NBSIR 76-1108

Fabrication of the Barium

Fluoride Film Humidity Sensor

by Industrial Firms

Frank E Jones

Heat Division

Institute for Basic Standards

National Bureau of Standards

Washington, D C. 20234

April 1977

Final

Prepared for Cambridge Air Force Geophysical Laboratories

Department of the Air Force

Hanscom Air Force Base

Bedford, Massachusetts 01731

NBSIR 76-1108

FABRICATION OF THE BARIUM

FLUORIDE FILM HUMIDITY SENSOR

BY INDUSTRIAL FIRMS

Frank E. Jones

Heat Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

April 1977

Final

Prepared for Cambridge Air Force Geophysical Laboratories

Department of the Air Force

Hanscom Air Force Base

Bedford, Massachusetts 01731

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Betsy Ancker-Johnson. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
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ABSTRACT

The barium fluoride film electric hygrometer element, which was

conceived and developed at the National Bureau of Standards as a fast

responding humidity sensor and which has been used in a variety of

research applications, has been successfully fabricated by several

commercial firms. This successful transfer of technology from the

Federal Government to the private sector should assure the availability

of the element for general use, including missile climatology and

routine radiosonde use. Calibration equations have been developed and

the analysis of calibration data has provided insight into the physical

processes involved in the functioning of the element.

It has been shown that the conductance - ^ isotherm (in itself

a Type II isotherm in the Brunauer designation of physical adsorption

isotherms) is a composite of a Type I and two Type III isotherms. The

two Type III isotherm equations are of the form of the Freundlich

isotherm equation. These results represent the solution of a long-standing

problem in adsorption and have general application to other adsorption

systems in addition to the water vapor-barium fluoride film system.

Key Words: Barium fluoride; calibration equations; fast response;

films; humidity sensor; industrial fabrication; isotherm

equations; physical adsorption; relative humidity; routine

radiosonde application.

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CONTENTS

ABSTRACT i

/

1. INTRODUCTION 1

2. COMMERCIAL SUPPLIERS OF ELECTRODE PATTERNS

AND BARIUM FLUORIDE FILMS 4

3. ROOM TEMPERATURE CALIBRATION 6

3.1 Calibration Equations 13

3.1.1 Development of Equation Relating

Element Conductance, G, to Relative

Pressure of Water Vapor, 13

^s

3.1.2 Development of Calibration Equations

Relating Element Resistance to

Relative Humidity 21

3.2 Low Temperature Calibrations 25

4. DISCUSSION 30

4.1 Physical Adsorption and Humidity Element

Functioning 33

5. CONCLUSIONS 36

6. REFERENCES 37

7. FIGURE CAPTIONS 39

8. LIST OF TABLES 40

9. APPENDIX A. ADDITIONAL FIGURES AND TABLES

I

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1. INTRODUCTION

The barium fluoride film electric hygrometer element [1,2] was

developed as a fast responding radiosonde humidity sensor. A series of

radiosonde flights [3] established the capability of the element for

radiosonde use on an experimental basis; however, the instability of the

element with time, as indicated by an observable shift in calibration in

a period as short as one day, precluded its use in routine radiosonde

flights at that state of its development. A study of the aging characteri sties

of the element and of possible causes of the drift of calibration with

time led to changes in fabrication procedures which substantially

improved the stability of the element [4].

The rapid response of the element to rapid changes or fluctuations

of humidity [5] make it a valuable research tool. The element has been

used in a field study of the effectiveness of monomolecular films

of alcohol mixtures for reducing evaporation of water from a lake

[6], for measurements, by an eddy correlation method, of evaporation

from a crop surface [7], mounted in a probe on an aircraft to determine

the horizontal profiles of humidity through fair weather clouds [8],

and in a laboratory determination of the humidity distribution with

height above a free water surface [9], These successful applications

established the suitability of the element for a variety of meteorological

applications that require detailed moisture fluctuation information,

e.g., as an improved radiosonde element for general application and

for particular application at missile test ranges.

1
In order to make the element generally available for various

applications, it was one of the objectives of the present work to

develop commercial sources of the element, i.e., to transfer the

fabrication technology to the private sector and to determine whether

there are firms with the capability of producing barium fluoride film electric

hygrometer elements which exhibit a performance that is equivalent to (or

better than) the performance of those developed and fabricated at NBS. The

procurement and calibration of a number of commercial ly-produced barium

fluoride elements was the other objective of the present work.

The barium fluoride film electric hygrometer element, illustrated

in figure 1, consists of a glass substrate on which a film of barium

fluoride, 0.3 ym thick, has been deposited by vapor deposition over

closely-spaced metallic film electrodes.

The production of a barium fluoride film element consists of two

separable operations: 1) the fabrication of the metallic film

electrode pattern on the substrate and 2) the deposition of the barium

fluoride film over the electrode pattern. In the development of the

element at NBS both operations were devised and performed (2) , therefore,

a potential cormercial supplier with competence in the deposition of

thin films could be expected to be capable of performing both operations.

However, it was considered for the present work to be more effective

and efficient to attempt to locate two categories of suppliers: 1)

those who could supply the substrates with electrode patterns and 2)

those who could deposit the barium fluoride films. The second of these

operation is by far the more critical.

2
3

FIGURE

1.

Barii^

fluoride

film

electric

hygrometer

element

construction

and

electrode

configuration.
2. COMMERCIAL SUPPLIERS OF ELECTRODE PATTERNS AND BARIUM

FLUORIDE FILMS.

Two suppliers were located who could and did produce satisfactory

electrode patterns by photoetching chromium film covered masking plates;

these suppliers were the sources of all of the substrates with electrode

patterns which were used for the deposition of the barium fluoride films.

Five firms were invited to deposit the barium fluoride films on a limited

number of substrates by the procedures described in references 2 and 4.

The procedures developed at NBS, described in references 2 and 4, will

be briefly outlined here in the interest of completeness. After the

electrode patterns were formed by the electro-etching process, the

substrates were cleaned by a detergent-and-water wash followed by rinses

in distilled water, in isopropyl alcohol and a vapor degreasing in an

isopropyl alcohol degreaser. The substrates were then placed, electrode

face down, on a support in the bell jar of an oil diffusion-pumped

vacuum evaporator. The source used for the deposition of the barium

fluoride film was a solid mass of barium fluoride, formed by vacuum

melting and subsequent cooling of reagent-grade barium fluoride powder,

in a molybdenum "boat." A junction of a platinum, platinum-rhodium

thermocouple was embedded in the solid mass. A glow discharge was

maintained for approximately 20 minutes, after which the pressure was

lowered to approximately 5 x 10"^ Torr. The barium fluoride charge,

covered by a tantalum baffle, was heated until the thermocouple

indication was 1160°C. The baffle was then removed for 5 minutes,

during which time the barium fluoride deposited on the substrates.

During the deposition, the electrical power to the "boat" was adjusted

4
to maintain the 1160°C temperature indication. The thickness of the

barium fluoride film was determined interferometrical ly to be 0.3

micrometer. The construction of the finished element is shown in

figure 1. The results of various experiments described in reference 4

and the considerations therein indicated the possibility that

contamination by diffusion pumping fluid was a source of the previously

observed drift of the calibration of the barium fluoride film element.

Therefore, the production procedures were modified as follows: 1) liquid

nitrogen was maintained in both the mechanicaT pump cold trap and the

oil diffusion pump trap throughout the production process; 2) the

distance between the evaporation source and the substrates was reduced

from 38 cm to 19 cm; 3) the substrates were exposed to a glow discharge

for approximately 76 minutes during which time the substrate temperature

increased to approximately 160°C. The glow discharge was produced by an

electrode assembly designed to expose the substrates to positive species

in the discharge and to reduce if not eliminate electron bombardment;

4) the deposition was started within 3 minutes after the glow discharge

power supply was turned off; 5) the time of deposition was reduced

from 300 sec to 180 sec; and 6) argon was introduced into the

evaporator as soon as possible after the deposition of the film to

bring the pressure to ambient in the relative absence of oxygen. The

pumping fluid in the diffusion pump was DC705 silicone and the bell

jar gasket was made of Vi ton.

5
The five suppliers of the barium fluoride films were provided with

copies of references 2 and 4 and asked to follow these procedures.

However, the availability of electron bombardment heating apparatus

and optical film thickness monitoring and control apparatus and other

refinements enabled the individual suppliers to depart from these

procedures without potential deleterious effects on the performance

of the finished elements.

3. ROOM TEMPERATURE CALIBRATION

The performance of the completed barium fluoride film electric

hygrometer elements as received from the five firms which deposited the

barium fluoride films was first investigated by performing room

temperature calibrations of the elements. The calibrations consist of

measurement of the electrical resistance of the elements at a series of

relative humidity (RH) points. The goal of the calibration was to

determine whether the performance of elements produced by commerical

suppliers was comparable to or better than that of those produced at NBS.

Prior to the calibration, the elements were subjected to a heat

treatment which had in earlier work resulted in considerable reduction

in element resistance at room temperature [2] and which had in

later work [4] been shown to be effective in reversing the effect of "aging"

on the calibration of the elements. The heat treatment consisted of

raising the temperature of the elements to temperatures in the range of

350°C to 400°C in a furnace for 1 hour then slowly returning the

elements to room temperature (usually overnight).

6
The elements were then exposed to 6 cycles of relative humidity, RH,

between near 0% RH (over barium oxide desiccant) and near 100%

RH (over distilled water), exposure at each RH was for 10 minutes. The

elements were then immediately passed through a series of RH points

established by saturated salt solutions in sealed glass jars; the

elements were maintained at each RH for 20 minutes. The sequence of

RH was one of alternation between high and low RH's, for example:

100, 29, 97, 33.5%, etc.

The calibration RH's and the salts used to establish them were:

12%, lithium chloride (LiCl); 29%, calcium chloride (CaCl

2

);

33.5%, magnesium chloride (MgCl

2

' 6 H

2 O) ; 38.5%, sodium iodide (Nal);

48.5%, lithium nitrate (LiNO^); 53.5%, magnesium nitrate (Mg(N02 ) 2

’ 6 H

2 O)

64.5%, sodium nitrite (NaN 02 ); 71.0%, strontium chloride (Sr Cl

2

* 6 H 20 );

75.5%, sodium chloride (NaCl); 80.5%, potassium bromide (KBr); 84.5%,

potassium chloride (KCl); 87.0%, zinc sulfate (ZnS 0 ^‘ 7 H 20 ) ; 90.5%,

barium chloride (BaCl

2

' 2820 ) ; 92.0%, potassium nitrate (KNO^) and 97.0%,

potassium sulfate (K

2

S 0 ^).

The electronic circuitry used for the room temperature calibration

had been designed by R. Bruce Uhlenhopp and was of the type used in

several research applications of the element [5, 6 , 8 , 9]. The circuit

was calibrated using resistance boxes and the output was measured using

a digital voltmeter. The room temperature calibrations were performed

on elements from four suppliers. A, B, C and D, on four successive

Saturdays. These four sessions of calibration made it possible to

calibrate a number of elements from each of the four suppliers and also

to provide information on the short-term stability of some of the

elements. 7
On four elements from each of three suppliers, designated

A, B, and C, were calibrated at a room temperature of 25®C and a room

RH of 49%. The elements from supplier C were found to be unsatisfactory

presumably due to exposure of the substrates to electron bombardment

during the glow discharge bombardment prior to deposition of the barium

fluoride film [4], and were eliminated from further investigation. On

9/13/75 the elements from supplier C were replaced by four additional

elements from supplier B; these, with the four elements each from

suppliers A and B calibrated on 9/6/75 were calibrated at room temperature..

On 9/20/75 the second set of elements from supplier B was replaced by

four elements from supplier D; these, with the others calibrated on

9/6/75 and 9/13/75 were calibrated at room temperature. On 9/27/75, due to

the limited capacity for calibrating elements, the set of four elements

from supplier D was replaced by the four elements from supplier B which

were replaced on 9/20/75 and reheated on 9/26/75; these, with the others

calibrated on 9/6/75 and 9/13/75 were calibrated at room temperature.

On 4/26/76, three elements from supplier E were calibrated at room temperature. The elements had been heated for 1 hour in Feb. 1976, and

remained in the muffle furnace at room temperature until they were removed

on 4/21/76. The RH cycling of the elements was performed on 4/26/76

before the calibration was made.

The calibration data (element resistance vs relative humidity) for

one element from supplier A are plotted in figure 2. The points for the

four successive weeks are indicated by different symbols. The data for the

remaining three elements from supplier A and for four elements each from

suppliers B, D and E are plotted in figures A-1 through A-14 in Appendix A.

(Figures not interleaved with the text are presented in Appendix A and

8
RESISTANCE,

0W1S

ELEMENT 1111, SUPPLIER A

lOOM.

-H-

-i-tT-^ !

±iitJ. i I !

io^_

IM

TTT

O 9/6/75

A 9/13/75 • 9/20/75

9/27/75

Least Squares fit, 9/6/75

Least Squares fit, element K2

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f

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"jrr-—

n

f ?

IK

*

1 —

L

'T- f —r ^

I ;

0 10 20 30 40 50 60 70 80 90 100

RELATIVE HUMIDITY, %

FIGURE 2. Room temperature calibration, element IIIl, supplier A.

9
are designated by the prefix A- with the number). Due to erratic

measurements, only six data points (closed circles) are available for

element III 3-E.

In previous work at NBS on barium fluoride elements [9] it was

found that the room temperature calibration data when plotted as logarithm of

the number of ohms of element resistance against relative humidity,

separated into three distinct regions. This is illustrated in figure 3.

As seen in the figure, the plot is curvilinear in Region I covering the

range "0" to 26% RH. In Region II covering the range 26 to 84.5% RH and

Region III covering the range 84.5% to 100% RH, the plot is linear.

In order to ascertain whether the characteristic shape of the calibration

curves for the conimerical ly manufactured elements was similar to that

for the elements produced at NBS, the calibration data in the present

work was plotted as shown in figure 2 and a straight line was fitted

to the data in Region II. The data for 9/6/75 calibration of the A and

B elements, for the 9/20/75 calibration of the D elements and for the

4/26/76 calibration of the E elements have been fitted in the region

29 to 84.5% RH by an equation of the form

In R = a = b RH (1)

by the method of least squares, where In R is the natural (Naperian)

logarithm of the number of ohms of resistance of the element. The

straight solid line in the figures is the plot of equation 1. For

comparison, the dashed line is a plot of a similar equation for an

element produced at NBS (element K2 of reference 9).

10
RESISTANCE.

OHMS

11
Although the room temperature calibrations in the present work

were made over the range 12 to 97%, there were very little data at

the 12% point since the circuitry was not calibrated for resistance

higher than 11 megohms. Also, since "shorting strips" (metallic strips

painted on or soldered to the electrode films) were not applied to

the elements, the resistances included the series resistance of the

electrode film and therefore at the high RH's (in the range above

approximately 90% RH) the resistance did not represent the optimum

performance of the elements. Therefore, the region chosen for

assessment of the room temperature performance of the elements was

that region, 29 to 84.5% RH, in which earlier work [9] has shown

that equation 1 applies.

12
3.1 Calibration Equations

3.1.1 Development of Equation Relating Element Conductance, 6, to

Relative Pressure of Water Vapor,

^

^s

In this section an empirical equation relating the electrical

conductance, G = i, to the relative pressure of water vapor,

^ K P I UU

will be developed. Conductance rather than resistance has been chosen

to represent the performance of the element since the physics of the

situation relates conductance to relative pressure. That is, in the

model adopted here water is adsorbed in the Bap

2

film and the mobility

of current carriers in the water increases with the "amount" of water adsorbed.

The "amount" of water adsorbed and, therefore, the conductance of the

Bap

2

film, increases with increasing RH. A plot of conductance versus

RH or ^ is similar in shape to a typical adsorption isotherm of Type II ^s

in the Brunauer designation [12]. In the present treatment the data

for Bap

2 films in reference 9 will be reanalyzed to develop a new empirical

equation relating G to

^

and to relate the terms in the equation to

conventional isotherm eouations, if possible.

It was shown in reference 9 that the room temperature calibration

for barium film elements, when plotted on semilogarithmic graph paper,

separates into three distinct regions. This separation is illustrated in

figure 3 in which the room temperature data for element K2 of the earlier

work are plotted.

In this analytical development, the appearance of three regions is

considered to indicate the existence of three different modes of adsorption

of water vapor (or of three different types of adsorption sites). The

conductance in region I is considered to represent the sum of the zero ^

13
conductance and the conductance due to mode I. In region II, the

adsorption mode of region I is considered to be present in addition to

a second mode; the conductance thus being the sum of that due to the two

modes. Similarly, in region III modes I and II are considered to be

present in addition to a third mode. III; the conductance thus being the

sum of that due to the three modes. Analytically then, one might expect

the relationship between element conductance, G, and relative pressure,

to be represented by an equation containing a constant term and three

^s

terms invol ving

Ps

The development of the empirical equation relating element

conductance G to relative water vapor pressure, will be illustrated

by the use of the +23°C room temperature calibration data for element K2

in reference 9. The data are tabulated in table 1 in which the units of

conductance G are micromhos [1 micromho = ( )].

10° ohms

In order to develop an equation relating G to ^ , the plot of the

Ps

calibration data is decomposed into three parts. In regions II and III

the data are represented by equations of the form

In G = a + B -P— . (2 ) Ps

Using the method of least squares on the data for region II

(B_ = 0.335 to 0.805), values = -2.14609 and 6jj +8.00790 result.

Ps

Equation 2 thus becomes

In Gjj = -2.14609 + 8.00790 ^ . (3)

14
Table 1. Room Temperature, 23®C, Calibration Data

for Element K2^ from^ Reference 9.

III O

Conductance, G,

in micromhos

0.120 0.500

0.175 0.714

0.225 0.855

0.335 1.61

0.385 2.56

0.485 5.35

0.535 8.70

0.645 21.1

0.710 36.4

0.755 48.8

0.805 75.2

0.845 108

0.870 152

0.920 270

0.955 465

0.970 513

The data for element K2 in reference 9 in the region ^ = 0.335 to 0.845

are fitted by the equation: In G = -2.22161 + 8.12993 ^ .

15
Rearranging equation 3,

^

= 0.2G800 + 0.12488 In Gjj

( 4 )

The values of and ^

calculated using equations 3 and 4, respectively,

are tabulated in table A-1 in Appendix A. (Tables not interleaved with

the text are presented in Appendix A and are designated by the prefix Abefore the number).

Using the method of least squares on the data for region III

(2_ = 0.845 to 0.970), values ajjj = -6.02090 and = 12.67352 result.

P s Equation 2 thus becomes

In G,,, - -6.02090 + 12.67352 £- . (5) III

Rearranging equation 5,

^ = 0.47508 + 0.078905 In G,„

Pc ni ( 6 )

The values of Gjjj and ^calculated using equations 5 and 6 ,

respectively, are tabulated in table A-2.

Setting equation 3 equal to equation 5, the point of intersection

of the straight line segments for regions II and III can be calculated:

-2.14609 + 8.00790

^ = -6.02090 + 12.67352 , Ps Ps

3.87481 = 4.66562

^ , Ps

Ps

0.831.

(7)

( 8 )

16
Recalling that it has been hypothesized that the "measured"

conductance, in region III is the, sum of the conductances due

to three adsorption modes, that the "measured" conductance in

region II is the sum of conductances due to two of the adsorption modes

and that conductances in parallel are additive, the conductance due

to mode III is equal to the difference between the conductances calculated

from equations 3 and 5, i.e., calc. - calc. G^^. In table A-3

this difference, designated G^, is tabulated.

The data for G^ can be represented by

Using the method of least squares, values c = 6.44573 and d = 24.99003

result. Equation 9 thus becomes

In G-, = c + d In

^ . ^ Pc

(9)

In G

3

= 6.44573 + 24.99003 In . Ps

( 10 )

Rearranging equation 10,

In

^ = -0.25793 + 0.04002 In G

Pc

( 11 )

Values of G- and ^calculated from equations 10 and 1 1 ,respecti vely

,

Pc are tabulated in table A-4.

The conductance for region I, i.e., for 0.120, 0.1 75 and 0.225 , is

^ cs essentially linear with In ^— and can, therefore, be represented by an

P cs

17
equation of the form

In f + h Gj. (12)

where is the "measured" conductance in region I. Using the method

of least squares, the values f = -3.00574 and h = +1.77011 result.

Thus, equation 12 becomes

In ^

= -3.00574 + 1.77011 G, . (13)

Ps ^

Rearranging equation 13,

G, = 1.69805 + 0.56494 In

^ . ’ Ps

(14)

Values of G, and ^ calculated from equation 14 and 13, respectively,

are tabulated in table A-5.

Again, recalling that it has been hypothesized that the conductance

Gjj in region II is the sum of the conductances due to two of the

adsorption modes, the conductance G^ due to mode II is equal

to the difference between the conductances calculated from equations

3 and 14, i.e., calc. Gjj - calc. Gj. In table A-6 this difference,

designated G

2

, is tabulated. The relationship between G^ and ^

in region II ( ^ = 0.335 to 0.805) can be represented by an equation

of the form

In Gp = k + m In . (15)

18

/
Using the method of least squares, the values k = 5.34400 and m = 5.31462

result. Thus, equation 15 becomes

In = 5.34400 + 5.31462 In ^

. (16)

Values of calculated from equation 16 are included in table A-6. The

sums of the calculated values of G^ and G

2 are tabulated in table A-7.

It is seen in table A-7 that the sum of G^ and G^ exceeds G, the

"measured" conductance, in region I. This is due to the fact that the

"measured" conductance, G^, in region I was used as a first estimate

of the conductance, G^, due to mode I and as such included some

conductance due to mode II. Therefore, new estimates of G^ , designated

G-| ' , were made by reducing G^ by the values calculated for G^ in

region I; thus, the values of G^ are: 0.500-0.003 = 0.497,

0.714-0.020 = 0.694, and 0.855-0.076 = 0.779. The equation resulting

from the treatment of the new estimates, G-j ' , by the method of least

squares is

G' = 1.46774 + 0.45439 In £- . (17)

^s

Values of G^' calculated from equation 17 are tabulated in table A-8.

The difference between G^ and the calculated values of Gjj, designated

G

2 ,is also tabulated in table A-8.

The equation resulting from the least squares treatment of G^ is

In G‘ = 5.29292 + 5.15798 In (18)

19
The values of calculated from equation 18 are tabulated in table A-8.

The sum of Gj and G^, calculated from equations 17 and 18, respectively,

are tabulated in table A-9 for region III ” 0.845 to 0.970). This

sum subtracted from the "measured" values G is designated G^ and

tabulated in table A-9. The equation resulting from the least squares

treatment of G^ is

In G' = 6.53675 + 19.38125 In . (19)

3 p

^ '

Recapitulating, equations have been developed relating the room

temperature conductance, ^=( pg^^'stance ^ ’ element K2 of reference

9 to the relative pressure of water vapor, ^

. In the region

0.12 to 0.225, equation 17 applies, in the region 0.335

P S P 5 to 0.805, equation 18 applies; and in the region

^ = 0.845 to

Ps

0.970, equation 19 applies. These three equations represent a

decomposition of the plot of G against To reconstruct the plot

then it is necessary only to combine the three equations. The combined

equation is the sum of the three equations, since conductances in series are

addi ti ve.

The combined equation is

G'= G‘ + G^ + G‘ , (20)

where G] is given by equation 17, G^ is found by solving equation 18,

and G^ is found by solving equation 19, viz.:

20
(17) S

=

g; =

1.46774 + 0.45439 In ^ , Ps

exp [5.29292 + 5.15798 In ^ ],

G: = 198.923

5.15798

G‘ =

g; =

exp [6.53675 + 19.38125 In ^ ] 19.38125

^

690.040 1 ^'

( 21 )

( 22 )

Combining equations 17, 21 and 22, ,

G'= 1.46774 + 0.45439 In ^ + 198.923

38125

+ 690.0401^1 (23)

Substituting the calibration values of ^

in equation 23, the

calculated values G' are tabulated in table 2 and compared to the

"measured" values of G.

3.1.2 Development of Calibration Equations Relating Element Resistance

to Relative Humidity.

Having developed an equation relating element conductance to relative

pressure of water vapor in the preceding section, we now turn to the

development of the conventional form of calibration equations relating

element resistance to relative humidity.

We return now to equations 3 and 5,

In G

II -2.14609 + 8.00790 ^ , Ps

(3)

21
Equation

23,

and

"Measured"

Values

of

G.

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4-0^ C c d ^ o ^ O

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00 00 txO 0) <0 0) pc PC PC

22

0.970
and

In Gtt (5) = -6.02090 + 12.67352 , 11 Ps

/

representing the two linear segments of the plot of conductance, G,

against relative pressure of water vapor,

^ . These equations can be

Ps

changed to represent the relationship between the common logarithm,

log, (i.e., logarithm to the base 10) of resistance, R, and relative

humidity, RH. Noting first that

In Gj

j = - In Rj j

,

In Rtt = 2.14609 - 8.00790 ' (24)

II Ps

Noting next that

*^II ^ 2.30259 ^ir

log Rtt = 0.93203 - 3.47778 ^ . (25) ^ II Ps

Noting then that ^

,

log Rjj = 0.93203 - 0.034778 RH, (26)

where R^j is in megohms . Similarly, equation 5 becomes

log = 2.61484 - 0.055040 RH. (27)

If desired in the application of the element, the plot for the region

covered by the linear segments, that is, from 24.5 percent to 97 percent RH,

23
can be linearized, that is, equation 26 can be made to apply to the

entire region, by adding a resistance in series with the element. In

the case of element K2 from reference 9 the series resistor would be

about 1800 ohms.

To estimate the lower limit for the region of applicability of

equation 25, and therefore, that region extended by adding the series

resistor, the conductance calculated from equations 3 and 14 are set

equal and -2— is solved for. The lower limit is estimated to be

0.245. Therefore, the linearized plot should apply to the RH

Ps

region 24.5% to 97.0% (and, presumably to 100%).

In region I (from ^ = 0 to

^ = 0.245), the relationship between

me asured" conductance Gj and is represented by equation 12,

In ^ = f + h G.. ( 12 )

Substituting RH for

^

and for Gt and the values determined for f

R

s 'I and h, equation 12 becomes

log RH = 0.69463 + 0.76875 . (28)

Taking the common logarithm of both sides of equation 28, the following

equation results,

log log

(5

^

23)

" O-ll'l^l - log Rj. (29)

The relative humidity corresponding to an element resistance of Rj could

be found from a plot of either log RH versus (where Rj is megohms)

24
or log log versus log .

Equations 26, 27, and 28 or 29 are of the forms of element

calibration equations. The values of the parameters in the equations

for elements produced elsewhere depend upon the capability of the

manufacturer of the elements to produce elements typical of those produced

at NBS.

3.2 Low Temperature Calibrations

Twenty elements, supplied by three of the suppliers, were

calibrated in the NBS Pressure Humidity Apparatus [10] at 25.5, 0.7,

-19.3 and -39.3°C. The performance of two of. the elements is

illustrated in figures 4 and 5. Because of the demonstrated

inadequacy of the circuitry used for measuring element resistance in this

series of calibrations, particularly at low temperatures, and because

of other uncertainties caused by the lack of information on its

performance, it is not possible to derive reliable quantitative

information. However, it can be observed that* the elements responded

to changes in RH at temperatures as low as -39.3°C, the lowest in the

calibration series; straight lines on the plots of logarithm of

resistance vs relative humidity appear to represent the data over the

range about 30 to 80% RH for temperatures down to -19.3°C; the

straight lines for the several temperatures tend to be parallel and

the resistance at a given RH increases with decreasing temperature.

The treatment in reference 9 in which the temperature dependence of the

resistance is assigned to the intercept of the straight line plot appears

to be valid for the data in this calibration series^

25
RESISTANCE,

OHMS

FIGURE 4. Calibration at several temperatures, element H3192.

26
RESISTANCE,

OHMS

FIGURE 5. Calibration at several temperatures, element H3194.

27
The treatment in reference 9 is briefly outlined here in the

interest of completeness. Calibration data from reference 2 for

elements calibrated at nominal temperatures of 40°, 20°, 0°, -20° and -40°C are treated. The data were fitted in the nominal region = 0.25 to

Ps

0.85 by an equation of the form

log R - a + b —

^S

(30)

It was determined that the values of b for the five temperatures were

not statistically significantly different, consequently, the value of b for

0°C was assigned as the slope for each of the calibration temperatures and the

values of the intercept were adjusted to correspond to this value of

the slope. Assigning the same slope for each of the curves permits

the assignment of the temperature dependence of 1og-|Q R to adjusted

intercepts, thus

log (T) + b'

where a' is the intercept adjusted to correspond to the assigned slope

b' . For each temperature, a straight line of slope b' was drawn

through the point at — =0.50. The intercepts of each of these

Ps

straight lines is a' for the particular temperature. The plot of a

'

against temperature is shown in figure 6. A functional relationship

between a' and T derived from curve-fitting the data of figure 6 would

permit automatic data processing of element resistance data to arrive

at indicated RH for any temperature in the range 40° to -40°C.

28
TEMPERATURE, °C

FIGURE 6. Plot of adjusted intercept, a', of equation 29 against temperature.

29
4. DISCUSSION

The values of the parameters a and b in the equation

lnR=a+b-^

relating element resistance, R, to the relative pressure of water

vapor, for the elements calibrated at room temperature on September 6, 1975

are tabulated in table 3. The values of the parameters for subsequent

calibrations are tabulated in tables A-10 through A-13. For comparison, the

parameters for element K2 of reference 9 for region II = 0.335 to 0.805)

are included in the tables. In the present work, equation 1 applies

to the range

^ = 0.29 to 0.845o

Ps

Application of the "t test" [11] indicates that the values of b

for elements from suppliers A and B in the tables are not statistically

significantly different, at the 1 percent level, from the value of b

for element K2 of reference 9. The values of b for 3 elements

(A3-D, A4-D and C2-D) from supplier Dare statistically significantly

different, at the 1 percent level, from the value of b for element

K2 of reference 9. Since the functional dependence of element resistance

on relative pressure of water vapor is reflected in the value of b, it

can be concluded that in respect to room temperature calibration the

elements produced by suppliers A and B are typical of those produced

at NBS. The elements supplied by suppliers D and E, although the values

of b depart significantly from that for element K2 of reference 9 and

from those for elements from suppliers A and B, are nevertheless useful.

30
Table 3. Room Temperature Calibration Parameters, a and b, for

Elements Calibrated on September 6, 1975. (In R = a + b

Element-Suppl ier b a

A1 - B -8.21568 15.31044

A2 - B -8.30881 15.75718

C3 - B -8.11827 15.92886

C4 - B -7.73982 15.85565

nil - A -S.;n530 14.85332

1 1 12 - A -7.G9423 M.898C1

III3 - A -7.76116 15.14089

III4 - A -7.92297 15.32379

mean for supplier B -8.09565 15.71303

mean for supplier A -7.84842 15.05415

(1) mean for 8 elements -7.97203 15.38359

estimate of standard deviation

for 8 elements 0.23115

estimate of standard deviation of

the mean for 8 elements 0.08172

(2) element K2 of reference 9 -8.12993 16.03712

(1)

(2)

0.98058 0.95925

31
The value of a, the intercept, in equation 1 is influenced by the

quality of the electrode patterns on the substrates and therefore is

not considered in detail here. It is desirable, however, that the

value of a be reasonably small since ultimately the problem

of measuring very high resistances is accentuated by this parameter.

The low temperature calibration data, although leaving much

to be desired due to the inadequacy of the circuitry used, give

qualitative encouragement that the low temperature performance of

Some of the elements might be typical of that of elements produced

at NBS.

The calibration equations derived above provide analytical

expressions relating element resistance (or conductance) to relative

humidity (or relative vapor pressure of water). The effecti veness 'of

the analysis is indicated by the agreement between calculated and

"measured" conductance (columns (4) and (5) in table 2) as expressed

from 0.948 to 1.103 (94.8 to 110.3%). The uncertainty in the

measurement of resistance is estimated to be about ± 5% over most of

the range of resistance. The uncertainty in resistance due to the

uncertainty in the values of the RH points established by the saturated

salt solutions (estimated to be ± 0.5% RH) is estimated to be ± 4%.

The uncertainty in the resistance measurement is considered to be random,

the uncertainty in the values of the RH points is considered to be

systematic. Combining the two uncertainties in resistance by addition,

results in an uncertainty of + 9%. On this basis the agreement between the

calculated and "measured" values of conductance, approximately -5 to +10%,

is seen to be quite satisfactory.

by the ratio of these The ratio is seen to range

32
4.1 Physical Adsorption and Humidity Element Functioning

Empirical equations of the form of equation 23,

G'= a + b ^

c

( 30 )

represent the relationship between element conductance, G, and

D RH

relative v^por pressure of water,

^ , and can be used to

Ps luu

generate calibration curves or equations, i.e., element resistance

versus relative humidity. These equations also provide insight

into the physical processes involved in the functioning of the

element.

It has been hypothesized that the element functions by the

physical adsorption of water vapor on the barium fluoride film, the

amount of adsorbed water vapor depending on the relative pressure of

water vapor. The adsorbed water vapor increases the surface conductance

of the film. A plot of conductance versus relative pressure of water

vapor should therefore represent an adsorption isotherm.

Many theoretical isotherm equations exist and attempts have been

made by others to apply them to physical adsorption data with varying

degrees of success. These include the isotherm equations of Langmuir,

BET (Brunauer, Emmett and Teller), Fruendlich, Harkins-Jura , Henry,

Frenkel-Halsey-Hill and many others. The approach taken in the present

work has been to decompose the "S-shaped" plot of conductance, G, versus relative pressure of water vapor, into its three constituent parts,

fit empirical equations to the parts and combine these empirical equations.

Following this empirical treatment of the data, we then inquire which, if

any, of the theoretical isotherm equations are represented by the

empirical equations.

33
It has been shown above that a plot of conductance versus ^

is a composite of three separate curves. The existence of the three

separate curves has been attributed to three distinct modes of physical

adsorption. It is tempting to describe these modes as the conventional

unimolecular and multimolecul ar adsorption and capillary condensation.

It is also possible to hypothesize the existence of three classes of

adsorption sites. We shall here adhere to referring to distinct modes

of adsorption.

A plot of conductance against ^ has the shape of the Type II

isotherm in the Brunauer designation [12]. A plot of the first two

terms of equation 30 has the shape of the Type I isotherm, a plot

of the third term and a plot of the fourth term have the shape of the

Type III isotherm. Therefore, the conductance - isotherm (in itself

Ps

a Type II isotherm) is a composite of a Type I isotherm and two Type III

isotherms. This is an important result of more general application.

The first two terms of equation 30, a + b In are an empirical

Ps

fit of the data in the 12 to 22.5% RH region with parameters adjusted

by iteration to apply to the entire range of RH. The third and fourth

terms expressed as conductances are

G

2

G

3

(31)

(32)

34
Equations 31 and 32 are of the form of the Freundlich equation [121

V = kp" , (33)

where v is the volume of gas adsorbed and p is the equilibrium pressure.

Therefore, the analysis of the data has produced an empirical equation for

the Tyoe I isotherm, equations of the form of the Freundlich equation for

two Type III isotherms and a decomposition of a Type II isotherm into a

Type I isotherm and two Type III isotherms.

35
5. CONCLUSIONS

Commercial sources for barium fluoride film electric hygrometer

elements have been developed. Elements produced by at least two of

these sources appear to be typical of those produced at NBS. This

represents the successful transfer of technology from the developer

of the element in the Federal Government to the private sector and

should insure the availability of the element for general use. This

general use includes missile climatology and routine radiosonde use.

Calibration equations for the elements have been developed and

insight into the physical processes involved in the functioning of the

element has been gained by analysis of calibration data. It has been

shown that the conductance - isotherm (in itself a Type II Isotherm

in the Brunauer designation of physical adsorption isotherms) is a

composite of a Type I isotherm and two Type III isotherms. The two

Type III isotherm equations are of the form of the Freundlich

theoretical isotherm equation. These results represent the solution

of a long-standing problem in adsorption and have general application

to other adsorption systems in addition to the water vapor-barium fluoride

film system.

It is estimated that in the intermediate RH region, 33.5 percent

to 80.5 percent, measurements of RH using the commercially produced

elements would be uncertain by about 5 percent RH. There is not

sufficient data to make estimates of the uncertainties in the

other regions.

36
6. REFERENCES

[1]

. F. E. Jones, "Hygrometer Elements,," U. S. Patent 3,058,079 (1962). [2]

. F. E. Jones and A. Wexler, "A Barium Fluoride Film Hygrometer

Element," J. Geophys. Res. 2087 (1960).

[3]

. F. E. Jones, "Performance of the Barium Fluoride Film Hygrometer

Element on Radiosonde Flights," J. Geophys. Res. 2735 (1963).

[4]

, F. E. Jones, "Study of the Storage Stability of the Barium Fluoride

Film Electric Hygrometer Element," J. Res. NBS 71C , 199 (1967).

[5]

. B. R. Bean and R. 0. Gilmer, "Comparison of Barium Fluoride Humidity

Element with the Microwave Refractometer for Studies of Rapid

Fluctuations of Atmospheric Humidity," Radio Science 1155 (1969).

[6]

. B. R. Bean and Q. L. Florey, "A Field Study of the Effectiveness of

Fatty Alcohol Mixtures as Evaporation Reducing Monomolecular Films,"

Water Resources Research 4, 206 (1968).

[7]

. S. M. Goltz, C. B. Tanner, G. W. Thurtell and F. E. Jones

, "Evaporation

Measurements by an Eddy Correlation Method," Water Resources Research

6, 440 (1970).

[8]

. H. K. Weickmann, A. R. Tebo and F. E. Jones, "Temperature and Humidity

Conditions in Cumulus Mediocris," Conference on Cloud Physics, Fort

Collins, Colorado, August 24-27, 1970, pp. 177, 178.

[9]

. F. E. Jones, "Barium Fluoride Film Humidity Element Calibration

Analysis, Applications and other Developments", NBS Report 10058,

July, 1969.

[10]. A. Wexler and R. D. Daniels, Jr., "Pressure-Humidity Apparatus,"

J. Res. NBS 269 (1952).

37
[n]. W. J. Youden, Statistical Methods for Chemists (John Wiley &

Sons, Inc., New York, 1951), pp. 47-49.

[12]. S. Brunauer, The Adsorption of Gases and Vapors , Vol . I,

Physical Adsorption (Princeton University Press, Princeton,

New Jersey, 1943), p. 150.

38
7. FIGURE CAPTIONS

Figure 1. Barium fluoride film electric hygrometer element

construction and electrode configuration. 3

Figure 2. Room temperature calibration, element IIIl, supplier A. 9

Figure 3. Room temperature calibration of element K2 of reference 9,

showing separation into three regions. 11

Figure 4. Calibration at several temperatures, element H3192. 26

Figure 5. Calibration at several temperatures , element H3194. 27

Figure 6. Plot of adjusted intercept, a', of equation 29 against

temperature. 29

Figure A-1. Room temperature calibration, element III2, supplier A. 42

Figure A-2. Room temperature calibration, element III3, supplier A. 43

Figure A-3. Room temperature calibration, element III4, supplier A. 44

Figure A-4. Room temperature calibration, element A1 , supplier B. 45

Figure A-5. Room temperature calibration, element A2, supplier B. 46

Figure A-6. Room temperature calibration, element C3, supplier B. 47

Figure A-7. Room temperature calibration, element C4, supplier B. 48

Figure A-8. Room temperature calibration, element A3, supplier D. 49

Figure A-9. Room temperature calibration, element A4, supplier D. 50

Figure A-10. Room temperature calibration, element Cl, supplier D. 51

Figure A-11. Room temperature calibration, element C2, supplier D. 52

Figure A-12. Room temperature calibration, element IIIl, supplier E. 53

Figure A-13. Room temperature calibration, elements III2 and III3,

suppl ier E. 54

Figure A-14. Room temperature calibration, element III4, supplier E. 55

39
8. LIST OF TABLES

Table 1.

Table 2.

Table 3.

Table A-1

.

Table A-2.

Table A-3.

Table A-4.

Table A-5.

Table A-6.

Table A-7.

Table A-8.

Table A-9.

Table A-10.

Table A-11

.

Table A-12.

Table A-13.

Room Temperature, 23°C, Calibration Data for Element

K2 from Reference 9.

Comparison of the Values of G' Calculated Using

Equation 23, and "Measured" Values of G.

Room Temperature Calibration Parameters, ^ and for

Elements Calibrated on September 6, 1975. (In R = a + b .

Values of G.. and

^

Calculated Using Equations 3 and 4.

Values of Gj^^ and ^

Calculated Usings Equations 5 and 6.

Values of G^ Calculated Using Equations 3 and 5.

Values of G^ and ^

Calculated Usings Equations 10 and 11.

Values of G-j and Calculated Using Equations 14 and 13.

Values of G

2 Calculated Using Equations 3, 14 and 16.

Values of G-j and G

2

Calculated Using Equations 14 and 16,

and the sum of G-j and G

2

.

Values of G-j and G^ Calculated Using Equations 17 and 18.

Values of G^ and G^ Calculated Using Equations 17 and 18,

and G^.

Room Temperature Calibration Parameters, §_ and for

Elements Calibrated on September 13, 1975. (In R = a + b ^)

.

Room Temperature Calibration Parameters, ^ and for Elements

Calibrated on September 20, 1975. (In R = a + b ^)

.

Room Temperature Calibration Parameters, ^ and for Elements

Calibrated on September 27, 1975. (In R = a + b ^)'

Room Temperature Calibration Parameters, ^ and b,^for

Elements from Supplier E Calibrated on April 26, 1976.

( 1 n R = a + b .

15

22

31

56

57

58

59

60

61

62

63

64

65

66

67

68

40
9. APPENDIX A

ADDITIONAL FIGURES AND TABLES

Figures and tables which have not' been interleaved with the

text are presented on the following pages of this appendix.

41
RESISTANCE.

OHMS

ELEMENT I I 12, SUPPLIER A

FIGURE A-1. Room temperature calibration, element 1 1 12, supplier A.

42
ELEMENT III3, SUPPLIER A

luun 1 > T

' ’

1- —_

— - -

^—1

- - r

1 1

’

• —TT' r~

! I

: i

i

. . t M :

/ — - ——— — • '

lOM

. ..1 o Qyfi/7«;

A 9/13/75 • 9/20/75

9/27/75

——Least Squares fit, 9/6/75

8- — 1“ '

r- —

—— - —

-—Least Squares fit. element K2

IM

1- !- \

f

• » —

! A

5 W

o

‘ ^ 1.

• > ^ 1\ 1 o ‘

- \

«/) \ V

UJ ^ a:

lOOK

\

A

• • • • \; ;

\ -V .... ® , $“1“

*1 C)

•

. . : X- \ * \

\

1

' ' V.

\ ! : i : i .

T

".—

\

1 3--, r : i : : r~"7 i ! :

10K

. . O \i

• — . *T ~

!

' ’

!-

t- - M

1- 1 ^

i S'!) i

• T

\ 4

57 . j ..... .

t

• -- - - - •

• V •

: 1

IK

— T

-

i

!

! i

1

iL

'Ji It) ZO 30 4 0 b TO 70 ^ 0 ^00

RELATIVE HUMIDITY, %

FIGURE A-2. Room temperature calibration, element III3, supplier A.

43
RESISTANCE,

OHMS

lOOMELEMENT I I 14, SUPPLIER A

lOM

o 9/6/75

A 9/13/75 • 9/20/75

9/27/75 •

Least Squares fit, 9/6/75

Least Squares fit, element K2

lOOK

40 50 60 70 80

RELATIVE HUMIDITY, %

FIGURE A-3. Room temperature calibration, element III4, supplier A.

44
RESISTANCE,

OHMS

FIGURE A-4. Room temperature calibration, element A1 , supplier B.

45
RESISTANCE,

OHMS

FIGURE A-5. Room temperature calibration, element ;\2, supplier B.

46
RESISTANCE,

OHMS

ELEMENT C3, SUPPLIER 6

FIGURE A-6. Room temperature calibration, element C3, supplier B.

47
RESISTANCE,

Of^S

REUTIVE HUMIDITY, %

lOOK,

!II

lOOM,

t

I

1

ELEMENT C4, SUPPLIER B

o 9/6/75

A 9/13/75 • 9/20/75

9/27/75 —Least Squares fit, 9/6/75 —Least Squares fit, element K2

• «

FIGURE A-7. Room temperature calibration, element C4, supplier B. 48
RESISTANCE,

OHMS

ELEMENT A3, SUPPLIER D

Room temperature calibration, element A3, supplier D.

49

FIGURE A-8
RESISTANCE,

OHMS

ELEMENT A4, SUPPLIER D

(l

lOOM

lOM

• 9/20/75 ^ Least Squares fit, 9/20/75

Least Squares fit, element K2

0 20 40 60 80 100

RELATIVE HUMIDITY, %

FIGURE A-9. Room temperature calibration, element A4, supplier D.

50
RESISTANCE,

OHMS

lOOM

I—

lOM

IM ,

1 1

V

-V

-^7

ELEMENT Cl , SUPPLIER D -.T~-

:J

• 9/20/75

Least Squares fit, 9/20/75

Least Squares fit, element K2

—

lOOK

lOK151

\

IK

T - I

- i

i

I

T

.

20 40 . 60 80

RELATIVE HUMIDITY, %

I ..I

100

FIGURE A-10. Room temperature calibration, element Cl, supplier D,

51
ELEMENT C2, SUPPLIER D lOOM

lOfi

Ifi

C/> 6 £ i

: 2:c•-

to J. UJ

1001^.

9-

Ih

ij10K.

IK

-i

I

'l-Ui

- - A

20

\

--v-

'"f *-4

-

...... ^

:e:::

• 9/20/75

Least Squares fit, 9/20/75 —Least Squares fit, element K2

--t--

T“i" —-1-

K i X T

—

t

40

-1 : : •

.. l._.

RELATIVE HUMIDITY. %

ioo'

FIGURE A-11. Room temperature calibration, element G2, supplier D,

52
RESISTANCE,

OHMS

FIGURE A-12. Room temperature calibration, element IIIl, supplier E.

53

MiNIIMliitSriliiiAi
RESISTANCE,

OHMS

FIGURE A-13. Room temperature calibration, elements III2 and III3, supplier E

54
RrsisTANcr,

niiMs

FIGURE A- 14. Room temperature calibration, element 1 1 14, supplier E.

55
Table A-1 . Values of Conductance in Region II,

and Relative Pressure of Water Vapor,

Calculated Using Equations 3 and 4.

(1)

^ir

mi cromohos

(2)

Ps

(3)

Cal c

. j

»

in micromhos

(4)

calc, pPs

HI

(4) - (2)

1.61 0.335 1.71 0.327 1.062 -0.008

2.56 0.385 2.55 0.385 0.996 0.000

5.35 0.485 5.68 0.477 1.062 -0.008

8.70 0.535 8.48 0.538 0.975 +0.003

21.1 0.645 20.47 0.649 0.970 +0.004

36.4 0.710 34.45 0.717 0.946 +0.007

48.8 0.755 49.40 0.753 1 .012 -0.002

75.2 0.805 73.72 0.807 0.980 +0.002

56
Table A-2. Values of Conductance in Region III,

and Relative Pressure of Water Vapor,

^s

Calculated Using Equations 5 and 6.

0) (2) (3) (4) W

(4) - (2)

L_ Cal c . ^

j j j

* calc. —

Pq

in micromhos *^s in micromhos s

108 0.845 108.7 0.845 1.006 0.000

152 0.870 149.2 0.871 0.982 +0.001

270 0.920 281.1 0.917 1.041 -0.003

465 0.955 438.0 0.960 0.942 +0.005

513 0.970 529.8 0.967 1.033 -0.003

57
Table A- 3. Values of G^, the Difference Between the

Values of the Conductance in Regions II and III,

Calculated Using Equations 3 and 5.

(I)

calc.

(2)

calc. G„^

Gj = (1) - (2), 2^

in micromhos in micromhos in micromhos

s

108.7 101.6 7.1 0.845

149.2 124.1 25.1 0.870

281.1 185.2 95 9

0.920

438.0 245.0 193.0

0.955

529.8 276.3 253.5 0.970

58
Table A-4. Values of G^, the Difference Between the

Calculated Values of the Conductance in Regions II and III, and

Calculated Using Equations 10 and 11.

(1)

in mfcromhos

(2)

£_

Ps

(3)

calc. G-,

in micrOmhos

!:ic. ^

Ps

(3)

TH

(4) - (2)

7.1 0.845 9.36 0.836 1.318 -0.009

25.1 0.870 19.41 0.879 0.773 +0.009

95.9 0.920 78.42 0.927 0.818 +0.007

193.0 0.955 199.4 0.954 1.033 -0.001

253.5 0.970 294.3 0.964 1.161 -0.006

59
Table A-5. Value of , the Calculated Value of the

Conductance in Region I, and ^ , Calculated Using Equations 14 and 13.

(1)

mi cf'omhos

(2)

£_

Ps

(3)

calc. Gj,

in micromhos Ps

TTT

(4) - (2)

0.500 0.120 0.500 0.120 1.000 0.000

0.714 0.175 0.713 0.175 0.999 0.000

0.855 0.225 0.855 0.225 1.000 0.000

60
Table A-6 . Values of G , ? the Conductance Due to

Adsorption Mode II, Calculated Using Equations 3, 14 and 16.

(1) (2)

/

. (3) (4)

calc. Gjj calc. Gj, Gj = (l)-(2), calc. G^ ft}

£_

in micromhos in micromhos in micromhos in micromhos ^s

0.306 0.500 0.120

Region I 0.475 0.713 0.175

0.709 0.855 0.225

t 1.710 1.080 0.630 0.626 0.994 0.335

2.552 1.159 1.393 1 .311 0.941 0.385

Region II 5.684 1.289 4.395 4.474 1 .018 0.485

8.464 1.345 7.119 7.537 1 .059 0.535

20.471 1.450 19.021 20.359 1 .070 0.645

34.450 1.505 32.945 33.413 1 .029 0.710

49.396 1.539 47.857 47.012 0.982 0.755

73.720 1.576 72.144 66.101 0.916 0.805

61

I
Table A-7. Values of and G

2

, The Values of Conductance Due

to Adsorption Modes I and II, Respectively, Calculated Using

Equations 14 and 16, and the Sum of Gj and G^.

t Region

I

I

t

Region

II

(1) (2)

(3) ( 4 ) ( 5 )

G,

calc. Gj calc. G

2

( 3 ) + ( 4 ) in micromhos Ps in micromhos in micromhos in micromhos

0.500 0.120 0.500 0.003 0.503

0.714 0.175 0.713 0.020 0.733

0.855 0.225 0.855 0.076 0.931

1.61 0.335 1.080 0.626 1.706

2.56 0.385 1.159 1.311 2.470

5.35 0.485 1.289 4.474 5.763

8.70 0.535 1.345 7.537 8.882

21.1 0.645 1.450 20.359 21.809

36.4 0.710 1.505 33.913 35.418

48.8 0.755 1.539 47.012 48.551

75.2 0.805 1.576 66.101 67.677

( 2 )

1 .006

1.027

1 .089

1 .060

0.965

1 .077

1 .021

1 .034

0.973

0.995

0.900

62
Table A-8. Values of , and G^, New Values of the Conducturice Due to

Adsorption Modes I and II, Respectively, Calculated Using Equations 17 and 18.

(1) (2) (3) (4) (5)

calc. Gj

,

calc. Ojj/ O' = (2)-(l), calc. G'

L. > (l)+(5),

in micromhos Ps in micromhos in micromhos in micromhos in micromhos

t 0.504 0.120 0.004 0.508

Region

I 0.676 0.175 0.025 0.701

V 0.790 0.225 0.091 0.881

0.971 0.335 1.710 0.739 0.706 1 .677

T 1.034 0.385 2.552 1.518 1.447 2.481

1.139 0.485 5.684 4.545 4.762 5.901

Region

II 1.184 0.535 8.464 7.280 7.898 9.082

1 1.268 0.645 20.471 19.203 20.720 21.988

1.312 0.710 34.450 33.138 34.000 35.312

1.340 0.755 49.396 48.056 46.681 48.021

1.369 0.805 73.720 72.351 64.980 66.349

63
Table A-9. Values of G^, the New Value of Conductance Due to

Adsorption Mode III, Calculated from the New Values of the Conductance

Due to Adsorption Modes I and II, Calculated Using Equations 17 and

18, and the "Measured" Value of Conductance, G.

(1) (2) (3) (4) (5)

calc. G1 , calc. Gp, (1) + (3) G, G; =(5)-(4),

in micromhos Ps in micromhos in micromhos in micromhos 1n micromhos

1 .391 0.845 83.448 84.84 108 23.2

1.404 0.870 96.990 98.39 152 53.6

1.430 0.920 129.391 130.82 270 134

1.447 0.955 156.871 158.32 465 307

1.454 0.970 170.002 171.46 513 342

64
Table A-lO.Room Temperature Calibration Parameters

,

and for Elements

Calibrated on September 13, 1975. (In R = a + b RH).

Element-Suppl ier b a

A1 - B -6.10005x10“^ 14.35188

A2 - B -8.09422x10"^ 16.13275

C4 - B -7.92993x10“^ 15.74331

nil - A -7.77542x10“^ 14.95634

III2 - A -7.09167x10“^ 15.11538

1113 - A -7.94441x10“^ 15.45438

III4 - A -8.17878x10“^ 15.49869

mean for A2-B and C4-B -8.01208x10“^ 15.93803

mean for supplier A -7.74757x10“^ 15.25620

mean for 6 elements -7.83574x10“^ 15.48348

estimate of standard deviation

for 6 elements 0.39050x10“^

estimate of standard deviation of

the mean for 6 elements 0.15942x10“^

element K2 of reference 9 -8.12993x10“^ 16.03712

ill

(2)

0.96381 0.96548

65
Table A-ll.koom Temperature Calibration Parameters , £ and for Elements

Calibrated on September 20, 1975. (In R

= a + b RH).

Element-Supplier b a

A1 - B -7.82767x10"^ 15.31730

A2 - B -8.40123x10"^ 16.73889

C3 - B -6.72384x10"^ 14.93656

C4 - B -8.13712x10"^ 15.96918

nil - A -8.19514x10"^ 15.05381

III2 - A -7.67538x10"^ 15.15096

III3 - A -8.22840x10"^ 15.57060

III4 - A -7.73869x10"^ 15.35507

A3 - D -7.01840x10"^ 14.90606

A4 - D -7.02122x10"^ 16.48222

*C1 - D

^-8.48717x10"^ *19.13051

C2 - D -7.15512x10"^ 17.19894

mean for supplier B -7.77246x10"^ 15.74048

mean for suppl ier A -7.95940x10"^ 15.28261

mean for supplier D* -7.06491x10"^ 16.19574

(1) mean for 8 elements from suppliers

B and A -7.86593x10"^ 15.51155

estimate of standard deviation for

8 elements from suppliers B and A 0.52891x10"^

estimate of standard deviation

of the mean

(2) element K2 of reference 9

0.18700x10“^

-8.12993x10"^ 16.03712

(1)

0.96753 0.96723

* excluded from mean.

66
idble A-12.Room Temperature Calibration Parameters, a_ and for

Elements Calibrated on September 27, 1975. (In R = a + b RH).

El enent-Suppl i er b a

A1 - B -9. 01400x10"^ 16.58506

a2 - 6 -7.95223x10"^ 16.80703

C3 - B -7.18793x10"^ 14.98036

nil - A -8.01244x10"^ 14.90439

III2 - A -8.41959x10"^ 15.39848

III3 - A -8.76682x10"^ 15.77972

III4 - A -8.48811x10"^ 15.53159

mean for supplier B -8.05139x10"^ 16.12415

mean for supplier A -8.42174x10"^ 15.40354

(1) mean for 7 elements -8.26302x10"^ 15.71238

estimate of standard deviation

for 7 elements 0.60665x10"^

estimate of standard deviation , ^-2

of tne mean for 7 elements 0.22929x10

(2) element K2 of reference 9 -8.12993x10"^ 16.03712

(1)

(2)

1.01637 0.97975

67
Table A-13.Roop Temperature Calibration Parameters, a and for Elements

from Supplier E Calibrated on April 26, 1976. (In P = a + b RH).

Element b a nil - E -10. 32980x10"^ 1 7 . 58000

III4 - E -10.12638x10'^ 17.17377

III2 - E -13.21357x10"^ 19.15191

Element K2 of reference 9 - 8.12993x10'^ 16.03712
NBS-1 14A (REV 7-73)

U.S. DEPT. OF v,OMM ] l>tm K A I ION OK RI-.PORT NO. 2. (...v’t Accession

bibliographic data No

sheet NBSIR 76-1108

3. Kr( ipunt*s Accession No.

4. 1 1 1 1.1 AND si 'H I ri 1 1- Fabrication of the Barium Fluoride Film Humidity

Sensor by Industrial Firms

5. Pub! R at ion Date August 1976

6. Performing Organization < ode

7. Al niORlSI

Frank E. Jones

9. pf;rfor.min(. ORC.ANI/ATION namf anii addrkss

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project / T ask / Work Unit No. 2216161

11. ( ontract /Orant No.

12. .Sponsoring Organization Name and ( omplete 'Vddress (Street, City, State, ZIP)

Cambridge Air Force Geophysical Laboratories

Department of the Air Force

Hanscom Air Force Base

Bedford, Massachusetts 01731

13. 1 ype of Report & Period

< overetl Final

14. Sponsoring Agency < ode

15. si;i^pu;mhntary noi ks

16. AHSTRA( I (A 200-word or less factual summary of most si^ificant in formation, ff document includes a significant

bibliography or I iterature survey, mention il here.)

The barium fluoride film electric hygrometer element, which was conceived and

developed at the National Bureau of Standards as a fast responding humidity sensor

and which has been used in a variety of research applications, has been

successfully fabricated by several commercial firms. This successful transfer of

technology from the Federal Government to the private sector should assure the

availability of the element for general use, including missile climatology and

routine radiosonde use. Calibration equations have been developed and the analysis

of calibration data has provided insight into the physical processes involved in the

functioning of the element.

It has been shown that the conductance - isotherm (in itself a Type II

isotherm in the Brunauer designation of physicll adsorption isotherms) is a composite of a Type I and two Type III isotherms. The two Type III isotherm

isotherm equations are of the form of the Freundlich isotherm equation. These

results represent the solution of a lonq-standinq problem in adsorption and have

general application to other adsorption systems in addition to the water vaporbarium fluoride film system.

17. KKY V'OKDS tsix to twelve entries; alphabetical order, capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Barium fluoride; calibration equations; fast response; films; humidity sensor;

industrial fabrication; isotherm equations; physical adsorption; relative humidity;

routine radiosonde application.

18. A . AILAHILITY X Unlimited 19, SECURITY CLASS

(THIS REPORT)

21, NO. OF PAGES

For Otficial Distribution. Do Not Release to NTT's UN( LAS.SIFIED 73

[ Order From .Sup. of Doc., U.S. Government Printing ('tfice 'Washington, D.( . 20 i02. SD (.at. No. (13

20. Sl ( URll Y ( LASS

(THIS PA(.F)

22. Price

fX Urder l'r.)m National 'Technical Information Service (NTIS)

Springfield, Virginia 22151 UNCLASSIFIED $4.50

USCOMM-DC 29042-P74
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