Vacuum Microbalance Techniques: Volume 8 Proceedings of the Wakefield Conference, June 12–13, 1969
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VACUUM MICROBALANCE TECHNIQUES
Volume 2 Washington,D.C., Conference-1961
Volume 5 Princeton Conference-1965 Edited by Klaus H. Behrndt
Volume 6 Newport Beach Conference-1966
Edited by A. W. Czanderna
Volume 7 Eindhoven Conference-1968
Edited by C. H. Massen and H. J . van Beckum
Volume 8 Wakefield Conference-1969 Edited by A. W. Czanderna
VACUUM MICROBALANCE TECHNIQUES VOLUME 8
Proceedings of the Wakefield Conference June 12-13. 1969
Edited by A. W.Czanderna
<:f? PLENUM PRESS • NEW YORK-LONDON • 1971
Library of Congress Catalog Card Number 61-8595
ISBN 978-1-4757-0135-7 ISBN 978-1-4757-0133-3 (eBook) DOl
10.1007/978-1-4757-0133-3
© 1971 Plenum Press, New York Soft cover reprint of the hardcover
1st edition 1971
A Division of Plenum Publishing Corporation 227 West 17th Street,
New York, N.Y. 10011
United Kingdom edition published by Plenum Press, London A Division
of Plenum Publishing Corporation, Ltd.
Da.vis House (4th Floor), 8 Scrubs Lane, Harlesden, NW10 6SE,
England
All rights reserved
No part of this publication may be reproduced in any form without
written permission from the publisher.
Introduction
This volume contains the proceedings of the Eighth Conference on
Vacuum Microbalance Techniques held at Wakefield, Massachusetts on
June 12 and 13, 1969. The tenth anniversary of the first confer
ence will be registered as this volume passes through the typeset
ting and proofreading stages. The eight volumes that have spawned
from this continuing series of conferences now contain a total of
125 papers. Thus, these volumes serve as a major repository of the
world's literature on vacuum microbalance techniques. The Ninth and
Tenth Conferences will be held in West Germany in June 1970 and in
Texas in 1971.
Each of the eight meetings has served as a forum where new
developments in this rapidly advancing fie ld can be presented and
discussed constructively within a conference atmosphere of cordial
informality. The interaction of the participants at the conferences
has led to the first treatise on ultra mlcrogravtmetry;' edited by
S. P. Wolsky and E. J. Zdanuk, with most of the fourteen chapters
written by steady contributors to the volumes on Vacuum Micro
balance Techniques. The number of research investigations and
published works in which a vacuum microbalance is utilized con
tinues to expand r apldly.f This is a direct result of several
types of automatic recording balances that are now available
commercial ly.3
The Eighth Conference was held to bring together again re search
scientists and engineers who exploit the measurement of mass as a
means of studying physical and chemical phenomena.
IS. P. Wolsky and E. J. Zda nuk, Ultra Mic ro Weight Determi nat
ion in Controlled En vironments. Intersci ence, New York,
1969.
2 A. W. Czanderna, "Utramicrobalance Review. " in: Wolsky and
Zdanuk , op. cit••p. 7.
3 D. Fox and M. Katz. "The Availability of Commerci a l
Microbalances and Quar tz Crystal Oscillators, " in: Wolsky and
Zdanuk , op. cit• •p. 465.
v
vi INTRODUCTION
Support for the conference was provided by the Army Research Of
fice - Durham.! Clarkson College of Technology, P, R. Mallory and
Co., Inc., and the Cahn Division of Ventron Instruments. Over 1500
users of microbalances were contacted by mail announcing the con
ference. In addition, the meeting was announced in the Journal of
Vacuum Science and Technology.! Chemical and Engineering News,6 and
Research/Development. 7
There were forty-six participants at the conference represent ing
Germany, Great Britain, and all regions of the United States.
Roughly, two-thirds of the attendees from the United States came
from the northeast, while the four scientists from Western Europe
provided an international character to the meeting. The attendees
were welcomed by the Conference Chairman, A. W. Czanderna, who
provided a brief historical sketch of the conferences and indicated
some of the benefits derived by the participants of previous
confer ences. In the technical program which followed, J. W.
Whalen, Th, Gast, E. J. Zdanuk, and Pat Gaskins served successively
as moder ators for the four sessions. The first session was opened
with an invited paper by E. A. Gulbransen and was followed by two
contri buted papers pertaining to oxidation. An invited paper was
presented in the second session by E. Robens on the genera] problem
of the mass defect produced by thermal gradients. In the third
session, W. H. King presented an invited paper on applications of
the crys tal oscillator microbalance. Of the nineteen papers
presented, seventeen are included in the proceedings and an
eighteenth was accepted for publication after the conference
because of its rele vance to the other papers in the volume.
Discussion questions and answers that followed each presentation
are incorporated at the end of each paper. The cooperation of the
participants and authors, which made it possible to document this
valuable material, is grate fully acknowledged. The format of the
volume, abbreviations, ref erences, etc., conform to that of
previous volumes as outlined by the publisher, Plenum Press. In
addition, the editor thanks all the authors for their cooperation
in using the definitions developed for
4Gram DA - ARO-D-31-124- G1l57 to Clarkson Coll ege of Technology
with A. VI. Czanderna as Principal Investigator.
5 Announcements, J . Vac . Sci. Tech. 6 : 277. 1969.
6Chem . Eng. News, Feb. 24. 1969, p. 96; May 19, 1969, p. 46. 7
Research /Development. May 1969. p. 46; June 1969, p. 40.
INTRODUCTION vii
microbalances 8 and the AVS standard symbols for vacuum sys
tems.i
It is a pleasure to thank all the people who contributed to the
success of the Eighth Conference. Two complete mailings of the
"Call for Papers n were handled by Pat Gaskins and Colin Williams
and the staff of the Cahn Division of the Ventron Instruments Com
pany. The papers for the technical program were selected by S. P.
Wolsky and A. W. Czanderna on the basis of abstracts submitted.
Local arrangements for the meeting at the Colonial Statler Hilton
were made by S. P. Wolsky, E. J. Zdanuk, and Mrs. M. Dor andi. The
participants enjoyed hospitality provided by the Cahn, Rodder,
Sartorius, and Worden Instrument Companies. Considerable typing and
secretarial contributions were made by Mrs. A. Hollister from the
planning stages to the publication of this volume. The painstak
ing task of copyediting the manuscripts and proofreading the
galleys fell on Mrs. A. Czanderna and her assistance is gratefully
acknowl edged. Finally, it is my pleasure to thank Dr. H. M. Davis
of the ARO-Durham, Dr . E . E . Anderson, Chairman of Physics at
Clark son College of Technology, and Dr. S. P, Wolsky, Director of
Re search at P, R. Mallory and Son, Inc., whose administrative
deci- s ions and / or expertise led to direct financial support
that made it possible to hold the E'ighth Conference on Vacuum
Microbalance Techniques.
Alvin W. Czanderna Potsdam, New York November 1969
8 Czanderna , op. cit. •p. 10-11. These definitions evolved from
an. original se t suggested by T. N. Rhodin and were an outgro wth
of interaction by S. P. Wolsky. R. L. Schwoebel, E. 1. Zdanuk, and
A. W. Czanderna. They are recommended for use by all workers in the
field .
9Graphic Symbols in Vacuu m Technology AVS Standard 7.1-1 966. J.
Vac. Sci. Tech. 4 : 139-142.1967.
Contents
E. A. Gulbransen
The Simultaneous Use of Mass Spectrometer and Micro balance
Techniques for the Carbon - Oxygen System . .. . . . . . . . . . .
. • . • . . . . . . . . . • . • 17
J . Graham Br own, John Dollimore , Clive M. Freedman, and Brian H.
Harrison
A System for the Determination of Oxidation- Reduction Kinetics in
Nonstoichiometr ic Metal Oxides . . • • . 29
I. Bransky and N. M. Ta llan
An Automated Bakeable Quartz Fiber Vacuum Ultra- microbalance .. ..
. ....... ....... •.••• 43
J. Rodder
Stanley E. Fink and Robert P. Merrill
The Effect of Thermal Gas Motion on Microbalance Measur ements
(Invited) ..•.........••...• 73
E. Robens
Gravimetric Adsorption Studies of Hydrogen on Granular Metal
Surfaces Using a Vacuum Microbalance 97
D. A. Cadenhead and N. J. Wagner
Gravimetric Measurement of the Molecular Area of Some Adsorbed
Gases .•..•.....••...•••• 111
E. Robens, G. Sandstede , and G. Walter
ix
x
CONTENTS
121
Momentum Artifacts in the Gravimetric Measurement of 131 Fast
Desorption .....•..•.......•.....•
Robert P. Merrill, Charles R. Arnold, and Andrew J. Robell
On the Development of Electromagnetic Balances in Recent Years
.....•..•...•.....•••.. 0 • 141
Tho Gast
Pressure of Light Used as Restoring Force on a Micro- balance .••.
0 0 0 •• 0 0 0 • 0 • 0 • 0 • 0 0 • 0 • 0 0 0 0 0 147
Karl P. Zinnow and Jens Po Dybwad
Vacuum Microbalance Apparatus for Rapid Determination of
Low-Temperature Vaporization Rates . 0 • • • • • 155
J, Gordon Davy
Wireless Temperature Measurement of a Sample in Vacuum. 0 0 0 • 0 0
0 0 • 0 0 0 0 0 • 0 0 • • • • • • • • • • • 173
G. Richard Blair
Applications of the Quartz Crystal Resonator (Invited) 183 Wo H.
King, Jr.
Thermal Degradation of Piperazine Copolyamides . . . . • 201
Stephen D. Bruck and Ashok Thadani
A Thermal Analysis System for Radioactive Materials. . 215 W. J.
Kerrigan, J. S. Byrd, and P. Do Holloway
Thermal Degradation of an Anhydride-Cured Epoxy Resin by Laser
Heating 0 0 •••••• 0 • 0 • 0 0 0 0 0 • 229
A. So Vlastaras
Laboratory P. O. Box 1663 Los Alamos, New Mexico 87544
Warren A. Anderson Sylvania Ltg. Center 100 Endicott Street
Danvers, Massachusetts 01923
Klaus Behrndt Granville-Phillips Co. 5675 E. Arapahoe Street
Boulder, Colorado 80302
Joseph R. Biegen Department of Physics Clarkson College of
Technology Potsdam, New York 13676
G. Richard Blair Hughes Aircraft Company Electron Dynamics Division
Torrance, California 90509
1. Bransky Wright-Patterson AFB ARL(ARZ) Bldg. 450 Ohio 45433
S. D. Bruck National Heart Institute National Institute of Health
Bethesda, Maryland 20014
xi
D. A. Cadenhead Department of Chemistry SUNY at Buffalo Buffalo,
New York 14214
Peter G. Chamy General Electric Company 6901 Elmwood Avenue
Materials Laboratory - 10-779 Philadelphia, Pennsylvania
19142
Edward G. Clarke, Jr. Department of Physics Clarkson College of
Technology Potsdam, New York 13676
A. W. Czanderna Department of Physics Clarkson College of
Technology Potsdam, New York 13676
J. Dollimore Dept. of Pure and Applied
Physics University of Salford Salford 5, Lancashire,England
Jens Peter Dybwad Space Physics Laboratory Air Force Cambridge
Research
Laboratories Bedford, Massachusetts 01730
Owen Fiet TRW Systems 1 Space Park Redondo Beach, California
90278
xii
Division 618 Glennan Building Case Western Reserve Univer-
sity Cleveland, Ohio 44106
Pat Gaskins, Consultant 11811 Marble Arch Drive Santa Ana,
California 92705
Theodor R. Gast Technische Universltat of Berlin Kurfiirstendamm
195/196 1 Berlin 15, Germany
Leonard J. Gordon MIT Lincoln Laboratory Space Communications D-013
Lexington, Massachusetts 02173
George P. Gray Systems Research Laboratories 7001 Indian Ripple
Road Dayton, Ohio 45440
Earl A. Gulbransen Westinghouse Research
Laboratories Pittsburgh, Pennsylvania 15235
Eugene A. Harlacher Continental Oil Company Ponca City, Oklahoma
74601
M. H. Houston Massachusetts lust. of
Technology Cambridge, Massachusetts
Donald W. Kemp American Cyanamid 1937 Main Street Stamford,
Connecticut
W. J. Kerrigan Savannah River Laboratory E. 1. du Pont de Nemours
and
Co. Aiken, South Carolina 29801
W. H. King, Jr. Esso Research and Engineering
Co. P. O. Box 121 Linden, New Jersey 07036
Morton Lieberman Sandia Corporation Sandia Base Albuquerque, New
Mexico 87115
Thomas D. McGee Iowa State University Ames, Iowa 50010
Robert P. Merrill Dept. of Chemical Engineering University of
California Berkeley, California 94720
Donald E. Meyer Texas Instruments p. O. Box 5012 MS-913 Dallas,
Texas 75238
Edward B. Murphy MIT Lincoln Laboratory Box 73 Lexington,
Massachusetts 02173
William Noakes Ventron Instruments Ltd. 27 Essex Road Dartford,
Kent , England
CONFERE NCE PARTICI PA ~T S xii i
Ray D. Worden Worden Quartz Products 6121 Hillcroft Houston, Texas
77036
Colin J. Williams Cahn Div, - Ventron Instruments
Co. 7fiOO Jefferson Street Paramount, California 90723
James W. Whalen Department of Chemistry University of Texas at El
Paso El Paso, Texas
Jerry Weil Cahn Dlv, - Ventron Instruments
Co. 7500 Jeffers on Street Paramount , California 90723
Nor man Wagner Department of Chemistry SUNY at Buffalo Buffalo, New
York 14214
J. Redder Rodder Instrument Company 775 Sunshine Dr ive Los Altos ,
California
Walter Tripp Systems Research Laboratory 7001 Indian Ripple Road
Dayton, Ohio 45440
Erich Robens Battelle-Institut e . V. 6 Frankfurt /Main - 90
Wiesbadener Strasse, Germany
Edward Zdanuk A. S. Vlastaras r . R. Mall or y and Company ,
General Electric Com pany Inc. 6901 Elmwood Avenue N. W. Ind. Park
Philadelphia, Penns ylvania 19142 Burlington,Massachusetts
01801
Peter H. Price AC Electronics Division General Motors Corporation
Wakefield, Massachusetts 01880
James S. Radawski Calm Div. - Ventron Inst, Corp. 7500 Jefferson
Street Paramount, California 90723
Daniel A. Rankin General Oceanology 27 Moulton Street Cambridge,
Massachusetts 02138
Karl P. Zinnow Space Physics Laboratory Air Force Cam br idge
Research
Laboratories Bedford, Massachusetts 01730
Earl A. Gulbransen
ABSTRACT
The use of sensitive microbalances enclosed in vacuum and reac
tion systems is at least 55 years old. Since World War II, use of
the vacuum microbalance method has grown rapidly and extended into
many new research areas. In the area of high-temperature oxidation,
it is essential to use thermochemical analysis and ki netic theory
in the planning and interpretation of microbalance studies. Studies
on the oxidat ion of silicon, chromium, and molyb denum are
discuss ed. It is concluded that detailed thermochemical analyses
must be used in planning the work and in interpreting the
experimental data.
INTRODUCTION
Many physical and chemical reactions occur in high-vacuum and
controlled-atmosphere reaction systems at high temperature. A major
problem is to minimize the extraneous reactions so the re action
of interest can be studied. Since most materials are capable of
reaction with gases in the reaction environment, a careful selec
tion must be made of furnace tubes, specimen support systems, re
active gases, and the preliminary treatments of the sample and
reaction system. If the rate of extraneous reactions is minimized,
then we can take the next step to plan the experimental program.
Finally, we have the problem of interpreting the experimental re
sults so that meaningful conclusions can be obtained.
1
2 E. A. GULBRANSEN
We have found thermochemical analysis to be a useful disci pline
at all stages in vacuum microbalance studies. The application of
thermochemical data can be simplified through the use of dia
grams. LogPMO vs logpoz and 10gPMO vs r/r diagrams arex x very
useful in high-temperature oxidation. Here PMO refers to
x the several elemental and oxide vapor species, For silicon and
chromium, these include Si, Siz, Si3, SiO, SiOz, Cr, CrO, CrOz, and
Cr03' These diagrams will be applied to three problems: (1) the use
of silica and mullite furnace tubes and silica support wires in
vacuum microbalance systems, (2) the interpretation of oxidation
studies on silicon, and (3) the interpretation of oxidation studies
on chromium.
Before considering these problems, we must consider the various
processes which can occur in the oxidation of materials over a wide
range of temperature and pressure,
TYPES OF OXIDATION PROCESSES
Kinetic studies on the oxidation of carbon,' molybdenum.! and
tungsten' >! have shown that there are at least six different
stages of reaction and four types of rate-controlling oxidation
processes. The six stages are as follows: (1) At low temperatures,
where ad herent oxide scale is formed, a Wagner-type diffusion of
metal or oxygen through the oxide film is present. (2) At higher
tempera tures, although a localized breakdown of the oxide occurs,
a Wagner type diffusion of metal or oxygen through the oxide film
is rate controlling. (3) At higher temperatures, where both oxide
volatility and oxide film-formation occur, either a Wagner-type
diffusion pro cess or a chemical-type oxidation process at the
metal- oxide in terface is rate controlling, (4) At higher
temperatures, where the oxide films volatilize, a chemical-type
oxidation process occurs at the metal interface. (5) At high
temperatures, where a dense bar rier layer of volatilized oxide
gases or condensed oxide crystals form, a transport of oxygen gas
through the barrier layer occurs. (6) At high temperatures, where
break-up of metal in the solid or liquid state occurs, transport of
oxygen gas through barrier layer is rate controlling.
For silicon and chromium where relatively high pressures of
volatile species develop at the element- oxide interface, an addi
tional type of oxidation process occurs, i.e., rapid transport
of
HIGH-TEMPERATURE OXIDATION OF MATERIALS 3
vapor species through a porous oxide film or ruptured oxide film.
If the oxide film or scale is molten, rapid transfer of oxygen oc
curs by means of convection currents in the liquid oxide. As a fur
ther complication, droplets of oxide can fall off the
specimen.
THERMOCHEMICAL PRINCIPLES
aA + f3 B ~ yC + oD
the mass action constant K is the ratio of the activities of each
mole of the reaction products to those for the reactants
(1)
(2)
For reaction (1) to occur , it must be thermochemically favorable.
The change in the Gibbs' free energy function boG used to express
chemical reactivity, is
boG = boH - TboS, (3)
where boH is the change in enthalpy, boS is the change in entropy,
and T is the absolute temperature of the reaction. When boG < 0,
a chem ical reaction is favored; at equilibrium, boG = 0; and when
boG > 0, the reverse reaction is favored.
The change in free energy of the reaction is connected with the
mass action constant by the equation
boG = boGo + RT InK,
where boGo is the free energy of reaction with each reactant and
product species in a standard state.
At equilibrium , K = Kp' where Kp is the equilibrium con stant,
and
The values of boGo and log Kp for a reaction are obtained fr om
a
(4)
(5)
4 E. A. GULBRANSEN
summation of the corresponding values for all of the different re
actants and products. For most purposes, it is convenient to de
velop log Kp values. This makes the determination of equilibrium
activities and pressures possible by using equation (2). The dia
grams presented here were constructed on the basis of such calcu
lations.
In recent years, a major stimulus has occurred in the compila tion
of thermochemical data in the form of tables by the use of com
puter techniques. Free energy, enthalpy, and equilibrium constant
data have been collected in the form of tables for many compounds
and molecular species over a wide range of temperatures, e.g., the
JANAF Tables. 5
THERMOCHEMICAL DATA
Tables 1 and 2 show the thermochemical data in units of logKp over
the temperature range for the several equilibria in the sili con-
oxygen system, mullite, and the chromium- oxygen systems.f Here,
(s), (l), and (g) refer to the solid, liquid, and gaseous phases.
Reactions of both the condensed and volatile oxide species are in
cluded. To simplify the interpretation of the complex equilibria
and to show the relationships between the equilibrium pressures of
the volatile species over the one or more condensed oxide and ele
mental phases and the oxygen pressure, log PMO VS log Po 2 dia-x
grams prepared at a series of temperatures are used. These dia-
grams were first used extensively by Kellogg" and independently by
Jansson and Gulbransen. 8
Plots of logP Mox vs, logPo2 at 1400 K for the Si- 0 and Cr - 0
systems are shown in Figs. 1 and 2. Similar diagrams were prepared
for the other temperatures given in Tables I and II to give a
complete thermochemical description of the Si - 0 and Cr - 0 sys
tems. High equilibrium pressures of volatile species occur at the
outer oxide - oxygen interface for the Cr - 0 system and at the in
ner element - oxide interface for both the Si - 0 and Cr - 0
systems.
To summarize the thermochemical data given in log p MOx vs, logPo2
diagrams, logP Mox vs lIT diagrams are used. Here, logP MOx is the
equilibrium element and oxide pressure at the ele ment- oxide and
oxide - oxygen interface or at any oxygen pres sure corresponding
to a given H2/H20 mixture.
T a b
C ?: J
tr t o :::: §Z > -l o Z o 'T J S; > -l
tT l i:8 ;> r C
/)
o: :J S; Z gj Z
HIGH-TEMPERA TURE OXIDATION OF MATERIALS 7
Log PH /PH°2 2 12 10 4 2 - 2 -4 -6 -S
5 1111 Si0 2
- 24 -
- 28
- 40 - 36 - 32 - 28 - 24 -20 - 16 -1 2 -8 -4 Log Po aim
2
Fig . 1- The rmoche mic al dia gram fo r the Si - °system, log PSiO
x
vs log P O 2 '
1400 K .
Cr tq)
-16 -14 - 12 - 10 Log po2atm
Fig. 2. Thermochem ical diagram for the Cr - ° syste m, logPCrO
x
vs log P0 2
M. P. Si 141ZOC
1.0 0.950.9 0.850.8
!x 103 T
Fig. 3. Plot of log PSiOx vs. liT for the volatile oxides at the
Si02(s, l) - O2 interface at 1 atm.
We now consider application of the thermochemical data to the use
of quartz and mullite as furnace tubes, to quartz as a spec imen
supporting material, and to the oxidation of silicon and chro
mium.
QUARTZ AND MULLITE AS FURNACE TUBE AND SPECIMEN SUPPORT
MATERIALS
A plot of logPSiOx vs liT is shown in Fig. 3 for the equilib rium
vapor species over Si02(s) for logP0
2 ::= O. A horizontal dashed
line is drawn at logP siO ::= -1). Our experience has shown thatx
volatility becomes appreciable at this value. At 1400 K (1127 C)
and logp0
2 ::= 0, logPSi0
similar diagram for logP0 2
::= -12, logp Si0 2
::= -13.15, and logPSiO ::=
-10.50. Thus, only a small loss of SiO(g) would occur in a high
quality vacuum system at temperatures up to 1400 K.
In a hydrogen-reducing atmosphere at 1400 K having logPH/PH20 ::=
4, logPSiO ::= -u.1, and, therefore, Si02(s) would not be reduced
but appreciable losses of Si and °would occur and
HIGH-TEMPERA TURE OXIDA l ION OF MATERIALS 9
the specimen would be contaminated with Si and 0. Quartz cannot be
used at 1400 K if the ratio of HdH20 is high.
Mullite, 3Al20 3 . 2Si02, is often used at temperatures above 1400
K to replace quartz furnace tubes. Thermochemical data'' show
mullite to be only slightly more stable than the component oxides
3Al203(s) and 2Si02(s). At 1400 K, logKp = -0.359 for the
reaction
(6)
So, Si02 in mullite behaves about the same, thermochemically, as
quartz. Hence, it is concluded that both quartz and mullite hang
down tubes can cause contamination problems under vacuum and
reducing conditions at 1400 K.
It is suggested that pure alumina, zirconia, hafnia, or thoria be
used as furnace tubes for temperatures of 1400 K and higher.
Thermochemically, hafnia and thoria appear to have best proper
ties for high-temperature furnace tubes.
OXIDATION OF SILICON
a. Thermochemical Predictions
The diagram log p sio, VS log P02 is plotted in Fig. 1 for the Si-O
system at 1400 K. Here, logP SiO = -4.2, so SiO(g) pres sures
develop at the Si(s)-Si02(s) interface. A logpsiO and logp Si VS 1
IT diagram is shown in Fig. 4 for the Si (s) - Si02(s) interface
together with values for log p Crand log PCrO at the Cr (s) Cr203
interface. The Si - ° system is unusual with the develop ment of
high gas pressures at internal interfaces.
It is seen in Fig. 1 that for logPo2 = 0, logPsioz and logPsio are
-13.15 and -16.50. At 1400 K, little direct volatility occurs. For
log p-, = -12, 10gPSiO and logPS iO are -13.15 and -10.50.
2 z Thus, even under high-vacuum conditions, little direct
volatility occurs.
High SiO(g) pressures at the element- oxide interface can lead to a
rapid transfer of SiO (g) through the porous film consum ing
Si02(s) and to a rupturing of the film when logps;o >
logpoz.
10 E. A. GULBRANSEN
1.2 1.1
700 gOO 900 1000 1100 1200 1300 1S00 1700 I I II ' 1
I I M.P. cr
2148°K
Fig. 4. The logPSiO' log PSi' logpCro and log PCrOvs l iT at the
element - oxide interface.
b. Experimental Studies
The oxidation behavior of high-purity silicon has been studied
extensively under conditions where protective oxides are formed.
Wagner'' was the first to recognize the nature of the transition
from active to passive oxidation for the oxidation of silicon in
inert-gas atmospheres containing low partial pressures of oxygen.
Wagner's analysis assumed that oxygen diffuses through a barrier
layer of volatilized SiO(g) to the silicon interface and that
SiO(g) diffuses away from the surface into the surrounding oxygen
gas. The maximum oxygen pressure for which a bare silicon sur face
could exist was given by the equation
1
)2 P SiO (eq),
where PSiO (eq) is the equilibrium pressure of SiO(g) at the Si(s)
Si02(s) interface and DSiO /D 02 is the ratio of diffusion
constants for SiO(g) and 02 in the boundary layer and is assigned
the value 0.64. Substituting, we have
P 02(max) = O.4PSiO (eq)
or
11
To ve To verifyWagner 's theoretical predictions, Gulbransen,
Andrew and Brassartl" studied the oxidation of high-purity silicon
under flow conditions and at oxygen pressures of 9 . 10-3, 4 .
10-2, and 10-1 torr. At 1100 C and 10-1 torr , a slow weight gain
of 1.1 3 .1016
atoms of Si reacting per cm2-sec was obser ved. At 1200 C and 10-1
torr, a rapid weight loss of 3 .51 • 1018 atoms of Si reacting per
cm2-sec was found. Rapid weight losses occurred in all of the ex
periments at 9 . 10-3 tor r and 4 . 10-2 torr and for the 1300 C
ex periment at 10- 1 torr. The rates of oxidation were nearly
independ ent of temperature and were nearly a linear function of
gas pres sure or gas flow.
In Fig. 5 there is a plot of log PS iO vs l/T for SiO(g) pres
sures at the Si (s) - Si02(s) interface. The experimental oxidation
data are plotted using logpoz as the ordinate and the values of 1/
T
Temp, ·C
~ :- 141 20C M. P. Si Is)
- 3 ,/ ':- 1109PSiO leQ )~.4)
/ Wa<j ner' < Condition
- 4 ® ®/ ® For Log PO
3' - 7
- 8 -
l. 0 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 O. 45
!x 103 T
Fig. 5. Active and passive regions for the oxidation of silicon on
a plot of log PSiO vs 1IT.
12 E. A. GULBRA NSEN
as abscissa. The P and A signs indicate passive (weight gain) and
active (weight loss) types of oxidation. The heavy diagonal line
gives the equilibrium pressures of SiO(g) at the Si(s)-Si02(s) in
terface. Areas of the diagram above and to the left of the line are
conditions where 10gp02 > 10gPSiO (eq), and areas below and to
the right of the line are conditions where log P02 < log
PSiO(eq). The kinetic data show the area to the left of the line is
the passive oxi dation region and the area to the right of the
line is the active oxi dation region. Rapid transfer of SiO(g)
occurs through the porous oxide film which is consumed by the
reaction. Rupturing of the oxide film also can occur when 10gP02
< 10gPsiO (eq).
Extremely rapid oxidation occurs in the active region since the
barrier layer of volatilized oxide species (according to the
equilibria of Fig. 2) consists of Si02(s) smoke (crystals) and not
SiO(g) gas as assumed by Wagner.9 Much higher oxidation rates can
occur when the barrier layer consists of oxide crystals rather than
gaseous oxides.
At 10-1 torr and 1200 C, 7100 Aof Si reacted per cm2-sec
using a flow rate of 1 . 1019 oxygen atoms/sec in the tube. At a
rate of 5350 cm/sec, 36.4% of the oxygen atoms flowing over the
sample reacted. For the reaction conditions, this is the highest
rate of oxidation we have measured. Wagner's condition for active
and passive oxidation is also shown in Fig. 5. We conclude that the
condition log P02 = log PSiO (eq) is the essential condition
separating active and passive oxidation of silicon.
OXIDATIONOF CHROMIUM
a. Thermochemical Predictions
It should be noted that Fig. 2 and other log PCrOx vs log P02
diagrams show volatile species are important for two reasons:
First, a relatively high pressure of Cr (g) can develop at the Cr
Cr203 interface, and second, relatively high pressures of Cr03 (g)
exist over the Cr203 (s) - O2(g) interface. In Fig. 4, there is a
plot of 10gPcr and 10gPcro vs l/T at the metal- oxide interface.
LogPCr:= -9 for a temperature of 975 C. Relatively high tempera
ture and low oxygen pressure must be used to observe the condi
tion where 10gPcr > 10gpo2• Thus, at 1530 C, 10gPCr = -4. Rapid
oxidation should occur for log P02 < -4.
HIGH-TEMPERATURE OXlD }\ n ON OF MA TERIA LS
Temp, °C
800 900 1000 llOO 1200 1300 1400 1500 1600 1700 1800
-4 M.P. Cr 1875°C
- 8
~ - 12
Ix 103 T
Fig. 6. Plot of the log PCrO vs 1IT for volatile species in the
oxidation x
of Cr at 0.1 atm 02 pressure.
13
In Fig. 6 there is a plot of logp c-o; vs liT for an oxygen
pressure of 0.1 atm. LogP Crz03 =~ for a temperature of 1000 C. At
this temperature, oxide volatility should be observed. As the
temperature is increased, oxide volatility increases although the
temperature coefficient is small. Even at the melting point of
chromium, logPc r0
3 and logP cr0
b. Experimental Studies
Unfortunately, complete oxidation studies have not been made. Both
oxygen consumption and weight-change experiments must be made to
evaluate the complex oxidation behavior. Two studies have been made
in our laboratories on the vapor pressure of chromium, the
transport of chromium vapor through oxide films, and the ki netics
of oxidati on at temperatures up to 1100 C.11,2 A plot of the
parabolic rate law constant vs. 1 IT in Fig. 7 sh ows a transforma
tion occurs near 1000 C. This was related to the equilibrium pres
sure of chromium at the metal- oxide interface. The transforma
tion point, C-B in Fig. 7, corresponds to the condition at which
the
14
1100
-10.5
-11.0
-11.5
! X103 T
Fig. 7. The log A vs l/T for the oxidation of Cr. From the slopes,
D.H C- D =37.5 keal/mole and D.HA-B = 59.4 keal/mole.
rate of evaporation is equal to the rate of chromium metal
diffusion in oxidation. Thus, the high vapor pressure of chromium
short cir cuits the normal diffusion processes and for these
conditions an in crease in the rate of oxidation occurs. The
volatility of Cr03 should begin to exert its influence at 1000 C on
the oxidation pro cess and on the stoichiometry of the oxide
although this has not been verified experimentally.
CONCLUSlONS
Thermochemical analysis of the nature of the volatile oxide
species, their equilibrium pressures , and the composition and sta
bility of the condensed oxide phases can be used to evaluate
furnace tubes and support wires for specimens, plan productive
experiments, and interpret the experimental measurements.
Quartz and mullite as furnace tubes and silica as a support fiber
were considered for use at 1400 K and at 02 pressures of 1 atm,
10-12 atm, and under reducing conditions. Both materials yield
volatile reaction products at 10-12 atm of 02 and under reduc ing
conditions.
HIGH-TEMPERAT URE OXIDATION OF MATERlALS 15
The active and passive regions of oxidation of silicon were
considered thermochemically. Active oxidation occurs when log P02
< log P SiO (eq), and passive oxidation occurs when log P02 >
log P SiO (eq). Rapid rates of oxidation are predicted and observed
experimentally.
Thermochemically, chromium should show a transition to a rapid
oxidation rate at 975 C where logPcr > -9. This was ob served
experimentally. Direct volatility of Cr03 (g) also should be
observed.
REFERENCES
1. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, The
oxidation of graphite at temperatures of 600 to 1500 C and at
pressures of 2 to 76 torr of oxygen, J. Electrochern. Soc., 110,476
(1963).
2. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, Oxida tion
of molybdenum 550 to 1700 C, J. Electrochem. Soc., 110 , 952
(1963).
3. E. A. Gulbransen and K. F. Andrew, Kinetics of oxidation of pure
tungsten from 500 to 1300 C, J. Electrochem. Soc., 107, 619
(1960).
4. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, Kinetics of
oxidation of pure tungsten, 1150-1615 C, J. Electrochem. Soc., 111,
103 (1964).
5. JANAF Tables of Thermochemical Data, Dow Chemical Com pany,
Midland, Michigan, including Supplement No. 30 dated Dec. 31,
1968.
6. C. E. Wicks and F. E. Block, Thermodynamic properties of 65
elements - their oxides, halides , carbides, and nitrides, Bur. of
Mines Bulletin No. 605, Washington, U. S. Government Printing
Office (1963).
7. H. H. Kellogg, Vaporization chemistry in extractive metal
lurgy, Trans. Met. Soc. AIME, 236, 602 (1966).
8. S. A. Jansson and E. A. Gulbransen, Evaluation of Gas Metal
Reactions by Means of Thermochemical Diagrams, Paper presented at
the International Congress on Corrosion, Amsterdam , Sept.
1969.
9. C. Wagner, Passivity during the oxidation of silicon at ele
vated temperatures, J. Appl, Phys. , 29, 1295 (1958).
16 E. A. GULBRANSEN
10. E. A. Gulbransen, K. F. Andrew, and F. A. Brassart, Oxida tion
of silicon at high temperatures and low pressure under flow
conditions and the vapor pressure of silicon, J. Electro chern,
Soc. , 113, 834 (1966).
11. E. A. Gulbransen and K. F. Andrew, Kinetics of the oxidation of
chromium, J. Electrochem, Soc., 104, 334 (1957).
DISCUSSION
D . E. Me y e r: How applicable are the techniques you describe to
the oxida tion studies where gaseous components such as
phosphorous and boron are also present?
E. A. G u I bra n sen: I see no majo r difficulties in the study of
materials where gaseous compounds of phosphorus and boron are
formed. The logpPOx and logpo diagram for phosphorus is one of the
very interesting oxide systems we have consid~red since high
pressures of volatile oxides develop at the phosphorus- oxygen
interface . These pressures explain the rapid oxidation reactions
of phosphorus. Some day we hope adsorption chemists will take a
look at phosphorus and relate their mea surements to
thermochemistry of the phosphorus- oxygen system.
The Simultaneous Use of Mass Spectrometer and Microbalance
Techniques for the Carbon-Oxygen System
J. Graham Brown, John Dollimore, Clive M. Freedman, and Brian H.
Harrison Department of Pure and Applied Physics Univer sity of
Salford Salford 5, Lancashire United Kingdom
ABSTRACT
The initial degassing of a high-surface-area graphite is character
ized using mass spectrometric and thermogravimetric weight-loss
measurements. It will be indicated how far the combination of these
allied techniques can be used to define the graphitic nature of the
material in terms of the extent of the basal and edge planes of the
graphite crystallite. The active surface area of the graphite was
measured by the formation of surface oxide during low-pres sure
oxygen chemisorption onto the clean surface of the material. By
subsequent thermal desorption of surface oxide an additional value
for the active surface area was obtained from the weight-loss data
and the known ratios of the desorbed gaseous species CO and CO2,
The utility of a mass spectrometer - microbalance system for the
study of gas - surface reactions is discussed.
INTRODUCTION
Microbalance techniques have been used extensively in the study of
the thermal decomposition of powdered materials. In many decom
position reactions, the evolution of various gaseous products
occurs in discrete stages, and weight-loss data are adequate to
character ize the process.
17
18 J. G. BROWN ET AL.
In the carbon- oxygen system, it has now been established that the
oxidation of various carbons and graphite proceeds from the
formation of a stable surface oxide to the production of gaseous CO
and CO2• Heating of this stable surface oxide results in its
thermal desorption as CO and CO2• One is therefore concerned with
the simultaneous evolution of CO and CO2 in both oxidation and
thermal desorption studies. This is particularly the case in the
temperature range 300-1000 C, so that the weight-loss data need to
be supplemented with other measurements.
The graphite surface oxide has been shown by many workers to be
associated with the reactive edge-plane carbon atoms of the
graphite crystallttea.lf On this basis, by making the assumption
that CO is the predominant gaseous product' due to thermal desorp
tion of surface oxide, weight-loss data were used to obtain
physical crystallographic data on the basal to edge plane ratio of
graphite during a grinding series. This technique of determining
crystallo graphic parameters has been improved, in the present
study, by the additional information obtained from the mass
spectrometer.
In the past, the mass spectrometer has been combined with
thermogravimetric measurements for the purpose of qualitatively
describing a process.4,5 The present work is intended to show the
varying degree of participation of the mass spectrometer in a study
of the thermal treatment of graphite and some of the proper ties
and stability of its surface oxide produced by reaction with
molecular oxygen. Finally, it will be demonstrated how the mass
spectrometer alone may be used as a microbalance, using the broader
meaning of this nomenclature.f
EXPERIMENT AL
Apparatus
The material used in this study was a ground sample of Ache son 's
graphite with a BET specific surface of 102 m2/g when measured by
nitrogen adsorption at 78 K. The grinding process reduced the
crystallite size and produced extensive graphite edge planes. Since
small sample masses are employed in vacuum microbalance work, this
particular high-area graphite enabled the mass spectrometer -
microbalance system to be matched readily based on high gas
evolution quantities.
MASS SPECTROMETER AND MICROBALA NCE TECHNIQUES
RGA MS 10
Vacuum Gas
storage Cahn RG Electrobalance Twin Furnace
Fig. 1. System for simultaneous use of a Cahn RG microbalance and
an AEI MS10 mass spectrometer.
19
The simultaneous TGA- MSA system is shown in Fig. 1. A Cahn RG
Electrobalance® was used and the enclosure could be evacuated to
10-6 torr using two cold traps, a 3-in. oil-diffusion pump, and
PTFE greaseless stopcocks. Viton O-ring seals were employed for the
symmetrical hangdown tubes which together with the crucibles and
suspension were made of high-purity silica. Sample temperatures
were measured with a chromel- alumel thermocouple situated on the
axis of the sample tube and just be low the sample. To prevent
interaction with gaseous products the thermocouple was enclosed in
a thin quartz tube sealed to the bot tom of the sample tube.
Gaseous products evolved from the sample were transferred, for
analysis, to the mass spectrometer system by a baffled 2-in.
oil-diffusion pump. The removal of gases from the microbalance
enclosure prevented spurious weight changes arising from TMF
effects 7 and also prevented readsorption and secondary reactions
from occurring. The mass spectrometer system, described else
where," consisted of a 5.5-liter reservoir connected to an AEI MS10
mass spectrometer via a fixed molecular leak of 10-2 torr liter /
sec at atmospheric differential. This fixed leak allowed par tial
pressures from 0.1 to 600 mtorr in the reservoir to be mea sured
on the mass spectrometer.
20 J. G. BROWN ET AL.
This type of system can be used either to obtain a qualitative
analysis of the gaseous products to supplement the weight-loss
data, or by accurate calibration of the reservoir volume and the
mass spectrometer senstttvtty." the mass of evolved gas can be
determined from the general gas law, PV = mRT. The direct cor
relation between the weight of gas evolved determined on both the
microbalance and mass spectrometer systems allows the mass
spectrometer to be used as a microbalance for chemisorption and
oxidation studies in the pressure regions where the conventional
microbalance is troubled by spurious weight changes.
Procedure
A 0.25-g sample of the original ground Acheson graphite was
degassed at room temperature for 12 hr to remove physical ly
adsorbed gases. The sample temperature was raised in tem perature
increments of 100 C up to 900 C. The gaseous products were
transferred to the mass spectrometer for analysis after half-hour
collection times at each increment. At the end of each temperature
increment, the evolved gas was removed from the reservoir by
evacuation before proceeding to the next tempera ture run. To
ensure a cleaned surface for chemisorption experi ments, the
sample was heated at 1000 C until a pressure of 10-6
torr was achieved. The sample was then lowered to the desired
reaction temperature before admission of oxygen to the required
pressure. The desorption of the surface oxide, formed by oxygen
chemisorption, was monitored in a manner similar to that de
scribed above but was continuous up to a collection time of 50 min
at selected temperature increments. Chemisorption and oxidation
experiments were carried out using just the mass spectrometer to
follow the change in the partial pressures of the gaseous compo
nents.
RESULTS AND DISCUSSION
The initial degassing of the Acheson's graphite is shown in Fig. 2
as a cumulative weight loss curve expressed in milligrams per gram
of sample. The weight of the major gaseous components detected
during degassing is also shown. The specific weights of CO and CO2
evolved can be used to estimate the extent of the graph ite edge
planes by determining the number of carbon atoms in the evolved
oxides of carbon.14 On this basis, the initial degassing gives a
coverage of 14.8 m2/g and 10.0 m2/g from CO and CO2,
MASS SPECTROMET ER AND MICROBALA NCE TECHNIQUES
20
21
800
Fig. 2. Cumulative weight loss showing major components on initial
degassing of a ground Acheson's graphite . Total Hz = 0.106 mg/g;
total HzO = 0.865 mg/g.
respectively, and a total edge-plane extent of 24.8 m2/g. Since
some of the coverage may, in fact, be due to "ground in" defects, a
more precise procedure of chemisorbing oxygen onto the clean
graphite surface was employed. In cleaning the graphite surface by
evacuation at 1000 C, the "ground in" defects are annealed out''
and the subsequent formation of surface oxide will then be confined
to the crystallographic edge planes. Oxygen was chemisorbed on the
sample at 250 C and 2 torr pressure for 1 hr, with less than 0.1%
"burn-off" occurring. From other studies,9 it was found that this
period was sufficient to obtain at least 95% of the saturation
coverage at 250 C. The desorption of the surface oxide was followed
using the simultaneous thermogravimetric and mass spectro metric
weight-loss technique.
Typical isothermal weight-loss curves are illustrated in Fig. 3 for
the 500, 650, and 800 C desorption runs with Fig. 4 show ing the
breakdown of gaseous components in the 500 C run. The cumulative
weight-loss data obtained from the desorption of the
22 J. G. BROWN ET AL.
0.20,----,-----,----,----,
0.05
o
Fig, 3. Typical isothermal desorption curves of 02 chemisorp tion
at 2 torr ~nd 250 C for 1 h.
surface oxide over the whole temperature range are presented in
Table I and shows the excellent agreement between calculated (MSA)
and measured (TGA) weight losses. The extent of surface oxide
coverage corresponded to 7.8 m2/g and 0.055 m2/ g for CO and CO2,
respectively, giving a total edge-plane extent of 7.85 m 2/g.
It is pertinent at this point to compare the quantity of CO2
evolved during the initial degassing with that obtained from a con
trolled oxygen chemisorption. The large quantity of CO2 found on
the initial degassing has been tentatively associated with defects
caused by the grinding process. Electron spin resonance methods '"
have shown an increase in the free spin concentration on grinding
and that subsequent thermal annealing at temperatures up to 1000 C
greatly reduces this concentratton.i Further work has also shown
the correlation between the production of CO2 and spin cen ters,11
and it is suggested that the large drop in CO2 evolution after the
initial degassing is, in fact, associated with the anneal ing out
of damage caused by the grinding process. Further evi dence for
this annealing is found in the reduction of the surface
MASS SPECTROMETER AND MICRO BALANCE TECHNIQUES
0.125.------,-----..,..------,-,
23
0.100 -
Ul
Fig. 4 . Component analysis of 500 C isothermal desorption
curve.
Table 1. Cumulative Weight Loss* - A Comparison of Simultane ous
Mass Spectrometer and Microbalance Data
CO, mg . C0 20 mg .
Cumulative total: MSA, mg
Temperature range, C
400- 500- 600- 650- 700- 750- 800- 900-
500 600 650 700 750 800 900 950
0.063 0.199 0.335 0.473 0.663 0.823 1.010 1.085 0.052 0.094 0.111
0.121 0.128 0.128 0.128 0.128
0.115 0.293 0.446 0.594 0.791 0.951 1.138 1.213
0.120 0.305 0.454 0.602 0.810 0.961 1.150 1.231
• From a 0.2662-g sample .
24 J. G. BROWN ET AL.
area after heat treatment to 1000 C. The initial surface area of
the sample after degassing at 300 C to remove adsorbed gases was
102 m2/ g; after heat treatment of the sample at 1000 C, the
surface area decreased to 90 m2/g in a reproducible manner. This
more than accounted for the surface oxide coverage associated with
the CO2 evolved.
It is als o possible to obtain surface area data on powders by
using the broadening of the lines on x-ray powder diffraction
photo graphs, and, therefore, such x-ray measurements were made to
provide comparative data. The photographs were obtained using a
quadruple Guinier focusing camera, and the pr ofiles of the powder
lines were obtained using a recording microdensitometer. The
quadruple camera permitted the simultaneous exposure of three
samples together with a suitable standard material for the evalua
tion of the instrumental line width so that the observed pr ofiles
could be corrected to give the pure diffraction widths. In this
way,
275 ~...... ~ -.::... E ~
... 15~.5 225 :::0
'" Ox Ql Ql 0...
~ 200 :::0 10 -e '"01 '" 0
>. Ql (J
'E 20 c:: Ql 0 '0 .c .~ ...
0 :::0 Uc:r
20 40 60 Time (minutes)
Fig. 5. Formation of graphite surface oxide at 300 C and 250 mtorr
of 0 2 on a cleaned surface of ground Acheson's graphite .
MASS SPECTROMETER AND MICROBALANCE TECHNIQUES 25
30
~ .~ Q)
OL4~O§0=::~§~=:;~==!==j~=~t~J
Fig. 6. Thermal decomposition of surface oxide after
1.70,10"burnoff" at 300 C.
using the (110) and (004) powder lines, values of the layer diam
eters La and the dimensions of the crystallites perpendicular to
the layers , Lc , were obtained. Surface areas could then be calcu
lated assuming that the particles are cylinders of diameter La and
height L c; the total surface area, the basal-plane area, and the
edge plane area can all be evaluated. It is necessary to assume a
value of the density of the graphite, and since the x-ray method
measures the extent of the regions of perfect crystallinity, the
appropriate value is the ideal x-ray density of 2.26 g/cm3• Using
these methods we find for the ground Acheson's graphite a total
specific surface area of about 100 m2/g and a specific edge-plane
area of about 46 m 2/ g.
In the present study, the mass spectrometer was used as a sensitive
microbalance during the oxidation process. Figure 5 shows the
buildup of surface oxide on the clean graphite surface at an
initial oxygen pressure of 250 mtorr and a temperature of 300 C.
The figure also shows the production of "burn-off" products CO and
CO2 and the continual depletion of oxygen during the first hour of
oxidation. The total "burn-off" of carbon amounted to 1.7% w/w of
sample after a 13-hr exposure to the oxygen. Figure 6 shows the
cumulative weight-loss data obtained in subsequent desorption of
the surface oxide up to 950 C. The total surface oxide coverage
corresponded to 38.2 m2/g and consisted of 36.9 m2/g and 1.3
m2/g
of CO and CO2, respectively.
26 J. G. BROWN ET AL.
The advantage of the mass spectrometer is apparent when one
considers that the conventional microbalance weight change would be
a complex function of oxygen chemisorption and carbon removal as CO
and CO2, Normally in microbalance studies at low oxygen pressures,
the oxygen is diluted with an inert gas 12 and the oxidation
process followed after the initial formation of surface oxide has
been completed. This restriction allows only tentative conclusions
to be drawn about the processes occurring in the ini tial period
of oxidation.
CONCLUSION
It has been demonstrated that a mass spectrometer may be used to
supplement microbalance data. Previous techniques, used to
determine edge-plane extents of ground graphite samples, could be
in error in the light of the present work. With ground samples, the
large proportion of CO2 evolved can lead to significant error in
the edge-plane extent, if weight-loss measurements are based sole
lyon the evolution of CO. Defects caused by the grinding process
appear to be associated with the majority of the evolved CO2,
In view of the good agreement for total surface area as mea sured
by physical adsorption and x-ray line-broadening techniques, it
must be concluded that not all the edge-plane surface can chemi
sorb oxygen. This would account for the low values of edge-plane
extent obtained from chemisorption studies when compared with the
values from x-ray data. The use of chemisorption studies to de
fine the edge-plane extent could therefore lead to many problems of
interpretation.
It is demonstrated by the present work that even as little as 2%
"burn-off" on the sample can alter by at least threefold the
measured edge-plane extent. This is most likely due to "internal
channeltng't'! arising from catalytic oxidation due to the 0.2%
iron content introduced in the grinding process.
A clearer insight into the energetic nature of the surface oxide
formed on graphite can be obtained'! from the present results by
careful analysis of the isothermal desorption kinetics using an
established technlque.P
ACKNOWLEDGME NTS
B. H. Harrison and C. M. Freedman would like to acknowl edge
financial assistance from the National Gas Council (UK) and The
University of Salford, respectively.
MASS SPECTROMETER AND !v!ICROBALANCE TECHNIQUES
REFERENCES
27
1. G. R. Hennig, Proceedings of the Fifth Conference on Carbon,
Vol. 1, Pergamon Press, Oxford (1963), p. 143.
2. E. A. C. Follet, Carbon, .!.' 329 (1964). 3. S. J. Gregg and J.
Hickman, Second Conference on Industrial
Carbon and Graphite, London, 1965 , Soc. Chern. Ind. (1966),
p.424.
4. F. Zitomer , Anal. Chern., 40, 1091 (1968). 5. W. W. Wendlandt
and T. M. Southern, Anal. Chim. Acta, 32,
405 (1965). 6. J. Dollimore, C. M. Freedman, and B. H. Harrison,
Seven
teenth Annual Conference on Mass Spectrometry and Allied Topic s,
Dallas, 1969.
7. A. W. Czanderna, in: Vacuum Microbalance Techniques, Vol. 4,
Plenum Press, New York (1965), p. 69.
8. H. Harker , J. B. Horsley, and A. Parkin, J. Nucl. Mater., 28,
202 (1968).
9. J. Dollimore , C. M. Freedman, and B. H. Harrison, unpub lished
work.
10. S. Mrozowski and J . F. Andrew, Proceedings of the Fourth
Conference on Carbon, Pergamon Press, Oxford (1960), p. 207.
11. H. Harker, J. T. Gallagher, and A. Parkin, Carbon, !' 401
(1966).
12. B. G. Tucker and l\L F. R. Mulcahy, Trans. Faraday Soc., 65,
274 (1969\.
13. G. R. Hennig, J. Inorg. Nucl. Chem., 24, 1129 (1962). 14. J.
Dollimore, C. M. Freedman, and B. H. Harrison, to be
published. 15. J. Dollimore, C. M. Freedman, and B. H. Harrison,
Ninth
Biennial Conference on Carbon, SP-26 (1969).
A System for the Determination of Oxidation-Reduction Kinetics in N
onstoichiometric Metal Oxides
I. Bransky*
and
ABSTRACT
The chemical diffusion coefficient can be determined from measure
ments of the kinetics of oxidation or reduction of a
nonstoichiomet ric metal oxide. To accomplish this
thermogravimetrically when the homogeneity range of the oxide is
small , all disturbing influ ences and sources of noise, such as
gas-flow irregularities and temperature gradient variations , must
be minimized. A system is described which delivers high gas flows
at constant pressure and flow rate to the furnace and switches
rapidly from one oxygen par t ial pressure to another with minimum
disturbance to the Cahn RG Electrobalance® us ed . The importance
of linear gas velocity and furnace geometry when using CO- CO2
mixtures is discussed and a satisfactory gas preheater is
described. An example of the ap plication of the apparatus to the
reduction of Mn01+x in steps of ~x ~ 0.2% is presented.
• Visiting Senior Research Physici st at Aerospace Research
Laborator ies .
29
INTRODUCTIO N
In recent years, a considerable amount of effort has been devoted
to the study of the oxidation - reduction kinetics of metal oxides,
with particular emphasis on the calculation of the chemical diffu
sion coefficient from the observed reaction rates. The chemical
diffusion coefficient :5 is defined as the proportionality constant
in Ftck's law
J = :5(dc/dx), (1)
where, since interdiffusion in the presence of a chemical potential
gradient is occurring, J is the total flux of all mobile species
and c , for a nonstoichiometric compound, is the excess
concentration of one of the components.
There are many practical and theoretical reasons for this in
terest in the values of D. The chemical diffusion coefficient is
im portant in the calculation of equilibration times for a
nonstoichlo metric semiconductor interacting with its vapor, in
diffusion-con trolled oxidation of metals, and in solid state
reactions between oxides. Furthermore, it is sometimes possible to
use values of :5 to estimate the self-diffusion coefficients of the
constituents of a compound'v and to compare these with values
obtained from tracer experiments. From a theoretical point of view,
these diffusion co efficients are of interest because they are
sensitive to the defect structure of the oxides under study. The
role of chemical diffu sion in sintering may be of particular
importance in ceramic tech nology . For example, Kuczynskl'' has
suggested that the sintering rates of various oxides are controlled
by the chemical diffusion co efficients of the oxides, rather than
by the self-diffusion coeffi cients of their constituents.
During the reduction of a metal-deficient oxide specimen in a
gaseous atmosphere, metal vacancies diffuse toward the oxide gas
interface. Since, for a metal oxide M,Oj,
_ a [V 0] _ a [00] -----,
ax ax
Ftck's first law, given in equation (1), can often be simplified
to
OXIDATION -REDUCTION KINETICS IN METAL OXIDES
J v = Doc/ax, M
is the flux of metal vacancies. This is particularly
true when the self-diffusion coefficient for oxygen vacancies is
much smaller than that for metal vacancies. If the surface reac
tions involved in the incorporation of oxygen from the gas phase
in to the crystal lattice are sufficiently rapid, then the change
in metal vacancy concentration is controlled by volume diffusion
and Fick's second law can be written
(3)
Levin and wagner! presented a very convenient simplified treat
ment of equation (3) in the analysis of their reduction experiments
on wiistite. Their mathematical solution assumed (1) a constant D,
and (2) that the surface of the specimen equilibrates instantly to
the composition required by the chemical potential of the oxygen in
the gas phase. Two integrated solutions of equation (3) were pre
sented. The first, which is valid during the initial part of the
com positional change , t.e ., when Dt/a2 -s 0.15, has a parabolic
form
(4)
where kp = 4fj(~c)2 / 1T and ~m = m - mo; m is the sample weight at
time t; mo the initial weight at t = 0; ~c the change in the cation
concentration; A the area of the specimen; and a the
half-thickness. The second integrated solution of equation (3) is
valid for the rest of the process, when f5t/a2 :::: 0.15, and it
has a logarithmic form
~m 8 1TDt log (1 - mf - m/ = log;2 - 2.3 (4a2) , (5)
where mf is the final weight at time t = 00. Both analyses are for
one-dimensional diffusion only. Edge corrections for finite samples
have been given by Landler and Komarek. 5 A survey of the
mathematical analysis of oxidation- reduction data, experi mental
techniques, and the recent studies of chemical diffusion co
efficients in metal oxides has been given by J. B. Wagner.6
32 I. BRAN SKY AND N. M. TALLAN
EXPERIME NTAL
Determination of Chemical Diffusion Coefficients
To determine the chemical diffusion coefficient from oxi dation or
reduction rates of an oxide, a specimen is equilibrated at a given
oxygen pressure at some temperature and then, at some arbitrary
time zero, the oxygen pressure is changed rapidly to a new value.
The isothermal rate of change of some physical prop erty, such as
electrical conductivity, 7,8,9 weight change ,4,5,10 or the density
of color centers.!' that is proportional to the rate of com
position equilibration must then be measured. It has been pointed
out by Campbell, Kass, and O'Keeffe9 that the apparent :5 is sensi
tive to the electrode configuration used in the conductivity
measure ments. It is therefore desirable, whenever possible, to
study rates of oxidation or reduction processes by a more direct
method, such as weight change, which follows the vacancy
concentration itself.
Design of the Thermogravimetric System
The chemical diffusion coefficient has been found to be strong ly
dependent on defect concentration in several metal
oxides4,5,10,12,13
and therefore it varies rapidly with stoichiometric deviation. It
is therefore extremely important for the thermogravimetric system
to have maximum sensibility to weight change to permit recording
the rates of oxidation or reduction in composition steps that are
suffi ciently small so that Dcan be considered constant.
Furthermore, to meet the requirement that the change in oxygen
partial pressure be as rapid as possible, the system should be
capable of handling high gas flows. At the same time, the gas flow
should be sufficient ly constant so the force exerted on the
sample does not vary with time, and the switching of the gas
mixtures at time zero, to change the oxygen partial pressure,
should disturb the balance as little as possible.
Description of the Thermogravimetric System
A schematic diagram of the system is shown in Fig. 1. The sample
12, in the form of a thin, single crystal disc, is suspended from a
Cahn RG Electrobalance®. For the study of MnG, a sap phire fiber
was used in contact with the specimen to minimize in teraction.
The balance was operated on the 10-mg mass range and in either the
200- or the 400-llg/mV output position. A Leeds and
OXIDATION- RE DUCTION KINE TICS IN METAL OXIDES
Gas I Gas n Gas I Gas n CO CO2 CO CO2
I,
33
CD '
16
8
Fig. 1 . A schematic diagram of the thermogravimetric system: 1)
Matheson Model 70 low-pressure regulator ; 2) purifiers; 3) valve ;
4) Matheson's Floating Spheres flow meters ; 5) gas mixer ; 6)
mercury manometer ; 7) two-way solenoid valves : 8) capil lary ;
9) preheater: 10) alumina cruci ble ; 11) alum ina furnace tube ;
12) sample; 13) sapphire fiber; 14) platinum or nichrome wire; 15)
radiation shields ; 16) balance; 17) toggle valve: 18) Cartesian
manostat No. 6; 19) vacuum pump; 20) outlet to ex haust.
Northrop AZAR recorder was used with I-mV full-scale input. The
furnace construction has been described elsewhere.I!
Mixtures of CO2 and CO were used to obtain oxygen partial pressure
in the range of 10-3 to 10-11 atm. The CO2 was purified by passing
the gas over copper turnings 2, heated to about 750 C. Floating
ball flow meters used to measure the flow of CO2 and CO were
calibrated for the gases used by timing the rise of a soap mem
brane in a burette. As seen in Fig. 1, two identical gas-mixing
sys tems were used, one to provide the initial oxygen partial
pressure and one to provide the oxygen pressure required for the
desired step change in composition. Two solenoid valves 7 were used
to switch from one mixture to the other. To conveniently maintain a
constant gas flow through the furnaces, a capillary which repre
sented the maximum restr iction in the line was used in conjunction
with a manostat 18 on the furnace and a manometer 6 on the mix- ing
chamber 5. Since the pressure drop across the capillary was
34 1. BRAN SKY AND N. M. TALLAN
constant, the flow through the system was essentially constant and
independent of the settings of other valves in the system used to
control the individual gas flow rates. While one mixture was flow
ing through the furnaces, the other one was vented into an exhaust
system. To minimize the disturbance to the balance when switch ing
gas mixtures, identical capillaries were used at the inlets to the
furnace and the exhaust system. The cartesian manostat, which was
used to maintain constant pressure in the furnace, was set
generally at a pressure between 150 and 200 torr to minimize
thermal fluctuations of the balance beam. A toggle valve 17 was
used to terminate the gas flow abruptly to permit weight measure
ments in a static rather than a dynamic gas environment when
necessary.
RESULTS
Operation of the System
A total gas flow of about 500 cc/min at atmospheric pres sure was
selected to obtain a favorable time constant for the pro cess of
exchanging the gas mixtures. With the 17-in.-long, 1} in.-diameter
furnace tube used, this flow rate would give a time constant of
about 6 sec if laminar flow were maintained. However, when this
flow was introduced directly into the bottom of the fur nace
during the initial trial measurements on MnO, obvious signs of
difficulty were observed. At 1300 C, the COdCO ratio was changed
from 90 to 50, a change which should have produced a mass loss of
about 400 J1.g on the specimen used, but no mass change was
detected. When the change in gas mixture involved lower COdCO
ratios , i.e. , higher CO contents, asymmetric amounts of oxidation
and reduction were obtained from switching back and forth between
the same two gas mixtures . This behavior was suggestive of two
effects associated with the possibility that the gas flowing
through the furnace tube at this high flow rate might not be
reaching the temperature of the furnace. First, if the gas striking
the sample surface is unheated, the rate of sur face reaction
might be slowed to a point where the oxidation and reduction
kinetics are no longer controlled by volume diffusion. Second,
unheated gas flowing past the sample might contain oxy gen present
in the incoming gas stream which is not removed by reaction with
the CO to produce CO2,
OXIDAnON- REDUCTION KINETICS IN METAL OXIDES 35
If we consider a furnace tube of radius R and a hot zone of length
Lt> the transit time of a gas molecule through the hot zone for
a flow rate F is given by 1TLtR
2IF. The diffusion time for a gas molecule from the center of the
furnace tube to the wall is es sentially given by R2l Ug, where Dg
is the interdiffusion coeffi cient of one gas in another. For
about 93% of the gas molecules to collide with the furnace wall and
thereby to reach the furnace temperature, the length of the hot
zone should be at least F I 1TDg•
For a flow of 500 cc/min measured at atmospheric pressure but
flowing in a furnace at 150 to 200 torr and a value of Dg of 0.3
cm2/sec for CO2 diffusing in CO at 1300 C, the hot zone should
therefore be at least about 40 cm long. Since the hot zone of the
furnace used was not more than 10 cm long, it is indeed quite
likely that much of the gas flowing past the sample was substan
tially colder than the indicated furnace temperature.
If the gas flow is constrained to a region near the furnace wall by
the insertion of a concentric tube of radius r < R, then it can
be shown that the required "constrained hot-zone" length is given
by
F (R - r) 141TDg (R + r).
By inserting a l%-in.-diameter crucible below the sample in a 11/
2-in.-diameter furnace tube, the required hot-zone length for the
same gas flow rate is reduced to only about 0.4 em,
Effective heating of the gas flow was assured in the system
described here by introducing the incoming gas stream through a
preheater (9 in Fig. 1) which supported an alumina crucible 10 in a
position immediately below the sample. The preheater was con
structed of concentric alumina tubes heated to about 1000 C by a
platinum wire heating element. The alumina crucible below the
sample contributed not only to the heating of the gas, as described
above, but also to the minimization of fluctuations in the weighing
of the sample caused by gas turbulence and to reduction in the
lift ing force exerted on the sample by the flowing gas. After
intro ducing the preheater and crucible, the spurious effects
noted earlier were not observed again; the oxidation and reduction
mea surements were always found to be essentially
symmetrical.
36 1. BRANSKY AND N. M. TALLA N
Ta1325'C COt/COa25IoCOlCOoI3
T=1275'C COt/COo 39 loC0z/COaI9
Fig . 2 . Recorded weight change of the reduction of Mn0 l-0054 to
Mn0 l.O040 at 1275, 130 0, and 1325 C
Determination of the Chemical Diffusion Coefficient in MnO
The first step in an actual measurement was the equilibra tion of
the sample at a given temperature with a predetermined CO2/CO
mixture within the MnO phase field. 15 After an equilibri um
weight was attained, the COdCO mixture was changed and the change
in sample weight due to oxidation or reduction was record ed
continuously. The results of reduction measurements on an MnO
single crystal disc, 0.9 mm thick with ( 100) crystallographic
faces 12 mm in diameter, are shown at three different tempera
tures in Fig. 2. The reduction corresponds in each case to a
OXIDATION - REDUCTION KINETICS IN METAL OXIDES 37
3000.---------r-----.-----,------....------,
400 500
Fig . 3a. Parabolic ra te of reduction of MnO l +X at 1300 C: 1. CO
zl CO = 142 .5
to codco = 81. 5; II . COz/CO = 53.6 to codco = 24.4.
MnO. 130 0 · C
0 ...J
0 20 0 300 400 500 Time(minl
Fig . 3b . Logarithmic rate of reduction of MnO!+x at 1300 C: 1.
COz/ CO =142 .5 to COz/CO = 81. 5; II . COz/CO = 53.6 to COz/CO =
24.4 .
38 I. BRANSKY AND N. M. TALLAN
change in composition from MnOt.0054 to MnOt.0040' It may be noted
from the recorder traces that the noise level , using all of the
fil tering available electronically in the balance circuit, was
about ±2 J.Lg. The uncertainty in the :5 values calculated from
equations (4) and (5) is largely due to the uncertainties in the
values of mo and mf determined from the recorder traces. It is
therefore necessary to determine the initial and final weights as
carefully as possible from data of the type shown in Fig. 2. It was
found to be particularly difficult to determine mo when the initial
reduction kinetics were very rapid. Static values of mo and mf were
always used to check the reliability of the values measured in
flowing gas atmospheres.
The chemical diffusion coefficient :5 was calculated from equations
(4) and (5) using a computer which also plotted the mea sured
weight change as both parabolic and logarithmic functions of the
time. Values of :5 were calculated from the slope of the linear
part of each plot by the method of least squares. The agree ment
between values of :5 calculated from the initial parabolic part of
the reduction rate and from the later-stage logarithmic partwas
usually within experimental error, but the parabolic values were
generally more consistent. Examples of the computer plots are shown
in Figs. 3a and 3b, where arrows have been used to indi cate the
end points of the linear parts from which :5 values were
calculated.
Since the integrated solutions of equation ~) which are used to
calculate :5 are obtained under the assumption that all surface
reactions involved are much more rapid than the volume diffusion
process, it is always important to determine that this condition is
satisfied for the material studied and for the experimental condi
tions used. This was accomplished for MnO by varying the flow rates
of the initial and final COdCO mixtures, by varying the total
pressures of the COdcO mixtures, and by diluting the COdCO mixtures
with argon. The initial and final CO2I CO ratios, and therefore the
step in composition, were the same in all cases. Al though the
kinetics of the reduction were not influenced by varia tions in
flow rate, they were significantly slowed down by either reduction
in the CO2leo total pressure or increase in argon di lution. These
effects will be discussed further in a separate pub lication on
the kinetics of MnO reduction in CO2I CO mlxtures.J''
OXIDATION- REDUCTION KINETICS IN METAL OXIDES
10,....--:---~-----r------,
9
8
o .0 15
Fig . 4. Chemical diffusion coefficient of Mn01+x at 1300 C as a
function of the deviation from stoic hiomet ry.
In Fig. 4, the chemical diffusion coefficient of Mn01+X is shown as
a function of x at 1300 C. The values shown were calcu lated from
composition steps of about Ax ~ 0.2%. It may be noted that :5
decreases with increasing stoichiometric deviation. This behavior
was also found in Fe01+x by other investigators4,5,10 us ing
gravimetric measurements in steps of about Ax = 1% and in Mn01+x by
Price12 using electrical conductivity measurements.
CONCLUSIONS
The gravimetric system described here, which has been found to be
sufficiently sensitive for the determination of chemical diffusion
coefficients in MnO from small changes in the composi tion , is
currently being used for additional studies of MnO and will be used
for future studies of CoO and U02. The system should, in fact,
prove to be valuable for similar studies in other materials where
the weight change accompanying oxidation or reduction is large
enough to permit gravimetric measurements to be used. A system of
the same design might also be applied to studies of the initial
stages of oxidation of metals.
40
REFERENCES
I. BRANSKY AND N. M. TALLAN
1. L. S. Darken, Diffusion, mobility, and their interrelation
through free energy in binary metallic systems, Trans. Am. Inst.
Min. Met. Engra., 175, 184 (1948).
2. C. Wagner, Uber den Zusammenhang zwischen Ionenbeweg Iichkeit
und Dlffuslonsgeschwlndigkett in festen Salzen, Z. Physik. Chem.,
Bll, 139 (1930); Beitrag zur Theorie des Anlaufvorganges. II, Z.
Physik. Chem., B32, 447 (1936).
3. G. C. Kuczynski, Grain boundaries and the phenomena of the
diffusion in oxides, Bull. Soc. Franc. Ceram., 80, 45 (1968).
4. R. Levin and J. B. Wagner, Jr., Reduction of undoped and
chromium-doped wtistite in carbon monoxide - carbon di oxide
mixtures, Trans. AIME, 233, 159 (1965).
5. P. F. Landler and K. L. Komarek, Reduction of wtistite within
the wtistite phase in H2- H20 mixtures, Trans. AIME, 236, 138
(1966).
6. J. B. Wagner, Jr., Chemical diffusion coefficients for some
nonstoichlometrtc metal oxides, Mass Transport in Oxides, Natl.
Bur. Stnds, Special Publication 296, P. 65 (1967), U.S. Department
of Commerce.
7. J. B. Price and J. B. Wagner, Jr., Determination of the chemical
diffusion coefficients in single crystal CoO and NiO, Z. Physik.
Chern., 49, 257 (1966).
8. K. W. Lay, The oxygen chemical diffusion coefficient of uranium
dioxide, Am. Ceramic Soc. Annual Meeting, Washington, D. C., May
1969.
9. R. H. Campbell, W. J. Kass, and M. °'Keeffe , Interdiffusion
coefficients from electronic conductivity measurements
application to CU20, Mass Transport in Oxides, Natl, Bur. Stds,
Special Publication 296, P. 173 (1967), U.S. Department of
Commerce.
10. P. L. Hembree and J. B. Wagner, Jr., Kinetics of reduction of
wtistite in CO2- CO mixtures at 1100"C, to be published.
11. J. Buyn, PhD Thesis, University of Notre Dame, Indiana
(1967).
12. J. B. Price, Chemical and radiotracer diffusion in Mn01+x' PhD
Thesis, Northwestern University, Evanston, Illinois (1968).
13. r, Bransky, M. Gvishi, and N. M. Tallan,
Thermogravimetric
OXIDATION -REDUCTION KINETICS IN METAL OXIDES 41
studies of chemical diffusion in MnO!+x, Am. Ceramic Soc. Annual
Meeting, Washington, D.C., May 1969.
14. W. C. Tripp, R. W. vest, and N. M. Tallan, System for measuring
microgram weight changes under controlled oxy gen partial pressure
to 1000°C, in: Vacuum Microbalance Techniques, Vol, 4 (1965), p.
141.
15. I. Bransky and N. M. Tallan, The phase field of Mn01+x in the
temperature range 1000°C-1400°C, to be published.
16. I. Bransky and N. M. Tallan, Kinetics of Mn01+x reduction in
COdCO mixtures, to be published.
DISCUSSION
E. A . Gu I bra n sen: What is the influence of volatile oxides of
manganese on your measurements?
min at 1500 C and co2/co = 6.3 . The kinetic studies reported here
were conducted in a range of temperatures and oxygen partial
pressures where evaporation could be neglected, as is seen in Fig.
2 from the constant weight at equilibrium . This conclu sion was
also verified many times during the course of these measurements by
simply reoxidizing the specimen in the initial gas mixture and
comparing its weight to the in itial weight before
reduction.
R. M. A I ire: How did you assure yourself that you had diffusion
in only one dimension, when your sample was a disc, which could
have diffusion in two dimensions? Did you establish what species
diffuses?
I. Bra n sky: The solutions of Fick 's laws used to determine the
chemical dif fusion coefficient in the present work do assume
one-dimensional diffusion . Corrections for edge effects have been
given by Landler and Komarek. f The samples used in this study were
thin enough that the corrections due to edge effects were within
the experi mental error.
No tracer diffusion expe riments were made in the present study to
evaluate the individual diffusivities of the oxygen and manganese
ions. However, the relatively high chemical diffusion coefficient
obtained in the single crystals studied indicates that the rate s
of oxidation and reduction are determined by the manganese ion
diffusiv ity rather than by the diffusivity of the slower oxygen
ion. The self-diffusion coeffi cient of Mn in MnO calculated from
the value of the chemical diffusion coefficient found in this study
(using the Darken relation and neglecting the oxygen diffusivity)
is about 10- 8 cm2/sec at 1300 C. Price12 found a value of 2.25 '
10- 8 cm 2/sec for the tracer diffusivity of Mn54 in MnO at 1141 C
in an oxygen partial pressure of 10- 7 atm .
An Automated Bakeable Quartz Fiber Vacuum Ultramicrobalance
J. Radder
ABSTRACT
An automated bakeable quartz fiber vacuum ultramicrobalance is
described. A precision of 5 • 10-9 g has been obtained with a 200
mg load yielding a load to precision ratio (LPR)1 of 4 . 107• The
load sensitivity product (LSp)t,2 is 1.2 . 106• The design of the
shock-resistant beam, its suspension, and its special housing are
described. Automatic operation is accomplished with flags mount ed
on the hangdown suspensions, two photocells , magnetic com
pensation, and the appropriate electronics. Causes of instabilities
encountered in high vacuum with the automatic system are dis
cussed and the methods used to eliminate the problems are
given.
INTRODUCTION
For many experiments it is necessary to measure submicrogram mass
changes. The balance desired was required to meet the fol lowing
specifications: 1) a stability of 10-8 g, 2) a ratio of capa city
to precision greater than 10 7, 3) a bake able system to permit
operation at pressures below 10- 9 torr, 4) construction from
glass-type materials wherever possible, and 5) a design that makes
it practical to use the instrument. Concerning 5), this means the
balance must be rugged, portable, and insensitive to the usual vi
brations found in the laboratory. One instrument which is able to
meet these qualifications is the quartz fiber torsion balance. As a
mechanical device , its sensitivity remains virtually
unchallenged.I As a beam balance, an LPR exceeding 107 is easily
attained.
43
44 J. RODDER
Bakeability and remarkable stability are assured because of the
nearly ideal physical properties of fused silica. Finally, if
proper ly designed and constructed, quartz fiber balances are
surprising ly rugged and the disadvantages offered4 can be
eliminated.
DESIGN OF THE BALANCE
Beam
Most quartz fiber balances are constructed with the torsion fibers
nearly horizontal. With this design, however, the quartz fibers are
sensitive to shock because they are under large stress. The
explanation for this can be understood by referring to Fig. I. It
is observed that the stress on the fiber is Fcsco when the fiber
supports a constant load 2F. This stress increases rapidly as the
fiber approaches a horizontal position, vlz.., CY - O. Thus, by in
creasing CY from 2° to 10°, the stress on the fiber is reduced by a
factor of ten.
Careful attention must be given to the design of the terminal
suspension, which is used for loading the beam via hangdowns, One
of the designs used frequently is a fine vertical fiber fused to a
rod as shown in Fig. 2. For high sensitivity the bending mo ment
of the fiber must be small, which requires a fiber diameter of
approximately 5 u , Although a 5tJ- fiber can sustain a load of 9
g, fracture occurs readily under the forces of steady mechanical
vibration or hard impact on the beam limit stops.
The torsion suspension shown in Fig. 3 is just as sensitive but
more shock resistant than the fine vertical fiber. This is be
cause the torsion suspension is strained over a much longer
length
Fig. 1. The stress on a fiber.
A N A UTOMA TED ULTRA MICROBALAN CE
f ig . 2. Early beam showing fragile terminal suspension.
45
than the bending of the fine vertical fiber at a point. Hence, a
larger-diameter fiber can be used without decreasing the sensi
tivity.
The principles indicated above were used to design the beam which
has been used in more than 75 commercial balances.! As illustrated
in Fig. 4, the trussed beam and each terminal suspen sion are
supported by a pair of fine fibers. To increase the sensi tivity
without sacrificing strength, the central pair, or torsion fibers,
are longer than those usually associated with this type of balance.
It is worth noting that the spring, sometimes found at the end of
the back torsion fiber, is absent in this design.
f ig . 3. Torsion terminal suspension.
46 J. RODDER
Fig. 5. Pic ture of a prototype microbalance .
AN AUTQI,1ATED ULTRA l>lI CROBA LAl\ CE
f ig . 6 Pic ture of microbalance after impact.
47
A prototype balance of the same beam design is shown in Fig. 5 with
the top and side of the housing removed . The beam is slightly
heavier on the s ide touching the beam arrest; other wise the
weight of the beam is carried by the torsi on fibers . It can be
see n that the beam is r athe r low with respect to the ends of the
tors ion fibers. The housing, with it s sus pended beam , was
lifted two inches above a wooden table and then dropped . Shor tly
after impact, the picture shown in Fig. 6 was taken . The torsi on
fiber is s lack, the far side of the beam has moved upward nearly
an inch , and the tr iangle of the rear te rminal sus pension has
moved to the r ight while r otat ing. It is evident that this sever
e test provided an excess s train for the fine fibers .
The beam used In a typical vacuum bal ance weighs 175 mg and is
constructed fr om fused s ilica r ods r anging in diamete r from
0.2 to 0.4 mm . With a zuo-mg sample load, the center of mass was
adjus ted to give a per iod of 45 sec and a deflection se ns iti
vity of 6· / "g.
48 J. RODDER
Housing
In order to accommodate the long torsion fibers, the design of the
glass housing presented some special problems. The diffi culties
were overcome as shown in Fig. 7. There are two posts inside to
which the torsion fibers are fused. After the adjustments on the
beam are completed and the subassemblies added, the four end caps
are sealed. While some care must be exercised in the assembly, the
result is a compact lightweight housing having a volume of less
than 1.5 liters. If desired, the sample hangdown tube can be sealed
to a vacuum flange which makes it easy to move the balance to a
different location.
Electronics
A photocell was chosen as the transducer to detect beam movement
for several reasons. First, it exerts no force on the beam. Second,
the photocell is located outside the vacuum sys tem and can be
removed during the bakeout, Finally, the associ ated electronic
circuitry is relatively simple. Small mass changes are determined
by using the well-known magnetic compensation method! in which the
magnetic field of a coil interacts with a per manent magnet
suspended from the beam. The beam is maintained in a null position
by an electronic feedback system whose output current to the coil
is a linear function of the weight change. A block diagram of the
electronic system is shown in Fig. 8. The electronic circuitry is
complicated by the tendency of the flexible quartz system to
Vibrate. As a consequence, the electronic com ponents must be
selected carefully.
RESULTS
The system was first tested at atmospheric pressure. The balance
drifted continually after initial equilibrium was established
because heat from the photocell lamp generated air currents within
the housing. Subsequent pumping to 10- 2 torr reduced the drift to
an acceptably small level. As a final check the system was pumped
to 10-6 torr. At approximately 10-4 torr the noise level at the
control system output increased abruptly. Apparently, at 10-2 torr
the air was still effective in damping the mechanical system, but
at 10-4 torr damping disappeared. At pressures less than 10-4 torr,
the slightest vibration caused up to a 2000-fold in crease in the
noise level of the system.
A ~ AtrTmtATED t 'LTRA\lI CROBALANCE 49
f ig. 7. Prororype vacuum balance .
50 J. RODDER
The magnitude of the vibration problem ruled out the usual brute
force method of mounting the balance on a massive support. The
problem can be solved if there exists a transducer which pro vides
a signal to the amplifier only if the beam rotates. Vertical
oscillations caused by vibration should contribute nothing to the
signal. This transducer can be realized in practice by using two
photocells as shown in Fig. 9. In this circuit the connection of
the photocells eliminates the signal due to the vertical
displacement of the beam. In addition to solving the vibration
problem, the two photocell system provides temperature compensation
and doubles the signal to the amplifier. To use the two photocell
system, the beam and housing were modified according to the diagram
shown in Fig. 10. The two flags interrupt the light to the
photocell.
Another effect can occur as the pressure is reduced below 10-4
torr; that is, the magnet begins to swing. The oscillations are
gradually amplified by the control system until the control loop
becomes unstable. This problem proved a most difficult one to
solve. Since the oscillations began only after air damping had been
removed, magnetic damping was tried first. This proved in
effective and also interfered with the beam magnet and coiL
Finally, it was postulated that even though the field in a
cylindrically wound coil diverges, there must be one position where
the field of the coil is axial to the field of the suspended
magnet. At this point no lateral forces are exerted on the mag
net. Such a relationship between the coil and magnet does exist.
With a properly positioned coil the total excursion of the magnet
can be decreased to less than 25 p.. Furthermore , a forced oscil
lation of the magnet can be damped within 20 min.
PERFORMANCE
The sensibility of the balance is a function of the distance be
tween the center of the coil and the poles of the permanent magnet.
By making the distance relatively long it is poss ible to obtain a
calibration that yields an output of 1 mV/0.5 p.g; thus , 5 . 10-9
g corresponds to a 1% movement on the I-mV scale. At this high
sensibility, it is necessary to tare the balance to within 400 p. g
of the absolute null because of the limited range of compensation
by the coil. The balance is insensitive to vibration so a sturdy
wood en table provides an adequate support. Even with the
vibrations from a compressor operating nearby, the balance
performed satis factorily. Finally, a balance of this type has
been used effectively
AN AUTOMATED ULTRAMICROBALANCE 51
Fig. 9. Wheatstone bridge circuit of two-photocell system.
Fig. 10. Components of the beam and housing: 1) sample tube; 2)
window; 3) flag : 4) magnet; 5) vacuum flange; 6) ring seal.
52 J. RODDER
as a tool for surface studies, which will be discussed in detail in
the paper by R. Merrill.6
CONCLUSION
A beam design has been developed with features not found in other
balances. First, when used as a torsion balance, the deflec tion
sensitivity varies only a few parts per 10,000 from no load to
maximum load. Second, the design of the terminal suspension pro
vides for a nonrotatable sample. Finally, as.a torsion fiber bal
ance, the design is unique regarding the ruggedness of the quartz
system.
ACKNOWLEDGEMENT
The author is indebted to Dr. D. Clark for his help in design ing
the electronic system.
REFERENCES
1. A. W. Czanderna, Ultramicrobalance review, in: S. P. Wolsky and
E. Zdanuk (eds.) , Ultra Micro Weight Determina tion in Controlled
Environment, Interscience, New York (1969), p. 11.
2. R. L. Schwoebel, Ultramicro