other    three programs on this    disc "'I$;"Atomic Packing and Crystal Structures"N$'''"   THE  END"ú òSb×"MENU":,ÝòINTRO:D%=30ô"PROCintro4ô*FX11,08ô turn off AUTO REPEAT9TY$=" Type your answer"<*FX212,200@*FX214,3Dô"REDUCE BELLaFI$=½17+½131+½17+½0:N$=½17+½128+½17+½3:No$=I$+½7+"No"+N$:û131:Û:û1:ñŠ10,2)" PC (CGA) Version "&HñŠ10,6)I$;"ATOMIC PACKING   &    "$LñŠ8,8)"CRYSTAL STRUCTURES 2.1  "FPñŠ10,12)"Interstitial Sites "Š5,14)"in Closest-packed Structures " Tû1:ñŠ12,18)"Copyright  1990"1XñŠ2,20)"L.S.Dent Glasser   &    K.M.Crennell"\òSb:û128:Û:û3 ´`ñ''"Program 1 considered the close-packing of equal spheres.  Only the structures  of single element solids such as the    noble gases or metals can be described  in this way."idñ''"Most crystals are built from more than  one kind of atom, and these atoms are ofdifferent sizes."³hñ''"  This program looks at some structures derived from closest-packing by filling the ";:û2:ñ"interstitial sites ";:û3:ñ"in an array of   closest packed atoms, and explores"qlñ"further the differences between         hexagonal and cubic closest packing.          ( HCP and CCP )":û128	pòSb:áq:
ÝòINIT"‘H%=0:P%=1:ô flagS for PROCD,&R’A%=48:ô"RADIUS OF SPHERE"”SX%=4*¨(A%/¶(48)+0.5):SY%=A%+4.–U%=248:V%=440:ô"LOCATION OF CENTRAL SPHERE"˜ã I%= 0 ¸ 15:óX%:c%(I%)=4*X%:íAšã I%=16 ¸ 70 ˆ 2:óX%,Y%:c%(I%)=X%*SX%+U%:c%(I%+1)=Y%*SY%+V%:íœã I%= 0 ¸ 8:q%(I%)=I%:í( ô"Define characters for superscripts¢ï23,255,8,8,62,8,8,0,0,0¤ï23,254,24,36,8,16,60,0,0,0¦ï23,253,0,0,0,24,36,8,16,60¨ï23,252,24,36,8,36,24,0,0,0©E%=0:F%=0	ªS%=72¬ã I%=18 ¸ 26
®÷ dpAG°ã J%=1 ¸ 3:óX,Y:c%(S%)=4*¨(X*I%)+U%:c%(S%+1)=4*¨(Y*I%)+V%:S%=S%+2:í²í I%P´÷ dpA:ã J%=1 ¸ 3:óX,Y:c%(S%)=4*¨(-X*26)+U%:c%(S%+1)=4*¨(-Y*26)+V%:S%=S%+2:í¶á·:5ºô LOOKUP TABLE FOR FOLLOWING TRANSLATIONS OF DATA¼ô index to c%¾ô 470 0Àô 472 6Âô 474 10Äô 478 16Æô 480 22Èô 482 28Êô 484 40Ìô 488 52Îô 490 54Ðô 492 66Òô 496 72Ôô"8 RANDOM SPHERES SC1ÖÜ30,40, 110,100, 130,160ØÜ 80,180, 40,110ÚÜ 20,160, 60,80,  140,40Üô"  1ST LAYERÞÜ 2,0, -1,-1, -1,1àÜ -4,0, 2,2, 2,-2)âÜ -4,2, -4,-2, 5,-1, 5,1, -1,-3, -1,3'äÜ 5,-3, 2,-4, -7,-1, -7,1, 2,4, 5,3æô" 2ND LAYER	èÜ 0,0&êÜ 3,-1, 0,-2, -3,-1, -3,1, 0,2,3,1ìÜ 6,0, -3,-3, -3,3 îô"Scene 14  LOCATIONS 72-131"ðÜ -1,0, 0.5,0.866,  0.5,-0.866ñ:XÝòS1>bòtxt:Ú:ñŠ0,5)"Atoms and ions"'"vary greatly in"'"size.":ï5JlA%=80:òdrn(0,0,2,4,3):A%=36:òdrn(6,0,2,4,2):A%=16:òdrn(10,0,2,4,3):òSbyvï4:ñ'"The relatively"'"large ones, such ascaesium or chlorideions, have radii ofalmost 2 Angstrom  units. (0.2nm)":ï5-€A%=96:òdrn(0,0,1,4,3):òSb:òdrn(0,0,2,4,3)gŠñ'"Some, such as oxideor fluoride ions,  are intermediate insize at just over  an Angstrom (0.1nm)"-”A%=48:òdrn(6,0,1,4,2):òSb:òdrn(6,0,2,4,2)ažñ'"And some, such as  Mg";½254;½255;" or Al";½252;½255;" are"'"tiny, less than an Angstrom."':¨A%=24:òdrn(10,0,1,4,3):òSb:òdrn(10,0,2,4,3):ï20:òSpr:á©:¼ÝòS5xÆï26,12:òtxt:ñ''"Many crystal"'"structures can be  described as a     closest-packed     array of one type  of atom,"tÐòdrn(16,0,0,3,18):òSb:A%=16:òdrn(52,0,1,4,-10):ñ'"with smaller ones  tucked into the    spaces between them":òSb}ÚA%=48:òdrn(16,0,2,4,-12):A%=16:òdrn(16,0,1,4,6):ñ'"The layers of big  atoms are shaded   differently for    clarity.":òSb<îñ'"Let us look more   closely at these   spaces.":òSpr:áï: ÝòS7J*ï26:Û:òtxt:ñ''"Here is a close-"'"packed layer.":òdrn(16,0,2,4,18):òSbŽ4ñ'"The next layer fitson top like this."':òdrn(52,0,0,7,-10):òSb:ñ"Only half the"'"hollows have"'"spheres on top; theothers have not.":òSb€>ñ'"Thus there are two"''"sorts of holes, or"''I$;"interstitial sites,";N$'"between the layers.":òSb:A%=12:òdrn(16,3,1,8,-12)eHñ"One sort- these -  are above the gaps in the bottom layerand below the gaps in the top one":òSbµRñ'"The other sort are above the atoms of the lower layer -":òdrn(16,3,1,8,-12):òdrn(16,3,3,8,18):òSb:ñ"or below those of  the upper layer."':òdrn(16,3,3,8,18):òdrn(52,3,1,8,-10)1\òSpr:A%=12:òdrn(52,3,1,8,-10):Û:çA$="R"å T~C°fï20:ñ'"Suppose the larger spheres are oxide  ions. Smaller ions - say Mg";½254;½255;" - fit   into the first typeof interstitial    site.":A%=20:òdrn(16,0,1,4,-1):A%=48:òSb…pñ'"How many oxide ionstouch the Mg? ";:ç ¤rt=6 ñ'"Yes";:åDxC ‹ñNo$", count again ";:ç ¤rt=6 ñ'"Yes";:åDxC ‹ñ'No$", there are 6"
xòSpr:áy:	„ÝòS14½Žï26:Û:òtxt:ñ''"The 6 oxide ions   are arranged aroundthe central Mg likethis."''"Repeated pressing  of SPACEBAR moves  the ions apart so  that you  can see  the structure more clearly."¬ã S%=72 ¸ 120 ˆ 6	®*FX19¬²A%=48:òdrn(52,0,0,8,1):A%=52:òdrn(S%,0,0,8,-3):A%=48:òdrn(S%,0,2,8,-2):òdrn(S%+4,0,2,4,-1):A%=24:òdrn(52,0,1,4,1):A%=52:òdrn(S%,0,0,8,3):A%=48:òdrn(S%,0,2,4,3):òSb:í   E¶ñ'"The ions lie at theapices of a regularpolyhedron.":ï5:òOCT:òSb¼*FX202,40e¾ñ'"What is it?"'"__________";:ï8,8,8,8,8,8,8,8,8,8:I%=¤rt:çÀA$,3)="OCT" „ ÀA$,3)="oct" Œ ñ'"Yes" gÀñ'"It is an "'I$"octahedron"N$'"we say the Mg is"'I$"  octahedrally  "'"  coordinated   "N$':òSpr:áÁ:	èÝòS17pòï26:Û:òtxt:ñ'"The Mg occupies"''"OCTAHEDRAL SITES"''"between two close-"'"packed layers of"'"oxide ions.":ï5Lüòdrn(16,0,2,4,18):A%=16:òdrn(16,0,1,4,-12):A%=48:òdrn(52,0,0,3,-10):òSb &ñ'"Now add a third"'"oxide layer."E%=72:òdrn(16,0,3,7,6):òSb*FX202,40–ñ'"Are the oxide ions HEXAGONAL or CUBIC close-packed?"'I$"(HCP or CCP)"N$;:I%=¤rt:ç A$=À"CCP",©(A$)) „ A$=À"ccp",©(A$)) € A$<>""ñ'"Yes"; ‹ ñ'No$;‘$ñ'"the oxide ions are CUBIC close-packed.":òSb:ñ"More Mg ions can"'"be fitted between"'"these top layers."'"Where do you think they go?"'"1";¢.E%=0:A%=16:ï5:ãL%=1¸5:òdrn(16,0,3,8,3):òP(2):òdrn(16,0,0,-207,3):òP(2):í:òSb:ñ;" or 2";:ï5:ã L%=1 ¸ 5:òdrn(16,0,3,8,-3):òP(2):òdrn(16,0,0,-206,-3):òP(2):í:òSb/ñ;" or 3":ï5}8ã L%=1 ¸ 5:òdrn(52,0,3,8,7):òP(2):òdrn(52,0,0,-205,7):òP(2):í:ï4:ñ"Which? ";:ç ¤rt=1 ñ'"Yes "; ‹ñ'No$" they are at 1.  ";:òSbRBñ"Thus...":òdrn(52,0,0,8,7):òdrn(16,0,0,8,-3):A%=16:òdrn(16,0,1,4,6):A%=48:òSb—Lï4:ñ'" How many Mg ions  touch each oxide"'"ion? ";:ç¤rt=6ñ"Yes"' ‹ñNo$", count again "':ç ¤rt<>6 ñNo$", 6 Mg ions toucheach oxide ion."' ‹ñ'"Yes"'
`òSpr:áa:	°ÝòS22Pºï26:Û:òtxt:ñ''"Look at these smallions surrounding a large oxide ion.":S%=72eÈA%=120:òdrn(52,0,0,8,1):A%=24:òdrn(S%,0,1,4,-3):A%=64:òdrn(52,0,2,4,1):A%=24:òdrn(S%,0,1,4,3):òSbgÎñ'"Which polyhedron dothey form? ";:I%=¤rt:W$=ÀA$,3):çW$="oct" „ W$="OCT" „ W$="Oct"ñ'"Yes" ‹ ñ'No$1Øñ'"It is an "I$"octahedron";:òOCT:òSb:û128:û3Žâï26,12:òtxt:ñ''"In the extended"'"array, 6 Mg ions   touch 6 oxides, and6 oxides touch eachMg."''"What is the formulaof the compound?   ";MãA%=48:òdrn(16,0,2,4,18):A%=16:òdrn(16,0,1,4,-12):A%=48:òdrn(52,0,0,3,-10)aèI%=¤rt:ç A$="MGO" „ A$="mgo" „ A$="MgO" „ A$="mGO" „ A$="mGo" ñ'"Yes" ‹ñ'No$", it is MgO":òSbXìòdrn(16,0,2,4,18):A%=16:òdrn(16,0,1,4,-3):òdrn(22,0,3,4,-9):A%=48:òdrn(52,0,0,3,-10)Çöñ'"In the extended"'"array, there are   equal numbers of   each kind of ion."'"Each is surrounded by an octahedron   formed by the otherkind.":òSb:ñ"For example, 6 Mg  ions surround each oxide."'! A%=16:òdrn(16,0,1,4,3):òSpr:á:	ÝòS25eï26,12:òtxt:ñ'"MgO is based on    cubic close packing -like this":F%=160:òA:òP(6):òB:òP(6):òC:òSbX(ñŠ0,20);"HEXAGONAL close    packing is"'"different":F%=-240:òA:òP(2):òB:òP(2):òA:òSb€2ï26,24,0;400;1279;799;16,26:òtxt:ñ''"When we fit atoms  into the octahedralsite in CCP, the   layers build up"'"like this." :<E%=120:F%=160:òA:òSb:òc:òP(9):òB:òP(6):òa:òP(9):òC:òSb×Fï26,24,0;400;1279;799;16,26:òtxt:ñ'"The layers of"'"interstitial atoms are staggered."''"Call them  a,b,c tocorrespond with theA,B,C of the large ones."''"Now press the"'"SPACEBAR to build  up the layers again" ¬Pï5:òA:ì0,460:ï65:òSb:ï5:òc:ì0,508:ñ"c over":òSb:òB:ï5:ì0,556:ñ"B over":òSb:ï5:òa:ì0,604:ñ"a over":òSb:ï5:òC:ì0,652:ñ"C over":òSpr:E%=120:F%=160:çA$="R" „ A$="r" Œ åDFEvdñŠ0,10);"The arrangement is still CUBIC.                          Watch what happens with the HCP array          "7nï26,24,0;0;1279;400;:Ú:òtxt:ñŠ0,18)" ":F%=-240:òSb ’xï4:ñ'"Here the small"'"atoms lie one abovethe other."':òA:òP(6):òc:òP(9):òB:òP(6):òc:òP(9):òA:ï4:ñ"Press the SPACEBAR to rebuild the HCP.":òSb›‚ï26,24,0;0;600;400;:Ú:òtxt:ï5:òA:ì0,90:ï65:òSb:ï5:òc:ì0,138:ñ"c over":òSb:ï5:òB:ì0,186:ñ"B over":òSb:ï5:òc:ì0,234:ñ"c over":òSb:ï5:òA:ì 0,282:ñ"A over"0ŒòSpr:E%=80:F%=-240:ç A$="R" „ A$="r" Œ åtBEÍ–ï26,4,28,21,24,39,10,12:ñ'''"In HCP the small   atoms are not      staggered."''"They form straight lines through the  structure."''"Because of this,   they are closer    together than in   CCP."':òSb R ñ"In HCP how many    small atoms touch  each large one? ";:ç¤rt=6ñ"Yes"':åt~Eªñ'No$", watch while we count them.";:ï24,0;0;600;400;16:òSb:òA:òP(2):òc:ï4:ñ'"3 little atoms":òSb:òB:ñ"touch the middle"'"large atom":òSb:òc*´ñ"which touches"'"3 more little atoms"
¾òSpr:á¿:ÒÝòS32:W%=3rÜï26:Û:òtxt:ñ''"There are three    small atoms just   below each large   atom, and three    just above.":ï5:òSb)æF%=160:òA:òc:òP(3):òB:òP(3):òc:òSb:ï4¡ðñ'"It is easier to seethe shape of the   group if we view itfrom different"'"angles."'':òIN(64):F%=-240:òD(20,60):ñI$+" Use the cursor    keys to rotate it."(úñ''N$+"Press RETURN to    continue";
*FX4,1Uõ:G%=¥:çG%=136òR(15,2) ‹ ç G%=137òR(-15,2) ‹ ç G%=138òR(-15,1) ‹ ç G%=139òR(15,1)6çG%>135 € G%<140 A%=120:òdrn(52,0,0,8,1):òD(20,60)"ý G%=13:*FX4,0”,A%=120:òdrn(52,0,0,8,1):E%=-160:òIN(64):òR(15,3):òR(70,1):òD(20,60):E%=160:òTRG:òD(20,0):ñŠ0,23)"Do the small"'"atoms form an"'"octahedron? Y/N"=6òg("YyNn"):ñ;A$:ç A$="N" „ A$="n" Œ ñ"Yes, "; ‹ ñNo$", ";C@ñ;"it is not an"'"octahedron. It is a"+I$+"trigonal prism."+N$'
JòSpr:áK:^ÝòS34:W%=3»hï26:Û:òtxt:ñ'''"So in HCP the smallatoms touch an"'I$+"octahedron"+N$+" of six  large ones.":F%=156:òdrn(126,0,1,4,2):òdrn(130,0,1,4,1):A%=24:òdrn(52,0,2,4,1):A%=52:òdrn(126,0,0,4,-3)yrA%=48:òdrn(126,0,1,4,-3):òOCT:òSb:ï4:ñŠ0,18)"But the large atomstouch a"'I$+"trigonal prism"'N$+"of six small ones." :|F%=-240:òIN(108):òR(15,3):òR(70,1):òD(24,60):òTRG:òSprá‘:šÝòS36:W%=3§¤ï26:Û:òtxt:ñ'"This arrangement isless symmetrical   than the cubic one."':òSb:ñ"Now we look roughlyalong the close-   packed planes to   see another"'"difference."®F%=160:E%=-160:P%=1:òIN(84):òR(60,6):òR(75,3):òR(70,1):òD(20,60):ï5:ì80,740:ñ"CCP       HCP":E%=160:òIN(84):òR(15,3):òR(70,1):òD(20,60):òSb™¸ñ''"Because the ions   in the trigonal    prism (of CCP) lie above one another, they are closer."''"Press the SPACEBAR to turn one into   the other."?Âï5:F%=-240:E%=216:òIN(128):òR(127,3):òR(70,1):òD(20,0):òTRGQÌE%=-96:ãM%=60¸0ˆ-10:ï24,0;60;300;500;:òIN(128):òR(M%,6):òR(127-M%,3):òR(70,1)ÖÚ:òD(20,0)@àòD(20,0):çE%=192òTRG:òOG:E%=-160:ï24,0;100;320;500;:òD(20,0)êòTRG:ç M%>30òOG	ôòSb:ícþï4:ñŠ0,25);I$;"To repeat press R  or SPACE continues";N$:A$=¾:çA$="R"Ú:ï28,21,31,39,25:Û:å dLFô PROCSpr	á
:ÐÝòS39:W%=3ÙÚï26:Û:òtxt:ñ'"Structures based onHCP occur if the   interstitial atoms attract one anotherfavouring the"'I$+"trigonal prism."+N$'"Atoms which repel  one another favour CCP because then   they are further   apart."‰äF%=192:E%=-120:òIN(108):òR(60,6):òR(-15,3):òR(80,1):òTRG:òOG:E%=160:òIN(108):òR(45,3):òR(80,1):òTRG:òSb:ï5:ì150,764:ñ"O         P":ï4îñ'"Try this experiment"'"Choose either an"'I$+"O"+N$+"ctahedron or a"'"Trigonal "I$+"P"+N$+"rism,"'"Press O or P ";:òg("OPop"):ñ;A$:C$=A$tøA%=32:ã F%=0 ¸ -120 ˆ -120:ã E%=-120+F%/40 ¸ 200-F%/40ˆ320-F%/20:òdrn(52,0,2,4,1):í:ìU%-88,V%+F%:ßU%+168,V%+F%:íUï5:ì40,V%+12:ñ"A";:æ0,1:ñ"   > > < <":æ0,3:ì40,V%-108:ñ"R";:æ0,1:ñ"   < < > >":ï4*FX202,40lñ'"A atoms "I$"A"N$"ttract"'"R atoms "I$"R"N$"epel"'"Which is likely to favour your"'"polyhedron? A/R ";» òg("ARar"):ñ;A$:ç (C$="O" „ C$="o") € (A$="R" „ A$="r") Œ ñ"Yes. R atoms repel,increase distance." ‹ ç (C$="P" „ C$="p") € (A$="A" „ A$="a") Œ ñ"Yes A atoms attractdecrease distance."‰*ç (C$="P" „ C$="p") € (A$="R" „ A$="r") Œ ñNo$". R atoms repel.." ‹ ç (C$="O" „ C$="o") € (A$="A" „ A$="a") Œ ñNo$" A atoms attract."k4ñI$+"Press R to repeat  the question, or   SPACEBAR continues"+N$:òg("R "):ñ':ç A$="R" „ A$="r" Œ ådnGÒ>ñ''"In ionic solids,   the small ions havethe same sign, and repel one another."''"What sort of"'"packing should thisfavour- CCP or HCP? ":I%=¤rt:çÀ"CCP",©(A$))=A$ „ À"ccp",©(A$))=A$ € A$<>""ñ"Yes"; ‹ ñNo$;¯Hñ" it is CCP":òSb:ñ'"HCP structures withatoms in octahedralsites are rare. An example is NiAs"'"where the Ni atoms are thought to"'"attract through"'"Ni-Ni "I$"covalent"N$+Rñ"or "I$;"semi-metallic";N$'"bonding."'\ï20:òSpr:á]:˜ÝòS43:F%=144:E%=-80{¢ï26:Û:òtxt:ñ'"At the beginning ofthis module, we sawthat there are"+I$+" two "+N$+"types of inter-    stitial sites."''½¬òdrn(16,0,1,4,12):òdrn(52,0,3,7,-7):òSb:ñ'"The "+I$+"octahedral"+N$'"sites are above thegaps in the lower  layer, and below   the gaps in the"'"upper layer.":A%=12:òdrn(16,3,2,8,-6):òSba¶òdrn(16,3,2,8,-6):òdrn(16,3,3,4,6):ñ'"Some other sites   lie above atoms of the lower layer."…Àñ'"How many large"'"atoms surround thistype of site? ";:ç¤rt=4ñ'"Yes" ‹ñ'No$", count again ";:ç¤rt=4ñ'"Yes" ‹ñ'No$", there are 4"“Êòdrn(16,3,3,8,6):òdrn(52,0,2,8,-7):E%=0:ñ'"The remaining siteslie below atoms of the upper layer.   How many large"'"atoms surround"'"these? ";QÔç ¤rt=4 ñ'"Yes" ‹ñ'No$", count again ";:ç ¤rt=4 ñ'"Yes" ‹ñ'No$", there are 4"OÞñ'"Atoms in these"'"sites touch a "'I$"tetrahedron"N$" of fourlarge atoms."kàE%=48:F%=-180:W%=4:òIN(112):òR(-35,1):òR(45,2):òTT(0,3):òSb:ñ'"A tetrahedron is   related to a cube."''eèòCU(7,1):òD(20,0):òSb:ñ"Try rotating this  using the cursor   keys."''"To continue, press RETURN"
ò*FX4,1MüG%=¥:çG%=136òR(9,2) ‹ çG%=137òR(-9,2) ‹ çG%=138 òR(-9,1) ‹ çG%=139òR(9,1)J	A%=176:òdrn(52,0,0,8,1):çG%=13åTPI ‹òCU(7,1):òTT(0,3)::òD(20,0):åd|H
	*FX4,0y	Û:ï4:ñ'"Suppose the large  spheres are oxide  ions. Small ions,  such as Li, can"'"fit into the"'"tetrahedral sites."O$	A%=48:E%=40:òdrn(16,0,1,4,-12):òdrn(52,0,3,7,7):A%=12:òdrn(16,0,2,8,-6):òSbW.	ñ'"To see how these   are arranged, buildup a cubic array   using the SPACEBAR":òSb°8	E%=520:A%=48:òA:ï26,5:ì1100,128:ñ"A":A%=20:òSb:ï5:òdrn(52,0,2,4,1):ì1100,160:ñ"b over":ì0,80:ñ"Tetrahedral site 1":òSb:ï5:òdrn(16,0,2,4,3):ì1036,160:ñ"a,":ì576,80:ñ"-2-3-4"pB	òSb:ï5:A%=48:òB:ì1100,192:ñ"B over":òSb:ï5:A%=20:òdrn(16,0,2,4,-3):ì1100,224:ñ"c over":ì768,80:ñ"-5-6-7":òSb^L	ï5:òdrn(52,0,2,4,1):ì1036,224:ñ"b,":ì960,80:ñ"-8":òSb:ï5:A%=48:òC:ì1100,256:ñ"C over":òSb -V	òSpr:ç A$="R" ï24,640;0;1279;620;:Ú:åTxIt	áu	:	Ä	ÝòS50ÄÎ	ï26:Û:òtxt:ñ'"Here is the cubic  array of oxide ionswith small Li ions in the tetrahedral sites.":F%=160:òdrn(16,0,0,3,6):òdrn(52,0,0,3,7):òa:A%=20:òdrn(52,0,2,4,1):A%=48:òdrn(16,0,0,3,-6):òSbØ	*FX202,48«â	ñ'"If there is a Li   ion in every"'"tetrahedral site,  each oxide ion"'"touches 8 Li, and  each Li touches 4  oxides."''"What is the formulaof this compound? ":I%=¤rtBì	ç A$="Li2O" „ A$="LI2O" „ A$="li2o" „ A$="lI2O"ñ'"Yes" ‹ ñ'No$ö	*FX202,40„ 
ñ"It is Li";:ï253:ñ"O"''"The 8 Li form a    cube around the    oxide.":òSb:F%=-240:E%=-80:òdrn(16,0,0,3,6):æ0,3:ï5:ì450,128:ñ"A"s

A%=20:òdrn(52,0,2,4,1):ì450,160:ñ"b over":òSb:ï5:òa:ì386,160:ñ"a,":òSb:W%=4:òIN(64):òR(135,3):òR(55,2):òCU(1,1)¹
ñ"Here is the"'"bottom corner of   the cube...":òSb:A%=48:òdrn(52,0,0,3,7):ñ"(now obscured by   the next layer)":ï5:æ0,3:ì450,192:ñ"B over":òSb:ï5:òc:ì450,224:ñ"c over":òSb:òCU(2,1)’
ñ"the next six"'"corners...":òSb:A%=20:òdrn(52,0,2,4,1):ï5:ì386,224:ñ"b,":ï4:ñ"and the last"'"corner.":òCU(4,1):òSb:A%=48:ï5:òdrn(16,0,0,3,-6)T(
æ0,3:ì450,256:ñ"C over":òSb:ñ"Now we redraw it   without the large  oxides.":òSb¾2
E%=-120:F%=-180:ï24,0;0;639;360;:Ú:A%=20:òdrn(52,0,2,4,1):òP(3):òdrn(16,0,2,4,3):òP(3):òCU(1,1):òdrn(52,0,2,4,1):òdrn(16,0,2,4,3):òP(3):òdrn(16,0,2,4,-3):òCU(3,1):òD(20,0):òP(3):òCU(7,1)'<
òD(20,0):òSb:E%=120:F%=-248:òT(1,0)
F
òSpr:áG
:	Œ
ÝòS52æ–
ï26:Û:òtxt:ñ''"If instead of Li";½255;", we put Be";½254;½255;" into   these sites, only  half of them are   filled, making BeO."''"(The charges would not balance if all sites were filled.)"'"First redraw the   LiO structure."£ 
òSb:ï26:E%=160:F%=140:òdrn(16,0,0,3,12):ï5:ì0,468:æ0,3:ñ"A":òSb:òb:ï26,5:ì64,500:ñ"b":òSb:A%=20:òdrn(16,0,2,4,12):ï26,5:ì0,500:ñ"a,":òSb:A%=48:òdrn(52,0,1,4,7)¢
ï26,5:ì0,532:æ0,3:ñ"B" Šª
òSb:òc:òb:ï5:ì0,564:ñ"b,c":òSb:òdrn(16,0,0,3,-3):ï5:ì0,596:æ0,3:ñ"C":òSb:A%=20:òdrn(16,0,2,4,-3):òdrn(16,0,2,4,3):ï5:ì0,628:ñ"c,a":òSb²
òtxt±´
ñŠ0,16)"Now the BeO"'"structure below":F%=-184:E%=-32:A%=48:òdrn(16,0,0,3,12):ï26,5:æ0,3:ì0,108:ñ"A":òSb:A%=20:òdrn(16,0,2,4,12):ï26,5:ì0,140:ñ"a":òSb:A%=48:òdrn(52,0,1,4,7)¶
ï26,5:ì0,172:æ0,3:ñ"B"„¾
òSb:òb:ï26,5:ì0,204:ñ"b":òSb:òdrn(16,0,0,3,-3):ï26,5:ì0,236:æ0,3:ñ"C":òSb:A%=20:òdrn(16,0,2,4,-3):ï26,5:ì0,268:ñ"c":òSb:ï26:òtxtRÈ
ñŠ0,19)"Make sure you can  see the differencesbetween these two  structures."'
Ò
òSpr:áÓ
:ð
ÝòS53:W%=4‡ú
ï26:Û:òtxt:ñ''"Each oxide is"'"surrounded by a"'"tetrahedron of Be."''"Now rebuild the"'"structure to see"'"this more clearly.":òSb™F%=160:òdrn(16,0,0,3,6):A%=20:òdrn(52,0,2,4,1):òSb:òdrn(16,0,1,7,3):ñ'"Outline circles    mark vacant sites.":òIN(64):òR(135,3):òR(55,2):òCU(1,1):òSb°A%=48:òdrn(52,0,0,3,7):òSb:òCU(2,1):òc:òSb:A%=20:òdrn(52,3,1,0,1):òCU(4,1):òSb:ñŠ0,10)"Here is the Be     arrangement again, with vacant sites  shown in different shades."'”E%=0:F%=-200:H%=1:òT(3,1):H%=0:ñ'"The filled sites   form a tetrahedron"':A%=144:òdrn(52,0,0,8,1):òD(20,-4):òCU(7,3):òTT(0,3):E%=E%+280:òTT(0,3)
"òSpr:á#:	TÝòS54©^ï26:Û:òtxt:ñ''''"In "+I$+" Hexagonal ClosePacking"+N$+" tetrahedralsites, like octa-  hedral ones, are   closer together."''"Use the SPACEBAR tobuild up the layers"'¥hï5:F%=120:E%=144:òA:ì64,400:ñ"A":A%=20:òSb:òdrn(52,0,2,4,1):ï26,5:ì64,432:ñ"b over":ì0,760:ñ"Tetrahedral site 1":òSb:òa:ï26,5:ì0,432:ñ"a,":ì576,760:ñ"-2-3-4":òSbˆrA%=48:òB:ï26,5:ì64,464:ñ"B over":òSb:A%=20:òdrn(16,0,2,4,1):ï26,5:ì64,496:ñ"a over":ì768,760:ñ"-5":òSb:òa:ï26,5:ì832,760:ñ"-6-7":òSbj|A%=20:òdrn(52,0,2,4,1):ï26,5:ì0,496:ñ"b,":ì960,760:ñ"-8":òSb:A%=48:ï26,5:ì64,528:ñ"A over":òA:òSb:òtxtà†ñŠ0,15)"Now this is redrawnwithout the big"'"spheres."''"Rotate it until yousee it as 2 inter- locking tetrahedra.":F%=-240:E%=0:H%=1:òT(-1,1):ñ''''''"Filling all these  sites is difficult,there are no known examples."''DA%=160:ñ"Filling half the"'"sites in an orderedway is possible."¹šòdrn(52,0,0,8,1):òTT(0,2):òD(20,-4):òSb:ñ'"Press R to re-draw the other"'"tetrahedron or"'"SPACE to continue"':A$=¾:çA$="R"„A$="r"A%=160:òdrn(52,0,0,8,1):òCU(3,-1):òD(20,4):òSb:H%=0R¤ï24,0;320;1279;799;16:ñŠ0,7)"ZnO is an example."''"Use SPACEBAR to"'"draw it."§®ï5:F%=120:E%=120:A%=48:òdrn(16,0,1,3,12):A%=20:òdrn(16,0,2,4,12):ì0,500:ñ"A":ì0,532:ñ"a over":òSb:A%=48:òB:ï26,5:ì0,564:ñ"B over":òSb:òb:ï26,5:ì0,596:ñ"b over":òSb4¸òdrn(16,0,1,3,12):ï26,5:ì0,628:ñ"A over":òSpr:á ¹:ÝòIntror:ï26,12!&ñŠ8,4)" STRUCTURE  REVISION "Â0ñ''Š7)"Now try making some of"'Š7)"your own structures."''''"You choose either ";:û129:ñ" hexagonal or cubic ";:û128:ñ''"closest packing for the large atoms, and":û130:û0:ñ "octahedral or ";>2ñ"tetrahedral";:û3:û128:ñ" sites for"''"the small ones."''S:ñ"Pressing the 'R' key at the at the end  of a question gets another one":òSb:á;:	€ÝòS59—Šï26:Û:F$=" ":òtxt:ñ''"Do you want the bigatoms, call them X,arranged HCP or CCP? ";:I%=¤rt:P$=ÀA$,1):ç P$<>"H" € P$<>"h" € P$<>"C" € P$<>"c" å tJLÕ”ñ'"If the small atoms are called M, whichtype of site do youwant them to fill?"'"(O for octahedral   T for tetrahedral)";:I%=¤rt:S$=ÀA$,1):çS$<>"O" € S$<>"o" € S$<>"T" € S$<>"t" åtTL ‹ ç S$="O" „ S$="o" åthLTžñ'"Do you want half orall of the sites   filled? H or A ";:òg("AHah"):F$=A$:ñA$;!¨òSb:òtxt:Û:ï5:L%=V%+F%-512:òA<²ç (P$="C" „ P$="c") € (S$="O" „ S$="o") òc:òB:òa:òC:P%=1<¼ç (P$="H" „ P$="h") € (S$="O" „ S$="o") òc:òB:òc:òA:P%=4VÆç (P$="C" „ P$="c") € (S$="T" „ S$="t") € (F$="A" „ F$="a") òb:òa:òB:òc:òb:òC:P%=2PÐç (P$="C" „ P$="c") € (S$="T" „ S$="t") € (F$="H" „ F$="h") òa:òB:òb:òC:P%=3VÚç (P$="H" „ P$="h") € (S$="T" „ S$="t") € (F$="A" „ F$="a") òb:òa:òB:òa:òb:òA:P%=5Päç (P$="H" „ P$="h") € (S$="T" „ S$="t") € (F$="H" „ F$="h") òb:òB:òa:òA:P%=6!îN%=0:ï4:ã I%=1 ¸ 6:q%(I%)=1:í4øõ:Q%=³(6):ý q%(Q%)=1:q%(Q%)=0:N%=N%+1:å(3320+Q%)*ùñ'"Is the formula MX  or M2X? ":å DHM*úñ'"How many X round   each M? ":å DHM*ûñ'"How many M round   each X? ":å DHM]üñ'"What sort of"'"polyhedron do the  large X atoms form around the small M ones? ":å T~M]ýñ'"What sort of"'"polyhedron do the  small M atoms form around the large X ones? ":å T~Meþñ'"Give an example of a compound (quoted in this module)    with this type of  structure.":å DHMƒ>ñI$;"C";N$;"ube,"'I$;"O";N$;"ctahedron,"'I$;"T";N$"etrahedron,"'"trigonal";I$"P";N$"rism, "'I$"N"N$"one of these?"'" C/O/T/P/N"Hç Q%<>6 å DfMR*FX202,48
\å DpMf*FX202,40
pI%=¤rtz*FX202,40„ç Q%=6 å drM
Ž÷ d@M(˜ç Q%>1 ã I%=2 ¸ Q%:ã J%=1 ¸ 6:óS$:í,¢ã I%=1 ¸ P%:óS$:í7¬ç ÀA$,©(S$))=S$ ñ'"Yes" ‹ ñ'No$'"The answer is ";S$
¶å D~NÀÜ MX,M2X,MX,MX,M2X,MXÊÜ 6,4,4,6,4,4ÔÜ 6,8,4,6,8,4ÞÜ O,T,T,O,T,TèÜ O,C,T,P,N,Tòô "ANSWERS TO QUESTION 6üç P%>1 å TZN@ç A$="MGO" „ A$="LIF" „ A$="NACL" „ A$="CAO" ñ'"Yes" ‹ ñ'No$5ñ'"MgO, LiF, NaCl, CaOhave this structure":å D~N:ç P%>2 å TnN ‹ ç A$="LI2O" „ A$="NA2O"ñ'"Yes" ‹ ñ'No$5$ñ'"Li2O, Na2O both    have this structure":å D~ND.ç P%>3 å DBN ‹ ç A$="BEO" „ A$="ZNS" „ A$="SIC" ñ'"Yes" ‹ ñ'No$B8ñ'"BeO and one form ofZnS and SiC have   this structure":åD~NLBç P%>4 å DVN ‹ ç A$="NIAS" ñ'"Yes" ‹ ñ'No$", NiAs has this  structure."
Lå D~N;Vç P%>5 å DjN ‹ ç A$="NONE" „ A$="none" ñ'"Yes" ‹ ñ'No$>`ñ"There are no known examples of this   structure.":å D~N4jç A$="ZNO" „ A$="ZNS" „ A$="SIC" ñ'"Yes" ‹ ñ'No$;tñ"ZnO  and one form  of ZnS and SiC havethis structure"~ç N%<3 å dxLAˆòSb:ï5:ô MOVE0,100:PRINTI$"More?"N$"Press R"':PROCSpr:ENDPROC
‰òSpr:áŠ:% ç Ÿ=17 ×"MENU" ‹ ö:ñ" AT LINE ";ž¡à¢: NÝòA:òdrn(16,0,1,3,6):á!N:&*NÝòa:A%=20:òdrn(16,0,2,4,3):A%=48:á+N:4NÝòB:òdrn(52,0,1,3,7):á5N:&>NÝòb:A%=20:òdrn(52,0,2,4,7):A%=48:á?N:HNÝòC:òdrn(16,0,1,3,-6):áIN:'RNÝòc:A%=20:òdrn(16,0,2,4,-3):A%=48:áSN:„NÝòCU(X%,K%)ŽNçK%<0 òTT(0,2):òTT(1,1):á˜Næ0,K%:ï29,U%+E%;V%+F%;U¢NçX%€ 1 ìX(0,1),X(1,1):ßX(0,0),X(1,0):ßX(0,5),X(1,5):ìX(0,0),X(1,0):ßX(0,3),X(1,3)q¬NçX%€2ìX(0,3),X(1,3):ßX(0,4),X(1,4):ßX(0,5),X(1,5):ßX(0,6),X(1,6):ßX(0,1),X(1,1):ßX(0,2),X(1,2):ßX(0,3),X(1,3)S¶NçX%€4ìX(0,6),X(1,6):ßX(0,7),X(1,7):ßX(0,2),X(1,2):ìX(0,7),X(1,7):ßX(0,4),X(1,4)ÀNï29,0;0;:áÁN:¡èNÝòD(a%,c%):ô"PLOT spheres radius a% at corners of cell in X(2,N%) in colour AND SIZE given by c% =0 all yellow =1 only odd in red  <0 only even >1 is a radii!òNN%=2*W%-1:st%=1:ç c%=-4 st%=2nüNA%=a%:g%=0:t%=4:ãI%=0¸N%ˆst%:çX(2,I%)<0 X%=U%+E%+¤I4(X(0,I%)):Y%=V%+F%+¤I4(X(1,I%)):k%=2-(H%€I%):æ0,k%:òd2Oí0Oçc%=60 æ0,1:k%=1:A%=c%:X%=U%+E%:Y%=V%+F%:òd2eOA%=a%:ãI%=0¸N%ˆst%:çX(2,I%)>=0 X%=U%+E%+¤I4(X(0,I%)):Y%=V%+F%+¤I4(X(1,I%)):k%=2-(H%€I%):æ0,k%:òd2$Oí:á%O:!LOÝòdrn(r%,g%,k%,t%,n%):çt%<0ï5VOæg%,k%:Z%=r%:ãJ%=1¸”(n%)C`Oçn%>0 Œ X%=c%(Z%):Y%=c%(Z%+1) ‹ X%=2*U%-c%(Z%):Y%=2*V%-c%(Z%+1)jOX%=X%+E%:Y%=Y%+F%*tOç t%<0 Œ ìX%-12,Y%+16:ñ½(256+t%) ‹ òd2~OZ%=Z%+2:í:çt%<0ï4ˆOá‰O::’OÝòd2:ô t%=3 outlines sphere, 4=sphere, 7=circle 8=diskœOìX%,Y%:o%=153:ç t%=7 o%=145¦Oðo%,A%-2,0:çt%>6á(°OìX%-A%2,Y%+A%2:æ0,3:ð153,.175*A%,0 ºOçt%<>4 ìX%,Y%:æ0,3:ð145,A%,0ÄOæg%,k%:áÅO:âOÝòg(a$):*FX15,1ìOõi%=¥:çi%>96i%=i%-32öOA$=½i%:ý§a$,A$):á÷O:sPÝòHEX(R%,N%):æ0,3:M%=c%(R%)+E%:K%=c%(R%+1)+F%:ìM%,K%:Q%=R%:ãL%=2¸N%:ßc%(Q%+2)+E%,c%(Q%+3)+F%:Q%=Q%+2:í:ßM%,K%:áP:3(PÝòIN(s%):ô read co-ords and scale by s%(pixels)2PçW%=3÷@PP ‹ ÷@ZP+<PãI%=0¸W%-1:J%=I%+W%:çW%=4 J%=4+(I%+1)ƒ4hFPóU,V:X(0,I%)=U*s%:X(0,J%)=X(0,I%):X(1,I%)=V*s%:X(1,J%)=X(1,I%):X(2,I%)=.5774*s%:X(2,J%)=-X(2,I%):í:áGP:+PPÜ-0.8165,0,0.4082,0.7071,0.4082,-0.7071;ZPÜ-.5774,.5774, .5774,.5774, .5774,-.5774, -.5774,-.5774[P:nPÝ¤I4(x):=(x 4)*4oP:‘xPÝòOCT:òHEX(120,3):ï29,E%;F%;:ßc%(128),c%(129):ßc%(124),c%(125):ßc%(126),c%(127):ßc%(122),c%(123):ßc%(130),c%(131):ßc%(120),c%(121):ï29,0;0;:áyP:ŒPÝòOG:æ0,3:ï29,U%+E%;V%+F%;]–PìX(0,0),X(1,0):ßX(0,4),X(1,4):ìX(0,1),X(1,1):ßX(0,5),X(1,5):ìX(0,2),X(1,2):ßX(0,3),X(1,3) Pï29,0;0;:á¡P:ªPÝòP(T%):I%=¦(T%*10):á«P:.¾PÝòR(A,X%):ô"ROTATE A degrees ABOUT AXIS X%bÈPS=µ(²(A)):C=›(²(A)):Y%=X%ƒ3:Z%=(Y%+1)ƒ3:N%=2*W%-1:st%=1:çX%>3N%=W%-1:ç P%<0 st%=2:ï7:N%=2*W%-1[ÒPã I%=0 ¸ N% ˆ st%:U=X(Y%,I%)*C+X(Z%,I%)*S:X(Z%,I%)=X(Z%,I%)*C-X(Y%,I%)*S:X(Y%,I%)=U:í:áÓP:‚ÜPÝ¤rt:ï5,24,0;0;576;40;:æ0,128+D%:D%=5-D%:æ0,0:Ú:ì0,32:ñTY$;:ï4:A$="":õ:òCHIN:ý —(G$)=13:æ0,128:Ú:ï24,0;0;1278;799;:æ0,3:=»(A$)ÝP:
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