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pTM May 2022 Thermo calc Vapor-Solid Distribution

PC 1760 / :

Constants

Ro 8.314 :

T0K 273.15 :

Temperature

T 750 T0K + :

P 20 :

Torr

Energy

T ΔGSi 435.78 1000 * T 267.7 * - :

SiGe Ωi

Ωi 15150 :

T ΔGP 486.6 1000 * T 260.1 * - :

Flows

ϕpt 20 :

ϕtl 20000 ϕpt - :

ϕP ϕpt 0.99999 * :

ϕH2 ϕtl ϕpt - :

pzpt ϕpt ϕtl / P PC / * :

pzH2 ϕH2 ϕtl / P PC / * :

pzP ϕP ϕtl / P PC / * :

Partial Pressures
atm

pzP pzSi pzpt pzP - :

xv pzP pzpt / :

Mole fraction vapor

pzP pSi pP x pzP pP - pzP pzSi pSi - pzP + pP - / :

Mole fraction solid

pzP pSi pP aSi 1 pzP pSi pP x - (e Ωi Ro T * / pzP pSi pP x (2^*^* :

Activities

pzP pSi pP aP pzP pSi pP x e Ωi Ro T * / 1 pzP pSi pP x - (2^*^* :

K0Si e T ΔGSi Ro T * / -^:

K0P e T ΔGP Ro T * / -^:

pzP pSi pP KSi pzP pSi pP aSi 2 pzP pzSi pSi - (* (2^* pSi / :

pzP pSi pP KP pzP pSi pP aP 2 pzP pP - (* (2^* pP / :

Given

x target pSi pP 12 mat x 1 el x 2 el 12 mat : pzP pSi pP KSi K0Si - pzP pSi pP KP K0P - 21 mat 21 line :

Jx x target x 12 range el vectorize Jacob :

x J Jx eval :

ε 1012 -^:

Solve

pzP guess f sol guess 0 ε target J al_nleqsolve : sol target normi ε sqrt < sol 00 stack if 21 line :

guess 101 -^101 -^21 mat :

pSi pP 21 mat pzP guess f : 0.0002 15.2151 21 mat

pzP pzSi 19124875 /

Output

pzpt 15.2152

pzP pzSi pSi pzP pzSi pSi - xv pzP pP pzP pP - pzP pSi pP x 24 mat 0.0002 0.0002 6.4725 107 -^* 1 15.2151 15.2151 4.4876 106 -^* 0.874 24 mat