NBSIR 74-355 C/?)

CARBON THIN FILM THERMOMETRY

R. S. Collier

L. L. Sparks

T. R. Strobridge

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1973

Final Report

Prepared for:

National Aeronautics and Space Administration

Marshall Space Flight Center

Huntsville, Alabama 35812

NBSIR 74-355

CARBON THIN FILM THERMOMETRY

R. S. Collier

L. L. Sparks

T. R. Strobridge

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1973

Final Report

Prepared for:

National Aeronautics and Space Administration

Marshall Space Flight Center

Huntsville, Alabama 35812

U.S. DEPARTTVIENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts Director

CONTENTS

INTRODUCTION 1

THIN FILM FABRICATION 1 THERMOMETER CALIBRATION 10

CONCLUSIONS AND RECOMMENDATIONS 14

REFERENCES 15

APPENDIX A. GRAPHICAL REPRESENTATIONS OF THE CALIBRATED FILMS A-1

APPENDIX B. DATA AND CURVE FITTING FOR THE CALIBRATED FILMS B1

APPENDIX C. THREE POINT CALIBRATION OF THE FILMS • . . . C-1

APPENDIX D. LIQUID GAS DISCRIMINATION SET POINTS D1

List of Figures

Figure 1. Carbon film deposit rate and thickness 6

Figure Z. Film properties - Effect of substrate temperature and

deposition rate 7

Figure 3. Film properties - Rate effect at 200° C 8

Figure 4. Film properties - Thickness effects 9

Figure 5. Calibrated cryostat 11

Figure 6. Electrical circuits 12

List of Tables

Table 1. Carbon film deposition parameters 5

111
ABSTRACT

This is a summary of work done on NASA (Marshall Space Flight Center)

purchase order H-92167A concerning Carbon Thin Film Thermometry. Optimum film deposition parameters were sought on an empirical basis for maximum stability of the films. One hundred films were fabricated for use at the

Marshall Space Flight Center; 10 of these films were given a precise quasicontinuous calibration of temperature vs. resistance with 22 intervals between

5 and 80 K using primary platinum and germanium thermometers. Sensitivity

curves were established and the remaining 90 films were given a three point

calibration and fitted to the established sensitivity curves. Hydrogen gas -liquid

discrimination set points are given for each film.

Keywords: Calibration; carbon films; low temperature; thermometry; vacuum

depos ition.

iv
INTRODUCTION

Thin film thermometry has attracted attention for a number of years,

primarily from the desire to know true surface temperatures under transient

conditions. Also, thin film sensors have the advantage that they can be fabri-

[1 2] cated quickly in large quantities. Previous work ' has shown that carbon

films can be used to give a high level signal in gas -liquid discrimination at

cryogenic temperatures; also, the resistance calibrations at the boiling points

of helium, hydrogen, and nitrogen and at room temperature suggest that the

resistance vs. temperature characteristic is nearly linear on a log-log scale.

This suggests that the carbon films could have useful thermometer properties

for the entire cryogenic range.

The purpose of the present work is to investigate and develop the

thermometry properties of carbon films particularly in the difficult range

from 14 to 20 kelvins and to provide MSFC with approximately 100 useful

sensors for further use and evaluation. The areas of effort include the optimization and refinement of the thin film deposition process, precision calibration

of ten of the carbon film sensors and three point calibration of the other 90

films

.

THIN FILM FABRICATION

The carbon films are fabricated in a vacuum system with pressures

- 6 - 8 between 10 and 10 torr. The carbon is vaporized by a high intensity

electron beam and the carbon vapor is condensed on an insulating substrate;

most commonly, this substrate may be quartz or pyrex glass.

The physical and electrical properties of the film are highly dependent

on the deposition parameters; namely, deposition rate, substrate temperature,

film thickness, background pressure, and the nature and cleanliness of the

substrate. The optical appearance of the films may range from a dull opaque

black to a shiny translucent blue. The surface adhesion of the films also vary;

some films may rub off easily and others are difficult to scratch with a steel
point. The electrical properties, resistance vs temperature, also vary; some

films are more sensitive to temperature than others. For some films, the

resistance is stable on thermal cycling to cryogenic temperatures; other

films are not stable. Most films seem to have an upward drift in resistance

due to aging at room temperature although there have been some films where

the drift is less than 0. 001 percent of the total resistance for periods of 15

[1] months or more.

It is known that the crystal structure of the films can take various

[3] forms. Gjonnes has found by electron diffraction studies that the film

structure contains a mixture of 6-ring and staggered 8-ring structures similar

[4] to those found in tetraphenylene. On the other hand, Jenkins, et al. have

o found mixtures of graphite and diamond crystalites on the order of 25-50 A dia

[5] meter. Also, Fischback reports a definite role of the substrate surface

condition in determining the crystal structure.

Presumably, it is the variety of possible crystal structures which

causes the great variety in the physical and electrical properties of the films;

and the great latitude in the film fabrication and vacuum deposition parameters

which makes such a variety possible. It remains to find those fabrication and

deposition parameters which will produce films with a useful temperature

sensitivity, which are stable on thermal cycling, and have no long term drift

due to room temperature annealing.

To relate these desirable properties to a particular film crystal

structure is beyond the scope of this present work; rather it was our task to

see if there is a semi- empirical relationship between the film deposition

parameters and the electrical properties of the films and to produce some

useful films (approximately 100) for further testing in NASA facilities.

At the request of NASA, a joint effort was arranged with an independent contractor under NASA contract NAS 8-25097 to fabricate the carbon films;

testing, calibration and evaluation were done at NBS.

2
Films were deposited under various deposition rates, thickness

and substrate temperature. It was found that the substrate temperature is

the primary factor in determining the temperature sensitivity; lower

substrate temperatures produce more sensitive films. The film deposition

rate seems to be the primary factor determining stability on thermal cycling;

high deposition rates tend to produce films which are unstable and often are

seen to crack and peel from the substrate. The condition of the substrate

also seems to be important in stability and drift, however, at present, there

is no clear qualitative guideline. The thickness also plays a role in stability

and sensitivity; the thicker films seem to be less sensitive.

The thickness of the films ranged from a few hundred to a few thousand

Angstroms; the deposition rate ranged from 1 to ZO Angstroms per minute;

and the substrate temperatures ranged from 100 to 300 centigrade.

The first parameter which was optimized was the substrate temperature

at or near ZOO centigrade. This was chosen so that the sensitivity of resistance

vs temperature is useful in the cryogenic range between 4 and 80 kelvin; if

the resistance ratio between room temperature and boiling nitrogen is on the

order of two, then the resistance vs temperature is nearly linear on a log-log

plot.

Secondly, the deposition rate was optimized. Initial efforts were concentrated at low deposition rates on the order of 1 Angstrom per minute since

it was known^^^ that at low deposition rates the films were more stable; however

at these low rates it was difficult to obtain reproducible results from run to run. This is possibly due to the effect of background gases in the deposition system;

the rate of Impingement of gas molecules being about 300 times the carbon

at these rates. At slightly higher rates, from 3 to 10 Angstroms per minute,

fairly reproducible results could be obtained in the film resistance and sensitivity from run to run, and also among the samples in the same run; however,

it appears that there Is some sacrifice in stability and drift in some of the films.

It was felt that reproducibility was the first achievement which should be m.ade

3
in order to study the s emi-erapirical relationship between deposition parameters

and electrical properties of the films.

Accordingly, eight deposition runs were made as production runs; the

deposition parameters for each run are listed in Table 1. The substrate

temperature was held at 200° C except for runs 001 and 002 which were held

at 155° C. The deposition rates were at 8 and 17 Angstroms per minute and

thicknesses ranged from 2300 to 8700 Angstroms as indicated in Figure 1. The

background pres sures during deposition were about 3x10° torr.

Figures 2, 3, and 4 show resistance vs temperature plotted on a log-log

scale with the resistance normalized to the room temperature value. The curves

are smooth lines connecting data points at room temperature and the boiling

points of nitrogen, hydrogen, and helium respectively. The brackets indicate

the spread among sensors deposited in the same batch. Figure 2 shows the

effect of substrate temperature on sensitivity and also the effect of deposition

rate at 155°C. Figure 3 shows the rate effect at 200° C; and Figure 4 shows

the effect of thickness.

Thirty three sensors were deposited in each run. The substrates were

modified transistor headers consisting of ground pyrex glass with Kovar pin

feedthroughs for electrical contact. Twenty five of the most stable sensors

were chosen from each of the four runs labeled 003, 005, 006 and 008 for a

total of 100 sensors. From each batch of 25, two sensors were chosen for

detailed calibration; they were designated 3-1, 3-2, 5-1, 5-2, 6-3, 6-5, 8-1

and 8-2. In addition there were two cylindrical samples 7-B and 7-C which

were calibrated; these tv/o samples were deposited previous to the present

work and were included for general interest.

4
TARLF. T

Carbon Filn T'eposition Pararr.eters

Batch (1) Tcr.p . "C

—'—' Pressure

Torr

rate Tine

Xours

Thickness (2)

: Ion i t o r Hz/Min

Sv.bst Monitor

Hz

Flat

oA

Cone

o Flat A

oA/Mir

Cone

0A/Min

001 155 3X10"" 11 17

... , 5.5 8;00 4700 7300 2300

i 002 155 2x10"^ 5.5 8.5 2.7 8:28 2725 4200 1400

003 200 3X1

0~^

11 17 5.5 7:35 5600 8700 2800:

004 200 3X10"^ 5.5 8.5 2.7 7:45 2600 4000 1300

005 . 200 3X10"^ 11 17 5.5 7:47 5450 8400 2700

006 200 3X10"^ 11 17 5.5 ^:00 2725 4200 1400

008 200 3X10"^ 11 17 5.5 2 :30 1500 2300 (3)

C-9 200 3X10"^ 11 17 5.5 4:13 2750

• 4300 1400

5

Di^jia XNionj 7 wiirvrf M^rna niuzajiq cci oa^c tin,1
*03 MlOtAStQ IMlOni 8 Hi^tf Hdvno NJoxAiid cci-ao»c OH

THERMOMETER CALIBRATIONS

It is seen in figures 2-4 that the three point calibrations suggest that

the resistance vs temperature is almost linear on a log-log scale if a smooth

curve is drawn through the three points.

Until this present work, there has been very little data (and no precision

data) at temperatures between the cryogen boiling points. Precision thermometry requires that intermediate points be known and that there be good interpolation formula between calibrated values. Also, from a qualitative point of

view, the thermometer engenders more confidence in its use if there are no

bumps or wiggles in the calibration curve.

With these points in mind, a precision calibration was obtained for 10

of the carbon films for temperatures between 6 and 80 K. Special attention

is given to the range 13-20 K which is approximately the interval between the

freezing and boiling points of hydrogen. It was expected that the carbon films

would be particularly useful in this range.

The calibration was done in the cryostat used for the NBS thermocouple

calibration program. This cryostat is described in detail in NBS Monograph

124 by Sparks, Powell, and Hall and is shown schematically in figure 5. A

very basic sketch of the system wiring is shown in figure 6. The carbon re- sistors were thermally connected to the variable temperature block by imbedding the resistors in a copper ring which was in turn clamped to the variable

temperature block.

The primary thermometers used to determine the temperature of the

variable temperature block were a capsule type platinum resistance thermometer

for temperatures above 20 K and a germanium resistance thermometer for temperatures below 20 K. Temperatures above T = 20 K are based on IPTS-68

while those below T = 20 K are based on NBS P2-20 (1965).

All measurements of resistance (primary and carbon thin film thermometers) were made using the standard four terminal method. The voltage measuring device was a Fluke model 8300A digital voltmeter. The mininum input
LIQUID Np

HEATER

COIL

METAL

DEVVAR

UPPER

CHAMBER

HELIUM GAS

THERMOMETER

BULB

FILL TUBE

LEAD WIRE

TUBE

VACUUM

CHAMBER

PLATINUM

THERMOMETER

76 K

TEMPERING

FOR LEADS

GAS VENT .

UPPER

TEMPERING

BLOCK

PLATINUM AND

GERMANIUM

THERMOMETERS.

COPPER

BLOCK

COPPER THERMAL

BY -PASS

RADIATION

SHIELD

LOWER

CHAMBER

LIQUID

LOWER

TEMPERING

RING

Figure 5, Calibrated cryostat.

11
INSULATED

JUNCTION

CRYOSTAT

L!0

THERMAL ANCHORING

at Liquid Nitrogen

Temperatures

VARIABLE TEMPERATURE BLOCK

for Thermometers

Multiple

Coils

A.

Leads to primary

Thermometers

Multiple coils

Copper extension

wires

Electrically shielded

wir"23 to Instrument

<-WAX SEAL

I?

I ! Multiple

Coils

Figure 6. Electrical circuits.

12
resistance of this device on the ranges used is 100 mega ohms; this high

input impedance allows this instrument to be used as a potentiometer in that

essentially no current flows in the measurement arms. The general approach

used in making all measurements was to pass current through a standard

resistor and the specimen and measure the voltage across each. A similar

set of voltages were taken with the current reversed through both the standard

resistor and the specimen. The average of the forward and reverse voltages

and knowledge of the resistance of the standard resistor allow the carbon thin

film resistance to be computed. Several runs were made at a given constant

temperature with different carbon resistor currents being used. No appreciable

current dependence was detected.

The results of the calibrations and also other data for the films are

contained in appendices to this report:

Appendix A contains the graphical representations of the data for the

10 calibrated films. The circles represent the data points and the line represents the fitted curve which is an expression of log T as a polynomial in log R.

Appendix B contains the coefficients of the polynomial and a comparison of the

calculated values with the experimental values. It is seen that the residuals

are on the order of a few hundredths of a degree which is about the same order

of accuracy as the calibrations.

Appendix C contains the three point calibrations for the other 90 films

as well as some data on the long term drift for each of the runs. This data

was taken over a period of 10 months. Appendix D contains information on the

hydrogen gas-liquid discrimination set points.

13
CONCLUSIONS AND RECOMMENDATIONS

The calibrations show that the carbon film resistance vs temperature

curve is smooth with no noticeable bumps or wiggles in the entire cryogenic

range between 6 and 80 kelvin. The films are sensitive in the subcooled

hydrogen range making these films useful for hydrogen slush applications.

The film deposition process has been refined to the point where reasonable

reproducibility and stability of the films may be achieved.

The empirical approach to carbon film fabrication has produced a film which should be useful for many temperature and phase sensing applications. It is felt that further refinement of the processes for precision

thermometry should be pursued in order to obtain films which are consistently

stable and free of drift; improvements could possibly be obtained by a study

of the film crystaline properties as obtained by electron diffraction and microscopy and relating these structural properties with the electrical properties;

a study of this nature has been beyond the scope of this project. Fundamental

research along these lines seems to be justified since there have been several

films produced "accidently" which are completely stable and have no measur

able long term drift. It is also possible that further semi-empirical variations

of the deposition parameters may produce these desired refinements; however,

it is our present view that a fundaraental study at this point would be

more productive.

14
REFERENCES

J. C, Jellison and R. S, Collier, Advances in Cryogenic Engineering,

Vol. 14, p 322-330 (1969).

R. S. Collier and J. C. Jellison, Advances in Cryogenic Engineering,

Vol. 15, p 251-261 (1970).

J. Gjonnes, Acta Cryst., Vol. 13(1):54 (I960).

G. M. Jenkins, J. A. TurnbuU and G. K. Williamson, J. Nuclear

Materials (Netherlands), Vol. 7(2):215 (1962).

D. B. Fischback, NASA Report CR- 97494.

15
APPENDIX A

GRAPHICAL REPRESENTATIONS OF THE CALIBRATED FILMS.

The following graphs show the resistance vs temperature for each of

the ten calibrated films. The dotted circles represent the data points and the

solid lines is the mathematical fit described in Appendix B.

A-1
I

i

RESISTANCE (Ohms)

RESISTOR R31

i

RESISTANCE (Ohms)

RESISTOR R51

A-4

RESISTANCE (Ohms) .13-

S •f£>!»5 RESISTOR RS3

A-6



A-10
I I ]

i 'i i i HI 11 ? " ' ' ' 1 " I ' > »

i

A-11
APPENDIX B

DATA AND CURVE FITTING FOR THE CALIBRATED FILMS

The following tables give the measured values of resistance and temperature as well as the coefficients and calculated values of the temperature

in terms of

2 3 4 5

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TH:: CCEFFlCiETUS-ruR AM EXPaNSIuN W 1 TK " 5 " TE":ri-S "ARE

1. D 5 6 152 32 55 + G a

2" - 1 . 5 9 3 5 9 i o u i + u -j 2

"'9.2"J3T539C3o^C71-

-2.^+3735^^107 + 001

' 2 * 4 u 3^5 -J A- ^ 4 ^• 5 + u U 'J'

COrrSTANT'

X**i

^ ^JI^-'^V X**3

THE COEFFICIENTS FOR A^i EXPANSION ^ilTH b TERHS ARE

A= -3.63i)ly3232^ + <] o2 CONSTANT

"IBTz: 7. Scu7T577T5 + i:G2 X'-^l

C= -G.7G501l7li7-n:d2 X**2

2 . 621 i+Ho35"3r+u G 2

" X-^*3' ^ -5. i sl j522o33t-j ul X**4

. itT 8u'o o 3o J 1"2 5 -F-sru G' ~ ~

B-5
rhlNi' FILM Ga^BON rH£R,^OHcTc^ 'RSY-Z'"

"

Y 15 TIflP. IM K _

,_X IS R£SlST_M_MGc

lcgio r Versus uugu r for k£sistor r32

" Tog X

2, 727363-f- uL u

2. 55 j565 + iC u 2/5i+6jIT-^-o

2, 51i2_9i-(-uCC

2. ^a32i9-HGQa

2. ^+6dUi5+uCi;

2, 39^205+aGa

'2 . 3 i+"5T."2 5" + a i7ir 2. 302318+00 u 2^"27u95u + iJi>u" 2* 2^.3 2 3+ jC G

log Y ~

" 7 . 7 J U 7 6 9 - C u_l_

J.

"X.

1.

5^i+b37-u01

ii3375^-GG0

Tb"2TWF'IiTnr

log YCALC log Y - log YCALC

7. 7S35Htf-0 Jl -1« 27"5501-0a3

d ; u 3 3 75- uTi 5:i! 5 6 5'3a - C

a"3 9.652G82-eul L 72^+^+9-0 G 2

1.. C 35531D + G0 (T

i.i76757+uGu

^1 , 2"j¥7Wi-17uV

1. 23G9&G + G0U

t; 2 5"5'5W+T;inr

i. 2 791'+2 + uuC

1.12C5 2b+uGG

i. i78Q56+G0 G T.l'95ir5 9+uur

i,23GQ7l+G0 0

1. 2 772bO + CQ D

-7. 153072-003

-1.299if 3.3-003

~"Trb5^rTb^!JU"3~

8, a tt 03 GO -0 0 it ""17^X2^^" GTS" 1. 351669-0u3

T7Z99/^+7 + o u G i.3 9G970+GOC

1 . 5 36^+^5 -t-u C b TVB-93 5i:T+uirU"

i.64-M-7G^<-uGG

1. 3988,^9 + GO 0

1'."'+ / i2i7TuuOi. 5 3 7^73 + J J C

1, 6i+i+Ci7 + LG 0

2. 329995-1; ijo

-7. 3786&a-0L)3

-l,3;iU3l/-UU3

-1. J28G08-GG3

'a-."2iTi3"'zr3T-u'Gir

2. I7!*i+1G + GG G "2.'i28lErg^^QGT

"37j Hnr2"9'T; -"CrjT?"

6. d730i+2-G0^

T7o37Zh3+uGu

1.7o733i+^-aGG

1 . 3 519 +• OTTT

1:T5^o515 + JGir

i« 768390 + 00 0

i,92i+722-i-uGu

rr2o8tti4-uuir

-1. 055bi+:J-0G3

1. / <^3U oo-u'CTT

-1. it732i+7-G G3

"?T3^351B'2^G"u5'

u99i78+ JG i. a232'+9f

G "l.^^"2G"&TFuGT x.^irr979+'uTn7

TH-: STA^MDARD Oc^yiAl'ION l;^ TH£ TRANSFORMcO \/AkIA9L£ IS 5.370-0 33

1 Ht' WEIGHTED ST5"N JAR 0 "DEVlATrON IN THE "TR'A^^iSFaRT1Za~VA-R^AB•CZ "TS GVOTS^t

B-6
> IS T_M.= . IN K

2E EXr^RI HENT

,X IS RiSISTAN'Jc IN OhHS

PCX I T S"A ;Nir " "5 TE rj-1 s

. ''

6 • 66 35 +

6 . i 2 U 1 +

5 . 35 73+

7Gb w +

3. 7iGl-i3"."527-r+"

3 « 515 3 t 3: 3 J 5^9 + 3. lo71+

3. :^Eit+

2.^377+

2. 2132+

2;7ir3"3T1. 3662+

T". 7 39-1+'

1

.

6h&3+

1, 3^49+

1T256"5 + 1. 233d+

uG2

JG 2

u u DC 2"

ut 2

0G2~

ju2

uor

0 G 2

u G 2

u u~2

u u 2

J G 2

ur2~

J G 2

t]D2~

GO 2

"3'« "99 5ir G^ T+ 3 Z'Z

"' 7»J0buGG + '.yGc 3 J J

5^ u C~ij + ij G L l.l3l4-a-a+LGl

TiZ 3oTU j + GGT "

i . 4-5 0 J +i; u 1

'1T5'0 Z317IFF"C~G 1

1 • 6 J 2 3tj G + u a 1

TVrD'2ruT+uGl^

1.3 MoGj + wlI

X.9 G 1 7Tra"+ uBi"'

1* 9 I*'*! u J +u 0 1

"ZTs-'o u"Z"oir* iim~

2.95G1GG+GG1

-Ti "^^i91"0lr+^J^r

3,92200G+uGi

'47 4 ITTuir+r;rr

" H«d6660 3+uGl

3 ^TZ'^'G'G + u G r~

7. 3'3 3 3C G +GG1

li • 3"cj"C"l'G'C + G"u 1

"

3. 75110G+Gul

YCALC

'"BVUToB H-5 + 7G l~ 6.9 23bod+uGG

' 9.'2 3ai36+'G j U 1. G bc279 + .u

1

"1. 3 iSoBl + G u r

i. ^fb56 66+u j1

~l'."'5 C"doT2'+ OlTT"

i.567Q7i+GGl

lo 693 5 23+GGl"

1. 796196+GGl

'1."B93i+ 7^ + u'Gl'

1. 9c3i+3G + JG 1

2. 959^9i+GG 1

3.-q:i?7 2-5tr+0jr

3. 6 9 HO 31 + G 31

- tf -G 5 TZ 2 + Utl r

H.353639+GG1

"-57-3-6 o 3+-utrr

7. 2 7 35i+i+ + jG 1

"67 AG'S 3 7 6 + GO 1

3. 7^9'+17 + GGl

Y-YG

•~I7T o ^''+"5 &

- a. i+3il7i+-

-2."2 5-133i+-

2. 112G 57-

-^i-i5oG"3-G-

-9. U5634-3-

- 4 . 5 -J 17X2--

3. 5229iG-

"3. if 768 ZS--

5. lG^+i^49-

-a7'2^1^;-7-9--

l. G&6g72-

-fF^-5T3^T3--

-9. 3312G3~

^3. r5C2^ ir^- 2. 736916-

-6v9^779-rZ=-

3»16G7j3-

2. 975593-

-2-,-ai+75 3-9-

1. 633G 93-

A L C

Cu 2

G u 1

G G1

CG2

D u^Z

G Q i

G

"• ?

GOi

GG2

tnr2~

OGl

rfr^-

GG2

Ctj"!

GGl

ocrTH - ~SX;ND mHO" 71117X471 0 N"Tr-r'THr"~aRTbT K A'r--\/^R'I A;SrE"-r S -2 723 6 703- 0 Ql '

B-7
-----T Hjn-r-Flrri-x'^A-^<^Jiv-i"Hii-^rtmTr1"Tr^-n<!ji:"- Z

i IS T£MP. IM .< ,X i:: f\£SISTAN3E lU OHMS

Z2 57XP£T?I>lcTjTAL" POINTS AiiD -Up-TC 6 TE.^HS;'

LOGIC K V£RbJ:> L.OGiu T FOR R£SISTOr< r<5 i

[He c C£F FTC i'E7;T^3~r c^—A"N~ '"'£ XF A :rsrarxr w TTFf

r x £\xi^-s-~vcci^

1. 571 1 25 66+ GO u CCTNSTAP^T"

FHE GCEFFIGIENTS FC^ AN EXPANSION HITH 2 TERHS AR£

7.5G7-n!d55 55 + QaG CONSTANT

FHE GO£FFICI£NTS FO^ AN EXPANSION WITH 3 TERMS ARE

i.i+3u532749b + bGl CONSTANT

-^", TW5'3'^^Z^ 76 + u u 0 ~ X** 1

1.67i22i3'-f J7 + 0GQ X»*2

FH crcHrrTC'irriTS-raT""^:^TrrxF^iTSTOTr-wTTH—i+-r£i<rrs-5-Rt

5".-0it Jj W56TB1-UG u

' Cai^STA-NT"

S.B'+'f'^^ j 75 J 3 + ud 0 X**l

, -SiTGij 52"j G r+ u G t X* »-2 l.ii27&oi^33+G u u X*-3

r H E G CE F F I C IE N TS F OR A rr £ X PA M S IX)T-i ^ W IT H ^-

J c K:n S- AR:£

. ... -Z .7722o-^J32 j7 + GG 2 CONSTAI^T"

5.o3o6o37j3bf0G2 X**l — 'hi Z G rrZ o"83 2 6^' 0 G 2 X^Z

1.3!joo^-^u5 3 7 + GJ2 X**3

r • fa 6 3 :r5 J-Z G J£t + u-j 1 x**-'+

7HE GOwFFlGlENTS FOR AN EXr'Af.SION NITH 6 TERMS

A= 2.Go2367uG^J+GG2 CONSTANT

B = - b . 3X5 3 27 3916+ GG 2 X*-^ r "

" C= 7.5^o5252d73+UG2 X**2

-D = -:t. HVJZ3663I3 + U GZ ' X**3

E= 1, 2b593o5> JH + u u 2 X'-^h

F = irr2-6 31^f J^3+-C-TJ1 x*^-

- - B---8--- -
X ^J-^^J IN K , X IS RtSISTANCe IN OHMS

22" EXPcRJMENTAL POINTS AND "b TtRfiS.

L03ie R VERSUS LOiiO T FOR RESISTOR R5i

log X

2. 22 6b&t» »oaa

2. eCiu 6u + 0 C li 2. 156905+GOO

2. C 95^*6 U + 0 0 0

"2. C/8/^2+J0u

2. 07£*lQ5-»-QQ0

'~2T1QX'+3 7b+oau

2> &550 9 ^»J00

2* C^556G + G0u

2. 03a776+3C0

2.03l7Sr+000

2. 002619+000

1. 977752^-000

i. 957367+QOu

~Tr9"¥QTr2TMT

1.925Q65+00Q

1, ti893'f7+aDu

i. 861765+000

1. 6^3111+000

log Y

7.7aG7a9-001

J»5^tit637-uiJl

"ITu 4 1'g^f 5 + u uD"

1.113375-*":ui:

l.ib2/i»^ + ubL

1.176757+000

TT2i3"^4TW+"uTrcr

1.230960+aDC

i.2555d6+uOu

i.279itf2 + bue

1.2997if7 + uOc

l»39Q9 70 + CiGu

1.536ifit5 + uuC

i,59JFDT+innr

l«&f*'+7Q^+ + LCD

TTF3TZ¥T+innr

1. 76733it + GCG

1.863519+Tri7u'

log YCALC

/. 78B5h3-G31

9. 552226-iJG 1

T# 0 '+"2b&2 + Ju 0 i. ll36b5 + jG 0

,1. 1760 98 + Liu C "X. ^1 bdc bavdixr

i. 23G7Hif+ua G T72^gT3+"j'u

1. 27d9d3+aQ 0 TT3 u(JUoD + dTO"

1.390176+uaQ

1. 5 3 68Ct + 0'j 0 T75'9T7Tir+'uTi'u"

log Y - log YCKIXr753936-0G^+

-7, 390336-00^*

7 ,1 7 1 5 5"5^in+~

-,5, 335'2'od-Ubif " 6. 5 620 31-00 It ~oT' OOT7T9-UU Vi

2. l5i+5 60-Q0C1

~=^'2.'3Z5gTr2^RroTn

1. 56629a-00itVi

"^^Tr3 31^/ 4-0:0

7•9t^23a6-aO'^^•]

1,923249+uQC

i.942Cb3=s^rcrr

"T7^^7o2b-U0b'|

-3. 549521-d04^

ir5^

1, 645264 + 0 J 0 -5. 796740-Qa4i

:nrC =^7 7Tby /'5-lju4:

l* 767246f.JG 8 . 6 129 61-0 05::

1,9249351- Ja o l.T9'4Tolc + c"u 0

""r;'9T481b-UUo

-1. &35714-003.:

--£r7-4"o 4"8Tr^^~

Trtd STANDARO

Trfr'WtrSKTED"

DEVIATION IN THE TRANSFORMED VARIABLE IS 9.503-334.

l^rmDlkRU UZVTATIOli IN" "THE" T RA w SFCKJIEO 'VATrLTrerFTS:"

B-9
IS TEMP. IN K ,X IS RtSISTANCil IN OhHS

'2 2" rXPcRTMrNTMr-T'iniTTS"'' A riiJ-'-e TERMS.

X y YCAi_G Y-YCALC

i--53-5-tr+Tr[7z Tr9iTOTraw[rtr~5Twg7rin-croD—-rroTztrztt-inrz

i«5a684-L)G2 aoaGGQ+UOij" 6. 98137G + J3 C 2.o6303o-CC2

"IVkZSZ-i-jUZ d', U a ?G"uT+u 9 7C2rT3B+"': aO' ^ -r;-5"33T7^tuZ

i, 3275 + jLZ i.i JlttJu + jCl 1. lC32204-0u 1 -1. 820359-0 u 2

i . 2Cf~8'5 3 OZ r: 296'Tinr+- J 01 r.-2 99765TtJtI I

- '-1. i+65 26 0^0 CTTl.ljB7 + a02 l.i+^itDUG + bOl 1. tf557i5 + 0ul -1. 11516 3-002

1;-! aB'l"-'' Tu "2 TTTsTZTUTn-"u U

1

1l-FuO u"? 5"^ : 71" "ZTZTST r5-0u2

I.i59ti + GG2 l.oJ23ua + uJl 1 . 5990 S^t+u a 1 3. 266i60-Gu2

- "1.-1 353-FO G-2 rrra Zuu-xn-^z-i 1 . 7 trri sst- aa i

isr-k-^rszT^^xxrs

1.1132+002 1.801300+001 1.002265+001 -9.6^9769-0 0 3

T.u^tf-i. air2 r."3 GTrc-tn^GX—i ; 9171gx-d-+o -ti e^^-^+irrs-s-^ tnro- 1.0759+002 1.99h1uO+OC1 1.99563G+001 -1. 530261-C Q

1 „

>

,j 5

3

-[.-g-trz 2.^6u25u+lC l ^tr5-5 7 G 5 + Jtrt tFTifWrrE^eij-?-

9. 5006+001 2. 95010 0 + 001 2. 950090+031 9. 833^+63-0 0 5

9~." J6 5 a-+-o —^3T-tf-3-9t-trimro^t -3 -.-^t t9-r2-+ra-t— 8:t 1 9^1-- irO-2

8.7159 + OCi 3.522000 + 001 3.9 2^+3 73 + 0:1 -2. 3733 66-0 0 2

o.wi ?z+ J oi: if ; ifTZTTrtr+ir1

1 «:^-9tr+ o" ui— 5v-8^j3-7^-3^ o^(r2

8. 1776 + 001 i+.366600+u01 870967 + 001 -i+. 1671 0 7- 0 0 2

77r5t-8-+:rm 5-;-35- 2 ttoo+ u in 5T"8-5-t2~3^+a-^-i imrb-o-s-j-a-i}^

7.27^+2 + 301 7. 303300+001 7. 2 70166 + OJl 3.313^+0 5-0 01

6T36'8-0"-Fi3 err 3V3^DTutr+0^0T-~'~8Ti+~l-2fe-91+utrt—-^-3T2-59tr5&^irtM"

6.8891 + 001 8.751100+001 8. 7^+2108+001 8. 992039-002

B-10
THl7r-rrtrrt-nrtttinJr^-THE?tTtOTi&TH'^-K^?^^

Y IS T^MP» lU K ,X 15 xESISTAMuc It* 0nM5

22 EXPERrMENrAL-pOINTS''" A:nO' OP TD" 5 "TlRMS."

Ll/GlG R - VckSUJ i.03iu T FOK i\LSI3T0R k52

1 H E 'IT GE FFTi: I z NTS' Ti: T"A rr^rxpA' r i 3 XCTN i-i Tivr- - 1 - T E R ri s~Air£—

1. orr3'7i26 55^oc'ir ~

: caNsiAvrrT'

TH£ CO^FFICItlNTS F0'< AM EXPANSION ' WITH 2 TERMS ARE

7.ifo5265'+i2^+^ Ou - COtNSTANT

g„_^^-^^2-+.r-j J -X^'^L

THt COEFFICIENTS FOR AM EXPANSION WITH 3 TERMS ARE

1 .35uiS72i+2^+Uui CONSTANT

--C TTSTJi 513 0 uTU OF X»-»r

l.i+02H727i6b + 0 J J X»*2

THE~CCEFF Tor-'A rrrrPTiTf jSTOTT-wTTH- - -Tr-rTRits—a-Rc-

-l.GaGS5327ifl+lj jG

- 2".' Z5 7T3"5 5

1" "J 1 +ir jX"

5.bc7^5i89JM--Uui

croNSTA-nTX**3

T H E"~C 0E F F reI EN r S F 0 R A ^^ E X P A riSI 0 N W rT r £ Rr! s- A R E

• i . 2 li ^ 1 5 : 7 5 6 + U 7

Z

2.^+6:52i556o5 + c0 2

• i & u Z ST^S 4 5 3 5"+'TrO"2 5,72ii j2323^<-33i

• 5'. 7 D 3^ 1 5 - 3 OD+U JiT'

CONSTANT

X**l

-x*-^-z —

X**3

THE CCZFFICIiiH rS F0< AH EXPANSION WITH TERMS AR;

K- -6 • 1 5 3 5 ^2 52 3 g+ u u

2

"B ~ '1 . ^ 2 7'5 7^65 i l -t- JTo"

C = -1,3-j61u5j2c>6 + Gj3

E^" - 5~. 9 5 i o o 3 ^2 J 5 + J C 2" E= -1. oi+o 7i27o^6-t-ua2

F"'^ 1.2 r'3T9'53i; j3^'b u T

CONSTANT

X**l

-

X**2

X**3

X*»^+

X*^5

B-11
THIN FIi_M GaxBO'M I r^z.k^O:^^J'^X

13 T_HP< IN ,< ,X L6 P.ilSiSrANGC IN QhM3

LOGIC \/Ik:iJi

POii-iTS AiNu 6 l^•r^2,

RISI:_TCR k5 2

log X log Y

'

' log YCALC ^^log'Y - log YCALTT

2 . 2 7 797 1 + J »: u"" 3 » -f 5 59 ^+ T- C C i i o ^ 5'2 2 7'9 - G' TI IT'b 52 To'^^Cu"^' ' c.252o7Drjuu . 3 '+H-0 5 7- . 0 1 . 5 h6l 26- o j 1 - i . i i 3 o 9 1- 0 li 2 . 1 9 3 1 9 6 -t- 0 C i . G 4- 1 5 ^ 5 f u G C" " 1 . u 1^3 h 1- j 3-" CT T." 1 2 bTI 5 - 0 0

5" " - 2» 17 ji+29+ jC J i.lli375 + L.'GL i« 11^1 76 + -J j Q -8. Q il66o-0 G ^

'2'.-i'5'2r7 5'+ J c: I .T~5"2T^r^i-T:^ I r. r5Z9Z"2T":~ u =ttj53"3'9'5- rr^'

2. Ii+7i36+ Ju . i,i7&75 7 + -u^ 1 . 1 765 3^++ u G C 2. 227^25-CCh

2. 137j51 + ju u i . 2 j 4'7'^'h- +"u'0"l I * 2 i7o 973-riJu-ij rr7"a oZ5'5~- C u'^'"'"""' 2,i273c5 + uOU i.2ju9bu+b0ij i, 23C7 9 2-t-uuO i,o77G6i-00^

' 2 . 1 Id it 2 6 + 0 u u i". 215 '5 5 S^d+I] cl7 1 . 2'5^ 7 5"C' +TJC -17 6^+3 S'Z'j'^iTu'^

"

2.iljl9i++uCu 1 . 2 79i'+2f : u L 1 . 2 7 89 62 + o w C 1.3:2639-00'+

~"2T iT29 2"5+Vinj i".T9T7"4TTTrru rr2'99"5HljTU''r(j 9T9T771 2 - U U b ; 2.u7i36i + 0Cu i,39ij97C+i.uG 1 . 3 91^+ 55 + j j C a^^+b 92-0 0 2 , "0SBTirr+ u i 7+ o 9 S 57T^ IV i^b 9711 2 + 13 Tl T:'2'W7"3T=TrTr5

2.G2356b + uGL; l»936i+'i-5 + uuC i»5 36776 + bCG -3» 3 3 7^4- 7- C C

" 2 u r5 o 2"o +1 u'C 1 . 5 9 3"5^uT+7 fil i". 5 9 3 G^lT+lj Tu ^+777 3W^7^ZZ^ ' 1.9o9322 + l)uu 1.64-H-70^+aGG i.&if^db6<-jJG -1.6130 6 7-00^+

^ 1 ,'^97o"i^t"5+ LilTu r,"o 572 f+ o+^G G"u 1 76 1 TTcc'tljIilj 777 ^ G 2 2 2^DTI'5

1. 951229 + JU- i. 7o733^ + u.. L 1 . 7b791i + b J C -5 , 769G 26-C G iV9222^3+GGG lVti 5 351 J+'GUT" "1. JSZU'kolrZZ'Z 17 117277^-1773"" ~ i.9G 32 C3 + UUU i,925249 + uGu 1.9 2^i+CQ^-GG0 -1. 150^7 G-CG5

1 , 1 9 7 91 o ^ JU G 1 79 h 2 u 6~3 G G O i . 9^151 6 + 7 G 7 57^^6 &5T'9-'u G 4

HE STmNOARJ G£^/i^Ti:jN IN Tht T^.^.. 9F0R;1E0 l'A^I.A6L.7 IS 5,7cl-u3if

H- W£IGhT29 ST7Nj^<a UIVT^TrCTi IN TH £ "TR A;] S Fd^fE O''' V lX'RT!XStZ~lS—'' Q.ZIJS

B-12
jV IS TcMP. IN K ,X IS ricSISTAMGc I OH'MS

! 2Z EXPERIMENTAL POrMTS 'MNu""' "6 TEF,MS." \

i . 7u 9 5-«-uC Z"" 1.5783 + C'CZ

1 * -+196+ JuZ

1. 57il+UCZ

l.ol55+uGZ

1. 267'++iJG2

-rrirso+^rz1. ilGu+a02

1. ol30+uG2

9.T5"Ti + .jinr8,36C7+dGi

ST-juzr+ijcr^

7« 90 53+ jC 1

7,0DjCuu+GGu

i<.lJi^c j + COl

i «29"o30 J +^G 01

i«^5^6GJ + -iJl

"r:~3'aTJirT+'JG'r

i.6J23Gu+^ 31

7 u 2'Crin?+ C"i~ 1.5jl5Uij+-iL;l

" I'o's Trnnn- J ci."^ 1 . 9 JM-IG J + J c. 1

'ZV^oTZ C J + G L i

2.95G103+UC1

-3Tir3 ynrrr u nr

3.922G0a+Gul

wr?rcrcr+ g lt

^•»d66£C'j+uL!l

~'5T3"5^'^n71j'*- u G

1" 7»5j35 3G + ijLl

~5'* 3 3 C rCJ ^TC~r

5. 75lliiC + GGl

"6» G C 7- G G 9 . Cu' 1. iC

1 . 3C

1. h5

rr ^ ± » J U 1.59

T.7 u 1. b C Te 9 G 1.9 9

2.9'+

-tTc 3. 91

4". if I

i+. e 6

5T0

6' 7.2 3

d • H t b. 7i+

YCAlC

13 52+' GO C

2C93+ J J C 7^+65 + u G u 1371 + u j 1

'To97l-"G71'

513G+Gj1

'L^-JT^ G7r9if 59+G : I

l-oi^^3"+G*l;T~

1962+ jG I t:9ri"+Gcri~

36H't + GG 1

Z^-o-r-JtTT

9255+ ju 1

rrztr+otnr

7692+00

1

'+3-ogT0-7r5933+GGi

a~IT9 +0^0-1"

5282+- Gj 1

2329'+jniG088+GG

1

Y-YGALC

~-2. 3 5TSZ j-Crtlo5. 9Co83a-CG3

-2.-^+"5 5 it 7 7- 0 03"

2.355617-GG^

- 2. 39 72 55- U U Z^

-5. 3ui+297-Gu3

7 ~7 T3tr7T-"u"Lro~

2. 8i+G65G-C G 2

-"6 VS7 1 r jr-"i^tr3-

-6 6192 7 5-G G 3 —7 « ^1 3Tr4--C u 3-

i+. 557573-GG3

---2r-.-7 ^+6-tr"r5-- 6. hS^'^+A-S-G G 3

--2 .0 ^0l- a 5-^ bTj-2-

i*. 3u8t+G 7-Gu2

^-r. o-392irr^cr2-

b. 5730 Sa-O G 3

-^7T-7-7-9-3-a-3--^-trG-2"- 1.3j18uh--GG1

-2v222ci7 7-CrG-r1. 1G1233-GG1

Tri 3 T:; ivcrprfcu-uri TrA rJxnr-Tr^'^rw—rr^^-iitAtr^kl-pr'^—i b> trrintr5-tir- Otr 2

I

B-13
...... ..j-^ -.;-jrxc^'tr5-?tstrN--'t-HfrH^^

5---^

- IN K ,X IS RESISTANG£ IN OHMS

EXPERIMENTAL •PurNTS'AT4Il"UP-rC7- 5-TERMSV

lI^iI versus logic r FOR KiZSISTOR R63

HE - CD c FFI CirNT S- POT" -AN"rX PTH^^-O N"~WrTH—1"'"TERTl-S—A-RE"

-

: r, 37'irjirXZ5 5

5"+"0 O GO U c r r 1 L 1 c fH 1 o r u i\ M n c A r M f J J> i u N - . c — u U SN J 1 M IN 1 -LB/iZ^ba/ZS + tlGU X**l

1 w r r - p p T r J r T F n ? AM r y P A N ^ T n

WITH 3 TFRM9 Hhi^

1.3j9 J7d£6ii+QG1 CONSTANT

-—• - — .1 .. ,.>.,,_

-5". 95"5Th?^TI J+ C 0 u 9»5£29d39925-Qai —x^*-r-

-X-CcFTx ^^T^TS^^^^-ATr-^X?^TTSTOT^ —£r-TErms—A-^t

- rrsru roZTisre^ c u i __ q-q.^^

-1.256^632740+0 Jl X**l

-3.0-5 2 5 o ^Id 3 5--F-3-a a X * *-2 -2,6u3/96u736-Liai X**3

i CC£ F P-ICI Er^ T S~F 0:<-mN-£ X-pM riSItJtr- WI T H 5- T ERftS-A^e

• r. To 3 3 5277 T^+ u jT"

H . lb 54^+506^+3+00 i

7.252i762230+GaC

'-CrO^I3TAN-T

X**i

X»*5

X+^i+-

CCiFFICIENrS FOR AN I XPAiNSION WITH 6 TERMS ARE

A = C = D = E =

3. ^+6^15 3640 7+0 01

5 « T"! u J 0 235 4 9 + (m"

4. 62560 j4i 71 + U 0

- 2 V nJ o 72 u 6 3 2 rU dT

4. 39 3 332414i+u.a

CONSTANT

X**2

X

s
Y IS T£i-1?, IN K ,A 13 \-3:;STAU3l ll^ OhhS

dZ 3Xr>- -ilNENTnu ' POI ITS ANiJ "6 TcKMb/

;_„G1C r< vcR;)J3 _03iJ T FOR. K^-SlLrCR Ko3

1logl-Y AV* log Y log I L^A±jV^ log Y - log YCALC - / 7 1 1 , 7 r( Q - 1 i , ^ 7 ,

f « 7 c- f] A ~ h - ] i] 1 0 u 0

> _ —' o H "'r 1 1 1 1 1 1 t i ^ « i+ 'J ^ 1 ; . i 1 O • n :t ? ^

^ U U J

£^ • 1 o u. ii A 7 — r 1 ^) - rL

r, ^ J J

- ''i y'' i"i v'S H T 4- ; I

' - i

• -r'^~j i|7^Cj 3 ^ _ I 1 ^ 5 7 1- ^ C G i, 7 n ' fi U ^ i- i i t-il 'i^7ST' i 1 .. i 1 5 2 1 C > - J L - 1 .

-^j 3 5 o - f:\i \j \js 2 • T^Tn 1 ^ ^ ^+^1 5 +' JL> tJ^ Li^ ^ • V-* t» ' • T ' J W W '163i;3"i+'+TG'D L Li 4- 7 ^ i 1 ! i 1 . 7 n 7 5 7 + J b

'

'

1. 176638-1-^0 G fi r i+ u u ^

. -"2 - l* ? A ^7 ^ •¥ A U J 2 u 2 5 3 i:? 4- u C

"o - 9" arc— f '."x "

i.' w 0 7 1 ^ rt ^ +

'

i 253^0 1 + e:J Li.— * \j 0 0 ^ 1.'^ c • \j ^ J \j ^ * www -X. 9 —> ^ \J ^ *J \^ <i "~ 1. 2 5 5 u 5 +7) 'o u U U H

C- •

Z". n 1 i t rt 4- n

("^ ^•^f i.275it+2 ^JL~l— +l^WO LiiJL; !• 27d'+l5 + ^ G

C- • n 7 t+ ^ 7 U + I i

i

. 1 ^

._ ^___

"iT

I»j9o97 0 + j^-.l i o 3j31ri^ + 3jC -2. 2 13 19 2-

1.4-b3c57T-i;LiL •T^'TS

'^ R ? 8 + u ? 1 1. 5 v3 7 3 o 6 + J U 0 -9.^363^3- G C M. ^ 2 . 5 2 i}iJ 13^- U U 1. 5935G3 + >jC c '5'9"2i^5+- J 3Tr

^

*' H 7 8 + •] • 1. 1 r (1

t- L 4-

C- • r. '6 5"7 OYSl-'u uT~

2. i«7o733^-"t'uGiJ 1. 76 6i2G-!-jjC -7» 3565 3 2- G G^^

ii+o jM-52 +'u O'-3"~ 1 . 6 63 5 19 + u' u C "

d6i525-t-D J G IVggtt3 3'3- 3 0

3'"' 2. 3c3359+ J'. C i,3232H'i+^ul; 1. i 2^+5^5-Huj L -1,2 j6i7:- »J 0 0

c * 3 7 62 ^5 + 3 t o i. 9 h'I 9 55+ J3 3 "X^Z'i 1 2 A 3-

TRAN -uA3Li IS 1,508

WETIGHTEu 51 \:OAR3 DcVImTTG N i. r THE" TRmnS FGRr-iE 0' V A RI A'

B-15
T H irr F TLTt'-aa <u jir-THc^-^or-r^rrr-c"i^d3-?

Y J.3 K;-!P. IN ,< ,X 13 ^£b^31-.MCh IN 0HH3

Z 2

' iXPcXiMENTAu Pai:«lTS 'AND- 6 TER-1S.

7, o^L;2 + JG'2"'

o » J J ^ J u

5, 3556+JG2

5, 1325+0X2

5. jj'. c5 + jC2

4- . 3 SHi-f riTH"

73iZ + >jL2

3. d573+ Ji) 2

0 "« tf Y'-i 5 + u tTt^"

' 3. 373u-t-jG2

'3 • 13 C 3 + u 172 3,u53^ + l102

2% o To I u'b~c 2. 5672+^fj2

2 . 4^1 7 5t j C'2

' 24,o7c2+uG2

7 J

ij 3 d I, J w +• , ^ L

. J G 5 G D J T C t u

'

i . 2 13 Tuu +- a C i

'

"1"V ^TZ oTTr'Tn " 1.oj25uu + -j-^1

1. 7 'J 2 u u 3 + C 1 1.3Jl3QGf.wl

1. 3 Jr7r:-i--UI•-

l•9^^lLl^J + 'jul

~2~» H b vj "2" ITC 'FL'TI"! 2.35uloU+.Gi

"'3«^3yt a"t;> -ul

3.j22CUG+uOi

^.'+iz7Trj 1-u jr^~

- -(•doooGG+oul

~'5 Vd 5"2^ u'j'V- 1

7,3j33tJ + _\.i

3.33 IT rCTu'+' r LT i

3a7 3llL;U+uijl

Y CALC

6."C 123 sT-Fr'o c"" 5« 963367+^ J L 9* 0^6 0 36 + GDC

l.luClc2+ojl

i. 3 C'3798-<-jaT

"

1 • H 5 59 15 + J 0 1

1* 59^*1724- Jul

lo 5 99313"+!: 7"!"

1, 799C97+C:

-1, 3 9 35T^+aT^r'

l. 3 897 93+ J u 1

-e-rtrr2-7 b9^+ JTrr2.9 5^-2 23 + 0^1

3T-if ^+-6561-+Sul~

3. 9l016i+uQi

^•. <j6516^-»-G J 1

7.26:jb5e + 3Gi

"5. vu5rt+8+ jiri:'^

U<,7^d922 + u 31

Y-YCALC

-1 , 3 397ifT- C ^72~

5 » 9 11 3 3

1 - G 0 2

3038^a-Cu?^

1„ 237833-002

- 5 . <+ 9 3 C 3'3'-"uTi'"2"

-2.3i51i:-GC2

""tf i l lUl'JT"- CU'j ~ d* i2753o-Cu2

"~ 2Vl367 7 3-C112-

2. 2C2&32-G 02 - 3T-r3•2^9T---i^t-2-

i+. 3 J6779-0 Q2

-^11-25-6-9-3-3^-trtri122 69 7-C 3 2

7i ^+^t;"b3'i+ - ttr2~

1. 13395 5- GGl

r. 17 3 ir9i+-^ 1. 5155Gi+-'G 32

lT-r-5^9iD-7-7-CiM3. 34-61 6o-C u 1

5G^^o l2-at^-l^-

2. 178if 50-G U2

r9NL7A Rj~Drv I ^ T "T^r-r Hr-QRi Grf-rA-crTiT"K:rA b-t-e-is r;-2-2*^«-e-s-- j oiB-16
TKi>r-"F-ttTt-tr^"CDtnM-rfTL-^icr^ -

IS TdHP. IN K ,X IS RLSlS'i AHO£ IN 0H^'3

22 EXPERIriETiT^'C "POINTS^ AUD'VF TC" 5 TERMSV

»G3iC T VikSUS uOSi.- R FOR R-.SISTUR R65

|-H rXtrZF PICTENTS-F 0 ;^~AK rxpp rru rON~ s-f rTH-" r-T E RM S' a:r^

lV37"rCiul2o&64^u 0 0

'. CONSTANT

HL COLFF ICi£iNT3 FOR AN EXPANSION WiTH 2 TERMS ARE

6. it2727iliJ6 + ': Q d

" CONSTANT

i rg 5 if Hh 3I57XWu 0"u " X* * r

HE COEFFICIENTS FO^ AN EXPANSION WITH 3 TERMS ARc

I.iti5io356i2 + u0i CONSTANT

-7, 9-0 7 73^^ 03 lV+17U"a X* *r "

l.li+23J j957i++G0L) X**2

Hf -o 0 £ F PI Gl ciTrS~"F-GR-A-M~ •£rX-P'.2VfNS"rON-- ft rTti—tr-T Erms-Ai^s

1 , 6 53 ^v 5 e9+ G iri — ' const a r;T

-1.2:j7..737i2o + uai X»*I

- ZiZ 7 7 01-772^2+ " X + + 2

-2.i+5d252733w-Ga 1 X^^o

iHE CCuFFl^^lLN rr- FOR - A N^cXP^AHSimr WTTK- '5 fERi^S- AR^ - -

-

-6, 1663 5 j93£tu + OCr '

' "CONSTANT

l.iu^SJ 9bU39+C02 X-^1

b ; 7T5"55-3 31 33^f LTu X

-~ -X * ^Z

1.7o53ap5136+Gai X**3

-

-

- -1.73?2ocG3 53+w3 J

"

- X**^-- -

HE C0:_FFIuiEivlT3 F G\ AN EXPANSION WiTH 6, TE.OiS ARE

A= 7. 339i+77t+iJl-^G:i CONSTANT

B= -l.'+oH362^j62 + b : 2

" X**!" ' C = 1 , 3t2 J d^i^+Q U2 X**2

D -5.7S3 j6a2255 + 30X ~"

' X**3

"

E= 1.27idGi3377+0 J 1 X*^^

""F = -i.Tro : 723F329"-Fa^-: - - x**-5

f. B-17
Ja^ ^' PI » J SISTAN Cl I N OHMS

2 2 EXP£RI MENTAL POINTS AND 6 TtRrlS.

.0510 T VERSUS !_QGiu R FOR RESI3TCR R65

"Tog X log Y log YCALC log Y - log yCALC

2

933639+OQG 7.75G7a9-cGl 7. 765a9if-aoi -5. 10550^--u GV

2. a8&5l3+uO U d.'+DS^Vi-uci 5. 4i+37^9-GGi 1. 2i916'+-Duo

2, 9.5'+^637-GUl 9. 552361-GOl -7,523i+'+d-0Gi+

2- 75235b + oG 0 1. G'+l^'+5~+yG C 1.

2 • 7Go575-t-oD u l.li3575+uCC 1. lii+C2i++Qa[i -6, ^890 7it-C Gif

"Z7"bB':2o2 + Juu 1 . Ib2/i+if + u U b 1. lbii65/ + du y 8. 7a!+i+9d-bub

2» 672556+UiJ u 1.176757+GGG 1. 176230 + 00 0 5. 2658 l^+-0 Qif

TV^57 0 5^+ u"D u 1.2ji+/''+i4-+UGU 1. 2L392b + ju 0 8. 191ul3-aO£t

2

6t+2^67 + aCa 1.230960+000 1. 23G622 + QG G 3. 3 75u 3 7-0

629 dr5Tf 3 0 G 1.25558b+GGG ± • 255661+CGC if57L62-CG5

2. 615738 + 00 u 1.2 791'+2 + 0DG 1. 2 790 35+OaO 1. 056832-00*+

'2. bCb05l+0G G 1.295747+aOG i. 209634+aGO 1.125209-bU4

2. 56j256>0Gu 1.3 3G970+UCG 1. 3 912 57+00

-2. 86^+738-0 0^+ 1 . '+69637 + GG U i. it7GG53 + CjO -2. 16o99i-GUi+

i2* i+92330 + JOu 1.536^+^+5 + 000 1. 536927 + Gu 0 -i+. 8 2Q2 3 8-C 0 '2. if"&73^>QGu 1,593505+ GOG i. "5'93455+uGO b.2i+Gi+b2-0bb

2. t+it5i32+QU0 1. 6kk93k-*-Qij(i -2. 2977^6- 0 0^

"27 1 • 5 ^7 2^0 +o 0 u X • b571^5 + i:iru 7.85ub/2-bdb

2, 39M-G '6+ U G u 1, 76733i+ + C0C 1. 767306 + 00 0 2.556^+11-005

2, 3t?t>b3i+ + uu u 1. ab351 J +UU G 1. 'o'o22oi++uO 0 1. 23i+8b5-UU3

2. 351^10+uOG 1.9232^+9 + 000 1. 92i+38if+00 0 -1.13^+9^+3-0 0 3

2. 3 2 4^6 3 G + G G G 1 . 9^2'u 63 + J iTu 1.9^16^Gif + J0 u 2.567082-00'+

ic STANDARD DEVIATION IN THE TRANSFORMED VARIABLE IS 6.805-0Qi+

4 E WE ^GHTED"^5^A:7^aA7^D~^rv^ATIrIT^^^^"-THE~TRT^rrsFCRM•EI^-v'AR^^ Q-.-0
1 IS T^MP.- IN < ,X lb' xHblS TA^lGd I iN OHMS

2 2 lXP£RIMENTAI:^ POI;nITS"' AND 6 T1£R^1S.

"&V53 30-FUUZ

7. 7l;u^-^jo2

6. ^'+5 5+ jCZ

5. o5tf G + UQ2

57111 3 + D C 2"

^. '/asa-^ .ja2

-~HVra'5T+ JQ"2~

A3^fG3+Jb2

^+.2565+ J02

- ^.13-75 + 01:2"

j369 + aG2

"-3-.-63"^3Tac^^-

3. 3333^-uu 2

-3. iar3+u(r2^

2. ^33^-+ jC 2

2'. 737u+^JC 2"

2.67^5+UC 2

"2, tfTrr+Tuz2. 269U + UU 2

~"Z::i£fV9+irb2^

2.1117+002

7. Juoouu + Lo'j

i * J J 5 u L i] + C u l.lJl^UG+CCl —1. 2^o3 G34-5Gr^

-"T;"5T2 G-uT"^

1.oj2oi,J + -u1 —rV"7 J2 uG u * uUT

1. jai3oa+uai —1-; -9 a iT^-u'+u trr'" 1. 9 Ji+lG j + J Ji

2.95G1IJ J + uGl - -3v-£+391Qt^^^U^•I " 3.922C0 J+uui

'4. ^i^Tur-j-ccri^""

i+.dobcuG + OCl

^ ,^

.- 2 y-r 7.3j33uC + -,u1

3.7511Ga+uGl

YoALG

6 • 9 0 3 3 5 5 + C d G 9 . G ZGoi3 + G - 1. iG272'+ + a01

lV3 0u2i+I>u01"

i. i+5^3..8+ .. Jl

1 G"n'^"o"C^"G~G"l"-" i. 5 :)92 oH-00 1

1. 7 C C6r7"e + u iri"

i«aui&G9+jai

1. 9 G 12 37^ G TI

1 . 9 9 3 5 c 3 + J J

1

2«95157G+jG1

-J; '+i+-29x9^.^r~

3.92l527^-Gul

!+15GI35 f 03r--

h* 66592C+Jai

7.2c2565 + G,]l

3* ^tU2G-2^+Ta r~

6. 7453o9+uul

Y-YCALC

-7; u56^+65--0^J•3

l. 9&i>5i+d-0G2

-1. SoiSz-z-rcH

-1. 323q50~C C2

-lV9i+132V-G"[r2—

2. 915137-003

3. U1917G-G02

--1-i -3 2216 3-^ G-C2--

-3, Qg319G-0G 3

'~'+V b27ri^?^ u uj—

5. 1653 25-U L 3

l~6-2-3-3-5-:r--eTDT~

-1, ^+70335-002

--3-.-ai 9 1-7 9-0-0-2---

^. 732237-G C 3

•-Z.^3-352d9-GG-Z3. 7 967 2 6-0 03

"3 r^q-tf i3 3

6--- Gnr3~

2. 073653-0 Gl

=2-.-l-g28 37^0Ct5, Zil^f 57-Ga2

"TH e: stattdard^ urTT'4Tro u-'in- t h t) ri g r f;A"L~v"ARrA-3L r—i- 7 re7~5VH-- J 32-

B-19
T hMTJ-f-JEtni—e 1 --ftfii-T^TtlJTttrTTnt-tc? "3^2

Y IS T£MP. IN K ,X IS ^£SI3TmNC£ IN OHMS

ZZ EXPERTMEHTm-l POIrrrS~A:iD UF^Tir~5"TERn3V

L.C310 R MIRS'JS LOGiu T FOr< .^lESISTCR R73 log T = P (log R)

1 H

-: ' CCETFITjriTrT3""'"F0:'r~A-N"''£^XFATrS"lT7rr-"^^^^^ 1 ri£ Kl^rS~H'Rt1 . J7I J0126 65+ J U C~' C0NJTAr4T'

FHc GOEFFIGIEi) rS FOR AN EX?A,WSIOt>i WITH 2 TERHS ARE

4. 326^9322 3a+GG G CONSTANT

- T, bT3'rn'S'Sl o'^-o'lST * i

THE COEFFICIENTS FOR AN EXPANSION WITH 3 TERMS ARE

9. C5cidi+7a^i3 + UuU CONSTANT

3.214377951^-001 X**2

T M

E

' cxrrrr 1 c-itTrnr-F

a

r—an-itx^- rrtrrotr- KiTt^

^ terms airt

"1 7 u 5 ^8-r73'5-4 -1^ aC-l eONS T A rtT- -9.527i7o355C+uQ0 X**l

17 5 0 3 o-'j-5 iftrcr7"-FC-tru x •-2

-i.3o2 J59l7d5-G. 1 X»*3

THE" COEFFICIENTS" FOR- Ar~E XPAMS-raN-rl ITU—5

" rE f'trtS- A-^RE-

! - 2,3Z32337ric: + uul ' -CONSTANT'

-1 . 59o7b242 Ji++ J Ci 1 X**i

- ^T^5 To rSJ3 ^ u't-ZT'C — X^*'2

-5.7l7J6+6D2u~Gul X**3

2.To?-Jo Ju^uC-z

THE COEFFICIENTS FOR AN EXPANSION WxTH 6 TERMS ARE

A = 2 . 5u 7Sb23u52+u J 1

B = --2;2-^"5o3-ir3ir-Fcrj-r-"

C= 75626ZS:}6C 0

E= 1,36653 3 S255-uGi

CONSTANT

X*

X**2 - X**3-

X**4

- —x^^5---~

B-2Q
x5 T_H?. IK < ,X

r<7 IS Kioj-ST^-N^^c if. OhhS

u.OSi. i

log X

o c r o i 3

5 5 oo 4- 5

o J o 5 o ^

9 5 5 J 3

35 Jd 5 7 7^335^

76 7430

c5 i7^c

5 7 Z4 5 5

5 0 + 7 H 1 ^ 5 5 9 6

^ C i 3 3 3

3 5 7 3 Zd

3 b ) 7 5

2 c 5 9 C 3

lcid75

»- a 1

+ u

-t- J I + Ji

-J ; + J ! + J + u

+ J

t- J

T J + J * o + d

7S^7i9-- C

1

T d L L

log Y

/J • •+ P 3 3 1 - - I- 1

:3»-3-+^c37-l,l1

i i J 4- 1 9 M- 5 - - ^ i • 11 J 5 7 5 + u o J 'TVI o 2 7 4^'+ C^'u

1 . 1 7 6 7 5 7 > J L C T.'z J 47 : 3"r

1.233S5U+0GG

1.255536 + ^ ju

1. 273li+2 + . u - T72iT7'4 7 rr

l,33J97j+-L,b

1 4- 6 ^ c j T + 1 <j ^ 1.536^^3 +

o

"i . 5 j'3 5l J +^\,Tr

i.6^i+7.. 4^... :

:

"I", o 3T 2 4 3' t ~ C "iT i»7o7534 + ouil

1.333 51 3^ I 3 Z 1. 923249 + J u u 1 .'9 42 C 6 3 r u Z C

log YCALC

7o78^237-c J 1

0 . 4 S> 1 8 2 : - J ^ 1 9« 5 nd l 46- u 3 1

1 » L; 422 C3 4 33 U I.xl3&3d4j.ju

1» X c'27ToV C J C

1. 1762221-:- J G T. 2"C"4i^"4-: : r

1. 2 3udl3 + J j C To' 2 557 70 + 0 J C

1 . 2 79216 + 3 J C "i^"'2^5T5cTrj r

1.39u632 + uJiJ

i . 4 139 9 35 4 J J C 1.33c796^jjb

~lo 59369c + 3j 3' 1 , 6^t^92 C + ^ J t

' 1 ."rJC ? i ir7"4 3 33" 1.7 t 7 3 3 ^ + J 3 L To 0 62 579 4 J 3 C" 1* 9243 774 u G C I. 9 4l7'55 + 3 3 C

log Y - -1. ^76

121

- 3 • 3 J 3

-2. 553

-2. 327

"'"iVl-C2

5. 5-t2

i. 463

-T7'33&

-7. 442

1. — 9^ 9 Jl

-3. 512

'-rrT-32

-2. 15d

""IT 3 5 3

3 • 0 J 3 ^ 9.35 99

-1, 123

""3. G7C+

log

^ 6'r'- 2o J3 7^-

2 77-

3 j7-

o' _

6 3 6-

635-

4' 99^

7 0 4-

loT17 3-

F33-

193-

23 J-

?3T19 7-

5 3 IYCALC"

C G 4

C 3

i+ G 3

C C M0 J 4

3

T

0 Oi+

0 3 4

G C 5

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THl STmNJhRJ G^vIaFIJ:* I:j THE TRhNS FORMED 7 A Kx ABLE IS 4.ci2a-0 Qi*

IHE WLIGHTEJ STM-JjAxT DEVIATKT^ IN T Hi" " T R A S F 0 £ JT' VARIABLE IS '

B-21
T K vr F ir?i ~ atrt^B^j^rTRErRTr 0 n£ rr:^-R:rd-=2

f IS T£MP- IN < ,X IS RESISTANGi IN OHMS

Zc £ X PcR I HENTli'L:~ POINTS" "A MCr"^"5~TERM S .

' 2 rC'3o9 + u u ^~ 1. i+a75<-aDH

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7. 3515 + uO 3

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2. 321Q+ j03

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1« o662 + JG 3

1. 52Cl+":Jtr3"—

1. ^77&+CG3

^Tgg'gTririr+u'iru'

7.0 joCuJ+CLu

37 u'u 5 b 0 [r+ 5 L iT" i.iji'+Qa+oiji

r.2 =

i.3j23Uu+Lcr

l,D023au+uGi

x;T:j2"DTnr'-f ocr

YCaLC

7. G C1353 + U C u

i.3ji3uu+uGl

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1. i+5i+5 63-»-aai

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1. 6iG290+aai

i. 5L2G62+jai

Y-YCALC

"5"2"-G'u3~

6. 6^7156-033

-6V36Zir5'5'=^Cr03"

-6. 553512-G Q3

3. 69l6ii-i]ui+

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2, 009937-002 —3Tr^5rzir-=irc-3-

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1 • 9 rZ!rZ6-+ U^I "^-37-25 9"3-i+5-^ Cir3-

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1. 995061+GOl

2.95G776 + L G

•3. ^t^fl"S-32^0a-l3. 923716+001

-i+vt+iff89-o>-aai--

i+.b652o& + G j1

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7, 257510+00

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a. 7iti+9C7 + aQ 1

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1. 576960-001

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6. 193033-002

B-22
IS T-rtP. IH K ,X IS RcSISTA.jCE IN OHMS

22 " EXPERIMENT4i:"P0Trrr5"A:^O O'F- TC"- 6 -TERMS,

lj310 R versus ^03ib T FOR R£SISTOR R7G

H E

" C aZF FXCTEN73-^0 R" " A rr"EKFAn o TO N" 1^ I T ri T TE .RH S"" ATR E

1 . 5T1 J u 12 55 6 + 0 OTT" : ' C 0 N ST T>l

'

HI CO£FFICIENTS FOR AN EXPANSION WITH

22 77 3 G 5535 + OOu

- 7 . 5 0 o

2~'4"3 175 Z - ff lTI"

2 TERMS ARE

CONSTANT

T*"»"I

iHE COEFFICIENTS FOR AN EXPANSION WITH 3 TERhS ARE

6 .fcif27i7ii5i+0U 0 -TrC 5 J 57ri + 0 Vo" 2.87671501^+8-001

CONSTANT

x**r

X**2

h^r'XCZrFICTrT^rS~T^OR:"Airz'X?-A-NSrON"WrTH r-TERMS~-A-Rc

^I V 5 6 u 75573 4 4- + GU 1" -8.12 32912186+000

i . 5 i+rr33 5 7'ju + G c r

-l.L23ci2 JG639-C01

CtrNST^rmx** ?

X»*3

ifHE CCEFFICIENr-S~FO=i AN^- EXPANSION W ITH "5 -reRriS-A-RS

! 3.36To3i5i57 + Ctri - COriSTAN-T

-2,6ii77i+6u25 + C^l X**l

2-+7 :7x55^:c>U T(r X-*-*2

]' -1.20 553i+99i'+ + COb X**3

" 6 . 7 61 657 37 j 3- G LT'Z —X**i+

[tHL COEFFICIENTS FOR AN EXPANSION WITH 6 TERMS ARE

A= 1.89M-6l35Ai3 + 001 CONSTANT

' B =-7. e2oo67ri^37+Dau ^ X**! ' C=-&.3A17710622-uui X**2

D= 1. G J7 21ii+i97-Ki;"Ju ' " X**3 "

'

I E = -2.07 J ica6:<72-G01 X**i+

|

- -- F =1.3^+0? J J-2i;JS-^U-a-2 X*-*5

B-23
K ( C ~ 2

y IS Tc'IP, IM K ,X IS ^LcSiSTA.;-! .- i.' T f. n L-i M -i? X rw u n n ,i > ''J LA.c.Kiri;:.iN 1 ML r U 1 M 1 o M ; U D Tlk _

it R VEkSUi L 0 J i r F 0 k R Sit: —:

iOg A Log Y iOg xL//iXj<vj log I - log 1 K^ALjK^

1. y M-H 11 / + U b U 7 7 1 . V Q n _ "1 ^ 7. 753G20-ijO 1 — Z> Z> > \ 7 ft A _ n r ; c« cai/00~b'L;HH • / HPlU 1+ U u L

. —

4 ^ i+ b 3 1 + J U G _/ t ^ T I V/ V i W y ^ 9

55i22C- C J

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7,

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/+. i.23u9&0+Cuj ^ ^H w W ^ W >J w u 1. 2306 G9+G0 C

1X n ii. Q 1 — n n • !7 U H-H J X~ u u *+ 0 • Q W 2* iT X \ 1 fi y O'+C C U * U U u 2~55Ti5+lj J G ~~

£f . 7 i 0 5 ""Ij 3 • ^^WwL_Jb ' WWW 1*2 791^2 + J C t 1. 2 77g36 + i; u C X» C jOtJXO UUO

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o • fill i C+UUu 'iiT3 9-3+ub U , X • tj o ^ o u 'J u b 0

C *3 1*1 "i G <~i _L n '1 l»3oDH'+r>TLl; b 1. 5380^6 + 00 C X« OjOP73 lJLiO o « P 0 Oii 1 C + J L U i 1 9¥3"5 + vJ 0 u o»vf jUPO~UUO

2o • C "I U 7 / » U i n i i ItOtH / U'+tUUU 1. oi+52u9-*-Uu G

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i. d 63 5I-5>C1j l i. £5 79'3 uo U !?»!?u003i bbO

3* 295773+OGO i.9232i+9 + uUb 1. ^ZSkkb-i- }\} C -2. 19&55i+-CU3

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THc STANDARO OcyiATION IN THc TRArSFORMdQ \/ARIABLZ IS 2-599

r H E W EI G H T E D

" 3 T AT J 3 A R l) D E / x AT1 0 * j ^ x ^ T H E" T R A S PG P. M E 0

' V A :U A BL E 'I S

B-24
IS T£MP. In .< ,X IS R£SI5TAMU£ IM OHMS

X Y YCALG Y-YCALC

cTzg^^-f-uX^ 5T9 9guirirFir[rc 5."a a2t)5"^t"+uTo

^rsr^-iiooxrr^uU'Z

5.56G3+GG4 7.006000 + 000 6.9967^+0 + 00 0 1, 126025-002

~ 3. 3;23it + 00 i+ j 05"I7u17VIj"uI; 9. G 15ZW*ZT^ - 1 rT2 3 o

6 -X

2.130b+jCM- i.i jli^O O + QOl l.G9969C+uGl 1.7J9797-CC2 —rrpr95+ u o^; 17^9 otuj "-Finri r, 3 jD&^^v-cnn

^.-ss^rm-usz

i.3177 + Q0H l.t+5i+600 + uol 1. ^+60^+35+ j 0 1 -5.33^+961-002

ivzsTTvuv'n 17572 50 u+iriri IT 5^i:5"tr7ZTtnri—=^7rix lo- oirz —1.1602+004 1.602300+001 1.566032+031 1.626756-001

IT J it 5 2+ 0 —1 . 7 J 2 0 c u + uiTi" iTTmxr-Fcnrr 57-035 irrr-ircr3

9.6^+32 + 00 3 1. 3J13U0 + UC1 1. 7993^+6 + 001 1. 95^+30 0-002

' b\3o6Z+'3Tr3 iT9inTtrir+-:ri 1 . s s6"-£+or+j-tri 5t2^ 8-irLr2

6.^+080 + 00 3 1.99^+100 + 001 1. 9663^+2 + 001 7. 757977-CQ2

6T3Z STTF u [^5 2"^+ o"~2T7T+Tci—"ZT^' 73BT2inrtn—=vrprorr3-^--trtri

5.i496+jL3 2. :«50100 + OG1 2.9573^+9 + 001 -7.2^+8718-0 0 2

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3. 8567+003 3.9220flO + uOl 3. 889365 + 001 3. 213^+96-0 0

1

3.-i+!i9 5+^0-3"-"'^—+T^+xz7 0 0 + 0 0 T^'^wi^iTSTT^nrm—=^5TT26"7^7r- inrz

3.1160+003 i+.d668;jO + -iJl ^t. 6 70686 + 00 1 -3. 885922-0 0 2

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B-25
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i IS T£MP. iN K ,X IS RdSISTANJc IN OHMS

22 ' EXPERT i-lENTHL-pOTNTS '^AIiO' D^ TO & TlRT^SV -- LOGIC R VcKS'JS LOGlu T FOR R£SISTOR R81

' - - T . 3riTrijr2Do6+u iTD ctiT4STftrnrHE COcFFICIlNTS for an expansion with .2 TERMS ARE

5.4+006377906 + 000 CONSTANT

- 1 . zrszzmk 5t+ o jto — x*-*'i

Frit: COEFFIGIlNTS for an expansion with 3 TERMS ARE

1 . u25 t»2 J373i + G a i CONSTANT

-h,! 4:1 o-lA-77T2'4--D-01] X*"^!

'+. 572 7i3o3-Ji+-uCl X»*2

- r3 ^tJ-7-3 sr r+tr o^r co n s-t a n^ r- 92^55'?235'++a j G X*»l

- 6. 7u r'?zji33 a-cri x^*-2

-2.2963437035-002 X**3

THE COEFFICIcNTS-FOR " Ait -EXPArTS-ItJN WiTH~^S T £ Rr^S-AiRE

- 1,1 5X7 3 3 9 5 5 3 + 0 c 2

~ CO NST ANT

-i.29761^762o+GG2 X**l

5 . 6-6 o 5 57a"3-J 7 -F tr 0"! -1.11^+0^97766 + 0 0 1 X**3

6.25733 ji343-irCl X**-^-'

FHE CC^iFFICIENl 3 FOR AN EXPANSION WITH 6 TERMS ARA =-i+. 725H7iH596+a J 2 _ _ COfiSTANT

B = T.i+o3 679 63 5H+ini2 X*»r

C= -£+.6b7 7710u36 + Cu2 _ D 1. ^+hh'+697567+Tj'J'2 " X**- -j E=-2.22333:iirH3G + 001

F = - I . 3 6-3-/ 7o27 35 i^a^ '

B-26
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"2£^'XxptRIR£^lTHL^"P0^^^^s 6 TEFMsr'

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log X

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7.736789-001

3, 5^h637-uU1

1. 113375 + 0 G L, 1.17575 7+ GOii

1.2 3u96Q+uGG

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1. 168269-

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Hl STANOARO 0£yiATION In THc TRAr.SFGRMEO \/ARIA5lE IS 7.177-0a3

"TH£ WEIGHTED STA-IDARU DEVIATTGH TM" THrE^TRA:-ISFOR,'^EO"VART^rBrE~I'S
-T HiTr-Fiu-M--c^:e^ir-Tnrf<na;r=Ttxn<:3^^^

Y IS T£MP. Lh < ,X IS RtSISTANCt IN OHMS

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6. a076+ULi3 7, 03«3L QG + GQ.U 6. 9itl5 59+ u G C 6.65bQ59-0u2

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3. 7555 + UU3 i . iu iif 0 C + l w l 1. C 9565it + .-j 1 5*7156^+3-0 0 2

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2.i+292 + G03 i.8Jl3ua + uGl 1, 7 915 1^++ Q 0 1 9,735572-002

2T 328 4 + 0 u 3 r. 2 3 I TO ir+ ^tr— 1 . 3 e2-7-2"7 + G U'l lT-89r31r2'--0131-

2.2'+^2+J33 i.99^1CJ + wGl 1, 9 66^+^*5 + J 1 2. 765^97-0 G 1

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1,6093+003 2.95G1GG+UU1 2,968292+UOl -1,81918 5-0 01

1 . £+3r7 + a ir3 3. 2+3^iur+ u u i 3. £+676 53 + jiri —^-2^ 5533^-- trtri1.332a + DC3 i,922CuC+uCl 3.32711G + Q01 9. *+a90 15-G 01

^i".'ZTi+9+"a 03 rr^rrzTuT+r: r uv^^iSToT-f-m-i—--^rt+-365T8- otrr

1. 1273 + 00 3 ^.6o68uJ + jG1 ^ . 3 7^+i+l2 + J 0 1 -7,6120 71-0 0 2

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0. 3382 + UL2 7.3333ja + uLi 7.129595 + jdl 1 . 737G 54-+ G 0 0 "7^T3To + JC2 ~":5-73l57X77F771 3 . H3679^r+'ClJl—-57t) 6^6135^ C'lnr

7, 7963+002 3, 75llOJ+bbl 8, 773933 + 001 -2. 2 383£+9-G 0 1

B-28
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IS T£MP, IN K ,X IS RESiSTArlCE IN OhMS

_j;ilQ VERSUS »G^iu T FOR R£3Iil OR R62

cnFTTtrTE i-rrr- r {TR-'-Ai^-E-KPt^rrs-i-ar^ •''HrTH-----r--T lk-as^-h^ki

i rrrrj j rz oo'+ttot; co nst a- n r

HE CC£FFICI£NTS FOR AN EXPANSION HITH 2 TERMS ARE

5.2lJ63J9i66 + QQQ COiMSTANT

-^TiXTuT^ 3il 3r* uTCT X»-»1

)H£ COEFFICIENTS FOR AN EXPANSION WITH 3 TERMS ARE

l.C167G29362+0Gi CONSTANT

-Tt ; Z53Zb '5J^ i+2>' cnrc —^

6963039539-0 01 X*»2

frr~c-OTF FTCTrrrr3~T-oT~ATr- irxfTt n-stott-^it-r—r-T-E-^fts-^£

7 1 .67^3" 3d o7-£f i*cTC tn ~ CtTN^j T A^r

-i.03u27062i3+GGl X*»l

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irf£- "CCE F F I CI E NT r F O.R- A N—E Xp-A' N Sl Cnr W I T H 5 T E RftS—A1R-£ "

2. 1661^4^33 2 a^irCX CaNSTAMT

-1.6i+: l532265 + 'Jol X**l

I 5 -.-rzo^n? 5 9 0 -j-e^tTiTG : x*^2-

-7.5^:.776i^:j2-0cl X**3 — V. 3o33H2 29-7o-ua-2- - X^^-^y

HE COEFFICIENTS FOR AN EXPANSION WITH 6 TE.^MS ARE

A= 5.do32b2i+oj3 + 0o;^ COMSTAiiT

B =- 7 . Q Hrr^4 9 Z2"32^ a\rj " ^'*'*^ ' C =-9.7l5ol7223u+U j J X»*2

D = 3.7 rro ooi5 JT + 0" ira -x* *-3—~ -- E =-b.^+6u 37^'+2^+bo-oul X**i+

F = tr/t ^i^3'J^^^b5-^'^-^i^c^ x'^'^

B-29-
T hIN TTLT1"'UARt3 JN'Tricf^'rtUf^rTc^i'^

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^ 2 ~£ X P £ R I Ml NT ATT^P OlrU S AN 0 d~T £ RH

lOGiO R VdR^Ui u03i-- T FOR RESISTGR R82

log X

3. 7imi+'JGG"

3. Sd'JiS^ + GC u 3. i+9&'5'5 9'+J0T

3. it229t+0-»-0Ga

"""3T 3 7Fu"3'B + 3 G j

3. 563557 + uG u o.'3 3cWSnTJ"

3. 3i37'+H-aC u

r^g Y . 7.73a789-Gai

3»5^^+337- o 01

1 . 1 1 3 3 7 5 + u 3 0

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7^76 51 83- a Gl_ a. iti^OT75'=^^'Lri

9* 55376'+-eai

l.ll^&13+uOC

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i . 176i+o6+C J 0

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"~T7Tuo'57u-CC3

~6.9^70i+8-00if

~2VW67"5ir=^(7I!'ii^

-1.238316-003

2. 6;52'+92-CCit

i.23Q960+uGu

"iTabJi+i+i+LnjTr

1.23u622-i-ua 0 T73Tr2'8 3b-Gu3

3. 375366-00^*

3. 29ib'2i + JQG

3. 27iGC2+ JG u

3. i7b'+87+0aQ

T:25'558&>uGl

1.2791'+2 + uG G 1.39G97a+Guu

Xr2"5537l + uGQ

1.27<i8'+6 + uaG

i.2993o7 + GijC

2. 9519h6-CQ^+

4. a98/2i-Uuif

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3. G6509a->-jGG

2. gd39't5 + 0OG

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2. 91 CJ2 0 5 + JG u oi+ ^7"15+ 0X

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B-31
APPENDIX C

DATA ON LONG TERM DRIFT AND THREE POINT

CALIBRATIONS OF THE FILMS

Figures C-1 and C-2 show examples of data on long term drift and thermal

cycling of the films between room temperature and the boiling point of liquid nitrogen (LN^). A total of 109 such data sheets were delivered (along with the films)

to the sponsor.

In addition, three point calibrations of the films at room temperature and

the boiling points of liquid nitrogen and liquid helium were obtained for 100 films

and delivered (along with the films) to the sponsor.

C-1
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C-3
APPENDIX D

LIQUID-GAS DISCRIMINATION SET POINTS

The liquid-gas discrimination set point is based on the transient

response of the carbon film to a constant current pulse of amplitude, I . dV ° A differentiating circuit measures the initital voltage transient —— given by

is large in gas and small in liquid, and the set point is some intermediate point which can be set in an electronic comparator.

For peak voltages on the order of 20 V the liquid initial transients for

all films at 20 kelvin is on the order of 10 volts/ sec; and in gas just above the

boiling point the initital transients are on the order of 1000 volts /sec; therefore

a sufficient set point for all the films anywhere near 100 volts/sec will give

rapid liquid-gas discrimination using circuits outlined in reference [Z],

o dt

dR

dR

D-1
FORM NBS-114A (1-7S) U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA tvttjcttd d ^ n a qcc

5i^E£j NBSIR Report 74-355

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Carbon Thin Film Thermometry

5. Publication Date Or f-nhp T- 1 Q7

(S. Performing Organization Code

7. AUTHOR(S)

R. S. Collier, L. L, Sparks and T. R. Strobridge

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS Boulder Labs

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Project/Task/Work Unit No. 2750460

11. Contract/Grant No. NASA Purchase

Order H-92167A

12. Sponsoring Organization Name and Address National Aeronautics and Space Administration

George C. Marshall Space Flight Center

Hunts ville, Alabama 3 5812

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This is a summary of work done on NASA(Marshall Space Flight Center)

purchase order H-92167A concerning Carbon Thin Film Thermometry. Optimum film deposition parameters were sought on an empirical basis for maximum stability of the films. One hundred films were fabricated for use at the

Marshall Space Flight Center; 10 of these films were given a precise quasicontinuous calibration of temperature vs. resistance with 22 intervals between

5 and 80 K using primary platinum and germanium thermometers. Sensitivity

curves were established and the remaining 90 films were given a three point

calibration and fitted to the established sensitivity curves. Hydrogen gas-liquid

discrimination set points are given for each film.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Calibration; carbon films; low temperature; thermometry; vacuum deposition.

18. AVAILABILITY STATEMENT 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

1 1 UNLIMITED.

UNCL ASSIFIED

[xl FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

USCOMM-DC 66244-P7I

USCOMM ' ERL