National Bureau of Standarflt Library E-01 Admin, BJdfc JAN 1 2S 19713/ OCA

NBS SPECIAL PUBLICATION ^uU^O

A 11 ID 3 0fl5bT3

Standard Reference Materials:

VISCOSITY OF A STANDARD

BOROSILICATE GLASS

I1

UNITED STATES DEPARTMENT OF COMMERCE Maurice H. Stans, Secretary NATIONAL BUREAU OF STANDARDS Lewis M. Branscomb, Director

Standard Reference Materials: Viscosity of a Standard

Borosilicate Glass

(Certification of Standard Reference Material 717)

A. Napolitano and E. G. Hawkins

Institute for Materials Research

National Bureau of Standards Washington, D.C. 20234

I National Bureau of Standards Special Publication 260-23

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-23, 10 pages (Dec. 1970) CODEN: XNBSA

Issued December 1970

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13.10:260-23), Price 25 cents
Library of Congress Catalog Card Number: 75-608432
Viscosity of a Standard Borosilicate Glass

A. Napolitano and E. G. Hawkins

The viscosity of a borosilicate glass has been measured at the National Bureau of Standards and four other laboratories. Determinations were made in the range 102 to 1016 poises (1525 to 470 °C). Measurements were made by the rotating cylinder, fiber elongation, beam bending, and

parallel-plate methods. The results have been evaluated and the glass has been issued as Standard

Reference Material No. 717. Key words: Beam-bending; borosilicate glass; glass viscosity; parallel-plate; rotating cylinder; standard reference material ; viscosity ; viscosity standard.

1. Introduction

In a continuing program of establishing well-char-

| acterized glasses as standard reference materials, a

| borosilicate glass has been selected and promoted as

! a third viscosity standard. This glass is also a type

I of glass that is usually produced commercially in

I large quantities, can be manufactured in homogenous

lots, and is stable in storage. In addition to its good

| optical quality, (i.e., free from severe cord, gas

! bubbles, stones, etc.) it has a low expansion and

I seals to Kovar1 metal. Its transformation point is

I rather low and its expansion closely matches that of

j the Kovar metal from its strain point to room tem-

[ perature.

| This report gives the results of the viscosity measI urements made at NBS and four laboratories2 that

participated in a "round robin" series of measurements. The data have been analyzed and tabulated

in a "Certificate of Viscosity Values" and the glass has been issued as Standard Reference Material No.

717.

1 Trade name for an iron, nickel, and cobalt alloy for glass-to-nietal seals.

* Corning Glass Works, Corning, New York (Mr. Eugene H. Fontana); Emhart Corporation, Hartford, Connecticut (Mr. Leo E. Stadler); Owens

Illinois, Toledo, Ohio (Mr. R. W. Beiswenger); Thatcher Glass Manufacturing Co., Inc. Elmira, N.Y. (Mr. Thomas M. Mike).

2. Glass Sample

Following the procedure used with the two pre- vious standard reference glasses, No. 710 (soda-limesilica) [l] 3 and No. 711 (lead-silica) '[2], a large quantity of borosilicate glass with the highest possible homogeneity was purchased. The lot consisted of about 545 kgs of glass in the form of strips having a

cross section of 4.2 cm by 4.2 cm and 60 cm long with

a few strips 45 cm long. All strips were numbered

consecutively to show the sequence of production and also marked with the hour of delivery from the

glass tank. There were several breaks in the contin- uous process where glass was discarded by the manufacturer, figure 1, because of striae, deviations from

the target index, die marks, surface imperfections,

or breakage. Before delivery of the glass the manufactuer used

136 kg of the strip glass to form rods 0.6 cm by 0.6 cm

and about 100 cm long by a reheating and drawing

process. The weight lost in this drawing process was

86 kg. The remaining 50 kg of glass in rod shape was

equivalent to approximately 650 lengths of 91.4 cm. The homogeneity of the glass was checked by measuring the index of refraction (iV/j-line) [1] on small samples of glass taken from each strip or every 2.5 kg

of glass. Sampling of the rod shaped glass was about

3 Figures in brackets indicate the literature references at the end of this publication.

WASTE | STRIf 6.0

o, 48

i It

R

PRODUCER'S ANNEAL

-VISCOSITY SAMPLES*,,

WASTE , STRIP ROD ROD ROD JBLJB

50 70 100 HO 130 140 150 180 2 0 2400 0300 0330 1100 230 250 260 STRIP NO. 2200 2350 TIME hr Figure 1. Index variation and production history of Standard Glass No. 717.

1
Table 1. Viscosities of five samples of glass selected from the total lot of glass No. 717 (see fig. 1)

Strip No. 70 Strip No. 100 Strip No. 125 Strip No. 85 Strip No. 260 Temp, °C LoglO^ObB Temp, °C Logio^obs Temp, °C Logl0>?0bs Temp, °C LogicWobs Temp, °C Logioiobs

Test Method: Fiber Elongation

485. 5" 14.603 515.

0

a 13.375 470.

9

a 15.236 539.5* 12.360 528. 7" 12.788 568.6 11.404 549.0 12.024 501.1- 13.917 556.0 11.796 555.2 11.756 580.9 10.970 564.4 11.517 560.0 11.636 574.4 11.168 564.0 11.523 600.4 10.318 577.6 11.075 580.8 10.982 590.4 10.660 585.5 10.795 614.9 9.932 610.8 10.028 600.2 10.309 596.0 10.440 605.0 10.209 620.7 9.792

Test Method: Rotating Cylinder

636.6 9.380 599.3 10.414 607.0 10.148 613.4 9.995 628.7 9.573

643.2 9.193 600.8 10.261 619.5 9.798 710.9 7.812 709.0 7.847 681.0 8.333 652.0 9.015 709.3 7.820 798.6 6.442 806.4 6.342 749.8 7.091 704.3 7.925 781.7 6.665 901.8 5.254 904.7 5.223

835.8 5.937 725.9 7.534 810.9 6.272 1010.7 4.332 1003.2 4.393 893.4 5.317 763.7 6.932 908.2 5.183 1104.3 3.736 1103.5 3.739 914.4 5.138 804.5 6.354 929.9 4.991- 1196.0 3.250 1220.7 3.132

1078.9 3.846 858.8 5.690 996.2 4.446 1302.6 2.795 1320.3 2.732

1177.5 3.314 909.8 5.155 1027.0 4.214 1400.1 2.460 1393.3 2.487

1283.5 2.850 935.0 4.949 1095.0 3.773

1359.6 2.569 983.2

1051.0

1144.2 1250.4

1300.3

1333.7

1401.2

4.534

4.032

3.513

2.975

2.813 2.690

2.455

1129.6

1195.3 1227.7

1294.7 1320.7 1377.0

1408.9

3.590

3.243

3.102

2.818 2.727

2.529 2.428

a Times held at indicated temperature before viscosity measurements were made are as follows: 485.5, 47 hr; 515.0, 19 hr; 470.9, 71 hr; 501.1, 70 hr; 539.5, 1 hr; and 528.7, 2 hr.

every 1 kg of glass. The index of refraction was measured before (as received) and after they had all been

given the same heat-treatment (annealing). The re- sults of these measurements are shown in figure 1. With the producer's anneal the index of refraction

for the total lot ranged from 1.48728 to 1.48760, a change of 0.00032. Closer examination reveals that about 80 percent of the glass in the lot ranges from

1.48740 to 1.48760, a change of 0.00020. The NBS

anneal gave comparable results: the index of refrac- tion for the lot ranging from 1.48748 to 1.48782, a change of 0.00034; and 80 percent of the lot ranging from 1.48762 to 1.48782, a change of 0.00020.

It has been shown that such a variation in index

for glass in this quantity [1, 2] denotes minimum

composition changes and is within acceptable toler- ances for the proposed physical property standard of

viscosity. It is well known that the uniformity of index is not necessarily a unique indicator of uni- formity of composition. In a continuous production

of a quantity of glass in strip form such as this, where no deliberate changes are made in the batch composition, it is unlikely that a significant change in composition would not be reflected by a concurrent change in index. In this case, figure 1, the index of

refraction does decrease slightly at the end of the

production run showing possible composition

changes. It will be shown later that these changes had no measurable effects on the viscosity of the

glass selected from this area. The nominal chemical composition4 for this glass

is as follows: Si02 —70 percent B203 -17 K20 -8

Na20-1

A1203 -3

Li20 -1

3. Apparatus and Method of Measurement

3.1. Laboratory A

The measurement of viscosity at the National Bureau of Standards was made by the rotating concentric cylinder and fiber elongation methods. The equipment for these measurements has been

described in detail in previous papers [1, 3].

4 This glass is not intended as a standard for ehemical analysis. The above

composition is offered only for information purposes.

2
Table 2. Fulcher equation constants forfive samples of

glass measured by Laboratory A (NBS)

Strip No. A B T0

70 -1.491 4680.33 205.2 0.017

100 -1.576 4831.33 194.9 .029 125 -1.542 4787.73 197.3 .017 185 -1.583 4849 . 19 194.0 .018 260 -1.618 4907.03 189.9 .025 Combined -1.562 4811.83 196.1 .023

Table 3. Comparison of temperatures corresponding

to nominal viscosities calculated from Fulcher

equation parameters for each of the five samples

Temperature, °C

Logioi? S-70 S-100 S-125 S-185 S-260 Comb.

2 25 1456 .4 1457 .8 1459 .9 1459 .2 1458 4 1458 4

2 50 1378 0 1380 .3 1381 .8 1381 .7 1381 4 1380 7 2 75 1308 9 1311 8 1312 8 1313 .2 1313 2 1312 0

3 00 1247 4 1250 8 1251 4 1252 .1 1252 4 1250 9

3 50 1143 0 1146 8 1146 9 1148 .0 1148 6 1146 7 4 00 1057 6 1061 4 1061 2 1062 6 1063 3 1061 3 4 50 986 5 990 1 989 7 991 2 991 9 989 9

5 00 926 3 929 6 929 2 930 6 931 3 929 4

5 50 874 7 877 7 877 2 878 6 879 2 877 5 6 00 830 0 832 7 832 1 833 5 834 0 832 5 6 50 790 9 793 2 792 7 793 9 794 3 793 0 7 00 756 4 758 3 757 8 759 0 759 3 758 1 7 50 725 7 727 3 726 8 727 9 728 0 727 1 8 00 698 3 699 5 699 1 700 0 700 1 699 4

8 50 673 6 674 4 674 1 674 9 674 8 674 4

9 00 651 3 651 8 651 5 652 2 652 0 651 7 9 50 631 0 631 1 630 9 631 5 631 2 631 1 10 00 612 5 612 3 612 1 612 6 612 2 612 3

10 50 595 5 595 0 594 9 595 3 594 8 595 1

11 00 579 9 579 1 579 1 579 4 578 8 579 2

11 50 565 5 564 4 564 4 564 6 563 9 564 5

12 00 552 1 550 8 550 9 551 0 550 2 550 9

3.2. Other Participating Laboratories The four other participating laboratories also made viscosity determinations at high temperatures

(725-1525 °C) by the rotating concentric cylinder method. The techniques and modifications used by

each laboratory have been described previously

[1, 2]. In the low-temperature region (495-850 °C) Laboratory C made extensive viscosity measure- ments by the beam-bending [4] and parallel-plate methods [5]. The beam-bending data were deter- mined at equilibrium temperatures and also at heat- ing and cooling rates of 5°/min. The parallel-plate data were determined only for 5°/mm. heating rate (630-850 °C).

All laboratories made the softening, annealing, and strain point determinations using the ASTM

Methods of Test [6, 7].

4. Results

4.1. Viscosity Measurements Made at NBS (Laboratory A)

In assuming that the index changes throughout

the lot are due to slight unintentional changes in composition, five samples of glass were selected from

the lot for viscosity measurements by laboratory A,

figure 1. Two samples were selected from the region

of the highest index, strips No. 70 and No. 100; one from the region of the lowest index, strip No. 260; and, two in the intermediate range, strips No. 125 and No. 185. The results of the viscosity measure- ments on the five samples selected from the lot are given in table 1. The' data from both the low-temperature fiber elongation method and the high-temperature rotat- ing concentric cylinder method for each of the five glasses were combined and fitted to the Fulcher

equation [8] by the method of least squares combined

with the Gauss-Newton iterative method. [9] The Fulcher equation has the form:

Logior? = A + B/(T - To) (1) where T = temperature in °C

rj = viscosity in poises and A, B, and TQ = constants. The constants A, B and T0 for each of the five glasses and also for the five samples combined are given

in table 2. Only data up to log10 12 and under

equilibrium conditions were used to determine these parameters. Using the constants derived for each glass, temperatures for nominal values of logio viscosity were

calculated, and are given in table 3. The results of

these calculations show that the temperatures for

strip No. 70 are slightly lower for the same logio viscosity values at the higher temperatures when

compared to the remaining four glasses. The last column of table 3 gives the temperatures calculated from the combined equation derived from the data

of all five glasses.

4.2. Viscosity Measurements Made at Participating Laboratories The results received from each laboratory are given in tables 4, 5A, 5B, 5C, and 6. Since the four

participating laboratories all used the rotating cylinder method at the higher temperatures these

results are given in table 4. Only Laboratory C

besides NBS made measurements at the lower temperatures, i.e., below the softening temperature. These data are given in tables 5A, 5B, 5C and 6. The data from each laboratory was treated in the

3
Table 4. High-temperature viscosities of Glass No. 71 7 from participating laboratories

I

ii

Rotating Cylinder

Laboratory B Laboratory C Laboratory D Laboratory E

LogioTJObs Temp, °C Logi, Temp, °C Logll Temp, °C

2.241 2.337

2.455 2.563

2.623 2.750

2.854

3.107 3.314

3.476

3.630

3.834

4.073 4.317

4.536

4.823

5.143

5.435

1375.0 1319.9

1293.5 1259.4

1221.4

1183.5

1144.4

1104.6

1068.6

1021.5 988.2

956.2

918.5

889.8

847.6

817.9

790.1

724.7

2.535 2.710

2.820

2.944

3.133 3.288

3.491 3.704

3.928

4.238

4.484

4.745

5.069

5.344 5.766

6.145

6.522

7.501

1521 2.10

1499 2.15

1479 2.20

1441 2.30

1406 2 .40 1377 2.50

1343 2 .60 1318 2.70

1291 2.80

1267 2.90

1243 3.00

1221 3.10

1197 3.20

1176 3.30

1154 3.40

1135 3.50

1117 3.60

1102 3.70

1088 3.80

1074 3.90

1060 4.00

1332 1250 1180

1107

1071 997

934

876

Table 5B. Log viscosities of SRM 717 by the beambending method (5 °C/min cooling rate)

Table 5A. Log viscosities of SRM 717 by the beambending method (5 °C/min heating rate)

Logi0 J?0bs Run 1 Run 2

13.805 13.580

13.410 13.220

13.033 12.828

12.631 12.452 12.238

12.033

11.812

11.742

13.677

13.500

13.220

13.045 12.892

12.702

12.491

12.283

Temp, °C

553 558

563 568

573 578

583 588

593 598

603

608

613

618

623

628

633 638

643 648

653

658

663 668

673

Logio»;obs —*

11 604

11 316

11 207

11 104

10 962

10 847

10 723

10 545

10 394

10 301

10 217

10 124

10 021

9 870

9 765

9 641

9 524

9 336

10.688

10.587

10.431 10.316

10.162 10.068 9.932 9.836

9.723 9.610

9.522

9.442 9.356

9.243

9.149

9.037

8.883

8.775

8.657

Temp, °C

<— Logi0r;obs —

>

Run 1 Run 2 Run 3 Run 4

557 11.669

552 11.874 11.852

547 12.107 12.079 11.939

542 12.312 12.253 12.164

537 12.509 12.471 12.401 532 12.693 12.632 12.547 12.583

527 12.870 12.848 12.754 12.769

522 13.045 13.025 12.931 12.926

517 13.220 13.161 13.114 13.114

512 13.389 13.334 13.294 13.290

507 13.496 13.490 13.430 13.455

502 13.634 13.606 13.628 13.623

497 13.841 13.782 13.846 13.788

Table 5C. Log viscosities of SRM 717 by the beambending method (equilibrium conditions)

Temp, °C LoglolObs

546.5 12.037 533.5 12.500

525.5 12.840 514.0 13.248 504.5 13.621 495.0 14.134

4
Table 6. Log viscosities of SRM 717 by the parallel- plate method (5 °C/min heating rate) Table 8. Comparison of logio viscosity versus tem- peratures data from each participating laboratory

Temp, °C Logio»/Obs

630 9 .447 640 9.241

650 9.013 660 8.764

670 8.545 680 9.310 690 8.064

700 7.847

710 7.652

720 7.483

730 7 .356 740 7.204

750 7.068

760 6.916

770 6.814

780 6 .703 790 6.594

800 6.446

810 6.299

820 6.233

830 6.146

840 5.961 850 5.859

Table 7. Fulcher equation constants from the data submitted by each laboratory

Laboratory Range, °C A B To er

A 550-1410 -1.562 4811.83 196.1 0.023 B 880-1475 -0.827 3603.35 305.6 .018 C 550-1375 -1.561 4814.88 192.6 .013 D 1060-1520 -0.612 3042.68 398.1 .011 E 875-1330 -1.528 4781.47 196.9 .017 Combined 550-1520 -1.546 4775.14 198.3 .029 A-E

same manner as that for Laboratory A. In the case of Laboratory C only equilibrium data were used to

solve for the best equation for that laboratory. Using the constants derived from each laboratory's

data, table 7, a comparison of temperatures for nominal values of logio viscosities are given in table 8. Calculations were made for each laboratory only in the temperature range in which the actual measure- ments were made. The data from all the laboratories was then combined and fitted to the Fulcher equation. This gave:

log10 tj = -1.546 + 4775.14/(T °C - 198.3) (2) with a standard error in log10 rj = 0.029. Using eq

(2), temperatures in the last column of table 8 were

calculated for the specific logio viscosities.

Logio

Viscosity

Poise'

2.00

2.10

2.25 2.50

2.75 3.00 3.50

4.00 4.50

5.00

5.50 6.00 6.50

7.00

7.50 8.00

8.50 9.00 9.50

10.00 10.50

11.00 11.50

12.00

Temperature, °C

Laboratories

1 158.4 1380.7 1312.0

1250.9

1146.7

1061.3 989.9 929.4

877.5

832.5 793.0

758.1

727.1 699.4

674.4

651.7

631.1

612.3

595.1 579.2

564.5

550.9

1476.5

1388.5

1312.8 1247.0

1138.3 1052.0 981.9 923.9

875.0

1378.2 1309.4

1248.2 1143.9 1058.4 986.9

926.4

874.4

829.4

789.9 755.0

723.9

696.1 671.1

648.5

627.9 609.0

591.8

575.9

561.2 547.6

1519.9

1461 .

1

1375.7

1303 . 1240.4 1138.0

1057.8

1381.0 1314.7

1252.9

1147.9

1061.9 990.1 929.4

877.3

Value from combined

equation

1545.1 1508.2

1456.4

1378.7 1310.0

1248.8

1144.7 1059.4 988.2 927.9

876.1

831.2 791.8

757.1

726.2 698.6

673.7

651.1 630.7

611.9

594.8

579.0 564.4

550.9 One poise is 1 g/cm s, which is equal to 0.1 kg/r

TEMPERATURE-"C X I0"2

Figure 2. Observed values of logw viscosity plotted against the function of temperature 4775.14/T°C-198.3 (1000-1520 °C).

5
TEMPERATURE-'CHO"*

Figure 3. Observed values of logio viscosity plotted against the Figure 4. Observed values of logio viscosity plotted against the function of temperature 4775.14/ T°C-19~8.3 (800-1050 °C). function of temperature 4775.14/T°C-198.3 (550-800 °C).

LOG,„ VISCOSITY - CALCULATED

PARTICIPATING LABORATORIES

o A-LAB » D-LAB

• B-LAB XE-LAB

A C-LAB

700 800 Figure 5. Differences in observed and calculated log\ 0 viscosities.

0 line represents the final equation, eq (2). The data from each laboratory has been plotted

against the temperature function of the final equation in figures 2, 3, and 4 between the values logio 2 and logio 12 viscosity. The differences between the observed and calculated logio viscosities frdm eq (2) have been plotted in figure 5 to indicate the magnitude of scatter. Most of the differences are within

the arbitrary limits of ±5 °C and ±10 percent vis- cosity except those at the very high temperatures, 1400 to 1525 °C. This ; departure of the observed

logio viscosities at the high temperatures from the

calculated values is partly due to the failure of the Fulchcr equation in fitting low-temperature (highviscosity) data [10].

The beam-bending data submitted by Laboratory C has been compared to the final equation (curve)

in figures 6 and 7. In these plots the dashed part of the curve is an extrapolation of the calculated curve (logio 2 to logio 12 viscosity). A comparison of the fiber elongation and beam bending data under

equilibrium conditions are shown in figure 8. Laboratory C also submitted viscosity data obtained by a new method, the parallel-plate viscometer, and this data is compared to the final curve in figure 9. The

agreement is very good especially in view of the fact that none of this data was used to calculate the curve.

6
Table 9. Softening, annealing, and strain points of Standard Glass No. 717

Temperature, °C

Laboratory A B C D E Average

Softening Point Annealing point

Strain Point

723 517 469

722 516

472

717 516 466

721 515 466

716

515

473

720 516

471

TEMPERATURE-T Figure 6. Beam-bending data (5 °C/min heating rate) compared

to the final equation, eq (2). Dashed line is extrapolation of final equation.

4.3. Softening, Annealing, and Strain Points The softening, annealing, and strain points were determined by all the participating laboratories and are given in table 9. The methods of test and

definitions of these points are given in the ASTM

Standards.

5. Summary

NBS has established a third Standard Reference

Material for the viscosity of glass: No. 717 (Borosilicate). Viscosity measurements have been made on this glass by five laboratories. The temperature range

covered was 495 to 1525 °C. The rotating cylinder,

fiber elongation, beam-bending, and parallel- late methods were used.

& 4775.14 T°C -198.3 -1.546-^/I*

500 540 TEMPERATURE-X FlGUBE 7. Beam-bending data (5 °C/min cooling rate) compared to the final equation, eq (2). Dashed line is extrapolation of final equation. 7
A viscosity temperature curve was determined from these measurements by fitting the data to the Fulcher equation by the method of least squares combined with the Gauss-Newton iterative method. The softening, annealing, and strain points of this glass have been determined by five participating

laboratories.

The authors wish to thank all the participating

laboratories for their cooperation in making viscosity measurements on this glass. They also acknowledge

the help received from Joseph H. Simmons for the computer calculations.

6. References

[1] Napolitano, A., and Hawkins, E. G., Viscosity of a stand- ard soda-lime-silica glass, J. Res. Nat. Bur. Stand.

(U.S.), 68A (Phys. & Chem.), No. 5, 439 (Sept.-Oct.

1964).

[2] Napolitano, A., and Hawkins, E. G., Viscosity of a

standard lead-silica glass, Nat. Bur. Stand. (U.S.)" Misc. Publ. 260-11, 1 (1966).

[3] Napolitano, A., Macedo, P. B., and Hawkins, E. G., A wide range (up to 1010 P) rotating cylinder viscometer, J. Res. Nat. Bur. Stand. (U.S.), 69A (Phys. &

Chem.), No. 5, 449 (Sept.-Oct. 1965).

[4] Hagy, H. E., Experimental evaluation of beam-bending method of determining glass viscosities in the range

108 to 1015 poises, J. Am. Ceram. Soc. 46, No. 2, 93

(1963).

[5] Fontana, E. H., A versatile parallel-plate viscometer for

glass viscosity measurements to 1000°C, Am. Ceram

Soc. Bull. 49, No. 6, 594 (1970).

[6] ASTM Standards, Softening Point of Glass ASTM Desig- nation C338-57 (Reapproved 68) Part 13 (1970).

[7] ASTM Standards, Annealing Point and Strain Point of

Glass, ASTM Designation C336-69 and ASTM Desig- nation C598-67T, Part 13 (1970).

[8] Fulcher, G. S., Analysis of recent measurements of vis- cosity of glass, J. Am. Ceram. Soc. 8, No. 6, 339 (1925);

8, No. 12, 789 (1925).

[9] Macedo,. P. B., Viscoelasticity of glasses, Mechanical and

Thermal Properties of Ceramics, Nat. Bur. Stand.

(U.S.), Spec. Publ. 303, 169 (1969).

[10] Macedo, P. B., and Napolitano, A., Inadequacies of vis- cosity theories for B203 , J. Chem. Phys. 49, No. 4, 1887 (1968).

* U.S. GOVERNMENT PRINTING OFFICE: 1971 O—402-008 8
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1 Bureau of Standards research and development in

j physics, mathematics, chemistry, and engineering.

I Comprehensive scientific papers give complete details

| of the work, including laboratory data, experimental

i procedures, and theoretical and mathematical analyI ses. Illustrated with photographs, drawings, and

charts.

j Published in three sections, available separately:

j • Physics and Chemistry

j Papers of interest primarily to scientists working in

! these fields. This section covers a broad range of

j physical and chemical research, with major emphasis

| on standards of physical measurement, fundamental

constants, and properties of matter. Issued six times

a year. Annual subscription: Domestic, $9.50; foreign, $11.75*. • Mathematical Sciences

! Studies and compilations designed mainly for the

j mathematician and theoretical physicist. Topics in mathematical statistics, theory of experiment design,

I numerical analysis, theoretical physics and chemistry, logical design and programming of computers and computer systems. Short numerical tables. Issued quarterly. Annual subscription: Domestic,

$5.00; foreign, $6.25*. • Engineering and Instrumentation

Reporting results of interest chiefly to the engineer and the applied scientist. This section includes many

of the new developments in instrumentation resulting from the Bureau's work in physical measurement,

data processing, and development of test methods.

It will also cover some of the work in acoustics, applied mechanics, building research, and cryogenic

engineering. Issued quarterly. Annual subscription: Domestic, $5.00; foreign, $6.25*. TECHNICAL NEWS BULLETIN

The best single source of information concerning the Bureau's research, developmental, cooperative and

publication activities, this monthly publication is designed for the industry-oriented individual whose

daily work involves intimate contact with science and

technology

for engineers, chemists, physicists, re- search managers, product-development managers, and company executives. Annual subscription: Domestic,

$3.00; foreign, $4.00*.

• Difference in price is due to extra cost of foreign mailing. Order NBS publications from:

Applied Mathematics Series. Mathematical tables, manuals, and studies. Building Science Series. Research results, test methods, and performance criteria of building materials, components, systems, and structures. Handbooks. Recommended codes of engineering and industrial practice (including safety codes) de- veloped in cooperation with interested industries, professional organizations, and regulatory bodies. Special Publications. Proceedings of NBS conferences, bibliographies, annual reports, wall charts, pamphlets, etc. Monographs. Major contributions to the technical

literature on various subjects related to the Bureau's

scientific and technical activities. National Standard Reference Data Series. NSRDS provides quantitive data on the physical and chemical properties of materials, compiled from

the world's literature and critically evaluated. Product Standards. Provide requirements for sizes, types, quality and methods for testing various industrial products. These standards are developed cooperatively with interested Government and industry groups and provide the basis for common understanding of product characteristics for both buyers and sellers. Their use is voluntary. Technical Notes. This series consists of communications and reports (covering both other agency and

NBS-sponsored work) of limited or transitory interest. Federal Information Processing Standards Publications. This series is the official publication within

the Federal Government for information on standards adopted and promulgated under the Public Law

89-306, and Bureau of the Budget Circular A-86

entitled, Standardization of Data Elements and Codes

in Data Systems.

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