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NAT'L INST. OF STAND & TECHi R IX

A111D5 3SMblb

NBS SPECIAL PUBLICATION 260-85

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

Standard Reference Materials:

A Look at Techniques for

the Dimensional Calibration of

Standard Microscopic Particles

-QC

100

.U57

#260-85

1983
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis lor equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities 2 — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering2 — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering2

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, M D, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
NBS

RESEARCH

INFORMATION CENTER Standard Reference Materials:

A Look at Techniques for the Dimensional

Calibration of Standard Microscopic Particles

Dennis A. Swyt

Mechanical Production Metrology Division

Center for Manufacturing Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued September 1983
Library of Congress Catalog Card Number: 83-600571

National Bureau of Standards Special Publication 260-85

Natl. Bur. Stand. (U.S.), Spec. Publ. 260-85, 150 pages (Sept. 1983)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1983

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

Price $5.50

(Add 25 percent for other than U.S. mailing)
PREFACE

Standard Reference Materials (SRM's) as defined by the

National Bureau of Standards are wel 1 -cha racteri zed materials

produced in quantity and certified for one or more physical

or chemical properties. They are used to assure the accuracy

and compatibility of measurements throughout the Nation.

SRM's are widely used as primary standards in many diverse

fields in science, industry, and technology, both within the

United States and throughout the world. They are also used

extensively in the fields of environmental and clinical analysis. In many applications, traceability of quality control

and measurement processes to the national measurement system

are carried out through the mechanism and use of SRM's. For

many of the Nation's scientists and technologists it is

therefore of more than passing interest to know the details

of the measurements made at NBS in arriving at the certified

values of the SRM's produced. An NBS series of papers, of

which this publication is a member, called the NBS Special

Publication - 260 Series , is reserved for this purpose.

This 260 Series is dedicated to the dissemination of

information on different phases of the preparation, measurement, certification and use of NBS-SRM's. In general, much

more detail will be found in these papers than is generally

allowed, or desirable, in scientific journal articles. This

enables the user to assess the validity and accuracy of the

measurement processes employed, to judge the statistical

analysis, and to learn details of techniques and methods

utilized for work entailing the greatest care and accuracy.

These papers also should provide sufficient additional information not found on the certificate so that new applications

in diverse fields not foreseen at the time the SRM was originally issued will be sought and found.

Inquiries concerning the technical content of this paper

should be directed to the author. Other questions concerned

with the availability, delivery, price, and so forth will

receive prompt attention from:

Office of Standard Reference Materials

National Bureau of Standards

Washington, D.C. 20234

Stanley D. Rasberry, Chief

Office of Standard Reference Materials
OTHER NBS PUBLICATIONS IN THIS SERIES

Catalog of NBS Standard Reference Materials (1981-83 edition). R. W. Seward, ed.. NBS

Spec. Publ. 260 (November 1981). Michaelis. R. E., and Wyman. L. L. Standard

Reference Materials: Preparation of White Cast

Iron Spectrochemical Standards. NBS Misc. Publ. 260-1 (June 1964). COM74- 1 1061 **

Michaelis, R. E., Wyman, L. L.. and Flitsch, R., Standard Reference Materials: Preparation of NBS Copper-Base Spectrochemical Standards. NBS Misc. Publ. 260-2 (October 1964). COM74-

1 1063**

Michaelis, R. E.. Yakowitz, H., and Moore, G. A., Standard Reference Materials: Metallographic

Characterization of an NBS Spectrometric LowAlloy Steel Standard. NBS Misc. Publ. 260-3 (October 1964). COM74-1 1060** Hague, J. L. Mears. T. W., and Michaelis, R. E., Standard Reference Materials: Sources of

Information, NBS Misc. Publ. 260-4 (February

1965). COM74-11059

Alvarez, R., and Flitsch R., Standard Reference

Materials: Accuracy of Solution X-Ray Spectrometric Analysis of Copper-Base Alloys. NBS

Misc. Publ. 260-5 (March 1965). PBI68068**

Shultz, J. L, Standard Reference Materials: Methods for the Chemical Analysis of White

Cast Iron Standards. NBS Misc. Publ. 260-6

(July 1975). COM74-1 1068**

Bell, R. K., Standard Reference Materials:

Methods for the Chemical Analysis of NBS

Copper-Base Spectrochemical Standards. NBS

Misc. Publ. 260-7 (October 1965). COM74-

1 1067** Richmond. M.S., Standard Reference Materials: Analysis of Uranium Concentrates at the

National Bureau of Standards. NBS Misc. Publ. 260-8 (December 1965). COM74- 1 1066** Anspach, S. C. Cavallo, L. M. Garfinkel. S. B. Hutchinson. J. M. R.. and Smith. C. N., Standard Reference Materials: Half Lives of Materials Used in the Preparation of Standard Reference Materials of Nineteen Radioactive Nuclides

Issued by the National Bureau of Standards NBS Misc. Publ. 260-9 (November 1965).

COM 74-1 1065**

Yakowitz, H., Vieth, D. L., Heinrich, K. F. J., and

Michaelis. R. E., Standard Reference Materials: Homogeneity Characterization on NBS Spectrometric Standards II: Cartridge Brass and LowAlloy Steel. NBS Misc. Publ. 260-10 (December

1965). COM 74- 1 1064** Napolitano. A., and Hawkins, E. G., Standard Reference Materials: Viscosity of Standard

Lead-Silica Glass, NBS Misc. Publ. 260-11 (November 1966). NBS Misc. Publ. 260-11** Yakowitz, H.. Vieth, D. L., and Michaelis, R. E., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards III: White Cast Iron and Stainless Steel Powder Compact, NBS Misc. Publ. 260-12

(September 1966). NBS Misc. Publ. 260-12** Spijkerman, J. L., Snediker, D. K., Ruegg, F. C,

and DeVoe, J. R.. Standard Reference Materials: Mossbauer Spectroscopy Standard for the Chemical Shift of Iron Compounds. NBS Misc. Publ. 260-13 (July 1967). NBS Misc. Publ.

260-13**

Menis, O., and Sterling, J. T., Standard Reference

Materials: Determination of Oxygen in Ferrous

Materials - SRM 1090, 1091, and 1092, NBS

Misc. Publ. 260-14 (September 1966). NBS Misc.

Publ. 260-14**

Passaglia, E., and Shouse, P. J. Standard Refer- ence Materials: Recommended Method of Use

of Standard Light-Sensitive Paper for Calibrat- ing Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Misc. Publ. 260-15 (June 1967). (Replaced by NBS Spec. Publ.

260-41.) Yakowitz, H., Michaelis. R. E., and Vieth, D. L.. Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards IV: Preparation and Microprobe Characterization of W-209? MO Alloy Fabricated by

Powder Metallurgical Methods, NBS Spec.

Publ. 260-16 (January 1969). COM74-1 1062** Catanzaro, E. J.. Champion, C. E., Garner, E. L.. Marinenko. G., Sappenfield. K. M.. and Shields, W. R. Standard Reference Materials: Boric

Acid: Isotopic and Assay Standard Reference

Materials. NBS Spec. Publ. 260-17 (February

1970). Out of Print

i v
Geller, S. B.. Mantek. P.A., and Cleveland, N. C. Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic Tape

(Computer Amplitude Reference) Using the Reference Tape Amplitude Measurement

"Process A, "NBS Spec. Publ. 260-18 (November

1969). (See NBS Spec. Publ. 260-29.) Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold (Certifica- tion of Standard Reference Material 745). NBS

Spec. Publ. 260-19 (January 1970). PBI9007I**

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressures of Cadmium and

Silver, NBS Spec. Publ. 260-21 (January 1971). COM74-1 1359** Yakowitz, H., Fiori, C. E., and Michaelis, R. E., Standard Reference Materials: Homogeneity

Characterization of Fe-3 Si Alloy, NBS Spec.

Publ. 260-22 (February 1971). COM74-1 1357** Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of a Standard

Borosilicate Glass, NBS Spec. Publ. 260-23 (December 1970). COM71-00I57**

Sappenfield. K. M., Marineko, G.. and Hague, J. L., Standard Reference Materials: Comparison

of Redox Standards, NBS Spec. Publ. 260-24 (January 1972). COM72-50058**

Hicho, G. E., Yakowit?, H., Rasberry, S. D., and

Michaelis, R. E., Standard Reference Materials: A Standard Reference Material Containing

Nominally Four Percent Austenite, NBS Spec. Publ. 260-25 (February 1971). COM74-1 1356** Martin, J. F., Standard Reference Materials:

National Bureau of Standards-US Steel Corportion Joint Program for Determining Oxygen and Nitrogen in Steel, NBS Spec. Publ. 260-26

(February 1971). 85 cents* PB 81 176620

Garner, E. L., Machlan, L. A., and Shields, W. R., Standard Reference Materials: Uranium

Isotopic Standard Reference Materials. NBS

Spec. Publ. 260-27 (April 1971). COM74-

11358**

Heinrich, K. F. J., Myklebust, R. L., Rasberry, S. D. . and Michaelis, R. E., Standard Reference Materials: Preparation and Evaluation of SRM's 481 and 482 Gold-Silver and GoldCopper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM71-50365**

Geller. S. B.. Standard Reference Materials: Cali- bration of NBS Secondary Standard MagneticTape (Computer Amplitude Reference) Using

the Reference Tape Amplitude Measurement

"Process A-Model 2," NBS Spec. Publ. 260-29

(June 1971). COM71-50282

Gorozhanina, R. S., Freedman. A. Y.. and

Shaievitch. A. B. (translated by M. C. Sclby). Standard Reference Materials: Standard

Samples Issued in the USSR (A Translation from the Russian). NBS Spec. Publ. 260-30 (June

1971). COM7I-50283**

Hust. J. G., and Sparks, L. L.. Standard Reference

Materials: Thermal Conductivity of Electrolytic Iron SRM 734 from 4 to 300 K. NBS Spec. Publ. 260-31 (November 1971). COM7I-50563**

Mavrodineanu. R.. and Lazar, J. W., Standard

Reference Materials: Standard Quartz Cuvettes,

for High Accuracy Spectrophotometry. NBS

Spec. Publ. 260-32 (December 1973). 55 cents* SN003-003-OI2I3-I Wagner. H. L., Standard Reference Materials: Comparison of Original and Supplemental

SRM 705, Narrow Molecular Weight Distri- bution Polystyrene. NBS Spec. Publ. 260-33 (May 1972). COM72-50526**

Sparks, L. L., and Hust, J. G., Standard Reference

Materials: Thermoelectric Voltage, NBS Spec.

Publ. 260-34. (April 1972). COM72-5037 1 ** Sparks. L. L., and Hust, J. G., Standard Refer- ence Materials: Thermal Conductivity of

Austenitic Stainless Steel. SRM 735 from 5 to 280 K, NBS Spec. Publ. 260-35 (April 1972.) 35 cents* COM72-50368**

Cali, J. P., Mandel, J., Moore, L. J., and Young, D.

S.. Standard Reference Materials: A Referee Method for the Determination of Calcium in Serum, NBS SRM 915, NBS Spec. Publ. 260-36 (May 1972). COM72-50527**

Shultz, J. I. Bell.. R. K. Rains, T. C, and Menis,

O., Standard Reference Materials: Methods of Analysis of NBS Clay Standards, NBS Spec. Publ. 260-37 (June 1972). COM72-50692**

Richmond, J. C. and Hsia. J. J.. Standard Refer- ence Materials: Preparation and Calibration of Standards of Spectral Specular Reflectance,

NBS Spec. Publ. 260-38 (May 1972). COM72-

50528**

Clark, A. F.. Denson. V.A.. Hust, J. G., and

Powell, R. L., Standard Reference Materials The Eddy Current Decay Method for Resistivity Characterization of High-Purity Metals, NBS

Spec. Publ. 260-39 (May 1972). COM72-50529**

V
McAdie. H. C. Garn, P.D., and Menis, O., Standard Reference Materials: Selection of Thermal

Analysis Temperature Standards Through a Cooperative Study (SRM 758, 759, 760). NBS

Spec. Publ. 260-40 (August 1972.) COM72-

50776** Wood. L. A., and Shouse, P. J.. Standard

Reference Materials: Use of Standard LightSensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for Colorfastness to

Light. NBS Spec. Publ. 260-41 (August 1972) COM72-50775**

Wagner, H. L. and Verdier, P. H., eds.. Standard

Reference Materials: The Characterization of Linear Polyethylene, SRM 1475. NBS Spec. Publ. 260-42 (September 1972). COM72-

50944**

Yakowitz, H.. Ruff, A. W., and Michaelis, R. E., Standard Reference Materials: Preparation and

Homogeneity Characterization of an Austenitic Iron-Chromium-Nickel Alloy. NBS Spec. Publ. 260-43 (November 1972). COM73-50760**

Schooley. J. F., Soulen, R. J., Jr.. and Evans, G. A.,

Jr.. Standard Reference Materials: Preparation

and Use of Superconductive Fixed Point

Devices. SRM 767, NBS Spec. Publ. 260-44 (December 1972). COM73-50037**

Greifer. B.. Maienthal, E. J. Rains, T. C, and

Rasberry, S. D., Standard Reference Materials: Powdered Lead-Based Paint. SRM 1579, NBS

Spec. Pubi. 260-45 (March 1973). COM73-

50226**

Hust, J. G.. and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and

Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 k, NBS Spec. Publ. 260-46 (March 1975). SN003-003-0I278-5

Hust, J. G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797, and Austenitic Stainless Steel, SRM 798, from 5 to 280 K, NBS Spec. Publ. 260-47 (February

1974). COM74-50I76**

Mangum, B. W.. and Wise, J. A., Standard Refer- ence Materials: Description and Use of Precision Thermometers for the Clinical Laboratory,

SRM 933 and SRM 934, NBS Spec. Publ. 260-48 (May 1974). 60 cents* SN003-003-0I278-5

Carpenter, B. S., and Reimer, G. M., Standard Reference Materials Calibrated Glass Standards for Fission Track Use, NBS Spec. Publ. 260-49 (November 1974). COM74-51I85

Hust. J. G., and Giarratano, P. J.. Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRM's 734 and 797 from 4 to 1000 K, NBS Spec. Publ. 260-50 (June 1975). $1.00* SN003-003-0 1425-7 Mavrodineanu. R.. and Baldwin, J. R., Standard

Reference Materials: Glass Filters As a Standard Reference Material for Spectrophotometry;

Selection; Preparation; Certification; Use-SRM

930, NBS Spec. Publ. 260-51 (November 1975). $1.90* SN003-003-0I481-8

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials 730 and 799. from 4 to 3000 K. NBS Spec. Publ. 260-52 (September 1975). $1.05* SN003-003-

01464-8 Durst. R. A., Standard Reference Materials: Standardization of pH Measurements, NBS

Spec. Publ. 260-53 (December 1975, Revised). $1.05 SN003-003-0I551-2

Burke, R. W., and Mavrodineanu, R. Standard

Reference Materials: Certification and Use of Acidic Potassium Dichromate Solutions as an

Ultraviolet Absorbance Standard. NBS Spec. Publ. 260-54 (August 1977). $3.00* SN003-003-

01828-7

Ditmars, D. A., Cezairliyan, A.. Ishihara, S., and

Douglas. T. B., Standard Reference Materials: Enthalpy and Heat Capacity; Molybdenum

SRM 781, from 273 to 2800 K, NBS Spec. Publ. 260-55 (September 1977). $2.20* SN003-003-

01836-8

Powell. R. L.. Sparks. L. L., and Hust. J. G.. Standard Reference Materials: Standard

Thermocouple Materials. Pt.67: SRM 1967, NBS

Spec. Publ. 260-56 (February 1978). $2.20* SN003-003-0 18864

Cali. J. P. and Plebanski, T.. Guide to United

States Reference Materials. NBS Spec. Publ. 260-57 (February 1978). $2.20* PB 277173

Barnes, J. D.. and Martin, G. M.. Standard Refer- ence Materials: Polyester Film for Oxygen Gas

Transmission Measurements SRM 1470. NBS

Spec. Publ. 260-58 (June 1979) $2.00* SN003-

003-02077 Chang, T., and Kahn, A. H. Standard Reference

Materials: Electron Paramagnetic Resonance

Intensity Standard; SRM 2601. NBS Spec. Publ. 260-59 (August 1978) $2.30* SN003-

003-01975-5

vi
Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., and Moody, J. R., Standard Refer- ence Materials: A Reference Method for the Determination of Sodium in Serum, NBS Spec.

Publ. 260-60 (August 1978). $3.00* SN003-003

01978-0

Verdier, P. H.. and Wagner. H. L., Standard Refer- ence Materials: The Characterization of Linear Polyethylene (SRM 1482, 1483, 1484). NBS

Spec. Publ. 260-61 (December 1978). $1.70* SN003-003-02006-1

Soulen, R. J., and Dove, R. B., Standard Reference

Materials: Temperature Reference Standard

for Use Below 0.5 K (SRM 768). NBS Spec.

Publ. 260-62 (April 1979). $2.30* SN003-003-

02047-8 Velapoldi, R. A.. Paule, R. C, Schaffer. R. Mandel, J.. Machlan, L. A., and Gramlich, J. W., Standard Reference Materials: A Reference Method for the Determination of Potassium in Serum. NBS Spec. Publ. 260-63 (May 1979). $3.75* SN003-003-02068

Velapoldi, R. A., and Mielenz, K. D., Standard

Reference Materials: A Fluorescence Standard

Reference Material Quinine Sulfate Dihydrate

(SRM 936), NBS Spec. Publ. 260-64 (January

1980). $4.25* SN003-003-02 148-2 Marinenko. R. B.. Heinrich, K. F. J., and Ruegg,

F. C, Standard Reference Materials: Micro- Homogeneity Studies of NBS Standard Reference

Materials. NBS Research Materials, and Other Related Samples. NBS Spec. Publ. 260-65

(September 1979). $3.50* SN003-003-021 14-1 Venable. W. H., Jr.. and Eckerle. K. L.. Standard

Reference Materials: Didymium Glass Filters for Calibrating the Wavelength Scale of Spectrophotometers (SRM 2009. 2010. 2013). NBS Spec.

Publ. 260-66 (October 1979). $3.50* SN003-003-

02127-0

Velapoldi, R. A., Paule. R. C, Schaffer, R., Mandel.

J.. Murphy, T. J., and Gramlich, J. W., Standard

Reference Materials: A Reference Method for the Determination of Chloride in Serum. NBS Spec.

Publ. 260-67 (November 1979). $3.75* SN003-

003-02136-9 Mavrodineanu. R. and Baldwin. J. R., Standard

Reference Materials: Metal-On-Quartz Filters as a Standard Reference Material for Spectrophotometry-SRM 2031. NBS Spec. Publ. 260-68

(April 1980). $4.25* SN003-003-02 167-9

Velapoldi. R. A., Paule, R. C. Schaffer. R., Mandel, J., Machlan, L. A., Garner, E. L., and

Rains, T. C Standard Reference Materials: A

Reference Method for the Determination of Lithium in Serum, NBS Spec. Publ. 260-69 (July)

1980). $4.25* SN003-003-022I4-4 Marinenko, R. B., Biancaniello, F., Boyer, P. A., Ruff, A. W., DeRobertis, L., Standard Reference

Materials: Preparation and Characterization of an Iron-Chromium-Nickel Alloy for Microanalysis, NBS Spec. Publ. 260-70 (May 1981). $2.50* SN003-003-02328-1

Seward, R. W., and Mavrodineanu, R., Standard

Reference Materials: Summary of the Clinical Laboratory Standards Issued by the National Bureau of Standards, NBS Spec. Publ. 260-71 (November 1981). $6.50* SN003-003-0238 1-7 Reeder, D.J., Coxon, B., Enagonio, D., Christensen,

R. O. Schaffer, R., Howell, B. F., Paule, R. C,

Mandel, J., Standard Reference Materials: SRM

900, Antiepilepsy Drug Level Assay Standard,

NBS Spec. Publ. 260-72 (June 1981). $4.25* SN003-003-02329-9

Interrante, C. G., and Hicho. G. E., Standard Refer- ence Materials: A Standard Reference Material Containing Nominally Fifteen Percent Austenite (SRM 486), NBS Spec. Publ. 260-73 (January

1982). $2.75* SN003-003-02386-8 Marinenko, R. B., Standard Reference Materials: Preparation and Characterization of K-411 and K-414 Mineral Glasses for Microanalysis: SRM

470. NBS Spec. Publ. 260-74 (April 1982). $3.50 SN003-003-023-95-7

Weidner, V. R.. Hsia. J. J., Standard Reference

Materials: Preparation and Calibration of First Surface Aluminum Mirror Specular Reflectance Standards (SRM 2003a). NBS Spec. Publ. 260-75 (May 1982). $3.75 SN003-003-023-99-0

Hicho. G. E. and Eaton, E. E., Standard Reference Materials: A Standard Reference Material

Containing Nominally Five Percent Austenite (SRM 485a), NBS Spec. Publ. 260-76 (August

1982). $3.50 SN003-003-024-33-3 Furukawa. G. T.. Riddle. J. L.. Bigge. W. G.. and

Pfieffer. E. R.. Standard Reference Materials: Application of Some Metal SRM's as Thermometric Fixed Points. NBS Spec. Publ. 260-77 (August 1982). $6.00 SN003-003-024-34-

1

vii
Hicho. G. E. and Eaton. E. E.. Standard Reference

Materials: Standard Reference Material Containing Nominally Thirty Percent Austenite (SRM

487). NBS Spec. Publ. 260-78 (September 1982). $3.75 SN0O3-O03-O24-35-O Richmond. J. C. Hsia. J. J.. Weidner. V. R.. and

Wilmering. D. B . Standard Reference Materials: Second Surface Mirror Standards of Specular

Spectral Reflectance (SRM's 2023. 2024. 2025). NBS Spec. Publ. 260-79 (October 1982). $4.50 SN003-003-024-47-3

Schaffer. R.. Mandel, J., Sun. T., Cohen, A., and

Hertz. H. S., Standard Reference Materials: Evaluation by an ID/ MS Method of the AACC

Reference Method for Serum Glucose. NBS

Spec. Publ. 260-80 (October 1982). $4.75SN003-

003-024-43-

1

Burke. R. W., Mavrodineanu, R. (NBS retired). Standard Reference Materials: Accuracy in Analytical Spectrophotometry. NBS Spec. Publ. 260-81 (April 1983). $6.00 SN003-003-024-84-8

Weidner. V. R., Standard Reference Materials: White Opal Glass Diffuse Spectral Reflectance Standards for the Visible Spectrum (SRM's 2015 and 2016). NBS Spec. Publ. 260-82 (April 1983). $3.75 SN-003-003-024-89-9

Bowers,. G. N., Jr., Alvarez, R.. Cali, J. P. (NBS

retired). Eberhardt, K. R . Reeder. D. J., Schaffer. R.. Uriano, G. A.. Standard Reference

Materials: The Measurement of the Catalytic

(Activity) Concentration of Seven Enzymes in NBS Human Serum SRM 909. NBS Spec.

Publ. 260-83 (June 1983). $4.50 SN003-003-024-

99-6

Gills. T. E., Seward. R. W.. Collins, R. J., and

Webster, W. C, Standard Reference Materials: Sampling, Materials Handling. Processing, and Packaging of NBS Sulfur in Coal Standard

Reference Materials, 2682, 2683. 2684, and 2685. NBS Spec. Publ. 260-84 (In Press). Swyt, D. A., Standard Reference Materials: A Look

at Techniques for the Dimensional Calibration of Standard Microscopic Particles, NBS Spec. Publ. 260-85 (In Press).

* Send order with remittance to Superintendent

of Documents. US Government Printing Office Washington. DC 20402. Remittance from

foreign countries should include an additional one-fourth of the purchase price for postage. ** May be ordered from: National Technical Information Services (NT1S). Springfield

Virginia 22151.
CONTENTS

Page

Executive Summary x

1. INTRODUCTION 2

A. Sample of Users' Needs 2

B. Current Techniques 3

1 .B.I. Available Instrumentation: Reviews 3 l.B.2. Documentary Standards 3 1. B 3. Standard Reference Particles 3

2. SUMMARY OVERVIEW OF ELEMENTS OF PARTICLE SIZE MEASUREMENT SYSTEMS . 8

A. The Object: States of Matter , 8

B. The Measuring Instruments 8

2. B.I. Size-Dependent Phenomena 8

2.B.2. Number of Particles Involved , 12 2.B.3. Separation of Particles by Size 12 2.B.4. Types of Dimensional Calibration ..... 12

C. Single Number Index to Characterize Particle Dimensions 18

2.C1. Characterizing a Single Particle 18

2. C.2. Giving an Average Size to a Group 20

3. CANDIDATE INSTRUMENTS FOR STANDARDS CALIBRATION .... 25

A. Needs of Calibration Scheme 25

B. Interrelationship of Three Candidate Measurement Methods . 25

3. B.I. Electron Microscopy

.

25 3.B.2. Light- Scattering 28

3. B.3. Automatic Counting (and Sizing) of Particles 33

4. INTERCOMPARISON OF MEASUREMENTS 38

A. Comparison of Latex Particle Measurements ........ 38

4. A.I. Specific Results Compared 38

4. A. 2. Generalization from Comparisons 70

5. REPORT CONCLUSION 85

6. BIBLIOGRAPHY 86

7. APPENDICES 99

A. Identified Domestic Suppliers of Standard Spherical

Particles or Test Dusts 99

B. Some International Suppliers of Particle-Size Related

Equipment 100

C. Documentary Standards Related to Microscopic Particle

Size Measurement 106

D. Literature Sources Consulted . 110

E. University and Industry People Contacted 112

F. NBS Certificate of Calibration for Glass Spheres SRM 1003,

1004, 1017a, 1018a; Scanning Electron Microscope Magnification

Standard (A Stage Micrometer Scale), SRM 484a 114

G. Tolerances Attached to the Average Quoted in Certain Tables 135

ix
Executive Summary

The purpose of this report is to examine the metrological capabilities of various

generic techniques suitable for use at NBS for the dimensional calibration of future NBS

particle size Standard Reference Materials (SRM's). At present, within the overall range

of sizes from 100 pm to 0.1 ym, some sized glass beads, spherical polymers, pollens, and test dusts are commercially available as reference materials. Currently, NBS provides

as SRMs only some wide-size-distribution glass beads. The intent is to develop other

particle-size SRMs: initially, narrow-distribution spherical polymers and, finally,

stable particulate matter of arbitrary shape and size distributions.

At the present level of development of calibration technology, the spherical polymers

are most suitable for an initial SRM. They are highly spherical, and have narrow size

distributions, thus providing for minimal ambiguity in measurements and maximal separation

of object and instrument variables. Batch-manufactured spherical polymers range in size

from less than 80 nm to over 100 ym with size distributions characterized by standard

deviations which range in a complex manner from about 5 nm for the smallest particles to 1-10 pm for the largest.

The report explicitly looks at various size-dependent phenomena which are the basis

for measurement techniques. It examines the way an individual particle is given one characteristic dimension, and how a collection of particles is given an average dimension.

Of the variety of techniques examined, three generic ones have been singled out from

those with individual characteristics which contribute to a comprehensive calibration

approach.

Microscopy which gives direct-imaging includes both optical which is limited by depth

of focus and electron which has high resolution and great depth of focus. Electron microscopy can provide direct-imaging, shape-verifying definitive measurements of limited numbers

of particles in vacuo . For polystyrene, a glassy polymer, there is evidence that the

required evacuation and electron-irradiation can be used without producing significant

dimensional changes. Transmission electron microscope measurements on polymer spheres by

the manufacturer over nearly three decades show consistency at 5 to 10 nm level with some indication of a systematic difference of 15 nm from an average of light-scatter and other

electron microscopy values.

Light-scattering techniques vary considerably in detail but generally are one of two

fundamentally different types: the first determines size from the intensity characteristics

of scattered light with analysis based on Mie calculations for scattering of a plane wave from a uniform dielectric sphere; the second determines size from the frequency characteristics of scattered light with analysis based on hydrodynamic calculations for objects

moving in fluids. The former, angular-intensity type, is of specific interest as a means

to obtain first-principle measurements potentially accurate at the 1% level on highlyspherical, narrow-distribution particles. The calculations assume particles are spheres

with a known index of refraction. Briefly noted in the report are other light-scattering

techniques with demonstrated capability for calibration quality particle size measurements

such as Rayleigh spectrometry, laser Doppler, and single-particle levitation; from among

the suitable techniques, the angular-intensity one has been chosed for initial calibrations

and for description here for reasons of directness in implementation, use, and interpretation.

Automatic liquid-borne particle counters measure some characteristic dimension of individual particles passing sequentially past a detector. There are two fundamentally different types: (1) the electri cal -resisti vity type measures the volume of electrolyte

displaced by a particle; and (2) the optical type which can be of two kinds: (a) one measures a projected shadow area; and (b) the other measures a Fraunhofer-dif fraction

pattern dimension. The optical types measure dimensions down to about 2 pm while the

electri cal -resisti vity types measure down to about 0.5 pm. All three devices can give

explicit histograms of size distributions but are comparators which require particles of

known size for calibration. Reproducibility of comparisons of mean diameters are of the

order of 1% to 3%.

Within the body and seven appendices, this report contains 50 tables of data, 250

x
literature references, and lists of 10 domestic commercial suppliers of sized particles,

30 principal and 40 secondary documentary standards on particles, 22 industry and university

contacts, and 125 domestic and foreign suppliers of particle-sizing equipment.

The report concludes that the definitive calibration of narrow-distribution polymer

spheres, a prerequisite first step toward size-calibration of irregularly-shaped matter,

can be obtained by a three-element, self-consistent approach involving the three techniques

named: electron microscopy to provide direct-view shape-verification and direct measurement of a limited sample of particles in va cuo; liquid-borne counting to provide an explicit

histogram verification of the broad size distribution in a sample liquid; and angularintensity light scattering to provide a nondestructive mean-size measurement of the original

population in the delivery vial. Under these conditions, an overall uncertainty in calibration of 0.005 ym or 1%, whichever is greater, is anticipated as achievable.

xi
List of Tables

Table No. Page No.

1. Examples of Commercial Sized Standard Particles . 6

2. NBS Standard Reference Materials Related to Particle Sizing 7

3. Some Definitions of Particle Size 19

4. Shape Factors and Shape Coefficients 21

5. Expressions for Various Mean Diameters 22

6. Various Techniques: Dow Nominal 2.956 pm Latex 39

7. Various Techniques: Dow Nominal 2.682 Pm Latex ...... 40

8. Various Techniques: Dow Nominal 1.192 Pm Latex 41

9. Various Techniques: Dow Nominal 0.796 Urn Latex 42

10. Various Techniques: Dow Nominal 0.264 pm Latex , 43

11. Various Techniques: Dow Nominal 0.088 pm Latex 44

12. Various Techniques: Eleven Other Dow Latexes 46

13. Resistance Counter I-vs-EM: Six Standard Latexes 47

14. Resistance Counter 1 1 I-vs-EM: Two PVC Latexes 48

15. Resistance Counter II-vs-EM: Six Standard Latexes 49

16. Resistance Counter I-vs-II: Four Standard Latexes 50

17. Resistance Counter Round-Robin: Three Devices, One Latex 51

18. Resistance Counter-vs-Optical Microscope: Four DVB . . 52

19. Visual Eyepiece, Array, SEM: Four DVB Latexes 53

20. Filar-Eyepiece Microscope-vs-EM: Seven Dow Latexes 54

21. Optical Array-vs-EM: Six PVC Latexes 55

22. EM of Shadow-vs-Particle Images: Five PVC Latexes 56

23. EM of Shadow-vs-Particle Images: Four DVB Latexes 57

24. Dark-Field Optical Microscope-vs-EM: Four PS Latexes 59

25. Disc Centrifuge-vs-EM: Six PVC Latexes 60

26. Fractional Creami ng-vs-EM: Four PVC Latexes 61

27. Flow Microscopy-vs-EM: Nine Dow Latexes 62

28. HOTS-vs-EM: Six PVC Latexes 63

29. HOTS-vs-EM: Six Dow Latexes 64

30. Light Scattering by Five Techniques and Same Workers: Eight Dow Latexes. ... 65

31. Rayleigh Li newi dth-vs-EM: Four Dow Latexes 66

xi i
32. Average of Light Scattering: 0.245 Dow Latex 67

33. Average of Light Scattering: 1.192 urn Dow Latex. 68

34. Average of Light Scattering: 2.956 urn Dow Latex. 69

35. Electron Microscopy (EM) of Dow-vs-Others: Twenty-One Latexes. 71

36. EM of Dow-vs-Davi dson, et al.: Nine Dow Latexes 72

37. Size Distributions of Nine Dow Latexes by Two EM Groups 73

38. Mean size of Nine Dow Latexes by Two EM Groups 74

39. EM of Dow-vs-Dobbi ns, et al.: Six Dow Latexes 75

40. EM of Dow-vs-Davi dson, Haller: Four Dow Latexes 76

41. EM Plate Image Size Measurement: Effect 77

42. EM Plate Image Size Measurement: Five Latexes 78

43. EM Dow-vs-EM Average of Others: Twenty-One Latexes 79

44. EM Dow-vs-LS Average: Fourteen Latexes 80

45. EM Other-vs-LS Average: Nine Latexes 81

46. Shadow EM-vs-Average EM and LS: Six Dow Latexes 83

47. EM Dow-vs-Combi ned LS-EM: Twenty-Four Latexes 84

List of Figures

Figure No. Page No.

1. The Width of the Particle Size Distribution (a) as a Function of

Mean Particle Diameter of the Distribution for Batch Grown Polymer

Spheres Produced by One Manufacturer 5

2. Alternative Ways of Measuring the Size of an Image 36

xi i i

A LOOK AT TECHNIQUES FOR THE DIMENSIONAL CALIBRATION

OF STANDARD MICROSCOPIC PARTICLES

Dennis A. Swyt

Mechanical Production Metrology Division

Center for Manufacturing Engineering

National Bureau of Standards

Washington, DC 20234

This report surveys generic techniques for the dimensional calibration of microscopic

particle size standards. It notes some user needs and available instrumentation, documentary

standards, and commercial, sized particles. It discusses the elements of the measurement

process, including the particle and medium, size-dependent phenomena, shape factors, singlenumber indices of average size, and means of length calibration. The report examines

systematic differences among published results of electron microscopy, liqht scattering,

particle counter, and other measurements on widely-used commercial polymer spheres. It concludes that the definitive calibration of narrow-distribution polymer spheres, a prerequisite first step toward cal i bration of irregularly-shaped matter, would best involve

a three-element approach involving the techniques named.

Key Words: Dimensional measurement; electron microscopy, flow-through particle counters;

latex spheres; light scatter; micrometrol ogy ; microscopic spheres; Mie scattering; particle

standards; optical microscopy; particle size calibration; polymer spheres; scanning electron

microscope; transmission electron microscope.

1
1. INTRODUCTION

Particle-size measurement is an inclusive term that encompasses a diversity of

measurements by a spectrum of techniques on a host of different particulate substances. To calibrate particle-size measuring devices, particles of "certified size" are available

from commercial sources. At the same time, requests for NBS-certif ied, particle-size

Standard Reference Materials (SRM's) have been insistent and recurrent (for example, Refs.

CI , K5, WO).

As part of an investigative-developmental project at NBS on such SRMs, this report has

been prepared. Its purpose is to look at those techniques which can potentially be used as

(1) reference methods for the definitive, primary dimensional -cal ibration of particle

standards and (2) comparison methods for convenient transfer calibration from the reference

method to bulk calibration method.

Guided by experience at NBS and the preponderance of work of a more fundamental nature

reported in the scientific literature, this report has of necessity focussed on the basic

techniques of electron microscopy and light scattering and the comparison techniques of

automatic particle counting. An underlying premise of the report is that in order to understand and manage the basic measurement techniques, the object-to-be-measured should be

as simple and lacking ambiguity as possible. Hence, because of their unique metrological

properties, latex spheres play a central role in the examination of individual techniques

and their i ntercomparisons.

In its structure, this report follows the topical outline given in the Table of

Contents. Part I is introductory background on particles and their size-measurement as generally practiced. Part II outlines some of the basic metrological factors of measurement

systems to be taken into explicit account. In Part III, candidate instruments are looked

at individually, and in Part IV their measurement results are intercompared. Part V summarizes the general conclusions of the report, and Part VI lists references. Part VII includes appendices on domestic suppliers of particle reference materials, equipment

suppliers, documentary standards, bibliographic sources used, and contacts at universities

and in industry. Also included is a note on how some quoted statistical uncertainties are computed.

A. Sample of Users' Needs

A vast spectrum of end-products, by-products, and waste-products or contaminants of

modern industrial technology are microscopic particles which require dimensional measurement. As end-products, particles can be constituents of anything from plastics to cement

to metal ores to photographic emulsions. As end products or by-products particles can be

the result of manufacturing processes as varied as milling, mining, refining, grinding,

spraying, or chemical precipitation. As contaminants, particles can occur in drugs and

intravenous fluids for medical use, in lithographic chemicals for microelectronics manufacture, in hydraulic fluids for aerospace systems, and in the atmospheres industrial

workers and the general population breathe.

Particles which require dimensional measurement vary greatly in range of size, chemical

composition, and uniformity of size and shape. What various workers refer to as particles

range in characteristic dimension over as many as six orders of magnitude: from 10,000 to 0.01 micrometers ( um) [A14]. They vary in physical make-up from complex-but-stable,

naturally-occurring minerals (asbestos) or biological material (cotton dust), to mixed and

dynamically changing smoke and combustion products, to pure and stable synthesized materials

such as polymers. Individual particles vary in shape from jagged irregular road dusts, to fibrous (actually rolled-plates) asbestos, to disc-like blood platelets, to spheroidal

bacteria or pollens, to spherical polymer resins. Populations of particles range from

Materials and instruments are identified in this paper in order to adequately specify the

experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or instrumentation is the best available for the purpose.

2
heterogenous mixtures of irregularly shaped debris of widely different average size to collections of nearly perfect spheres of nearly identical sizes.

B. Current Techniques

l.B.l. Available Instrumentation: Reviews

The instrumentation developed to dimensional ly measure these diverse particles - apart from the equipment to collect and separate them - is as varied as the particles

themselves. The instruments vary in fundamental principle of operation, the size-dependent

attribute of the particle measured, range of sizes measurable, resolution, precision and

accuracy. Physical phenomena used as bases for dimensional measurements include: direct

imaging by ligiit and electron optics; light scattering of a multitude of types; X ray, Y ray, ultrasonic and acoustic attenuation; pressure, flow, magnetic, electrostatic, or resistivity variations; and settling, sieving, separation, diffusion, and other properties.

Over the last few years, reviews of particle-size measurement instrumentation have

been published in archival journals, trade magazines, monographs, and engineering text

books. For example:

A comprehensive survey of instrumentation was reported by Davies in 1974-75 [Dll, D12,

D13]. It was further updated and revised in 1978 [D8]. A popularized view of some commercial

instruments and related techniques was given by Austin [A14] and Carver [CI]. Stockham and

Fochtman [S10] discussed, among other aspects of particle size analysis, a range of

instruments and techniques [S10]. Collins, et al . , [C21] reviewed the common methods of

measurement while other reviewers such as Kratohvil [K13] considered a general technique,

such as 1 ight scattering , as it applied to particle-size measurement. Others, who will be

referenced later in this report, compared specific techniques with each other. Finally,

Allen [A3], in his textbook on particle-size measurement, provided a detailed and referenced

discussion of phenomena, instruments, and techniques. Taken with the articles of Davies,

Allen's compilation of commercial suppliers of instruments [Appendix B] provides a comprehensive list of available equipment and their sources.

I.B.2. Documentary Standards

Faced with a broad array of instruments and techniques which (after measuring different

dimensional attributes of collections of irregularly shaped and compositional ly varied

particles) yield numbers called "particle size", industry takes the normal recourse and

seeks suitable documentary and physical standards. Documentary standards are written

descriptions of methods, procedures or specifications, for example, how to specify or test

the performance of an instrument. Physical standards are artifacts, e.g., a particle of

known size, by which one calibrates or tests an instrument or process.

The American National Standards Institute (ANSI) and the American Society for Testing

and Materials (ASTM) as well as the National Fluid Power Association (NFPA) and the Society

of Automotive Engineers (SAE) have documentary standards relating to particle size

measurement. Appendix C lists seventeen ANSI, thirteen ASTM (existing or in draft), and

three NFPA standards, as well as an SAE and an ISO (International Organization for

Standardization) standard. It also gives the identification numbers of thirty-seven other

ASTM standards, twenty-two of which are on material characterization and fifteen on system

characterization.

I.B.3. Standard Reference Particles

Some of the documentary standards refer to physical reference materials; that is,

sized, standard, and uniform particles or test dusts. Ten organizations have been identified

as commercial domestic sources of sized particles [Appendix A]. These include: particle

supply firms who make and/or handle standard reference particles as their primary business;

manufacturers of particle-measuring instruments who make and/or supply reference particles

for instrument calibration; and manufacturers of other products who produce sized-standard

reference particles or dusts as a sideline.

3
There are four major types of commercially available, sized-standard reference particles suitable for calibration of particle-size measuring instruments. These include:

test dusts; naturally occurring, spherical pollens; uniform glass beads or microspheres;

and various polymer "latex" spheres. Examples of the characteristic dimensions of these

various types of reference materials are given in Table 1. Commercial test dust is a collection of coarse, irregularly shaped particles primarily used to simulate the matter

removed by filtration from hydraulic systems. Pollen, glass, and latex-type polymer particles are used as spherical particles to calibrate, for example, various flow-through

particle counters, light scattering, and other particle-sizing instruments. Latex-type

polymer spheres of small diameters are used as electron-microscope calibration standards.

Latex-like polymers and glass beads are most widely used as sized, spherical calibration

reference materials, and each has physical properties which are advantageous in some applications, and drawbacks in others. The following sketches of their properties are drawn from a technical article by NBS workers on glass beads for calibrations [H18], glass

bead and latex supplier's literature [Appendix C], and undocumented accounts by NBS workers

and particle manufacturers.

Glass beads have the following properties: appear fairly spherical in direct observation; are transparent with a high index of refraction; are rigid solids without cleavage

planes; are somewhat surface-tempered; and have impact strength. In addition, the glass

beads can have voids and/or an onion-like layer structure, can shatter or fragment, can agglomerate in the presence of atmospheric moisture, have a broad distribution of sizes

within a sample and mean sizes for the population typically which range from about 5 ym

(or as low as 1 ym) to 100 ym.

Latex-like spheres (polystyrene, polyvinyl toluene, etc.) appear highly spherical,

have low-or-moderate specific gravity, are translucent-to-opaque, are glassy-to plastic

solids, and can distort in shape when dried or irradiated. Further, the latex-like spheres

can have dimensions and properties dependent on surface-active and dispersal agents, cannot be airborne above about 3 ym in size, and can agglomerate in pairs, triads, or clumps.

Mass-produced, batch-grown spheres can have a single, relatively narrow distribution of

sizes while limited-production, droplet-grown spheres can have a very narrow "main-mode"

size with "satellite modes," one below and one above the main-mode. Latexes cover the

range 0.01 to 100 pm with distribution of size within populations strongly dependent on mean size. Batch-produced latex spheres have population standard deviations (o) characterized as in Fig. 1 (drawn from a manufacturer's technical data sheets): below 1 ym mean

size, is of the order of 0.005 ym; it rises at 1 ym to about 0.01 ym and remains at 1% or

so up to 2 ym, rising to 5% or 0.15 ym at 3 ym, 10% at 5 ym, and 20% at 10-20ym. Dropletproduced latex spheres are reported by another manufacturer to have a "main-mode" distribution of less than 1.5% over the range of 5 to 100 ym. ("Satellite-modes" are not counted

in the computation of this narrow width.)

At present, NBS provides, as standard reference materials, the sized glass beads and

spheres described in Table 2, as well as a stage-micrometer also described. The basic

method of calibration of the glass spheres and beads is described in Ref. H18 and in the

certificates of calibration (example in Appendix G) which accompany the materials.

Also reported to be available from other sources are: encapsulated, graduated rows of

individually selected particles [T4]; dyed latexes and ones to whose surface chemicals can

be atomically bonded [B2, B3]; and specially sieved, narrow-distribution glass beads [C22].

Potentially available sometime after 1982 [E2] are narrow-distribution, large-diameter

latex spheres batch grown in the gravity-free environment of the space shuttle [K8].

Among particle reference materials, latex-like polymer spheres play a central metrological role; and among the suppliers of latex-like spheres, the metrological role of the

Dow-Diagnostic Division of Dow-Chemical Company* is unique. For over 25 years, latex

spheres with individual particle diameters measured by electron microscopy and with mean diameters covering at close intervals the range from sub-0.1 ym to over 1 ym,have been

distributed by Dow [B2, B3]. From 1954 until 1979, published values of latex diameters

*Please note disclaimer at beginning of Introduction.

4
have been measured at Dow by the same basic technique and often by the same individual

[B16, R10J. Within the industrial and scientific communities, these latex particles have

been measured by numerous other workers and techniques, and published accounts and results

of these measurements provide a systematic and comprehensive body of metrological data and

form a major portion of this report. Various aspects of the measurement techniques and

instruments will be discussed in Parts II and III of the report while Part IV will present

an examination of some of that data.

i i i i 0.1 1 10 100

MEAN DIAMETER Cum)

Figure 1. The width of the particle size distribution (a) as a function of mean particle

diameter of the distribution for batch grown polymer spheres produced by one manufacturer [Ref. B3].

5
Table 1

Examples of Commercially Available Sized Standard Particles

Material Mean Size (pm) Range About Mean (ym)

Polymer Spheres

Polystyrene (PS)

Polyvinyl-Toluene (PVT) (Great variety with size-dependent range;

Poly sty rene-Di vinyl Benzene (DVB) see figure 1 for typical values)*

Polystyrene-Butadiene (PSB)

Uniform Glass Microspheres**

1-3

1-5

7 1-30

1.8 0.5-6

8.0 4-14

10 5-15

100 90-115

Spherical Pollens**

Paper Mul berry 1 3-1

4

Ragweed 19-21

Bermuda Grass 22-30

Walnut 40-50

Corn 65-75

Test Dust**

AC Fine 1-45

AC Fine 45-80

*Suppliers Bulletin (Dow Diagnostics; see note below).

**Suppliers Bulletin (Duke Standards Inc.; for identified suppliers of

standard particles see Appendix A.)

6
Table 2

NBS Standard Reference Materials Used

in Particle Size Measurement

Standard Reference

Material Number

Type Dimensions

( um

)

SRM 1003 glass spheres 5-30

SRM 1004 glass beads 34-120

SRM 1017a glass beads 100-310

SRM 1018a glass beads 225-780

SRM 484a SEM stage micrometer 1,2,3,5,50*

*Spacings calibrated to + 0.04 ym in 1-5 urn range and 0.48 for 50 urn.

7
2. SUMMARY OVERVIEW OF ELEMENTS OF PARTICLE SIZE MEASUREMENT SYSTEMS

The purpose of particle-size measurement is to associate with the particles a number,

that is, a "size," which characterizes some important dimensional property of the particles.

The measurement process involves the particles as an object, the measuring instrument and a conceptual model of how it interacts with the object, and the mathematical manipulations

done with the data collected on the particles.

This section will look at some of the combinations of object-instrument-mathematical

models which give rise to different operational definitions of particle size. Specifically,

the section briefly examines various kinds of particles and their environments, some measuring instruments and the size-dependent phenomena they exploit, conceptual definitions

of particle size, and mathematical definitions of mean particle size.

A. The Object: State of Matter

Particles to be sized can be any one of the three states of matter as can the medium

in which the particles exist. In aerosols, the medium is gaseous and the particles can be

liquid drops or solids. In hydrosols, the medium is liquid and the particles are most

often solids, although they may be drops of other liquids or air bubbles. When not suspended

in a gaseous or liquid medium, solid particles can be in the form of a dry powder or dry

individual particles. And finally, both liquid drops and solid particles can exist in an extremely low-pressure gaseous or vacuum medium.

As candidates for sized particle reference materials, solids have the attribute that

they may be used in liquid, gaseous, or vacuum media with some degree of mechanical size

and shape stability. For example, polymer spheres in water solution may be measured in

that solution by (1) laser-light scattering, (2) in an electrolyte solution by a resistivetype, flow-through counter, (3) air-dried and on a substrate by an optical microscope, and

(4) evacuated and irradiated in an electron microscope. By comparing sizes measured by

different techniques, the effect on the size and shape of the particle by the change of

medium can and should be considered explicitly.

B. The Measuring Instruments

At the heart of each operational definition of a particle size is a device which

responds to some size-dependent property of the particles. The size-dependent phenomena

may involve one or more particles at a time or may involve a physical separation of particles

by size. Thus, some calibration by which the basic unit of length is associated with that

phenomena is required. This section examines some of these phenomena, the number of

particles involved, any separation process used, and the types of calibrations possible and

useful

.

2.B.I. Size-Dependent Phenomena

Initially, particle-size measuring instruments detect some signal which is assumed to be related to the size-property of the particle. For imagi ng-i nstruments, the intensity

distribution in the directly viewable, magnified image of the microscopic particle is the

signal. For non-imaging instruments, the nature of the signal depends on the phenomena

exploi ted.

a. Imaging: Optical and Electron

Microscopes, both light-optical or electron-opticaT, are valuable for particle-size

analysis because they present a direct-image of the particles to the investigator for visual

examination. The visual image can contain information on shape, surface features, and

debris present, as well as dimensional information. The reliability of the dimensional

information obtained from microscopy depends, among other things, upon specifics of the

instrument and technique. These specifics include the familiar matters of magnification,

resolution limit, and depth of focus, and the less familiar matter of edge-location, with

its dependence on a selection criterion and its variation with focus and other system

variables. -
In optical microscopy, the magnification in the image plane can be up to 1000 or 1500

X so that particles as small as 0.5 pm or so can be imaged. In reflected light, the surface

features of the object and the shape of the plane section of the object perpendicular to the optical axis of the microscope are viewed, while in transmitted light, only the plane

section can be seen.

In electron microscopy, the maximum magnification in the image plane depends on the

type of microscope: for the scanning electron microscope (SEM), which forms images of the

surface of solid objects, the magnification can be up to about 100,000 X while for the

transmission electron microscope (TEM), which forms images from electrons which pass through

thin specimens, the maximum magnification is typically 300,000 X but can reach 800,000 X. SEM's can image particles as small as 0.015 ym, while the TEM's can image those as small

as 0.001 urn. As with the optical microscope with reflected light, the SEM images the

surface and the plane section, while like the optical microscope with transmitted light,

the TEM images the plane section only.

In addition to surpassing the optical microscope in maximum magnification by orders of

magnitude, electron microscopes have the major advantage of sharper focus and greater depth

of focus. Microscope images, whether optical or electron, do not have sharp, discontinuous

edges, but are bounded by blurred transition regions. The width of the blur-region is a variable which depends on the instrument resolution and depth of focus capabilities as well

as a subjective judgment of best focus.

In a dimensional measurement of an extended object, such as a particle or a planar

feature, the apparent width depends on where in the blur region one decides the edge lies.

The location of the edge therefore changes with the subjective criterion of edge location

within the blur region and the location of the blur region varies with focus settings.

There is clear evidence that fi lar-eyepi eces, image-shearing (i.e. split image) eyepieces,

and automatic-image analyzers, such as TV-microscope systems, locate the edges of optical

images on different levels within the blur region [Sll,12].

For an ideal object with square edges, the width of the blur region for an optical

microscope is determined by the object and by diffraction phenomena modulated by the performance characteristics and focus setting of the microscope; for a real optical microscope

and real object, the blur region will be greater than that for an ideal laminar object

imaged by a diffraction-limited lens system. As a rule of thumb, the smallest blur attainable will be wider than about 0.25 ym [N5]. The location of each of two edges which define

the width of an object's image (e.g., the diameter of a particle) is ambiguous by an amount

twice as great or up to the f ull -di f fraction spot, i.e., 0.5 ym or more, depending on edgelocation criteria, focus choice, and instrument operating conditions.

It has been demonstrated that the apparent size of microscopic objects as measured by

optical microscopy depends systematically on lens and diaphragm apertures [C8, N5, S3],

illumination levels [C9], focus conditions [N5, S3] and image-measurement device type

[SI 2]. It has been demonstrated experimentally that automatic-TV-microscope systems, filareyepiece visual microscopes, and image-sheari ng visual microscopes can yield size-measurements on identical 1 to 10 ym planar objects that differ systematically from -0.25 to +0.25 ym, depending on image polarity [S12]. Further, a related study [Sll] showed systematic differences among measurement results from several industrial laboratories on a 3 ym

planar object of up to 0.6 ym. In these cases, the thickness of the object ( 0.1 ym) was advantageously small compared to the depth of focus of the optical microscope. In particle

size measurement, this is not the case.

Classically, the depth of focus of an optical microscope is on the order of 0.5 ym at 1000 X (and, for example, 10 ym at 100 X). In such a situation, the depth of focus is a significant fraction of the large particles in a field of view (and can exceed the size of

small ones in the same field). Attainment of an acceptable, albeit arbitrary, "best focus"

is a major limitation on particle size measurement by optical microscopy, although it is not the only limitation on dimensional accuracy.

Electron microscopes surpass optical microscopes not only in overall magnification but

also in greater depth of focus, while at the same time, on a different scale of dimensions,

9
are more susceptible to edge-location difficulties. As a rule of thumb, the depth of focus

of an electron microscope is equal to the width of the field of view. At 1000 X, this

corresponds to about 100 ym (compared to 0.5 ym for the optical microscope). At a typical

magnification for particle size, e.g., 20,000 X, the depth of focus is on the order of 5 ym. The width of the blur-region in electron microscope imaging is correspondingly smaller

but still significant in proportion to the size of the objects measured. For an SEM, the

blur-region width is of the order of the electron-beam spot size, and can be as small as 5 nm in high-resolution systems or as large as 50 nm. The lower limit applies only in the case of transmission electron detectors. Edge location uncertainties of 10 nm and larger can be anticipated for secondary and backscattered electron detection. For a TEM, the

blur-region width is on the order of 1-2 nm for ordinary instruments. Thus, while the

optical microscope as described above has an edge-location ambiguity in width measurements

of up to 0.5 ym, the electron microscopes have an ambiguity at least ten times less or about 0.05 ym for an ordinary SEM and about 2 nm for a not-unusual TEM.

The significance of edge-location ambiguity is this: similar objects measured with

similar microscopes can have apparent sizes which differ systematically by as much as double

the width of the blur region depending on the arbitrary choice of edge-location and focus

setting alone. In an optical microscope, systematic differences of the order of 0.5 ym in

size measurements could be attributed to just these effects. These are not errors inherent

to the instrument but rather are systematic errors which are not removed by line-scale

calibration. Other calibration techniques, involving either comparison to extended objects

of known size or theoretical modeling of the image process, can reduce or eliminate these

effects. This topic will be discussed more thoroughly in another section of the report.

As a note, for a number of reasons, including attempts to eliminate changes in polymer

particle dimensions for certain PVC latexes due to evacuation and irradiation in electron

microscopy [C20, D5] and also to reduce depth of focus problems in optical microscopy

[C9], metal vapor deposition has been used to produce shadows of polymer spheres, where

measurements are subsequently made on the circular openings in the deposited film rather

than on the original polymer sphere [C9, C20, D5],

b. Non-imaging size phenomena

Apart from i nstruments which produce direct images, there are i nstruments which exploit

other size-dependent phenomena for particle measurements. Most of these other phenomena

involve the particles' radiation scattering properties, velocity, or volume displacement.

The vol ume-di spl acement type of particle-size instrument is the one which has been

variously described as an electrical-sensing-zone [A3] or electrical-resistance [Dll]

particle counter. Such an instrument scales and counts the current pulses produced as individual particles pass sequentially through an aperture, on either side of which is an electrode, and thereby displace a volume of electrolyte through which current flows.

Versions of the basic device were patented and first marketed by Coulter Electronics Inc. over two decades ago and have been available from at least six manufacturers in the U.S.,

West Germany, Japan, and Eastern Europe [A3, Appendix B].

In principle, the measured change in current due to the particles' presence between

the electrodes is directly proportional to the volume of the fluid displaced which is

identical to the volume which the material of the particle occupies. Allen devotes a textbook chapter to the instrument, reviewing the equation form Ai - v(l - a/A)~l, where

v is the volume of of fluid displaced, Ai is a change in current, and a and A are crosssectional areas of the particle and aperture, respectively.

Allen reports that for spherical particles which are large compared to the aperture

(particle diameter about 0.4 times aperture diameter), "the error involved in assuming a linear relationship is about 5.5%." He also reports "discrepancies of unspecified degrees

between computed weight of particles counted and weight in suspension as being usually

explained by differences between the envelope of the particle being measured, as opposed

to the true vol ume.

Coincidence effects, which affect flow-through counters of both the light-blockage

[W10] as well as the electrical-sensing-zone types, have been studied extensively as

L0
indicated by the citations in, for example, Coulter's Industrial Bibliography* and Allen's

text [A3]. Two types of coincidence errors are postulated: primary or horizontal coincidence due to two particles which give rise to two overlapping pulses; and secondary or vertical coincidence due to two particles below threshold which give rise to one pulse of

a single large particle. Besides these error sources in counting, Allen (A3) covers the

work of others and his own work on factors which distort the basic volume displacement

proportionality [A3]. These factors include: the conductivities of the particle and

electrolyte; the effective volumes of the aperture and the particle; the particle shape

and its orientation during passage through the aperture; the presence of more than one particle in the sensing zone (coincidence); pulse shape dependence on wall effects and

hydrodynamic focusing; and means of end-point determination.

Apparently, in practice, instrument response is independent of the resistivity of the

particle and Berg, quoted in Ref» A3, suggest that this is due to the Helmholtz electrical

double layer and associated solvent molecules at the surface of the particle.

While instruments involving electromagnetic scattering include examples such as x-ray, Y-ray, or ultrasound [see, for example, Refs. D8, Dll-14], light scatteri ng and specifically

visible-light scattering are the most common instruments currently in use.

Similarly to the term particle-size, light scattering is an inclusive one that

encompasses a broad range of instrumentation, techniques, and physical phenomena. In general, there is an incoming light beam incident on one or a collection of particles and a measurement of some property of the scattered outgoing light. The outgoing light, like the

incident light, is characterized by amplitude or intensity, phase, frequency, direction of

propagation and state of polarization. A theoretical model is used to relate some combination of these parameters of the scattered light to the size of the particle or particles

doing the scattering. In some instruments, the relevant theory is explicit and detailed

enough to provide a direct measurement of particle size, i.e., one in which the size is calculated directly from the basic mode; in other light-scattering instruments, the model

is sufficient only to allow comparisons of particles of unknown size to those of known

sizes. Because of their significance as potential candidate instruments for the calibration

of particle reference materials, the function and theory of light-scattering instruments

will be examined in more detail below in Section 3.B.

Instruments which determine particle-size via the measurement of size-dependent velocity of motion do so by various means. The means differ according to the cause of the

motion and how the velocity is measured. The size-dependent velocity can be due to, for

example: settling with buoyancy under gravity [C4, C5]; centrifugation or flow under pressure [D8, Dll-13]; Brownian motion [R7, L13]; or forced-vibration of sinusoidal [S2] or non-sinusoidal types [SI]. The size-dependent velocity can be measured, for example, by:

transit-times or separation due to velocity differences [D8, Dll-13], doppl er-f requencyshift [C4, C5], or time-correlation [L13, G10].

While some of these techniques and their variations use light, even scattered light,

for the particle velocity determination, these techniques are distinguished from what is

here called angular-intensity light-scattering because the size-dependent phenomena is principally described by aerodynamic or hydrodynamic equations for objects moving in fluids

rather than by equations for electromagnetic waves scattered from spheres.

Velocity-dependent light-scattering as a means of particle size measurement, especially

applied to liquid-drop aerosols, is well-established with a literature of its own. It includes the doppler-shif t instruments and techniques variously described, for example, as: laser doppler velocimetry [F5], doppler shift spectroscopy [C4, C5, F4, H12, H13], or simply

laser doppler systems [SI, S2, D22]. For the most part, these systems, with the exception

of those of Refs. SI and S2, deal with flow or settling. Where the particle velocity is

due to Brownian motion, a related family of techniques includes those variously described,

for example, as: photon correlation [CI 1 , G10], homodyne [H14], optical self-beating [L13];

or Rayleigh-li newi dth [RIO] spectroscopy.

^Available from Coulter Electronics, Inc., Hialeah, Fla.

11
2.B.2. Number of Particles Involved

The number of scatterings involved in most light scattering techniques is usually a single one; that is, the light which reaches the detector has been scattered only once. Single-scattering is the basis of techniques which look at one isolated particle at a time

in a single event [e.g., W15-W16], at one isolated particle at a time in a rapid series

[e.g., W12], or at many particles at one time for single-scattering from multiple particles

in parallel [e.g. , R7],

2.B.3. Separation of Particles By Size

Another factor about particle-size instruments which bears on their performance as measuring devices is whether they involve intentional separation of particles by size.

Such separation can be achieved in a number of ways, for example, mechanically, aerodynamical ly, or hydrodynamically.

Sieving is a technique for mechanically separating particulate matter into size

intervals and is used both for mass-handling of tons of large particle materials and microhandling of fine particle materials as small as 1 ym in size. For sieves with openings of

known dimensions, the sieving operation is one of successive separations into groups smaller

and larger than those which just fit through the openings. It is a conventional way of

sizing standard glass beads and microspheres [H18, C22]. It gives a name to those particles

smaller than those which can be satisfactorily sized by sieving; particles in the "subsieve" category [01], however, can be larger than the smallest sized by sieving.

Impactor-sizing is a technique for aerodynamically separating particulate matter into

size intervals; impactors are used most often for the characterization of airborne contaminants such as dusts and smokes. In such devices particulate matter is deposited on collectors

according to the aerodynamic momentum associated with the particles. For a fixed velocity,

separation by momentum corresponds to separation by mass, which for a known density

corresponds to separation by volume, which for an assumed spherical shape corresponds to separation by diameter. Relatively recent designs for variable-slit [C24] and low-pressure

[H7] impactors have provided a means to measure aerodynamic particle sizes over continuous

or discrete ranges down to diameters of 0.05 ym or less.

Sedimentation and centrif ugation are techniques for hydrodynamically separating particulate matter into size intervals and, most often in laboratories, are used for the

smaller, <1 ym, particles [01, Dll-14]. In such devices the concentration of particles

suspended at various depths is determined as a function of settling time. Concentrations

are determined, for examples, by light [D12], x-ray [01] or Y-ray [D12] attenuation at various depths or times.

2.B.4. Types of Dimensional Calibration

Instruments which measure particle-size do so by a comparison, indirect or direct,

with the basic dimensional unit of length. This comparison requires explicitly or implicitly

the use of some practical length standard, which can be a particle of known size, a linescale

or a wavelength of light. Direct-imaging instruments can use any of the three; non-imaging

instruments can use only the first and last.

a. Direct-imaging instruments

Electron and optical microscopes are usually calibrated for dimensional measurements

by a ratio technique either using a linescale such as a stage micrometer or replica

grating [e.g., in Refs. B16, Rll, H4], or using particles of a known size [e.g., in Ref.

H4, C8]. While each of the two approaches, linescale or particles of known size, follows

the same procedure, there is a consequential if subtle difference in them which results in differences and varying degrees of dimensional errors. Where the magnification Ms of a microscope is calibrated by means of a linescale of known spacing S 0

, the measured dimension

of the unknown, D x

, is given in terms of the dimensions of the images of the known spacing

and the unknown particles, s 0 and d

x respectively:

12
d

< la ) D ¥ (Um) = x

| mm) S n (um), or

x

s (mm) 0

(lb) D

x

(urn) = M

~* d

x (pm), where

s (lc) |v] - o(mm)

s S Q (ym)

Where the magnification M

p of a microscope is calibrated by means of particles of known

dimension D0

, the measured dimension of the unknown, D

x

, is given in terms of the dimensions

of the images of the known and unknown particles, d

0 and d

x respectively:

d

( 2a ) D x (urn) = x

\ mm] D (ym), or

* dQ (mm) 0

(2b) Dy (ym) = M~ ] d y (ym), where

p

d (2c) m = o (mm ) . P D

0 (ym)

The analogous equations for the measurement of unknown line spacings in terms of

known ones are:

s (mm)

( 3a > S

x (ym) = S„(ym), or

s 0 (mm)

(3b) S v (ym) = s v (mm), where

A $ A

s (mm)

(3c) m = Q . s S Q (ym)

Equations la and 2a are usually implicitly and erroneously assumed to yield results

identical to each other and to Eq. 3a. But because of the edge location phenomena described

earlier, they can and do give greatly different results. Rearrangement of Eqs. la, 2a,

and 3a into explicit ratios begins to show the basis for the differences which occur:

D d (4a) _x = _x

D

0

do

13
(4b) x = x Sq s O

(4c) _x = _x

So s o

Here it is at least formally explicit that calibration with particles of known size,

as in Eq. 4a, consists of comparing widths-to-widths while calibration for particle measurements with a linescale as in Eq. 4b consists of comparing widths-to-spacings in dissimilar

objects.

Calibration for spacing measurements with a linescale as in Eq. 4c consists of comparing spacings-to-spaci ngs.

It has been demonstrated that in an optical microscope, the apparent width of an object's image depends on the edge location criterion, focussing, and instrument operating

conditions [C9, N5, Sll-12]. Further, it has been demonstrated, for both spherical particles [C9] and planar objects [S12], that the apparent width d

1 can differ from the

geometrical -optical width d by an increment A which depends on edge-location criteria,

etc., but is relatively constant over a range of object sizes (e.g., from 0.2 to 2 ym

[Ref. C9] and similarly 1 to 10 pm [S12]). Thus,

(5a) d* = d + A.

In the same imaging systems, the apparent spacings of a linescale are in practice to a very high degree free of these effects and in principle are independent of them [Sll, S12].

Thus

,

(6) s' = s.

Substitution of Eqs. 5a and 6 as appropriate into Eqs. 4a-4c results in expressions for

the ratios of object and image dimensions.

D d +A

x = _x

D 0 V

D d +A

X = X

S os O

S s X = X

s os o

For a difference in size between the known and unknown particles of Eq. 7a given by

d

x

= d 0 + 5 and for a geometrical -optical magnification M given by Eqs. lc through 3c, the

difference in the object size corresponding to the difference between the apparent and the

geometrical -optics image size, becomes for the three cases shown in Eqs. 7a-7c:

(7a)

(7b)

(7c)

14
Case I. Particles of unknown size measured by ratio to particles of known size.

(8a) C=D _ _x = A . 6 x M M "d^

Case II . Particles of unknown size measured by ratio to lines of known spacings.

(8b) £= D_ _x_=A - (l) = 6. x MM M

Case III. Lines of unknown spacing measured by ratio to lines of known spacing.

e = S - JL = A • (0) = 0 . x M M

Eqs. 8a, b, and c can be used to examine how systematic error which can arise in microscope measurements of dimensions due to ambiguities in image edge location is affected by

various calibration techniques. The basis for such errors is the distance A/2 between the

apparent edge of an object's image and that determined by geometrical (electron or light)

optics; the corresponding ambiguity for the object edge is A/2M and for the object width

A/M. Based on the discussion earlier, A/m can be of the order of 0.25 ym or more for an optical microscope [e.g., in Refs. C4, Sll, and 12] while for an electron microscope, the

author would anticipate A/M to be of the order of one-tenth that amount or 0.01 urn or so for an ideal object.

Given a non-zero A/M then, in a measurement of an unknown linespacing against a known

one, the error due to edge location as represented by Eq. 8c is zero. In a measurement

of an extended object, either against a similar extended object or against a linespacing,

the error due to edge location as represented by Eqs. 8a and 8b is non-zero. For calibration with a linescale, the error in the dimensions of a particle could be on the order

of 0.25 ym for an optical microscope measurement and on the order of 0.02 ym for a scanning

electron microscope measurement independent of particle size (based just on considerations

of what goes on in the image plane; other effects can mitigate or compound these errors).

For calibration with particles of known size, the error depends also on the difference in size between the unknown and known particles. For example, in the measurement of an (unknown) 15 ym particle against a (known) 10 ym particle, the error in size according to

Eq. 8a for an optical microscope measurement might be:

(9) e = 0.25 (1°J±5) = 0.125 ym

and for an electron microscope measurement:

(10) £ = o.02 (l°-ll5) = 0.01 ym HO

while for a measurement of a 10.1 ym (unknown) against a 10 ym (known) the respective

errors might be:

(ID e = 0.25 ( 10.1-10 ) = 0.025 ym

TO

15
Both the formal relationships of Eq. 8a, b, and c and the numerical examples just

given illustrate some major points about the calibration of microscopes for dimensional

measurements. First, there is sound evidence that edge-location ambiguities should lead

one to anticipate systematic errors on the order of many tenths of a ym in optical microscope

measurements and on the order of a hundredth of a ym in electron microscope measurements

of the dimensions of extended objects such as particles. Second, these errors can be

reduced, but not eliminated, by calibration against known spheres and only if the knowns

and unknowns are close in size. Since these errors depend on the specific means by which

an imaged apparent edge is located with respect to the geometric edge, one further way to

deal with them is via a theoretical model of the microscope and its interaction with the

object, a model which quantitatively describes the relation between the image profile and

the object. In formal terms such a model mathematically describes, for example, the (light

or electron) intensity distribution within the image as a function of position x and

variables of the instrument, e.g.

(13) I = I(x, a, 3).

Such a model and a linear displacement measuring device allow scanning of a microscope

image and the location of the intensities, Ig, corresponding to those determined by geometric

optics. The measured width of an object corresponds then to the distance between the

points on the image at those intensities:

(14) w = x( I-, ) - x(I 2

).

The displacement measuring device for such a measurement can be a calibrated transducer

[N5] or an interferometer which can relate the measurements directly to the wavelength

of light [SI 3].

b. Non-imaging instruments

While imaging instruments can be dimensional ly calibrated by linescales (or displacement-measuring devices), non-imaging are usually calibrated by one or the other of the two remaining methods: explicit comparison of particles against other particles of known

size or implicit comparison against a wavelength of light.

Commercial flow-through counters of the volume-displacement type [C25], the light

shadow-projection type [W10], or other light-ratio types [W12] are calibrated using particles

of known mean size and size distributions. Some commercial single-particle light scatter

instruments of the levitation [W15] or flow-through type [W18] compare against the wavelength

of the light source. Most laser light-scattering instruments, including those which scatter

light from suspensions [Dll-14, W12, Gl ] as well as the single-particle types just mentioned,

make implicit comparison against the light wavelength which appears as an input parameter

to a theoretical -analytical calculation of instrument response.

For angular-intensity light-scattering instruments, the calculation involves complex

equations requiring computer numerical evaluation techniques. As such, no simple descriptive form of the dependence of intensity I vs. angles 9 and cj> , particle size d, and light

wavelength A and complex index of refraction m can be given. Formally, however,

(15) I = 1(6, .t», x, m. . .)

where the size parameter x = i\d/\ and d is the diameter of the spherical particle. Here

the comparison of particle size vs wavelength is calcul ationally direct.

In particle-velocity light-scattering instruments, the calculation, in special cases,

can be independent of angular-intensity theory and involve only hydrodynamic motion theories:

for example, in first-order calculations, measurements on collections of particles of

L6
nearly identical size [C4]. The most analytically simple case will demonstrate a point

about dimensional calibration against the wavelength of light in velocity systems. For

example, for particles following Stokes behavior, the viscous force F is given by

(16) F = 6Trnav

where a is particle radius, n is the viscosity, and v is the particle velocity. A more

specific example is for spherical particles of density, p, settling under gravity g, at terminal velocity in air, where the viscous and gravitational forces are equal and

6-rTnRv = 4 TrR 3 pg

and

(18) w = 2pgR 2 9

For a Doppler shift given in terms of the vector velocity v and the light propagation

vector k:

(19) f = 1_ v • k

where

(20) )k | = air sin e

Combination of the Stokes and Doppler equations gives the measurable frequency shift of

the scattered light as a function of the particle size r and the wavelength of the light

X, as well as other system variables:

(2D Af = ^(2Pi) (4nna1p ) sin 1

1?.

or

(22) f _r£

X

The most significant point to be made concerns dimensional calibration, and is that while

the particle size in aerodynamic or hydrodynamic velocity measurements is determined in

terms of the wavelength of light, it is done in a way different than in angular-intensity

light scattering where the size information and dimensional calibration is in the scaling

parameter x = 2 nr/X.

Calibration of flow-through counters against particles of known size can be accomplished

in at least two ways: a single-point (one ratio) technique and a multiple-point (two or more ratio) technique. A single-point technique can accomodate scale-factor (i.e. multiplicative) effects if no off-set (i.e. additive) effects are present. In the presence of

off-set effects, at least a two-point calibration is required. Some models of commercial

flow-through counters of both light-blockage and electrical -sensing-zone types can be

adjusted in at least two-point calibrations. Further, there is a technique for determining

17
the fraction of the total particles in a sample which are smaller in size than that which

can be detected, sized, and counted [A3].

2.C. Single-Number Index to Characterize Particle Dimensions

Individual particles of matter are three-dimensional objects and dusts, powders, and

suspensions are collections of vast numbers of individual particles. The determination of

a characteristic particle size for a collection of particles therefore involves defining

and measuring a size of one particle and defining and measuring a size of a population of

particles.

2.C.I. Characterizing a Single Particle

An individual particle is a real three-dimensional object which has no one unique

dimension which to call its size. As a geometrical object it is complex and irregular. As

an object-to-be-measured, it is the receiver of action in one of many operational definitions

where other operational definitions yield other sizes because they treat other geometrical

representations of the particle. Most often the geometry is described in terms of the

diameter of an equivalent circle or sphere; a sample of twelve ^uch diameters with their

definitions is listed in Table 3.

Microscopes, both optical and electron, and one type of flow-through counter [W10], measure particle size by scaling a two-dimensional plane projection of the three-dimensional

particle. In a microscope, a non-circular image can be characterized in various ways:

Feret's diameter dp which is the distance between parallel tangent. s to the outline of the

projected image; Martin's diameter, a mean chord length; or, one not shown in Table 3,

a shear diameter, d£, which is obtained with an image splitting eyepiece and is the Feret's

diameter parallel to the eyepiece axis independent of the particle orientation [S10]. In the light-blockage type of particle counter, the particle size is given as the diameter

dpMAX °f tne C1rc l e equal in area to the maximum projected area of a tumbling particle

[WlO]. Note that maximum projected area diameters dpf^x differs from the random-orientation

projected area diameters, dp r

, the latter being for a particle lying on a substrate in a microscope. Besides being characterized in terms of a straight line chord-type dimension

or an area-type dimension, projected plane images can be characterised by their perimeter.

Electrical -sensing-zone particle counters and one special -type of light scattering

instrument measure particle size in terms of the individual particle's volume. For the

former, the effect is the volume of liquid electrolyte displaced [C25]; for the latter, the

effect is the Rayliegh scattering in which an electronic polarizabil ity gives rise to a dipole moment proportional in strength to the volume of the particle [A3].

Hydrodynamic and aerodynamic velocity-dependent particle-size measuring devices,

ranging from Doppler-shift spectrometers [C4] to precipitation impactors [C24, A7], measure

particle size via Stokes'-type equations which involve volume-surface phenomena. The linear

dimension in a Stokes-equation of the form: force = (shape factor) x (dimension) x (velocity) appears as the result of evaluation of complex-boundary conditions integrated over

the surface of the object moving in the fluid [A3]. Further, where terminal velocities

such as those due to gravity are measured, the Stokes force is equated to a buoyant force

which is proportional to volume displacement:

(gravity) x (density) x (volume) = (shape) x (dimension) x (velocity).

Solution of this form of equation for a specific object shape yields the size vs velocity

equation upon which size measurements are based. Other size-dependent phenomena which

involve surface effects, such as gas adsorption, are used in commercial and laboratoryprototype devices [Dll-14, D8, A3].

In almost all particle measurements, and i nciependent of the physical phenomena and

geometrical effects involved, the resulting single-number characterization of the non-ideal

irregular, three-dimensional particle is given as the diameter of a(n) (equivalent) sphere.

Where the particle is perfectly spherical, many of bhe geometrical effects would in form be

the same - for example, the plane projection of a sphere is a circle whose diameters, whether

1 8
Table 3

Definitions of Particle Size [A3]

Symbol

d

v

dsv

df

Name

Volume diameter

Surface diameter

Surface volume

diameter

Drag diameter

Free-fal ling

di ameter

Stokes 1 diameter

Projected area

di ameter

Projected area

di ameter

Perimeter

di ameter

Sieve diameter

Feret's diameter

Martin's diameter

Def i ni tion

Diameter of a sphere having the same volume as the particle

Diameter of a sphere having the same surface as the particle

Diameter of a sphere having the same external surface to volume

ratio as a sphere

Diameter of a sphere having the same resistance to motion as the

particle in a fluid of the same viscosity and at the same velocity

(dj approximates to D

s when R e

is

small)

Diameter of a sphere having the same

density and the same free-falling

speed as the particle in a fluid

of the same density and viscosity

The free-falling diameter of a particle in the laminar flow region

(R

e <0.2)

Diameter of a circle having the same

area as the projected area of the

particle resting in a stable position

Diameter of a circle having the same

area as the projected area of the

particle in random orientation

Diameter of a circle having the same perimeter as the projected outline of

the particle

The width of the minimum square aperture

through which the particle will pass

The mean value of the distance between

pairs of parallel tangents to the

projected outline of the particle

The mean chord length of the projected

outline of the particle

19
Feret or Martin's or image-shear, is the equatorial diameter. The diameter of the projected

area in a maximum, random or stable orientation is the same diameter, as is the diameter

of the sphere of equivalent surface area.

Two points are worth keeping in mind in the evaluation and i ntercompari son of experimental measurements on real particles, especially nearly-spherical real particles. One

point is that particles are spherical only in relation to an individual technique's ability

to detect deviations from sphericity. The second point is that even highly spherical

particles have different equivalent spherical diameters according to the physical phenomenon

and operational definition by which the various diameters are measured. A particle does

not have a simple "true size" or an "absolute diameter" but rather these operationally

defined sizes. Increases in precision can reveal systematic differences between variouslydefined sizes while at the same time refinement and sophistication in theoretical modelling

can produce convergence. Later in Section 4 on the intercomparison of particle sizes

measured by various techniques, both the presence of systematic differences and the possibility of obtaining convergence will be apparent.

While this report is concerned primarily with spherical particles which can potentially

serve as sized standard reference particles, Table 4 is given to illustrate some shape

factors or coefficients and their definitions [A3, S10]. The factors have practical importance, especially in dealing with industrial powders, suspensions, dusts and atmospheres

which are made up of irregularly-shaped particles. For spherical particles, the factors

and coefficients reduce to unity or appropriate multiples of tt.

As a practical matter, deviations from sphericity at even a low-level have a consequence

on the precise determination of the mean size and population standard deviation (monodispersity) of highly spherical standard particles. Some observations that have been made about

shape effects are worth keeping in mind in the evaluation of systematic error effects in

the calibration of standard particles. In electron microscopy, the shape of the equatorial

plane of the particle in a stable rest position on a substrate is viewed; and apparent

particle shape can be changed by pin-cushion, barrel distortion, and related astigmatic

effects on the two-dimensional imagery. Further, some evidence has been given that latex

particles may distort in shape upon electron irradiation [Tl]. In light scattering, the

basic Mie theory only describes scattering from perfectly spherical objects [Bll , K7, V4].

Techniques for dealing with light-scattering from nearly spherical particles such as oblate

and prolate spheroids [A6, L3] and ellipsoids [L5] treat deviations from sphericity as perturbations on complex mathematical formulations [Bll, K7, V4]. In flow-through particle

counting of either the light-obscuration [CI, W10] or electrical sensing zone types [C25],

particle shape determines the apparent size, changing the form and location of the size

distribution curve for non-spherical particles relative to that for spherical ones [A3,

W10]. The probable effect of a particle's asphericity on a measurement, whether by electron

microscopy, light scattering, or flow- through counting, is to increase the apparent width

of the size distribution, increase the uncertainty in the mean size, and shift the apparent

mean size to some degree as well.

2.C.2. Giving an Average Size to a Group

Commercially and environmentally important microscopic particles occur seldom, if ever, individually or in small numbers having practically equal sizes, but instead occur in

groups of great numbers having measurably different sizes. The common practical requirement

that such a complex system be describable by a single index is reflected in the wish to characterize that population of a large number of irregularly-shaped, three-dimensional

particles by one number, that is, by some average particle size. While the problem of

defining a size of an individual particle is geometrical -physical , the problem of defining

an average size for a population is statistical -physical

A conventional manner of describing, with one number, a population of particles having

different sizes is by means of a particle size distribution function. In tabular, graphical,

or equation form, the size distribution describes the amount of particulate matter which

occurs for a given size or size interval. The amount can be given in terms of mass; thus

there is a number size distribution and a mass size distribution. Either distribution, by mass or number, can be characterized by an arithmetic average (or arithmetic mean) size

d

a > by a geometric mean (or geometric average) size d

q , by a median size d m , or by other

20
Table 4

Table of Shape Factors and Shape Coefficients [A3]

Shape Factors Definition Coefficients

Sphericity The ratio of the surface area of a sphere

having the same volume as the particle to its actual area; the reciprocal is known as the coefficient of rugosity or angularity

< 1

Circularity The ratio of the perimeter of a circle

having the same area as the projected

area of the particle to its actual perimeter

x < 1

Surface-shape Coefficient of proportionality relating

coefficient the surface area of the particle with the

square of its measured diameter

S

= a s,Ad

a'

Volume-shape Coefficient of proportionality relating

coefficient the volume of the particle with the cube

of its measured diameter

V

= av,Ad A

:

Surfacevolume shape

coefficient

Ratio of surface to volume shape

coefficient

a s,v,A =

S ' A

av,A

21
Table 5

Mathematical Expressions of Various Mean Diameters of a Distribution

Number-length mean diameter x NL

Number-surface mean diameter

Number-volume mean diameter

Surface-volume mean diameter

Volume-moment mean diameter

Weight, moment mean diameter

X NS

X NV

Length-surface mean diameter XY LS

Length-volume mean diameter X* LV

; SV

^XM

EdL ExdN

EdN EdN

V/EdS\ /Ax2 dN

\ EdN/ ¥ \EdN

3/AdV\ 3//Ex3

dN'

EdS Ex 2 dN

EdL ExdN

V/EdV\ //Ex 3 dN\

y EdL/ * yExdN I

EdV Ex 3 dN

EdS Ex

2 dN

EdM Ex^dN

EdV Ex

3 dN

EdM ExdW Ex4 dN

EdW EdW Ex

3 dN

22
types of averages or means based on either number or mass, as will be discussed later. In some cases, the distribution is characterized by a mode size.

The differences among mean, median, and mode values of particle size are of practical

metrological importance. Most measurement processes and calculations yield one of many

types of mean size, as will be discussed shortly; a recommended way of calibrating flowthrough counters employs a median size; and at least one manufacturer of standard reference

particles characterizes them in terms of a main-mode size. The use of a median or a mode

requires an explicit graphical representation of the size distribution, such as a histogram.

If the distribution of sizes shows a peak, that is, if some size d-| has more particles

occurring at it than at nearby sizes above and below it, the size with more particles is

a mode and the distribution is modal. Some processes produce particles which have a dominant

single mode as, for example, batch grown latex particles. In contrast, other processes,

such as vibrating-ori f ice generators, have been observed to produce particle distributions

with two, three, or more modes [C4]; droplet-grown latex particles with tri-modal distributions have even been reported by manufacturers.

Some natural and industrial processes result in well-behaved single mode distributions

which are symmetric and monotonically and asymptotically approach zero at sizes well above

and below the modal size. For narrow-distribution particles such as polymer spheres, the

distribution is symmetric in the linear dimension and can be described well for most

applications by the Gaussian or normal distribution [A3]; for many ground or milled powders

and glass beads, the distribution is symmetric in the log of the dimension and can be

described by the log normal distribution [G2]; certain sub-0.1 ym polymer sphere distributions have been best described in hydrodynamic studies by symmetric but non-Gaussian

distribution functions [Cll].

The most commonly used mathematical distribution function is the Gaussian or normal

distribution and its explicit use or implicit applicability is conveyed by the term "standard

deviation" as the index of the width of the distribution. The standard deviation is the

limiting value of the root-meansquare (RMS) average deviation of an infinitely large,

normally distributed population. In metrology the standard deviation is a measure of the

random scatter in measurement data, while in common usage in particle-size measurement,

the standard deviation is a measure of the distribution of sizes in a population. Failure

to clearly distinguish the variations associated with the measurements from the variations

associated with the particle population can be troublesome and misleading.

In a measurement process statistical control is a must to yield valid results, and

the variations in measurements are random and characterizable by a standard deviation om. In a particle population with a normal distribution of sizes, that variation among sizes

is characterized by a standard deviation Op. In a first order model of the results of

applying the in-control measurement process to the normally-distributed particle population,

the standard deviation <7j. of measurements on the population will be the quadrature combination of the two:

for measurements on N particles, the standard deviation on the mean of the measurements

will be:

Given that is an observed scatter in measurement results, o m

is the component of

that scatter due to variations in size among the particles in the distribution, and o

p is

the component due to variations in the measurement process itself, some caution in interpreting results is required. For example, if one measures the apparent diameters of a

(23) 2 =(a

p

2 +0m

2)l/2

(24)

23
great number of particles as images on TEM plates and computes an RMS average deviation from

the mean diameter, one obtains an estimate of o

t

. Without moving, refocusing, reimaging,

and remeasuring one single unvarying particle to obtain an estimate of a

p

, one cannot

determine o" m , the quantity of interest.

The two equations above formally illustrate two points about measurements of particle

size distributions. First, Eq. 23 shows that a standard deviation computed from measurement data for a distribution of particles is equal to the particle distribution standard

deviation o

D only in the limit of small measurement uncertainty, or:

(25) o

t ~ a„ if and only if o >> a,

Since a mcan be determined only by a separate determination, such as by repeated measurements on one particle, the assumption that a

p >> ani should be questioned. However, given

the absence from the literature of data upon which estimates of the variability o for

the different measurement techniques, one can only keep the difference between and o m

in mind and treat o-j- as an upper limit for om

. As a second point, since the effective

number of particles N involved in multiple-particle phenomena (such as that seen in many

forms of light-scattering) is not known, the uncertainty in mean particle size cannot be

easily reduced without separate redeterminations. Further, the assumption of a normal

distribution of particle sizes for real populations of particles should be made with

reserve.

Caution and special mathematical techniques are also required to deal with multi-mode

or unsymmetric, skewed distributions [A3]. An expediency is to treat the dominant mode as

a single mode, ignoring parts of the distribution. Number averages are most susceptible

to the biasing effect of small particles which can occur in large numbers and would be

counted in one technique and would go undetected or intentionally uncounted in another

technique; mass averages are most susceptible to the biasing effect of large particles

which carry proportionally so much more mass than many small particles.

While number-average and mass-average mean diameter are most commonly used, they are only two of the many moments of a distribution which can be computed and which find use.

Table 5 shows eight such moment-mean diameters, with their general and specific

expressions for spherical particles. In general these moment-means are of the form:

sum (number x weighting factor #1 x size)

(26) wmean

= sum (number x weighting factor #2)

where the sum is over the sizes or intervals, the number is the number of particles for a given size or interval, and the weighting factors are geometrical factors such as length,

area, volume, or weight. The physical and formal differences among these various mean diameters is of metrological consequence since different particle-size measurement techniques, either inherently or by convention or convenience, determine different types of mean

diameters; for example, microscope measurements of diameters lead directly to a numberlength mean diameter; certain light-scattering techniques including extinction and laserDoppler velocimetry yield a number-area mean diameter; and mass-deposition devices, such

as impactors yield a number-mass (or weight) mean diameter.

Part II of this report, now concluded, has been an overview of those elements of

particle-size measurement systems which contribute significantly to the measurement process

and produce a number called a particle size. The particles of central interest to this

report are those which are spherical and monosize. The measurement techniques of central

interest are the three techniques by which such particles can be dimensional ly calibrated

in a consistent and compatible scheme.

2U
3. CANDIDATE INSTRUMENTS FOR STANDARDS CALIBRATION

A. Needs of Calibration Scheme

The needs and capabilities of industry and science with regard to sized particle

reference materials place stringent demands on the method of calibration in regard to the

dimensional measurements by which the particles are calibrated and their size is certified.

The measurements must be definitive in the sense that they are accurate to a degree com- mensurate with users present and near-future capabilities. In more specific terms, this means that a calibration technique must yield high-resolution measurements of some defined

particle size, and still, to a high degree, be independent of time and technique. Besides

being accurate, the techniques also need to be reasonably fast and economical.

No single current measurement techni que meets all these general requirements. Electron

microscopy can provide high-resolution, unambiguous imaging and dimensional measurement of even sub-0.1 ym individual particles. It can provide direct-image information on particle

shape and surface features and on the presence of agglomeration or debris. It can provide

via image-analysis of either manual or automatic form, an explicit histogram of particle

size distribution. However, it has the disadvantages that it is slow, necessarily involves

limited sampling of the population, and subjects the particles to vacuum and electron

i rradi ation.

Light-scattering from a suspension can provide high-resolution, dimensional information

averaged over a large number of particles in their normal environment. The method is fast,

non-intrusive, and can provide mean size and population standard deviation. It is advantageous in that it is based on a well-established theory. But the method is model -dependent

and requires prior knowledge or assumptions, usually that the particles are spherical,

homogenous, normally-distributed in size, and have a certain index of refraction. Also

scattering from a suspension cannot well distinguish agglomeration or debris or deviations

from sphericity.

Flow-through liquid-borne particle counters can provide moderately high resolution,

and fast, sequential measurements of individual particles in a sample of a liquid suspension.

They can provide an explicit, built-up histogram and so distinguish normal distributions

from skewed or multimodal ones. They also are comparators which require particles of known

size for their calibration, with the lower limit of the range of commercial devices at about 0.5 um. The electrical-sensing zone type requires that particles be in an electrolyte

solution. This type and the optical type involve consumption of the sample, and although

they cannot distinguish debris, they do give evidence when agglomeration occurs.

While other particle-size measurement techniques are avai lable, the three aforementioned complement each other in a scheme which promises to provide measurements which are accurate, fast, economical, and independent of method to a degree sufficient to meet the

needs of today's seekers of sized standard reference particles.

Because both electron microscopy and certain forms of light-scattering are direct-measurement techniques (that is, they yield dimensional measurements of particle size without

requiring particles of known size for comparison), each could be a primary calibration

technique in its own right. However, because the two techniques involve independent operational definitions of particle size which do not necessarily yield corresponding results,

i ntercomparison and refinement of the techniques, theoretical models, mathematical algorithms, and formal definitions to achieve such correspondence may be required. Flow-through

counters could then provide more information for the refinement process and be used for a rapid, convenient, secondary calibration in which particles of unknown sizes are calibrated

by comparison against particles of known sizes from a primary calibration. In this context,

these three generic techniques will now be examined in more detail.

B. Interrelationships of Three Candidate Measurement Methods

3.B.I. Electron Microscopy

In electron microscope measurement of particle size, electrons from a source are focused via electron optics onto the particle and either electrons transmitted and attenuated

25
by the particle (as in a TEM) or "reflected" (actually either backscattered electrons or different secondary emission electrons) by the particle as in an SEM are imaged. In a TEM

the imaging is usually done directly onto an electron-sensitive photographic plate; in an SEM the imaging is done by detecting the electrons and forming an image on a cathrode-ray

tube where intensity is proportional to the current detected. TEM requires a measurement

of the directly-exposed image on the plate, usually done visually with a reticle or with

some form of semi- or fully-automated image analyzer. SEM requires a measurement of either

an image on a photograph of the CRT screen or some form of scaling of the electron intensity

profile. In general, analytical models of the imaging process are not used and apparently

not thought to be required.

Early innovative work on electron microscope measurements of polymer sphere diameters

was done by Bradford and Vanderhoff at Dow in 1954 [B16]. Bradford has continued to the

present [Rll] work which is the basis for the mean particle sizes attributed to the more

than sixty Dow latexes marketed since 1947 [B2].

The basic technique, apart from some changes in instruments and calibration materials,

has been unchanged [Rll]. At the heart of the technique is the measurement of the apparent

diameter of the TEM image of a particle against the apparent spacings of the TEM image of

the lines of a replica grating upon which the particle rests. In the 1954 paper, the

authors report using a shadowed silicon monoxide replica grating with 1134 lines per mm

mounted on a stainless steel grid. The choice of the silicon monoxide stainless steel

combination was made after they observed that collodion shrank 5% after five minutes of

irradiation and that in a similar period 0.34 ym polystyrene spheres on collodion replica

on a copper grid could grow in size by 15% (0.007 ym). In that report the effects and

levels of beam current, contamination growth, and pumping rate were not known.

In the 1979 paper, the author reports using a new instrument with a shadowed carbon

replica grating of 2160 lines/mm. By private communication he reports that particles to be

measured are air-dried on the replica grating, evacuated to 10"5 Torr, and irradiated with

50 Kev electrons at magnifications of 7000X - 20,000X; the resulting photographic plate

shows particle images 1-4 mm in diameter against a background showing about nine lines of

the grating replica. The apparent diameters of the particle images and apparent spacings

of the grating are measured visually with an eyepiece magnifier to a precision of about

+0.02 mm. A range of from 70 to 300 particles are measured and the mean and standard

"deviation are calculated directly from the data. A typical standard deviation is +0.005 ura for particles in the range 0.1 to 1.0 ym, independent of mean size, and the standard deviation

is attributed wholly to the distribution in particle sizes, on the apparent premise that

the standard deviation of the measurement is much smaller than that of the particle size

distribution. In 1979, the mean diameter of the Dow LS-1028-E latex, previously measured

by Dow and found to be 1.099 ym, was remeasured by them and reported without comment to be

1 .192 um [Rll].

In the last few years, independent and sometimes very thorough electron microscope

measurements on polystyrene spheres and Dow latexes in particular have been reported by

various workers [A4, Cll, C20, C23, D3, D6, D20, H4], Of these, some data from comparisons

by Davidson and Haller [D3], Heard [H4], Dobbins [D21] and Davidson, et al . [D6] will be

examined in some detail later in this report. For the moment, two of the reports of work,

which like that of Bradford [B16], systematically investigated error effects in TEM

measurements of particle-size, will be described in brief.

Heard, et al

.

, measured mean particle sizes of nine Dow latexes and reported results

in a paper entitled "A Redetermination of the Diameters of Dow Polystyrene Latices" [H4].

They reported that they used a carbon replica grating, 300 A° thick, gold-palladium shadowed,

having 30,000 lines per inch (1181 lines per mm), and mounted on copper 200 mesh grids. To minimize radiation damage to the spheres, measurements were made at 100 Kev accelerating

voltage at the lowest beam current giving acceptable images with three second exposures.

To minimize contamination, a cold-finger stage was used. For 0.5 to 1 ym spheres, the TEM

magnification was 10,000 to 20,000X while for 0.3 to 0.8 ym spheres the magnification was 30,000 to 50,000X. A measurement at 12,500X on the screen gave 25,000X on the photographic

print, and on such a print the apparent diameters of images of latex spheres was 17 to 28 mm against an apparent spacing of 20 mm for six grating lines on the print. Diameters and

spacings for images on print were measured with a reticle to precisions of +0.2 mm.

26
Among other effects, Heard reported that fidelity of reproduction of the replica grid

was demonstrated by direct measurement (29,900 + 100 lines/inch measured for replica compared

to 30,000 quoted for the master by the manufacturer). In addition, there was no detectable

change in replica grating spacing on irradiation (<0.2% change in 10 min.), and no detectable change in sphere size on irradiation at normal beam currents. However, 1 u m spheres

decreased in size by 2% in the first minute and 5% in 10 minutes at beam currents of four

times normal, corresponding to magnifications of twice normal; the decrease was about half

as much for 0.1 ym spheres.

In Heard's measurements of particles against replica gratings and against other

particles in a ratio technique, it was quoted that there were estimated total uncertainties

(lo) of +0.008 ym for 0.365 ym particles up to +0.016 ym for 1.16 ym particles. These

variations were attributed wholly to the measurements and not at all to the particle

population.

Davidson and various co-workers, in allied papers [D2-7], performed measurements on various polystyrene latexes (including Dow latexes) using various techniques, including

light-scattering and electron microscopy. One paper by Davidson and Haller, entitled "Latex

Particle Size Analysis: V. Analysis of Errors in Electron Microscopy", deals systematically

with the subject [D3]. Among the effects experimentally measured were those due to grid

material, ion exchange of the latex, vacuum conditions, magnification variation over time,

method of measuring the photographic images including filar eyepiece and spot-projecting

image analyzer, and image reproduction by contact print and enlargement.

Among other conclusions, Davidson and Haller decided the following: neither grid type

nor ion exchange "had much effect" on measured diameters; the effects of irradiation and

pumping rate were negligible if micrographs were made within one minute of initial beam

exposure; changes in pumping rate could cause apparent particle diameter to increase,

decrease, or remain constant with beam exposure; sizing of images by means of a filar

micrometer eyepiece gave diameters "very close to those from other methods"; the projectedspot image analyzer (Zeiss TGZ-3) gave results comparable to the filar if enlarged

transparencies were counted which showed the latex particles as black dots against a white

background; and if negatives were counted directly (white dots against black background),

the diameters so obtained were often lower than those obtained by filar counting. Finally,

it was concluded that "the magnitude of the various errors in electron microscopy of

polystyrene latex for sharp negatives" is at the 90% confidence level +3% in magnification,

+3% on average diameter of sample, +3% for filar micrometer sizing, +5% for Zeiss TGZ-3

sizing of 5 mm black spots, and the combined total error is approximately 5% for filar

counting and 7% for the projected-spot counting.

On the important issue of changes in the diameter of polymer latex spheres during

exposure to the electron beam in an electron microscope, the evidence is not overwhelming

but seems to indicate that polystyrene latex spheres can be measured with a negligible (but

unspecified) change in size if the exposure is at a low beam current and brief. Early on, Davidson and Haller [D3] reported that the apparent size could increase, decrease, or remain

the same depending on pumping rates; they speculated that a no-change situation corresponded

to a balance between diameter decrease due to mass loss and diameter increase due to con- tamination deposition. Talmon and Miller [Tl] reported that while "soft" latexes, such as benzene-plasticized polystyrene, required special techniques such as an 85 °K cold stage

and embedding between polyimide sheets, "glassy" latexes such as unplasticized polystyrene

could be measured well just by spraying, drying, and normal handling. Similarly, Claver

and Farnham [C20], while reporting decreases in diameters of polystyrene spheres of from 2 to 9% upon intense exposure for many minutes, conclude that "a maximum (mass) loss from

polystyrene is negligibly small for all but the most precise measurements". Finally,

Heard, et al . [H4], in the most explicit statement of the magnitude of the effect for

normal exposures lasting up to ten minutes, report a "negligibly small" decrease in size

with an upper limit of 0.2% for 1 ym spheres and 0.1% for smaller ones.

Five potential sources of significant systematic error are apparent in the reports of

electron microscope measurements of latex spheres drawn from liquid suspension as described

above. First, there is the change in particle diameter due to drying in air and subsequent

evacuation. Second, there is the decrease in particle diameter due to loss of mass due to irradiation by high energy electrons. Third, there is the increase in particle diameter

27
due to deposition of contamination by the electron beam. Fourth, there is the determination

of the point-to-point magnification of the electron image. And finally, there is the matter

of properly measuring the image corresponding to that determined by geometrical -optics.

Each of these potential sources of error would need to be investigated and managed in order

to obtain definitive measurements from the technique.

3.B.2. Light-Scattering

As a candidate technique for direct measurement of particle sizes, especially highly

spherical monosize particles in liquid or aerosol suspension, light-scattering in one or more of its many forms has conspicuous advantages. For example, it can measure such

particles in their own environment, can average instantaneously over a great number of

particles, and via a wel 1 -devel oped theory, can yield dimensional information without

requiring comparison to particles of known size. Light-scattering, however, is not one

thing. Rather, in contrast to the technique of electron microscope measurements of particle

size, light-scattering measurements encompass a wide array of seemingly unrelated techniques

and a complex of theoretical -analytical models. This report will only touch on some of the

instruments and theoretical treatments in order to provide some context for the intercomparison of results and a discussion of the potential calibration techniques.

a. Light-scattering instrument systems

A major reason for the diversity of techniques and theoretical treatments of lightscattering as applied to particle size measurement is the nature of light and the number of

its properties capable of carrying dimensional information about the particle which scattered

it. These properties include amplitude (or intensity or photon count), phase, frequency

(or wavelength) , direction of polarization, and direction of propagation. In general the

technique is to deduce particle size from the dependence of one of these properties upon

a second one which varies as the remaining are held fixed or ignored. Some of the major

types of light-scattering techniques for particle size measurements based on this type of

independent-dependent variable categorization include:

° intensity-vs-direction of propagation measurements (referred to as angular scattering); some variations of this classic technique and their capabilities will be discussed

shortly.

° intensity-vs-phase type measurements, which includes laser interferometry [Rl,

R2]; holography with one-wavelength [HI 6, K9] or two-wavelength [M8] illumination in normal wide-angle or forward-scatter [S9] or with computer-synthesized holographs

[T6]; and array-diffraction [F3, P2].

0 f requency-vs-direction type measurements, which includes various Doppler shift

techniques [C3].

° photon count-vs-time measurements, which includes various photon correlation techniques [C12, G10, H14, L13].

° intensi ty-vs-presence/absence of particles, which includes the optical extinction

and turbidity techniques [D15, 18, 19, 21]; this technique involves measurement in the forward-direction with scattering as one of the attenuation mechanisms for the

change in intensity, but it is distinguished from forward (or near-forward or low-angle)

scattering [B12, D15, Lll, S6] since the unscattered beam carries the information;

0 intensi ty-vs-microscope quasi-imaging, including interference contrast microscopy

[S8], dark-field microscopy [D2], and array-counting [K15, R3] techniques.

Among these various light-scattering techniques with demonstrated capabilities for

measurement of particle size to uncertainties in the range 100 down to 3 nm, there are, for

example, angular-intensity techniques to be discussed below, laser-Doppler techniques (with

reported uncertainties of about 1% for 5-15 um particles [eg. B17], photon-counting

Rayleigh-spectrometer techniques (with reported uncertainties of 0.003 um particles [H3a]),

and, for measurements of single particles, deviation techniques [eg. C24, Ml, W17]. Of

28
these, angular intensity scattering is most interesting since it: (1) can be applied to collections of particles in suspension; (2) is suited to dimensional measurement of highly

spherical, homogenous particles in the range 1-10 um as chosen for initial standard reference

particles; (3) can be implemented and theoretically treated in a straight-forward convenient

way; and (4) can also add to fundamental understanding of electromagnetic scattering

phenomena.

Angular scattering, which is the classic technique of light scattering for particle

size measurements involving i ntensi ty-versus-angl e, is applied with various ways of extracting dimensional information from the angular intensity distribution, that is, from the

scattering pattern. For example, early work on latex spheres used 90° scatter, polarization ratio, extremum location, dissymmetry ratio, and spectral transmittance to obtain

dimensional information [D19]. This pre-laser work achieved agreement among mean diameters

as measured by the various techniques which could often be considered to be good (each

within, for example, 0.01 or 0.02 ym of an average) and was occasionally strikingly good

(for examples, mean diameters of a latex by the four methods of 0.808, 0.802, 0.803, and

0.805 um) [D19].

The technique of angular scattering has been applied continually with refinements of sources (from mercury lamps [D19] to HeNe CW lasers [Gl] to wavelength-tunable dye lasers

[A7]), detection, and data processing techniques [Kl , K2]. Kratohvil, who has published

continually over the period and maintained contact with the literature, reviewed lightscattering measurements in general in 1964 [K13] and, along with original measurements

[Kll , K12, K14, W6, W7, W8], has compared the results of some latex sphere diameter

measurements by the variety of light-scattering techniques [K10]. Gebhart, et al . have

discussed the various light-scattering instruments capable of high-resolution, direct

measurement of particle size which they describe as particle-size spectrometers [Gl], while

Willeke and Liv discussed various light-scattering instruments which are usually limited to comparison measurements, and they describe as optical particle counters [W12]. Most of the

particle counters are fixed angle, i ntensi ty-ratioi ng devices in which the design choice is to gain simplicity and speed by trading-off angle-scanning.

Angular-scattering measurements on standard spherical particles have been made using

commercial and laboratory prototype instruments which scan various segments of the angular

distribution. More or less full circle devices are referred to by Marshall, et al . [Ml]

and Powell, et al . [R10]. That reported by Marshall has been used to scan continuously

over the angular ranges 5°-175° and 185°-355° with a 2° angular acceptance at the detector

[Ml], while that reported on by Powell has been used to scan over an assumedly large part

of the full circle at 1° intervals with a 5° acceptance [R10]. Angular-scattering instruments which scan more-or-less the half circle are those used or described by Wyatt [W15,

16], Kerker, and Powell [R10]. In the devices of Wyatt and Kerker, which are from the same manufacturer and differ only in that the former measures electrostatically-levitated

individual particles [W15, 16] while the latter measures- particles in suspension, the

scanning range is typically 8° to 172° with a 2° acceptance. Powell's instrument was used

in a modified form to scan from 45° to 115° at 5° intervals with a 5° acceptance [R10].

For each of these five angular-scattering instruments, the size of the particle doing

the scattering is determined from a comparison of the observed i ntensi ty-vs-angl e distribution with a theoretical distribution calculated for a specific particle size-index of

refraction combination. In essence, it is a two-parameter fit of observed-vs-calcul ated

curves. As an example of a fast measurement and achievable results, the Gucker instrument

[Ml, R10] uses an ellipsoidal mirror for collecting the light-scattering by a particle at its focus and a second moving mirror to scan 360° in 20 msec; uncertainties in the measurement of the diameters of individual particles ranging from 0.3 to 11 ym in size are given

as 0.5 to <1%; the resulting mean diameter for a Dow (LS-1028-E) latex is given as D

= 1.189 ym with a = 0.008 ym and an index of m = 1 .588.

Both types of angular intensity light scattering techniques, i.e., scattering from

single levitated particles and scattering from collections of particles in suspension, can yield values for the distributions of particle size about a mean diameter. In singleparticle scattering methods such as in Ref. C24, particles are measured serially and a mean diameter and distribution about the mean calculated from individual measured diameters.

In scattering-from-suspensions methods: (1) a mean diameter alone can be determined by

29
a single best-fit match between an observed angular intensity pattern and one calculated

for one diameter of sphere, or (2) a mean diameter and a distribution can be determined

by a fit between an observed pattern and a pattern calculated as the average of a number

of individual patterns for different size spheres [see, for example, Ref. Kll, K12].

Potential sources of measurement uncertainty in angular intensity light scattering

determinations of particle size include the effects of

(1) deviations from sphericity of individual particles;

(2) deviations of the index of refractions of individual microscopic particles from the

known value for the bulk material;

(3) deviations in the wavelength of the light used from the assumed value;

(4) errors in angle measurement;

(5) errors in intensity measurement;

(6) finite acceptance angles detector;

(7) deviations from planarity of incident light;

(8) deviations from monochromatici ty of incident light; and

(9) fundamental light and limitations of Mie theory.

Quantitative determination of the systematic effects of these factors require extensive

analysis which is beyond the scope of this work. Estimates of variability in results have

been made, however, by numerous authors; estimates of the magnitude of systematic effects

can be made, for example, by intercomparisons of results from various laboratories, such as

in Ref. RIO and in this work. By inference, it appears that systematic errors of the order of

1-3% for the 1 ym particles can be encountered, while overall uncertainties of 1% (including

observed variability with estimates of systematic errors) appear to be attainable.

b. Applicable theories of light-scattering

The interaction of light with real microscopic particles is a complex physical phenomenon which can be described mathematically only in restricted, approximate forms. As applied

to particle size measurement, basic theory usually treats light which is elastically scattered from, at most, one homogenous dielectric sphere. Different theoretical models are used to quantitatively describe the behavior of the light scattered from such a spherical

particle and to extract the dimensional information about the particle. The choice of

models depends on the dimensions of the real particle relative to the wavelength of the

light (x = 2 Tra/X) and on the effective index of refraction of the particle relative to the medium (m = n particle/nmedium )

.

In the limit of very small particle diameters (0<<x) and the limit of very large particle

diameters (D>>A), the relevant models treat them as geometrical objects which do not interact

with the electromagnetic wave. Within each of these limits, the next order approximations,

for particles nearer in dimension to A, add phase-shifts which depend on the index of

refraction. For intermediate size particles, the most accurate theory treats the complex

interaction of the dielectric sphere with the electromagnetic wave which describes the light.

Various elements of the five basic models have been described by, among others, Allen

[A3], Born and Wolf [Bll], Chu [C12], Deirmendjian [D16], Gebhart [Gl], Kerker [K7], Van de

Hulst [V4], and Willeke [W12], from whom this discussion is drawn. The names associated

with these various models vary according to the vagaries of history and the inclinations

of workers reporting (see Kerker [K7] for a discussion).

Rayleigh -scattering applies to very small particles such as air molecules. In terms

of the size parameter x and the relative index m, the approximation applies for

if)
(27) (m-1 ) -> 0

(28) x = 2ttt < o.3.

X

In this approximation, the particle is treated as a point dipole with a dipole strength

proportional to particle volume. From Van de Hulst [V4], the intensity I at angle 9 is

given by

(29) I, = |a|2 2tt 4 (l+cos

2 6)

6 Xm 2Z4

where a is the volume polarizability, z is the distance from particle to detector, and X m

is the wavelength in the medium. For homogenous spheres:

(30) q

= 3(m2 -l) v (m2+2) 4

which for the condition(m - l) -» 0 reduces to

< 31 > a = 2(m-l) v

Since v ~ r 3 and I ~ a?,

(32) I e ~ r6(l+cos2e)

where the angle-dependent and angle-independent terms correspond to two polarizations. In Rayleigh scattering, the intensity distribution is symmetric about 90°.

Rayleigh-Gans (or Rayleigh-Debye or Rayleigh-Gans-Debye) scattering applies to particles somewhat larger than air molecules, such as macromolecules. In this approximation, the

dipole scattering of the Rayleigh approximation is modified to take into account phase-shifts

of the differential volume elements over the finite volume of the sphere. Here the con- straints are relaxed somewhat and the approximation applies to either:

(33) small spheres where D << A

or a particle with an index close to that of the medium:

(34) (m-1) -0,

while the overall constraint is maintained:

(35) 2tt3

( m_i ) << i . X

According to Van de Hulst [A3, V4], the intensity varies in the form:

31
(36)

where

kV(m-l) 2

8itZ' (siny-ycosy) (l+cos 2

6)

(37) 2 TT D Am

sin 9 and k = *L

7 Am

Here the scattering intensity is asymmetric about 90° and shows maxima and minima. At the

other end of the size spectrum are large particles, where D >> A is the basic diffraction

scattering and its phase-shift modification.

Fraunhofer diffraction applies to particles large in comparison to the wavelength,

D >> A, and treats the particle in the limit as a circular disc. The intensity pattern is

described by the familiar Bessel function equation of the Airy pattern:

(38)

I ~

J-j(xsine)'

xsine

where again x = 2iTa/A m

. The intensity shows maxima and minima, with the first zero of

the function at sin = 1.22 /2a.

Anomalous diffraction applies to particles large in comparison to the wavelength D>A,

but not at the limit of geometric diffraction. In this approximation:

(39) x >> 1

while

(40) (m - 1 ) + 0.

Phenomenologically, the model treats a transparent sphere as having an incident ray which

passes through the sphere without reflection or refraction but has a significant phase

shift because of the long path length through the sphere. The total scattered field results

from the interference of the Fraunhofer-contribution and the forward-scattered phasedelayed contribution.

Resonant scattering occurs when the incident electromagnetic wave physically interacts

with the material of the scatterer in such a way so as to produce in the scattering properties

maxima and minima which cannot be accounted for by diffraction and interference phenomena

alone. The current theory best suited to handle this situation is one variously described

as Mie [V4], Lorentz-Mie [RIO], or Debye [K7].

Mie theory treats plane electromagnetic waves incident on and scattered from homogeneous dielectric spheres described by a size parameter x = 2-n-a/A and a complex index of

refraction m. Scattered fields are determined from solutions of Maxwell's equations with

boundary conditions consisting of continuity of field vector components at mathematical

discontinuous boundaries [K7]. The resulting expressions for the angular intensity distributions for the two polarizations are:

(41 ) i] (x, m, 0) i 2 (x, m, 9)

32
These are infinite series whose terms are functions of spherical Bessel and Le Gendre

polynomials. The response R of a light-scattering instrument in terms of f-j, i2, f

s P)

(the source spectral emission function), f(j(x) (the detector spectral sensitivity function),

fq(9, tfc ) (the source-particle-detector geometry function), and k (a scale factor) is:

While classic texts such as those by Born and Wolf [Bll], Kerker [K7], and Van de

Hulst [V4] show the behavior of scattering functions from Mie theory calculations for

many values of the parameters m, 6, A, and x, particle size measurements based on such calculations have serious practical limitations. First, they apply only to spheres;

second, they apply solely to collections of identical spheres; third, they predict angular

intensity from known index and size parameters, not vice versa; and finally, they require

extensive computer calculations to numerically evaluate the series.

As a result of this latter condition, particle-size determination via Mie theory has

been done in a number of ways: the most common being manual -visual matching, with interpolation, of experimentally-measured intensity curves against theoretical curves such as those in textbooks [V4] or instrument-manufacturers catalogue of curves [W5]: similar

matching against individually calculated curves with best-guess input values of m and x: and computer best-fit determinations [RIO],

In the evaluation of the results of the particle size determination via the Mie

calculations, a number of factors have been pointed out and examined as sources of systematic

error. An important source is the effect of particle non-sphericity and this subject has

been extensively treated theoretically and experimentally for the cases of ellipsoids,

oblate and prolate spheroids [A6, L3, L5, L7, C14, C16, W16]. The effect of a finite

width of size distribution [W5] and the assumed shape of the distribution [W3, Cll] has

been examined, while an effect of finite detector acceptance angle has been calculated and

compared using experimental results [RIO].

3.B.3. Automatic Counting (and Sizing) of Particles.

a. Particle counters

The capabilities of automatic liquid-borne particle counters for providing fast,

explicit histogram measurements of particle sizes over ranges of about 5 ym up to 100 ym

makes them attractive as candidates for comparison calibrations of standard particles such

as latex spheres and glass microbeads. Both types, optical and electrical -resistance, have

comparable basic capabilities although they differ significantly in specifics. Commercially

available instruments are described by Allen [A3], Davies [D8] and Willeke [W10].

Electrical-sensing-zone (or electrical resistance) particle size instruments, based on the original device by Coulter [C25], measure an effective particle volume in terms of a change in resistivity of an electrolyte from which some fraction is displaced by the

particle. In a first-order model [A3], the change in resistance due to the presence of a particle in the orifice of the device can be expressed in terms of the resistivities of the

electrolyte fluid e and the particle p, the cross-sectional areas of the aperture A a and

the particle Ap, and the effective fraction of the particle dimension e subtended by the

aperture. This change in resistance is given by [A3]:

(42) R(m, x, q, (j), a,) = kf s (A)fd (x)f

g

(e, <|>)

x (i,(m, 0, x) + i 2 (m, 6, x)) .

(43)

33
According to Allen, terms p e / Pp can be neglected since, in practice, the response is

independent of the resistivity of the particle. The equation above then reduces to

I 44 ' 4rW_V|x (Ad

61) x 1 - V

or

R ~ (particle volume) x 1 •

The magnitude of the deviation from a straight volume proportionality is shape- and

size-dependent, causing a 6% effect for rod-shaped particles as well as a 5.5% error

for large spherical particles (Dp >^ 0.4 D aperture) [A3].

Characteristic precisions, attributed to such instruments by their manufacturers and

evidenced by round-robin intercomparison [ASTM Circular C690], include repeatabil ities of

+1% (at 95% confidence, for all size levels) and reproducibilities of +3%. As mentioned

earlier, the literature on the technique, its systematic effects, and error sources is

extensive, with Al len 's treatment [A3], the manufacturer's technical literature including

the Coulter, Inc. bibliography, and other sources [S10, D8-13], providing input.

Optical particle counters vary in the way they measure particle dimensions, although

many are characterized as measuring some projected area [Gl , D81. Using more than fifty

1 iterature citations, Willeke and Liu [W12] identify laboratory prototype and commercial

devices, discuss them in terms of the effects of angular geometries, theoretical response

calculations, calibration techniques, sampling efficiency, particle shape and refractive

index, counting accuracy, coincidences, pulse processing, and size resolution.

In general the response R of most optical counters can be described formally as an integral over the instrument geometry, its spectral response f

s and the Mie scattering

functions and their variables as described in Section 3.B.2.b. such that:

(46) R(m,x) = JJJ

[kfs U)fg

(e, <j>)

x (i,(m, 6, x) + i 2 (m, j, x))]d6d<WA.

Resulting theoretical response functions for specific optical counters are given in graphs,

discussed, or cited in the literature by Willeke [W12]. Two instruments described by

Gebhart [Gl] are relatively representative of the basic capabilities. One instrument,

designed for particles small compared to the wavelength of light, uses a laser source and

near-forward collection described as giving a volume-equivalent size independent of

shape but dependent of the index of refraction in a scaling-factor type behavior; the

second instrument, for particles large in comparison to wavelength, uses a white

light source and low-angle collection described as giving a projected area size independent

of both shape and index of refraction. A major reason for using white light is to average

out the theory-based oscillations in instrument response to monochromatic light which can

give apparently multivalued particle size [Gl , B12]. The laser instrument is described as being able to measure particles over the size range 0.05 \im to 0.7 ym with an uncertainty

of 2%; the white light instrument's range is given as 0.7 to 6 m [Gl]. A new addition to the field is a commercial optical aerosol size instrument which masks and measures segments

of the Fraunhofer diffraction pattern to obtain second, third and fourth power of radius

dependence [W18].

Some of the more apparent potential sources of systematic error in flow-through particle

counters as reported in the literature are common to both optical and electrical -sensing

types. Among these are errors in accurately counting and characterizing the whole particle

34
population distribution due to, for example, more than one particle in the sensing zone (coincidence), electronic noise, preferential sampling of sizes, non-discrimination of

debris or agglomeration, finite-width size-interval channels, and a fine size lower detection limit.

Other potential sources of systematic error in flow-through counters are specific to the type. Among those for electrical sensing instruments, for example, are finite size of

particle relative to aperture dimensions and pulse-shape dependence on wal 1 -proximity

effects. Potential error sources specific to optical counters are possible non-unique

response as a function of particle size and unaccounted for dependence on particle shape or index of refraction. In comparisons of measurements by the two devices, there is the

difference in vol ume-versus-area (or other power of radius) dependence. Some of the more apparent sources of systematic error are reported in the literature.

b. Image analyzers

Image analyzers, as adjuncts to optical or electron microscopes, can provide some degree of automatic counting and sizing of the magnified images from the microscopes. Like

flow-through particle counters, they allow explicit histograms of particle size distributions to be derived from counts of individual particles of measured sizes. There are two major types of image analyzers, and they are distinguished by their basic method of measuring

image size and the degree of automation in the process; in the first type of image analyzer,

operator judgment is the basis of size measurement, while in the other type, the decision

is machine-made.

Projected-spot image analyzers are machine-assist devices which project a variablesize light spot onto a photographic print or negative and record the aperture size

corresponding to the one which the operator decides gives the best fit between the size of

the projected spot and the photographic image of the particle. The device is a conventional means of semi -automatical ly sizing and counting images of particles on TEM plates or optical

microscope photos and has been applied to the sizing of latex spheres [A5, B3, C3, D3].

The second type of image analyzer is a machine-decision device and includes both

digital computer-based and analog circuitry-based image processing. For either one, there

are two types according to whether the image produced by the microscope is measured directly

or whether the image is photographed and the photographic image is measured. Image analyzers

of each type are available commercially, and their application to particle size measurement

has been discussed in the literature [A3, Dll-14, S10],

The relationship of image analyzers of various types to each other and to other ways

of measuring the size of microscope images of particles is shown in Figure 2. Starting

with particle, (A), as an object, the figure shows that the image, (B), produced by the

electron or optical microscope can be processed one of three ways. In an optical microscope,

the image can be viewed (C) by eye directly and the size of the light image measured

with a visual eyepiece such as a reticle, a movable cross-hair filar, or an image-splitting

(shearing) device. It is also possible to photograph the light image (D) and scan it by

a photodetector (E). In an electron microscope, the electron beam image can be recorded

directly onto a photographic plate, as in a TEM, collected to produce an image on a CRT

which is in turn photographed (D), or collected for electronic processing (E).

Whether the images are recordings of the light in an optical microscope, the electrons

in a TEM. or the light from the CRT screen of an SEM, photomicrographs (D) can be analyzed

in one of two ways. They can be viewed (F) under low-power optical magnification and

measured as in (C), a project-spot can be matched to the image size as discussed previously,

or the photographs can be reimaged and scanned with a photodetector (G). A vidicon as a detector can be used to produce a TV image which has a movable electronic-crosshair for

visual settings (H), or a vidicon, together with an apertured photomultipl ier, a diode

array, or other photodetector can be used to generate digitized or analog waveforms for a machine-based judgment of image size (I). This process, which eliminates the operator's

subjective judgment of image size, can be applied directly to the original microscope

image (as opposed to the photographed image), as in E to I

.

35
Figure 2 . Alternative Ways of Mesuring the Size of an Image

A. Extended-Object

Imaged by Optical or Electron System

to produce

B . Primary Light (or Electron) Image

which is processed one of three (or two) ways

, Viewed by Eye

which measures

Light Image Size

by Visual Judgment

(Reticle, Filar, or

Ima ge-Shear

)

Photograph

which is

processed by one of

two ways

r E. Photo- (or Electron-)

Detector

which measures Light

(or Electron) Image

Size at GeometricThreshold Levels on Intensity Profile or

an Abritrary Level

Viewed by Eye

which measures Photograph Image

Size by Visual

Judgment

a. Reticle

b. Filar

c. Image Shear

d. Projected-Spot

Matching

G. Scanned by PhotoDetector which

processes the Re - Imaged Photograph

Image by one of two ways

I

H. Viewed by Eye

which measures

TV Image Size

by Visual Judgment

(Electronic CrossHair)

I . Waveform Analysis

which measures Image - of -an- Image Size by

Machine Judgment on

a. Analog Waveform

b. Digitized Image

36
Systematic errors related to different edge-location criteria and related effects were discussed earlier, and image-analyzers are also susceptible. Since the effects depend on the relation of the edge-region to the image as a whole, they can be relatively independent

of the microscope magnification and are observed over a range of particle sizes. For 3 ym latexes, the manufacturer reports that TEM measurements using a projected-spot analyzer

differ by about 0.5 ym or about 20% from those obtained using a reticle directly on the TEM

plates [B3]. For 0.25 ym latexes, another manufacturer's laboratory reports difference up to 0.05 ym or about 20% for the same two techniques [D3], depending on the size and polarity

(clear spot on opaque background or vice versa) of the images processed by the analyzer.

Similar systematic differences among filar, image-shearing, and TV-microscope systems, as well as a discussion of polarity-dependence, have been reported for the related case of

planar objects, where differences on the order of 0.25 ym for measurements directly on the

light images of 1 , 3, and 10 ym objects were observed [Sll, S12].

Two methods of overcoming the arbitrariness of such systematic differences have been

reported. For TEM measurements on the 0.25 ym latexes, the reticle measurements were reported

as producing the best agreement between the TEM results and those from other unspecified

methods [D3]. For optical microscope measurements on clear and opaque planar objects, no one optical method other than photometric scanning using, for example, a theoreticallypredicted threshold on the image for object-size determination, was found acceptable and

free from large systematic error [N5, Sll].

ooo

This brief examination of automatic particle counting techniques, especially those of

flow-through counters, follows a similar examination of light-scattering and electron

microscopy techniques. Each has strengths and weaknesses which complement the other two. Taken together, the three provide an attractive scheme for primary and secondary calibration

of microscopic particle size reference materials, especially standard spherical particles

such as polymer and glass microspheres.

Electron microscopy with its unambiguous, high-resolution, high depth of focus imaging, can yield precise and potentially accurate dimensional measurements on individual particles,

in vacuo , and explicitly differentiates among particles of different shapes and morphological

composition. Light-scattering can determine mean size of narrow-distribution spherical

particles in their original liquid environment, averaging over many particles more or less

instantaneously. Flow-through counters can provide histograms of distributions as verification of the validity of the assumptions made in light-scattering as well as rapid comparison

calibrations of particles of unknown size against particles of known size as determined by

electron microscopy and light-scattering taken together.

With this potential complementary relationship of electron microscopy, lightscattering, and flow-through counting as a back-drop, Part 4 of this report presents

reported intercomparison measurements by these techniques on polymer spheres. As was noted in the introduction to this report, in order to best understand the behavior of a measurement technique itself, the object-to-be-measured should be as simple and lacking

ambiguity as possible. Polymer spheres are in general highly spherical and therefore

susceptible to dimensional characterization by a single number, the diameter; further,

the distribution of sizes in a population can be very narrow (1%); and the spheres are assumedly dimensionally stable under a variety of handling conditions and over time.

Further, the latex spheres marketed by Dow [B2, B3] over a period of two and nearly three

decades have been measured using the same basic technique and even the same people [B16,

RIO]. This history has provided a metrological baseline for detailed comparisons of

measurements over a range of particle sizes from <0.1 ym, most often to 1 ym, but ranging

up to as much as 100 ym. This next section looks at the results of measurements on these

materials, specifically the mean particle size of a number of Dow latexes as determined by

different techniques. From these data, conclusions are drawn about the techniques and the

materials themselves, and these conclusions are summarized in the fifth and final section

of the body of this report.

37
4. I NTERCOMPARI SON OF MEASUREMENTS

This section of the report summarizes and discusses results of particle-size measurements by a number of techniques on polymer spheres, primarily Dow latex spheres, over a range of sizes from 0.08 ym to 3 ym or more. In most cases, the results are given in

tables of mean diameter measured by one technique versus mean diameter measured by a second

technique. The second technique is usually that of electron microscopy and is performed

by the manufacturer of the polymers. Also given in most tables are the incremental- and

percent fractional-differences between the apparent diameters measured by the different

techniques. In order of presentation, the tabular data deal first with an overviewcomparison of results for six latexes which span the range of sizes, then with flow-through

counter results, followed by light-scattering results, and finally with electron microscopy

measurements.

A. Comparisons of Latex Particle Measurements.

4.A.1 Specific Results Compared

Polymer spheres, especially Dow latexes, have been measured independently by various

techniques and workers. They have especially desirable properties, which include a high

order of sphericity, narrow size distribution, and, in many cases, a nominal size measured

by the manufacturer, quoted, and assumedly accurate to hundredths or even thousandths of a micrometer (the implied accuracies are in range 0.01 to 0.001 ym) [B16].

In order to provide some estimate of the scatter among results by different techniques,

Tables 6 through 11 show redrafted published compilations of mean diameters of six Dow

latexes as measured by various techniques. The measurement methods include those of electron microscopy, light scattering of a number of types, and other specific techniques as indicated. Inspection of the individual tables indicates a relatively wide variation

among reported values. As a basis for comparison without selecting or excluding values,

the following table gives (in rounded-off numbers) the average of the values in each table,

the number which constitutes the average, the RMS (root-mean-square) average deviation in ym and percent, and the range of values in ym and percent.

Mean Number in Average Range of

Val ue Average Deviation Val ues

(ym) (ym) m (ym) m

3.02 12 0.048 1 .6 0.08 2.6

2.70 5 0.013 0.5 0.03 1.1

1 .18 16 0.058" 4.9 0.26 22 0.80 9 0.033 4.1 0.09 11 0.025 16 0.008 3.2 0.026 10

0.078 6 0.005 6.4 0.014 18

Some general observations about the data in Tables 6-11 can be made based on the

summary table, above. First, for the four latexes with mean diameters of less than 1.2 ym,

the average deviation (which describes the spread of the results from the various techniques) is on the order of 5% and the range is on the order of 15%; as for random variations, the range of ten measurements here is about three times the average deviation

[Appendix F]. Second, while there are large variations from the behavior for the smallest

and largest latexes, the average deviation is very comparable to the standard deviation of

the particle distributions for the latexes (as determined by electron microscopy measurements

of the manufacturer, see p. 7 of the report). Third, a cursory inspection shows no readily

apparent systematic relationships as, for example, between the electron microscopy and light

scattering values. Finally, the data alone does not suggest which if any method is more

def ini ti ve.

Table 12 shows a compilation of some other latexes for which one or more measurements besides the manufacturer's have been reported. Again, no readily apparent

systematic behavior is present. Later, it will be seen that where published data has

38
Table 6

Diameter of Dow Latex LS-1358-38 Spheres

Measured by Various Workers [Ref. K10]

Measurement Method Mean Diameter (ym)

Microscopy

Electron 2.958a 3.075b 3.036C

Optical (See Array)

Angular Light Scatter

Indiv. particles 3.01

1

e (Dry)

Collections

Light Scatter Other 2.96f 2.975f 3.02 d

Flow-Through

Resistance

Light Blockage

Light Scatter 3.128<=

Array

Length-Count 3.00^ 3.02^ (Dry)

Diffraction 3.03& 3.04f (Dry)

Centrifuge

Spiral

Ultra

Sedimentation

Turbi di ty/Exti nction

a. Dow quoted Ref. K10

b. Krieger, O'Neill 1968 [Ref.KlO]

c. Davidson, et al. 1967 [Ref. D6]

d. Wallace, Kratohvil [in Ref. W6]

e. Marshall, et al. 1976 [Ref. Ml]

f. Robillard,Patitsas 1973 [Ref. R5]

39
Table 7

Diameter of Dow Latex (LS-642-6) Spheres

Measured by Various Workers [Ref. R4]

Measurement Method Mean Diameter (pm)

Mi croscopy

Electron

Opti cal 2.682*(See Array Count)

Angular Light Scatter

Indiv. particles

Collections 2.714

2.696

Light Scatter Other

Flow-Through

Resistance

Light Blockage

Light Scatter

Array

Length-Count 2.708 (Dry)

Diffraction 2.688 (Dry)

Centrifuge

Spi ral Ultra

Sedimentation

Turbi di ty /Extinction

* Attributed to Dow

40
Table 8

Diameter of Dow Latex LS-1028-E Spheres

Measured by Various Workers [Ref. RIO]

Measurement Method Mean Diameter (pm)

Microscopy

Electron l.ioa 1.19a i.igb 1.17c i.ied l.26e

Optical

Angular Light Scatter

Indiv. particles 1 . 20^ 1.209 1.19h Collections 1.201 1.21 J

Light Scatter Other 1.20J

Flow-Through

Resistance

Light Blockage

Light Scatter 1.21 b

Array

Leng th-Count

Diffraction 1.20k

Centrifuge

Spiral 1.22e

Ultra 1.00 1

Sedimentation

Turbi di ty /Extinction

X-Ray Scatter

a. Bradford 1979 [Ref. RIO]

b. Davidson, et al. 1967 [Ref. D6]

c. Porstendorfer 1971 [Ref. RIO]

d. Heard, et al. 1970 [Ref. H4]

e. Stober, Flaschart 1971 [Ref. RIO]

f. Phillips, et al. 1970 [Ref. RIO]

g. Gucker, et al. 1973 [Ref. RIO]

h. Marshall, et al. [in Ref. Ml]

i. Wims, Meyer 1972 [Ref. RIO]

j. Rowel 1, et al. [Ref. RIO]

k. Bierhuizen, Ferron 1975 [Ref. RIO]

1. Van den Hul., Vanderhoff 1971

[Ref .RIO]

41
Table 9

Diameter of Dow Latex 449E Spheres

Measured by Various Workers [Ref. C23]

Measurement Method Mean Diameter (pm)

Microscopy

El ectron

Optical

0.796a 0.777b Q.765C 0.850d

Angular Light Scatter

Indiv. particles

Col lections

0.784e

0.797e

0.764e

0.773f

Light Scatter Other

Flow-Through

Resistance

Light Blockage

Light Scatter 0.849C

Array

Length-Count

Diffraction

Centri f uge

Spiral

Ultra

Sedimentation

Turbi di ty/Exti nction

X-Ray Scatter

a. Attributed to Dow e. Cooke, Kerker 1973

b. Robbins, Jizmagian 1966 f. Kratohvil, Wallace 1973

c. Davidson, et al. 1967

d. Cooper, Parfitt 1968

42
Table 10

Diameter of Dow Latex LS-057-A Spheres

Measured by Various Workers [Ref. K10]

Measurement Method Mean Diameter (urn)

Microscopy

Electron

Opti cal

Angular Light Scatter

Indiv. particles

Col lections

Light Scatter Other

Flow-Through

Resistance

Light Blockage

Light Scatter

Array

Length-Count

Diffraction

Random Diffraction

Centrifuge

Spiral

Ultra

Sedimentation

Turbi di ty/Exti nction

X-Ray Scatter

a. Bradford 1955 [Ref.B16]

b. Dobbins 1966 [Ref.D20]

c. Davidson, et al. 1967 [Ref. D6]

d. Davidson, Haller 1974 [Ref. D3]

e. Kratohvil, Wallace 1970 [Ref.K12]

f. Querfeld, et al. 1972 [Ref.KlO]

g. Dezelic, Kratohvil 1961 [Ref. D19]

0.264a 0.262b 0.262C 0.245 d

0.242e 0.245f 0.2459 0.25^

0.2381 0.2441

0.248J

0.245 - 0.259k 0.2491

0. 254m 0.248"

h. Jennings, Plummer 1968 [Ref.KlO]

1. Davidson, et al. 1971 [Ref.D5]

j. McCormick 1964 [Ref.KlO]

k. Bateman, et al. 1963 [Ref.KlO]

1. Dezelic, et al. 1963 [Ref.D18]

m. Bonse, Hart 1966 [Ref.KlO]

n. Brady, Gravatt 1971 [Ref. K10]

43
Table 11

Diameter of Dow Latex LS-040-A Spheres

Measured by Various Workers [Ref. D3]

Measurement Method Mean Diameter (win)

Microscopy

Electron

Optical

0.088a 0.078b

Angular Light Scatter

Indiv. particles

Col lection 0.076C

Light Scatter Other

Flow-Through

Resistance

Light Blockage

Light Scatter 0.074^

Array

Length-Count

Diffraction

Centrifuge

Spi ral Ultra

Sedimentation 0.074 e

Turbi di ty/Exti nction

X-Ray Scatter 0.078 f

a. Bradford 1955 [Ref.B16] d. Davidson, Collins 1972 [in Ref. D4]

b. Davidson, Haller 1974 [Ref. D3] e. McCormick 1964 [in Ref. D3]

c. Kratohvil, et al. [in Ref. D3] f. Bonse, Hart 1966 [in Ref. D3]
allowed comparisons of the same individual techniques over a series of latexes of different

sizes, systematic differences are manifest. In the next three sections, illustrative

comparisons are made for resistive-counters, light-scattering, and electron microscopy.

a. Resistive Counter Measurements

Most flow- through particle counters are comparators which can provide precise measurement of particles of unknown size relative to particles of known size against which the

instruments are calibrated. Tables 13-18 show reported results for measurements made on polymer spheres with flow-through counters or calibrated against other such spheres.

These tables are included here as a sampling of the levels of agreement that have been

observed and reported for such measurements.

Tables 13-16 are extracted from one study involving polymer spheres from three suppliers, two different resistive-type counters, and a special electron microscopy technique

[A5]. (As noted earlier, the special technique involves measurement of the shadow, through

an opening in a metal film, cast by a particle as a result of metal vapor deposition [C9,

C20, D5]). Over the range 0.8ym to 11.5 ym of the six latexes in Table 13, the resistive

counter measurements agree with the special electron-microscopy measurements to within +5%

or so, with an arithmetic average deviation of +0.25% and an RMS average deviation of

4.3%. Some hint of systematic effects appear in the correlation of the error sign with

latex source for two of the three cases; these apparent incremental differences also appear

in Table 14 for two other latexes. Over the same range, 0.8 ym to 1 1 .5 u m of latexes, in

Table 15, a second resistive counter's measurements agree with the special electron microscopy measurements within 5% or so, with an arithmetic average difference of -1.2% and an RMS average deviation of 3%.

Direct comparison of the two counters for four latexes over the 0.8 ym to 11.5 ym

range in Table 16, shows agreement within 5% or so, with an arithmetic average deviation

of 0.25% and an RMS deviation of 3.2%. Differences this large exceed the precision reported

to be characteristic of the devices themselves. For comparisons of the same types of

counters, repeatabi 1 i ties of 1% (95% confidence) and reproducibilities of 3% (95% confidence)

are reported (ASTM circular C90), such agreement being consistent with results in Table 17 for one company's comparison of instruments at sites in three countries. For the 6.6 ym

latex shown, the three instruments produced results which agree with an RMS deviation of

0.9% on median size. (They also agree with an RMS deviation of 2% on the size distribution

index Dg^/^g, which is the ratio of the size greater than that of 84% of the population

to the size greater than 50%).

b. Optical Microscope Measurements

In tables 18-23, measurements on polymer spheres made by three different optical

microscope techniques are compared with other methods. In Table 18, the comparison is for some large (10 ym to 20 ym) DVB latexes and is between flow-through counter measurements

and optical microscope/projected-spot analyzer measurements [A5]. Here the difference

is clearly systematic, with the optical microscope measurements always exceeding the

counter measurements by 2 to 11%, corresponding to 0.3 ym to 2.5 ym.

Table 19 shows results for nominally 5, 10, and 20 ym DVB latexes using visual imagesplitting optical microscopy, visual array-counting optical microscopy, and scaled-photography scanning electron microscopy [S5]. With observed variations on the order of 0.2 ym

for both the visual eyepiece and SF.M measurements and 0.5 ym for the array count, the 0%

to 6.5% differences between entries is on the order of the combined uncertainties and is

apparently non-systematic.

While the optical microscope-vs-electron microscope comparison for large spheres in Table 19 shows some level of agreement, a more detailed and precise comparison for small

spheres [C8, C9] given in Table 20 shows large systematic disagreement. Table 19, which

applies to wide-distribution DVB latexes from 5 to 20 m in size, shows optical microscope

measurements (with an image-splitting eyepiece) within +0.3 ym of some (scaled photograph)

SEM measurements. Table 20, which applies to narrow-distribution PS latexes from 0.5 to 3.5 ym in size, shows (using a filar eyepiece) optical microscope measurements differing

45
Table 12

Mean Particle Size of Ten Dow Latexes

by Various Methods

Latex Value Attributed Value By Various Scattering

Designation to Dow EM Related Techni ques

LS-1132-B 0.091 0.085a (0.094R)* 0

LS-055-A 0.188 0.171FC 0.175Ld

LS-1047-A 0.234 0.210Xe

LS-1010-E 0.357 0.343R3

LS-06-A 0.365 0.339Lf 0.342H9

LS-15N-8 0.511 0.503Lh 0.515H9

LS-06-A 0.557 0.537Lh 0.594FC 0.561H9

LS- 0.822 0.82A 1

' 0.80Z1

LS-113-B 1.011 1.04A1 1.02Z.1

LS-067-A 1.171 1.120L" 1.136LJ 1.1 46L k 1.160L9

LS-464-E 1.305 1.276Lh 1.242FC

R: Rayleigh li newi dth H: Higher-order-Tyndal 1 F: Flow microscopy Z: Various settli ng

L: Angular light scatter A: Array

X: X-Ray scatter *: Ambiguous value

a. Lee, et al. 1972 [Ref.L13]. f. Davidson, Haller 1974 [Ref. D3].

b. Gulari, et al. 1979 [Ref.GlO]. g. Pierce, Maron 1964 [Ref. P4].

c. Davidson, et al. 1967 [Ref. D6]. h. Wallace, Kratohvil 1972 [Ref. W3].

d. Dezelic, et al. 1963 [Ref.D18]. i. Ferron 1975 [Ref. F3],

e. Hachisu, S. 1976 [Ref. H2]. j. Rowel 1, et al. 1967 [Ref. RIO].

46
Table 13

Mean Particle Size of Some Standard Polymer Spheres

by Shadowed TEM and Coulter Counter [Ref. A5]

Latex Source

Shadowed

TEM Value

Coulter

Counter Value

Difference

\im °lo

Coul ter

Coul ter

Dow

Dow

Duke

Duke

0.84

1.31

1.81

3.36

5.10

11.55

0.80

1.35

1.90

3.54

4.89

11.26

-0.04

+0.04

+0.09

+0.18

-0.21

-0.29

-5.0

+3.0

+5.0

+5.4

-4.3

-2.5

47
Table 14

Mean Particle Size of Two PVC Latexes by

Shadowed TEM and Coulter Counter [Ref. A5]

Latex Shadowed Coulter Difference

TEM Value Counter Value pm %

PVC 0.87 0.99 +0.08 10.7

0.98 1.09 +0.10 15.9

48
Table 15

Mean Particle Size of Some Standard Polymer Spheres

by EM and Celloscope [Ref. A5]

Latex

Source

Shadowed

TEM Value

Celloscope

Value

Difference

Coul ter

Coul ter

Coulter

Duke

Duke

Duke

0.84

1.31

3.59

3.63

5.10

11.55

0.82

1.28

3.45

3.45

5.00

11.45

0.02

0.03

-0.14

-0.18

-0.10

-0.10

2.5

2.3

-3.9

-5.0

-2.0

-0.9

49
Table 16

Mean Particle Size of Some Standard Polymer Spheres

by Coulter Counter and Celloscope [Ref. A5]

Latex

Source

Coulter

Counter

Coul ter

Coulter

Duke

Duke

0.80

1.35

4.89

11.26

CelloScopeDifference

pm %

0.82

1.28

5.00

11.45

+0.02 2.5

-0.07 -5.2

+0.11 2.2

+0.17 1.5

50
Table 17

Intercompari son of Coulter Counters

in Round-Robin [Ref. A5] (ym)

Location D 50 D 84/°50 D 84 0

USA 6.6 1.35 8.90 2.31

GB 6.7 1.34 8.98 2.28

GDR 6.6 1.30 8.58 1.98

51
Table 18

Sizes of Some DVB Latexes by

Various Techniques [Ref. A5]

Image-Analyzer

Optical Microscope

Coulter

Counter

Difference

ym %

10.2 ym 9.9 ym +0.3 2.9

13.4 13.1 +0.3 2.2

22.9 21.9 +1.0 4.4

22.2 19.7 +2.5 11.3

b2
Table 19

Sizes of Some DVB Latexes

Various Techniques [Ref.

by

Visual-Eyepi ece Optical MicroscopyArray

Count

Scanni ng Electron Microscope

5.1 + 0.2 M m 5.1 + 0.5 y m 5.2 + 0.2 ym

10.2 + 0.1 10.4 + 0.1 10.5 + 0.1

19.7 + 0.1 20.8 + 0.5 19.5 + 0.2

53
Table 20

Mean Particle Size of Seven Dow Latexes by Filar-Eyepiece

Optical Microscope and Electron Microscope [Ref. C9]

Latex

Designation

Electron

Microscope*

Optical

Microscope

(Filar)

Difference

(ym)

Lb-Ob/-A U. £04 U.4DD 0.202

LS-061-A 0.365 0.576 0.211

LS-15N-8 0.511 0.824 0.313

LS-063-A 0.556 0.818 0.362

LS-066-A 0.814 1.181 0.367

LS-067-A 1.171 1.553 0.382

LS-886-43 1.83 2.7 0.340

LS-? 2.79 3.49 0.70

*Note: Presumedly Dow latexes of these designations; author identifies

them only as polystyrene spheres and gives the values here

associated with Dow EM.

54
Table 21

TEM and Optical Array Values of

Some PVC Latex Sizes [Ref. D7]

TEM-Image Optical Difference

of Shadow Array pin lo

0.484 0.491 -0.007 - 1.5

0.503 0.510 -0.007 -1.3

0.662 0.694 -0.032 - 4.8

0.868 0.991 -0.123 -14.1

0.938 0.996 -0.058 - 6.2

0.976 1.03 -0.058 - 5.5

55
Table 22

TEM-Measured Metal -Vapor Shadowed

PVC Latex Particles [Ref. D7]

Size of Images

of Shadows

Size of Images

of Particles

Difference

pm 1

0.198 0.166 -0.032 16.2

0.200 0.161 -0.039 19.5

0.662 0.560 -0.102 15.4

0.938 0.773 -0.165 17.6

0.976 0.816 -0.160 16.4

56
Table 23

Sizes of Some DVB Latexes by

Various Techniques [Ref. Tl]

TEM Images

of Shadows

TEM Images

of Particles

Difference

P m 7o

0.43 0.35 0.08 18.6

0.54 0.37 0.17 31.5

0.70 0.52 0.18 25.7

1.20 0.91 0.29 24.2

57
systematically from +0.2 to +0.7 ym from (replica-grating) TEM measurements. In this latter

case, the largest portion of the sytematic difference is attributable to error in the

optical measurements which are due to, first, edge-location effects and, second, limiting

resolution [C8, N5, Sll-12]. An application of the array-counting technique to overcome

these limitations is illustrated in Table 21 [D7]. Here special TEM measurements and

optical array measurements on 0.5 to 1 urn latexes agree within 0.01 to 0.1 ym or so.

The special TEM technique of Table 21 is the vapor-shadowing one briefly described

earlier. In this technique, an anticipated change in particular diameter due to shrinkage

upon exposure to the electron beam is avoided by measurement of the diameter of the shadow

of the particle produced by metal vapor deposition prior to electron irradiation. Table 22

shows the apparent diameters of the particles and their shadows for five PVC latexes [D7];

the shadow diameters are larger by a fairly consistent 17%. Table 23 shows similar data

for four DVB latexes [Tl]; again the shadow diameters are larger, this time by an average

25%. In the tables which follow, those electron microscopy (EM) measurements which use the

vapor-shadow technique are indicated, and the shrinkage and compensation effects should be

kept in mind when comparisons are made.

c. Various Optical Techniques versus Electron Microscopy

In the next eleven tables (24-34), the results of measurements on polymer spheres by

various light-scattering-based techniques are given and, in most cases, compared with

results from electron microscopy. For the majority of cases, the differences among results

are sizable and, while often random-appearing, they occasionally hint at systematic

behavior.

In Table 24 are results for four styrene latexes measured by EM and dark-field

microscopy, a light-scattering technique using annular illumination or collection in an optical microscope-differences range from -24% to +12% with no apparent systematic behavior.

In table 25, differences between disc centifuge and TEM shadow measurements range between

-10% and +10%. In Table 26, results for fractional creaming [D2] are similar.

However, in Table 24, for eight of nine Dow latexes, results from the flow ultramicroscope, another type of angular scattering device, are consistently an average 8%

above the TEM shadow values. A similar systematic difference which averages 9% is manifest for the light-scattering values from the higher-order Tyndall spectra (HOTS) for six

PVC latexes in Table 28. (In Table 29, a few HOTS measurements on six DOW latexes do not

exhibit such systematic behavior.)

Table 30 summarizes an early, pre-laser-era comparison of results from five lightscattering techniques on eleven latexes, including eight Dow latexes, and it first demonstrated probable systematic differences between results from light-scattering measurements

and electron-microscopy measurements made by the latex manufacturer. The light-scattering

(LS) techniques included transmi ttance , 90° scatteri ng, di ssymmetry ratio, polarization

ratio, and location of extrema in the angular scattering patterns. Averages for the various

LS techniques appear in column 8; for the eight Dow latexes, the mean LS values systematically differ from the EM values in column 2, with the EM values being greater by an average

0.016 ym.

The comprehensiveness of measurements such as those summarized in Table 30 allows

comparisons and conclusions which more limited data collection do not. For example, in

Table 31, the few results available for Rayleigh linewidth light-scattering measurements,

based on Stokes* size-dependent velocity equations rather than Mie-type scattering equations,

do not show consistent behavior. Enough internal consistency among various light-scattering

results does exist, however, to make averages over various LS techniques legitimate. The

degree of consistency is shown in Tables 32-34 for individual latexes.

Table 32 shows the mean values at 95% confidence limits of the particle size of a nominally 0.25 urn Dow latex using various light scattering techniques. The mean of the

twelve entries for various techniques (Table 10) is 0.247 +_ 0.005 ym, a value which overlaps

all but the flow ul tramicroscopy values. Table 33 shows similar results for a nominal

1.2 pm latex, with the average of seven mean LS values being 1.196 + 0.009 ym. Table 34

for nominal 3 ym spheres, which have size distributions about 10% oT nominal (Figure 1),

58
Table 24

Mean Particle Size of Some Styrene Latexes by

Electron and Dark-Field Optical Microscopy [Ref. D2]

Styrene Electron Dark Field Difference

Latex Microscopy Optical M. ym %

S39 0.213 0.265 -0.052 -24.4

S39 0.126 0.140 -0.014 -11.1

S37 0.091 0.078 +0.013 +14.2

S36 0.074 0.065 +0.009 +12.2

59
Table 25

TEM and Disc Centrifuge Value of

Some PVC Latex Sizes [D7]

TEM Image Disc Difference

of Shadow Centrifuge %

0.0525 0.0471 0.0054 10.3

0.0822 0.0780 0.0042 5.1

0.200 0.215 -0.015 - 7.5

0.285 0.289 -0.004 - 1.4

0.484 0.543 -0.059 -12.2

0.503 0.552 -0.049 - 9.7

60
Table 26

TEM and

of Sftmp

Fractional Creaming Values

PVC Latex Sizes [Ref. D7]

TEM Shadow

of Image

Fractional

Creami ng Difference\im %

0.0525 0.0490 0.0035 6. 7

0.0822 0.0840 -0.0018 - 2. 2

0.200 0.195 0.005 2. 5

0.662 0.770 -0.108 -16. 3

61
i

I

Table 27

Mean Particle Size of Some Dow Latexes by

TEM and Light-Scatter Technique [Ref. D5,D6]

Latex TEM- Image Flow-Ultra- Difference

Designation of Shadow Microscope ym %

LS-055-A 0.177 0.171 0.006 3.4

LS-057-A 0.262 0.280 -0.018 - 6.9

LS-061-A 0.350 0.365 -0.015 - 4.3

LS-063-A 0.510 0.594 -0.084 -16.5

LS-449-E 0.765 0.849 -0.084 -11.0

LS-464-E 1.087 1.242 -0.155 -14.3

LS-1028-E 1.183 1.213 -0.030 - 2.5

L6064-36 2.024 2.211 -0.187 - 9.2

EP-1 358-36 3.036 3.128 -0.092 - 3.0

62
Table 28

TEM and Higher-Order Tyndall

Values of Some PVC Latex Sizes

Spectra

[Ref. D7]

TEM-Image

of Shadow

Higher Order

T-Spectra

Difference

vim %

0.285 0.326 -0.041 -14.4

0.484 0.512 -0.028 - 5.8

0.503 0.548 -0.045 - 8.9

0.662 0.720 -0.058 - 8.8

0.868 0.953 -0.085 - 8.9

0.976 1.04 -0.064 - 6.6

63
Table 29

Mean Particle Diameter of Six Dow Latexes

by Higher-Order-Tyndal 1 Spectra [Ref. P4]

Latex Value Attributed HOTS* Difference

Designation to Dow EM Value %

LS15N-7 0.340 0.329 -0.011 -3.2

LS-061-A 0.365 0.342 -0.023 -6.3

LS-15N-8 0.511 0.515 +0.004 7.8

LS-063-A 0.557 0.561 +0.004 7.2

LS-066-A 0.814 0.799 -0.015 -1.8

LS-067-A 1.171 1.160 -0.011 0.9

^Entries are single value or average of two which differ from 0.2 to 21

64
Table 30

Comparison of Mean Particle Diameter of Eleven Dow and non-Dow Latexes

by Various Light-Scattering Techniques by Same Workers* [Ref. 19]

Latex

Numbers

EM Value

Light

Trans

90

Scttr

Dissym

Ratio

Polar

Rati o ExtrmLoca t Mean

LS

BASF-1** 0.037** 0.030 0.029 — — — 0.029

BASF- 2** 0.047** 0.042 0.042 0.050 — — 0.045

BASF-3** 0.072** 0.069 0.058 — — — 0.064

LS-040-A 0.088 0.076 0.073

0.074

0.078

0.080 — 0.076 0.076

LS-15N-23 0.138 0.120 0.118

0.120

0.124

0.120

--- 0.118 0.120

LS-055-A 0.188 0.167 0.182

0.176

0.175 0.175

LS-057-A 0.264 0.240 0.249

0.240

0.241

0.242

0.254 0.248 0.245

LS-061-A 0.365 0.329 0.333

0.338

0.346

0.334

0.331 0.360 0.339

LS-063-A 0.557 0.522 0.526

0.537

0.552 0.534 0.531 0.534

LS-066-A 0.814 0.784 0.808

0.807

0.802

0.805

0.803 0.805

0.808

0.803

LS-067-A 1.171 1.185 1.156

1.180

1.164

1.190

1.146 1.158

1.155

1.167

* Dezelic and Kratohvil 1961 [Ref. 19] ** Non-Dow latexes; all others Dow latexes with electron microscopy by Dow. Note: Second values at different wavelengths of mercury arc source

(col. 4,5) or different angular widths of the detector acceptance

aperture (col. 7)

65
Table 31

Mean Particle Size of Some Dow Latexes lay RayleighLinewidth Light Scatter and Electron Microscopy

Latex EM Rayleigh Difference

Designation Li new i dth p m %

LS-1028-E 1.1923 1.20b -0.01 +0.7

LS-1010-E 0.357C 0.343C +0.018 -3.9

LS-1047-E 0.234 [moments only]d

LS-1132-B 0.091 0.0847C +0.063 -6.9

LS-"910"d 70.0884^ 0.0942d +0.006 +6.6

a. Bradford 1979 in Ref. RIO d. Gulari, et al. 1978 [Ref. G10]

b. Rowel 1, et al. 1979 [Ref. RIO e. Chu, et al. 1979 [Ref. Cll]

c. Lee, et al. 1972 [Ref. L13]

66
Table 32

Averaged Values of Mean Particle Size of Dow Latex LS-057-A

from Various Optical Techniques [Table 10]

Method of

Measurement

Number in

Average

Average

of Means

Tolerance

of Average*

Angular Scatter

Flow Microscopy

Other-Light-Type**

X-Ray Scatter

All But X-Ray

4

6

2

2

4

2

12

0.245 ym

0.247

0.241

0.249

0.250

0.251

0.247

+0.004p m

+0.007

+0.008

+0.001

+0.006

+0.008

+0.005

*See Appendix G for method of calculating tolerances.

**Sedimentation and turbidity entries of Table 10.
I

Table 33

Averaged Values of Mean Particle Size of Dow Latex LS-1028-E

from Various Optical Techniques [Table 8]

Method of

Measurement

Number in

Average

Average

of Means

Tolerance

of Average*

Angular Scatter 7 1.196 Pm +0.009 v m

Array Diffraction 1 1 .20

Flow Microscopy 1 1.213

Other-Li ght-Type 1 1 .220

*See Appendix G for method of calculating tolerances.

68
Table 34

Averaged Values of Mean Particle Size of Dow Latex LS-1 358-38

from Various Optical Techniques [Table 6]

Method of

Measurement

Number in

Avera ge Average

of Means

Tolerance

of Average*

Angular Scatter

Array Count

Array Diffraction

Flow Microscopy

2.992 ym

3.010

3.035

3.128

+0.027 pm

+0.025

+0.013

*See Appendix G for method of calculating tolerances.

69
also shows light-scattering values agreeing within about 1% at the 95% confidence level.

It is the consistency of data such as these which permits combining mean values from various

light-scattering techniques to obtain an aggregate "light-scattering value" of particle

diameter which may be compared, as it later will be, with an electron microscopy value. In the next eight tables (35-42), the internal consistency of electron microscopy results are examined.

d. Intercomparison of Electron Microscopy Results

Table 35 shows electron-microscope values of mean particle size for twenty-one Dow

latexes as measured by Dow and various others with thirteen different workers. For latexes

nominally 0.09 ym to 3.5 ym in size, the results differ from -7% to +16% and -0.08 ym to +0.22 ym. Of the thirty-si x entries in Table 35, the differences between the size attributed

to Dow EM and those of others is negative in only six of the thirty-six. Thus, there is a suggestion that the mean diameters as measured by Dow are systematically higher than those

by other EM workers. In the next five tables, comparisons are made between results of Dow

and those of four other workers for a series of latexes over a range of sizes.

Table 3 shows EM results for nine Dow latexes from Dow EM measurements and as measured

by Davidson, et al. [D5, D6]. Except for three latexes where results are suspect because

widely different distributions in sizes were observed (see Table 37), the six latexes have

Dow EM values which are an average 0.021 ym greater. Table 38 shows EM results for another

group of nine Dow latexes in a comparison of Dow results and those of Heard, et al . [H4].

Except for one of the nine latexes, the mean particle diameters attributed to measurements

by Dow are greater by an average of 0.02 ym. While the measurements on six latexes by

Dobbin in Table 29 show three values which are greater than Dow and three which are less,

the results on four latexes by Davidson and Haller in Table 40 are less than the Dow values

by an average of 0.02 ym.

The likely cause of systematic differences in the measurements of mean particle size

by various electron microscopy groups lies in the edge-location aspect of dimensional

measurements by imaging techniques as discussed earl i er. The effect of choosing, explicitly

or implicitly, a different relative intensity level on an image intensity profile is shown

in Tables 41 and 42. Table 41 shows that the apparent size of a nominal 0.25 ym particle

imaged with a TEM varies by up to 20% depending on the method used to measure the size of

the image on the plate: with a filar eyepiece or an image analyzer, and whether directly

on the plate, a contact print, or an enlargement photo. Analogously, Table 42 shows that

the apparent size of a nominal 3 ym particle imaged with a TEM varies by up to 30% depending

on whether a reticle eyepiece or projected-spot analyzer is used to measure the size of the

image. With these potential effects as background, the final five tables (43-47) show

comparisons between various light-scattering and electron microscopy results for a number

of Dow latexes.

4. A. 2. Generalizations from Compari sons

Table 43 is a compilation of electron microscopy and light-scattering results for

twenty-five Dow latexes covering a range of sizes from nominally 0.09 ym to 3.5 ym. In columns 2 through 4 are given mean particle diameters for the latexes as attributed to Dow's electron microscopy measurements as an average electron microscopy measurements by

other groups, and as an average of various light-scattering techniques. Where averages are given, the number of means averaged, the average mean, the 95% confidence limits, and the source tables are indicated. Of the twenty-five latexes, twenty-one have two or more independent electron microscopy measurements, fifteen have light-scattering measurements,

and ten have two independent electron microscopy measurements as well as light scattering

measurements. In Table 43, comparison of the Dow EM and other EM entries indicates that in sixteen of the twenty-one cases, the Dow value is greater than the other.

In the next two tables, comparisons are made between the average light scattering

results and the Dow and non-Dow EM results. Table 44 shows a comparison of Dow electron

microscopy values and average angular light-scatter values for the mean particle diameter

of twelve Dow latexes over a range of sizes from nominally 0.09 ym to 1.2 ym. In eleven of

the twelve cases, the Dow EM values are greater than the light-scatter value, the average

difference being 0.014 ym. Table 45 shows a comparison of non-Dow electron microscopy

70
Table 35

Electron-Microscope Values of Mean Particle Size

of Some Dow Latexes by Various Workers

Latex Size Attributed Size By Difference

Designation to Dow EM Others EM vim %

LS-040-A3 0.088 0.078b 0.01 11.3

LS-1132-B 0.091 0.085k 0.01 6.9

LS-1044-E 0.109 0.100e 0.01 8.3

LS-052-A 0.126 0.119 c 0.01 5.6

LS-1045-E 0.176 0.16 e 0.02 9.1

LS-055-A 0.188 0.177 d 0.01 5.9

LS-1047-E 0.234 0.22 e 0.01 6.0

LS-057-A a 0.264 0.262 d 0.00 0.8

0.264 0.262C 0.00 0.8

0.264 0.245 b 0.02 7.2

LS-1010-E 0.357 0.3431 0.01 3.9

0.357 0.33e 0.03 7.9

LS-061-A 0.365 0.33 e 0.04 9.6

0.365 0.350 d 0.02 4.1

0.365 0.33f 0.04 9.6

0.365 0.336 b 0.03 8.0

0.365 0.368C 0.00 0.8

LS-1029-E 0.500 0.50e 0.00 0.0

LS-063-A 3 0.557 0.510 d 0.05 8.4

0.557 0.587C -0.03 -5.4

L O 1 U 1 L. — L O 714 0.74 e -0.03 -3.6

LS-449-E 0.796 0.777C 0.02 2.5

0.796 0.765 d 0.03 3.9

0.796 0.850J -0.05 -6.8

0.790 0.760 b 0.03 3.8

LS-1114-B 0.813 0.76e 0.05 6.5

LS-1028-E 1.1921 1.183 d 0.01 0.8

1.192 1.17"1 0.02 1.8

1.192 1.1 6e 0.03 2.7

1.192 1.26" -0.07 -5.7

LS-464-E 1.305 1.087 d 0.22 16.8

1.305 1.343C -0.04 -2.9

LS-886-43 1.81 1 .81

J

0.00 0.0

LS-6064-36 2.050 2.024 d 0.03 1.3

LS-1 358-38 2.958 3.036 d -0.08 -2.6

EP-1 358-35 3.49 3.36J 0.13 3.7

a. Bradford, Vanderhoff 1955 [Ref.B16] h. Kerker 1973 [Ref.C23]

b. Davidson, Haller 1974 [Ref. D3] i. Bradford 1979 [in Ref. R10]

c. Dobbins 1966 [Ref.D20] j. Aliet 1976 [Ref. A4]

d. Davidson, et al. 1967 [Ref. D6] k. Chu, et al. 1979 [Ref.Cll]

e. Heard, et al. 1970 [Ref. H4] 1. Lee, et al. 1972 [Ref.L13]

f. Claver,Farnham 1972 [Ref.C20] m. Porstendorf er 1972 [in h]

g. Cooper 1968 [in h] n. Stober, et al. 1971 [in h]

71
Table 36

Electron-Microscope Values of Mean Particle Size of Some Dow latexes

by Two Workers

Latex Dow-Bradford Davidson, etal. Difference

Designation EM [Ref. B16] EM [Ref.D5,D6] um %

LS-055-A 0.1881 0.1770 0.011 5.8

LS-057-A 0.2638 0.2617 0.002 0.8

LS-061-A 0.3646 0.3499 0.015 4.0

LS-063-A 0.5567 0.5101 0.047 8.4

LS-449-E 0.7962 0.7646 0.032 4.0

LS-464-E 1.3046 1.0867 0.218 16.7

LS-1028-E (1.0992) (1.1827) (-0.084) (-7.6)

1.199* 1.1827 0.016 1.4

L6064-36 2.049 2.0240 0.025 1.2

EP-1 358-36 2.9583 3.0356 -0.077 -2.6

*Redetermi nation [Ref. R10]

72
Table 37

Comparison of Size Distribution Standard Deviations

of Some Dow Latexes by Two Workers [Ref. D5,D6]

Latex Normal Distribution (ym) Ratio

Designation Size (pm) Dow-Bradford I Davidson, et al.

I

LS-055-A 0.19 0.0076 0.0106 1.4

LS-057-A 0.26 0.006 0.0144 2.4

LS-061-A 0.37 0.0079 0.0198 2.5

LS-063-A 0.56 0.0108 0.0267 3.4

LS-449-E 0.80 0.0083 0.0624 7.5

LS-464-E 1.30 0.0158 0.2348 14.9

LS-1028-E 1.20 0.0159 0.636 40.0

L-6064-36 2.05 0.0180 0.1088 6.0

EP-1 358-38 2.96 0.0150 0.1904 12.7

73
Table 38

Electron-Microscope Values of Mean Particle Size

of Some Dow Latexes by Two Workers [Ref. H4]

Latex Bradford-Dow Heard, et al. Difference

Designation EM EM ym %

LS-1044-E 0.109 (0.103)* (0.006) 5.5

0.100* 0.009 8.3

LS-1045-E 0.176 0.16* 0.016 9.1

LS-1047-E 0.234 0.22* 0.014 6.0

LS-1010-E 0.357 0.33 0.027 7.6

(LS-061-A) 0.365 (0.33)* (0.035) (9.6)

LS-1029-E 0.500 0.50 0.00 0.0

LS-1012-E 0.714 0.74 -0.026 -3.6

LS-1114-E 0.813 0.76 0.053 6.5

LS-1028-E (1.099) (1.16) (-0.061

)

(-5.6)

1.192** 1.16 0.032 2.7

*Dimensionally measured by ratio of image size with other particles;

other unstarred entries were scaled with grating replica.

**Redetermi nation by Dow [Ref. R10]

74
Table 39

Electron-Microscope Values of Mean Particle Size

of Some Dow Latexes By Two Workers [Ref. D20]

Latex Value Dobbins, et al. Difference

Designation Dow EM EM pm %

LS-052-A 0.126 0.119 -0.007 -5.6

LS-057-A 0.264 0.262 -0.002 -0.8

LS-061-A 0.365 0.368 +0.003 +0.8

LS-063-A 0.557 0.587 +0.030 +5.4

LS-449-E 0.796 0.777 -0.019 -2.4

LS-404-E 1.305 1.343 +0.038 +2.9

7 5
Table 40

Electron-Microscope Values of Mean Particle

Size of Some Dow Latexes by Two Workers [Ref. D2, D3]

Latex

Designation

Dow-Bradford

EM Davidson, HallerEM Difference

LS-040-A

LS-057-A

LS-061-A

LS-449-E

0.088

0.264

0.365

0.796

0.078

0.245

0.336

0.760

+0.01 11.4

+0.02 7.2

+0.03 8.0

+0.04 3.8

76
Table 41

Dependence of Apparent Particle Size on Method of Sizing Image on TEM Plate [Ref. D3]

Method of Image Sharpness Apparent Relative Size

Sizing Image I ndex Size Difference

Ratio °lo

Filar Eyepiece

Orig. negative 1.0 0.254 1 .03 + 3 with

clear spot 0.9 0.249 1 .01 +1 of

3mm di ameter 0.6 0.247 1.00

Oriq. neqative 1.0

wi th opaque spot 0.9 0.218 0.88 -12

of

3mm diameter 0.6 0.215 0.87 -13

Contact print 1.0 0.219,0.202 0.89,0.82 -IV-18 wi th clear spot 0.9 0.222,0.212 0.90,0.86 -10,--14 of

3mm diameter 0.6 0.199,0.196 0.80,0.79 -20,--21 Image Analyzer

Enlargement* 1.0* 0.247 1.00* 0%

with

clear spot 0.9 0.242 0.98 -rio of

6-8 mm diameter 0.6 0.220 0.89 -n%

* Method recommended by authors quoted

77
Table 42

Dependence of Apparent Particle Size of Four Dow Latexes on Method of Sizing Images on TEM Plate: Reticle EyepieceVersus-Automatic Projected Spot Analyzer [B3]

Reticle Eyepiece Projected-Spot RE/PS Difference

Dn °n On °n

2.82 0.25 3.72 0.27 1.1 -0.9 +32

3.00 0.12 3.20 0.19 1.6 -0.2 + 7

3.08 0.21 3.55 0.23 1.1 -0.5 +15

3.14 0.28 3.61 0.24 0.9 -0.5 +15

6.4 2.0 6.8 1 .9 0.9 -0.4 + 6

78
Table 43

Comparison of Dow Electron Microscopy Values

with Other EM and Light-Scattering

Latex Value Other EM a Light-Scatter

Designation Dow EM Number Average Number Average

i c n/i n a Lb-U4U-A n no o U . Uoo 1 n n"7 o U. U/o c

O U . (J/D +

n nn o h U . UU<: U

1 C 1 1 "3 0 D Lb- 1 1 6tL-D n nm u . uy 1 1 n no c U. (Job

i1 U • (Job Lb- 1 vm-t n l no u . i uy 1 n i nn U. 1 UU

1LS-15N-23 C 1 C 1 1 01 n 1 m 0.002b 0. 138 6 U. 1^0 +

\ c no a Lb-UbZ-A 1 n nin u. 1 1 y LS-1045-E 0.176 1 0.160

0.007b LS-057-A 0.188 1 0.177 5 0.175 +

1 C 1 A/17 C Lb- 1 U4/-L (J. £ J4 1 n oon U. ££U

Lb-Ub/-A U . ^04 O0 n oca x n nil U. dbo + U.U 1

o

i n1 U T Lo- I U 1 U-t U . Jj / O

C

ii U . J^ o 0.008 b LS-061-A 0.365 5 0.335 + 0.008 7 0.339 + LS-1029-E 0.500 1 0.50

LS-15N-8 0.511 1 0.503

0.007b LS-063-A 0.557 2 0.549 + 0.096 6 0.534 + LS-1012-E 0.714 1 0.74

LS-449-E 0.796 3 0.788 + 0.046 4 0.780 + 0.014^

LS-1114-E 0.813 1 0.76

0.006b LS-066-A 0.814 8 0.803 + LS-067-A 1.171 8 1.167 + 0.011b

LS-1028-E 1.192 4 1.193 + 0.050 6 1.195 + 0.009e LS-464-E 1 .305 1 1.215 1 1.276

LS-886-43 1.81 1 1.81

LS-6064-36 2.050 1 2.024

0.027f LS-1 358-38 2.958 1 3.036 4 2.992 + EP-1 358-35 3.49 1 3.36

a. Table 35 d. Table 9 b. Table 19 e. Table 33

c. Tables 32 f. Table 34

79
Table 44

Comparison of Dow Electron Microscopy and Average Angular Light Scatter

Values of Mean Particle Size for Twelve Dow Latexes [Table 43]

Latex Value Attributed Average Value Difference

Designation to Dow EM Light Scatter ym

LS-040-A 0.088 0.076 0.012

LS-1132-B 0.091 0.085 0.006

LS-15N-23 0.138 0.120 0.018

LS-055-A 0.188 0.175 0.013

LS-057-A 0.264 0.245 0.019

LS-1010-E 0.357 0.343 0.014

LS-061-A 0.365 0.339 0.026

LS-15N-8 0.511 0.503 0.008

LS-063-A 0.557 0.534 0.023

LS-449-E 0.796 0.780 0.016

LS-067-A 1.171 1.167 0.004

LS-1028-E 1.192 1.196 -0.004

HO
Table 45

Comparison of Non-Dow Electron Microscopy and Average Light Scatter

Values of Mean Particle Size for Eight Dow Latexes [Table 43]

Latex Average of Average

Designation Non-Dow EM Light Scatter

LS-040-A 0.078 0.076 + 0.002

LS-1132-B 0.085 0.085

LS-055-A 0.177 0.175 + 0.007

LS-057-A 0.256 + 0.013 0.245 + 0.004

LS-1010-A 0.337 + 0.016 0.343

LS-061-A 0.335 + 0.008 0.339 + 0.008

LS-063-A 0.544 + 0.096 0.534

LS-1012-E 0.788 + 0.046 0.780 + 0.014

LS-1028-E 1.193 + 0.050 1.196 + 0.009

81
values and average angular light-scatter values for nine Dow latexes over the same range of

sizes as in Table 44. For these nine latexes, there is no significant difference between

the light-scattering and non-Dow EM values, and in most cases, the respective values agree

within the uncertainty of either value. It can be seen from Tables 44 and 45 that other

non-Dow EM values are in essential agreement with LS values. As a result, a comparison was made between Dow EM values and a combined average of other EM and LS values.

Table 46 shows the comparison for twenty-four Dow latexes between the mean particle

diameter as attributed to Dow electron microscopy and the average value of light-scattering

and other electron microscopy values as compiled in this report. For twenty-one of the

twenty-four latexes, the Dow EM value is greater than the average other-EM and LS value,

and for the twenty-four latexes shown, the average difference, computed as a number (n)-

weighted average, is +0.0130 urn. For the seventeen narrow-distribution particles, that is those with mean diameters of less than 1 urn, the number (n)-weighted average difference is 0.0158 ym. Based on this table, the conclusion drawn is that the mean particle diameters

measured by the manufacturer of the latexes is systematically different from other EM and

LS values by about 0.015 urn and that this difference may be a result of systematic effects

in the EM values. This conclusion is in accord with the observations made by Kratohvil (as in Table 7 here) except that it is a more restricted one; for as Tables 44 and 45 indicate,

EM values can be in accord with LS values, although Dow's EM values in these cases may not

be.

As a note on the efficacy of vapor-shadow techniques, Table 47 shows results for six

Dow latexes by TEM shadow and the average of LS and other EM. While the arithmetic average

difference is +0.0015 um, the large RMS average difference of 0.015 ym makes it impossible

to conclude whether the vapor-shadow method yields results more in agreement with other

techniques than the direct EM measurements on particles themselves.

82
Table 46

Comparison of Vapor-Shadow Diameter and

Average of Light Scatter and Other EM Values

Latex TEM Shadow Av. LS + Difference

Designation Image* Other EM (pm)

LS-055-A 0.177 0.175 +0.002

LS-057-A 0.262 0.248 +0.014

LS-061-A 0.350 0.337 +0.013

LS-063-A 0.510 0.538 -0.028

LS-449-E 0.765 0.783 +0.018

LS-1028E 1.183 1.193 -0.010

83
Table 47

Comparison of Mean Particle Size Attributed to Dow EM and Average Value

from Light-Scattering and Others' Electron Microscopy [Tables 44 and 45]

Latex Value Attributed Av. LS & Other EM Difference*

Designation to Dow EM n Value vim

LS- 040-A 0.088 7 0.076 0.012

LS-1132-B 0.091 2 0.085 0.006

LS-1044-E 0.109 1 0.100 0.009

LS- 052-A 0. 126 1 0.1 19 0.007

LS- 15N-7 0.138 6 0.120 0.018

LS-1045-E 0. 176 1 0. 160 0.016

LS- 055-A 0.188 6 0.175 0.013

LS-1047-E 0.234 1 0.220 0.014

LS- 057-A 0.264 13 0.248 0.016

LS-1010-E 0.357 3 0.339 0.018

LS- 061 -A 0.365 12 0.337 0.028

LS-1029-E 0.500 1 0.500 0.000

LS- 15N-8 0.511 1 0.503 0.008

LS- 063-A 0.557 8 0.538 0.019

LS-1012-E 0.714 1 0.74 -0.026

LS- 449-E 0.796 7 0.783 0.013

LS-1114-B 0.813 1 0.76 0.053

LS- 067-A 1.171 4 1.167 0.004

LS-1028-E 1.192 10 1.195 -0.003

LS- 464-E 1.305 2 1.246 0.059

LS-886-43 1.81 1 1.81 0.000

LS6064-36 2.050 1 2.024 0.026

LSI 358-38 2.958 5 3.001 -0.043

EP1 358-35 3.49 1 3.36 0.13

^Average deviation, computed from the number-n weighted differences

for the 17 latexes of D<1 \im is + 0.0158 ym; for the 24 latexes

shown, the average is + 0.0130 urn.

84
5. REPORT CONCLUSIONS

The purpose of this report has been to look at those particle measurement techniques

which potentially can be used as:

(1) reference methods for definitive primary dimensional-calibration of microscopic spherical particle reference materials; and

(2) comparison methods for convenient transfer calibrations from the reference method to

bulk calibrations.

The impressive consistency of measurements of mean particle diameters of Dow polystyrene latex sphere by transmission electron microscopy in the laboratories of the latexes'

manufacturer has provided a substantial basis for conclusions regarding both reference and

comparison techniques.

From comparisons among EM measurements by the manufacturer, EM measurements by

independent workers, and LS measurements by various groups, the following conclusions were

drawn:

- Electron microscopy and light-scattering can yield mean particle diameters for narrow- distribution populations of polystyrene spheres which agree within the combined uncertainties and sometimes at the level of a few thousandths of a micrometer, i.e. nanometers.

- The electron microscopy values attributed to Dow differ systematically by an average

value of approximately 0.015 ym from the average of other electron microscopy and lightscatter values.

- Electron microscopy and light-scattering measurements provide good cross-checks of

each other and the two in combination can provide a definitive reference method for particle

diameter calibrations.

- Flow-through particle counters can provide effective comparison transfer calibrations. The three methods complement each other, each yielding unique information. Electron microscopy can give definitive measurements of a limited number of particles; lightscattering can give an average diameter for a narrow distribution of particles in their

normal liquid environment; flow-through counters can give an explicit histogram of the

size distribution of the population, whenever the instrumental uncertainty is significantly

less than the population distribution.

Final ly, compari son of results by various techniques indicates that by means of the

complementary electron microscopy - light scatter - flow-through counter approach, narrow distribution spherical polymer particles with mean diameters in the range 0.1 ym to 0.5 ym

can be calibrated with total uncertainties on the order of +0.005 ym, 1 ym particles with

an uncertainty of 0.01 ym, and larger particles with total uncertainties on the order of

the width of the total population distribution.

In conclusion, the evidence compiled in this report concerning some of the advantages,

disadvantages, and relative performance characteristics of light-scattering, flow-through

counting, and electron microscopy has lead to developmental work at NBS on these techniques

for calibration of particle size standard reference materials.

85
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73-78 (July 1974).

T4. Taylor, D. L., "An Absolute Standard for the Calibration of Automatic Particle Computers

Using Liquid Media," Filt. and Sep. (May 1976).

T5. Trolinger, J. D., "Particle Field Holography," Opt. Eng. 1_4, 383-392 (Sept. 1975).

T6. Tschudi, T., G. Herziger, and A. Engle, "Particle Size Analysis Using ComputerSynthesized Holograms," Appl. Opt. U, 245-248 (Feb. 1974).

T7. Turner, G. A., M. E. Fayed, and K. Zachariah, "Examination of Fine Particulates by SEM: Preparation of Samples," Powder Tech. 6, 33-38 (July 1972).

Ul. Ushakov, V. V., "Annular Method of Recording the Scattering Indicatrix in a Diffraction

Structometer," J. Appl. Spectrosc (USA) 28, 382-384 (March 1978).

U2. Ushakov, V. V., "Ring Method for Recording Scattering Indices in a Laser Diffraction

Structometer," J. Appl. Spectrosc (USA) 28, 551-554 (Mar. 1978).

VI. Van Den Hul , H. J. and J. W. Vanderhoff, "Inferences on Mechanism of Emulsion

Polymerization of Styrene...," J. Br. Polym. 1, 121-127 (Mar. 1970).

V2. Van Den Hul, H. J. and J. W. Vanderhoff, "Well -Characterized Monodisperse Latices," J. Coll. Interf. Sci. 28, 336-337 (Oct. 1968).
V3. Van Den Hul , H. J. and J. W. Vanderhoff, "Contaminant Removal From Latex By Ion-Exchange

Resin Treatment," J. Coll. Interf. Sci. 28, 336 (1968).

V4. Van De Hulst, H. C, Light Scattering By Small Particles , Wiley, NY (1 957).

V5. Venolia, A. W. , "Resistive-Pulse Particle Sizing Instrument," Anal. Chem. 50, 1275-

1279 (Aug. 1978).

V6. Vogelsgesang, R., "Particle Size Measurement Using Image Analyzing Devices," St. R. Luft (Ger) 32, 368-372 (Sept. 1972).

Wl. Walker, D. R., "Misconceptions About Automatic Particle Counters," Contam. Control, 15-

21 (Sept. 1964).

W2. Wallace, T. P., "Size Distribution of Polymer Latex Systems By Use of Unpolarized and

Horizontally-Polarized Scattered Light," J. Polymer. Sci. A2, J_0, 527 (1972).

W3. Wallace, T. P. and J. P. Kratohvil, "Particle Size Analysis of Polymer Latexes by

Light Scattering: V. Significance of Assumed Distribution in Analysis of Angular

Scattering Data," J. Polymer Sci. A2, JO, 631-645 (1972).

W4. Wallace, T. P., "Size Distribution of Polymer Latex Systems by Polarization Ratio of

Scattered Light," J. Polymer. Sci. A-2 9, 595 (1971).

W5. Wallace, T. P., "Size Distribution of Polymer Latex Systems By Use of Extrema in

Angular Light Scattering Patterns," J. Polymer Sci. A2, 8, 1425 (1970).

W6. Wallace, T. P. and J. P. Kratohvil, "Particle Size Analysis of Polymer Latexes by

Light Scattering By Use of Extrema in Angular Light Scattering Intensity," J. Polymer. Sci. A2, 8, 1425-1441 (1970).

W7. Wallace, T. P. and J. P. Kratohvil, "Comments on Comparison of Scattering of Coherent

and Incoherent Light By Polydispersed Spheres With Mie Theory," Appl. Opt. 8, 824-

826 (April 1969).

W8. Wallace, T. P. and J. P. Kratohvil, "Particle Size Analysis of Polymer Latexes By

Light Scattering: II. Computer Analysis," J. Polymer Sci. C, 25, 89-98 (1968).

W9. Wang, Y. L., "Contamination Removal from Latex by Centrifugation and Redispersion," J. Coll. Interf. Sci. 32, 633 (1970).

W10. Welch, R. M. and S. K. Cox, "Non-Spherical Extinction and Absorption Efficiencies",

Appl. Opt. 17, 3159-67, 1978.

Wll. West, G. C, "Standards for Calibration of Automatic Particle Counters," Hydr. and Pneum. (July 1975).

W12. Weiss, E. L. and H. N. Frock, "Rapid Analysis of Particle Size Distributions by Laser

Light Scattering," Powder Tech. J_4, 287-294 (July 1976).

W13. Willeke, K. and B. Y. H. Liu, "Single Particle Optical Counter: Principle, and

Application," Fine Particles , Academic Press (1976).

W14. Worthman, Donald E., "Possible Use of Two Laser Beams to Determine Particle-Size

Distribution," Harry Diamond Laboratory, 55 pp (Jan. 1979).

W15. Wu, J., "Fast-Moving Suspended Particles: Measurements of Size and Velocity," Appl.

Opt. 1_6, 596-600 (Mar. 1977).

W16. Wyatt, P. J., "A New Instrument for the Study of Individual Aerosol Particles," J. Coll. Interf. Sci. 34, 125 (1972).

97
W17. Wyatt, P. J., "Measurement of the Lorentz-Mie - Scatteri ng of a Single Particle:

Polystyrene Latex," J. Coll. Interf. Sci. 34, 159 (1970).

W18. Wertheimer, A. and M. Trainer, "Polarization Dependent Light Scattering for Sizing

Submicron Particles," J. Opt. Soc. Amer. 69, p. 1451, 1979.

Yl. Yates, D. E ., R. H. Ottewill, and J. W. Goodwin, "Purification of Polymer Latices," J. Coll. Interf. Sci. 62, 356-358 (Nov. 1977).

11. Zhulanqv, Y. V., "Laser Spectrometer for Submicron Aerosols," Coll. J. USSR (USA) 3_9, 936-941 (Nov. 1977).

98
Appendix A Identified Domestic Suppliers of Standard

Spherical Particles or Test Dusts

- AC Spark Plug Division

General Motors Corporation

AC Spark Plug Bldg.

Flint, MI 48556

- Coulter Electronics

590 West 20th Street

Hialeah, FL 33010

- Dow-Diagnostics Division

Dow Chemical Company

Box 68511

Indianapolis, IN 46268

- Duke Scientific Corporation

445 Sherman Avenue

Palo Alto, CA 94306

- Fluid Power Research Center

Oklahoma State University

Stillwater, OK 74074

- HIAC Division

Pacific Scientific Company

4719 West Brook Street

Montclair, CA 91763

- Microspheres Incorporated

14930 East Romona Blvd.

Baldwin Park, CA 91706

- Particle Information Service Incorporated

2957 Woodland Park Road

Grants Pass, OR 97526

- Poly Sciences

Paul Valley Industrial Park

Warrington, PA 18976

- Royco Instrument Company

141 Jefferson Drive

Menlo Park, CA 94025

99
I

I

Appendix B. Some International Suppliers of ParticleSize-Related Equipment [Ref. A3]

Part I. Manufacturers and Addresses

Adams, L. Ltd, Minerva Road, London, NW10.

Addy Products Ltd, Solent Industrial Estate, Botley, Hampshire S03 2FQ.

Aerograph Co., Lower Sydenham, London SW26.

Agar, Alan, W., 127 Rye Street, Bishop's Stortford, Hertfordshire.

Airflow Development, 31 Lancaster Road, High Wycombe, Buckinghamshire.

Airsupply International Gateway House, 302-8 High Street, Slough, Berkshire.

Alpine, Augsberg, W. Germany.

Ameresco Inc., 101 Park Street, Montclair, New Jersey 07042, U.S.A.

American Instruments Co., 8030 Georgia Avenue, Silver Springs, Maryland, U.S.A.

Anderson 2000 Inc., P.O. Box 20769, Atlanta, Georgia 30320, U.S.A.

Applied Research Laboratories, Wingate Road, Luton, Bedfordshire.

A.T.M. Corporation, Sonic Sifter Division, P.O. Box 2405, Milwaukee, Wisconsin 53214,

U.S.A.

Bailey Meters and Controls, 218 Purley Way, Croydon, Surrey.

Bausch & Lomb Inc., 820 Linden Avenue, 30320 Rochester, New York 14625, U.S.A.

Bendix Vacuum Ltd, Scientific Instruments and Equipment Division, Easthead Avenue,

Wokingham, Berkshire RG11 2PW.

Berg, R., Particle Data Inc., P.O. Box 265, Elmhurst, Illinois 60126, U.S.A.

Brezina, J., Hauptstrasse 68, D-6901 Wal dhi 1 sbach, W. Germany.

British Rema, P.O. Box 31, Imperial Steel Works, Sheffield S9 IRA. Buckbee Mears Co., 245 East 6th Street, St. Paul 1, Minnesota, U.S.A.

Bush, G. F. & Associates, Princeton, New Jersey, U.S.A.

Carl Zeiss, 7082 Oberkochen, W. Germany.

Carl Zeiss Jena Ltd, VEB Carl Zeiss, Jena, W. Germany; also England House, 93-7 New Cavendish Street, London Wl.

Carlo Erba, via Carlo Imbonati 24, 20159, Milan, Italy.

Casella, C. F. & Co., Regent House, Britannia Walk, London Nl. Charles Austin Pumps, Petersham Works, 100 Royston Road, Byfleet, Surrey.

Chemishes Laboratorium fur Torn" ndustri e, Goslar, Harz, W. Germany.

Cristison, Albany Road, East Gateshead Industrial Estate, Gateshead, Co. Durham NE8 3AT.

Coleman Instruments Inc., 42 Madison Street, Maywood, Illinois, U.S.A.

Coulter Electronics, High Street, Dunstable, Bedfordshire.

Coulter Electronics, 590 West 20th Street, Hialeah, Florida, U.S.A.

Degenhardt & Co. Ltd, 6 Cavendish Square, London Wl.

Delviljem (London) Ltd, Delviljim House, Shakespeare Road, Finchley, Middlesex.

Dietert, H. & Co., 9330 Roselawn Avenue, Detroit, Michigan, U.S.A.

Donaldson Co. Inc., 1400 West 94th Street, Minneapolis, Minnesota 55431, U.S.A.

Draeger Normalair Ltd, Kitty Brewster, Blythe, Northumberland.

Dragerwerk Lubeck, D-24 Lubeck 1, P.O. Box 1339, Moislinger Allee 53-55, W. Germany.

Endecottes Ltd, Lombard Road, London SW19.

Erwin Sick Opti k-Elektroni k, D-7808 Waldkirch, W. Germany, An der Allee 7-9, Postfach 310.

Evans Electroselenium Ltd, Halstead, Essex.

Ficklen, Joseph, B. , 1848 East Mountain Street, Pasadena 7, California, U.S.A.

Fisher Scientific Co., Pittsburgh 19, Pennsylvania, U.S.A.

Fleming Instruments Ltd, Lever Street, Bolton, Lancashire BL3 6BJ.

Foster Instruments, Sydney Road, Muswell Hill, London N10.

Franklin Electronics Inc., Bridgeport, Pennsylvania, U.S.A.

Freeman Labs Inc., 9290 Evenhouse Avenue, Rosemount, Illinois 60018, U.S.A.

Fritsch, Albert & Co., D6580 Idar-Oberstei n 1, W. Germany.

Gallenkamp Ltd, Portrack Lane, Stockton-on-Tees, Co. Durham.

Gardner Laboratory, Bethesda, Maryland, U.S.A.

100
Gelman Hawksley, 12 Peter Road, Lancing, Sussex.

Gelman Instruments Co., 600 South Wagner Road, Ann Arbor, Michigan 48106, U.S.A.

General Electric Co., Schenectady, New York, U.S.A.

Glass Developments Ltd, Sudbourne Road, Brixton Hill, London SW2.

Glen Creston, The Red House, Broadway, Stanmore, Middlesex.

Goring Kerr Ltd, Hanover Way, Windsor, Berkshire.

Greenings, Britannia Works, Printing House Lane, Hayes, Middlesex.

Griffin & George Ltd, Wembley, Middlesex.

Hawksley & Sons Ltd, 12 Peter Road, Lancing, Sussex.

High Accuracy Products, Corp., 141 Spring Street, Claremont, California 91711, U.S.A.

Hird-Brown Ltd, Lever Street, Bolton, Lancashire BL3 6BJ.

Howe, V. A. & Co. Ltd, 88 Peterborough Road, London SW6.

Image Analysing Computers Ltd, Melbourne, Royston SG6 6ET, Hertfordshire; also 40 Robert

Pitt Drive, Monsey, New York 10952, U.S.A.

Imperial Chemical Industries Ltd, Nobel Division, Stevenston, Ayshire, Scotland.

Infrasizers Ltd, Toronto, Ontario, Canada.

Japan Electron Optics Ltd, Jealco House, Grove Park, Edgware Road, Collindale, London NW9;

also 477 Riverside Avenue, Medford, Massachusetts 02155, U.S.A.

Joyce Loebl Ltd, Princesway, Team Valley, Gateshead 11, Co. Durham.

Kek Ltd, Hully Road, Hurdsfield Industrial Estate, Macclesfield, Cheshire SK10 2ND.

La Pine Scientific Co., Chicago 29, Illinois, U.S.A.

Lars, A. B. Ljungberg & Co., Stockholm, Sweden.

Laser Associates Ltd, Paynes Lane, Rugby, Warwickshire.

Lavino, Garrard House, 31-45 Gresham Street, London EC2.

Manufacturing Engineering and Equipment Corporation, Warrington, Pennsylvania, U.S.A.

Mason & Morton Ltd, 32-40 Headstone Drive, Wealdstone, Harrow, Middlesex.

Metals Research Ltd, 91 King Street, Cambridge.

Micromeretics Instrum Corporation, 800 Goshen Springs Road, Norcroft, Georgia 30071, U.S.A.

Microscal Ltd, 20 Mattock Lane, Ealing, London.

Millipore Corp., Ashby Road, Bedford, Massachusetts 01730, U.S.A.

Mines Safety Appliances Co. Ltd, Greenford, Middlesex.

Mines Safety Appliances Co. Ltd, 201 Braddock Avenue, Pittsburgh 8, Pennsylvania, U.S.A.

Mullard Equipment Ltd, Manor Royal, Crawley, Sussex.

Nautamix, N. V., P.O. Box 773, Haarlem, Holland.

Nethreler & Hinz. GmbH, Hamburg, W. Germany.

NEU Engineering Ltd, 32-4 Baker Street, Weybridge, Surrey.

NEU, Etablissement, P.O. Box 28, Lille, France.

Northgate Traders Ltd, London EC2.

Nuclepore Corp., 7035 Commerce Circle, Pleasanton, California 64566, U.S.A.

Numek Instruments and Controls Corporation, Appolo, Pennsylvania, U.S.A.

Numinco, 300 Seco Road, Monroeville, Pennsylvania 15146, U.S.A.

Pascal! Ltd, Gatwick Road, Crawley, Sussex.

Pearson Panke Ltd, 1-3 Halegrove Gardens, London NW7.

Pennwalt Ltd, Doman Road, Camberley, Surrey.

Perkin Elmer Ltd, Beaconsfi el d, Buckinghamshire.

Phoenix Precision Instrument Co., 3803 Fifth Street, Philadelphia, Pennsylvania 19140,

U.S.A.

Photoelectroni cs Ltd, Arcail House, Restmor Way, Hockbridge, Wallington, Surrey.

Pola Laboratory Supplies Inc., New York 7, U.S.A.

Polaron, 4 Shakespeare Road, Finchley, London N3.

Polymer Consultants Ltd, London.

Procedyne Corporation, 221 Somerset Street, New Brunswick, New Jersey, U.S.A.

Production Sales and Services Ltd, New Maiden, Surrey.

Prosser Scientific Instruments Ltd, Lady Lane Industrial Estate, Hadleigh, Ipswich, Suffolk

IP7 6DQ.

101
Quantachrome Corp., 337 Glen Cove Road, Greenvale, New York 11548, U.S.A.

Rao Instrument Co. Ltd, Brooklyn, New York, U.S.A.

Research Appliance Co., Route 8, Gibsonia, Pennsylvania 15044, U.S.A.

Ronald Trist Controls Ltd, Bath Road, Slough Berkshire.

Rotheroe & Mitchell Ltd, Aintree Road, Greenford, Middlesex.

Royco Instruments, 141 Jefferson Drive, Menlo Park, California 94025, U.S.A.

Sartorious Werke, GmbH, D-34 Gottingen, W. Germany.

Schaar & Co., Chicago, Illinois, U.S.A.

Science Spectrum, 1216 State Street, P.O. Box 3003, Santa Barbara, California, U.S.A.

Sharpies Centrifuges, Ltd, Camberley, Surrey.

Shimadzu Seisakusho Ltd, Kanda, Mi toshirocho, Chiyodra-Ku, Tokyo, Japan.

Simon Carves Ltd, Stockport, Lancashire.

Societe Fransaise d' Instruments de Controle et d'Analuses, Le Mesmil, Saint Denise, France.

Sondes Place Research Institute, Dorking, Surrey.

Strohline, Dusseldorf, W. Germany.

Systems and Components Ltd, Broadway, Market Lavington, Devizes, Wiltshire.

Techmation Ltd, 58 Edgware Way, Edgware, Middlesex.

Telefunken, A. E. G., 79 Ulm, Eli sabethstrasse 3, W. Germany.

Thermal Control Co. Ltd, 138 Old Shoreham Road, Hove, Sussex.

Thermo-Systems Inc. 2500 Cleveland Avenue, North St. Pauls, Minnesota 55113, U.S.A.

T0A Electric Co., Kobe, Japan.

Ultrasonics Ltd, Otley Road, Bradford, Yorkshire.

V.E.B. Transformratoren und Rontegemwerk, 48 Overbeckstrasse 8030, Dresden, West Germany.

Veco N. V. Zeefplatenf abri ck, Eerbeck (Veluive), The Netherlands.

Vickers Instruments Ltd, Haxby Road, York.

Walther & Co., Akti engesel 1 schaf t, 5 Koln-Del lbruck, W. Germany.

Warmain International Pty Ltd, Artarman, N. S. W., Australia.

Watson, W. & Sons Ltd, Barnet, Hertfordshire.

Zimney Corporation, Monrovia, California, U.S.A.

Part II. Partizle-Size-Related Equipment Noted in Ref. A3.

SAMPLING DEVICES

Spinning Riffler

Sample Divider

Rotary Riffler

Rotary Sample Divider

Sample Splitter

FLUE SAMPLERS

Smoke Dust Monitor

BCURA Gas Flow Monitor

Smoke Density meter(chimneys/ducts

)

Stack Monitors

In Stack Samplers

Dust Samplers

Smoke Density Measuring Instruments

C.E.R.L. Flue Dust Monitor

High Sensitivity Air Monitor

AEROSOL SAMPLERS

Thermal Precipitators (Standard

and Long Term)

Gravimetric Dust Sampler

Cascade Impactor, Hexhlet

Microscal

Pascal

Freeman Laboratories

Glen Creston

Fritsch (Christison)

Airflow Development

Bailey Meters and Controls

Research Appliance Company

Ander son Anderson

Erwin Sick, Pearson Panke

Foster Instruments

Photoelectronics

Casel la

(U.S. Agents M.S. A. (U.S. Agents M.S. A.

102
Wrights T. P. Hami 1 tons T. P. Konisampler T. P. British Standard Deposit Gauge

Continuous Oscillating and

Gravimetric T. P. Thermoposi tor Drager Dust Sampler

Thermal Precipitors, Konimeter,

Dust

Collectors, Gravicon, Porticon

Dust Sampler (filters)

Electrostatic Air Sampler Kit

01 in Particle Mass Monitor

Electrostatic Air Sampler

Smoke Pollution Sampler

Cascade Centri peter

Membrane Fi 1 ters Membrane Fi Iters Settlement Dust Counter

Hexhlet Gravimetric Personal

Sampler

Settlement Dust Sampler

Cascade Impactor

Portable Dust Sampler

Periodic Air Sampler

Personal Sampler

Cascade Sampler

Aerosol Gravimetric Spectrometer

Air Pollution Monitors

Particle Sampling Unit

Dust Sampling Unit

Millipore Sampling Set

Konimeter

AERA Portable Air Sampler

Light Scattering Counters

Light Reflectance Monitor

Aerosol Spectrometers

Sigrist Dust Measuring Equip.

Electricon Smoke Monitor

Coulter Contamination Counter

LIDAR, Smoke Plume Tracking

Laser Light Scattering Particle

Counter

SIEVING EQUIPMENT

Woven Wire Sieves

Inclyno Sieve Shaker, Turbine Sifter

Electroformed Sieves

Electroformed Sieves

Electroformed Sieves

Fisher Wheeler Sieve Shaker

Sieve Shakers

Sieve Shakers

Allen-Bradley Sonic Sifter

Small Portable Sieve Shaker

Tyler Ro Tap

Alpine Air Jet

Wet and Dry Sieve Shakers

Adams

Adams

Ficklen

Glass Developments

American Instruments

American Instruments

Dragerwerk

Sartorious (Howe)

Bendi x Thermo-Sy stems, Proner

Thermo-Systems, Proner

Charles Austin

Bird and Tole

Nuclepore

Gelman, Millipore

Casella, M.S. A. Casella, M.S. A.

Research Appliances

Research Appliances

Rotheroe and Mitchell

Rotheroe and Mitchell

Anderson

Anderson

Flemi ng Flemi ng Flemi ng

F 1 emi ng Thermal Control

Carl Zeiss Jena

Addy Products

High Accuracy Products (Air Supply)

Royco (Hawksley)

Bausch and Lomb (Applied Research

Laboratories)

Research Appliance

Sartorious

(Howe)

Ronal d Tri st

Coul ter Laser Associates

Endecattes, Pascal 1, Greenings

Pascal 1 Buckbee Mears (Production Sales and

Services)

Veco

Endecottes

Fisher

American Instruments, Pascal 1 Endecottes

ATM Corporation (Kek)

La Pine

La Pine

Alpine, Lavino

Fritsch (Howe)

103
MICROSCOPES

Watson Image Splitting

Push Button Counter

Vicker Image Shearing Eyepiece

Zeiss Endter P.S.A.

Metals Research P.S.A.

Quantimet

MCSpri Analyser

Superscope Electron Microscope

(also SEMs)

Magnif i ers E.M. Grids

Aides for E.M. The Timbrel! Analyser

The Q.M.S. System

Watson

Casel la Vickers

Carl Zeiss (Degenhardt)

Metals Research

Image Analysing Computors

Mi 1 lipore

Sondes Place Research

Polaron

Maron and Morton

Alan Agar

Coulter U.S.A.

Bausch and Lomb

MISCELLANEOUS DISPERSING EQUIPMENT

Ultrasonic Dispersers

Pyknometers

Ultrasonic Cleaner

Helium Air Pyknometer

Anti-Static Agent M441

Spraygun for Electron Microscopy

SEDIMENTATION EQUIPMENT

Pipettes and Hydrometers

Granulometer

WASP Photosedimentometer

Wagner Turbidimeter

EEL Photosedimentometer

Bound Brook Photosedimentometer

Micromerograph

Shimadzu Sedimentograph

Satorious Sedimentation Balance

Micron Particle Di stri butometer

Palo-Travis Particle Size Apparatus

Fisher Dotts Apparatus

Travis Method of Two Layer Analysis

LADAL X-Ray Sedimentometer

Sedi graph X-Ray Sedimentometer

CLASSIFIERS

Walther

Cascade Elutriator

Microsplit Separator

Major Classifier

Centrifugal Classifier

Andrews Kinetic Water

Gonel

1

Haul tain Infrasizer

Rol ler

Bahco

Hexhlet Collector(Walton' s Horizontal)

Microplex Classifier

Nauta Hosokawa Classifier

Alanysette 8

Donaldson Classifier

Mullard, Ultrasonics

Numi nco Fritsch (Christison)

Micrometetics (Coulter UK)

I.C.I.

Aerography

Gal lenkamp

Brezi na Microscal

La Pine

Evans Goring Kerr

Frankli n Shimadzu

Northgate Traders

Sartorious

Bush GF Pola

Fi sher

Schaar

Microscal

Micromeretics (Coulter UK)

Walther

American Instrument

British Rema

Donal dson

Micromeretics

Grif f i n and George

Chemisches Laboratori urn Inf rasizers

American Instrument

Dietert (Neu)

Casel la Lavi no Nautami x Fritsch (Howe)

Donal dsons

CENTRIFUGES

Simcar

Joyce Loebl Disc

Simon Carves

Joyce Loebl

104
Kaye Disc

Sharpies Centrifuge

Whitby Apparatus

LADAL X-Ray

Modified Pipette

Martin Sweeny

Pennwalt Appliances (U.S.A.)

Mines Safety

Mi croscal

Allen

STREAMING PRINCIPLE

Coulter Counter

Cel loscope

P.D. Analyser

Particle Volume Detector

TOA Microcel lcounter

Granulometer

Coul ter Lars

Berg

Telefunken

Toa

V.E.B.

LIGHT SCATTERING (see also Aerosol Samplers)

Shimadzu Light Scattering Photometer Shimadzu

Sinclair Phoenix Forward

Scattering Light Photometer

Brice-Phoeni x L.S.P.

Absolute L.S.P.

Photo-Nephelometers

Recording Turbidimeter

Scattermaster

Photometers

Differential Light Scatteri ng Photometers

Atlas of Light Scattering Curve

Phoeni x Phoenix

Phoeni x American Instruments

Coleman

General Electric Company

Manufacturing Engineering Company

Shimadzu, Societe Francaise, Nethreler

Polymer Consultants

Science Spectrum

Science Spectrum

PERMEAMETRY

Fisher Sub-Sieve Sizer Kek

Rigden Apparatus Gallenkamp

Knudsen Flow Permeameter Micromeretics

The Griffin Surface Area of Powders Griffin and George

Apparatus

GAS ADSORPTION (Surface Area and

Perkin-Elmer Shell Sorptometer

Strohline Areameter

Quantasorb and Monosorb

Gravimat

A Range of Instruments

Sorptomatic

Areatron

Air Displacement Porometer

Surface Area and Gas Adsorption

Equipment

Flow Mi crocalori meter

Mercury Porosimeters

simetry

)

Perki n-Elmer

Strohli n Ameresco, Quantachrome Corporation

Sartorious

Micromeretics (Coulters UK)

Carlo Erba (Systems and Components)

Leybol d Numi nco Numi nco

Microscal

American Instrument, Carlo Erba

(Systems and Components),

Micromeretics (Coulters UK),

Carlo Erba

105
Appendix C Documentary Standards Related to

Microscopic Particle-Size Measurement

A. American National Standards Institute

ANSI B93.28 1973

"Method for Calibration of Liquid Automatic Particle Counters Using AC Fine Test Dust"

ANSI B93.30 1973

"Method of Reporting Contamination Analysis Data of Hydraulic Fluid Power Systems"

ANSI B93.31 1973

"Multi-Pass Method for Evaluating the Filtration Performance of a Fine Hydraulic Fluid

Power Filter Element"

ANSI Z168.1

"Analysis by Microscopical Methods for Particle-Size Distribution of Particulate Substances

of Sub-Sieve Sizes"

ANSI Z173.31

"Method of Test for Continuous Sizing and Counting of Airborne Particles in Dust-Controlled

Areas Based on Light-Scattering Principles"

ANSI Z146.1

"Method for Measuring and Counting Particulate Contamination on Surfaces"

ANSI Z173.5 (1973)

"Method for Sizing and Counting of Airborne Particulate Contamination in Clean Rooms and

Other Dust-Controlled Areas Designed for Electronic and Similar Applications"

ANSI 173.16 (1973)

"Method for Sizing and Counting Particulate Contaminants in and on Clean Room Garments"

ANSI B93.19

"Method for Extracting Fluid Samples from the Lines of an Operating Hydraulic Fluid Power

System (For Particulate Contamination Analysis)"

ANSI Z173.9

"Method for Identification of Minute Crystalline Particle Contaminants by X-Ray Diffraction"

ANSI PTC28-1973

"Determining the Properties of Fine Particle Matter"

ANSI Z257.3

"Sampling Stalks for Particulate Matter"

106
B. American Society of Testing and Materials

ASTM E20-68 (1974)

"Analysis by Microscopical Methods for Particle-Size Distribution of Particulate Substances

of Sub-Sieve Sizes"

ASTM F321 -70T

"Automatic Particle Counter Size Setting"

ASTM F323

"Precision Classif icaiton of Particles"

ASTM F490

"Microscopical Sizing and Counting of Particles on Membrane Filters Using Image Shear"

ASTM F312 - 1969

"Microscopic Counting and Sizing of Particles from Aerospace Fluids on Membrane Filters"

ASTM F21.13 Draft in Committee

"Recommended Practice for Particle Count and Size Distribution Measurement in Batch Samples

for Filter Evaluation Using an Optical Particle Counter"

ASTM F21.13 Draft in Committee

"Standard Practice for Comparing the Particle-Size Distribution of Solids in a Powder or Suspended in Liquid by Means of Automatic Particle Counters"

ASTM F21.13 Draft in Committee

"Method for the Measurement of Particle Count and Size Distribution in Batch Samples for

Filter Evaluation Using an Electrical-Resistance Particle Counter"

ASTM Draft in Committee (F. 07. 01 .05-10)

"Median Method for Particle Counter Single Point Size Calibration"

ASTM Draft in Committee (F. 07. 01 .05-12)

"Practice for Defining Counting and Size Accuracy of a Liquid Borne Particle Counter Using

Near-Monodisperse Spherical Particulate Materials"

ASTM Draft in Committee (F. 07. 01 .05-1 3)

"Recommended Practice for On-Site Calibration of Liquid Borne Automatic Particle Counters

with Adjustable Individual Size Thresholds"

ASTM Draft in Committee (F. 07. 01 .05-14)

"Method for Determining the Quality of Calibration Particles for Automatic Particle Counters"

C. National Fluid Power Association

NFPA T2.9.6 1972

"Method for Calibation of Liquid Automatic Particle Counters Using AC Fine Test Dust"

107
NFPA T3.10.8.8 1973

"Multi-Pass Method for Evaluating the Filtration Performance of a Fine Hydraulic Fluid

Power Filter Element"

NFPA T2.9.3 1973

"Method for Reporting the Contamination Analysis Data of Hydraulic Fluid Power Systems"

D. Society of Automotive Engineers

SAE ARP 1192

"Method for Calibration and Verification of Automatic Liquid Borne Counter (Light Method)"

ISO TC 131/SC (USA) N-12

"Method for Calibration of Liquid Automatic Particle Counters Using AC Fine Test Dust"

E. Other ASTM Standards Related to Particle-Size Measurements

1. Material Characterization

Refractory Metals

Fishersi zer

Turbidimetry

Atmospheric Particles

Optical Sizing

Electronic Counter

Alundum Thimble

Pigment -Vehicles

Print Inks

Polymers/Chlori de

Soi Is

Whiteware Clays

Alumina, Quartz

Air Permeability

Electronic Counter

Centr. Sedimentation

Activated Carbon

White Extender Pigment

Multicolor Lacquers

2. System Characterization

Airborne Collected in Liquid D3365

B330 Airborne Collected in Thimble D3563

B430

Glass-Blow Down Systems

D2009 Automatic Counter F327

D336 5 Manual Measure F308

D3563 Aerospace Fluids

D1210 Metal/Fiber Ident F314

D1316 Microelectronic Components

D1705 Ring Oven Technique F59

D422 Non-Cryogenic Fluid Sampling F301

C775 Particles/Matter in Water D1883

Aviation Turbine Fuels D2276

C721 Surfaces F24

C690 Aerospace Fluids/Convolutes F304

C678 Man-Accessible Aerospace Tanks F306

D2862 Reservoir-Type Pressure Sensors F305

B3360 Aerospace Fluids/Membranes F311

D2338 Sampling Stacks D2928

108
1 . Material Characterization (con't)

Soap/Detergents D502

Metal Ores E383

Plastics D1921

Resins D2451

Asbestos By Screens D2947

Metal Powders B293

TFE-Fluorocarbon Matl's. Dl 457
Appendix D Literature Sources Consulted

During the preparation of this report, a number of bibliographic sources have been

used. These include science and engineering indices, books and articles with extensive

references, instrument company application notes, and individual journals.

Comp uter Literature Sear ch

The science abstracts and the engineering i ndex entries for the period 1969 to September 1979 were searched on the key words related to the dimensional measurement of

particles, and including instruments, techniques, and calibration methods. Approximately

150 titles and abstracts of papers having varying degrees of relevance were compiled.

Published Sources With Extensive References

Stockham and Fochtman's monograph, Particle Size Analysis (Ann Arbor Science, 1977)

contains 58 cited and 42 uncited references on the general subject of its title.

Among the numerous references in the 1976 volume Fine Particles , Willeke and Liu give

50 references related to single particle optical counters and Gebhart and his co-authors

give 50 related to optical aerosol size spectrometry above and below the wavelength of

light.

Kratohvil's review of the literature on "Light Scattering", which appeared in Analytical

Chemistry in 1966, provides 338 references on that subject with explicit consideration

given to work on scattering by spherical and nonspherical particles including latexes.

Allen's scholarly chemical -engineering textbook, Particle Size Measurement (Wiley,

1975), contains over 950 references closely related to various aspects of the title subject

and also contains names and addresses of international manufacturers and suppliers of

particle sampling and size measurement equipment.

Davies' four articles on "Rapid Response Instrumentation" (American Laboratory, Dec. 1973 - Feb. 1974 and April 1978) include over 150 references primarily on equipment

commercially available at those times.

McCrone and Delly's encyclopedia of techniques for small particle identification, The

Particle Atlas (Edition III, Volume 4, 1973), lists over 2000 references up to 1972 on subjects related to the general subject of particle characterization.

Instrument Company Bibliographies

Coulter Electronics Company provides a listing of over 560 references up to 1975 on the applications of their electrical -resistance type liquid-borne counter such subjects as air contamination and water and sewage.

Pacific Scientific Company provides a listing of nearly 200 references up to 1975 on the application of their HIAC light-obscuration type liquid borne counter on subjects

ranging from basic technology to military specifications.

Science Spectrum Company provides a listing of over 70 references up to 1978 on the

application of their various light-scattering type instruments on subjects such as microbiology and molecular weights.

Thermo Systems Incorporated provides a listing of 77 references into 1974 on the

theory, practice, and applications of instruments such as theirs used for laser doppler

veloci timetry

.

Journal

s

Articles on the most fundamental aspects of particle size measurement have appeared

most frequently in Powder Technology, The Journal of Colloid and Interface Science, Applied

110
Optics, The Journal of the Optical Society of America, Review of Scientific Instruments,

and The Journal of Microscopy and Microscope.

ill
Appendix E University and Industry People Contacted

Dr. Arthur Ashkin

Room 4E422

Bell Telephone Laboratories

Holmdell, NJ 07733

(201) 949-2673

Dr. Leigh Bangs

Dow Diagnostic Division

Dow Chemical Co. U.S.A.

Box 68511

Indianapolis, IN 46268

(317) 873-7108

Dr. William S. Bickel

Department of Physics

University of Arizona

Tucson, AZ 85721

(602) 626-1984

Dr. Michael Box Institute for Atmospheric Optics

and Remote Sensi ng P.O. Box P Hampton, VA 23666

Mr. Edward Bradford

Physical Research Laboratory

Dow Chemical Company

Midland, MI 48640

(517) 636-5082

Dr. Petr Chylek

Dept. of Meteorology

Massachusetts Institute of Technology

Cambridge, MA

Dr. Benjami n Chu

Dept. of Chemistry

University of NY - Stonybrook

Stonybrook, NY (516) 246-7792

Dr. Al Brunsting

Coulter Electronics Co. Hialeah, FL 33010

(305) 885-0131

Dr. C. A. Daniels

B. F. Goodrich Company

Avon Lake, OH

(216) 933-6181

Dr. Stanley Duke

Duke Scientific Corp.

445 Sherman Ave. Palo Alto, CA 94306

(415) 328-2400

Dr. Brian Kaye

Institute of Fine Particles Research

Laurentian University

Sudbury, Ontario Canada

(705) 675-1151 ext. 529

Prof. Milton Kerker

Dept. of Chemistry and Institute of

Colloid and Surface Science

Clarkson College of Technology

Potsdam, NY 13676

(315) 268-2390

Mr. Shephard Kinsman

Coulter Electronics Co. 590 W. Twentieth Street

Hialeah, FL 33010

(800) 327-6531

Prof. Jiosip Kratohvil

Dept. of Chemistry and Institute of

Colloid and Surface Science

Clarkson College of Technology

Potsdam, NY 13676

(315) 268-2353

Prof. Irving Krieger

Dept. of Macromolecular Science

Case-Western Reserve University

Cleveland, OH 44106

Mr. Earl Knutson

Environmental Research Lab

U.S. Dept. of Energy

376 Hudson Street

New York, NY (212) 620-3655

Dr. Paul Latimer

Dept. of Physics

Auburn University

Auburn, AL 36830

(205) 826-4264

Dr. Benjamin Y. H. Liu

Particle Technology Laboratory

Mechanical Engineering Dept.

University of Minnesota

Minneapolis, MN 55455

(612) 373-3043

Prof. Robert L. Rowel 1 Dept. of Chemistry

University of Massachusetts

Amherst, MA 01003

(415) 545-0247

112
Prof. Emil Wolf

Dept. of Physics and

Institute of Optics

University of Rochester

Rochester, NY

Mr. Jerry West

HIAC Instruments Co. 4719 W. Brook Street

Montclair, CA 91763

(714) 621-3965

Dr. John Vanderhoff

Leheigh University

Sinclair Science Lab #7

Room 205C

Bethlehem, PA 18015
Appendix F

U. S. Department; of Commerce

John T. <vonjH}rr^Secretary

National BiireaiiHef, Standards

A. V. I Astt#v Director Certificate of Calibration

Standard Reference Material 1003

Calibrated Glass Spheres

(5 to 30 Microns)

This standard sample of microscopically measured beads is issued for use in calibrating equipment and in evaluating methods for measuring particle size in the 5 to 30 micron range. The values given are based on measurements of 10,000 particles, of which 96 percent by volume are spheres. Four particle-size distributions are given with this sample in the form of graphs. These graphs represent

a distribution according to volume (figure 1), a distribution according to weight (figure 2), and two Stokes' law distributions (figures 3 and 4). The volume distribution permits comparison with electronic particle counters which respond according to the volume of the particle. The weight distribution permits comparison

with ultrafine sieves, and the Stokes' law distributions permit comparison with certain types of sedimentation and elutriation methods. Four distributions instead of one arise from the fact that some of the beads contain spherical gas voids which are large enough to affect the weight and sedimentation rate of the bead. Void diameters have been measured and corrections applied. The diameters given in the weight and volume distribution (figures 1 and

2) are actual physical diameters. Those given in the Stokes' law distributions (figures 3 and 4) are diameters corresponding to an equivalent distribution of solid spheres, which, on a weight basis, would settle at the same rate as the actual sample. Comparison of figures 3 and 4 shows the effect of a comparatively large change in the density of the sedimentation medium on the calculated Stokes' law distribution of the sample. The vertical lines in the graph are an estimate of reproducibility based on three times the standard error

of the mean for ten samples of 1,000 beads, each of which represents ten subsamples of 100 beads. This

corresponds to less than ±4 percent of the particle diameter for particles smaller than 20 microns with some- what greater uncertainty for particles larger than this size. The average specific gravity of the beads for purposes of weight-to-volume conversions is 2.39 ±0.01. The

specific gravity of the solid glass for Stokes' law calculations is 2.54 based on measuremens of a single prism

of the same glass. The specific surface computed from microscopic measurements is 1730 ±50 cm-/g, which

corresponds with a specific-surface mean diameter of 14.5 ±0.4 microns. The sample contains between

500,000 and 600,000 particles per milligram.

Two bottles of beads are provided. It is recommended that each bottle be shaken vigorously for a minute

before sampling, and beads be taken from a number of places in each. When the results of the two bottles are analyzed separately, there should be no systematic difference between the two sets of results in excess of the reported reproducibility limits of the sample. The surface of the glass in these beads can react with atmospheric moisture, which, with time, tends to make them more difficult to disperse. Direct exposure to relative humidities above 90 percent will produce a

noticeable effect on dispersibility within three days, whereas the effect is exceedingly slow at relative humidities less than 50 percent, and can be minimized, if not eliminated entirely by storing the beads in a desiccated atmosphere.

Washington, D. C. July 1, 1965.

20234 W. Wayne Meinke, Chief,

Office of Standard Reference Materials

114
FIG. I. VOLUME DISTRIBUTION

115
FIG. 2. WEIGHT DISTRIBUTION

116
FIG. 3. STOKES' LAW DISTRIBUTION

(CALCULATED FOR WATER)

117
118
U. S. Depart/tear^ of Commerce

Peter QjjPeterson Rational T&mmu of Standards

(Certificate of (ttalibratiort

Standard Reference Material 1004

Calibrated Glass Beads

R. K. Kirby

This Standard Reference Material is intended for use in the evaluation of the effective opening of

wire-cloth sieves in the range 34 /um through 120 /mi (Test Sieve Nos. 400, 325, 270, 230, 200,

170, and 140). The weight of glass beads in each bottle is about 63 g. While most of the beads are spherical about 6 percent by number range from nearly spherical beads to ellipsoidal beads and

fused beads.

The distribution of sizes in this SRM as determined by microscopic measurement is given in Table 1 as the weight percent of glass beads that are smaller than those that have the indicated diameter.

Over 13,000 beads were measured in the course of this calibration. These beads were sampled

from 6 bottles that were selected at intervals throughout the bottling process. Repeat measurements

were made on 2 of the bottles. The beads in these bottles were also carefully compared by sieving

with the beads from 21 other bottles, also selected at random. These intercomparisons show no

significant difference between beads from all 27 bottles. Considering the values of percent finer to be exact, the mean of the standard deviations associated with each diameter is 0.9 ± 0.4 jitm. This

error includes those errors due to the bottling and measuring processes and is to be expected when a given sieve is calibrated with different bottles of this SRM. In addition to this error, the user may

impose a sieving error of about ± 2 ;um, the result of differing ambient conditions. The reproducibility is, of course, dependent upon the sieving method and the care exercised by the operator.

The method that was used in the preparation of these calibrated glass beads (U.S. Patent No. 2,693,706, November 9, 1954) is described in a paper by F. G. Carpenter and V. R. Deitz, Glass Spheres for the Measurement of the Effective Opening of Testing Sieves, J. Research NBS 47,

139(1951).

The overall coordination and evaluation of data leading to certification of this SRM was per- formed by R. K. Kirby.

The technical and support aspects involved in the preparation, certification, and issuance of this Standard Reference Material were coordinated through the Office of Standard Reference Materials by W. P. Reed.

Washington. D. C. 20234 J. Paul Cali, Chief- April 3, 1972 Office of Standard Reference Materials

(over)

119
Table 1

Cumulative Size Distribution by Weight

Weight Diameter Weight Diameter Weight Diameter

percent (Effective percent (Effective percent (Effective

finer sieve finer sieve finer sieve opening) opening) opening)

% Mm % Mm % Mm

2 28 34 61 68 89

4 31 36 62 70 90

6 34 38 63

8 36 40 65 72 92

to 38 74 94

42 67 76 96

12 40 44 69 78 100

14 42 46 71 80 105

16 45 48 74

18 47 50 76 82 109

20 49 84 111

52 78 86 113

22 51 54 80 88 115

24 53 56 82 90 117

26 55 58 83

28 56 60 84 92 119

30 58 94 121 62 86 96 123

32 59 64 87 98 126

66 88

Directions for Using Calibrated Glass Beads for the Evaluation of the Effective Opening of Sieves

The Calibration Process

The aperture size of a sieve can be determined as the average size of the openings in the sieve. However, the purpose of a sieve is to measure the size of part; cles, and therefore, it is the effective opening that must be determined. This is done by using particles of known size. Thus the effective opening is determined by the size of calibrated glass beads that will just pass through the sieve. This

in turn permits the measurement of the particle size of an unknown material that will also just pass through the sieve.

The openings of a sieve are not all the same size, and particles that are coarser than the average opening can pass through the larger holes. Thus, the effective opening is generally larger than the average opening. In addition, the separation achieved by a sieve is not sharp. A few particles capable

of passing the sieve are always retained. The number of particles retained or passed depends upon

the manner and time of shaking, and any measurement of the effective opening must take these

variables into account. To a large extent, the glass bead method of calibration automatically

includes these effects because the sieves are shaken in the same manner when calibrated as when

measuring an unknown material.

120
The sieve openings are essentially square in shape and particles of irregular shape can pass through even though one of the dimensions of the particle is considerably larger than the diameter

of the opening. This is especially true for needlelike shapes. The average diameter of such irregular

particles that pass a sieve cannot be considered equal to the effective opening of the sieve as measured by the diameter of spheres that just pass.

For the application of the calibrated glass beads to sieve analysis, see Carpenter, F. G., and Deitz, V. R., Methods of Sieve Analysis with Particular Reference to Bone Char, J. Research NBS 45, 328

(1950).

Calibration Procedure

To evaluate the effective opening of testing sieves with glass beads, the entire standard is placed on the top sieve. The sieves are then shaken in a shaking device, or by hand, in exactly the same manner as that to be followed in routine analysis.

After the shaking has been completed, the stack of sieves is disassembled, and the beads are removed from each sieve and placed into a suitable weighing bottle. Experience has shown that loss of beads is very likely to occur during this operation. Therefore, the whole operation should be

carried out over a large piece of glazed paper to permit recovery of any beads that may accidently

be spilled. Such loss can also be minimized by the use of a funnel large enough to completely

contain the sieve. The stem of the funnel should be fitted snugly into the mouth of the weighing

bottle so that none of the beads can escape. The sieve is inverted into the top of the funnel and all of the glass beads are removed with a soft brush. Any beads that stick to the funnel should be swept

into the weighing bottle with the brush.

Each of the sieve fractions is weighed to the nearest 0.01 g. After weighing, all beads are returned to the original container and kept for reuse. The weight percent retained on each sieve is calculated from the weights of the sieve fractions. The percent passing through each sieve is deter- mined by subtracting the percentage on the coarsest sieve from 100 percent, the percentage on the next sieve from that result, and so on. The effective size of the sieve opening is determined by

interpolation between the nearest values given in the calibration table.

Example of Calculation Procedure

An example of data and calculations are shown below. Seven sieves were calibrated at the same

time. The original weight of the glass beads was 63.30 g. It may be noted that the sum of the weights shows a loss of 0.09 g. This loss is assumed to be evenly distributed and the sum of the weights is used to evaluate the percentages.

121
Example of calculation for effective opening

U.S.

sieve No.

Weight on sieve

Weight percent Opening of sieve

On sieve Finer than

sieve

Effective3 Nominal

140 9.99 g 15.81 84.2 111 nm 106 fim 170 5.88 9.30 74.9 95 90

200 14.86 23.50 51.4 77 75

230 8.12 12.84 38.6 64 63

270 6.44 10.19 28.4 56 53

325 7.73 12.23 16.1 45 45

400 3.29 5.21 10.9 39 38

Pan 6.90 10.92 63.21

a Determined by interpolation between values given in the calibration table.

Foreign Material and Dirt

If the sieves are not cleaned sufficiently before the calibration, some foreign material will be

found among the glass beads. If possible, this foreign material must be removed by hand. A dirty appearance of the glass beads indicates that they have picked up a small amount of dust. The weight

of the dust is usually so small that only a negligible error is introduced.

If the sieves to be calibrated have been used they may be cleaned thoroughly with a soft brush, soap and water or solvents. Under no circumstance should a sharp object be used to dislodge

particles that are stuck in the meshes.

Loss of Weight with Use

Experience has shown that there is a loss in weight of the beads with use. How great a loss can be

tolerated without introducing large errors in the calibration is difficult to state. However, a quick

check of the accuracy of the beads can be made by "cross-calibrating" a single sieve with the questionable beads and new or relatively little used beads. A variation significantly greater than

± 3 jum would indicate that the accuracy of the questionable beads has suffered from a loss of

v/eight. If an SRM is ruined by either repeated use or accident, the only recourse is to purchase a new SRM from the National Bureau of Standards.

122
U. S. Department of Commerce

MauriceJH. Stans

Sr. retM-v

National BurealS of Standards

L. M. Branscomb, Director

Rational ^itram of jltartctartta

Certificate of Calibration

Standard Reference Material 1017a

Calibrated Glass Beads

R. K. Kirby

This Standard Reference Material is intended for use in the evaluation of the effective opening of

wire-cloth sieves in the range 100 Mm through 310 jum (Test Sieves Nos. 140, 120, 100, 80, 70, 60,

and 50). The weight of glass beads in each bottle is about 84 g. While most of the beads are spherical about 8 percent by number range from nearly spherical beads to ellipsoidal beads and a few conglomerates.

The distribution of sizes in this SRM as determined by microscopic measurement is given in Table 1 as the weight percent of glass beads that are smaller than those that have the indicated diameter.

Over 60,000 beads were measured in the course of this calibration. These beads were sampled

from 24 bottles that were selected at intervals throughout the bottling process. Repeat measure- ments were made on 7 of the bottles. Considering the values of percent finer to be exact, the mean

of the standard deviations associated with each diameter is 4.6 ± 2.0 /im. This error includes those

errors due to the bottling and measuring processes and is to be expected when a given sieve is calibrated with different bottles of this SRM. In addition to this error, the user may impose a sieving error of about ±3.5 /im, the result of differing ambient conditions. The reproducibility is, of

course, dependent upon the sieving method and the care exercised by the operator.

The method that was used in the preparation of these calibrated glass beads (U.S. Patent No.

2,693,706, November 9, 1954) is described in a paper by F.G. Carpenter and V. R. Deitz, Glass Spheres for the Measurement of the Effective Opening of Testing Sieves, j. Research NBS 47,

139(1951).

The overall coordination and evaluation of data leading to certification of this SRM was per formed by R. K. Kiiby.

The technical and support aspects involved in the preparation, certification, and issuance of this Standard Reference Material were coordinated through the Office of Standard Reference Materials by W. P. Reed.

Washington, D. C. 20234 J. Paul Cali, Chief

September 24, 1971 Office of Standard Reference Materials

(over)

123
Table 1

Cumulative Size Distribution by Weight

iVeight Diameter Weight Diameter Weight Diameter

lercent (Effective percent (Effective percent (Effective

liner sieve finer sieve finer sieve opening) opening) opening)

% pin % fim % /im

1 82 34 163 67 219

2 88 35 165 68 222

3 92 69 226

4 94 36 167 70 229

5 97 37 169

38 170 71 232

6 100 39' -> y 172 72 235

104 40 173 73 238

107 74 240

o 1 1

0

41 175 75 243

to 111^1 9 42 1 76

43 178 764 V> 245

1

1

11 14. It1 44 77

1 9 11U 1 1 6 4^ iuu 7ft

J KJ 1 1 8 79 252

1 1 Q 1 Q 1

1 O 1 ftO

1 C

1 o 1—iU 4- i Aft ftl 0

1

9^Q

16 122 49 185 82 263

17 123 50 186 83 269

L8 124 84 274

1" 125 51 187 85 279

20 127 52 189

53 190 86 283

21 128 54 191 87 287

22 130 55 193 88 291

23 131 89 295

24 133 56 194 90 299

25 135 57 196

58 197 91 303

26 137 59 199 92 308

27 140 60 201 93 312

28 143 94 316

29 146 61 203 95 320

30 150 62 205

63 207 96 324

3] 153 64 210 97 328

32 157 65 213 98 333

33 160 99 341

66 216

124
Directions for Using Calibrated Glass Beads for the Evaluation of the Effective Opening of Sieves

The Calibration Process

The aperture size of a sieve can be determined as the average size of the openings in the sieve. However, the purpose of a sieve is to measure the size of particles, and therefore, it is the effective opening that must be determined. This is done by using particles of known size. Thus the effective opening is determined by the size of calibrated glass beads that will just pass through the sieve. This

in turn permits the measurement of the particle size of an unknown material that will also just pass through the sieve.

The openings of a sieve are not all the same size, and particles that are coarser than the average opening can pass through the larger holes. Thus, the effective opening is generally larger than the average opening. In addition, the separation achieved by a sieve is not sharp. A few particles capable

of passing the sieve are always retained. The number of particles retained or passed depends upon

the manner and time of shaking, and any measurement of the effective opening must take these

variables into account. To a large extent, the glass bead method of calibration automatically in- cludes these effects because the sieves are shaken in the same manner when calibrated as when

measuring an unknown material.

The sieve openings are essentially square in shape and particles of irregular shape can pass through even though one of the dimensions of the particle is considerably larger than the diameter

of the opening. This is especially true for needlelike shapes. The average diameter of such irregular

particles that pass a sieve cannot be considered equal to the effective opening of the sieve as measured by the diameter of spheres that just pass.

For the application of the calibrated glass beads to sieve analysis, see Carpenter, F. G., and Deitz, V. R., Methods of Sieve Analysis with Particular Reference to Bone Char, J. Research NBS 45,

328 (1950).

Calibration Procedure

To evaluate the effective opening of testing sieves with glass beads, the entire standard is placed on the top sieve. The sieves are then shaken in a shaking device, or by hand, in exactly the same manner as that to be followed in routine analysis.

After the shaking has been completed the stack of sieves is disassembled, and the beads are removed from each sieve and placed into a suitable weighing bottle. Experience has shown that loss of beads is very likely to occur during this operation. Therefore, the whole operation should be

carried out over a large piece of paper to permit recovery of any beads that may accidently be

spilled. Such loss can also be minimized by the use of a funnel large enough to completely contain

the sieve. The stem of the funnel should be fitted snugly into the mouth of the weighing bottle so

that no beads can bounce out. The sieve is inverted into the top of the funnel and all of the glass beads are removed with a stiff brush.

Each of the sieve fractions is weighed to the nearest 0.01 g. After weighing, all beads are returned to the original container and kept for reuse. The weight percent retained on each sieve is calculated from the weights of the sieve fractions. The percent passing through each sieve is deter- mined by subtracting the percentage on the coarsest sieve from 100 percent, the percentage on the next sieve from that result, and so on. The effective size of the sieve opening is determined by

interpolation between the nearest values given in the calibration table.

125
Example of Calculation Procedure

An example of data and calculations are shown below. Seven sieves were calibrated at the same

time. The original weight of the glass beads was 87.46 g. It may be noted that the sum of the weights shows a loss of 0.11 g. This loss is assumed to be evenly distributed and the sum of the weights is used to evaluate the percentages.

Example of calculation for effective opening

U.S.

sieve No.

Weight on sieve

Weight percent Opening of sieve

On sieve Finer than

sieve

Effective* Nominal

50 7.81 g 8.94 91.1 304 nm 300 Mm

60 11.24 12.87 78.2 250 250

70 9.79 11.21 67.0 219 212

80 19.29 22.09 44.9 180 180

100 12.86 14.72 30.2 150 150

120 8.54 9.77 20.4 127 125

140 11.32 12.96 7.4 105 106 Pan 6.50 7.44 87.35

Determined by interpolation between values given in the calibration table.

Foreign Material and Dirt

If the sieves are not cleaned sufficiently before the calibration, some foreign material will be found among the glass beads. If possible, this foreign material must be removed by hand. A dirty appearance of the glass beads indicates that they have picked up a small amount of dust. The weight

of the dust is usually so small that only a negligible error is introduced.

If the sieves to be calibrated have been used they may be cleaned thoroughly with a sturdy

brush, not too stiff, soap and water or solvents. Under no circumstance should a sharp object be used to dislodge particles that arc stuck in the meshes.

Loss of Weight with Use

Experience has shown that there is a loss in weight of the beads with use. How great a loss can be

tolerated without introducing large errors in the calibration is difficult to stale. However, a quick

check of the accuracy of the beads can be made by "cross-calibrating" a single sieve with the questionable beads and new or relatively little used beads. A variation significantly greater than ± 5

jum would indicate that the accuracy of the questionable beads has suffered from a loss of weight. If an SR.M is ruined by either repeated use or accident, the only recourse is to purchase a new SRM

from the National Bureau of Standards.

126
U. S. Department of Commerce

Frederick B. Dent

Secretary

National Bureau of Standards

Richard W. Roberta, Director Rational J&nxtan of Standards

(Certificate of Calibration

Standard Reference Material 1018a

Calibrated Glass Beads

R. K. Kirby

This Standard Reference Material is intended for use in the evaluation of the effective opening of

wire-cloth sieves in the range 225 Mm through 780 Mm (Test Sieve Nos. 60, 50, 45, 40, 35, 30, and

25). The weight of glass beads in each bottle is about 74 g. While most of the beads arc spherical

about 6 percent by number range from nearly spherical beads to elliposidal beads and fused beads.

The distribution of sizes in this SRM as determined by microscopic measurement is given in Table 1 as the weight percent of glass beads that are smaller than those that have the indicated diameter.

Over 18,000 beads were measured in the course of this calibration. These beads were sampled

from 10 bottles that were selected at intervals throughout the bottling process. The beads in these

bottles were also carefully compared by sieving with the beads from 20 other bottles, also selected

at random. These intercomparisons show no significant difference between beads from all 30

bottles. Considering the values of percent finer to be exact, the standard deviation associated with each test sieve is: No. 60, 2.1 Mm; No. 50, 2.5 Mm; No. 45, 2.9 Mm; No. 40, 2.7 Mm; No. 35, 3.8 Mm;

No. 30, 3.3 Mm; and No. 25, 4.5 Mm. It was assumed that the effective opening would be within the

permissible variation of average opening as specified in the ASTM Standard Specification for Wire- Cloth Sieves, El 1-70. This error includes those errors due to the bottling and measuring processes and is to be expected when a given sieve is calibrated with different bottles of this SRM. In addition

to this error, the user may impose a sieving error of about ± 2 Mm, the result of differing ambient

conditions. The reproducibility is, of course, dependent upon the sieving method and the care exercised by the operator.

The method that was used in the preparation of these calibrated glass beads (U. S. Patent No.

2,693,706, November 9, 1954) is described in a paper by F. G. Carpenter and V. R. Deitz, Glass Spheres for the Measurement of the Effective Opening of Testing Sieves, J. Res. NBS 47, 139

(1951).

The overall coordination and evaluation of data leading to certification of this SRM was per- formed by R. K. Kirby.

The technical and support aspects involved in the preparation, certification, and issuance of this Standard Reference Material were coordinated through the Office of Standard Reference Materials by W. P. Reed.

Washington. D. C. 20234 J. Paul Cali, Chief

May 16, 1973 Office of Standard Reference Materials

(over)

127
Directions for Using Calibrated Glass Beads for the Evaluation of the Effective Opening of Sieves The Calibration Process

The aperture size of a sieve can be determined as the average size of the openings in the sieve. However, the purpose of a sieve is to measure the size of particles, and therefore, it is the effective opening that must be determined. This is done by using particles of known size. Thus the effective opening is determined by the size of calibrated glass beads that will just pass through the sieve. This

in turn permits the measurement of the particle size of an unknown material that will also just pass through the sieve.

The openings of a sieve are not all the same size, and particles that are coarser than the average opening can pass through the larger holes. Thus, the effective opening is generally larger than the average opening. In addition, the separation achieved by a sieve is not sharp. A few particles capable

of passing the sieve are always retained. The number of particles retained or passed depends upon

the manner and time of shaking, and any measurement of the effective opening must take these

variables into account. To a large extent, the glass bead method of calibration automatically in- cludes these effects because the sieves are shaken in the same manner when calibrated as when

measuring an unknown material.

The sieve openings are essentially square in shape and particles of irregualr shape can pass through even though one of the dimensions of the particle is considerably larger than the diameter

of the opening. This is especially true for needlelike shapes. The average diameter of such irregular

particles that pass a sieve cannot be considered equal to the effective opening of the sieve as measured by the diameter of spheres that just pass.

For the application of the calibrated glass beads to sieve analysis, see Carpenter, F. G. and Deitz, V. R. Methods of Sieve Analysis with Particular Reference to Bone Char, J. Res. NBS 45, 328

(1950).

Calibration Procedure

To evaluate the effective opening of testing sieves with this SRM all of the glass beads are placed on the top sieve. The sieves are then shaken in a shaking device, or by hand, in exactly the same manner as that to be followed in routine analysis.

After the shaking has been completed the stack of sieves is disassembled, and the beads are removed from each sieve and placed into a suitable weighing bottle. Experience has shown that loss of beads is very likely to occur during this operation. Therefore, the whole operation should be

carried out over a large piece of paper to permit recovery of any beads that may accidently be

spilled. Such loss can also be minimized by the use of a funnel large enough to completely contain

the sieve. The stem of the funnel should be fitted snugly into the mouth of the weighing bottle so

that no beads can bounce out. The sieve is inverted into the top of the funnel and all of the glass beads are removed with a stiff brush.

Each of the sieve fractions is weighed to the nearest 0.01 g. After weighing, all beads are returned to the original container and kept for reuse. The weight percent retained on each sieve is calculated from the weights of the sieve fractions. The percent passing through each sieve is deter- mined by subtracting the percentage on the coarsest sieve from 100 percent, the percentage on the next sieve from that result, and so on. The effective size of the sieve opening is determined by

interpolation between the nearest values given in the calibration table.

128
Table 1

Cumulative Size Distribution by Weight

Weight Diameter Weight Diameter Weight Diameter

percent (Effective percent (Effective percent (effective

finer sieve finer sieve finer sieve opening) opening) opening)

% nm % Aim % Mm

1 200 34 349 67 581

2 207 35 354 68 583

3 212 69 585

4 217 36 360 70 588

5 221 37 367

38 375 71 590

6 225 39 385 72 592

7 229 40 396 73 595

8 233 74 598

9 236 41 408 75 602

10 239 42 420

43 432 76 606

11 242 44 444 77 611

12 245 45 454 78 617

13 249 79 627

14 253 46 462 80 646

15 257 47 469

48 475 81 680

16 262 49 480 82 692

17 267 50 486 83 700

18 274 84 706

19 281 51 493 85 712

20 289 52 500

53 507 86 717

21 296 54 515 87 723

22 302 55 523 88 729

23 307 89 736

24 312 56 531 90 743

25 316 57 539

58 546 91 750

26 320 59 552 92 759

27 323 60 557 93 769

28 326 94 779

29 329 61 561 95 791

30 332 62 565

63 569 96 803

31 336 64 572 97 817

32 340 65 575 98 832

33 344 99 849

66 578

129
Example of Calculation Procedure

An example of data and calculations are shown below. Seven sieves were calibrated at the same

time. The original weight of the glass beads was 73.91 g. It may be noted that the sum of the weights shows a loss of 0.02 g. This loss is assumed to be evenly distributed and the sum of the weights is used to evaluate the percentages.

Example of calculation for effective opening

Weight

Weight percent Opening of sieve

U.S. on sieve

sieve No. On sieve Finer than Effective" Nomina

sieve

25 8.43 g 11.41 88.6 733 /urn 710/jm

30 7.76 10.50 78.1 618 600

35 18.63 25.21 52.9 506 500

40 7.86 10.64 42.2 422 425

45 4.63 6.27 36.0 360 355

50 10.48 14.18 21.8 301 300

60 5.99 8.11 13.7 252 250

Pan 10.11 13.68 73.89

a Determined by interpolation between values given in the calibration table.

Foreign Material and Dirt

If the sieves are not cleaned sufficiently before the calibration, some foreign material will be

found among the glass beads. If possible, this foreign material must be removed by hand. A dirty appearance of the glass beads indicates that they have picked up a small amount of dust. The weight

of the dust is usually so small that only a negligible error is introduced.

If the sieves to be calibrated have been used they may be cleaned thoroughly with a sturdy

brush, not too stiff, soap and water or solvents. Under no circumstance should a sharp object be

used to dislodge particles that are stuck in the meshes.

Loss of Weight with Use

Experience has shown that there is a loss of weight of the beads with use. How great a loss can

be tolerated without introducing large errors in the calibration is difficult to state. However, the

variation of the accuracy of the "working sample" can be monitored by periodically calibrating a

set of sieves with it and one or two others that are kept in reserve. A variation significantly greater than ± 5 /im would indicate that the accuracy of the questionable beads has suffered from a loss of

weight. If an SRM is ruined by either repeated use or accident, the only recourse is to purchase a new SRM from the National Bureau of Standards.

130
U. S. Department of Commerce

Philip M. Klutznick

Secretary

National Bureau of Standards

Ernest Ambler. Director

Rational ^Bureau of Standards

diertifttate

Standard Reference Material 484b

Scanning Electron Microscope Magnification Standard

(A Stage Micrometer Scale)

David B. Ballard and Fielding Ogburn

This Standard Reference Material is intended for use in calibrating the scanning electron microscope (SEM) magnification scale to an accuracy of 5% or better within the range of l,000to 20,000X. Each SRM bears an identification number

and has been individually measured. The certified distances between the centers of specific lines opposite the Knoop indentation (see the sketch on page 2) are provided with each SRM together with a photomicrograph that shows the area used in the measurement. The certifica- tion is valid within an area 24 /im wide centered about a line extending from the Knoop indentation. The distances between the lines were determined from measurements made on photographs taken with an SEM in which

each SRM was compared by substitution with a Master Standard; thus each reported interval has been corrected for SEM magnification drift. The operating conditions of the SEM were monitored and a resolution of 0.050 /urn was

maintained using an SEM resolution test specimen.

The Master Standard was calibrated by an interferometry technique using a helium-neon iodine-stabilized laser as the length standard in the NBS Mechanical Processes Division. The uncertainty of this calibration, based on 160 independent measurements on each spacing, is 0.006 fim for distances fronY 1 to 50 /xm. The total uncertainty for the distances between line pairs 0 *! and 0-»2 (nominal distances of 1 and 2 fxm) is 0.032 /tm, between line pairs 2 -»3 and 3 -+4 (nominal distances of 3 and 5 /nm) is 0.056 fim, and for the distance between line pair 0 -»6 (nominal distance of 50 txm) is 0. 580 iim. These total uncertainties are the linear sums of errors associated with the Master Standard calibration and the comparison of each SRM with the Master Standard. The technical and support aspects involved in the certification and issuance of this Standard Reference Material were

coordinated through the Office of Standard Reference Materials by R.K. Kirby.

Washington, D.C. 20234 November 26, 1980

(over)

George A. Uriano, Chief

Office of Standard Reference Materials

131
Gold Lines

Knoop Indentation

3/i.n

5/j.tn Nickel

ZOfim-

-50^.m-

-40/j.mK

o

Ol Ido«

a.

Q.OO

Line 012 3 4

The polished surface of each SRM has been carefully ground and polished using metallographic techniques. The

carbonaceous contamination (a product of SEM electron beam bombardment) can be removed by light hand polishing on a stationary surface covered with micro cloth using metallographic 0.05-jim -y-alumina powder. This cleaning process does not alter the certified spacing of the lines by more than 0.010 /urn. Other cleaning techniques that remove surface material sufficient to obliterate the Knoop indentation will void the calibrated distance values. A recommended procedure for calibrating the magnification of the SEM using SRM 484b is given on the following page and by ASTM E766-80 Practice for Calibrating the Magnification of SEM Using SRM 484. It is suggested that the user extend the calibration to adjacent areas outside of the certified area on the SRM for routine use as a "Working

Standard." A list of parameters that may affect the resultant magnification of an SEM is given on page 4. The significant contributions of the following NBS staff members are hereby acknowledged: J. P. Young for techniques

of electroplating; D.R. Black for metallographic services; J.S. Beers for calibration of the Master Standard; and

M.C. Croarkin for statistical analysis.

SRM 484b

Page 2

132
The operational steps indicated by the manufacturers of scanning electron microscopes to calibrate the magnification

scale are different and often do not consider all the instrument parameters that may change the resultant magnification

(see next page). The following procedure details the use of NBS SRM 484b to calibrate one particular SEM, but may be used as a guide for calibration of other SEMs.

Outline of Procedure for Calibrating SEM Magnification Scale

1. After the surface of the SRM 484b has been inspected for cleanliness rigidly mount it on an SEM stub with electrically conductive cement or clamp it onto the SEM stage.

2. The surface of SRM 484b should be normal to the electron beam or the tilt axis of the stage should be perpendicular

to the gold lines of the SRM.

3. A clean vacuum of 10

2 Pa (10

4 Torr) or better is necessary to keep the contamination rate as low as possible.

4. Allow a 30-minute or more warm-up of electronic circuits to achieve operational stability.

5. Adjust electron gun voltage (between 5 to 30 kV), saturate filament, and check filament alignment.

6. Adjust all lens currents at a resettable value. Cycle lens circuit OFF-ON 3 times to minimize hysteresis effects.

7. Adjust lens apertures and stigmator for optimum resolution (minimum astigmatism).

o

8. SEM resolution should be a minimum of 0.05 (jm (500 A), or better.

9. Position the SRM, at a nominal magnification of 1 KX, so that the image of the Knoop indentation is centered at one

edge of the viewing cathode ray tube (CRT). The width of the gold line calibrated area extends 12 nm above and

below this indentation.

10. The same working distance or magnification scale of the SEM can be reproducibly obtained by focusing on the image of the gold lines with Z axis control at highest possible magnification to minimize depth of focus. An alternate focus method is to use single line wave form ("y" mode) and adjust Z axis for maximum signal height.

1 1. To minimize the effect of linear distortions produced by the recording system, the procedure is as follows: The SRM

is substituted for the unknown sample and photographed. The lines on the SRM to be used in the calibration should

be chosen so that the distance between them matches the length of the object to be measured with both images

positioned in the same area on the CRT. A millimeter scale taped onto the edges of the CRT in the x and y directions

will assist in the relocation of the respective images.

12. Add contrast, if necessary, S/N ratio should be 2:1 minimum.

13. After photo recording, if using Polaroid, allow prints to dry 15 to 20 minutes or more to minimize effects due to emulsion and coating shrinkage.

14. Measure the perpendicular distance between the lines using the CENTER of each line image on the photograph

with a TEM Diffraction Plate Reader or use an equivalent instrument, the precision of which (about 0.2 mm) is suitable for this purpose.

15. Repeat measurements 3 times on each photograph to determine the average spacing.

, , . . . „ . Distance measured between image lines on photograph

16. Magnification = ^

. c , .. ? 2 rr*- 2—E—

Certified distance between same lines

17. To determine the SEM stability and reproducibility, repeat all steps at hourly or daily intervals or after adjustments and repairs.

SRM 484b

Page 3

133
PARAMETERS THAT INFLUENCE THE RESULTANT MAGNIFICATION OF AN SEM

The parameters listed below may interact with each other. They are considered in order of their location in the instrument from electron source to the recorded photograph.

1. Electron gun high-voltage instability can change the wavelength of the electrons and thus the final focus.

2. Different condenser-lens strength combinations change the focal point of the final lens.

3. Uncorrected final lens astigmatism can give a false indication of exact focus.

4. Residual magnetic hysteresis, particularly in the final lens, can change the focal conditions.

5. Long depth of focus, particularly at low magnification and small beam divergence controlled by lens and aperture

selection, can lead to incorrect focus.

6. Nonorthogonal deflection (x-y axis) can be produced by scan coils.

7. Scan generator circuits may be nonlinear and/or change with aging of circuit components.

8. Zoom control of magnification can be nonlinear.

9. Nonlinearity of scan rotation accessory can distort magnification at different degrees of rotation.

10. Distortion of the electron beam sweep may occur from extraneous magnetic and electrostatic fields.

11. The percent error in magnification may be different for each magnification range.

12. A tilted sample surface (not perpendicular to the beam axis ) will introduce foreshortening and magnification

variation.

13. The tilt correction applied may not be relative to the tilt axis of the sample or of a particular area on the sample

surface.

14. Signal processing, particularly differentiation or homomorphic processing, can give a false impression of focus. DC suppression (sometimes called differential amplification, black level/gain, dark level or contrast expansion)

may be used because of the isotropic affect on the image.

15. The objective lens on some instruments may be electrically coupled to the magnification meter, thus focus and

magnification are operator dependent.

16. For the same apparent magnification, two different combinations of working distance and beam scan-raster will produce different linear magnification.

17. Thermal and electronic drift of circuit components related to the above parameters can affect magnification with time in a random manner.

18. Distortion of faceplate and nonorthogonal beam deflection of the CRT can produce nonlinear magnification.

19. Camera lens distortion and change of photo image-to-CRT atio can lead to magnification errors.

20. Expansion or contraction of photographic material, photographic enlarging, and control of contrast, can all have

a significant affect on final apparent image magnification.

SRM 484b

Page 4

134
Appendix G Tolerances Attached to the

Average Quoted in Certain Tables

The uncertainties attached to the averages are the "2 o^" uncertainties in the mean. The average of N values, assumed to be independent, is given by:

3

x = 1 I x- N

L

The sample standard deviation o

s is given by

1/2

where N is very large.

The "2o;v]" uncertainty is given by:

2oM

- k-|as

where a

s is the sample deviation, is the standard deviation or the mean of the population, and k-| is the factor which relates the sample average deviation and the population

standard deviation.

For N small (i.e., less than about 30), the "2a limit" differs significantly from the

"95% confidence limit". The factor k 2 relates the sample average deviation and the 95%

confidence interval:

(95% confidence interval) = l<2a s

•

Only as N > 30, does K = k -| /k 2 have a value within about 1% of unity.

135
The Factors lq, K]_, l<2, and K2 are Given in the Following Table

for Various Values of n from 2 to 60

Number of Unbiased 2om Sample 95% Mean 95%

Determinations Estimator Estimator Confidence Confidence

n k

n ci: "l k2 [2] k 2 k

2

c 0. 797 1 .77 11 £.1 ? 71/ 1 a QQJ J 0 2D

3 0. 886 1 .30 4.30 2. 48 0 .52

4 0. 921 1 .09 3.18 1

.

59 0 .69

5 0. 940 0 .95 2.78 1. 24 0 .77

6 0. 952 0 .86 2.57 1. 05 0 .82

7 0. 959 0 .79 2.45 0. 93 0 .85

8 0. 965 0 .73 2.37 0. 84 0 .87

20 0. 987 0 .45 2.09 0. 47 0 .94

30 0. 991 0 .37 2.04 0. 37 1 .00

60 0. 996 0 .26 2.00 0. 26 1 .00

1. Natrella, M. G. and C. Eisenhart, "Basic Statistical Concepts and

Preliminary Considerations," NBS Handbook 91 (1966).*

2. Ku, H., "Statistical Concepts in Metrology," Handbook of Industrial

Metrology , ASTME, Prentice Hall (1967).*

* Reprinted in Precision Measurement and Calibration: Statistical

Concepts and Procedures , NBS SP-300, Vol. I (Feb. 1969).

U.S. GOVERNMENT PRINTING OFFICE : 1983 O—380-997 (5185)

136
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

SHEET (See instructions) NBS SP 260--35 September 1983

4. title and subtitle Standard Reference Materials:

A Look at Techniques for the Dimensional Calibration of Standard Microscopic

Particles

5. AUTHOR(S)

Dennis A. Swyt

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234 Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

Same as in item 6 above.

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 83-600571

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

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

bibliography or literature survey, mention it here)

This report surveys generic techniques for the dimensional calibration of microscopic

particle size standards. It notes some user needs and available instrumentation,

documentary standards, and commercial, sized particles. It discusses the elements

of the measurement process, including the particle and medium, size-dependent

phenomena, shape factors, single-number indices of average size, and means of length

calibration. The report examines systematic differences among published results of

electron microscopy, light scattering, particle counter, and other measurements on widely-used commercial polymer spheres. It concludes that the definitive calibration

of narrow-distribution polymer spheres, a prerequisite first step toward calibration

of irregularly-shaped matter, would best involve a three-element approach involving

the techniques named.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

dimensional measurement; electron microscopy; flow-through particle counters; latex

spheres; light scatter; micrometrology; microscopic spheres; Mie scattering; optical

microscopy; particle standards; particle size calibration; polymer spheres;

scanning electron microscope; transmission electron microscope.

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150

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