^ecUnical v2ote 178

AN INTERPOLATION PROCEDURE FOR CALCULATING

ATMOSPHERIC BAND ABSORPTIONS FROM LABORATORY DATA

LEANN DROPPLEMAN, LAWRENCE R. MEGILL

AND ROBERT F. CALFEE

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

technical ^Ylote 178

ISSUED JUNE 3, 1963

AN INTERPOLATION PROCEDURE FOR CALCULATING

ATMOSPHERIC BAND ABSORPTIONS FROM LABORATORY DATA

LeAnn Droppleman, Lawrence R. Megill and Robert F. Calfee

Collision Processes Laboratory

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. Price 20 cents
CONTENTS

Page

1. Introduction 1

2. Resume of Interpolation Method 2

3. Results 6

4. Conclusions 7

5. References 7

li
An Interpolation Procedure for Calculating Atmospheric Band

Absorptions From Laboratory Data

LeAnn Drcppleman, Lawrence R, Megill, and Robert F. Calfee

A technique used for the calculation of absorption of

the 4.3u band of CO2 has Deen extended to the 2. On, 2.7u> and

15u bands of CO2. Results obtained agree favorably with the

experimental data available.

la Introduction

In recent years there has been an increased interest in problems

associated with absorption of infrared radiation by constituents of

the earth's atmosphere. Theoretical as well as experimental approaches

have been made to the problem. One such attempt is that of Megill

and Jamnick Fl96l] which makes use of laboratory data to determine,

by means of a regular band model, the atmospheric absorption due to

the COp band at U.3u- In another part of this paper a resume of their

technique is given for the convenience of the reader.

This method has been employed for further determinations of

atmospheric absorption by C02 for the 2u, 2-7u, U.3u and 15u bands.

The laboratory data used for these analyses are those of Howard,

Burch, and Williams r 195J+I , hereafter referred to as HBW. The HBW

report gives the results of investigations made with a low resolution

instrument. The spectrometer slits were set approximately 2000u apart.

In all the determinations made for the various CO bands, the

effective transmission values were measured from the laboratory

data at ten wave number (10 cm" ) intervals. An average value of

a. = 0.06^ cm" was assumed for the half -width of the lines at standard atmospheric conditions p_ and 6 . An average line spacing
6 = I.56 cm was used. Following Megill and Jamnick, corrections to

the half-width were made only for pressure variations, using a constant

p value of temperature, 6~ ~ 290° K . That is a = « — . From these °P

values the absorption coefficients were calculated and used to determine the integrated band absorption/ A

v d u.

2, Resume of Interpolation Method

The following is a brief review of the contents of the paper by

Megill and Jamnick with some changes in notation which will be compatible with the present paper.

The basic relationship governing the absorption of energy is

given by

I(") = I ( y ) exp [- k (u) ml. (1)

This equation states that for radiation at any wave number u, the flux

per unit area of radiation I, which has passed through a mass of

material m is given as the product of the incident energy flux (l )

and the exponential of the negative product of the mass m and an

absorption coefficient k(u) characteristic of that material. The

application of this simple relationship can result in a very complex

problem when one attempts to calculate k(v) for a given material.

This is especially true for an infrared band of a complex molecule.

Here a technique will be described which has been developed to allow
one to extrapolate from laboratory data to fairly general atmospheric

conditions

The calculation of k(v) involves knowledge of the position, the

strength and the shape of all absorption lines near enough to the

point v to affect the calculation . The summation of the effect of all

these lines is used to arrive at a total value for k(v). The integrated intensity and position are nearly independent of pressure and

temperature for many applications, but the shape is a function of both.

The problem of specific concern is the absorption of infrared

radiation through a non-uniform path such as the earth's atmosphere.

Many molecules have a band structure consisting of nearly regularly

spaced lines whose intensity varies slowly with wave number. This

type of band has been studied by a number of authors - Elsasser [1938J,

Kaplan [1952], and Plass [1958] • Here the assumption is made that each

portion of band can be represented by such a model with k(v) being

calculated from

k(u) =Jj ^

i M =^Soi b (v - vQi ) (2)

i i

where k. (v) is the contribution from the i'th line of intensity S -• 01

with its line center at position r

u .. The function b (v - v .) 01 v 01

describes the line shape. It is further assumed that the pressure

is such that only the Lorentz broadening need be considered so that
M«-

M > -?: ~ > (3)

;oi *[(»- u.)2 + a

2

3

where a is the half-width of the line. The assumption of a regular

band allows u . to he expressed as 01

v. . = v + n 6, (i+)

01 o

'

where v is taken at the center of an arbitrary line and 6 is the line

spacing. Here n takes on positive and negative integral values.

Assuming all the S . are equal, they will be denoted as S . Under these oi o conditions the absorption coefficient may be written

OP

{v) 'I tf ; —ra—

_5^ Lw - (" + n 6)J~ + a"

(5)

It has been shown by Elsasser [1938] that, given the above

expression, the transmittance of the region is

i

T = fexp [-2 * y y ^-?J2 ] dx , ( 6 ) £

cosh 2ny - cos 2 jt x ~2

where x = u/6, y = a/6, and y = S m/2 n a. The temperature and

pressure dependencies are included in the value used for a-
These pressure and temperature dependencies of a are given by

a = a

Q

(P )&> )*, (7)

where a is the line width at pressure P and temperature 6 • o o o Implicit in the above are the assumptions that the absorbing gas

is dilute and that the population of the various states does not

change with temperature; i.e., S is not a function of temperature.

o Utilizing the regular band model (Eq. 6), the atmospheric

transmittance was calculated from data taken from low resolution

experimentally determined absorption curves. An equivalent line

intensity S at intervals of ten wave numbers was calculated for each

pressure for which data were available. A plot of these values as a

function of pressure was then made. If Eq. (6) were an accurate

representation of the physical facts, then S (u,P) should be independo ent of pressure. It was found from these plots that S as here calculated is a function of pressure. Therefore, an equivalent line

strength S (v,P) was defined such that

S

c (v,p) =K (v) P

a

. (8) o

The absorptance in non-uniform paths was then calculated by:

l) assuming a regular band model; and 2) calculating the absorptance

due to a large number of "slabs", each of which is assumed to have a
Q . . distinct temperature and pressure. The values of S (v,P) are

o calculated for each slab from the empirically determined table of K's

and a's. In this fashion the principal effects are taken account of

by theory, while a second-order correction is made using the empirically determined parameters.

After determining the emergent flux I(v), the total band

absorptance was calculated by summing the effects of each of the ten

cm intervals. This result can then be compared to experimental

data. Megill and Jamnick [1961] made a comparison between calculations

of absorptance in the atmosphere by this technique based on the data

of HBW and data obtained on a balloon flight reported by Murcray,

Brooks, Murcray, and Williams ["i960].

3 . Results

For the present study of atmospheric absorption by the several

00 bands, the integrated absorptions were computed for each of the

layers in the atmosphere. Table 1 gives a list of pressures and C02

concentrations for which laboratory data were available. Table 2 lists

the least squares fit values of K and a from which the effective line

e strengths S were calculated. Table 3 shows the values of total

o. absorption A/ A^di? du calculated for each of the several layers in the

r -1 atmosphere. Plots of the total absorption / Aydu in cm as a function

of the product of pressure, P, in millimeters of mercury, and mass, m,

expressed as a fraction of the atmosphere traversed are shown in

6
figures 1, 2, 3, and h. In addition the results from data obtained

by balloon flight are also shown on the same graphs with the appropriate predicted results.

4. Conclusions

In the cases where comparisons with atmospheric data were made

the agreement is good. Thus the method appears to be a feasible means

of predicting atmospheric absorption by constituents which can be described by the regular band model and for which Lorentzian broadening

of the lines is the principal factor in determining line shapes.

Possibly, further refinements in the procedure could be attained by

including temperature corrections to the line broadening. From the

degree of success achieved in the case of the regular band, it seems

that it may be feasible to use a similar approach to the random band

model which is applicable to water vapor for example.

5. References

Elsasser, W. M., (1938). Phys. Rev. 54, 126.

Howard, J. N., D. E. Burch, and D. Williams, (1954) « Geophysics

Research Directoral, Ohio State University Research Foundation.

Kaplan, L. D., (1952). J. Meteorol. 9.

Megill, L. R., and P. M. Jamnick, (1961). J. Opt. Soc. Am. 51, 1294.

Murcray, D. G., J. N. Brooks, F. H. Murcray and W. J. Williams, (I960).

J. Opt. Soc. Am. 50, 107.

Plass, G. N., (1958). J. Opt. Soc. Am. 48, 690.
TABLE 1

Combinations of pressure P and concentration of COp w used for

e -1

calculating effective line strengths Sq at intervals of 10 cm .

C02 Band

2u

2.7u

P total P partial w P total P partial w

(mm Hg) (mm Hg) (atmo-cm) (mm Hg) (mm Hg) (atmo-cm)

10 10 1730 100 50 8630

35 35 378 200 10 108

35 35 755 200 10 432

35 35 1510 200 50 540

35 35 3020 200 10 1730

50 50 540 200 50 2160

50 50 2160 200 50 8630

50 50 8630 400 10 108

75 75 809 400 10 432

75 75 1620 400 10 1730

75 75 3240 470 50 540

75 75 6476 470 50 2160

100 10 432 470 50 8630

100 50 540 76O 50 540

100 10 1730 760 50 2160

100 50 2160 760 50 8630

1 1 11 120 10 432

1 1 22 120 10 863

1 1 43 120 10 1619

1 1 86 126 0.4 25

4 k 43 140 4 43

4 4 86 140 4 86

5 4 173 140 4 173

5 4 345 140 4 345

5 4 518 300 1 11

6 0.1+ 25 300 1 22

10 10 108 500 0.4 25

10 10 216 300 1 43

10 10 432 300 1 86

10 10 863 506 4 43

10 10 1619 306 4 86

25 1 11 306 4 173

25 1 22 306 4 345

25 0.4 25 306 4 648

25 1 43 737 1 11

25 1 86 737 1 92

57 1 11 737 1 43

57 1 22 737 1 86

8
Table 1 continued

C0

p

Band P total

(nun Hg)

P partial w P total P partial w (mm Hg) (atmo-cm) (mm fig) (mm Hg) (atmo

(2.7U 57 1 45 740 4 43

cont'd) 57 h 45 740 4 86

57 i 86 740 4 173

57 4 86 740 4 345

57 k 173 740 4 518

57 4 345 740 4 648

120 1 11 747 10 108

120 1 22 747 10 863

120 1 43 755 10 216

120 1 86 755 10 432

120 10 108 755 10 1619

120 10 216

4-3u 1 1 18 731 1 46

1 1 182 731 1 64

4 4 364 731 1 82

5 1 18 734 1 91

10 9.8 104 734 9.8 1043

10 k 364 735 1 9

10 9.8 1043 735 1 18

20 1 18 735 1 27

20 1 182 735 1 36

52 1 18 735 1 46

100 9.8 104 735 1 55

100 9.8 209 735 1 91

100 9.8 1040 735 9.8 104

100 9.8 1043 735 1 137

103 1 182 735 1 182

10U 1 18 735 9.8 313

199 1 18 735 9.8 626

396 9-8 104 735 9.8 1040

396 9.8 1043 735 9.8 1570

398 1 18 742 9.8 104

731 1 18
Table 1 continued

C02 Band P total P partial w P total P partial i (mm Hg) (mm Hg) (atmo-cm) (mm Hg) (mm Hg) (atmo

15 u 20 20 216 125 4 173

20 20 432 125 20 216

20 20 863 125 20 432

50 1 11 125 20 863

50 1 22 350 1 11

50 1 43 350 1 22

50 4 43 375 1 43

50 4 86 375 4 43

50 4 173 375 4 86

125 1 11 375 4 173

125 1 22 375 20 216

125 1 43 745 4 43

125 4 43 745 4 86

125 4 86 745 4 173

w

10
TABLE 2

Least square fit values of K and a from which the effective line

strengths S

e

= K P

a were calculated. P is expressed in millimeters

of mercury.

co2

Band

2u

(cm"1

)

U710

4720

'+730

U71+O

1+750

1+760

V770

1+780

1+790

1+800

1+810

i+820

i+830

1+81+0 1+850

1+860

1+870

1+880

1+890

1+900

1+910

1+920

;+930

1+91+0 1+950

1+960

i+970

i+980

1+990

5000

K

-'+ 1.93x10

l.ll+xlO -1

1.22x10-3

1.56xl0-2

i+.28xl0"2

1.38x10"!

3.17x10"!

7.78X10-1

1.2cxlOu 2.78x10°

5-22x10°

3-95x10°

6 .27x10^

6.10x10°

6.15x10°

5.69x10°

5-23x10°

5.1+8x10°

6.10x10°

7-56x10°

1.02X101

1.51X101

2.38X101

1+.22X101

1+.67X101

l+^^xlO1

3.59x10?-

2.78xl0|

2.15X101

I.63XIO1

1+.07X10"1

-6.19x10"!

2.l+9xl0"] -3-99x10

-8.86x10

-2

-2

-1.81+xlO"1

-2.21+xlO-1

-2.87xl0_1

-2.91X10"1

-3.1+tao-1

-i+.OOxlO-1

-2.75x10"!

-3.06x10"!

-2.65x10"!

-2. kk xlO"1

-2.21X10"1

-2.08x10"!

-2. 25X10"1

-2.6lxl0_1

-2.96xl0_1

-3.35X10"1

-3-73x10-1

-k. 13xl0_1

-1+.71X10-1

-1+.51X10"1

-l+.lOxlO-1

-3.61x10"!

-3-18x10-1

-2.93x10

-2.92x10

-1

-1

(cm"1

)

5010

5020

5030

501+0

5050

5060

5070

5080

5090

5100

5110

5120

5130

511+0

5150

5160

5170

5180

5190

5200

5210

5220

5230

521+0

5250

5260

5270

5280

5290

1. 3J+X101

1.06X101

6.75x10°

1+. 66x10°

1+. 00x10°

3-7^x10°

3.36xlOu

l+. 01x10°

5-87x10°

6.83x10°

6.13x10°

l+. 97x10°

3-21+xlO

3-1+0x10°

1.59x10°

9-58x10-1

5- 1+6x10

-1

2.23x10-1

1.12x10-1

2.83xl0-2

I.l6xl0-2

8.72x10-5

3-93x10-5

6.22x10-3

1.05x10-5

1. 1+1+ xl0"5

3.62x10"^

2.10x10"^

1.02xl0~5

a

-3.^+3x10-1

-3-68x10"!

-3.36X10"1

-3-01+xlO"!

-2.87x10-1

-2.67x10"!

-2.18x10"!

-2.13x10"!

-2.1+5xl0 _]

-1

—J. -1

-2.1+8x10

-2.26x10

-2.02x10

-1.66X10"-

1 -1.86x10"!

-1.65x10"!

-1.57x10"!

-1.23x10-1

-5-00x10-2

-1.85x10-2

1.33x10-1

1.96x10-1

1.53x10"!

2.11x10"!

1.37x10-1

3-1+2x10-1

3-15x10-1

l+.71xl0"l

l+. 63x10-1

8.92x10"!

11
Table 2 continued

co2

Band

v (cm~l

2.7u 3410

3420

3430

3440

3450

3460

3470

3480

3490

3500

3510

3520

35-30

3540

3550

3560

3570

3580

3590

3600

3610

3620

3630

3640

-1

2.75x10"^

1.36xlO-2

7.28xl0-2

1.25xl0"

J 2.35x10

1.67x10°

3.81x10°

1.86X101

3.76X101

7.82X101

1.52xl02

2.78xl02

4.17xl02

6. 31x1 2

8.24xl02

l.OlxlO5

1.34xlo5

1.63xl05

1.66x105

1.30xl05

1.35xlo5

1.05xl05

8.66 xlO2

7. 95x1 2

2.00x10"!

7.20xl0~2

-8.54xlO-2

-7.23xlO~2

-4.86xlO"2

-2.62x10"!

-2.96x10"!

-4. 64x10 "1

-4.89x10"!

-5-26x10"!

-5-45xlO_l

-5-41x10-1

-5.12xlO_1

-4.96x10"!

-4.60x10-1

-4.29x10"!

-4.17x10"!

r4.01xlO_1

-3.78X10-1

-3-05x10-1

-3- 28x10-!

-3.16x10"!

-3.25x10"!

-3.36xlO-1

(cm 1

)

3650

366O

3670

3680

3690

3700

3710

3720

3730

3740

3750

3760

3770

3780

3790

3800

3810

3820

3830

3840

3850

3860

3870

3880

K

8.46x10^

1.08xl05

1.55xK>5

2.11xKT

2.56xl05

2.90x10^

2.32xlo5

1.51x10^

4.67xl02

1.56xl02

4 .03X101

1 .19X101

1 .21x10°

3 .60x10"!

4.l8xlO"2

3.36xlO"2

9-56xlO"5

1.96x10-5

8.19x10-5

2.07x10-5

1.62x10"^

1.74x10"!

2.58xlO"2

4.53xlO"5

-3. 51x10"!

-3-80x10"!

-4.14X10-1

-4.39x10-1

-4.56x10"!

-4.90x10-1

-4.91x10"!

-4.32x10"!

-3-84x10"!

-2.9OXIO"1

-1.80x10-1

-1.19x10"!

1. 28X10"1

2.03x10"!

4.52x10"!

4.08x10"!

4.73x10-1

6.72x10"!

3.66x10"!

4.98x10-1

8.59x10"!

-3.08x10"!

-7.01xl0"2

5. 30x10

2

4.3u 2200

2210

2220

2230

2240

2250

2260

2270

2280

2290

2300

2310

2320

5-55x10^

1.26xKT

1.07xl02

5-67xl02

1.15x105

1.01xlo5

4.58x105

7-97x10?

1.51xl04

2.57x10^-

1.49xl04

3.68x10^

6.40X1011

-2.26x10"!

-6.65x10"!

-4.48x10"!

-5-59x10-1

-5-53x10-1

-3.34x10-1

-4.50x10"!

-4.45x10-1

-4.48x10"!

-5-60x10-1

-3.32x10-1

-3-31x10-1

-3.39x10-1

2330

2340

2350

236O

2370

2380

2390

2400

2410

2420

2430

2440

5-06x10^

7.4OXIO7

8.37x10^

8.42x10^

6.75x10^

1.79x107

1.73x10^

4.28x105

1.25xl02

5.96xlol

2.95x10°

1.31x10°

-5. 50x10

~1

0.0

0.0

-3-39x10-1

-7.79x10"!

-7.71x10"!

-8.89XIO"1

-8.87x10"!

-4.43x10-1

-4.48x10"!

-12.0x10"!

-5-56xlO"2

12
Table 2 continued

CO2

Band

15u

(cm-1

)

580

590

600

610

620

630

6h0

650

660

670

680

690

700

1 .69xl02

9.38XIO1

i+.27xl01

8.89XIO1

3- 44x1 2

U.25xl05

2. 3^x105

8.31xlOp

1.8+xlCT

3.65x10^

l.U9xl04

9.J+9xl05

4.50xl05

-6.3UXIO-1

-3.00xl0-1

-3.88X10"1

-6.50xlO-1

-2.06x10°

-6.04x10°

-2.34x10°

-3.34x10°

-4.13x10°

-5.29xlOU

-3-52x10°

-3.13xlOu -2.93x10°

v (cm"1

)

710

720

730

740

750

760

770

780

790

800

810

820

830

2.67x105

1.15xl05

5-32xl02

2.85xl02

1.53xl02

1.36xl02

U.89XIO1

2.U6xloJ

8.16x10°

5.96x10^

2.15x10°

5.65xlO-1

6.96xlO-2

-3-65x10°

-3.35x10"

-3-08x10°

-2.67x10°

-2.09x10°

-2.87x10°

-3-27x10°

-3.66x10^

-2.77x10°

-2.83x10°

-1.67x10°

-9.81+xlO"2

2.14x10°

13
TABLE 5

Values of / A^dv determined for the various layers in the atmosphere as a function of the product of pressure, P, in millimeters of

mercury and the mass, m, expressed as a fraction of the atmosphere

traversed.

P m 2u Band 2.7u Band l+.5u Band 15u Band

(ram Hg)

0.019 1.11 5.92 19.7 7-5

0.076 1.1k 9.96 55-6 12.8

0.171 2.52 15-6 1+5.5 17.7

0.501+ 2.86 17.1 55-

21.2

0.1+75 5.59 20.5 61+. 26.1+

0.681+ 5-90 25.5 71.2 50.1+

0.951 1+.1+0 26.5 77.1+ 51+.2

1.22 5.56 52.1+ 87.5 1+1.1+ 1.90 5.82 55-2 91.7 1+1+.8 2.50 6.28 57.9 95.1+ 1+8.0

2.74 6.71+ 1+0.6 98.8 51.1

5.21 7.19 1+5.2 102. 5i+.

1

5.72 7.65 1+5.8 105. 56.9

1+.28 8.07 1+8.5 108. 59-7

1+.86 8.50 50.8 110. 62.5

5.^9 8.95 55.5 112. 6i+.

9

6.16 9-55 55.7 115. 67.1+

6.86 9-77 58.1 117. 69-7

7.60 10.2 60.1+ 119. 72.0

17.1 11+.5 82.5 151+

91.2

50.1+ 18.1 102. 11+5. 105.

V7.5 21.7 118. 150. 115.

68.1+ 25.5 13^' 156. 125.

95.1 28.7 11+7. 160. 150.

122. 52.1 159- 161+

.

156.

151+. 55.^ 170. 167. ll+2.

190. 58.6 180. 170. U7-

250. 1+1.7 188. 172. 151.

27!+

1+1+.8 196. 176. 155.

521. 1+7-9 205. 177. 159.

572. 51-0 209. 179- 162.

1+28. 55.9 215. 181. 166.

1+86. 56.9 220. 182. 169.

5^9. 59-8 221+

.

181+. 171.

616. 62.6 228. 185. 17*+.

686. 65.5 252. 187. 176.

760. 68.2 256. 188. 178.

11+
ATMOSPHERIC ABSORPTION BY 2/1 C0 2

Figure 1. The total absorption of the 2.0|i band of C0 2 as

a function of the pressure in an isothermal atmosphere.

15
ATMOSPHERIC ABSORPTION BY 2.7/a C02

Figure 2. Atmospheric absorption of the 2.7\i band of CO2 is

shown as a function of pressure. The data obtained from the

balloon flight of Murcray et. al, are represented by x. An

isothermal atmosphere is assumed.

16
ATMOSPHERIC ABSORPTION BY 4.3 /x C02

50 100 300

/'

150

Aj, dv (cm -1

) Figure 3. Atmospheric absorption of the 4.3p band of CO2 is

shown as a function of pressure. The data obtained from the

balloon flight of Murcray et. al. are represented by x. An

isothermal atmosphere is assumed.

17
ATMOSPHERIC ABSORPTION BY 15/i C02

50 150

J A„ 6v (cm -1

)

300

Figure 4, The total absorption of the 15p. band of CC>2 as

a function of the pressure in an isothermal atmosphere.

18

ii U. S. GOVERNMENT PRINTING OFFICE : 1963 O - IJ86202
DEPARTMENT OF COMMERCE

Luther 11. II

\l. Bl REAU OF STANDARDS

A. V. Astin,

THE NATIONAL BUREAU OF STANDARDS

e of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and suggested in the following listing of the divisions and sections engaged in technical work.

I. each section carries out specialized research, development, and engineering in the field indicated by

rief description of the activities, and of the resultant publications, appears on the inside of the

OT.

iSIIINUTOrN, U.C.

tricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

s. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology. ^^Ht and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment,

eonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Re fer- Materials. Applied Analytical Research. Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

rols. Polymers. Macromolecules: Synthesis and Structure. Polymer Chemistry. Polymer Physics. Polymer Characation. Polymer Evaluation and Testing. Applied Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Microscopy and Diffraction. Metal Reactions. Metal Physics. Electrolysis Metal Deposition.

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-tallography.

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Engineering Applications. Systems Analysis.

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ics. Atomic Physics. Plasma Spectroscopy.

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Office of Weights and Measures. BOULDER, COLO.

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Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval Standards. Radio Plasma. Millimeter-Wave Research.

Circuit Standards. High Frequency Electrical Standards. High Frequency Calibration Services. High Frequency

iance Standards. Microwave Calibration Services. Microwave Circuit Standards. Low Frequency Calibration

Services.
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