Equations for Matse 201 Penn State

8/21/2019 Equations for Matse 201 Penn State

1/34

Elementary charge 1.60E-19 coulombs

Boltz 8.62E-05 eV/K

Avogadro 6.02E+23 atoms/mol

Plancks 6.63E-34 J-s

Speed of light 3.00E+08 m/s

Gas cnst 8.31E+00 J/K-mol

permittivity of free space 8.85E-12 F/mmass of an electron 9.11E-31 kg

Q (watts) Area (cubic meter)

3333 0.5

Q total Q3 (watts) Q2

47.69 15.90 15.90

Enthalpy Change H Change U

0

Heat Capactiy Heat Cv Change Temp#DIV/0!

Heat Cp Change Temp

#DIV/0!

linearCoefficent of Thermal expansion material A

(1/degrees C)

initial Volume formaterial A (cubic

cm)

Final Volume for material A

(cubic cm)

7.60E-06 1 0.9938

look up

Thermal Stress

(mpa) coeff. Linear expansion


2/34

compressive (Tf>Ti), thermal stress


3/34

Dependence of creep strain rate on stress AND

Temperature 19588 140

percent IonicityElectronegetivity of

more EN element

Electronegetivity of less EN

element

0.99502% 2.1 1.9

XRD for BCCsqrt of sum of

squares hkl d (nm)

find d given R and hkl x 0.1655find d and R, given hkl, diff angle, lamda x 0.1655

find sqrt of sum of squares hkl given DA, R, and lambda 3 0.1655

Find DA, given hkl, R, and lamda X 0.1655

XRD for FCCsqrt of sum of

squares hkl d (nm)

find d given R and hkl 11 0.1183

find d and R, given hkl, diff angle, lamda 11 0.1183

find sqrt of sum of squares hkl given DA, R, and lambda 11 0.1183

Find DA, given hkl, R, and lamda 11 0.1183

Density BCC (g/cc) a (cm) R (cm)7.90E+00 2.86E-08 1.24E-08

7.90E+00 2.86E-08 x

Density FCC (g/cc) a (cm) R (cm)22.44 3.84666E-08 1.36E-08

22.44 3.85E-08 x


4/34

Vacancy equationsFraction of atom

sites

Vacancys per cubic

centimeter

2.41E-05 1.99E+18

Schottky/FrenkelFraction of atom

sites defects per cubic centimeter

3.36E-09 5.30E+13

Kic( Mpa-sqrt(m))

crack propagation or critical

stress at fracture (Mpa)

find flaw size given crit stress 40 400

find crit stressgiven max flaw size 40 400

Flexural strength

(mpa) Width (mm)

find loadgiven strength and dimensions 150 8

find flex strength given load and dimensions 150 8

Flexural strength

(mpa) Radius (mm)

find loadgiven strength and dimensions 150 8find flex strength given load and dimensions 150 8

Voltage (V) Resistance (ohms)

find V 20 4

Find R 20 4

Find I 20 4

Resistance (ohm) Diameter (cm)

Find cond between voltmeterand resistance of the entire

lengthwith given values 125.00 0.510

Flexural Strength (circular)

Flexural Strength (rectanglular)

Ohm's Law


5/34

Find minimum Diameter for wire to exp 1.5V drop over it's

entire length 125.00 0.510

Find Resistance, current, current density, and the magnitude

of the electric field. All over its entire length. 125.00 0.51

Find max wire length. 125 0.51

Thickness (cm) Length (cm)

Step 1, use dimensions and ohms law to determine the

conductivity and resistivity of the semi conductor 0.1 1.5

Step 2. Dope with [Al] for a p-type semiconductor and find

the mobility of the majority carriers (holes). x x

Ec = energy of the

bottom edge of the

conduction band

(eV)

Ev = energy of the top edge

of the valence band (eV)

example (silicon intrinsic) ni increases with temp 1 1

Electron

concentration (m^-

3) Drift Velocity (m/s)

3.00E+18 100

3.00E+18 100

3.00E+18 100

3.00E+18 100

Hole concentration

(m^-3) Hole Mobility (m^2/V-s)

5.00E+22 0.03

5.00E+22 0.02

Extrinsic Semi Cond


6/34

Material Resistivity at 20C rt(m)

Aluminum

(annealed) 2.83E-08

Copper (annealed

standard) 1.72E-08

Gold 2.44E-08

Iron (99.99+%) 9.71E-08

Lead (99.73+%) 2.06E-07

Magnesium

*99.80%) 4.46E-08

Mercury 9.58E-07

Nickel (99.95% +

Co) 6.84E-08

Nichrone (66% Ni +

Cr and Fe) 1.00E-06

Platinum (99.99%) 1.06E-07

Silver (99.78%) 1.59E-08

1.07E-07

1.75E-07

Tungsten 5.51E-08

Zinc 5.92E-08

Steel (wire)


7/34

1.38E-16 erg/K 1.38E-23 J/K

5.189eV/K-mol

Kglass T1 T2 Xglass (m)

2 5 15 0.003

Q1 Area (cubic meter) Kgas (w/m-K) Kglass T1

15.90 0.5 0.016 2 5

Change P Volume Final Length (m)

Original Length

(m)

0.2 0.1

0.2 0.1

change U 0.2 0.10.2 0.1

Change H 0.2 0.1

Initial Density for

material A (g/cc)

final density for

material A (g/cc)

Mass for material

A (g)

Initial Temperature

for Material A

FinalTemperature for

material A

4.000 4.0249 4 573 302.02

look up

Modulus elasticity

(mpa) Temp, final Temp, intitial Change in temp

Double pain with argon gas steady state

Single Pane

Vol

li


8/34

100000 106 20 -86

100000 20 106 86

area (m^2) time (s/hr)

diffusion

coefficent (m^2/s) Ca (kg/cubic meter)

Cb (kg/cubic

meter)

0.2 3600 3.95E-11 0.9441 0.5901

0.2 3600 3.95E-11 0.9441 0.5901

density A (g/cc) density B (g/cc) A Kg/cubic meter B kg/cubic meter

grams to kg

factor

2.25 7.87 0.9441 0.5901 1000

Surface Concentration

(Cs) depth (x) meters time (t) sec Diffusion erf(z)

1.3 x x x 0.7727

x x x 1.94E-11 x

x 0.002 70561 1.94E-11 x

x 0.002 70561 1.94E-11 x

Diffusion depth (x) meters time (s)

diffusion coeff.

(D)

1.94E-11 x 70561.1 1.94E-11

1.94E-11 0.002 70561.1

1.94E-11 0.002 70561.1

Strain Rate 1 (1/hour)

Strain Rate 2

(1/hour)

1.00E-07 8.00E-06

K1=cnst n=cnst K2=cnst Qc (J/mol-K) Temperature (K)

1 2 x x x

rce

percent weight to kg/m^3

Fick's Second Law Case 1; cnst surface concentration (infinite source)


9/34

x 2 1 10 2000

a (nm) R (nm) h k l

0.2866 0.1241 1 1 10.2866 0.1241 1 1 1

0.287 0.1241 x x x

0.287 0.1241 1 1 1

a (nm) R (nm) h k l

0.3923 0.1387 1 1 3

0.3923 0.1387 1 1 3

0.3923 0.1387 x x x

0.3923 0.1387 1 1 3

Atomic Weight

(g/mol) Volume atoms/cell

55.85 2.35E-23 2

55.85 2.35E-23 2

Atomic Weight

(g/mol) Volume atoms/cell

192.2 5.69E-23 4

192.2 5.69E-23 4


10/34

atoms/cc density (g/cc)

atomic weigth

(g/mol) Temp (kelvin)

Activation

energy

(eV/atom)

8.24584E+22 7.65 55.85 600 0.55

atoms/ccdensity elment

1+element 2 (g/cc)atomic weigth

(g/mol) Temp (kelvin)

Activation

energy(eV/atom)

1.57E+22 1.95 74.55 773 2.6

Max flaw size (mm) strain z at fracture Yield Strength Mpa Modulus Mpa lo

3.183 0.478 400 200000 48.8

3.183

height (mm) Length (mm) Failure Load (N)

2.5 25 200

2.5 25 200

Length (mm) Failure Load (N)

25 965125 9651

Current (amps)

5

5

5

Area (cm^2)

Length of specimen

(cm)

Distance between

+/- on voltmeter

(cm) Voltage (V)

Current (amps or

coulombs/sec)

0.2043 5.1 12.5 0.1

Fracture Toughness

Electrical Conductivity using ohms law


11/34

0.2043 5.1 12.5 0.1

0.2043 5.1 12.5 0.1

0.2043 5.1

Area (cm^2) Width (cm) Voltage (V) Current (amps)

Resistance

(ohms)

0.05 0.5 1 0.019 52.63

x x x x x

Ef =

Eg= band gap

energy (eV)

Nv= effective

density of states in

valence bonds 1/cc

Nc= effective

density of states in

conduction band

1/cc

Temperature

(kelvin)

1.18 1.12 1.20E+19 2.80E+19 200

Electric Field (V/m)

Electron Mobility

(m^2/V-s)

Conductivity (ohm-

m)^-1 Current Density

500 0.2 0.0961200 48.06

500 0.2 0.09612 48.06

500 0.2 0.09612 48.06

500 0.2 0.09612 48.06

Temperature Conductivity

300 240.3

400 160.2

Intrinsic Semiconductor

Electrical Resistivity of Metals

ctor (p-type)

Extrinsic Semi Conductor (n-type)


12/34

Temperature

coefficient of

resistivity at 20C

(C-1

) Temperature Final Temperature Initial

Change in

Temperature Resistivity

0.0039 1000 200 800 1.17E-07

0.00393 1000 200 800 7.14E-08

0.0034 1000 200 800 9.08E-08

0.00651 1000 200 800 6.03E-07

0.00336 1000 200 800 7.61E-07

0.01784 1000 200 800 6.81E-07

0.00089 1000 200 800 1.64E-06

0.0069 1000 200 800 4.46E-07

0.0004 1000 200 800 1.32E-06

0.003923 1000 200 800 4.39E-07

0.0041 1000 200 800 6.81E-08

0.006 1000 200 800 6.21E-07

0.0036 1000 200 800 6.79E-07

0.0045 1000 200 800 2.53E-07

0.00419 1000 200 800 2.57E-07


13/34

T2 T3 T4 Xglass (m) Xgas (m)

5.0318 14.9682 15 0.002 0.005

Final

Temperature

Initial

Temperature

Linear Coefficent of

Thermal expansion

(1/degrees C)

100 20 0.0125

100 20 0.0125

100 20 0.0125100 20 0.0125

100 20 0.0125

Heat capcity Cpfor material A (J/g-

k) Q (J)

% change in density

material A

initial Volume for

material B (cubic cm)

Final Volume for


0.775 840.04 0.6% 50 50.04

look up

umetric thermal expansion

ear thermal expansion


14/34

change in

concentration

(kg/cubic meter)

change in depth

(m) concentration gradient

0.354 0.001 354

0.354 0.001 354

z D0 (m2/s) Temperature (K) Activation Qd (J/mol)z

0.854 x x x 0

x 2.30E-05 1273 148000 0.025

0.854 x x x 0.05

0.854 x x x 0.1

0.15

0.2

Temp indpendent

const (D0)

Activation

energy Qd

(J/mol) Temperature (Kelvin)0.25

2.30E-05 148000 1273 0.3

0.35

0.4

0.45

0.5

Diffusion given Qd, D0, and temp


15/34

2*theta

(diffraction angle,

DA) degrees 2*theta, radians lamda (nm) Energy (J) Frequency (Hz)

24.81 0.433 0.0711 2.80E-15 4.22E+1724.81 0.433 0.0711 2.80E-15 4.22E+17

24.81 0.433 0.0711 2.80E-15 4.22E+17

24.81 0.433 0.0711 2.80E-15 4.22E+17

2*theta

(diffraction angle,

DA) radians

2*theta,

DEGREES lamda Energy Frequency

1.42 81.36 0.1542 1.29E-15 1.945E+17

1.42 81.36 0.1542 1.29E-15 1.95E+17

1.42 81.36 0.1542 1.29E-15 1.95E+17

1.42 81.36 0.1542 1.29E-15 1.95E+17


16/34

Lf or fracture

length (mm) strain y Ao (area prior) Do (mm) Af

72.14 -0.141 128.7 12.8 95.03

Conductivity

(ohm-cm)^-1

Resistivity (ohm-

cm)

Current Density

(amps/cm^2)

Electric field intensity

(volts/cm)

Force on a single charge

(N)

0.1997 5.0069 0.49 2.45 3.93E-17


17/34

0.1997 5.007 0.49 2.45 3.93E-17

0.1997 5.0069 0.49 2.45 3.93E-17

5.0069

Resistivity (ohm-

cm)

Conductivity

(ohm-cm)^-1

Carrier concentration

of dopant (cm^-3)

Hole Mobility (cm^2/V-

s)

1.75 0.57 x

x 0.57 1.00E+17 35.6

ni = carrier

concentration

(intrinsic) 1/cc

n = carrier

concentration

(n-type

extrinsic) 1/cc

p = carrier

concentration (p-type

extrinsic) 1/cc n*p ni^2

1.43E+05 8.18E+14 4.11E+23 3.36E+38 2.05E+10

Doping parameters (p-type)


18/34


19/34

Initial Densityfor material B

(g/cc)

final densityfor material B

(g/cc)

Initial Mass for

material B (g)

InitialTemperature for

Material B

Final

Temperature for

material B

Heat

capcity Cp

formaterial B

(J/g-K)

1 0.9991 50 298 302.02 4.18

look up


20/34

er f(z) z er f(z) z erf (z)

0 0.55 0.5633 1.3 0.934

0.0282 0.6 0.6039 1.4 0.9523

0.0564 0.65 0.642 1.5 0.9661

0.1125 0.7 0.6778 1.6 0.9763

0.168 0.75 0.7112 1.7 0.9838

0.2227 0.8 0.7421 1.8 0.9891

0.2763 0.85 0.7707 1.9 0.9928

0.3286 0.9 0.797 2 0.9953

0.3794 0.95 0.8209 2.2 0.9981

0.4284 1 0.8427 2.4 0.9993

0.4755 1.1 0.8802 2.6 0.9998

0.5205 1.2 0.9103 2.8 0.9999


21/34


22/34

Df or fracture

dia. (mm) v

11 0.294

acceleration of

a single charge

(m/s^2)

charge Flux

(Volt-meters) charge

number of

electrons

4.31E+13 0.005011831 4.44E-14 2.77E+05


23/34

4.31E+13

4.31E+13


24/34


25/34


Thermal expansionmaterial B

(1/degrees C)

% changein density

material A

7.13E-05 0.09%

look up


26/34

Elementary charge 1.60E-19 coulombs

Boltz 8.62E-05 eV/K

Avogadro 6.02E+23 atoms/mol

Plancks 6.63E-34 J-s

Speed of light 3.00E+08 m/s

Gas cnst 8.31E+00 J/K-mol

permittivity of free space 8.85E-12 F/mmass of an electron 9.11E-31 kg

Q (watts) Area (cubic meter)

3333 0.5

Q total Q3 (watts) Q2

47.69 15.90 15.90

Enthalpy Change H Change U

0

Heat Capactiy Heat Cv Change Temp#DIV/0!

Heat Cp Change Temp

#DIV/0!

linearCoefficent of Thermal expansion material A

(1/degrees C)

initial Volume for

material A (cubic

cm)

Final Volume for material A

(cubic cm)

7.60E-06 1 0.993821641

look up

Thermal Stress

(mpa) coeff. Linear expansioncompressive (Tf>Ti), thermal stress


27/34

tension 172 0.00002

Activation energy for CREEP (Qc) J/mol-K

Temperature 1

(Kelvin) Temperature 2 (kelvin0

186329.2125 700 811

MORE CREEP: Strain Rate (1/hr) stress (Mpa)

Dependence of creep strain rate on stress 19600 140

Dependence of creep strain rate on stress AND

Temperature 19588 140


28/34

1.38E-16 erg/K 1.38E-23 J/K

5.189eV/K-mol

Kglass T1 T2 Xglass (m)

2 5 15 0.003

Q1 Area (cubic meter) Kgas (w/m-K) Kglass T1

15.90 0.5 0.016 2 5

Change P Volume Final Length (m)

Original Length

(m)

0.2 0.1

0.2 0.1

change U 0.2 0.10.2 0.1

Change H 0.2 0.1

Initial Density for

material A (g/cc)

final density for

material A (g/cc)

Mass for material

A (g)

Initial Temperature

for Material A

Final

Temperature for

material A

4 4.024867075 4 573 302.0193305

look up

Modulus elasticity

(mpa) Temp, final Temp, intitial Change in temp

100000 106 20 -86

Single Pane

Double pain with argon gas steady state

li

Vol


29/34

100000 20 106 86

Strain Rate 1 (1/hour)

Strain Rate 2

(1/hour)

1.00E-07 8.00E-06

K1=cnst n=cnst K2=cnst Qc (J/mol-K) Temperature (K)

1 2 x x x

x 2 1 10 2000


30/34

T2 T3 T4 Xglass (m) Xgas (m)

5.031796502 14.96820 15 0.002 0.005

Final

Temperature

Initial

Temperature


Thermal expansion

(1/degrees C)

100 20 0.0125

100 20 0.0125

100 20 0.0125100 20 0.0125

100 20 0.0125

Heat capcity Cp

for material A (J/g-

k) Q (J)

% change in density

material A

initial Volume for


Final Volume for


0.775 840.0400754 0.6% 50 50.04

look up

ear thermal expansion

umetric thermal expansion


31/34


32/34

Initial Density

for material B

(g/cc)

final density

for material B

(g/cc)

Initial Mass for

material B (g)

Initial

Temperature for

Material B

Final

Temperat

ure for

material B

Heat

capcity Cp

for

material B

(J/g-K)

1 0.999140606 50 298 302.0193 4.18

look up


33/34


34/34


Thermal expansion

material B

(1/degrees C)

% change

in density

material A

7.13E-05 0.09%

look up

Equations for Matse 201 Penn State

Documents

Transcript of Equations for Matse 201 Penn State