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A new method to determine the mass of microfine particles
Volume 23. number 5
PHYSICS
LETTERS
31 October 1966
A general analysis of the instability condition becomes too involved in instances of that sort. When the plasma is very rarefied, w$ << ~2, and the plasma exerts virtually no action on the high-frequency field, it is readily seen from (2) and (3) that - provided the plasma density decreases with decreasing intensity of the high-frequency field, the instability is possible solely for frequencies higher than the electron cyclotron frequency (v > Sz,) from a certain critical magnetic field upward’ the latter can be calculted from a cubic equation with respect to 0:. Generally speaking, for v2 > w.4 the discharge becomes unstable in this case at any arbitrary intensity of the high-frequency field whenever the magnetic fields are in the neighbourhood of fiz - v2 - w$. We should like to also point out that a high-frequency field that does not satisfy the conditions of instability, displays a stabilizing effect and can serve for suppressing the drift-dissipative instabilities caused by other radial forces (e.g. by an electric field or inhomogeneity of an magnetic field [7]) such as that in the Penning discharge. It is difficult to state authoritatively at the present time whether or not the instabilities that have been observed experimentally are in any way linked with the mechanism just outlined. The author wishes to express
his thanks to K. Jungwirth and R. Klima for their valuable
comments.
References 1. 2. 3. 4. 5. 6. 7.
V.I.Perel and J.M.Pinski, J. Tech. Phys. 36 (1966) 1021. S.D.Vagner, A.I. Zudov and A.D.Khakhaev. J. Tech. Phys. 31 (1961) 336. R.Geller, Phys. Rev. Letters 9 (1962) 248. F. C.Hoh, Phys. Fluids 6 (1963) 1184. H.A.H.Boot and R.B.R.Shersly-Harvie. Nature 180 (1957) 1187. A. V.Gaponov and M.A.MilIcr. Zh. Exp. i Theor. Fiz. 34 (1958) 242. V.Kopeck$. Czech. J. Phys., to be publsihed.
*****
A NEW
METHOD
TO
DETERMINE
THE
MASS
OF
MICROFINE
PARTICLES
Y. MURAYAMA Hitachi
Central
Research Received
Laboratory,
Kokubunji,
10 September
Tokyo,
Japan
1966
A possibility is suggested how to measure the mass of microfine particles, using MBssbauer type resonant emission or absorption of y-rays. In contrast to bulky specimens. they-ray spectrum of fine particles may suffer any shift due to recoil.
Since Mijssbauer [l] discovered the recoilless emission of y-rays from radioactive nuclei, this process has been always considered to be accompanied by no recoil as a whole of the matter. As is well known, the emission spectrum accompanying one or multi-phonon process spreads from the level spacing energy E, towards lower energies due to the phonon excitation. The uppermost part of the spectrum comes from zero phonon process, and is unshifted if the emission is recoil-free. However, if the emitter of y-rays is a microfine particle, this zero phonon part will be dis332
placed, because the center of mass suffers a recoil. The situation is the same in case a particle is the absorber of y-rays. The resonant absorption occurs at an energy shifted by the recoil. This is the basic idea to apply to how the total mass of a fine particle is determined. The way of measurement is no other than that for the ordinary Miissbauer effect. An emitter or an absorber must be forced to move to attain proper amount of the Doppler shift. The condition of the resonant absorption is 6E=* Mv2 = E$/2Mc2, where M is the total mass of a particle, 2, the Doppler velocity.
PHYSICS
Volume 23, number 5
The possibility of measurement is bounded by the line widthr . The requirement is E!/2Mc2 ?, 2 IT. Take a hoton to be 14.4 keV from 57Fe, then F = lo- EpeV. So we can measure the mass less than about 2 X 10-17g N 107MH, with MH the mass of a hydrogen atom. Then the minimum velocity 2’ for the maximum measurable mass equals some hundredths centimeters per second. This must be a limit to mechanical control in available experiments. It is also a problem whether a number of atoms involved behave as a whole or not [2]. If an particle can transmit an information throughout in a lifetime T with the velocity us (velocity of sound), the linear dimension L of the particle must satisfy and inequality F =Z/T 2 tiv s/L. For r N 10-7s (57Fe), L <, 10-2 cm. This is obviously satisfied in case the particles of concern are not recoil-free. This condition is also interpreted as that an emission process of a phonon of the fundamental wave-length L is far off from the process as a whole (i.e., the zero phonon process) in its spectrum. Hence, the resonant absorption experiment is more advantageous on fine particles than in the bulk. Next we compare the recoil of the fine particles with the Brownian motion. The energy 6E estimated about 1 eV for Fe. If kBT << 1 eV = N 104K, the broadening of the absorption or emission line due to the Brownian random motion is much smaller than the shift. If the particles do not contain any radioactive isotopes, we have to dope a small amount of them. Let’s take the particles to be absorbers as is usual and take 57Fe for instance, then the total cross section o = 2 x lo-1302 is so large [3].If we define the collision rate by l/f, (in set-1) and
IMPROVEMENTS
R. J. COLLIER
a packing factor of the powder by q and consider that the natural abundance of the isotope is 2.250/o, the necessary content of iron is given by (l~-ll/~t~ )s. This quantity is small enough not to disturb the intrinsic properties of the substance, even if we let the emission-absorption process occur more than lo6 times per sec. We limited our discussion to be the isotope of iron, but any other radioactive isotopes will do. The available narrowest gamma ray spectrum from 57Zn with T = 10-5 s will make it possible to measure mass as far as 1010 times of MH. However, the corresponding Doppler velocity estimated gives 10_5cm/s. Maybe this magnitude will be out of our mechanical accuracy of significance. So far we confined ourselves to an ensemble of particles of the same size. When there is a distribution in the ensemble of concern, the variety of the sizes will appear on the spectrum, where the relative intensity shows the proportion of the particles contained in the ensemble.
References 1. R.L.M&sbauer. Zeits. Phys. 151 (1958) 124. 2. G. K. Wertheim, Mijssbauer effect, principle and applications, (Academic Press, N.Y., 1964). 3. A. J. F.Boyle and H.E.Hall, Rep. Progr. Phys. 25 (1962) 441.
on the sensitivity
University
22 September
and frequency
Gambling and Wilmshurst [l] have described an electron-spin resonance spectrometer opera-
ELECTRON
SPIN
and T. H. WILMSHURST
of Electronics, Received
are reported
31 October 19G6
TO THE AMMONIA MASER RESONANCE SPECTROMETER
Department
Improvement;
LETTERS
of Southampton 1966
stability
of a previously
described
spectrometer.
ting at 24Gc/s and incorporating an ammonia maser amplifier to improve the sensitivity. The 333
PHYSICS
LETTERS
31 October 1966
A general analysis of the instability condition becomes too involved in instances of that sort. When the plasma is very rarefied, w$ << ~2, and the plasma exerts virtually no action on the high-frequency field, it is readily seen from (2) and (3) that - provided the plasma density decreases with decreasing intensity of the high-frequency field, the instability is possible solely for frequencies higher than the electron cyclotron frequency (v > Sz,) from a certain critical magnetic field upward’ the latter can be calculted from a cubic equation with respect to 0:. Generally speaking, for v2 > w.4 the discharge becomes unstable in this case at any arbitrary intensity of the high-frequency field whenever the magnetic fields are in the neighbourhood of fiz - v2 - w$. We should like to also point out that a high-frequency field that does not satisfy the conditions of instability, displays a stabilizing effect and can serve for suppressing the drift-dissipative instabilities caused by other radial forces (e.g. by an electric field or inhomogeneity of an magnetic field [7]) such as that in the Penning discharge. It is difficult to state authoritatively at the present time whether or not the instabilities that have been observed experimentally are in any way linked with the mechanism just outlined. The author wishes to express
his thanks to K. Jungwirth and R. Klima for their valuable
comments.
References 1. 2. 3. 4. 5. 6. 7.
V.I.Perel and J.M.Pinski, J. Tech. Phys. 36 (1966) 1021. S.D.Vagner, A.I. Zudov and A.D.Khakhaev. J. Tech. Phys. 31 (1961) 336. R.Geller, Phys. Rev. Letters 9 (1962) 248. F. C.Hoh, Phys. Fluids 6 (1963) 1184. H.A.H.Boot and R.B.R.Shersly-Harvie. Nature 180 (1957) 1187. A. V.Gaponov and M.A.MilIcr. Zh. Exp. i Theor. Fiz. 34 (1958) 242. V.Kopeck$. Czech. J. Phys., to be publsihed.
*****
A NEW
METHOD
TO
DETERMINE
THE
MASS
OF
MICROFINE
PARTICLES
Y. MURAYAMA Hitachi
Central
Research Received
Laboratory,
Kokubunji,
10 September
Tokyo,
Japan
1966
A possibility is suggested how to measure the mass of microfine particles, using MBssbauer type resonant emission or absorption of y-rays. In contrast to bulky specimens. they-ray spectrum of fine particles may suffer any shift due to recoil.
Since Mijssbauer [l] discovered the recoilless emission of y-rays from radioactive nuclei, this process has been always considered to be accompanied by no recoil as a whole of the matter. As is well known, the emission spectrum accompanying one or multi-phonon process spreads from the level spacing energy E, towards lower energies due to the phonon excitation. The uppermost part of the spectrum comes from zero phonon process, and is unshifted if the emission is recoil-free. However, if the emitter of y-rays is a microfine particle, this zero phonon part will be dis332
placed, because the center of mass suffers a recoil. The situation is the same in case a particle is the absorber of y-rays. The resonant absorption occurs at an energy shifted by the recoil. This is the basic idea to apply to how the total mass of a fine particle is determined. The way of measurement is no other than that for the ordinary Miissbauer effect. An emitter or an absorber must be forced to move to attain proper amount of the Doppler shift. The condition of the resonant absorption is 6E=* Mv2 = E$/2Mc2, where M is the total mass of a particle, 2, the Doppler velocity.
PHYSICS
Volume 23, number 5
The possibility of measurement is bounded by the line widthr . The requirement is E!/2Mc2 ?, 2 IT. Take a hoton to be 14.4 keV from 57Fe, then F = lo- EpeV. So we can measure the mass less than about 2 X 10-17g N 107MH, with MH the mass of a hydrogen atom. Then the minimum velocity 2’ for the maximum measurable mass equals some hundredths centimeters per second. This must be a limit to mechanical control in available experiments. It is also a problem whether a number of atoms involved behave as a whole or not [2]. If an particle can transmit an information throughout in a lifetime T with the velocity us (velocity of sound), the linear dimension L of the particle must satisfy and inequality F =Z/T 2 tiv s/L. For r N 10-7s (57Fe), L <, 10-2 cm. This is obviously satisfied in case the particles of concern are not recoil-free. This condition is also interpreted as that an emission process of a phonon of the fundamental wave-length L is far off from the process as a whole (i.e., the zero phonon process) in its spectrum. Hence, the resonant absorption experiment is more advantageous on fine particles than in the bulk. Next we compare the recoil of the fine particles with the Brownian motion. The energy 6E estimated about 1 eV for Fe. If kBT << 1 eV = N 104K, the broadening of the absorption or emission line due to the Brownian random motion is much smaller than the shift. If the particles do not contain any radioactive isotopes, we have to dope a small amount of them. Let’s take the particles to be absorbers as is usual and take 57Fe for instance, then the total cross section o = 2 x lo-1302 is so large [3].If we define the collision rate by l/f, (in set-1) and
IMPROVEMENTS
R. J. COLLIER
a packing factor of the powder by q and consider that the natural abundance of the isotope is 2.250/o, the necessary content of iron is given by (l~-ll/~t~ )s. This quantity is small enough not to disturb the intrinsic properties of the substance, even if we let the emission-absorption process occur more than lo6 times per sec. We limited our discussion to be the isotope of iron, but any other radioactive isotopes will do. The available narrowest gamma ray spectrum from 57Zn with T = 10-5 s will make it possible to measure mass as far as 1010 times of MH. However, the corresponding Doppler velocity estimated gives 10_5cm/s. Maybe this magnitude will be out of our mechanical accuracy of significance. So far we confined ourselves to an ensemble of particles of the same size. When there is a distribution in the ensemble of concern, the variety of the sizes will appear on the spectrum, where the relative intensity shows the proportion of the particles contained in the ensemble.
References 1. R.L.M&sbauer. Zeits. Phys. 151 (1958) 124. 2. G. K. Wertheim, Mijssbauer effect, principle and applications, (Academic Press, N.Y., 1964). 3. A. J. F.Boyle and H.E.Hall, Rep. Progr. Phys. 25 (1962) 441.
on the sensitivity
University
22 September
and frequency
Gambling and Wilmshurst [l] have described an electron-spin resonance spectrometer opera-
ELECTRON
SPIN
and T. H. WILMSHURST
of Electronics, Received
are reported
31 October 19G6
TO THE AMMONIA MASER RESONANCE SPECTROMETER
Department
Improvement;
LETTERS
of Southampton 1966
stability
of a previously
described
spectrometer.
ting at 24Gc/s and incorporating an ammonia maser amplifier to improve the sensitivity. The 333