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1
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0042152285
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W. A. Harrison, Phys. Rev. 118, 1182 (1960); 118, 1190 (1960).
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Phys. Rev.
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Harrison, W.A.1
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2
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0043261125
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W. A. Harrison, Phys. Rev. 118, 1182 (1960); 118, 1190 (1960).
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Phys. Rev.
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3
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84996151608
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N. W. Ashcroft, Philos. Mag. 8, 2055 (1963); N. W. Ashcroft and K. Sturm, Phys. Rev. B 3, 1898 (1971).
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Philos. Mag.
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Ashcroft, N.W.1
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9
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16244382284
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S. Krishnan and P. C. Nordine, Phys. Rev. B 47, 11780 (1993); 48, 4130 (1993).
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Phys. Rev. B
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10
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0001408367
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There has also been work done using fast x rays as a gas-gun diagnostic, but only for structural transformations involving simple crystalline phases. For recent work in this area, see P. A. Rigg and Y. M. Gupta, Appl. Phys. Lett. 73, 1655 (1998).
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(1998)
Appl. Phys. Lett.
, vol.73
, pp. 1655
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Rigg, P.A.1
Gupta, Y.M.2
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16244379451
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note
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We use "T=0" to mean motionless ions fixed on the fcc lattice sites. This is not truly T=0, for zero-point motion is neglected here. Rather, we are performing calculations for infinite ionic mass (and T-Q). This distinction is unimportant for our purposes here.
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12
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0042113153
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2(ω) for fcc Al at T=0 as calculated from the randomphase approximation with one-electron states from LDA, see Fig. 7 of L. X. Benedict, C. D. Spataru, and S. G. Louie, Phys. Rev. B 66, 085116 (2002). This should be compared to the experimental low-T result shown in Fig. 3 of this work. For finite-T density-functional calculations on the liquid at lower densities, see P. L. Silvestrelli, ibid. 60, 16382 (1999).
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(1965)
Phys. Rev.
, vol.140
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Kohn, W.1
Sham, L.J.2
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13
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0037104444
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2(ω) for fcc Al at T=0 as calculated from the randomphase approximation with one-electron states from LDA, see Fig. 7 of L. X. Benedict, C. D. Spataru, and S. G. Louie, Phys. Rev. B 66, 085116 (2002). This should be compared to the experimental low-T result shown in Fig. 3 of this work. For finite-T density-functional calculations on the liquid at lower densities, see P. L. Silvestrelli, ibid. 60, 16382 (1999).
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(2002)
Phys. Rev. B
, vol.66
, pp. 085116
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Benedict, L.X.1
Spataru, C.D.2
Louie, S.G.3
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14
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0000082350
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2(ω) for fcc Al at T=0 as calculated from the randomphase approximation with one-electron states from LDA, see Fig. 7 of L. X. Benedict, C. D. Spataru, and S. G. Louie, Phys. Rev. B 66, 085116 (2002). This should be compared to the experimental low-T result shown in Fig. 3 of this work. For finite-T density-functional calculations on the liquid at lower densities, see P. L. Silvestrelli, ibid. 60, 16382 (1999).
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(1999)
Phys. Rev. B
, vol.60
, pp. 16382
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Silvestrelli, P.L.1
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16244399417
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For Al in ambient conditions, peaks arise from transitions between nearly-free-electron bands split by the periodic potential at the BZ faces. For fee, two faces contribute strongly ([111], [200]), giving rise to two peaks, one of which is in the energy range of interest (at ∼1.5 eV). In bcc only the [110] face contributes strongly, and its resulting peak is at lower energy (<0.5 eV), while for hep several BZ faces contribute, resulting in a complex of peaks at energies below 1 eV.
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We have also performed calculations for 108 atom cells at T =550 K and 1000 K, and have obtained results almost indistinguishable from those performed with 32 atom cells.
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20
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16244362616
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2(ω), given the Lorentzian broadening we use (see below). In addition, we apply a special k-point shift to our mesh so that different k points are rendered symmetrically inequivalent.
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22
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16244368689
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Y. S. Touloukian, R. K. Kirby, R. E. Taylor, and T. Y. R. Lee, Therm. Prop. Mat. 4, 12 (1970).
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(1970)
Therm. Prop. Mat.
, vol.4
, pp. 12
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Touloukian, Y.S.1
Kirby, R.K.2
Taylor, R.E.3
Lee, T.Y.R.4
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5544225142
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[High Temp. 4, 348 (1966)].
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(1966)
High Temp.
, vol.4
, pp. 348
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25
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16244371238
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v(k) are band energies, and f(v,k) are Fermi-Dirac occupancies.
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26
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note
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2], with a width characterized by η=0.1 eV.
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27
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16244367675
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c= 1.125 ̊A), the pseudo-potential form factor for q=(η/a)[111] is smaller than it should be, resulting in a low-energy peak (below 0.5 eV) which is too low in energy compared to that of LDA. This accounts for much of the discrepancy in the region of the dip at ∼ 1.0 eV. Note also that the high-energy wiggles in the LDA results are due to incomplete k-point convergence.
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It should be pointed out that the experimental peaks (say, e.g., the 198 K one) look broader than those of our calculation. This may be due to the presence of overlayers or surface roughness in the experimental work. The LDA-RPA result for T=0 predicts a peak which is very sharp indeed and (intrinsic) quasiparticle lifetime broadening should be very small (Ref. 9).
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