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The maximum transient temperature rise can be estimated using the expression Q (1-R) /AC ζ′, where Q is the energy of a single incident optical pump pulse, R≈0.7 is the optical reflectance of the pump beam from the sample (including the front face of the sapphire), A=π w2 /2 is the pump beam-spot area, C is the specific heat per unit volume of liquid Hg, and ζ′ is the effective penetration depth of the pump beam into the Hg, taken to be ∼20 nm (as explained in Sec. 3). The spot radius w=17.5 μm is obtained from the pump beam lateral intensity profile, given by I (r) =exp (-2 r2 / w2). There is a simple relation between w and the full intensity width at half maximum D in this case: w≈0.85D. In our case Q (1-R) is equal to 0.7 nJ
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For the transparent sapphire, the exponential term in the integral of Eq. 5 ensures that only acoustic waves at frequency 2 ns v1′ /λ are detected.
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For the transparent sapphire, the exponential term in the integral of Eq. 5 ensures that only acoustic waves at frequency 2 ns v1′ /λ are detected.
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The ratio of the height of the ρ echo to the step of the δ echo was observed to be 1.4 for the data of Figs. 4 5. Some variation in this ratio was observed over different measurements, so the absolute values of dn/dη and dk/dη are subject to a ∼40% error.
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We have estimated the effect of the frequency-dependent sound velocity and ultrasonic attenuation on the acoustic reflection coefficient rac (ω) using the simple models of relaxational processes described in Sec. 5. We find that the contribution to the apparent velocity dispersion and ultrasonic attenuation in the measured data from this source in our case is negligible.
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We have estimated the effect of the frequency-dependent sound velocity and ultrasonic attenuation on the acoustic reflection coefficient rac (ω) using the simple models of relaxational processes described in Sec. 5. We find that the contribution to the apparent velocity dispersion and ultrasonic attenuation in the measured data from this source in our case is negligible.
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The accuracy of the analysis for the determination of the dispersion in velocity and attenuation was checked using synthesized acoustic pulses with dispersion and attenuation similar to that of Hg. The numerical error in this process is negligible compared to the scatter in the data for different Hg films.
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-
-
Strictly speaking, an independent measurement of z′ is required to determine the dispersion. However, if the velocity dispersion is small, as is expected to be the case for liquid Hg below 10 GHz, it is a good approximation to estimate z′ from the time between the maxima of the first and second echoes and from the known low-frequency sound velocity.
-
Strictly speaking, an independent measurement of z′ is required to determine the dispersion. However, if the velocity dispersion is small, as is expected to be the case for liquid Hg below 10 GHz, it is a good approximation to estimate z′ from the time between the maxima of the first and second echoes and from the known low-frequency sound velocity.
-
-
-
-
69
-
-
0345073195
-
-
JNCSBJ 0022-3093
-
Y. Ohmasa, Y. Kajihara, H. Kohno, Y. Hiejima, and M. Yao, J. Non-Cryst. Solids JNCSBJ 0022-3093 250-252, 209 (1999).
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, pp. 209
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-
Ohmasa, Y.1
Kajihara, Y.2
Kohno, H.3
Hiejima, Y.4
Yao, M.5
-
71
-
-
48749094756
-
-
This estimate is based on a Gaussian distribution of surface heights for the two sapphire surfaces.
-
This estimate is based on a Gaussian distribution of surface heights for the two sapphire surfaces.
-
-
-
-
72
-
-
84927282685
-
-
SOPUAP 0038-5670 10.1070/PU1992v035n03ABEH002221
-
S. A. Akhmanov and V. E. Gusev, Sov. Phys. Usp. SOPUAP 0038-5670 10.1070/PU1992v035n03ABEH002221 35, 153 (1992).
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Sov. Phys. Usp.
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, pp. 153
-
-
Akhmanov, S.A.1
Gusev, V.E.2
-
73
-
-
48749121787
-
-
The gradient of the positive dispersion dv/dω is known to an accuracy ∼50%.
-
The gradient of the positive dispersion dv/dω is known to an accuracy ∼50%.
-
-
-
-
75
-
-
0344178971
-
-
PPSOAU 0370-1328 10.1088/0370-1328/81/4/317
-
J. Jarzynski, Proc. Phys. Soc. London PPSOAU 0370-1328 10.1088/0370-1328/81/4/317 81, 745 (1963).
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Proc. Phys. Soc. London
, vol.81
, pp. 745
-
-
Jarzynski, J.1
-
76
-
-
48749108496
-
-
The thermal contribution can be simply estimated with the help of the relation γ-1=T β2 B/ CV =T β2 ρ0 vl2 / CV.
-
The thermal contribution can be simply estimated with the help of the relation γ-1=T β2 B/ CV =T β2 ρ0 vl2 / CV.
-
-
-
-
77
-
-
0002387086
-
-
This can be seen by Taylor expansion of the solution of a biquadratic equation proposed by Thurston: edited by W. P. Mason (Academic, New York
-
This can be seen by Taylor expansion of the solution of a biquadratic equation proposed by Thurston: R. N. Thurston, in Physical Acoustics, edited by, W. P. Mason, (Academic, New York, 1964), Vol. 1A, p. 1. See Eq. (258).
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(1964)
Physical Acoustics
, vol.1
, pp. 1
-
-
Thurston, R.N.1
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78
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-
17044410234
-
-
JNCSBJ 0022-3093
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L. E. Bove, F. Sacchetti, C. Petrillo, B. Dorner, F. Formisano, M. Sampoli, and F. Barocchi, J. Non-Cryst. Solids JNCSBJ 0022-3093 307-310, 842 (2002).
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, vol.307-310
, pp. 842
-
-
Bove, L.E.1
Sacchetti, F.2
Petrillo, C.3
Dorner, B.4
Formisano, F.5
Sampoli, M.6
Barocchi, F.7
-
79
-
-
0008116442
-
-
JCPSA6 0021-9606 10.1063/1.1670184
-
W. H. Nichols and E. F. Carome, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1670184 49, 1000 (1968).
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(1968)
J. Chem. Phys.
, vol.49
, pp. 1000
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-
Nichols, W.H.1
Carome, E.F.2
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81
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-
34548822080
-
-
JMAPAQ 0022-2488 10.1063/1.525164
-
R. L. Weaver and Y.-H. Pao, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.525164 22, 1909 (1981).
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(1981)
J. Math. Phys.
, vol.22
, pp. 1909
-
-
Weaver, R.L.1
Pao, Y.-H.2
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82
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-
0028976328
-
-
JASMAN 0001-4966 10.1121/1.412332
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T. L. Szabo, J. Acoust. Soc. Am. JASMAN 0001-4966 10.1121/1.412332 97, 14 (1995).
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(1995)
J. Acoust. Soc. Am.
, vol.97
, pp. 14
-
-
Szabo, T.L.1
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83
-
-
0033889221
-
-
JASMAN 0001-4966 10.1121/1.429586
-
K. R. Waters, M. S. Hughes, J. Mobley, G. H. Brandenburger, and J. G. Miller, J. Acoust. Soc. Am. JASMAN 0001-4966 10.1121/1.429586 108, 556 (2000).
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J. Acoust. Soc. Am.
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Waters, K.R.1
Hughes, M.S.2
Mobley, J.3
Brandenburger, G.H.4
Miller, J.G.5
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