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pTM January 2023 Thermo calc Vapor-Solid Distribution

System

Sys AB_:

PC 1760 / :

Constants

Ro 8.314 :

T0K 273.15 :

HSC 2 :

Temperature

°K T 800 T0K + : 1073.15

Torr P 50 :

Energy

T ΔGA 4001000 * T 190 * - :

A-B Ωi 2500 :

T ΔGB 3801000 * T 210 * - :

Flows

ϕpt 50 :

ϕtl 12500 :

ϕB ϕpt 0.01 * :

ϕH2 ϕtl ϕpt - :

pzpt ϕpt ϕtl / P PC / * :

pzH2 ϕH2 ϕtl / P PC / * :

pzB ϕB ϕtl / P PC / * :

Partial Pressuresatm

pzB pzA pzpt pzB - :

xv pzB pzpt / :

Mole fraction vapor

pzB pA pB x pzB pB - pzB pzA pA - pzB + pB - / :

Mole fraction solid

pzB pA pB aA 1 pzB pA pB x - (e Ωi Ro T * / pzB pA pB x (2^*^* :

Activities

pzB pA pB aB pzB pA pB x e Ωi Ro T * / 1 pzB pA pB x - (2^*^* :

K0A e T ΔGA Ro T * / -^:

K0B e T ΔGB Ro T * / -^:

EquilibriumConstants

pzB pA pB KA pzB pA pB aA 2 pzB pzA pA - (* (2^* pA / :

pzB pA pB KB pzB pA pB aB 2 pzB pB - (* (2^* pB / :

pzB 1.52

recast the system x y KA pzB x y aA 2 pzB pzA x - (* (2^* x / : x y KB pzB x y aB 2 pzB y - (* (2^* y / : 21 sys

x 0 KA x 0.001 KB 2 1 sys

recast the system x y KA pzB x y aA 2 pzB pzA x - (* (2^* x / : x y KB pzB x y aB 2 pzB y - (* (2^* y / : 21 sys

pzB 1.52

Locate 1rst exact value in vector V x col FindIdx j 1 : V j col el x ≠ j j 1 + : while j 0 ≡ inexistant j V j col el 12 mat if 31 line :

x 0.1 24 0.25 range :

x rows 160

0.1 1000 KB 4736

U1 x x 84 KA vectorize augment :

U1 U1 eval :

U2 x x 72 KA vectorize augment :

U2 U2 eval :

U3 x x 60 KA vectorize augment :

U3 :eval(U3

U1 U2 U3 23.65 100000 23.65 50000 - 2 2 mat 4 1 sys

U x x 84 KA vectorize x 72 KB vectorize - augment :

U U eval :

U 23 100000 23 50000 - 2 2 mat 2 1 sys

N x x 100 KB vectorize augment :

N N eval :

U1 1 row U2 1 row U3 1 row 31 mat 0.1 3029153.6 12 mat 0.1 2117243.6 12 mat 0.1 1658024.6 12 mat 31 mat

N 1 row 0.1 7737.1 - 12 mat

idxkey U1 U1 2 col Min 2 FindIdx :

idx U U 2 col Min 2 FindIdx :

idxkey 158 20506.27 12 mat

idx 1542191012 mat

U1 idxkey 11 el row 23.65 20506.27 12 mat

U idx 11 el row 232191012 mat

https://digital.library.unt.edu/ark:/67531/metadc666909/m2/1/high_res_d/2056.pdf

On that Flow Experimental Model, Deposition Rate (μm/min) vs Distance Along Wafer (cm) looks a simpler function than the model offered below from invented data set.

data list ListCollect ct 1 : i list a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 31 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

list 1234571015254070110158113 mat :

XY U1 list ListCollect :

XY XY eval :

Ge XY :

Minimize Conjugate-Gradient

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

XY f φ β Minimize XY f φ β LS X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line : β 1 el init : i 1 : i iter ≤ β i 1 + el XY f φ β i el LS : i i 1 + : 21 line while β β iter el : 41 line β 31 line :

Vector Gradient ... Optimiz Symbolic
seemingly a scalar kernel  not 
recognized in program loop x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

corr Pearson correlation χ X Mean : μ Y Mean : n XY rows : 13 mat X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

correlation between [X,Y data]

correlation ... [X,fitted model]

Absolute  residuals observer
fetches β from calculated δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 XY rows sum :

Otherwise Pearson independent of f(x,ParameterName) x y corr n x length : xy x y * vectorize : x2 x x * vectorize : y2 y y * vectorize : n xy sum (* x sum (y sum (* - n x2 sum (* x sum (2^- (n y2 sum (* y sum (2^- (* (sqrt / 51 line :

Fit ii 1 n range Fit ii el X ii el β f : for Fit 21 line :

Genfit Germanium

x β f β 1 el β 2 el x 1.125^/ + β 3 el x 2.25^/ + β 4 el x 3.375^/ + β 5 el x 1^/ + β 6 el x 0.5^/ + β 7 el x 0.25^/ + β 8 el x 0.125^/ + :

<= ConjugateGradient Vector Fnct x β φ x β f 8 φ :

X Ge 1 col : Y Ge 2 col : 12 mat XY X Y augment : data Ge o 7 black plot : n Ge rows : 41 sys

init 1111111118 mat transpose :

iter 7 :

algo solving for β β XY f φ β Minimize :

assign/isolate .. β β :

SSD 74726.88

β 1.9 106^* 1.5 106^* - 8023.1 171.6 - 2.7 106^* 3.9 106^* - 8.6 106^* 7.6 106^* - 81 mat

β β 1 round vectorize : 1949788.6 1491132 - 8023.1 171.6 - 2706372.2 3892609.2 - 8597321.5 7572755.7 - 81 mat

corr 1.00001

x λ 1 0.1 x ≤ (x 30 ≤ (& cases :

Pearson correlation corr 1.00001

Data set U1 fitted ... Export the black for else publishing

data x β f x λ * 2 1 sys

XY 0.1 3029154 0.25 1212935 0.4 758892 0.55 552517 0.7 4345951304896 1.45 211001 2.2 139915 3.7 84310 5.95 53665 10.45 32473 16.45 23270 23.65 20506132 mat :

β 1949788.6 1491132 - 8023.1 171.6 - 2706372.2 3892609.2 - 8597321.5 7572755.7 - 81 mat :

x β f β 1 el β 2 el x 1.125^/ + β 3 el x 2.25^/ + β 4 el x 3.375^/ + β 5 el x 1^/ + β 6 el x 0.5^/ + β 7 el x 0.25^/ + β 8 el x 0.125^/ + :

0.1 0.25 0.4 0.55 0.7 1 1.45 2.2 3.7 5.95 10.45 16.45 23.65 131 mat 302915412129357588925525174345953048962110011399158431053665324732327020506131 mat augment 0.1 3029154 0.25 1212935 0.4 758892 0.55 552517 0.7 4345951304896 1.45 211001 2.2 139915 3.7 84310 5.95 53665 10.45 32473 16.45 23270 23.65 20506132 mat

XY 2 col 302915412129357588925525174345953048962110011399158431053665324732327020506131 mat

... GR-50-AA ... Ge Ω °K 35000 0.05 2320 0.1 364.6 0.2 164 0.3 73.75 0.5 33.55 1 24.73 1.4 19.32 2 13.66 4.2 102 mat :

Germanium RTD

]]>

°C 1 :

https://www.lakeshore.com/Documents/LSTC_Germanium_l.pdf Lake Shore germanium resistance temperature sensors are recognized as “Secondary Standard Thermometers” and have been employed in the measurement of temperature from 0.05 K to 30 K for more than 40 years.

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Ge Ge 210 range 12 range el :

About Quantum Computers

Quantum computing requires extremely cold temperatures, as sub-atomic particles must be as close as

possible to a stationary state to be measured. The cores of D-Wave quantum computers operate at -273 °C,

which is 0.02 °C away from absolute zero.Feb 23, 2018

Reduction of the temperature of the computing environment below approximately 80mK is required for

the processor to function, and generally performance increases as temperature is lowered -

the lower the temperature, the better. The latest generation D-Wave 2000Q system has an operating

temperture of about 15 millikelvin. The QPU and parts of the input/output (I/O) system, comprising

roughly 10kg of material, is cooled to this temperature, which is approximately 180 times colder than

interstellar space! Most of the physical volume of the current system is due to the large size of the

refrigeration system. The refrigeration system used to cool the processors is known as a

dilution refrigerator.

To reach the near-absolute zero temperatures at which the system operates, the refrigerators use liquid

helium as a coolant. The type of refrigerator inside the D-Wave system is known as a "dry" dilution

refrigerator. This means that all the liquid helium resides inside a closed cycle system, where it is

recycled and recondensed using a pulse-tube technology. This makes them suited to remote deployment,

as there is no requirement for liquid helium replenishment on-site.

The specialized equipment to allow cooling to these temperatures is available commercially and runs

reliably. The refrigeration technology is also mature enough that the system has a turnkey operation.

The computer can be cooled down to operating temperature within several hours, and once this temperature

is reached remain cold for months or years.

]]> Genfit Utilities

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Applicable parts are: Optimiz "numeric" XY f φ β Minimize X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

Genfit Germanium

x α f α 1 el α 2 el x 1.125^/ + α 3 el x 2.25^/ + α 4 el x 3.375^/ + α 5 el x 1^/ + α 6 el x 0.5^/ + α 7 el x 0.25^/ + α 8 el x 0.125^/ + :

<= ConjugateGradient Vector Fnct x α φ x α f 8 φ :

X Ge 1 col : Y Ge 2 col : 12 mat XY X Y augment : data Ge o 7 black plot : n Ge rows : x c 1 13.66 x ≤ (x 35000 ≤ (& cases : 51 sys

α α 1 el 1111111118 mat transpose : iter 9 : i 1 : i iter ≤ α i 1 + el XY f φ α i el Minimize : i i 1 + : 21 line while α α iter el : 51 line :

assign to isolate α α :

α α 4 round vectorize : 3.844 - 2401.821 5401.639 - 52172.807 1901.257 - 172.7 82.887 - 33.532 81 mat

Conformity from absolute residuals δ i 1 Ge rows range Δ i el Y i el X i el α f - 3 round eval : for Ge X Y Δ augment : Header Ω °K Δ°K 13 mat : Header Ge stack 41 line :

Observe . . . @ 4.2 °K, switch to

GR-300-AA . . . Pt100 subcryo .

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Quick linfit GR-50-AA ... a most remarkable fit ± 0.001°K

data x α f x c * 2 1 sys

δ Ω °K Δ°K 35000 0.05 02320 0.1 0 364.6 0.2 0164 0.3 0.001 73.75 0.5 0.001 - 33.55 1 0.001 24.73 1.4 0.001 - 19.32 20 13.66 4.2 0103 mat