- Email: [email protected]
Densities of carbon foils
94
Nuclear Instruments and Methods m Physics Research A303 (1991) 94-98 North-Holland
Densities of carbon foils John O. Stoner, Jr.
ACF-Metals, Arizona Carbon Foil Co., Inc., 2239 E Klemdale Road, Tucson, AZ 85719-2440, USA and Physics Department, Bldg. 81, University of Arizona, Tucson, AZ 85721, USA
The densities of arc-evaporated carbon target foils have been measured by several methods. The density depends upon the method used to measure it ; for the same surface density, values obtained by different measurement techniques may differ by fifty percent or more . The most reliable density measurements are by flotation, yielding a density of 2.01±0.03 gcm -3, and mterferometnc step height with the surface density known from auxiliary measurements, yielding a density of 2.61±0.4 g cm -3 . The difference between these density values may be due in part to the compressive stresses that carbon films have while still on their substrates, uncertainties in the optical calibration of surface densities of carbon foils, and systematic errors m step-height measurements. Mechanical thickness measurements by micrometer caliper are unreliable due to nonplanarity of these foils.
1. Introduction
3. Measurements and discussion
The density of a target foil may be needed by an experimenter to obtain the stopping power (dE/d x) for projectiles of interest, or to develop models for the
Flotation is currently the most precise method for density measurements. Mixtures of bromoform and
develop well-characterized carbon targets, it has been
rate to 0.1% or better . Fragments of carbon foils were scraped from coated microscope slides and placed in such liquids; the fragments floated or sank depending
optical calibration of target-foil thickness. In order to
necessary to compare several methods for measuring
density of carbon foils #' .
Methods for finding the density of a thin foil fall into two classes: methods that rely upon Archimedes' principle, and methods that require separate measure-
ments of the surface density and thickness of a foil . The surface density may be measured by a variety of methods including weighing, particle backscattering, X-ray absorption, transmitted-particle energy loss, or optical transmission
previously
calibrated
by some
method .
Thickness may be measured by numerous methods in-
cluding step-height interferometry, physical micrometry (including stylus methods), electron microscopy, and ellipsometry (requiring knowledge of the optical con. stants)-2
carbon tetrachloride were used, for which careful weight and volume measurements yielded liquid densities accu-
upon whether the liquid was more or less dense than the foil . It was straightforward to ignore anomalous fragments that stuck to the container or always floated on
the surface. The transition between which many fragments sank, and none sank to the bottom of a container
typically corresponded to a density change of about 0 .05 g cm -3 , and with fluids of several densities prepared through such a range, the uncertainty could be reduced to 0.02 g cm -3 .
Table 1 Techniques for measuring carbon foil densities Method
Methods used Combinations of techniques used in this work to
measure the densities of carbon foils produced by arcevaporation [1-31 are summarized in table 1 . A synopsis of the results is shown in fig. 1 . ni
Some of these results have been reported informally in newsletters of the International Nuclear Target Development Society.
Flotation to liquids having a range of densities Weight loss m water Interferometric step height and optically calibrated surface density Scanning electron microscopy and optically calibrated surface density Micrometer and optically calibrated surface density Micrometer and weighings
0168-9002/91/$03 .50 U 1991 - Elsevier Science Publishers B.V . (North-Holland)
Surface densities tested [lig cm -2 ] 20 200 000 9-88 20 20-90 200-1600
95
J. O. Stoner / Densities of carbon foils
3 .5
3 .0
2 .5
POI
0
0 .5
2
5
10
20
50
100
200
500
1000
Surface Density (lcg/cm 2 )
Fig. 1. Density of carbon vs surface density. (o) Interferometric step-height thickness measurements with optical surface density measurements, (0) flotation measurements ; (X) nucrometer-caliper thickness measurements with optical surface density measurements below 100 w g cm -2 , weighed surface densities above 100 Pg cm -2. (a) Ref. [4], (b) ref. [5], (c) ref. [6], (d) ref. [7], (e) ref. [8]. An uncertainty of ± -20% on the surface density has arbitrarily been assumed for the foils of ref. [8], since no details of that uncertainty were reported in that paper.
The final flotation measurements were done with samples that were permitted to stabilize in a darkened box. Liquids containing carbon fragments were observed to undergo turbulence when exposed to room lights . In these, the neutral-buoyancy condition could still be identified easily; the density measurements for samples stored in lighted areas was not significantly different from those stored in the dark. The result for foils having nominal surface density of 20 ltg cm -2 was a density of 2.01 f 0.03 g cm -3 , where the uncertainty covers all measurements . This may be compared with the flotation results of Kennedy et al . [8], who found densities of their evaporated carbon foils at 50 and 125 wg cm -2 to be 1.82 ± 0.1 g cm -3 . Ballistic-aggregation simulations [9,10] suggest that thinner foils have higher density because they have
fewer entirely closed voids inaccessible to the flotation fluid, compared to thicker foils. The difference between the present results and those of ref. [8] may be in part attributed to such effects; in addition, differences in the deposition conditions and methods of removal from the substrate may have contributed to the differences in density. During several months of carbon evaporations, layers having thicknesses approaching 1 mm were built up on the deposition apparatus. A piece of such material was weighed in air and in water to obtain a gravimetric value for the density of 1.83 ± 0.03 g cm -3. This value for "bulk" carbon foils is in agreement with the results of ref. [8] and with a variety of other values for densities of amorphous and graphitic carbon [4-7] (see fig. 1) . Comparing this density to that of foils at 20 Wg cm -2 Il . CARBON STRIPPER FOILS
J. 0. Stoner / Densities of carbon foils
96 Mi cromap ACF1 .D5
512x128
SURFACE PROFILE DISPLAY 10X 632"
Standard Instrunent 14 :23 6/20/90
nn
-20 -30 -40 -50 .0
19 .2
a.2
10 .4
s
nn
Fig . 2 . Interferometric scan over a carbon step nominally 64 nm high on glass, overcoated with aluminium.
suggests that "bulk" evaporated carbon (which may include foils as thin as 50 FLg cm -Z ) has voids amounting to about 10% of the total volume. Thicknesses of carbon-film steps evaporated onto glass substrates and overcoated with aluminum were measured with an interference microscope #2, calibrated with a standard step traceable to the US National Institute of Standards and Technology . Typically, such measurements are accurate to 5% or better . A typical scan over a step is shown in fig . 2. The surface densities of such films were known from their optical transmittances [2,3] to within about 10%, so the volume densities could be calculated using the measured thicknesses . In this way the resulting densities were known to approximately ±15% . Aside from any systematic uncertainties, the mean value of the density from interferometric measurements, 2 .61 g cm -3 , has an uncertainty not greater than about 0 .4 g cm -3 to cover the spread in the interferometric measurements and account for uncertainties mentioned above. This measurement differs from the flotation measurements by an amount greater than the sum of the experimental uncertainties, and is greater than densities usually assumed for amorphous or graphitic carbon. Several possible sources of this discrepancy have been considered . The simplest would be an overestimate uz Interference-microscopy measurements were kindly done with a Micromap Surface Metrology System through the courtesy of Micromap, Inc ., 4725 E . Sunrise, Suite 432, Tucson, AZ 85718, USA .
by 20% in the optical measurement of carbon foil surface density . However, auxiliary Rutherford backscattering (RBS) measurements [11,12] of the surface densities of carbon foils do not support this explanation . Other possible errors might involve miscalibration of the step-height scale, currently believed to be accurate to ±5% and therefore to introduce an error not more than five percent in the density, and the possibility that thinner coatings of aluminum resulted on the carbon steps than on the glass substrates because of a possibly lower sticking probability of aluminum on carbon . A fourth possible source of error involves the observation that evaporated carbon foils are in compressive stress while on their substrates ; this suggests that their density while on their substrates is greater than their density after they are removed . However, previously obtained optical data rule out a density difference greater than about 5% between unsupported carbon foils and foils on their substrates . Nonlinear least-squares fits to transmission data for such foils [3] show that the absorption part (imaginary component) of the refractive index, which scales directly with the assumed density, is not changed significantly be removing them from their substrates. A 5% difference in the absorption parts of the refractive indices would shown up clearly . The greater scatter in the measurements of the real component of the refractive index would be consistent with a somewhat larger density change between unsupported foils and foils on their substrates, but not so large as 10% . It is therefore suggested tentatively then that the observed discrepancy of about 20% between the stepheight and flotation densities is due primarily to uncertainties in the step-height density measurements, in turn
97
J. O Stoner /Densities of carbon foils
Fig. 3. Carbon foil (354 hg cm -z ) released from its substrate, showing pattern of distortion due to stress
resulting from a combination of uncertainties in the step-height calibration and optical calibration, and possible compression of the foil on its substrate, in roughly equal amounts . By stacking several nominally identical foils, mechanical measurement of thickness was possible with an ordinary micrometer caliper. Foils having surface densities greater than 200 wg cm -2 were baked at 600 K to release them from their substrates, cut into squares and stacked ten layers deep for measurement. Foils having surface densities in the range 20-100 Ng cm -Z were not baked; they were floated off their substrates in the conventional manner, picked up on rings, allowed to dry, and stacked 50 layers deep . Measurements of the thickness of a stack, together with the surface density known from optical calibrations yielded values of the volume density (fig . 1) systematically far lower than values obtained by other methods, typically in the range 0.5 to 0.8 g cm -3 . However, such foils were observed to sink when immersed in water. The probable explanation for the anomalously low densities can be seen in fig. 3, which shows a relatively thick carbon foil with a deformation pattern on it . Such patterns, commonly seen on carbon foils of all thicknesses as they are removed from their substrates, result from the relief of compressive stresses arising during the deposition process. Such patterns remain in the foil after removal, rendering it nonplanar. It is probable that the mild pressure (typically only 0.001 of the Young's modulus) applied by a micrometer caliper in measuring such foils is insufficient to flatten these nonplanarities. Thus, the foils in a stack presumably had voids between them, and the density obtained by such measurements will always be seriously in error. Alternative explanations for the anomalous density measured by micrometer were considered and rejected :
Production of large numbers of voids and/or an extensive pore structure in the evaporation process could yield a spongy or fluffy foil whose averaged density was very low, yet would sink in water. However, a scanning-electron-microscope measurement on the cross section of a 20 wg cm - Z foil showed no such structure; indeed, the thickness of the foil was measured to be 100 ± 20 nm, corresponding to a density of 2.0 ± 0.4 g cm -3 , consistent with both flotation and step-height measurements . Others' measurements [13] of the thicknesses of carbon foils by transmission electron microscopy also showed no anomalies. (b) An evaporated foil is expected to have surface roughness and protrusions at its free surface that result from the ballistic nature of the deposition . A micrometer measurement of the thickness might record the maximum height of roughness or protrusions, or the distance from the substrate side of the foil at which the density became a very small fraction (perhaps 0.001) of the mean thickness. However, the roughness would then be expected to scale approximately with the square root of the thickness of the foil [14], causing a similar variation in the difference between the observed density and the bulk density. No such systematic variation is evident in the present measurements (fig . 1), and no unusual surface roughness has been seen in the step-height measurements (cf. fig. 2) . (a)
4. Conclusions Densities of carbon foils measured by ourselves and others using Archimedes' principle are in the range 1.82-2.01 g cm -3 , with some indication that the density is greater at lower surface densities. Such a variation is consistent with ballistic aggregation calculations . InterIt . CARBON STRIPPER FOILS
J O. Stoner / Densities of carbon foils
98
ferometric step-height measurements yield a mean density of 2.6 ± 0.4 g cm -3 , outside the range of flotation
measurements . The difference between the flotation and
Company is gratefully acknowledged . We appreciate comments on the manuscript by G. Thomas .
step-height densities is tentatively ascribed to a combi-
nation of calibration uncertainties in the optically mea-
sured surface density and the step-height, with a possi-
ble contribution by compressive strain in the foil while it is on its substrate. When a carbon foil is removed from its substrate, these strains relax in part, causing nonplanarities that (tan interfere with mechanical measurements of their thickness, and possibly diminishing
References [1] [2] [3] [4]
the density by a few~l percent.
Note added in proof: M. Shiojtn, Y. Saito, H. Okada and H. Sasaki reported in Jpn. J. Appl . Phys . 18 (1979)
1931 that the density of carbon foils on quartz sub-
strates ranged from 1 .93 to 2.76 gcm -3 with no clear dependence upon surface density in the range 3 .9 to
[5] [6] [7] [8]
gcm-3 , is consistent with our interferometric values but
[9] [10] [11]
Acknowledgements
[12] [13]
68 .6 Wgcm -2 . Their mean value for density, 2.45 ± 0.24 not with our flotation measurements .
Robert Stoner did much of the analysis of the flota-
tion data . The assistance of Russell Marsh of Micromap
[14]
G. Dearnaley, Rev. Sci. Instr. 31 (1960) 197. J.O . Stoner, Jr., J. Appl . Phys . 40 (1969) 707. J.O . Stoner, Jr., Nucl . Instr . and Meth . A236 (1985) 662 Poco Graphite Inc., 1601 State Street, Decatur, TX 76234, USA, commercial literature on types CZR to DFP graphite (1985) . R. Weast (ed.), Handbook of Chemistry and Physics, 66th ed ., (CRC Press, Boco Raton, FL, 1985) p. B-84. Ibid, p. B-12 . Ibid, p. B-199. E F Kennedy, D.H . Youngblood and A.E . Blaugrund, Phys . Rev. 158 (1967) 897. J.O . Stoner, Jr, Nucl . Instr. and Meth . A282 (1989) 242. J.O . Stoner, Jr., SPIE 1324 (1990) 202. K.C. Hsieh, B.R . Sande], V.A . Drake and R.S. King, Transnuttance of thin C and Si/C foils at 1216 .4, submitted to Nucl . Instr. and Meth. L.C . McIntyre and J A. Leavitt, private communication. R.C Moretz, H.M . Johnson and D.F . Parsons, J. Appl . Phys. 39 (1968) 5421 . B. Yang, B.L . Walden, R. Messier and W.B . White, SPIE 821 (1987) 68 .
Nuclear Instruments and Methods m Physics Research A303 (1991) 94-98 North-Holland
Densities of carbon foils John O. Stoner, Jr.
ACF-Metals, Arizona Carbon Foil Co., Inc., 2239 E Klemdale Road, Tucson, AZ 85719-2440, USA and Physics Department, Bldg. 81, University of Arizona, Tucson, AZ 85721, USA
The densities of arc-evaporated carbon target foils have been measured by several methods. The density depends upon the method used to measure it ; for the same surface density, values obtained by different measurement techniques may differ by fifty percent or more . The most reliable density measurements are by flotation, yielding a density of 2.01±0.03 gcm -3, and mterferometnc step height with the surface density known from auxiliary measurements, yielding a density of 2.61±0.4 g cm -3 . The difference between these density values may be due in part to the compressive stresses that carbon films have while still on their substrates, uncertainties in the optical calibration of surface densities of carbon foils, and systematic errors m step-height measurements. Mechanical thickness measurements by micrometer caliper are unreliable due to nonplanarity of these foils.
1. Introduction
3. Measurements and discussion
The density of a target foil may be needed by an experimenter to obtain the stopping power (dE/d x) for projectiles of interest, or to develop models for the
Flotation is currently the most precise method for density measurements. Mixtures of bromoform and
develop well-characterized carbon targets, it has been
rate to 0.1% or better . Fragments of carbon foils were scraped from coated microscope slides and placed in such liquids; the fragments floated or sank depending
optical calibration of target-foil thickness. In order to
necessary to compare several methods for measuring
density of carbon foils #' .
Methods for finding the density of a thin foil fall into two classes: methods that rely upon Archimedes' principle, and methods that require separate measure-
ments of the surface density and thickness of a foil . The surface density may be measured by a variety of methods including weighing, particle backscattering, X-ray absorption, transmitted-particle energy loss, or optical transmission
previously
calibrated
by some
method .
Thickness may be measured by numerous methods in-
cluding step-height interferometry, physical micrometry (including stylus methods), electron microscopy, and ellipsometry (requiring knowledge of the optical con. stants)-2
carbon tetrachloride were used, for which careful weight and volume measurements yielded liquid densities accu-
upon whether the liquid was more or less dense than the foil . It was straightforward to ignore anomalous fragments that stuck to the container or always floated on
the surface. The transition between which many fragments sank, and none sank to the bottom of a container
typically corresponded to a density change of about 0 .05 g cm -3 , and with fluids of several densities prepared through such a range, the uncertainty could be reduced to 0.02 g cm -3 .
Table 1 Techniques for measuring carbon foil densities Method
Methods used Combinations of techniques used in this work to
measure the densities of carbon foils produced by arcevaporation [1-31 are summarized in table 1 . A synopsis of the results is shown in fig. 1 . ni
Some of these results have been reported informally in newsletters of the International Nuclear Target Development Society.
Flotation to liquids having a range of densities Weight loss m water Interferometric step height and optically calibrated surface density Scanning electron microscopy and optically calibrated surface density Micrometer and optically calibrated surface density Micrometer and weighings
0168-9002/91/$03 .50 U 1991 - Elsevier Science Publishers B.V . (North-Holland)
Surface densities tested [lig cm -2 ] 20 200 000 9-88 20 20-90 200-1600
95
J. O. Stoner / Densities of carbon foils
3 .5
3 .0
2 .5
POI
0
0 .5
2
5
10
20
50
100
200
500
1000
Surface Density (lcg/cm 2 )
Fig. 1. Density of carbon vs surface density. (o) Interferometric step-height thickness measurements with optical surface density measurements, (0) flotation measurements ; (X) nucrometer-caliper thickness measurements with optical surface density measurements below 100 w g cm -2 , weighed surface densities above 100 Pg cm -2. (a) Ref. [4], (b) ref. [5], (c) ref. [6], (d) ref. [7], (e) ref. [8]. An uncertainty of ± -20% on the surface density has arbitrarily been assumed for the foils of ref. [8], since no details of that uncertainty were reported in that paper.
The final flotation measurements were done with samples that were permitted to stabilize in a darkened box. Liquids containing carbon fragments were observed to undergo turbulence when exposed to room lights . In these, the neutral-buoyancy condition could still be identified easily; the density measurements for samples stored in lighted areas was not significantly different from those stored in the dark. The result for foils having nominal surface density of 20 ltg cm -2 was a density of 2.01 f 0.03 g cm -3 , where the uncertainty covers all measurements . This may be compared with the flotation results of Kennedy et al . [8], who found densities of their evaporated carbon foils at 50 and 125 wg cm -2 to be 1.82 ± 0.1 g cm -3 . Ballistic-aggregation simulations [9,10] suggest that thinner foils have higher density because they have
fewer entirely closed voids inaccessible to the flotation fluid, compared to thicker foils. The difference between the present results and those of ref. [8] may be in part attributed to such effects; in addition, differences in the deposition conditions and methods of removal from the substrate may have contributed to the differences in density. During several months of carbon evaporations, layers having thicknesses approaching 1 mm were built up on the deposition apparatus. A piece of such material was weighed in air and in water to obtain a gravimetric value for the density of 1.83 ± 0.03 g cm -3. This value for "bulk" carbon foils is in agreement with the results of ref. [8] and with a variety of other values for densities of amorphous and graphitic carbon [4-7] (see fig. 1) . Comparing this density to that of foils at 20 Wg cm -2 Il . CARBON STRIPPER FOILS
J. 0. Stoner / Densities of carbon foils
96 Mi cromap ACF1 .D5
512x128
SURFACE PROFILE DISPLAY 10X 632"
Standard Instrunent 14 :23 6/20/90
nn
-20 -30 -40 -50 .0
19 .2
a.2
10 .4
s
nn
Fig . 2 . Interferometric scan over a carbon step nominally 64 nm high on glass, overcoated with aluminium.
suggests that "bulk" evaporated carbon (which may include foils as thin as 50 FLg cm -Z ) has voids amounting to about 10% of the total volume. Thicknesses of carbon-film steps evaporated onto glass substrates and overcoated with aluminum were measured with an interference microscope #2, calibrated with a standard step traceable to the US National Institute of Standards and Technology . Typically, such measurements are accurate to 5% or better . A typical scan over a step is shown in fig . 2. The surface densities of such films were known from their optical transmittances [2,3] to within about 10%, so the volume densities could be calculated using the measured thicknesses . In this way the resulting densities were known to approximately ±15% . Aside from any systematic uncertainties, the mean value of the density from interferometric measurements, 2 .61 g cm -3 , has an uncertainty not greater than about 0 .4 g cm -3 to cover the spread in the interferometric measurements and account for uncertainties mentioned above. This measurement differs from the flotation measurements by an amount greater than the sum of the experimental uncertainties, and is greater than densities usually assumed for amorphous or graphitic carbon. Several possible sources of this discrepancy have been considered . The simplest would be an overestimate uz Interference-microscopy measurements were kindly done with a Micromap Surface Metrology System through the courtesy of Micromap, Inc ., 4725 E . Sunrise, Suite 432, Tucson, AZ 85718, USA .
by 20% in the optical measurement of carbon foil surface density . However, auxiliary Rutherford backscattering (RBS) measurements [11,12] of the surface densities of carbon foils do not support this explanation . Other possible errors might involve miscalibration of the step-height scale, currently believed to be accurate to ±5% and therefore to introduce an error not more than five percent in the density, and the possibility that thinner coatings of aluminum resulted on the carbon steps than on the glass substrates because of a possibly lower sticking probability of aluminum on carbon . A fourth possible source of error involves the observation that evaporated carbon foils are in compressive stress while on their substrates ; this suggests that their density while on their substrates is greater than their density after they are removed . However, previously obtained optical data rule out a density difference greater than about 5% between unsupported carbon foils and foils on their substrates . Nonlinear least-squares fits to transmission data for such foils [3] show that the absorption part (imaginary component) of the refractive index, which scales directly with the assumed density, is not changed significantly be removing them from their substrates. A 5% difference in the absorption parts of the refractive indices would shown up clearly . The greater scatter in the measurements of the real component of the refractive index would be consistent with a somewhat larger density change between unsupported foils and foils on their substrates, but not so large as 10% . It is therefore suggested tentatively then that the observed discrepancy of about 20% between the stepheight and flotation densities is due primarily to uncertainties in the step-height density measurements, in turn
97
J. O Stoner /Densities of carbon foils
Fig. 3. Carbon foil (354 hg cm -z ) released from its substrate, showing pattern of distortion due to stress
resulting from a combination of uncertainties in the step-height calibration and optical calibration, and possible compression of the foil on its substrate, in roughly equal amounts . By stacking several nominally identical foils, mechanical measurement of thickness was possible with an ordinary micrometer caliper. Foils having surface densities greater than 200 wg cm -2 were baked at 600 K to release them from their substrates, cut into squares and stacked ten layers deep for measurement. Foils having surface densities in the range 20-100 Ng cm -Z were not baked; they were floated off their substrates in the conventional manner, picked up on rings, allowed to dry, and stacked 50 layers deep . Measurements of the thickness of a stack, together with the surface density known from optical calibrations yielded values of the volume density (fig . 1) systematically far lower than values obtained by other methods, typically in the range 0.5 to 0.8 g cm -3 . However, such foils were observed to sink when immersed in water. The probable explanation for the anomalously low densities can be seen in fig. 3, which shows a relatively thick carbon foil with a deformation pattern on it . Such patterns, commonly seen on carbon foils of all thicknesses as they are removed from their substrates, result from the relief of compressive stresses arising during the deposition process. Such patterns remain in the foil after removal, rendering it nonplanar. It is probable that the mild pressure (typically only 0.001 of the Young's modulus) applied by a micrometer caliper in measuring such foils is insufficient to flatten these nonplanarities. Thus, the foils in a stack presumably had voids between them, and the density obtained by such measurements will always be seriously in error. Alternative explanations for the anomalous density measured by micrometer were considered and rejected :
Production of large numbers of voids and/or an extensive pore structure in the evaporation process could yield a spongy or fluffy foil whose averaged density was very low, yet would sink in water. However, a scanning-electron-microscope measurement on the cross section of a 20 wg cm - Z foil showed no such structure; indeed, the thickness of the foil was measured to be 100 ± 20 nm, corresponding to a density of 2.0 ± 0.4 g cm -3 , consistent with both flotation and step-height measurements . Others' measurements [13] of the thicknesses of carbon foils by transmission electron microscopy also showed no anomalies. (b) An evaporated foil is expected to have surface roughness and protrusions at its free surface that result from the ballistic nature of the deposition . A micrometer measurement of the thickness might record the maximum height of roughness or protrusions, or the distance from the substrate side of the foil at which the density became a very small fraction (perhaps 0.001) of the mean thickness. However, the roughness would then be expected to scale approximately with the square root of the thickness of the foil [14], causing a similar variation in the difference between the observed density and the bulk density. No such systematic variation is evident in the present measurements (fig . 1), and no unusual surface roughness has been seen in the step-height measurements (cf. fig. 2) . (a)
4. Conclusions Densities of carbon foils measured by ourselves and others using Archimedes' principle are in the range 1.82-2.01 g cm -3 , with some indication that the density is greater at lower surface densities. Such a variation is consistent with ballistic aggregation calculations . InterIt . CARBON STRIPPER FOILS
J O. Stoner / Densities of carbon foils
98
ferometric step-height measurements yield a mean density of 2.6 ± 0.4 g cm -3 , outside the range of flotation
measurements . The difference between the flotation and
Company is gratefully acknowledged . We appreciate comments on the manuscript by G. Thomas .
step-height densities is tentatively ascribed to a combi-
nation of calibration uncertainties in the optically mea-
sured surface density and the step-height, with a possi-
ble contribution by compressive strain in the foil while it is on its substrate. When a carbon foil is removed from its substrate, these strains relax in part, causing nonplanarities that (tan interfere with mechanical measurements of their thickness, and possibly diminishing
References [1] [2] [3] [4]
the density by a few~l percent.
Note added in proof: M. Shiojtn, Y. Saito, H. Okada and H. Sasaki reported in Jpn. J. Appl . Phys . 18 (1979)
1931 that the density of carbon foils on quartz sub-
strates ranged from 1 .93 to 2.76 gcm -3 with no clear dependence upon surface density in the range 3 .9 to
[5] [6] [7] [8]
gcm-3 , is consistent with our interferometric values but
[9] [10] [11]
Acknowledgements
[12] [13]
68 .6 Wgcm -2 . Their mean value for density, 2.45 ± 0.24 not with our flotation measurements .
Robert Stoner did much of the analysis of the flota-
tion data . The assistance of Russell Marsh of Micromap
[14]
G. Dearnaley, Rev. Sci. Instr. 31 (1960) 197. J.O . Stoner, Jr., J. Appl . Phys . 40 (1969) 707. J.O . Stoner, Jr., Nucl . Instr . and Meth . A236 (1985) 662 Poco Graphite Inc., 1601 State Street, Decatur, TX 76234, USA, commercial literature on types CZR to DFP graphite (1985) . R. Weast (ed.), Handbook of Chemistry and Physics, 66th ed ., (CRC Press, Boco Raton, FL, 1985) p. B-84. Ibid, p. B-12 . Ibid, p. B-199. E F Kennedy, D.H . Youngblood and A.E . Blaugrund, Phys . Rev. 158 (1967) 897. J.O . Stoner, Jr, Nucl . Instr. and Meth . A282 (1989) 242. J.O . Stoner, Jr., SPIE 1324 (1990) 202. K.C. Hsieh, B.R . Sande], V.A . Drake and R.S. King, Transnuttance of thin C and Si/C foils at 1216 .4, submitted to Nucl . Instr. and Meth. L.C . McIntyre and J A. Leavitt, private communication. R.C Moretz, H.M . Johnson and D.F . Parsons, J. Appl . Phys. 39 (1968) 5421 . B. Yang, B.L . Walden, R. Messier and W.B . White, SPIE 821 (1987) 68 .