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Unformatted text preview: ࡱ> uO"zRoot Entry FߡBbP@Data WDWordDocumentObjectPoolf?bb`@  !"#$%&'()*+,-./0123456789:;<=>?ABCDEFGHIJKLMNWlQRSTVXZx[^_cbdevgikmpnoqrstwzxy|{~}      !)123456789:;<=>?@ABCDEFGHIJKLMNOXYZ[\^Uth}jOlePres000(Ole10NativemOle10FmtProgID  1TableZJSummaryInformation(DocumentSummaryInformation8(CompObjX0Table0> [0@0NormalCJOJQJmH @`@ Heading 1$$h@&5CJ<`< Heading 2$h@&5CJ<A@<Default Paragraph Font, @,Footer  !,@,Header  !,>`,Title$ 56CJ<C`"<Body Text Indent $h1%  (I) Zn diffusion through Ir-Zn is the rate limiting step; (II) Zn diffusion through the growing ZnS film is the rate limiting step; and (III) the chemical reaction at the gas/film interface is the rate limiting step? By comparing the times that you estimated from (I), (II) and (III), determine which step is the actual rate limiting step?  Fig. 1 DATA: Atomic weights: Zn: 65.4 g mol-1 S: 32.1 g mol-1 Densities: ZnS: 4.09 g cm-3 Vapor Pressure:  EMBED "Equation" "Word Object1" \* mergeformat  in equilibrium with molten sulfur at 400C = 10-2 atm Diffusivities: DZn in Ir-Zn = 8x10-13 cm2 s-1 DZn in ZnS = 8x10-16 cm2 s-1 DIr and DS in ZnS are effectively zero. Composition and Solubilities: Composition of Ir-Zn alloy: 25 at %Zn (2.02 g Zn cm-3) Maximum solubility of Zn in ZnS = 7 at% = 0.192 g cm-3 Chemical Reaction Data: 1/2S2(gas) + Zn  EMBED "Equation" "Word Object3" \* mergeformat  ZnS (irreversible) At 400C dx/dt = k ( EMBED "Equation" "Word Object1" \* mergeformat )1/2 [Zn] dx/dt = rate of film growth, cm s-1 k = rate constant = 10-11 (cm s-1)(atm)-1/2(g cm-3)-1  EMBED "Equation" "Word Object1" \* mergeformat  = pressure of S2 gas, atm [Zn] = concentration of Zn in ZnS, g cm-3. 1. This is a transient, non-steady-state diffusion problem and we have to apply the Fick's second law,  EMBED "Equation" "Word Object1" \* mergeformat  (1) a) During predeposition the surface concentration of boron is maintained constant. Hence, to derive the concentration profile as a function of time, we set up the coordinate system as shown in Fig. 2 and assume the following initial and boundary conditions:  EMBED "Equation" "Word Object1" \* mergeformat   EMBED "Equation" "Word Object2" \* mergeformat  (2)  EMBED "Equation" "Word Object3" \* mergeformat   Fig. 1 (please note that the substrate is n-type, so the background concentration is the concentration of, e.g., phosphorus atoms, not the boron atoms). With surface concentration fixed and semi-infinite system, we may apply the error function solution  EMBED "Equation" "Word Object4" \* mergeformat  (3) Using the boundary condition (2) to determine the constants, A and B.  EMBED "Equation" "Word Object5" \* mergeformat   EMBED "Equation" "Word Object6" \* mergeformat  Therefore the concentration profile is given by  EMBED "Equation" "Word Object7" \* mergeformat  (4) At 950C,  EMBED "Equation" "Word Object8" \* mergeformat  Substituting the surface concentration, the time for predeposition, and the diffusion coefficient at 950C, the concentration profile is given by  EMBED "Equation" "Word Object9" \* mergeformat  The junction depth is found by setting the value of the boron concentration profile equal to the background value of phosphorous concentration, i.e.,  EMBED "Equation" "Word Object10" \* mergeformat  (5) where xj is the junction depth and t1 is the predeposition time. We may rewrite (5) as  EMBED "Equation" "Word Object11" \* mergeformat  (6) By using the error function table from Shewmon's book, we have  EMBED "Equation" "Word Object2" \* mergeformat  To find the total amount of dopant entering the substrate, one way to do it is to integrate the concentration profile from 0 to ". However, there is a much simpler way if we do not know how to integrate erfc() function, as we discussed in the class. First, we find the flux at x = 0, which, according to the Fick's first law, is simply  EMBED "Equation" "Word Object12" \* mergeformat  (7)  EMBED "Equation" "Word Object13" \* mergeformat  (8) Then, the total amount of dopant entering the substrate is given by  EMBED "Equation" "Word Object14" \* mergeformat  (9) b) During drive-in, we may assume the predeposited dopants form a very thin layer, so we can use the thin film solution,  EMBED "Equation" "Word Object15" \* mergeformat  (10) where W is the total amount of dopant given by (9). Substitute (9) into (10), we have,  EMBED "Equation" "Word Object16" \* mergeformat  (11) At 1050C, the diffusion coefficient is  EMBED "Equation" "Word Object8" \* mergeformat  Therefore, the profile at 60 min. is given by  EMBED "Equation" "Word Object17" \* mergeformat  (12) The junction depth is given by  EMBED "Equation" "Word Object18" \* mergeformat  (13) where t1 and t2 are the predeposition time and drive-in time, respectively, Cs is the surface concentration during the predeposition stage. Substituting the relevant values into (13), we get the junction depth after the drive-in stage:  EMBED "Equation" "Word Object3" \* mergeformat  ---------------------------------------------------------------------------------------------------------------------- 2. (I) Assuming Zn diffusion through Ir-Zn is the rate limiting step  Fig. 2  EMBED "Equation" "Word Object4" \* mergeformat  With surface concentration fixed and semi-infinite system, we may apply the error function solution for the concentration profile Zn in IrZn alloy,  EMBED "Equation" "Word Object4" \* mergeformat  (1) Using the boundary conditions to determine the constants, A and B.  EMBED "Equation" "Word Object5" \* mergeformat   EMBED "Equation" "Word Object6" \* mergeformat  Therefore the concentration profile of Zn in IrZn is given by  EMBED "Equation" "Word Object7" \* mergeformat  (2) Then, the flux at the IrZn/ZnS interface is given by  EMBED "Equation" "Word Object12" \* mergeformat  (3) Substituting (2) into (3), we have  EMBED "Equation" "Word Object13" \* mergeformat  (4) The amount of Zn diffuses through the IrZn/ZnS interface is given by  EMBED "Equation" "Word Object14" \* mergeformat  (5) The amount of Zn contained in a ZnS film of 10-6 cm thick is equal to  EMBED "Equation" "Word Object1" \* mergeformat  (6) where  EMBED "Equation" "Word Object16" \* mergeformat  is density of ZnS, MZn and MZnS are the molecular weight of Zn and ZnS, respectively. Equating (5) and (6), we get  EMBED "Equation" "Word Object2" \* mergeformat  Therefore,  EMBED "Equation" "Word Object3" \* mergeformat  = EMBED "Equation" "Word Object4" \* mergeformat  =1.81s (II) Assuming Zn diffusion across the ZnS film is the rate limiting step In this case, we can assume (quasi-) steady state diffusion of Zn through ZnS and the concentration profile is schemtically shown in Fig. 3. The maximum solubility of excess Zn in ZnS, [Zn]max, is 0.192g/cm3  Fig. 3 Assuming a steady state diffusion,  EMBED "Equation" "Word Object5" \* mergeformat   EMBED "Equation" "Word Object6" \* mergeformat  (6) On the other hand, mass balance gives  EMBED "Equation" "Word Object7" \* mergeformat  and hence  EMBED "Equation" "Word Object8" \* mergeformat  (7) Rearranging (7), we have  EMBED "Equation" "Word Object9" \* mergeformat  (8) Integrating both sides of (8),  EMBED "Equation" "Word Object9" \* mergeformat  (9) which gives,  EMBED "Equation" "Word Object10" \* mergeformat  (10) Solving (10) for t2, we arrive at  EMBED "Equation" "Word Object11" \* mergeformat  (11) Plugging the numbers into (11), we have the result,  EMBED "Equation" "Word Object12" \* mergeformat  (III) Assuming that the chemical reaction at the film/gas interface is the rate limiting step From the problem, we have dx/dt = k ( EMBED "Equation" "Word Object1" \* mergeformat )1/2 [Zn] (12) where dx/dt = rate of film growth, cm s-1 k = rate constant = 10-11 (cm s-1)(atm)-1/2(g cm-3)-1  EMBED "Equation" "Word Object1" \* mergeformat  = pressure of S2 gas, atm [Zn] = concentration of Zn in ZnS, g cm-3. If the chemical reaction is rate limiting, [Zn] = [Zn]max = 0.192 g/cm3 and the rate of film growth is given by dx/dt = 10-11(cm s-1)(atm)-1/2(g cm-3)-1 x(10-2atm)1/2x0.192 g/cm3 = 1.92x10-13 cm/s (13) Rearranging (13) and integrating it, we get  EMBED "Equation" "Word Object13" \* mergeformat  (14) Solving (14) for t3,  EMBED "Equation" "Word Object14" \* mergeformat   EMBED "Equation" "Word Object15" \* mergeformat   EMBED "Equation" "Word Object17" \* mergeformat  Therefore, since t3 >> t1 and t2, the actual rate limiting step is the chemical reaction at the film/gas interface. 48:f i XYtx"(*.2NR^`HL~Żиjqo/< EHUVjqo/< UVEHjro/< EHUVjro/< UVEH jUjOJQJUCJEHjso/< EHUVEH j EHUCJEH56A45668 l m n o @ VWXZ[\cd$hh$45668 l m n o @ VWXZ[\cd4P-TvB~  BCyz  ?@P"Q"" d&$($*$,$$%d%f%h%j%%%&& &!&V&W&&&&&&&&&&&''''F'G'''(((((((((Ⱦ軳覞{ypjOJQJU5jm/< EHUVEH jEHUCJEHjm/< EHUVjm/< UVEHjm/< EHUVjm/< UVEHjm/< EHUVjm/< UVEHjm/< EHUVjm/< UVEH jUjm/< EHUVjm/< UV,(((((((((((!)")))))>*?*u*v*****/+0+e+$h$hh())) 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,,B,C,D,~,,,,,,Q-W-}--.4.5..../ /L/M//////%0001 1&&&&&&&&///////////   !"#$%'+,023456789:<CEFGHIJKMTVWXYZ[\^`gijklmnopqsz|}~T$dxpr  $"$ currentpoint ",Times .+D +B (()T)), Symbol)=) 0).)76) exp)-( d3).)46) eV(lk +B (wT"c#.( U * (U (  * ( .+ )[)cm (2 +/)s)X30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 6016 div 1152 3 -1 roll exch div scale currentpoint translate 64 53 translate 10 619 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (D) show 272 715 moveto 224 ns (B) show 443 619 moveto 384 /Times-Roman f1 (\() show 579 619 moveto 384 /Times-Italic f1 (T) show 831 619 moveto 384 /Times-Roman f1 (\)) show 1048 619 moveto 384 /Symbol f1 (=) show 1357 619 moveto 384 /Times-Roman f1 (0) show 1545 619 moveto 384 /Times-Roman f1 (.) show 1672 619 moveto 384 /Times-Roman f1 (76) show 2099 619 moveto 384 /Times-Roman f1 (exp) show 2853 619 moveto 384 /Symbol f1 (-) show 3138 380 moveto 384 /Times-Roman f1 (3) show 3309 380 moveto 384 /Times-Roman f1 (.) show 3439 380 moveto 384 /Times-Roman f1 (46) show 3829 380 moveto 384 /Times-Italic f1 (eV) show 3422 912 moveto (k) show 3602 1008 moveto 224 ns (B) show 3747 912 moveto 384 ns (T) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 3122 520 moveto 1162 0 rlineto stroke 2658 355 moveto 384 /Symbol f1 (\346) show 2658 928 moveto (\350) show 2658 709 moveto (\347) show 4296 355 moveto (\366) show 4296 928 moveto (\370) show 4296 709 moveto (\367) show 4500 619 moveto 384 /Times-Roman f1 ( ) show 4595 619 moveto 384 /Times-Roman f1 ([) show 4729 619 moveto 384 /Times-Italic f1 (cm) show 5193 448 moveto 224 /Times-Roman f1 (2) show 5431 619 moveto 384 /Times-Roman f1 (/) show 5636 619 moveto 384 /Times-Italic f1 (s) show 5795 619 moveto 384 /Times-Roman f1 (]) show end dMATH D B (T)=0.76exp-3.46eVk B T() [cm 2 /s{eFMicrosoft Equation 3.01ELO Equation.3CompObj &RObjInfo(OlePres000 )(Ole10Native * D B (T)=0.76exp-3.46eVk B T() [cm 2 /s EquationTWT Ddxpr  " currentpoint ",Times .+ P +S +2z30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 640 div 544 3 -1 roll exch div scale currentpoint translate 64 59 translate -4 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (P) PICT 1DCompObj;RObjInfo=OlePres000>(?????????????????????????????????'!'!'!'!'!'!'!'!'!'!'!'!'!'!'! 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EquationTWTDdxpr  " currentpoint ",Times .+ P +S +2z30 dict begin currentpoint 3 -1 roll sub neg 3 1 roOle RPIC  "STPICT UDCompObj!%_Rll sub 640 div 544 3 -1 roll exch div scale currentpoint translate 64 59 translate -4 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (P) show 224 357 moveto 288 ns (S) show 391 429 moveto 224 ns (2) show end d1MATH% P S 2 1 FMicrosoft Equation 3.01ELO '!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!ObjInfoaOlePres000$&b(Ole10Native'c)Ole10FmtProgID d '!'!'!'!'!'!'!'!'!'!z&$(,/N256,02479;=?AGOd`#(e+.2'7PҜ-/1368:<@BHP"w07.5>UnknownLong-QingDdxpr  " currentpoint ",Times .+ P +S +2z30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 640 div 544 3 -1 roll exch div scale currentpoint translate 64 59 translate -4 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (P) show 224 357 moveto 288 ns (S) show 391 429 moveto 224 ns (2) sh Chen Danan FanCeleste Drewien Mark T. Lusk Julie Clausen Lynn SanchezTECHNOLOGY TRANSFER Gary FergusonCarol A. MurraySNLSandia National LaboratoriesDottie Brockman Rob Banwart;OQqUik lP j #%6CompObj*.rRObjInfotOlePres000-/u(Ole10Native0v)Ole10FmtProgID w _1009741300:(5FbbOle xPIC 24yTT"X_@dxpr  @"@ currentpoint ", Symbol .+ ,Times)C()t"(=) D( * (12 +C(+)x (82")30 dict begin currentpoint 3 -1 roll sub neg 3 1 rollPICT {_CompObj37RObjInfoOlePres00068( sub 2048 div 960 3 -1 roll exch div scale currentpoint translate 64 46 translate 23 323 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (\266) show 231 323 moveto 384 /Times-Italic f1 (C) show 93 855 moveto 384 /Symbol f2 (\266) show 301 855 moveto 384 /Times-Italic f1 (t) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 463 moveto 513 0 rlineto stroke 621 562 moveto 384 /Symbol f1 (=) show 949 562 moveto 384 /Times-Italic f1 (D) show 1293 323 moveto 384 /Symbol f2 (\266) show 1533 152 moveto 224 /Times-Roman f1 (2) show 1659 323 moveto 384 /Times-Italic f1 (C) show 1329 855 moveto 384 /Symbol f2 (\266) show 1537 855 moveto 384 /Times-Italic f1 (x) show 1735 684 moveto 224 /Times-Roman f1 (2) show 1270 463 moveto 671 0 rlineto stroke end d^MATHR i Ct=D 2 Cx 2alFMicrosoft Equation 3.01ELO Equation.3R Ct=D 2 Cx 2 EquationOle10Native9VOle10FmtProgID  _1009741299>FbbOle TL_7dxpr  7"7 currentpoint ",Times .+ C)()x),)0)), Symbol)=) 0s30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1760 div 448 3 -1 roll exch div scale currentpoint translate 64 59 translate -12 26PIC ;=TPICT _CompObj<@RObjInfo1 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 252 261 moveto 384 /Times-Roman f1 (\() show 411 261 moveto 384 /Times-Italic f1 (x) show 591 261 moveto 384 /Times-Roman f1 (,) show 723 261 moveto 384 /Times-Roman f1 (0) show 926 261 moveto 384 /Times-Roman f1 (\)) show 1143 261 moveto 384 /Symbol f1 (=) show 1452 261 moveto 384 /Times-Roman f1 (0) show end d-MATH!6 C(x,0)=0g FMicrosoft Equation 3.01ELO Equation.3! C(x,0)=0 EquationRoot Entry F ,BbP@Data WDWordDocument|ObjectPoolf?bbOle PIC DFTPICT CompObjEIRT`,8dxpr  8"8 currentpoint ",Times .+ C)()0),)t)), Symbol)=) C +s30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1792 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate -12 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 252 261 moveto 384 /Times-Roman f1 (\() show 391 261 moveto 384 /Times-Roman f1 (0) show 581 261 moveto 384 /Times-Roman f1 (,) show 708 261 moveto 384 /Times-Italic f1 (t) show 839 261 moveto 384 /Times-Roman f1 (\)) show 1056 261 moveto 384 /Symbol f1 (=) show 1362 261 moveto 384 /Times-Italic f1 (C) show 1607 357 moveto 224 ns (s) show end d9MATH- C(0,t)=C subFMicrosoft Equation 3.01ELO Equation.3- C(0,t)=C s EquationObjInfoOlePres000HJ(Ole10NativeK1Ole10FmtProgID  _1009741297PFpbpbOle PIC MOTPICT cTq8c6dxpr  6"6 currentpoint ",Times .+ C)(, Symbol)),)t)))=) 0q30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1728 div 448 3 -1 roll exch div scale currentpoint translate 64 59 translate -12 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 252 261 moveto 384 /Times-Roman f1 (\() show 391 261 moveto 384 /Symbol f1 (\245) show 663 261 moveto 384 /Times-Roman f1 (,) show 790 261 moveto 384 /Times-Italic f1 (t) show 921 261 moveto 384 /Times-Roman f1 (\)) show 1138 261 moveto 384 /Symbol f1 (=) show 1447 261 moveto 384 /Times-Roman f1 (0) show end d-MATH! C(,t)=0g CompObjNRRObjInfoOlePres000QS(Ole10NativeT%FMicrosoft Equation 3.01ELO Equation.3! C(,t)=0 EquationT h< Ole10FmtProgID  _1009741295^LYFpbpbOle PIC VXTN dxpr  " currentpoint ",Times .+C) x),)t, Symbol ( ()))=) A) +) Berf( jx(^2)Dt"e#"i# "^.( W * ( | *  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4192 div 1024 3 -1 roll exch div scale currentpoint translate 64PICT NCompObjW[RObjInfoOlePres000Z\(  !"#$%&'(*.2456789:;<=>?@ABCDEFGHIJKLMNOQUY[\^_`abcdefghijklmnopqrstuvwxyz{|}~ 50 translate -12 558 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 558 moveto (x) show 588 558 moveto 384 /Times-Roman f1 (,) show 715 558 moveto 384 /Times-Italic f1 (t) show 250 568 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 846 568 moveto (\)) show 1060 558 moveto 384 /Symbol f1 (=) show 1395 558 moveto 384 /Times-Italic f1 (A) show 1704 558 moveto 384 /Symbol f1 (+) show 2016 558 moveto 384 /Times-Italic f1 (Berf) show 3343 319 moveto (x) show 2965 851 moveto 384 /Times-Roman f1 (2) show 3451 851 moveto 384 /Times-Italic f1 (Dt) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 691 376 384 3179 886 16 sqr /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 2944 459 moveto 958 0 rlineto stroke 2745 355 moveto 384 /Symbol f1 (\346) show 2745 806 moveto (\350) show 2745 587 moveto (\347) show 3914 355 moveto (\366) show 3914 806 moveto (\370) show 3914 587 moveto (\367) show end doMATHc Cx,t()=A+Berfx2 Dt  () tFMicrosoft Equation 3.01ELO Equation.3c Cx,t()=A+BerfOle10NativegOle10FmtProgID   _1009741294bFpbpbOle  x2 Dt  () EquationTd4 @dxpr  , aThomsona .* " currentpoint ",Times( C) 0),)t, Symbol ( PIC _a TPICT  CompObj`d)RObjInfo+()))=) A) +) B) ) 0) =) C +sa ( q ) a) )A) =) C +s30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5664 div 512 3 -1 roll exch div scale currentpoint translate 64 60 translate -12 292 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 388 292 moveto 384 /Times-Roman f1 (0) show 578 292 moveto 384 /Times-Roman f1 (,) show 705 292 moveto 384 /Times-Italic f1 (t) show 250 302 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 836 302 moveto (\)) show 1050 292 moveto 384 /Symbol f1 (=) show 1385 292 moveto 384 /Times-Italic f1 (A) show 1694 292 moveto 384 /Symbol f1 (+) show 2006 292 moveto 384 /Times-Italic f1 (B) show 2311 292 moveto 384 /Symbol f1 (\264) show 2602 292 moveto 384 /Times-Roman f1 (0) show 2892 292 moveto 384 /Symbol f1 (=) show 3198 292 moveto 384 /Times-Italic f1 (C) show 3443 388 moveto 224 ns (s) show 3557 292 moveto 384 /Thomson f1 ( ) show 3940 292 moveto 384 /Symbol f1 (\336) show 4418 292 moveto 384 /Thomson f1 ( ) show 4610 292 moveto 384 /Times-Italic f1 (A) show 4934 292 moveto 384 /Symbol f1 (=) show 5240 292 moveto 384 /Times-Italic f1 (C) show 5485 388 moveto 224 ns (s) show end dzMATHn C0,t()=A+B0=C s      A=C s4 FMicrosoft Equation 3.01ELO Equation.3n C0,t()=A+B0=C s      A=C s EquationOlePres000ce,(Ole10Nativef-rOle10FmtProgID / _1009741292yUkF) b) bOle 0PIC hj1TPICT 3CompObjimPRTR4@dxpr  , aThomsona .* " currentpoint ",Times( C, Symbol) ),)t ( ()))=) A) +) B) )1)=) 0a) )a) )B) =) -)C +sa (  130 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 6112 div 512 3 -1 roll exch div scale currentpoint translate 64 60 translate -12 292 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 388 292 moveto 384 /Symbol f1 (\245) show 660 292 moveto 384 /Times-Roman f1 (,) show 787 292 moveto 384 /Times-Italic f1 (t) show 250 302 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 918 302 moveto (\)) show 1132 292 moveto 384 /Symbol f1 (=) show 1467 292 moveto 384 /Times-Italic f1 (A) show 1776 292 moveto 384 /Symbol f1 (+) show 2088 292 moveto 384 /Times-Italic f1 (B) show 2393 292 moveto 384 /Symbol f1 (\264) show 2651 292 moveto 384 /Times-Roman f1 (1) show 2910 292 moveto 384 /Symbol f1 (=) show 3219 292 moveto 384 /Times-Roman f1 (0) show 3433 292 moveto 384 /Thomson f1 ( ) show 4008 292 moveto 384 /Symbol f1 (\336) show 4486 292 moveto 384 /Thomson f1 ( ) show 4678 292 moveto 384 /Times-Italic f1 (B) show 5001 292 moveto 384 /Symbol f1 (=) show 5315 292 moveto (-) show 5540 292 moveto 384 /Times-Italic f1 (C) show 5785 388 moveto 224 ns (s) show 5899 292 moveto 384 /Thomson f1 ( ) show end dzMATHn C,t()=A+B1=0       B=-C s  4 FMicrosoft Equation 3.01ELO Equation.3n C,t()=A+B1=0       B=-C s  EquationObjInfoROlePres000lnS(Ole10NativeoTrOle10FmtProgID V _1009741291tF) b) bOle WPIC qsXTPICT ZW T^ P WDdxpr  D, aThomsona .*D "D currentpoint ",Times(C) x),)t, Symbol ( ()))=) C +s (:-) C +s (Nerf( px(d2)Dt"k#"o#"d.( ^ * (  *  a.(6 )!=) C +s (67erfc(/x(@Q2)Dt"=X#"@\# "3P.(/J * (1o *  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4384 div 2176 3 -1 roll exch div scale currentpoint translate 64 51 translate -12 558 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 558 moveto (x) show 588 558 moveto 384 /Times-Roman f1 (,) show 715 558 moveto 384 /Times-Italic f1 (t) show 250 568 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 846 568 moveto (\)) show 1060 558 moveto 384 /Symbol f1 (=) show 1366 558 moveto 384 /Times-Italic f1 (C) show 1611 654 moveto 224 ns (s) show 1817 558 moveto 384 /Symbol f1 (-) show 2106 558 moveto 384 /Times-Italic f1 (C) show 2351 654 moveto 224 ns (s) show 2452 558 moveto 384 ns (erf) show 3545 319 moveto (x) show 3167 851 moveto 384 /Times-Roman f1 (2) show 3653 851 moveto 384 /Times-Italic f1 (Dt) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 691 376 384 3381 886 16 sqr /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 3146 459 moveto 958 0 rlineto stroke 2947 355 moveto 384 /Symbol f1 (\346) show 2947 806 moveto (\350) show 2947 587 moveto (\347) show 4116 355 moveto (\366) show 4116 806 moveto (\370) show 4116 587 moveto (\367) show 0 1708 moveto 384 /Thomson f1 ( ) show 1068 1708 moveto 384 /Symbol f1 (=) show 1374 1708 moveto 384 /Times-Italic f1 (C) show 1619 1804 moveto 224 ns (s) show 1720 1708 moveto 384 ns (erfc) show 2921 1469 moveto (x) show 2543 2001 moveto 384 /Times-Roman f1 (2) show 43029 2001 moveto 384 /Times-Italic f1 (Dt) show 691 376 384 2757 2036 16 sqr 2522 1609 moveto 958 0 rlineto stroke 2323 1505 moveto 384 /Symbol f1 (\346) show 2323 1956 moveto (\350) show 2323 1737 moveto (\347) show 3492 1505 moveto (\366) show 3492 1956 moveto (\370) show 3492 1737 moveto (\367) show end dMATH&  Cx,t()=C s -C s erfx2 Dt  ()          =C s erfcx2 Dt  ()34FMicrosoft Equation 3.01ELO Equation.3CompObjrvRObjInfoOlePres000uw(Ole10Nativex Cx,t()=C s -C s erfx2 Dt  ()          =C s erfcx2 Dt  () EquationTk Ole10FmtProgID  _1009741290p}F) b) bOle PIC z|TPICT CompObj{RObjInfoOlePres000~(edxpr-  e"e currentpoint ",Times .+D +950) )C, Symbol (=) 0).)76) exp)-( 3).)46) eV(`1).)38))10 (-)23 + J) /)K) )1223)K"`|.( R * (  *  .(8 ) =) 0).)76)exp)-(0S3).)46))1).)6) )10 (+-)19 + J(AN1).)38))10 (;z-)23 + )1223)J"4O_.(/@ * (4@ (1 * .(Z ) =) 4).)32))10 (UD-)15 +  (WXcm (Qf2"Mr + s (^T[)&30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 7296 div 3232 3 -1 roll exch div scale currentpoint translate 64 36 translate 10 564 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (D) show 260 662 moveto 224 /Times-Roman f1 (950) show 596 662 moveto 224 /Times-Roman f1 (\312) show 670 662 moveto 224 /Times-Italic f1 (C) show 956 564 moveto 384 /Symbol f1 (=) show 1265 564 moveto 384 /Times-Roman f1 (0) show 1453 564 moveto 384 /Times-Roman f1 (.) show 1580 564 moveto 384 /Times-Roman f1 (76) show 2007 564 moveto 384 /Times-Roman f1 (exp) show 2761 564 moveto 384 /Symbol f1 (-) show 4455 325 moveto 384 /Times-Roman f1 (3) show 4626 325 moveto 384 /Times-Roman f1 (.) show 4756 325 moveto 384 /Times-Roman f1 (46) show 5146 325 moveto 384 /Times-Italic f1 (eV) show 3020 857 moveto 384 /Times-Roman f1 (1) show 3177 857 moveto 384 /Times-Roman f1 (.) show 3295 857 moveto 384 /Times-Roman f1 (38) show 3746 857 moveto 384 /Symbol f1 (\264) show 4004 857 moveto 384 /Times-Roman f1 (10) show 4408 686 moveto 224 /Symbol f1 (-) show 4530 686 moveto 224 /Times-Roman f1 (23) show 4815 857 moveto 384 /Times-Italic f1 (J) show 5098 857 moveto 384 /Times-Roman f1 (/) show 5314 857 moveto 384 /Times-Italic f1 (K) show 5673 857 moveto 384 /Symbol f1 (\264) show 5931 857 moveto 384 /Times-Roman f1 (1223) show 6709 857 moveto 384 /Times-Italic f1 (K) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 3030 465 moveto 3980 0 rlineto stroke 2566 355 moveto 384 /Symbol f1 (\346) show 2566 818 moveto (\350) show 2566 599 moveto (\347) show 7022 355 moveto (\366) show 7022 818 moveto (\370) show 7022 599 moveto (\367) show 0 1756 moveto 384 /Times-Roman f1 ( ) show 396 1756 moveto 384 /Symbol f1 (=) show 705 1756 moveto 384 /Times-Roman f1 (0) show 893 1756 moveto 384 /Times-Roman f1 (.) show 1020 1756 moveto 384 /Times-Roman f1 (76) show 1447 1756 moveto 384 /Times-Roman f1 (exp) show 2201 1756 moveto 384 /Symbol f1 (-) show 2593 1517 moveto 384 /Times-Roman f1 (3) show 2764 1517 moveto 384 /Times-Roman f1 (.) show 2894 1517 moveto 384 /Times-Roman f1 (46) show 3355 1517 moveto 384 /Symbol f1 (\264) show 3613 1517 moveto 384 /Times-Roman f1 (1) show 3770 1517 moveto 384 /Times-Roman f1 (.) show 3891 1517 moveto 384 /Times-Roman f1 (6) show 4160 1517 moveto 384 /Symbol f1 (\264) show 4418 1517 moveto 384 /Times-Roman f1 (10) show 4822 1346 moveto 224 /Symbol f1 (-) show 4944 1346 moveto 224 /Times-Roman f1 (19) show 5236 1517 moveto 384 /Times-Italic f1 (J) show 2460 2049 moveto 384 /Times-Roman f1 (1) show 2617 2049 moveto 384 /Times-Roman f1 (.) show 2735 2049 moveto 384 /Times-Roman f1 (38) show 3186 2049 moveto 384 /Symbol f1 (\264) show 3444 2049 moveto 384 /Times-Roman f1 (10) show 3848 1878 moveto 224 /Symbol f1 (-) show 3970 1878 moveto 224 /Times-Roman f1 (23) show 4300 2049 moveto 384 /Symbol f1 (\264) show 4558 2049 moveto 384 /Times-Roman f1 (1223) show 5344 2049 moveto 384 /Times-Italic f1 (J) show 2470 1657 moveto 3089 0 rlineto stroke 2006 1517 moveto 384 /Symbol f1 (\346) show 2006 2040 moveto (\350) show 2006 1821 moveto (\347) show 5571 1517 moveto (\366) show 5571 2040 moveto (\370) show 5571 1821 moveto (\367) show 0 2858 moveto 384 /Times-Roman f1 ( ) show 396 2858 moveto 384 /Symbol f1 (=) show 710 2858 moveto 384 /Times-Roman f1 (4) show 897 2858 moveto 384 /Times-Roman f1 (.) show 1015 2858 moveto 384 /Times-Roman f1 (32) show 1479 2858 moveto 384 /Symbol f1 (\264) show 1737 2858 moveto 384 /Times-Roman f1 (10) show 2141 2687 moveto 224 /Symbol f1 (-) show 2263 2687 moveto 224 /Times-Roman f1 (15) show 2537 2858 moveto 384 /Times-Roman f1 ( ) show 2766 2755 moveto 384 /Times-Italic f1 (cm) show 3230 2584 moveto 224 /Times-Roman f1 (2) show /stb { newpath moveto 0 setlinewidth 2 copy rlineto } def /enb { rlineto neg exch neg exch rlineto closepath fill } def /hb { stb 0 thick enb } def /vb { stb thick 0 enb } def -478 671 3631 2432 vb 3705 2858 moveto 384 /Times-Italic f1 (s) show 2632 2995 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 2369 /Symbol f3 ([) show 3865 2995 moveto (]) show end dMATHX D 950C =0.76exp-3.46eV1.3810 -23 J/K1223K()   =0.76exp-3.461.610 -19 J1.3810 -23 1223J()   =4.3210 -15  )cm 2 s[34FMicrosoft Equation 3.01ELO Equation.3 D 950C =0.76exp-3.46eV1.3810 -23 J/K1223K()   =0.76exp-3.461.61Ole10NativeOle10FmtProgID  _1009741288F) b) bOle 0 -19 J1.3810 -23 1223J()   =4.3210 -15  )cm 2 s[ EquationT&"XPIC TPICT  CompObjRObjInfo dxpr  , aThomsona .* " currentpoint ",Times(C) x),)t, Symbol)=) 30)min). ( ()B))=) 1).)8))10 ( 20 +erfc( x(5).)57))10 (-)6"5 .(  *  (  *  a.( )atoms)/)cm ( 3n30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 9024 div 960 3 -1 roll exch div scale currentpoint translate 64 44 translate -12 532 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 532 moveto (x) show 588 532 moveto 384 /Times-Roman f1 (,) show 715 532 moveto 384 /Times-Italic f1 (t) show 933 532 moveto 384 /Symbol f1 (=) show 1235 532 moveto 384 /Times-Roman f1 (30) show 1669 532 moveto 384 /Times-Roman f1 (min) show 2267 532 moveto (.) show 250 542 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 2358 542 moveto (\)) show 2572 532 moveto 384 /Symbol f1 (=) show 2848 532 moveto 384 /Times-Roman f1 (1) show 3005 532 moveto 384 /Times-Roman f1 (.) show 3119 532 moveto 384 /Times-Roman f1 (8) show 3378 532 moveto 384 /Symbol f1 (\264) show 3636 532 moveto 384 /Times-Roman f1 (10) show 4036 362 moveto 224 ns (20) show 4305 532 moveto 38^dxpr,  ^"^ currentpoint ",Times .+x +j, Symbol (=) 2)4).)32))10 (T-)15 + ) 30)) 60"#"##h)) erfc( 1).)5)) 10 (16 (1).)8))10 (20", .(  * ( (  * .(3 )) 2)4).)32))10 (.V-)15 + ) 30)) 60"0!#"4%#h)) 2).)8(G )=) 1).)56))10 (BE-)5 + cm(Z )=) 0).)156)m)m30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 7456 div 3008 3 -1 roll exch div scale currentpoint translate 64 36 translate 11 594 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (x) show 217 690 moveto 224 ns (j) show 421 594 moveto 384 /Symbol f1 (=) show 728 594 moveto 384 /Times-Roman f1 (2) show 1200 594 moveto (4) show 1387 594 moveto 384 /Times-Roman f1 (.) show 1505 594 moveto 384 /Times-Roman f1 (32) show 1969 594 moveto 384 /Symbol f1 (\264) show 2227 594 moveto 384 /Times-Roman f1 (10) show 2631 423 moveto 224 /Symbol f1 (-) show 2753 423 moveto 224 /Times-Roman f1 (15) show 3085 594 moveto 384 /Symbol f1 (\264) show 3369 594 moveto 384 /Times-Roman f1 (30) show 3833 594 moveto 384 /Symbol f1 (\264) show 4120 594 moveto 384 /Times-Roman f1 (60) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 3584 442 384 942 631 16 sqr 4616 594 moveto 384 /Symbol f1 (\264) show 4903 594 moveto 384 /Times-Italic f1 (erfc) show 5702 355 moveto 384 /Times-Roman f1 (1) show 5859 355 moveto 384 /Times-Roman f1 (.) show 5981 355 moveto 384 /Times-Roman f1 (5) show 6239 355 moveto 384 /Symbol f1 (\264) show 6497 355 moveto 384 /Times-Roman f1 (10) show 6879 184 moveto 224 ns (16) show 5695 887 moveto 384 ns (1) show 5852 887 moveto 384 /Times-Roman f1 (.) show 5966 887 moveto 384 /Times-Roman f1 (8) show 6225 887 moveto 384 /Symbol f1 (\264) show 6483 887 moveto 384 /Times-Roman f1 (10) show 6883 716 moveto 224 ns (20) show /thick 0 def /th { dup setlinewidth /thick exch def } def J16 th 5705 495 moveto 1460 0 rlineto stroke 5506 355 moveto 384 /Symbol f1 (\346) show 5506 878 moveto (\350) show 5506 659 moveto (\347) show 7177 355 moveto (\366) show 7177 878 moveto (\370) show 7177 659 moveto (\367) show 0 1627 moveto 384 /Times-Roman f1 ( ) show 491 1627 moveto 384 /Symbol f1 (\273) show 794 1627 moveto 384 /Times-Roman f1 (2) show 1266 1627 moveto (4) show 1453 1627 moveto 384 /Times-Roman f1 (.) show 1571 1627 moveto 384 /Times-Roman f1 (32) show 2035 1627 moveto 384 /Symbol f1 (\264) show 2293 1627 moveto 384 /Times-Roman f1 (10) show 2697 1456 moveto 224 /Symbol f1 (-) show 2819 1456 moveto 224 /Times-Roman f1 (15) show 3151 1627 moveto 384 /Symbol f1 (\264) show 3435 1627 moveto 384 /Times-Roman f1 (30) show 3899 1627 moveto 384 /Symbol f1 (\264) show 4186 1627 moveto 384 /Times-Roman f1 (60) show 3584 442 384 1008 1664 16 sqr 4682 1627 moveto 384 /Symbol f1 (\264) show 4971 1627 moveto 384 /Times-Roman f1 (2) show 5159 1627 moveto 384 /Times-Roman f1 (.) show 5273 1627 moveto 384 /Times-Roman f1 (8) show 0 2267 moveto 384 /Times-Roman f1 ( ) show 492 2267 moveto 384 /Symbol f1 (=) show 768 2267 moveto 384 /Times-Roman f1 (1) show 925 2267 moveto 384 /Times-Roman f1 (.) show 1047 2267 moveto 384 /Times-Roman f1 (56) show 1508 2267 moveto 384 /Symbs (x) show 3086 947 moveto 224 /Symbol f1 (=) show 3233 947 moveto 224 /Times-Roman f1 (0) show end dMATHy Jb x=0 =-DdCx,t()dxb x=0laFMicrosoft Equation 3.01ELO Equation.3OlePres000g(Ole10Nativeh}Ole10FmtProgID j _1009741281FV:bV:by Jb x=0 =-DdCx,t()dxb x=0 EquationT8 !dxpr  !"! currentpoint ",Times .+J"Ole kPIC lTPICT n CompObjR +x, Symbol)=)0 (=) -)D)-)C +s ( U2+p"O#"S# "N( o1(c2)Dt"j#"n#"c.( 5 * (  * .(=) C +s ( D(p)t" "# "# 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5824 div 1056 3 -1 roll exch div scale currentpoint translate 64 60 translate 13 580 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (J) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 236 287 moveto 0 388 rlineto stroke 282 694 moveto 224 ns (x) show 412 694 moveto 224 /Symbol f1 (=) show 559 694 moveto 224 /Times-Roman f1 (0) show 805 580 moveto 384 /Symbol f1 (=) show 1119 580 moveto (-) show 1366 580 moveto 384 /Times-Italic f1 (D) show 1813 580 moveto 384 /Symbol f1 (-) show 2038 580 moveto 384 /Times-Italic f1 (C) show 2283 676 moveto 224 ns (s) show 2656 341 moveto 384 /Times-Roman f1 (2) show 2752 873 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 518 380 384 2493 912 16 sqr 2461 481 moveto 582 0 rlineto stroke 3490 341 moveto 384 /Times-Roman f1 (1) show 3128 873 moveto (2) show 3614 873 moveto 384 /Times-Italic f1 (Dt) show 691 376 384 3342 908 16 sqr 3107 481 moveto 958 0 rlineto stroke 1655 373 moveto 384 /Symbol f1 (\351) show 1655 914 moveto (\353) show 1655 742 moveto (\352) show 4090 373 moveto (\371) show 4090 914 moveto (\373) show 4090 742 moveto (\372) show 4336 580 moveto (=) show 4642 580 moveto 384 /Times-Italic f1 (C) show 4887 676 moveto 224 ns (s) show 5368 341 moveto 384 ns (D) show 5324 873 moveto 384 /Symbol f2 (p) show 5546 873 moveto 384 /Times-Italic f1 (t) show E5295 481 moveto 393 0 rlineto stroke 687 912 384 5033 912 16 sqr end dMATH_ Jb x=0 =-D-C s 2 p  12 Dt  [=C s  Dpt  mFMicrosoft Equation 3.01ELO Equation.3 Jb x=0 =-D-C s 2 p  12 Dt ObjInfoOlePres000(Ole10NativeOle10FmtProgID  [=C s  Dpt  EquationT FMicrosoft Equation 3.01ELO Equation.3_1009741280FV:bV:bOle PIC TPICT dxpr=  " currentpoint ",Times .+W, Symbol)=)Jdt)=)C +s("=0(=t +1 (= ("0(t +1 ( ( ZD(Yp)t"X "P# "T# (edt(; )=) 2)C +s (47D +950) )C (4Pt +1 (DCp"85"";-# "E1#$(a )=) 2) )1).)8))10 (\P20 + (Zm4).)32))10 (T-)15 + ) 30))60(j3).)14"lh"`d# "jh#j(} )=) 5).)66))10 (wF14 +  atoms)"/)cm (w230 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 6912 div 4096 3 -1 roll exch div scale currentpoint translate 64 43 translate -13 633 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (W) show 431 633 moveto 384 /Symbol f1 (=) show 992 633 moveto 384 /Times-Italic f1 (Jdt) show 1572 633 moveto 384 /Symbol f1 (=) show 2108 633 moveto 384 /Times-Italic f1 (C) show 2353 729 moveto 224 ns (s) show 1918 1052 moveto 224 /Times-Roman f1 (0) show 1890 152 moveto 224 /Times-Italic f1 (t) show 1953 208 moveto 160 /Times-Roman f1 (1) show 1889 767 moveto 576 /Symbol f1 (\362) show 777 1052 moveto 224 /Times-Roman f1 (0) show 749 152 moveto 224 /Times-Italic f1 (t) show 812 208 moveto 160 /Times-Roman f1 (1) show 748 767 moveto 576 /Symbol f1 (\362) show 2834 394 moveto 384 /Times-Italic f1 (D) show 2790 926 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show 3012 926 moveto 384 /Times-Italic f1 (t) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 2761 534 moveto 393 0 rlineto stroke /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 687 912 384 2499 965 16 sqr 3181 633 moveto (dt) show 0 1870 moveto 384 /Times-Roman f1 ( ) show 492 1870 moveto 384 /Symbol f1 (=) show 799 1870 moveto 384 /Times-Roman f1 (2) show 1001 1870 moveto 384 /Times-Italic f1 (C) show 1246 1966 moveto 224 ns (s) show 1696 1628 moveto 384 ns (D) show 1946 1726 moveto 224 /Times-Roman f1 (950) show 2282 1726 moveto 224 /Times-Roman f1 (\312) show g2356 1726 moveto 224 /Times-Italic f1 (C) show 2520 1628 moveto 384 ns (t) show 2611 1724 moveto 224 /Times-Roman f1 (1) show 2093 2163 moveto 384 /Symbol f2 (p) show 1654 1771 moveto 1109 0 rlineto stroke 1403 915 384 1392 2202 16 sqr 0 3078 moveto 384 /Times-Roman f1 ( ) show 492 3078 moveto 384 /Symbol f1 (=) show 799 3078 moveto 384 /Times-Roman f1 (2) show 1071 3078 moveto 384 /Symbol f1 (\264) show 1329 3078 moveto 384 /Times-Roman f1 (1) show 1486 3078 moveto 384 /Times-Roman f1 (.) show 1600 3078 moveto 384 /Times-Roman f1 (8) show 1859 3078 moveto 384 /Symbol f1 (\264) show 2117 3078 moveto 384 /Times-Roman f1 (10) show 2517 2907 moveto 224 ns (20) show 2857 3078 moveto 384 /Symbol f1 (\264) show 3447 2839 moveto 384 /Times-Roman f1 (4) show 3634 2839 moveto 384 /Times-Roman f1 (.) show 3752 2839 moveto 384 /Times-Roman f1 (32) show 4216 2839 moveto 384 /Symbol f1 (\264) show 4474 2839 moveto 384 /Times-Roman f1 (10) show 4878 2668 moveto 224 /Symbol f1 (-) show 5000 2668 moveto 224 /Times-Roman f1 (15) show 5332 2839 moveto 384 /Symbol f1 (\264) show 5616 2839 moveto 384 /Times-Roman f1 (30) show 6080 2839 moveto 384 /Symbol f1 (\264) show 6367 2839 moveto 384 /Times-Roman f1 (60) show 4770 3371 moveto (3) show 4941 3371 moveto 384 /Times-Roman f1 (.) show 5033 3371 moveto 384 /Times-Roman f1 (14) show 3419 2979 moveto 3354 0 rlineto stroke 3648 974 384 3157 3408 16 sqr 0 3963 moveto 384 /Times-Roman f1 ( ) show 492 3963 moveto 384 /Symbol f1 (=) show 798 3963 moveto 384 /Times-Roman f1 (5) show 972 3963 moveto 384 /Times-Roman f1 (.) show 1093 3963 moveto 384 /Times-Roman f1 (66) show 1554 3963 moveto 384 /Symbol f1 (\264) show 1812 3963 moveto 384 /Times-Roman f1 (10) show 2194 3792 moveto 224 ns (14) show 2475 3963 moveto 384 /Times-Roman f1 ( atoms) show 3570 3963 moveto (/) show 3772 3963 moveto (cm) show 4261 3792 moveto 224 ns (2) show end dMATHUR W=Jdt=C s0t 1  0t 1   Dpt  dt    =2C s  D 950C t 1 p      =21.810 20  4.3210 -15 30603.14      =5.6610 14  atoms/cm 2 1CompObjRObjInfoOlePres000(Ole10Native W=Jdt=C s0t 1  0t 1   Dpt  dt    =2C s  D 950C t 1 p      =21.810 20  4.3210 -15 30603.14      =5.6610 14  atoms/cm 2 EquationT  "dxpr  """ currentpoint ",Times .+C) x),)t, Symbol ( ()))=Ole10FmtProgID  _1009741278FV:bV:bOle PIC TPICT  CompObjRObjInfoOlePres000(     G)( !"#$%&'+*-,4./012356DC89:;<=>?@ABEFMH_IJKLNOPUQRSTVWYXZ[\`^ewabcdfghmijklonspqrtuxv~yz{|}( 6W*p)Dt".#"2#"-(Lexp)-( rx (x2 (m4)Dt"l.( ^ * (^ (  * 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4384 div 1088 3 -1 roll exch div scale currentpoint translate 64 47 translate -12 593 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 593 moveto (x) show 588 593 moveto 384 /Times-Roman f1 (,) show 715 593 moveto 384 /Times-Italic f1 (t) show 250 603 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 846 603 moveto (\)) show 1060 593 moveto 384 /Symbol f1 (=) show 1686 354 moveto 384 /Times-Italic f1 (W) show 1669 886 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show 1891 886 moveto 384 /Times-Italic f1 (Dt) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 900 380 384 1410 925 16 sqr /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1378 494 moveto 964 0 rlineto stroke 2398 593 moveto 384 /Times-Roman f1 (exp) show 3152 593 moveto 384 /Symbol f1 (-) show 3594 354 moveto 384 /Times-Italic f1 (x) show 3792 184 moveto 224 /Times-Roman f1 (2) show 3449 886 moveto 384 ns (4) show 3672 886 moveto 384 /Times-Italic f1 (Dt) show 3421 494 moveto 670 0 rlineto stroke 2957 355 moveto 384 /Symbol f1 (\346) show 2957 876 moveto (\350) show 2957 657 moveto (\347) show 4103 355 moveto (\366) show 4103 876 moveto (\370) show 4103 657 moveto (\367) show end dMATH Cx,t()=W pDt  exp-x 2 4Dt()12FMicrosoft Equation 3.01ELO Equation.3Ole10NativeOle10FmtProgID  _1009741277FbbOle  Cx,t()=W pDt  exp-x 2 4Dt() EquationT FMicrosoft Equation 3.01ELO PIC TPICT CompObjRObjInfoHdxpr!  H"H currentpoint ",Times .+C) x),)t, Symbol ( ())(#=) 2)C +s ( HD +950) )C ( bt +1 (Up"G""?# "C#$( y1(vp)Dt"n#"r#"m(exp)-( x (2 (4)Dt".(  * ( (  * .(: )!=(2-2)C +s (C3p"6-(2LD +950) )C (2et +1 (CVDt"6J""9B# "CF#$(:pexp)-(2x (-2 (C4)Dt"6.(1 * (6 (3 * 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 6432 div 2304 3 -1 roll exch div scale currentpoint translate 64 43 translate -12 594 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 594 moveto (x) show 588 594 moveto 384 /Times-Roman f1 (,) show 715 594 moveto 384 /Times-Italic f1 (t) show 250 604 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 846 604 moveto (\)) show 1060 594 moveto 384 /Symbol f1 (=) show 1367 594 moveto 384 /Times-Roman f1 (2) show 1569 594 moveto 384 /Times-Italic f1 (C) show 1814 690 moveto 224 ns (s) show 2264 352 moveto 384 ns (D) show 2514 450 moveto 224 /Times-Roman f1 (950) show 2850 450 moveto 224 /Times-Roman f1 (\312) show 2924 450 moveto 224 /Times-Italic f1 (C) show 3088 352 moveto 384 ns (t) show 3179 448 moveto 224 /Times-Roman f1 (1) show 2661 887 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 2222 495 moveto 1109 0 rlineto stroke /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 1403 915 384 1960 926 16 sqr 3813 355 moveto 384 /Times-Roman f1 (1) show 3718 887 moveto 384 /Symbol f2 (p) show 3940 887 moveto 384 /Times-Italic f1 (Dt) show 900 380 384 3459 926 16 sqr 3427 495 moveto 964 0 rlineto stroke 4447 594 moveto 384 /Times-Roman f1 (exp) show 5201 594 moveto 384 /Symbol f1 (-) show 5643 355 moveto 384 /Times-Italic f1 (x) show 5841 184 moveto 224 /Times-Roman f1 (2) show 5498 887 moveto 384 ns (4) show 5721 887 moveto 384 /Times-Italic f1 (Dt) show 5470 495 moveto 670 0 rlineto stroke 5006 355 moveto 384 /Symbol f1 (\346) show 5006 878 moveto (\350) show 5006 659 moveto (\347) show 6152 355 moveto (\366) show 6152 878 moveto (\370) show 6152 659 moveto (\367) show 0 1816 moveto 384 /Times-Roman f1 ( ) show 1068 1816 moveto 384 /Symbol f1 (=) show 1407 1577 moveto 384 /Times-Roman f1 (2) show 1609 1577 moveto 384 /Times-Italic f1 (C) show 1854 1673 moveto 224 ns (s) show 1578 2109 moveto 384 /Symbol f2 (p) show 1386 1717 moveto 614 0 rlineto stroke 2368 1574 moveto 384 /Times-Italic f1 (D) show 2618 1672 moveto 224 /Times-Roman f1 (950) show 2954 1672 moveto 224 /Times-Roman f1 (\312) show 3028 1672 moveto 224 /Times-Italic f1 (C) show 3192 1574 moveto 384 ns (t) show 3283 1670 moveto 224 /Times-Roman f1 (1) show 2692 2109 moveto 384 /Times-Italic f1 (Dt) show 2326 1717 moveto 1109 0 rlineto stroke 1403 911 384 2064 2144 16 sqr 3523 1816 moveto 384 /Times-Roman f1 (exp) show 4277 1816 moveto 384 /Symbol f1 (-) show 4719 1577 moveto 384 /Times-Italic f1 (x) show 4917 1406 moveto 224 /Times-Roman f1 (2) show 4574 2109 moveto 384 ns (4) show 4797 2109 moveto 384 /Times-Italic f1 (Dt) show 4546 1717 moveto 670 0 rlineto stroke 4082 1577 moveto 384 /Symbol f1 (\346) show 4082 2100 moveto (\350) show 4082 1881 moveto (\347) show 5228 1577 moveto (\366) show 5228 2100 moveto (\370) show 5228 1881 moveto (\367) show end dMATH= Cx,t()=2C s  D 950C t 1 p  1 pDt  exp-x 2 4Dt()          =2C s p D 950C t 1 Dt  exp-x 2 4Dt()o Equation.3 Cx,t()=2C s  D 950C t 1 p  1 pDt  exp-x 2 4Dt()          =2C s p D 950COlePres000(Ole10NativeOle10FmtProgID  _1009741276Fbb t 1 Dt  exp-x 2 4Dt() EquationTJ dxpr  " currentpoint ",Times .+D +Ole PIC TPICT CompObjR      $%&'()*.0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\^`defjlpqrstuvz|}~1050))C, Symbol ("=) 5).)15))10 ( W-)14 +  ( kcm (y2 +s" (g[) 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4480 div 832 3 -1 roll exch div scale currentpoint translate 64 55 translate 10 457 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (D) show 242 555 moveto 224 /Times-Roman f1 (1050) show 690 555 moveto 224 /Times-Roman f1 (\312) show 764 555 moveto 224 /Times-Italic f1 (C) show 1050 457 moveto 384 /Symbol f1 (=) show 1356 457 moveto 384 /Times-Roman f1 (5) show 1530 457 moveto 384 /Times-Roman f1 (.) show 1622 457 moveto 384 /Times-Roman f1 (15) show 2072 457 moveto 384 /Symbol f1 (\264) show 2330 457 moveto 384 /Times-Roman f1 (10) show 2734 286 moveto 224 /Symbol f1 (-) show 2856 286 moveto 224 /Times-Roman f1 (14) show 3137 457 moveto 384 /Times-Roman f1 ( ) show 3366 354 moveto 384 /Times-Italic f1 (cm) show 3830 183 moveto 224 /Times-Roman f1 (2) show 4037 619 moveto 384 /Times-Italic f1 (s) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th /stb { newpath moveto 0 setlinewidth 2 copy rlineto } def /enb { rlineto neg exch neg exch rlineto closepath fill } def /hb { stb 0 thick enb } def /vb { stb thick 0 enb } def -423 593 4231 31 vb 3232 583 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 2263 /Symbol f3 ([) show 4267 583 moveto (]) show end dMATH D 1050C =5.1510 -14  )cm 2 s[7 FMicrosoft Equation 3.01ELO Equation.3ObjInfoOlePres000(Ole10NativeOle10FmtProgID   D 1050C =5.1510 -14  )cm 2 s[ EquationT22 \FMicrosoft Equation 3.01ELO _1009741274FbbOle PIC TPICT Jkdxpr"  Jk"Jk currentpoint ",Times .+C) x),)t, Symbol ( ())(#=(-2) )1).)8))10 (c20 (Ip"->(w4).)32))10 (-)15 + ) 30(w5).)15))10 (-)14 + ) 60"vP"n# "r#R(exp)-(!x ((2 (4)) 5).)15))10 ('-)14 + ) 60)) 60"x.(  * ( (c * .(; )!=) 2).)35))10 (6X19 +  )exp)-(4x (/2 (E7).)416))10 (?-)10"8? .(3w * (8w (5 * 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 11616 div 2368 3 -1 roll exch div scale currentpoint translate 64 50 translate -12 644 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 644 moveto (x) show 588 644 moveto 384 /Times-Roman f1 (,) show 715 644 moveto 384 /Times-Italic f1 (t) show 250 654 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 846 654 moveto (\)) show 1060 644 moveto 384 /Symbol f1 (=) show 1399 405 moveto 384 /Times-Roman f1 (2) show 1671 405 moveto 384 /Symbol f1 (\264) show 1929 405 moveto 384 /Times-Roman f1 (1) show 2086 405 moveto 384 /Times-Roman f1 (.) show 2200 405 moveto 384 /Times-Roman f1 (8) show 2459 405 moveto 384 /Symbol f1 (\264) show 2717 405 moveto 384 /Times-Roman f1 (10) show 3117 234 moveto 224 ns (20) show 2273 937 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1378 545 moveto 2021 0 rlineto stroke 3753 405 moveto 384 /Times-Roman f1 (4) show 3940 405 moveto 384 /Times-Roman f1 (.) show 4058 405 moveto 384 /Times-Roman f1 (32) show 4522 405 moveto 384 /Symbol f1 (\264) show 4780 405 moveto 384 /Times-Roman f1 (10) show 5184 234 moveto 224 /Symbol f1 (-) show 5306 234 moveto 224 /Times-Roman f1 (15) show 5638 405 moveto 384 /Symbol f1 (\264) show 5922 405 moveto 384 /Times-Roman f1 (30) show 3770 937 moveto (5) show 3944 937 moveto 384 /Times-Roman f1 (.) show 4036 937 moveto 384 /Times-Roman f1 (15) show 4486 937 moveto 384 /Symbol f1 (\264) show 4744 937 moveto 384 /Times-Roman f1 (10) show 5148 766 moveto 224 /Symbol f1 (-) show 5270 766 moveto 224 /Times-Roman f1 (14) show 5609 937 moveto 384 /Symbol f1 (\264) show 5896 937 moveto 384 /Times-Roman f1 (60) show 3725 545 moveto 2603 0 rlineto stroke /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 2897 974 384 3463 974 16 sqr 6416 644 moveto 384 /Times-Roman f1 (exp) show 7170 644 moveto 384 /Symbol f1 (-) show 9212 405 moveto 384 /Times-Italic f1 (x) show 9410 234 moveto 224 /Times-Roman f1 (2) show 7467 937 moveto 384 ns (4) show 7738 937 moveto 384 /Symbol f1 (\264) show 8026 937 moveto 384 /Times-Roman f1 (5) show 8200 937 moveto 384 /Times-Roman f1 (.) show 8292 937 moveto 384 /Times-Roman f1 (15) show 8742 937 moveto 384 /Symbol f1 (\264) show 9000 937 moveto 384 /Times-Roman f1 (10) show 9404 766 moveto 224 /Symbol f1 (-) show 9526 766 moveto 224 /Times-Roman f1 (14) show 9865 937 moveto 384 /Symbol f1 (\264) show 10152 937 moveto 384 /Times-Roman f1 (60) show 10616 937 moveto 384 /Symbol f1 (\264) show 10903 937 moveto 384 /Times-Roman f1 (60) show 7439 545 moveto 3870 0 rlineto stroke 6975 405 moveto 384 /Symbol f1 (\346) show 6975 928 moveto (\350) show 6975 709 moveto (\347) show 11321 405 moveto (\366) show 11321 928 moveto (\370) show 11321 709 moveto (\367) show 0 1866 moveto 384 /Times-Roman f1 ( ) show 1068 1866 moveto 384 /Symbol f1 (=) show 1375 1866 moveto 384 /Times-Roman f1 (2) show 1563 1866 moveto 384 /Times-Roman f1 (.) show 1681 1866 moveto 384 /Times-Roman f1 (35) show 2131 1866 moveto 384 /Symbol f1 (\264) show 2389 1866 moveto 384 /Times-Roman f1 (10) show 2771 1695 moveto 224 ns (19) show 3050 1866 moveto 384 /Times-Roman f1 ( ) show 3202 1866 moveto 384 /Times-Roman f1 (exp) show 3956 1866 moveto 384 /Symbol f1 (-) show 5089 1627 moveto 384 /Times-Italic f1 (x) show 5287 1456 moveto 224 /Times-Roman f1 (2) show 4250 2159 moveto 384 ns (7) show 4428 2159 moveto 384 /Times-Roman f1 (.) show 4558 2159 moveto 384 /Times-Roman f1 (416) show 5211 2159 moveto 384 /Symbol f1 (\264) show 5469 2159 moveto 384 /Times-Roman f1 (10) show 5873 1988 moveto 224 /Symbol f1 (-) show 5995 1988 moveto 224 /Times-Roman f1 (10) show 4225 1767 moveto 2052 0 rlineto stroke 3761 1627 moveto 384 /Symbol f1 (\346) show 3761 2150 moveto (\350) show 3761 1931 moveto (\347) show 6289 1627 moveto (\366) show 6289 2150 moveto (\370) show 6289 1931 moveto (\367) show end dMATH[: Cx,t()=21.810 20 p 4.3210 -15 305.1510 -14 60  exp-x 2 45.1510 -14 6060()          =2.3510 19  exp-x 2 7.41610 -10 ()owCompObjRObjInfo!OlePres000"(Ole10Native#Equation.3 Cx,t()=21.810 20 p 4.3210 -15 305.1510 -14 60  exp-x 2 45.1510 -14 6060()          =2.3510 19  exp-x 2 7.41610 -10 () EquationT H *dxpr  *"*Ole10FmtProgID + _1009741273FbbOle ,PIC -TPICT / CompObj_RObjInfoaOlePres000b( currentpoint ",Times .+x +j, Symbol (=)-)4)Dt + 2 (@ln(QC +sub (cp("U2)C +s"P (wD +1050))C (t +2 ("yD +950) )C ("t +1"u&"m# "%q#( .(J * (J ( * ( "#"'!30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5312 div 1344 3 -1 roll exch div scale currentpoint translate 64 62 translate 11 738 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (x) show 217 834 moveto 224 ns (j) show 421 738 moveto 384 /Symbol f1 (=) show 997 738 moveto (-) show 1207 738 moveto 384 /Times-Roman f1 (4) show 1430 738 moveto 384 /Times-Italic f1 (Dt) show 1816 834 moveto 224 /Times-Roman f1 (2) show 2011 738 moveto 384 /Times-Roman f1 (ln) show 2541 499 moveto 384 /Times-Italic f1 (C) show 2786 595 moveto 224 ns (sub) show 3120 499 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show 2664 1031 moveto 384 /Times-Roman f1 (2) show 2866 1031 moveto 384 /Times-Italic f1 (C) show 3111 1127 moveto 224 ns (s) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 2521 639 moveto 858 0 rlineto stroke 3747 496 moveto 384 ns (D) show 3979 594 moveto 224 /Times-Roman f1 (1050) show 4427 594 moveto 224 /Times-Roman f1 (\312) show 4501 594 moveto 224 /Times-Italic f1 (C) show 4665 496 moveto 384 ns (t) show 4774 592 moveto 224 /Times-Roman f1 (2) show 3812 1031 moveto 384 /Times-Italic f1 (D) show 4062 1129 moveto 224 /Times-Roman f1 (950) show 4398 1129 moveto 224 /Times-Roman f1 (\312) show 4472 1129 moveto 224 /Times-Italic f1 (C) show 4636 1031 moveto 384 ns (t) show 4727 1127 moveto 224 /Times-Roman f1 (1) show 3705 639 moveto 1239 0 rlineto stroke /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 1533 1011 384 3443 1166 16 sqr 2322 435 moveto 384 /Symbol f1 (\346) show 2322 1086 moveto (\350) show 2322 867 moveto (\347) show 4988 435 moveto (\366) show 4988 1086 moveto (\370) show 4988 867 moveto (\367) show 4453 1230 384 739 1230 16 sqr end dMATH" x j = -4Dt 2 lnC sub p2C s  D 1050C t 2 D 950C t 1 () exFMicrosoft Equation 3.01ELO Equation.3 x j = -4Dt 2 lnC sub p2C s  D 1050C t 2 D 950C t 1 ()  EquationOle10NativecOle10FmtProgID g _1009741271FkbkbOle hTf3 $@FMicrosoft Equation 3.01ELO Equation.3 x j = -45.15PIC iTPICT 7 CompObjkRObjInfom Pudxpr  Pu"Pu currentpoint ",Times .+x +j, Symbol (=)-)4) ) 5).)15))10 (d-)14 + ) 60)) 60)) ln(1).)5))10 ( 16 + ) p(!2) )1).)8))10 (20"@ ((5).)15))10 ( ;-)14 + )3600(!4).)32))10 (=-)15 + )1800"\"# "" #^.(  * ( (m * (m "#"'!r.(: ) =) 6).)54)) 10 (4D-)5 + cm(L ) =) 0).)654) )m)m30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 11936 div 2560 3 -1 roll exch div scale currentpoint translate 64 37 translate 11 754 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (x) show 217 850 moveto 224 ns (j) show 421 754 moveto 384 /Symbol f1 (=) show 997 754 moveto (-) show 1207 754 moveto 384 /Times-Roman f1 (4) show 1478 754 moveto 384 /Symbol f1 (\264) show 1766 754 moveto 384 /Times-Roman f1 (5) show 1940 754 moveto 384 /Times-Roman f1 (.) show 2032 754 moveto 384 /Times-Roman f1 (15) show 2482 754 moveto 384 /Symbol f1 (\264) show 2740 754 moveto 384 /Times-Roman f1 (10) show 3144 583 moveto 224 /Symbol f1 (-) show 3266 583 moveto 224 /Times-Roman f1 (14) show 3605 754 moveto 384 /Symbol f1 (\264) show 3892 754 moveto 384 /Times-Roman f1 (60) show 4356 754 moveto 384 /Symbol f1 (\264) show 4643 754 moveto 384 /Times-Roman f1 (60) show 5107 754 moveto 384 /Symbol f1 (\264) show 5400 754 moveto 384 /Times-Roman f1 (ln) show 5900 515 moveto 384 /Times-Roman f1 (1) show 6057 515 moveto 384 /Times-Roman f1 (.) show 6179 515 moveto 384 /Times-Roman f1 (5) show 6437 515 moveto 384 /Symbol f1 (\264) show 6695 515 moveto 384 /Times-Roman f1 (10) show 7077 344 moveto 224 ns (16) show 7415 515 moveto 384 /Symbol f1 (\264) show 7712 515 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show 5951 1047 moveto 384 /Times-Roman f1 (2) show 6223 1047 moveto 384 /Symbol f1 (\264) show 6481 1047 moveto 384 /Times-Roman f1 (1) show 6638 1047 moveto 384 /Times-Roman f1 (.) show 6752 1047 moveto 384 /Times-Roman f1 (8) show 7011 1047 moveto 384 /Symbol f1 (\264) show 7269 1047 moveto 384 /Times-Roman f1 (10) show 7669 876 moveto 224 ns (20) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 5910 655 moveto 2061 0 rlineto stroke 8061 754 moveto 384 /Symbol f1 (\264) show 8657 515 moveto 384 /Times-Roman f1 (5) show 8831 515 moveto 384 /Times-Roman f1 (.) show 8923 515 moveto 384 /Times-Roman f1 (15) show 9373 515 moveto 384 /Symbol f1 (\264) show 9631 515 moveto 384 /Times-Roman f1 (10) show 10035 344 moveto 224 /Symbol f1 (-) show 10157 344 moveto 224 /Times-Roman f1 (14) show 10496 515 moveto 384 /Symbol f1 (\264) show 10780 515 moveto 384 /Times-Roman f1 (3600) show 8651 1047 moveto (4) show 8838 1047 moveto 384 /Times-Roman f1 (.) show 8956 1047 moveto 384 /Times-Roman f1 (32) show 9420 1047 moveto 384 /Symbol f1 (\264) show 9678 1047 moveto 384 /Times-Roman f1 (10) show 10082 876 moveto 224 /Symbol f1 (-) show 10204 876 moveto 224 /Times-Roman f1 (15) show 10536 1047 moveto 384 /Symbol f1 (\264) show 10794 1047 moveto 384 /Times-Roman f1 (1800) show 8623 655 moveto 2961 0 rlineto stroke /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 3255 972 384 8361 1084 16 sqr 5711 435 moveto 384 /Symbol f1 (\346) show 5711 1118 moveto (\350) show 5711 886 moveto (\347) show 11628 435 moveto (\366) show 11628 1118 moveto (\370) show 11628 886 moveto (\367) show 11093 1262 384 739 1262 16 sqr 0 1819 moveto 384 /Times-Roman f1 ( ) show 396 1819 moveto 384 /Symbol f1 (=) show 701 1819 moveto 384 /Times-Roman f1 (6) show 886 1819 moveto 384 /Times-Roman f1 (.) show 1008 1819 moveto 384 /Times-Roman f1 (54) show 1471 1819 moveto 384 /Symbol f1 (\264) show 1729 1819 moveto 384 /Times-Roman f1 (10) show 2133 1648 moveto 224 /Symbol f1 (-) show 2255 1648 moveto 224 /Times-Roman f1 (5) show 2417 1819 moveto 384 /Times-Roman f1 ( cm) show 0 2398 moveto ( ) show 396 2398 moveto 384 /Symbol f1 (=) show 705 2398 moveto 384 /Times-Roman f1 (0) show 893 2398 moveto 384 /Times-Roman f1 (.) show 1014 2398 moveto 384 /Times-Roman f1 (654) show 1611 2398 moveto 384 /Times-Roman f1 ( ) show 1707 2398 moveto 384 /Symbol f2 (m) show 1940 2398 moveto 384 /Times-Roman f1 (m) show end dMATHX x j = -45.1510 -14 6060ln1.510 16 p21.810 20  5.1510 -14 36004.3210 -15 1800  ()     =6.5410 -5  cm   =0.654 mmhoOlePres000n(Ole10NativeoOle10FmtProgID w _1009741270 Fkbkb10 -14 6060ln1.510 16 p21.810 20  5.1510 -14 36004.3210 -15 1800  ()     =6.5410 -5  cm   =0.654 mm EquationOle xPIC yTPICT { CompObjRT_  'dxpr  '"' currentpoint ",Times .+ C)()x),)0)), Symbol)=) C +0 ( ?=) 2).)02) g) /)cm (|3 + for )x) <) 0("C)()0),)t)))=) C +s (";=) 0)g)/)cm (i3 + for )x)>) 030 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5600 div 1248 3 -1 roll exch div scale currentpoint translate 64 58 translate -12 363 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 252 363 moveto 384 /Times-Roman f1 (\() show 411 363 moveto 384 /Times-Italic f1 (x) show 591 363 moveto 384 /Times-Roman f1 (,) show 723 363 moveto 384 /Times-Roman f1 (0) show 926 363 moveto 384 /Times-Roman f1 (\)) show 1143 363 moveto 384 /Symbol f1 (=) show 1449 363 moveto 384 /Times-Italic f1 (C) show 1691 459 moveto 288 /Times-Roman f1 (0) show 1968 363 moveto 384 /Symbol f1 (=) show 2275 363 moveto 384 /Times-Roman f1 (2) show 2463 363 moveto 384 /Times-Roman f1 (.) show 2588 363 moveto 384 /Times-Roman f1 (02) show 2991 363 moveto 384 /Times-Italic f1 (g) show 3271 363 moveto 384 /Times-Roman f1 (/) show 3470 363 moveto 384 /Times-Italic f1 (cm) show 3928 195 moveto 288 /Times-Roman f1 (3) show 4084 363 moveto 384 /Times-Roman f1 ( for ) show 4722 363 moveto 384 /Times-Italic f1 (x) show 4997 363 moveto 384 /Symbol f1 (<) show 5300 363 moveto 384 /Times-Roman f1 (0) show -12 1058 moveto 384 /Times-Italic f1 (C) show 252 1058 moveto 384 /Times-Roman f1 (\() show 391 1058 moveto 384 /Times-Roman f1 (0) show 581 1058 moveto 384 /Times-Roman f1 (,) show 708 1058 moveto 384 /Times-Italic f1 (t) show 839 1058 moveto 384 /Times-Roman f1 (\)) show 1056 1058 moveto 384 /Symbol f1 (=) show 1362 1058 moveto 384 /Times-Italic f1 (C) show 1606 1154 moveto 288 ns (s) show 1851 1058 moveto 384 /Symbol f1 (=) show 2160 1058 moveto 384 /Times-Roman f1 (0) show 2371 1058 moveto 384 /Times-Italic f1 (g) show 2651 1058 moveto 384 /Times-Roman f1 (/) show 2850 1058 moveto 384 /Times-Italic f1 (cm) show 3308 890 moveto 288 /Times-Roman f1 (3) show 3464 1058 moveto 384 /Times-Roman f1 ( for ) show 4102 1058 moveto 384 /Times-Italic f1 (x) show 4377 1058 moveto 384 /Symbol f1 (>) show 4680 1058 moveto !384 /Times-Roman f1 (0) show end dMATH*| C(x,0)=C 0 =2.02g/cm 3  for x<0C(0,t)=C s =0g/cm 3  for x>0seFMicrosoft Equation 3.01ELO Equation.3ObjInfoOlePres000(Ole10NativeOle10FmtProgID   C(x,0)=C 0 =2.02g/cm 3  for x<0C(0,t)=C s =0g/cm 3  for x>0 Equation_1009741269FkbkbOle PIC TPICT NT h< N dxpr  " currentpoint ",Times .+C) x),)t, Symbol ( ()))=) A) +) Berf( jx(^2)Dt"e#"i# "^.( W * ( | *  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4192 div 1024 3 -1 roll exch div scale currentpoint translate 64 50 translate -12 558 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 558 moveto (x) show 588 558 moveto 384 /Times-Roman f1 (,) show 715 558 moveto 384 /Times-Italic f1 (t) show 250 568 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 846 568 moveto (\)) show 1060 558 moveto 384 /Symbol f1 (=) show 1395 558 moveto 384 /Times-Italic f1 (A) show 1704 558 moveto 384 /Symbol f1 (+) show 2016 558 moveto 384 /Times-Italic f1 (Berf) show 3343 319 moveto (x) show 2965 851 moveto 384 /Times-Roman f1 (2) show 3451 851 moveto 384 /Times-Italic f1 (Dt) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 691 376 384 3179 886 16 sqr /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 2944 459 moveto 958 0 rlineto stroke 2745 355 moveto 384 /Symbol f1 (\346) show 2745 806 moveto (\350) show 2745 587 moveto (\347) show 3914 355 moveto (\366) show 3914 806 moveto (\370) show 3914 587 moveto (\367) show end doMATHc Cx,t()=A+Berfx2 Dt  () tFMicrosoft Equation 3.01ELO Equation.3CompObjRObjInfoOlePres000(Ole10Nativegc Cx,t()=A+Berfx2 Dt  () EquationTI4 ,hdxpr  " currentpoint ",Times .+ C) 0Ole10FmtProgID  _1009741267 FkbkbOle PIC   TPICT hCompObj RObjInfoOlePres000(),)t, Symbol ( ()))=) A) +) B) ) 0) =) 0) ) ) )A) =) 030 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5408 div 480 3 -1 roll exch div scale currentpoint translate 64 60 translate -12 292 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 388 292 moveto 384 /Times-Roman f1 (0) show 578 292 moveto 384 /Times-Roman f1 (,) show 705 292 moveto 384 /Times-Italic f1 (t) show 250 302 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 836 302 moveto (\)) show 1050 292 moveto 384 /Symbol f1 (=) show 1385 292 moveto 384 /Times-Italic f1 (A) show 1694 292 moveto 384 /Symbol f1 (+) show 2006 292 moveto 384 /Times-Italic f1 (B) show 2311 292 moveto 384 /Symbol f1 (\264) show 2602 292 moveto 384 /Times-Roman f1 (0) show 2892 292 moveto 384 /Symbol f1 (=) show 3201 292 moveto 384 /Times-Roman f1 (0) show 3415 292 moveto 384 /Times-Roman f1 ( ) show 3798 292 moveto 384 /Symbol f1 (\336) show 4276 292 moveto 384 /Times-Roman f1 ( ) show 4468 292 moveto 384 /Times-Italic f1 (A) show 4792 292 moveto 384 /Symbol f1 (=) show 5101 292 moveto 384 /Times-Roman f1 (0) show end daMATHUd C0,t()=A+B0=0     A=0 cFMicrosoft Equation 3.01ELO Equation.3U C0,t()=A+B0=0     A=0 EquationOle10NativeYOle10FmtProgID  _1009741266FbbOle PIC TPICT CompObj"RObjInfo$      !#'(,./0123456789:;<=>?@ABCDEFGHIJKLMNPTXZ[\^_`abcdefghijklmnopqrtx|~T 4@dxpr  " currentpoint ",Times .+ C, Symbol) -)),)t ( ()))=) A) +) B) )()-)1)))=) C +0 (  )) )B) =) -)C +030 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 6976 div 512 3 -1 roll exch div scale currentpoint translate 64 60 translate -12 292 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 393 292 moveto 384 /Symbol f1 (-) show 621 292 moveto (\245) show 893 292 moveto 384 /Times-Roman f1 (,) show 1020 292 moveto 384 /Times-Italic f1 (t) show 250 302 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 1151 302 moveto (\)) show 1365 292 moveto 384 /Symbol f1 (=) show 1700 292 moveto 384 /Times-Italic f1 (A) show 2009 292 moveto 384 /Symbol f1 (+) show 2321 292 moveto 384 /Times-Italic f1 (B) show 2626 292 moveto 384 /Symbol f1 (\264) show 2908 292 moveto 384 /Times-Roman f1 (\() show 3052 292 moveto 384 /Symbol f1 (-) show 3262 292 moveto 384 /Times-Roman f1 (1) show 3434 292 moveto 384 /Times-Roman f1 (\)) show 3651 292 moveto 384 /Symbol f1 (=) show 3957 292 moveto 384 /Times-Italic f1 (C) show 4199 388 moveto 288 /Times-Roman f1 (0) show 4368 292 moveto 384 /Times-Roman f1 ( ) show 4943 292 moveto 384 /Symbol f1 (\336) show 5421 292 moveto 384 /Times-Roman f1 ( ) show 5613 292 moveto 384 /Times-Italic f1 (B) show 5936 292 moveto 384 /Symbol f1 (=) show 6250 292 moveto (-) show 6475 292 moveto 384 /Times-Italic f1 (C) show 6717 388 moveto 288 /Times-Roman f1 (0) show end dMATH C-,t()=A+B(-1)=C 0        B=-C 02 FMicrosoft Equation 3.01ELO Equation.3 C-,t()=A+B(-1)=C 0        B=-C OlePres000%(Ole10Native&Ole10FmtProgID ) _1009741265cFbb0 EquationTh | {dxpr  {" { currentpoint ",Times .+C) x),)t, Symbol ( ()))=) -Ole *PIC +TPICT -|CompObj!OR)C +0 (@erf( bx(V2)Dt"#"a#"V.( O * ( t *  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3936 div 1024 3 -1 roll exch div scale currentpoint translate 64 50 translate -12 558 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (C) show 408 558 moveto (x) show 588 558 moveto 384 /Times-Roman f1 (,) show 715 558 moveto 384 /Times-Italic f1 (t) show 250 568 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 846 568 moveto (\)) show 1060 558 moveto 384 /Symbol f1 (=) show 1374 558 moveto (-) show 1599 558 moveto 384 /Times-Italic f1 (C) show 1841 654 moveto 288 /Times-Roman f1 (0) show 1997 558 moveto 384 /Times-Italic f1 (erf) show 3090 319 moveto (x) show 2712 851 moveto 384 /Times-Roman f1 (2) show 3198 851 moveto 384 /Times-Italic f1 (Dt) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 691 376 384 2926 886 16 sqr /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 2691 459 moveto 958 0 rlineto stroke 2492 355 moveto 384 /Symbol f1 (\346) show 2492 806 moveto (\350) show 2492 587 moveto (\347) show 3661 355 moveto (\366) show 3661 806 moveto (\370) show 3661 587 moveto (\367) show end dyMATHm Cx,t()=-C 0 erfx2 Dt  () 6FMicrosoft Equation 3.01ELO Equation.3m Cx,t()=-C 0 erfx2 Dt  () EquationTpObjInfoQOlePres000 "R(Ole10Native#SqOle10FmtProgID U _1009741263(FbbOle VPIC %'WTPICT Yuu!ldxpr  !l"!l currentpoint ",Times .+J" +x, Symbol)=)0 (=) -)D( 6dC)x),)t ( D())(Bdx"5%"\ +x)=)030 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3456 div 1056 3 -1 roll exch div scale currentpoint translate 64 45 translate 13 563 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (J) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 236 270 moveto 0 388 rlineto stroke 282 677 moveto 224 ns (x) show 412 677 moveto 224 /Symbol f1 (=) show 559 677 moveto 224 /Times-Roman f1 (0) show 805 563 moveto 384 /Symbol f1 (=) show 1119 563 moveto (-) show 1366 563 moveto 384 /Times-Italic f1 (D) show 1682 324 moveto (dC) show 2294 324 moveto (x) show 2474 324 moveto 384 /Times-Roman f1 (,) show 2601 324 moveto 384 /Times-Italic f1 (t) show 2136 334 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 2732 334 moveto (\)) show 2078 856 moveto 384 /Times-Italic f1 (dx) show 1655 464 moveto 1215 0 rlineto stroke 2910 0 moveto 0 928 rlineto stroke 2956 947 moveto 224 ns (x) show 3086 947 moveto 224 /Symbol f1 (=) show 3233 947 moveto 224 /Times-Roman f1 (0) show end dMATHy Jb x=0 =-DdCx,t()dxb x=0laFMicrosoft Equation 3.01ELO Equation.3y Jb x=0 =-DCompObj&*sRObjInfouOlePres000)+v(Ole10Native,w}dCx,t()dxb x=0 EquationT !dxpr  !"! currentpoint ",Times .+J" +x, Symbol)=)0 (=) -Ole10FmtProgID y _10097412626$1FbbOle zPIC .0{TPICT } CompObj/3RObjInfoOlePres00024()D)-)C +0 ( Y2+p"T#"X#"S( s1(h2)Dt"o#"s# "g.( 8 * (  * .(=) C +0 ( D(p)t" "# "# 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 6016 div 1056 3 -1 roll exch div scale currentpoint translate 64 60 translate 13 580 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (J) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 236 287 moveto 0 388 rlineto stroke 284 711 moveto 288 ns (x) show 442 711 moveto 288 /Symbol f1 (=) show 622 711 moveto 288 /Times-Roman f1 (0) show 899 580 moveto 384 /Symbol f1 (=) show 1213 580 moveto (-) show 1460 580 moveto 384 /Times-Italic f1 (D) show 1907 580 moveto 384 /Symbol f1 (-) show 2132 580 moveto 384 /Times-Italic f1 (C) show 2374 676 moveto 288 /Times-Roman f1 (0) show 2802 341 moveto 384 ns (2) show 2898 873 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 518 380 384 2639 912 16 sqr 2607 481 moveto 582 0 rlineto stroke 3636 341 moveto 384 /Times-Roman f1 (1) show 3274 873 moveto (2) show 3760 873 moveto 384 /Times-Italic f1 (Dt) show 691 376 384 3488 908 16 sqr 3253 481 moveto 958 0 rlineto stroke 1749 373 moveto 384 /Symbol f1 (\351) show 1749 914 moveto (\353) show 1749 742 moveto (\352) show 4236 373 moveto (\371) show 4236 914 moveto (\373) show 4236 742 moveto (\372) show 4482 580 moveto (=) show 4788 580 moveto 384 /Times-Italic f1 (C) show 5030 676 moveto 288 /Times-Roman f1 (0) show 5566 341 moveto 384 /Times-Italic f1 (D) show 5522 873 moveto 384 /Symbol f2 (p) show 5744 873 moveto 384 /Times-Italic f1 N(t) show 5493 481 moveto 393 0 rlineto stroke 687 912 384 5231 912 16 sqr end dMATH Jb x=0 =-D-C 0 2 p  12 Dt  [=C 0  Dpt  mFMicrosoft Equation 3.01ELO Equation.3 Jb x=0 =-D-C 0 2 p  12 Dt Ole10Native5Ole10FmtProgID  _1009741260:FbbOle  [=C 0  Dpt  EquationTS d x Fdxpr  F"F currentpoint ",Times .+W, Symbol)=)J" ' +x)=)0 hjt,.1ce#VX4gix24\3fhx ! !{!!!U"""&#X#Z#####$$[$$$$% %>%q%s%%%%S&&&&&&G'y'{''''''(g))))))*A*C*T******+G+I+e+++PIC 79TPICT  CompObj8<RObjInfo (9dt) =)C +0( P0(Ot +1 (Q ( 0(t +1 (( nD(mp)t"l "d# "h# (ydt(9 )=) 2)C +0 (28D +Zn (2Jt +1 (BAp"67"9/# "C3#30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4256 div 2240 3 -1 roll exch div scale currentpoint translate 64 54 translate -13 594 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (W) show 431 594 moveto 384 /Symbol f1 (=) show 972 594 moveto 384 /Times-Italic f1 (J) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1195 301 moveto 0 388 rlineto stroke 1243 725 moveto 288 ns (x) show 1401 725 moveto 288 /Symbol f1 (=) show 1581 725 moveto 288 /Times-Roman f1 (0) show 1777 594 moveto 384 /Times-Italic f1 (dt) show 2187 594 moveto 384 /Symbol f1 (=) show 2703 594 moveto 384 /Times-Italic f1 (C) show 2945 690 moveto 288 /Times-Roman f1 (0) show 2524 979 moveto (0) show 2495 195 moveto 288 /Times-Italic f1 (t) show 2565 267 moveto 224 /Times-Roman f1 (1) show 2540 650 moveto 384 /Symbol f1 (\362) show 768 979 moveto 288 /Times-Roman f1 (0) show 739 195 moveto 288 /Times-Italic f1 (t) show 809 267 moveto 224 /Times-Roman f1 (1) show 784 650 moveto 384 /Symbol f1 (\362) show 3481 355 moveto 384 /Times-Italic f1 (D) show 3437 887 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show 3659 887 moveto 384 /Times-Italic f1 (t) show 3408 495 moveto 393 0 rlineto stroke /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 687 912 384 3146 926 16 sqr 3828 594 moveto (dt) show 0 1795 moveto 384 /Times-Roman f1 ( ) show 492 1795 moveto 384 /Symbol f1 (=) show 799 1795 moveto 384 /Times-Roman f1 (2) show 1001 1795 moveto 384 /Times-Italic f1 (C) show 1243 1891 moveto 288 /Times-Roman f1 (0) show 1748 1556 moveto 384 /Times-Italic f1 (D) show 2009 1652 moveto 288 ns (Zn) show 2322 1556 moveto 384 ns (t) show 2406 1652 moveto 288 /Times-Roman f1 (1) show 2029 2088 moveto 384 /Symbol f2 (p) show 1706 1696 moveto 877 0 rlineto stroke 1171 912 384 1444 2127 16 sqr end dMATH $ W=Jb x=0 dt=C 00t 1  0t 1   Dpt  dt    =2C 0  D Zn t 1 p 06FMicrosoft Equation 3.01ELO Equation.3  W=Jb x=0 dt=C 00t 1  0t 1   Dpt  dt    =2C 0  D Zn t 1OlePres000;=(Ole10Native>Ole10FmtProgID  _1009741259Q-CFbb p  EquationTl dxpr  " currentpoint ",Times .*10, Symbol ( -)6 + cm (())Ole PIC @BTPICT  CompObjAER     !"#')*+,-./013:<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\^_`abcdfjklprstuvwxyz{|}~)) r +ZnS (Tg) cm (n3"^   (O()%)(z) M + Zn (g (() )) M + ZnS (g (() )"  (()W)30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 7136 div 704 3 -1 roll exch div scale currentpoint translate 64 54 translate -42 394 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (10) show 361 226 moveto 288 /Symbol f1 (-) show 519 226 moveto 288 /Times-Roman f1 (6) show 832 394 moveto 384 /Times-Italic f1 (cm) show 697 404 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() show 1291 404 moveto (\)) show 1487 394 moveto 384 /Symbol f1 (\264) show 1768 394 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 1997 490 moveto 288 /Times-Italic f1 (ZnS) show 2628 394 moveto 384 ns (g) show 3014 394 moveto (cm) show 3472 226 moveto 288 /Times-Roman f1 (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th /stb { newpath moveto 0 setlinewidth 2 copy rlineto } def /enb { rlineto neg exch neg exch rlineto closepath fill } def /hb { stb 0 thick enb } def /vb { stb thick 0 enb } def -142 446 2980 31 vb 2484 460 moveto 384 1000 1786 /Symbol f3 (\() show 3649 460 moveto (\)) show 3845 394 moveto 384 /Symbol f1 (\264) show 4281 394 moveto 384 /Times-Italic f1 (M) show 4611 490 moveto 288 ns (Zn) show 5094 394 moveto 384 ns (g) show 4950 413 moveto 384 1000 1273 /Symbol f3 (\() show 5295 413 moveto (\)) show 5621 394 moveto 384 /Times-Italic f1 (M) show 5951 490 moveto 288 ns (ZnS) show 6582 394 moveto 384 ns (g) show 6438 413 moveto 384 1000 1273 /Symbol f3 (\() show 6783 413 moveto (\)) show 16 th -135 420 5566 85 vb 4125 430 moveto 384 1000 1460 /Symbol f3 (\() show 6910 430 moveto (\)) show end dMATH  10 -6 cm()r ZnS )gcm 3 ())M Zn g()M ZnS g()()efFMicrosoft Equation 3.01ELO Equation.3ObjInfoOlePres000DF(Ole10NativeG Ole10FmtProgID $  10 -6 cm()r ZnS )gcm 3 ())M Zn g()M ZnS g()() EquationTN,_1009741258LFbbOle %PIC IK&TPICT (zzdxpr  " currentpoint ", Symbol .+ r,Times +ZnS30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 768 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate -19 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 210 357 moveto 288 /Times-Italic f1 (ZnS) show end d*MATH r ZnS nFMicrosoft Equation 3.01ELO Equation.3 r ZnS EquationCompObjJN2RObjInfo4OlePres000MO5(Ole10NativeP6"Ole10FmtProgID 7 _1009741256ZHUFbG5bOle 8PIC RT9TT A$dxpr  $"$ currentpoint ",Times .+W, Symbol)=) 2)C +0 ( 6D +Zn ( Ht +1 (?p"5"-# "1#(U=)10 (j-)6 +r PICT ;A CompObjSWeRObjInfogOlePres000VXh(+ZnS ( M + Zn (M + ZnS" .(  * ( (  * ( 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5760 div 1152 3 -1 roll exch div scale currentpoint translate 64 47 translate -13 625 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (W) show 431 625 moveto 384 /Symbol f1 (=) show 738 625 moveto 384 /Times-Roman f1 (2) show 940 625 moveto 384 /Times-Italic f1 (C) show 1182 721 moveto 288 /Times-Roman f1 (0) show 1687 386 moveto 384 /Times-Italic f1 (D) show 1948 482 moveto 288 ns (Zn) show 2261 386 moveto 384 ns (t) show 2345 482 moveto 288 /Times-Roman f1 (1) show 1968 918 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1645 526 moveto 877 0 rlineto stroke /sqr { 3 index div /thick exch def gsave translate dup dup neg scale dup 4 -1 roll exch div 3 1 roll div 0 setlinewidth newpath 0 0 moveto dup .395 mul 0 exch lineto .375 .214 rlineto dup thick add dup .375 exch lineto 2 index exch lineto dup thick 2 div sub dup 3 index exch lineto .6 exch lineto .375 0 lineto clip thick setlinewidth newpath dup .395 mul 0 exch moveto .15 .085 rlineto .375 0 lineto thick 2 div sub dup .6 exch lineto lineto stroke grestore } def 1171 912 384 1383 957 16 sqr 2662 625 moveto 384 /Symbol f1 (=) show 2938 625 moveto 384 /Times-Roman f1 (10) show 3341 457 moveto 288 /Symbol f1 (-) show 3499 457 moveto 288 /Times-Roman f1 (6) show 3678 625 moveto 384 /Symbol f2 (r) show 3907 721 moveto 288 /Times-Italic f1 (ZnS) show 4713 386 moveto 384 ns (M) show 5043 482 moveto 288 ns (Zn) show 4639 918 moveto 384 ns (M) show 4969 1014 moveto 288 ns (ZnS) show 4598 526 moveto 878 0 rlineto stroke 4399 355 moveto 384 /Symbol f1 (\346) show 4399 940 moveto (\350) show 4399 721 moveto (\347) show 5488 355 moveto (\366) show 5488 940 moveto (\370) show 5488 721 moveto (\367) show end dMATH W=2C 0  D Zn t 1 p  =10 -6 r ZnS M Zn M ZnS ()keFMicrosoft Equation 3.01ELO Equation.3 W=2C 0  D Zn t 1 p  =10 -6 r ZnS M Zn M ZnS () EquationT9_ Ole10NativeYiOle10FmtProgID m _1009741255^FG5bG5bOle nPIC [oTPICT q,CompObj\`RObjInfo,'}dxpr  '}"'} currentpoint ",Times .+t +1, Symbol ( =(p(!D +Zn" (210 ( >-)6 +r +Zn (ZM + Zn (!;2)C +0 (!NM + ZnS"2= .(, * (, (p * (p  .(v230 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4000 div 1248 3 -1 roll exch div scale currentpoint translate 64 50 translate -14 718 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (t) show 70 814 moveto 288 /Times-Roman f1 (1) show 323 718 moveto 384 /Symbol f1 (=) show 857 479 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show 683 1011 moveto 384 /Times-Italic f1 (D) show 944 1107 moveto 288 ns (Zn) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 641 619 moveto 662 0 rlineto stroke 1541 479 moveto 384 /Times-Roman f1 (10) show 1944 311 moveto 288 /Symbol f1 (-) show 2102 311 moveto 288 /Times-Roman f1 (6) show 2281 479 moveto 384 /Symbol f2 (r) show 2510 575 moveto 288 /Times-Italic f1 (Zn) show 2846 479 moveto 384 ns (M) show 3176 575 moveto 288 ns (Zn) show 1824 1011 moveto 384 /Times-Roman f1 (2) show 2026 1011 moveto 384 /Times-Italic f1 (C) show 2268 1107 moveto 288 /Times-Roman f1 (0) show 2446 1011 moveto 384 /Times-Italic f1 (M) show 2776 1107 moveto 288 ns (ZnS) show 1551 619 moveto 1984 0 rlineto stroke 1352 438 moveto 384 /Symbol f1 (\346) show 1352 1043 moveto (\350) show 1352 824 moveto (\347) show 3547 438 moveto (\366) show 3547 1043 moveto (\370) show 3547 824 moveto (\367) show 3743 195 moveto 288 /Times-Roman f1 (2) show end dMATH7 t 1 =pD Zn 10 -6 r Zn M Zn 2C 0 M ZnS () 2caFMicrosoft Equation 3.01ELO Equation.3 t 1 =pD Zn 10 -6 r Zn M ZnOlePres000_a(Ole10NativebOle10FmtProgID  _1009741253?gFG5bG5b 2C 0 M ZnS () 2 EquationT&w$dxpr  $"$ currentpoint ", Symbol .+& p,Ole PIC dfTPICT wCompObjeiRTimes(8))10 (-)13 + cm (<2 +s (F-)1"N ( 10 (i-)6 +cm)) 4).)09) gcm (-)3 +) 65) .)4)gmol (-)1 (Y2) ) 2).)02) gcm (-)3 +) 65) .)4)+) 32) .)1 (()9))gmol (-)1 Y  .( R * (R (   * (  30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 8832 div 1152 3 -1 roll exch div scale currentpoint translate 64 37 translate 1154 396 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) show 12 939 moveto 384 /Times-Roman f1 (8) show 271 939 moveto 384 /Symbol f1 (\264) show 529 939 moveto 384 /Times-Roman f1 (10) show 932 771 moveto 288 /Symbol f1 (-) show 1090 771 moveto 288 /Times-Roman f1 (13) show 1410 939 moveto 384 /Times-Italic f1 (cm) show 1872 771 moveto 288 /Times-Roman f1 (2) show 2034 939 moveto 384 /Times-Italic f1 (s) show 2203 771 moveto 288 /Symbol f1 (-) show 2361 771 moveto 288 /Times-Roman f1 (1) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 536 moveto 2538 0 rlineto stroke 2918 396 moveto 384 ns (10) show 3321 228 moveto 288 /Symbol f1 (-) show 3479 228 moveto 288 /Times-Roman f1 (6) show 3665 396 moveto 384 /Times-Italic f1 (cm) show 4193 396 moveto 384 /Symbol f1 (\264) show 4489 396 moveto 384 /Times-Roman f1 (4) show 4676 396 moveto 384 /Times-Roman f1 (.) show 4801 396 moveto 384 /Times-Roman f1 (09) show 5198 396 moveto 384 /Times-Italic f1 (gcm) show 5857 228 moveto 288 /Symbol f1 (-) show 6015 228 moveto 288 /Times-Roman f1 (3) show 6261 396 moveto 384 /Symbol f1 (\264) show 6548 396 moveto 384 /Times-Roman f1 (65) show 6914 396 moveto 384 /Times-Roman f1 (.) show 7044 396 moveto 384 /Times-Roman f1 (4) show 7254 396 moveto 384 /Times-Italic f1 (gmol) show 8049 228 moveto 288 /Symbol f1 (-) show 8207 228 moveto 288 /Times-Roman f1 (1) show 2807 939 moveto 384 ns (2) show 3079 939 moveto 384 /Symbol f1 (\264) show 3368 939 moveto 384 /Times-Roman f1 (2) show 3556 939 moveto 384 /Times-Roman f1 (.) show 3681 939 moveto 384 /Times-Roman f1 (02) show 4084 939 moveto 384 /Times-Italic f1 (gcm) show 4743 771 moveto 288 /Symbol f1 (-) show 4901 771 moveto 288 /Times-Roman f1 (3) show 5147 939 moveto 384 /Symbol f1 (\264) show 5561 939 moveto 384 /Times-Roman f1 (65) show 5927 939 moveto 384 /Times-Roman f1 (.) show 6057 939 moveto 384 /Times-Roman f1 (4) show 6331 939 moveto 384 /Symbol f1 (+) show 6617 939 moveto 384 /Times-Roman f1 (32) show 6997 939 moveto 384 /Times-Roman f1 (.) show 7089 939 moveto 384 /Times-Roman f1 (1) show 5427 951 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1190 /Symbol f3 (\() show 7261 951 moveto (\)) show 7396 939 moveto 384 /Times-Italic f1 (gmol) show 8191 771 moveto 288 /Symbol f1 (-) show 8349 771 moveto 288 /Times-Roman f1 (1) show 2786 536 moveto 5740 0 rlineto stroke 2587 355 moveto 384 /Symbol f1 (\346) show 2587 960 moveto (\350) show 2587 741 moveto (\347) show 8538 355 moveto (\366) show 8538 960 moveto (\370) show 8538 741 moveto (\367) show end dMATHQ>[ p810 -13 cm 2 s -1 10 -6 cm4.09gcm -3 65.4gmol -1 22.02gcm -3 65.4+32.1()gmol -1 ()omFMicrosoft Equation 3.01ELO Equation.3ObjInfoOlePres000hj(Ole10NativekUOle10FmtProgID  Q p810 -13 cm 2 s -1 10 -6 cm4.09gcm -3 65.4gmol -1 22.02gcm -3 65.4+32.1()gmol -1 () Equation_1009741252pFG5bG5bOle PIC moTPICT Tx4Didxpr  i"i currentpoint ",Times .+J, Symbol) =) -)D( ')C())x"'(:=) -)D( VD)C(XD)x"VF30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3360 div 928 3 -1 roll exch div scale current    !"#$%&'(*./356789:;<=>?@ABCEIMOPQRSTUVWXYZ[\^_`abceijnpqrstuvwxyz{|}~point translate 64 51 translate 13 525 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (J) show 304 525 moveto 384 /Symbol f1 (=) show 618 525 moveto (-) show 865 525 moveto 384 /Times-Italic f1 (D) show 1209 286 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (\266) show 1417 286 moveto 384 /Times-Italic f1 (C) show 1248 818 moveto 384 /Symbol f2 (\266) show 1456 818 moveto 384 /Times-Italic f1 (x) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1186 426 moveto 513 0 rlineto stroke 1807 525 moveto 384 /Symbol f1 (=) show 2121 525 moveto (-) show 2368 525 moveto 384 /Times-Italic f1 (D) show 2719 286 moveto 384 /Symbol f1 (D) show 2954 286 moveto 384 /Times-Italic f1 (C) show 2758 818 moveto 384 /Symbol f1 (D) show 2993 818 moveto 384 /Times-Italic f1 (x) show 2689 426 moveto 547 0 rlineto stroke end dTMATHH  J=-DCx=-DDCDxxcFMicrosoft Equation 3.01ELO Equation.3H J=-DCx=-DDCDx EquationCompObjnrRObjInfoOlePres000qs(Ole10NativetLOle10FmtProgID  _1009741251~lyFbbOle PIC vx TT"8X{dxpr  " currentpoint ", Symbol .+=) -,Times)D +Zn( ZnS ( .0)-) Zn ( ?[) +max (Fh"-7(i=) D +Zn( |ZnS ( ZnPICT  {CompObjw{)RObjInfo+OlePres000z|,( ( [) +max (h"&-30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5824 div 960 3 -1 roll exch div scale currentpoint translate 64 44 translate -4 564 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Symbol f1 (=) show 310 564 moveto (-) show 557 564 moveto 384 /Times-Italic f1 (D) show 818 660 moveto 288 ns (Zn) show 851 396 moveto (ZnS) show 1413 292 moveto 384 /Times-Roman f1 (0) show 1687 292 moveto 384 /Symbol f1 (-) show 2108 292 moveto 384 /Times-Italic f1 (Zn) show 1955 315 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1223 /Symbol f3 ([) show 2521 315 moveto (]) show 2644 423 moveto 288 /Times-Roman f1 (max) show 2199 857 moveto 384 /Times-Italic f1 (h) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1390 465 moveto 1806 0 rlineto stroke 3304 564 moveto 384 /Symbol f1 (=) show 3632 564 moveto 384 /Times-Italic f1 (D) show 3893 660 moveto 288 ns (Zn) show 3926 396 moveto (ZnS) show 4617 292 moveto 384 ns (Zn) show 4464 315 moveto 384 1000 1223 /Symbol f3 ([) show 5030 315 moveto (]) show 5153 423 moveto 288 /Times-Roman f1 (max) show 4991 857 moveto 384 /Times-Italic f1 (h) show 4465 465 moveto 1240 0 rlineto stroke end dMATH =-D ZnZnS 0-Zn[ max h=D ZnZnS Zn[ max hg FMicrosoft Equation 3.01ELO Equation.3 =-D ZnZnS 0-Zn[ max h=D ZnZnS Zn[ max hOle10Native}-Ole10FmtProgID 0 _1009741249FbbOle 1 EquationT!0;dxpr  ;"; currentpoint ",Times .+J, Symbol) =( dh+dt"  ($r +Zn( ,ZnS30 dict begin currentpoint 3 -1 roll sub neg 3PIC 2TPICT 4CompObjDRObjInfoF 1 roll sub 1888 div 896 3 -1 roll exch div scale currentpoint translate 64 43 translate 13 501 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (J) show 304 501 moveto 384 /Symbol f1 (=) show 649 262 moveto 384 /Times-Italic f1 (dh) show 685 794 moveto (dt) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 622 402 moveto 432 0 rlineto stroke 1099 501 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 1328 597 moveto 288 /Times-Italic f1 (Zn) show 1348 333 moveto (ZnS) show end dLMATH@  J=dhdtr ZnZnS1 FMicrosoft Equation 3.01ELO Equation.3OlePres000G(Ole10NativeHDOle10FmtProgID J _1009741248uFbb@ J=dhdtr ZnZnS EquationTxE4lwidxpr  i"i currentpoint ",Times .+D +Ole KPIC LTPICT NwCompObjdRZn( ZnS ( S +Zn(#max +h", Symbol(8=( Cdh+dt"B (Qr +Zn(YZnS30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3360 div 992 3 -1 roll exch div scale currentpoint translate 64 38 translate 10 602 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (D) show 271 698 moveto 288 ns (Zn) show 304 434 moveto (ZnS) show 872 363 moveto 384 ns (S) show 1060 459 moveto 288 ns (Zn) show 1086 195 moveto 288 /Times-Roman f1 (max) show 1146 895 moveto 384 /Times-Italic f1 (h) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 843 503 moveto 795 0 rlineto stroke 1746 602 moveto 384 /Symbol f1 (=) show 2091 363 moveto 384 /Times-Italic f1 (dh) show 2127 895 moveto (dt) show 2064 503 moveto 432 0 rlineto stroke 2541 602 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 2770 698 moveto 288 /Times-Italic f1 (Zn) show 2790 434 moveto (ZnS) show end dMATH D ZnZnS S Znmax h=dhdtr ZnZnS mFMicrosoft Equation 3.01ELO Equation.3ObjInfofOlePres000g(Ole10NativehOle10FmtProgID k  D ZnZnS S Znmax h=dhdtr ZnZnS EquationT l"_dxpr  "_""__1009741246FbbOle lPIC mTPICT o currentpoint ",Times .+hdh, Symbol)=( "D +Zn(+ZnS +S +Zn(@max (-r +Zn(5ZnS" 0 (Sdt30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3040 div 1088 3 -1 roll exch div scale currentpoint translate 64 38 translate -8 602 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (hdh) show 665 602 moveto 384 /Symbol f1 (=) show 1025 363 moveto 384 /Times-Italic f1 (D) show 1286 459 moveto 288 ns (Zn) show 1319 195 moveto (ZnS) show 1791 363 moveto 384 ns (S) show 1979 459 moveto 288 ns (Zn) show 2005 195 moveto 288 /Times-Roman f1 (max) show 1399 906 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 1628 1002 moveto 288 /Times-Italic f1 (Zn) show 1648 738 moveto (ZnS) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 983 503 moveto 1574 0 rlineto stroke 2616 602 moveto 384 ns (dt) show end dMATH{ hdh=D ZnZnS S Znmax r ZnZnS dtteFMicrosoft Equation 3.01ELO Equation.3CompObjRObjInfoOlePres000(Ole10Native{ hdh=D ZnZnS S Znmax r ZnZnS dt EquationTp"ldxpr  "l""l currentpoint ",Times .+hdh Ole10FmtProgID  _1009741245FtfbtfbOle PIC TPICT CompObjRObjInfoOlePres000( ( 0(h, Symbol + (=( .D + Zn(8ZnS +S +Zn(Mmax (:r +Zn(BZnS"-0 (`dt ( '0(&t +2 * 30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3456 div 1088 3 -1 roll exch div scale currentpoint translate 64 38 translate 177 602 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (hdh) show -6 987 moveto 288 /Times-Roman f1 (0) show -6 235 moveto 288 /Times-Italic f1 (h) show 10 658 moveto 384 /Symbol f1 (\362) show 850 602 moveto (=) show 1438 363 moveto 384 /Times-Italic f1 (D) show 1699 459 moveto 288 ns (Zn) show 1732 195 moveto (ZnS) show 2204 363 moveto 384 ns (S) show 2392 459 moveto 288 ns (Zn) show 2418 195 moveto 288 /Times-Roman f1 (max) show 1812 906 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 2041 1002 moveto 288 /Times-Italic f1 (Zn) show 2061 738 moveto (ZnS) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1396 503 moveto 1574 0 rlineto stroke 3029 602 moveto 384 ns (dt) show 1205 987 moveto 288 /Times-Roman f1 (0) show 1158 203 moveto 288 /Times-Italic f1 (t) show 1246 275 moveto 224 /Times-Roman f1 (2) show 1221 658 moveto 384 /Symbol f1 (\362) show end dMATHs hdh 0h  =D ZnZnS S Znmax r ZnZnS dt 0t 2 p FMicrosoft Equation 3.01ELO Equation.3 hdh 0h  =D ZnZnS S Znmax r ZOle10NativeOle10FmtProgID  _1009741244FtfbtfbOle nZnS dt 0t 2  EquationTC "Ydxpr  "Y""Y currentpoint ",Times .+ h ( 2 (2" , Symbol(=( D PIC TPICT CompObjRObjInfo +Zn('ZnS +S +Zn(<max ()r +Zn(1ZnS"0 (Ot +230 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2848 div 1088 3 -1 roll exch div scale currentpoint translate 64 38 translate 24 363 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (h) show 229 195 moveto 288 /Times-Roman f1 (2) show 118 895 moveto 384 ns (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 503 moveto 429 0 rlineto stroke 537 602 moveto 384 /Symbol f1 (=) show 897 363 moveto 384 /Times-Italic f1 (D) show 1158 459 moveto 288 ns (Zn) show 1191 195 moveto (ZnS) show 1663 363 moveto 384 ns (S) show 1851 459 moveto 288 ns (Zn) show 1877 195 moveto 288 /Times-Roman f1 (max) show 1271 906 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 1500 1002 moveto 288 /Times-Italic f1 (Zn) show 1520 738 moveto (ZnS) show 855 503 moveto 1574 0 rlineto stroke 2479 602 moveto 384 ns (t) show 2586 698 moveto 288 /Times-Roman f1 (2) show end dMATHc h 2 2=D ZnZnS S Znmax r ZnZnS t 2sfFMicrosoft Equation 3.01ELO Equation.3OlePres000(Ole10NativeOle10FmtProgID  _1009741242Ftfbtfb h 2 2=D ZnZnS S Znmax r ZnZnS t 2 EquationT @Ole PIC TPICT CompObjR"Pdxpr  "P""P currentpoint ",Times .+t +2, Symbol ( =( "h ((2 +r +Zn(5ZnS (2)D +Zn((ZnS +S +Zn(=max"730 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2560 div 1088 3 -1 roll exch div scale currentpoint translate 64 38 translate -14 602 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (t) show 93 698 moveto 288 /Times-Roman f1 (2) show 369 602 moveto 384 /Symbol f1 (=) show 1032 363 moveto 384 /Times-Italic f1 (h) show 1237 195 moveto 288 /Times-Roman f1 (2) show 1386 363 moveto /f2 {findfont matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (r) show 1615 459 moveto 288 /Times-Italic f1 (Zn) show 1635 195 moveto (ZnS) show 708 906 moveto 384 /Times-Roman f1 (2) show 932 906 moveto 384 /Times-Italic f1 (D) show 1193 1002 moveto 288 ns (Zn) show 1226 738 moveto (ZnS) show 1698 906 moveto 384 ns (S) show 1886 1002 moveto 288 ns (Zn) show 1912 738 moveto 288 /Times-Roman f1 (max) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 687 503 moveto 1777 0 rlineto stroke end dMATHP t 2 =h 2 r ZnZnS 2D ZnZnS S ZnmaxfsFMicrosoft Equation 3.01ELO Equation.3 t 2 =h 2 r ZnZnS 2D ZnZnS S Znmax EquationObjInfoOlePres000(Ole10NativeOle10FmtProgID  _1009741241FtfbtfbOle PIC TPICT [T)gFMicrosoft Equation 3.01ELO Equation.3 t 2 =10 -6 [=/dxpr  =/"=/ currentpoint ",Times .+!t +2, Symbol (! =(10 ( '-)6 +cm (())) (D2 + ) 4).)09( ngZnS+cm (3" m (( 65) .)4)gZn(97) .)5)gZnS" /(1%2)) 8))10 (,S-)16 (*dcm (%s2 (;ls".c(1|) 0).)192(*gZn*cm (63".  (!@) 8).)9))10 (3 +s)@) 2).)5)hrs30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 9696 div 1952 3 -1 roll exch div scale currentpoint translate 64 41 translate -14 1015 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (t) show 93 1111 moveto 288 /Times-Roman f1 (2) show 369 1015 moveto 384 /Symbol f1 (=) show 804 503 moveto 384 /Times-Roman f1 (10) show 1207 335 moveto 288 /Symbol f1 (-) show 1365 335 moveto 288 /Times-Roman f1 (6) show 1551 503 moveto 384 /Times-Italic f1 (cm) show 699 570 moveto /f3 {findfont 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1794 /Symbol f3 (\() show 2010 570 moveto (\)) show 2140 220 moveto 288 /Times-Roman f1 (2) show 2398 503 moveto 384 /Symbol f1 (\264) show 2694 503 moveto 384 /Times-Roman f1 (4) show 2881 503 moveto 384 /Times-Roman f1 (.) show 3006 503 moveto 384 /Times-Roman f1 (09) show 3467 264 moveto 384 /Times-Italic f1 (gZnS) show 3546 807 moveto (cm) show 4004 639 moveto 288 /Times-Roman f1 (3) show /thick 0 def /th { dup setlinewidth /thick exch def } def 8 th 3438 404 moveto 843 0 rlineto stroke 4371 503 moveto 384 /Symbol f1 (\264) show 4781 264 moveto 384 /Times-Roman f1 (65) show 5147 264 moveto 384 /Times-Roman f1 (.) show 5277 264 moveto 384 /Times-Roman f1 (4) show 5487 264 moveto 384 /Times-Italic f1 (gZn) show 4692 796 moveto 384 /Times-Roman f1 (97) show 5062 796 moveto 384 /Times-Roman f1 (.) show 5184 796 moveto 384 /Times-Roman f1 (5) show 5381 796 moveto 384 /Times-Italic f1 (gZnS) show 4671 404 moveto 1524 0 rlineto stroke 1130 1558 moveto 384 /Times-Roman f1 (2) show 1402 1558 moveto 384 /Symbol f1 (\264) show 1682 1558 moveto 384 /Times-Roman f1 (8) show 1941 1558 moveto 384 /Symbol f1 (\264) show 2199 1558 moveto 384 /Times-Roman f1 (10) show 2602 1390 moveto 288 /Symbol f1 (-) show 2760 1390 moveto 288 /Times-Roman f1 (16) show 3154 1319 moveto 384 /Times-Italic f1 (cm) show 3616 1151 moveto 288 /Times-Roman f1 &(2) show 3402 1851 moveto 384 /Times-Italic f1 (s) show 3134 1459 moveto 682 0 rlineto stroke 3906 1558 moveto 384 /Symbol f1 (\264) show 4197 1558 moveto 384 /Times-Roman f1 (0) show 4385 1558 moveto 384 /Times-Roman f1 (.) show 4477 1558 moveto 384 /Times-Roman f1 (192) show 5146 1319 moveto 384 /Times-Italic f1 (gZn) show 5127 1862 moveto (cm) show 5585 1694 moveto 288 /Times-Roman f1 (3) show 5107 1459 moveto 666 0 rlineto stroke 16 th 687 916 moveto 5540 0 rlineto stroke 6335 1015 moveto 384 /Symbol f1 (@) show 6633 1015 moveto 384 /Times-Roman f1 (8) show 6808 1015 moveto 384 /Times-Roman f1 (.) show 6931 1015 moveto 384 /Times-Roman f1 (9) show 7197 1015 moveto 384 /Symbol f1 (\264) show 7455 1015 moveto 384 /Times-Roman f1 (10) show 7849 847 moveto 288 ns (3) show 8031 1015 moveto 384 /Times-Italic f1 (s) show 8279 1015 moveto 384 /Symbol f1 (@) show 8586 1015 moveto 384 /Times-Roman f1 (2) show 8774 1015 moveto 384 /Times-Roman f1 (.) show 8896 1015 moveto 384 /Times-Roman f1 (5) show 9088 1015 moveto 384 /Times-Italic f1 (hrs) show end dMATHG t 2 =10 -6 cm() 2 4.09gZnScm 3 65.4gZn97.5gZnS2810 -16 cm 2 s0.192gZncm 3 @8.910 3 s@2.5hrs sCompObjRObjInfoOlePres000(Ole10Native     !"#$%&(/123456789:;<=>?@ABCDEFHLPRSTUVWXYZ[\^_`abcdefghijkmquwxyz{|}~cm() 2 4.09gZnScm 3 65.4gZn97.5gZnS2810 -16 cm 2 s0.192gZncm 3 @8.910 3 s@2.5hrs EquationOle10FmtProgID  _1009741240F b bOle PIC TTWTDdxpr  " currentpoint ",Times .+ P +S +2z30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 640 div 544 3 -1 roll exch div scale currentpoint translate 64 59 translate -4 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dPICT  DCompObjRObjInfoOlePres000(up /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (P) show 224 357 moveto 288 ns (S) show 391 429 moveto 224 ns (2) show end d1MATH% P S 2 1 FMicrosoft Equation 3.01ELO Equation.3Ole10Native)Ole10FmtProgID  _1009741238F b bOle % P S 2  EquationTWTDdxpr  " currentpoint ",Times .+ P +S +2z30 dict begin currentpoint 3 -1 roll sub neg 3 1 ro+,,G,z,|, -<->----R///////!0#0Z0001::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: @CPIC TPICT DCompObj'RObjInfo)ll sub 640 div 544 3 -1 roll exch div scale currentpoint translate 64 59 translate -4 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (P) show 224 357 moveto 288 ns (S) show 391 429 moveto 224 ns (2) show end d1MATH% P S 2 1 FMicrosoft Equation 3.01ELO Equation.3% P S 2  EquationTpOlePres000*(Ole10Native+)Ole10FmtProgID , _1009741237F b bOle -PIC .TPICT 0CompObjGR"ldxpr  "l""l currentpoint ",Times .+dx ( 0(h, Symbol + (=) 1).)92))10 (J-)13 +dt ( [0(Yt +3 ([30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3456 div 1088 3 -1 roll exch div scale currentpoint translate 64 43 translate 180 597 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (dx) show -6 982 moveto 288 /Times-Roman f1 (0) show -6 230 moveto 288 /Times-Italic f1 (h) show 10 653 moveto 384 /Symbol f1 (\362) show 652 597 moveto (=) show 928 597 moveto 384 /Times-Roman f1 (1) show 1085 597 moveto 384 /Times-Roman f1 (.) show 1208 597 moveto 384 /Times-Roman f1 (92) show 1672 597 moveto 384 /Symbol f1 (\264) show 1930 597 moveto 384 /Times-Roman f1 (10) show 2333 429 moveto 288 /Symbol f1 (-) show 2491 429 moveto 288 /Times-Roman f1 (13) show 3039 597 moveto 384 /Times-Italic f1 (dt) show 2853 982 moveto 288 /Times-Roman f1 (0) show 2813 195 moveto 288 /Times-Italic f1 (t) show 2898 267 moveto 224 /Times-Roman f1 (3) show 2869 653 moveto 384 /Symbol f1 (\362) show end dMATHy dx 0h  =1.9210 -13 dt 0t 3 laFMicrosoft Equation 3.01ELO Equation.3y dx 0h  =1.9210 -13 dt 0t 3  EquationTHObjInfoIOlePres000J(Ole10NativeK}Ole10FmtProgID M _1009741236F b bOle NPIC OTPICT Q!jdxpr  !j"!j currentpoint ",Times .+t +3, Symbol ( =( 1h)()cm))(1).)92))10 (B-)13 + cm+s"f" Q30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3392 div 1056 3 -1 roll exch div scale currentpoint translate 64 43 translate -14 501 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (t) show 89 597 moveto 288 /Times-Roman f1 (3) show 353 501 moveto 384 /Symbol f1 (=) show 1519 262 moveto 384 /Times-Italic f1 (h) show 1714 262 moveto 384 /Times-Roman f1 (\() show 1850 262 moveto 384 /Times-Italic f1 (cm) show 2309 262 moveto 384 /Times-Roman f1 (\)) show 661 806 moveto 384 /Times-Roman f1 (1) show 818 806 moveto 384 /Times-Roman f1 (.) show 941 806 moveto 384 /Times-Roman f1 (92) show 1405 806 moveto 384 /Symbol f1 (\264) show 1663 806 moveto 384 /Times-Roman f1 (10) show 2066 638 moveto 288 /Symbol f1 (-) show 2224 638 moveto 288 /Times-Roman f1 (13) show 2576 703 moveto 384 /Times-Italic f1 (cm) show 3075 968 moveto (s) show /thick 0 def /th { dup setlinewidth /thick exch def } def 8 th /stb { newpath moveto 0 setlinewidth 2 copy rlineto } def /enb { rlineto neg exch neg exch rlineto closepath fill } def /hb { stb 0 thick enb } def /vb { stb thick 0 enb } def -379 531 3233 442 vb 16 th 671 402 moveto 2602 0 rlineto stroke end dzMATHnj t 3 =h(cm)1.9210 -13 )cms64FMicrosoft Equation 3.01ELO Equation.3CompObjlRObjInfonOlePres000o(Ole10Nativeprn t 3 =h(cm)1.9210 -13 )cms EquationT: $"`dxpr  "`""` currentpoint ", Symbol .+=,TOle10FmtProgID r _1009741234FbbOle sPIC tTPICT v$CompObjRObjInfoOlePres000(ad#&  ! . R _   Q W S`dpqx#MZDS  ,.MPegps(+.;>@DIikor + - 1 4 9 < u w imes( "10 (.-)6 +cm( 1).)92))10 (7-)13 + cm)s"W " S30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3072 div 1088 3 -1 roll exch div scale currentpoint translate 64 37 translate -4 603 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Symbol f1 (=) show 1032 364 moveto 384 /Times-Roman f1 (10) show 1435 196 moveto 288 /Symbol f1 (-) show 1593 196 moveto 288 /Times-Roman f1 (6) show 1779 364 moveto 384 /Times-Italic f1 (cm) show 304 907 moveto 384 /Times-Roman f1 (1) show 461 907 moveto 384 /Times-Roman f1 (.) show 584 907 moveto 384 /Times-Roman f1 (92) show 1048 907 moveto 384 /Symbol f1 (\264) show 1306 907 moveto 384 /Times-Roman f1 (10) show 1709 739 moveto 288 /Symbol f1 (-) show 1867 739 moveto 288 /Times-Roman f1 (13) show 2219 907 moveto 384 /Times-Italic f1 (cm) show 2804 907 moveto (s) show /thick 0 def /th { dup setlinewidth /thick exch def } def 8 th /stb { newpath moveto 0 setlinewidth 2 copy rlineto } def /enb { rlineto neg exch neg exch rlineto closepath fill } def /hb { stb 0 thick enb } def /vb { stb thick 0 enb } def -110 344 2772 646 vb 16 th 314 504 moveto 2662 0 rlineto stroke end dwMATHk8 =10 -6 cm1.9210 -13 )cmsteFMicrosoft Equation 3.01ELO Equation.3k =10 -6 cm1.9210 -13 )cms EquationTOle10NativeoOle10FmtProgID  _1009741233FbbOle PIC TPICT CompObjRObjInfo3>dxpr  3>"3> currentpoint ", Symbol .+ @,Times) 5).)2) )10 (16 +s(@) 1445)hrs(1@) 2) monthso30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1984 div 1632 3 -1 roll exch div scale currentpoint translate 64 49 translate -4 364 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Symbol f1 (@) show 302 364 moveto 384 /Times-Roman f1 (5) show 476 364 moveto 384 /Times-Roman f1 (.) show 599 364 moveto 384 /Times-Roman f1 (2) show 871 364 moveto 384 /Symbol f1 (\264) show 1129 364 moveto 384 /Times-Roman f1 (10) show 1525 196 moveto 288 ns (6) show 1717 364 moveto 384 /Times-Italic f1 (s) show -4 943 moveto 384 /Symbol f1 (@) show 272 943 moveto 384 /Times-Roman f1 (1445) show 1040 943 moveto 384 /Times-Italic f1 (hrs) show -4 1519 moveto 384 /Symbol f1 (@) show 303 1519 moveto 384 /Times-Roman f1 (2) show 517 1519 moveto 384 /Times-Roman f1 ( months) show end duMATHiZ @5.210 6 s@1445hrs@2 monthslaFMicrosoft Equation 3.01ELO Equation.3@  !"#$%&'()*+,-./0123456789:;<=>?ABCDEFGHIJKLMNWlQRSTVXZx[^_cbdevgikmpnoqrstw`zxy|{~}!!!!! !e!h!!!!!!!!!""("-"####>$@$D$H$$$$$%%%%%%&&'&*&&&&&&& ' '''#(%(;(>((((((()))))),---E-G-Y-[-\-^---.. . .!.#.'.*.a.c.h.j.........1 1 D qx1 1Long-Qing Chen<Macintosh HD:chen:pennstate:matsc503:matsc503.00:example1_00@BB/B mf$F$GCJOJQJmH 56CJGCJOJQJmH FGCJOJQJmH $hC$Eƀb'$FhF0J F5CJGCJOJQJmH hF5CJGCJOJQJmH hC$Eƀ     $| !)#&'(*+,-./PQRSTUV_XYZ[\^aUbcdefghijklmnopqrutwh}yjSummaryInformation(DocumentSummaryInformation8(CompObjX0Table%fJOlePres000(Ole10NativemOle10FmtProgID  1TableZJ [0@0NormalCJOJQJmH @`@ Heading 1$$h@&5CJ<`< Heading 2$h@&5CJ<A@<Default Paragraph Font, @,Footer  !,@,Header  !,>`,Title$ 56CJ<C`"<Body Text Indent $h 1   cw $3)E, 16 LD: EFGQ<TbcdnrVnm\^_`abcdeo P  mopwx  o1hibc.s=>?W1pqcd      CDFGHOPw-. 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Lusk Julie Clausen Lynn SanchezTECHNOLOGY TRANSFER Gary FergusonCarol A. MurraySNLSandia National LaboratoriesDottie Brockman Rob Banwart';=0bdJ|~    H J T   C E ~ e68GIX<oqFHv35LNg!SU I K  !;!=!!!!! " """"""# #?#A#$$$$%%P%%%%%%%$&&&V&&&&&&'A'C''''K(}(((*),)****"+$+/+b+d++++I,::::::::::::::::::::::::::::::::::::::::::::::::::::::::::,/=@pweqryx2?R*hw#1.94Darrell G. SchlomLong-Qing Chen=>?WX12pqcd      CDFGHOPw-. M N g !@!y!!!!!""I"J"L"M"T"U"""!#"#e#f#####$$V$W$$$$$%%9%:%|%}%%%&&N&O&&&$'%'B'C'~'''((((_(`(2)3)5)6)=)>)?)b)))) * *F*P****++S+`+++,,C,D,E,,,,,,,R-X-~--.5.6.... /!/M/N//////&0001 1&&&&&&&&/////////// ?????????????????????_1009741683Ff?bf?bOle PIC TPICT ????????????'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!'!z&$(,/N256,02479;=?AGOd`#(e+.2'7PҜ-/1368:<@BHP"w07.5>UnknownLong-Qing Chen Danan FanCeleste Drewien Mark T. Lusk Julie Clausen Lynn SanchezTECHNOLOGY TRANSFER Gary FergusonCarol A. MurraySNLSandia National LaboratoriesDottie Brockman Rob Banwart<PRrVjlmQ k $&7iku-/2df$WY5hjy354giy !!|!!!V"""'#Y#[#####$$\$$$$ % %?%r%t%%%%T&&&&&&H'z'|''''''(h))))))*B*D*U******+H+J+f++++,,H,{,}, -=-?----S///////"0$0[000 1::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: be$'  " / S `  R X Taeqry$N[ET  -/NQfhqt),/<?AEJjlps  , . 2 5 : = v x !!!!!!!f!i!!!!!!!!!"")"."####?$A$E$I$$$$$%%%%%%&&(&+&&&&&&& ' '''$(&(<(?((((((())))))----F-H-Z-\--_---.. . .".$.(.+.b.d.i.k.........1 1 E ry1 1Long-Qing Chen<Macintosh HD:chen:pennstate:matsc503:matsc503.00:example1_00@/mf$F$GCJOJQJmH 56CJGCJOJQJmH FGCJOJQJmH $hC$Eƀb'$FhF0J F5CJGCJOJQJmH hF5CJGCJOJQJmH hC$Eƀb' BCg!CDEFGNQRSTv;<=>DOPQRSTZ[jIabdmn*:;=_`dirstz)*;UVWX^ijklmn ?cmnou[\deno 5   D !!!!"""111 1:? B*bb,*ktr Tl*bb,*k$ !:x}Sn@'@"C\'iK9 *TU*qDN:w& *W^ f׉\i3|3띩#a Tk0%lٓBC~ 5Z <VK%=9Eq7As3͌7a 1 O>WP `P)-YΊsL|~?)zj۟]v:?: ,d-9TC;%3MB†LST3K[&E-žu0H"@skcsf^hhaEWhnQJZY9Cgh.<)47f^2B&9ɹs";CÓ?藘ĘɌteQ wxa\hSqi0 qTԨdsCkϙ}E.9T<z8!UO^֫6z9d?[email protected]q>( wX."uf>|y{vV}S qSn_Q_ C DdhB Z S A>? B^5 J{Z|j: r T25 J{Z|j dD|x}VoDm7mRӦjT!評.zۇ@ T mލ]۬4QTB#p CompObj RObjInfoEquation Native X_1009765524 'FI BbI Bb_1009744860FdIbdIb_1009745279 FdIbdIb_1009745181FdIbdIbOle _1009765535#FI BbI Bb_1009765393FI BbI Bb_1009765755 FI BbI Bb_1009765808FI BbI BbOle10FmtProgID - _1009741682Ff?b bOle .PIC /TOlePres000O(Ole10NativePOle10FmtProgID Q _10097416801 #Ff?b b_1009765924  FI BbI Bb_1009766296FI BbߡBbOle CompObjRҜԜ֜؜ڜܜޜ$h$hs ,7jbjb kk1,,,8,dV-djFhl/r3333333H:J:J:J:J:J:J:,GIvv: 33333v:933-999333H:h^h3H:99H:H:-IjP,v94H:Solutions to Problem Set #1 - Matsc 503 - Spring 95 1. There are two ways of introducing dopants into silicon by diffusion. The first is called predeposition during which the surface concentration of dopant atoms is maintained constant by a vapor source; and the second is called the redistribution or drive-in which is used to move predeposited dopants to the desired junction depth. a) Assume the substrate is n-type with a background doping level of 1.5x1016 atoms/cm3 and the diffusion coefficient of boron in silicon is given by  EMBED "Equation" "Word Object1" \* mergeformat  where kB is the Boltzmann constant and T is temperature. The boron surface concentration is maintained at a constant value of 1.8x1020 atoms/cm3 during predeposition at 950C in a neutral ambient. If predeposition is performed for 30 min., calculate: (I) the diffusion profile; (II) the junction depth; and (III) the total amount of dopant entering the substrate. b) If, after the predeposition, the same substrate is subjected to a neutral ambient drive-in at 1050C for 60 min., calculate the diffusion profile and junction depth. You may assume that the predeposited impurities or dopants form a very thin layer. (Note: The junction depth is defined as the distance at which the Boron diffusion profile is equal to the substrate background (usually Phosphorus) concentration, csub.) 2. In order to prepare a specimen for a superconducting tunneling experiment, it is necessary to cover the top surface of a superconducting metal, an Ir-Zn alloy, with a thin insulating film of ZnS. (Fig. 1) ObjInfo)Equation Native " dpdt=3.8 p H =3.810 -8  8.7  =1.1210 -7  (atm/s)FMicrosoft Equation 3.0DNQE Equation.3 dp H dt=RTVJ tot =0.08267316.910 -10  p H =3.810 -8  p H  (atm/s)FMicrosoft Equation 3.0DNQE Equation.3n J tot =dndt=VRTdp H dtFMicrosoft Equation 3.0DNQE Equation.37 J tot =dndtFMicrosoft Equation 3.0DNQE Equation.3^ J tot =JA=2.310 -12  p H 61000 )13 () 2 =1.3810 -9  p H  (g/s)=6.910 -10  p H  mol/s()FMicrosoft Equation 3.0DNQE Equation.3 J=-Ddcdx=-10 -8 0-2.3210 -5  p H 0.1=2.310 -12  p HFMicrosoft Equation 3.0DNQE Equation.3 c=3 p H  (ppm)=310 -6 7.73 p H   (g/cm 3 )=2.3210 -5  p H (g/cm 3 )FMicrosoft Equation 3.0DNQE Equation.3 FMicrosoft Equation 3.0DNQE Equation.3s <7jbjb |kk1,,,8,dV-djFhl/r3333333H:J:J:J:J:J:J:,GIvv: 33333v:933-999333H:h^h3H:99H:H:-JjP,v94H:Solutions to Problem Set #1 - Matsc 503 - Spring 95 1. There are two ways of introducing dopants into silicon by diffusion. The first is called predeposition during which the surface concentration of dopant atoms is maintained constant by a vapor source; and the second is called the redistribution or drive-in which is used to move predeposited dopants to the desired junction depth. a) Assume the substrate is n-type with a background doping level of 1.5x1016 atoms/cm3 and the diffusion coefficient of boron in silicon is given by  EMBED "Equation" "Word Object1" \* mergeformat  where kB is the Boltzmann constant and T is temperature. The boron surface concentration is maintained at a constant value of 1.8x1020 atoms/cm3 during predeposition at 950C in a neutral ambient. If predeposition is performed for 30 min., calculate: (I) the diffusion profile; (II) the junction depth; and (III) the total amount of dopant entering the substrate. b) If, after the predeposition, the same substrate is subjected to a neutral ambient drive-in at 1050C for 60 min., calculate the diffusion profile and junction depth. You may assume that the predeposited impurities or dopants form a very thin layer. (Note: The junction depth is defined as the distance at which ...
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This note was uploaded on 01/19/2010 for the course MAT SCI 503 taught by Professor Chen during the Spring '02 term at Penn State.

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