Abstract

A method has been developed of deriving the fundamental absorption spectra of solids directly from experimental infrared data without having to resort to computational evaluation. These characteristic lattice absorption spectra represent the true energy absorption spectra of solids. As opposed to the traditional absorption coefficient (k) vs frequency curve, which is regarded as the absorption spectrum for solids in the region of anomalous dispersion, the spectra, as derived by the proposed method, clearly resolve the transverse and longitudinal modes of vibration. They also exhibit the characteristics of anharmonicity and damping. The method uses the combined reflection and transmission data on single-crystal and thin-film specimens. Its validity has been verified on a wide variety of solids. The most recent data obtained from emission, laser-Raman, or cold neutron scattering techniques, is in complete agreement with the derived values. A method of calculating the various modes of vibration of solids, directly from elastic constants, is also advanced. It is simultaneously used to render further support for the developed characteristic energy absorption spectra. The importance of these spectra is discussed with regard to some problems in solid state physics.

© 1970 Optical Society of America

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References

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  1. J. N. Plendl, AFCRL-69-0353, Phys. Sci. Res. Paper No. 393 (1969).
  2. R. B. Barnes, M. Czerny, Z. Phys. 72, 447 (1931).
    [CrossRef]
  3. M. Czerny, Z. Phys. 56, 600 (1930).
  4. A. Mitsuishi, H. Yoshinaga, S. Fujita, J. Phys. Soc. Japan 14, 110 (1959).
    [CrossRef]
  5. E. Madelung, Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 100 (1909); Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 43 (1910).
  6. R. W. Pohl, Optik (Springer Verlag, Berlin, 1940), p. 43.
  7. J. N. Plendl, “Resonance Vibrations of the Ionic Lattice from the Mechanical Aspect,” presented at the European Conference of Molecular Spectroscopists” at Freiburg (Br.), Germany, 1957.
  8. J. de Klerk, Rev. Sci. Instrum. 36, 1540 (1965).
    [CrossRef]
  9. W. P. Mason, in Lattice Dynamics (Academic Press, New York, 1965), Vol. III/B.
  10. G. Simmons, J. Graduate Res. Center, Dallas, Texas, Vol. 34, Nos. 1 and 2 (March1965).
  11. C. H. Perry, Diss., Queen Mary College, London1960; and spectral measurements, MIT Reports on AFCRL Contract No. AF19(628)-6066 (1966/68).
    [PubMed]
  12. R. B. Barnes, Z. Phys. 75, 723 (1932).
    [CrossRef]
  13. J. R. Aronson, H. G. McLinden, spectral measurements, A. D. Little, Inc. Reports on AFCRL Contract No. AF19-(604)-8504 (1961/65).
  14. J. R. Jasperse et al., Phys. Rev. 146, 526 (1966).
    [CrossRef]
  15. A. Hadni, spectral measurements, Univ. de Nancy Reports on AFCRL Contract No. AF61(052)-518 and AF61(052)-957 (1961/69).
  16. A. D. B. Woods et al., Phys. Rev. 131, 1025 (1963).
    [CrossRef]
  17. J. E. Mooij, Phys. Lett. 24A, 249, (1967).
  18. D. W. Berreman, Phys. Rev. 130, 2193 (1963).
    [CrossRef]
  19. G. Dolling et al., Phys. Rev. 168, 972 (1968).
    [CrossRef]
  20. H. Boutin, H. Prask, Surface Sci. 2, 261 (1964).
    [CrossRef]
  21. R. E. Schmunk, Bull. Amer. Phys. Soc. 12, 281 (1967).
  22. W. J. L. Buyers, Phys. Rev. 153, 923 (1967).
    [CrossRef]
  23. B. Stone, D. Hill, Phys. Rev. Lett. 4, 282 (1960).
    [CrossRef]
  24. P. J. Gielisse et al., Phys. Rev. 155, 1039 (1967).
    [CrossRef]
  25. O. Brafman et al., Solid State Commun. 6, 523 (1968).
    [CrossRef]
  26. P. Tarte, spectral measurements, Univ. de Liège Reports on AFCRL Contract No. AF61(052)-917 (1966/69).
  27. J. R. Jasperse, spectral measurements, A. D. Little, Inc. Reports on AFCRL Contract No. AF19(628)-4351 (1964/65).
  28. S. M. Shapiro et al., Phys. Rev. Lett. 19, 361 (1967).
    [CrossRef]
  29. H. Yoshinaga, R. A. Oetjen, J. Opt. Soc. Amer. 45, 1085 (1955).
    [CrossRef]
  30. G. Picus, in Advan. Electronics and Electron Phys., 7, 24 (1955), E. Burstein, P. E. Egli, Eds.
  31. O. Brafman, S. S. Mitra, Phys. Rev. 171, 931 (1968).
    [CrossRef]
  32. W. G. Spitzer et al., Silicon Carbide (Pergamon Press, Oxford, 1960), p. 347.
  33. J. S. Ziomek, P. B. Pickar, Phys. Stat. Sol. 21, 271 (1967).
    [CrossRef]
  34. K. D. Moeller, S. T. Varma, spectral measurements, Fairleigh Dickinson Univ. Reports on AFCRL Contract No. AF19(628)-4084 (1964/69).
  35. A. Hadni et al., in Quantum Electronics 3, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964).
  36. J. N. Plendl et al., Appl. Opt. 5, 397 (1966).
    [CrossRef] [PubMed]
  37. P. J. Gielisse et al., J. Appl. Phys. 36, 2446 (1965).
    [CrossRef]
  38. J. N. Plendl et al., Solid State Comm. 7, 109 (1969).
    [CrossRef]
  39. P. Tarte, Rev. Silicates Industriels, 7–8, 1 (1963).
  40. A. S. Barker, Phys. Rev. 132, 1474 (1963).
    [CrossRef]
  41. C. R. Renneke, D. W. Lynch, Phys. Rev. 138, A530 (1965).
    [CrossRef]
  42. J. N. Plendl, Phys. Rev. 123, 1172 (1961).
    [CrossRef]
  43. J. N. Plendl, P. J. Gielisse, Appl. Opt. 3, 943 (1964).
    [CrossRef]
  44. J. N. Plendl, P. J. Gielisse, Appl. Opt. 4, 853 (1965).
    [CrossRef]
  45. J. N. Plendl, P. J. Gielisse, Z. Kristal. 118, 404 (1963).
    [CrossRef]
  46. J. N. Plendl, “New Concepts in the Physics of Solids,” Monograph, Spec. AFCRL Report No. 52 (1966).
  47. J. N. Plendl, P. J. Gielisse, AFCRL-69-0429, Phys. Sci. Res. Papers #395; also being published in Phys. Chem. Sol. 31, 874 (1970).
  48. P. Tarte, Acad. Roy. Belgique, Memoirs 35 (1965).
  49. Landolt-Boernstein, Atom und Molekularphysik (Springer Verlag, Berlin, 1955), Vol. 4/I
  50. G. R. Hunt, C. H. Perry, J. Ferguson, Phys. Rev. 134, A688 (1964).
    [CrossRef]
  51. J. E. Hiller, Kristallchemie (W. De Gruyter Verlag, Berlin, 1952).
  52. J. N. Plendl, P. J. Gielisse, Phys. Stat. Sol. 35, K151 (1969).
    [CrossRef]

1969

J. N. Plendl et al., Solid State Comm. 7, 109 (1969).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Phys. Stat. Sol. 35, K151 (1969).
[CrossRef]

1968

O. Brafman, S. S. Mitra, Phys. Rev. 171, 931 (1968).
[CrossRef]

G. Dolling et al., Phys. Rev. 168, 972 (1968).
[CrossRef]

O. Brafman et al., Solid State Commun. 6, 523 (1968).
[CrossRef]

1967

S. M. Shapiro et al., Phys. Rev. Lett. 19, 361 (1967).
[CrossRef]

R. E. Schmunk, Bull. Amer. Phys. Soc. 12, 281 (1967).

W. J. L. Buyers, Phys. Rev. 153, 923 (1967).
[CrossRef]

J. E. Mooij, Phys. Lett. 24A, 249, (1967).

J. S. Ziomek, P. B. Pickar, Phys. Stat. Sol. 21, 271 (1967).
[CrossRef]

P. J. Gielisse et al., Phys. Rev. 155, 1039 (1967).
[CrossRef]

1966

J. N. Plendl et al., Appl. Opt. 5, 397 (1966).
[CrossRef] [PubMed]

J. R. Jasperse et al., Phys. Rev. 146, 526 (1966).
[CrossRef]

1965

J. de Klerk, Rev. Sci. Instrum. 36, 1540 (1965).
[CrossRef]

G. Simmons, J. Graduate Res. Center, Dallas, Texas, Vol. 34, Nos. 1 and 2 (March1965).

J. N. Plendl, P. J. Gielisse, Appl. Opt. 4, 853 (1965).
[CrossRef]

P. Tarte, Acad. Roy. Belgique, Memoirs 35 (1965).

C. R. Renneke, D. W. Lynch, Phys. Rev. 138, A530 (1965).
[CrossRef]

P. J. Gielisse et al., J. Appl. Phys. 36, 2446 (1965).
[CrossRef]

1964

G. R. Hunt, C. H. Perry, J. Ferguson, Phys. Rev. 134, A688 (1964).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Appl. Opt. 3, 943 (1964).
[CrossRef]

H. Boutin, H. Prask, Surface Sci. 2, 261 (1964).
[CrossRef]

1963

D. W. Berreman, Phys. Rev. 130, 2193 (1963).
[CrossRef]

A. D. B. Woods et al., Phys. Rev. 131, 1025 (1963).
[CrossRef]

P. Tarte, Rev. Silicates Industriels, 7–8, 1 (1963).

A. S. Barker, Phys. Rev. 132, 1474 (1963).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Z. Kristal. 118, 404 (1963).
[CrossRef]

1961

J. N. Plendl, Phys. Rev. 123, 1172 (1961).
[CrossRef]

1960

B. Stone, D. Hill, Phys. Rev. Lett. 4, 282 (1960).
[CrossRef]

1959

A. Mitsuishi, H. Yoshinaga, S. Fujita, J. Phys. Soc. Japan 14, 110 (1959).
[CrossRef]

1955

H. Yoshinaga, R. A. Oetjen, J. Opt. Soc. Amer. 45, 1085 (1955).
[CrossRef]

1932

R. B. Barnes, Z. Phys. 75, 723 (1932).
[CrossRef]

1931

R. B. Barnes, M. Czerny, Z. Phys. 72, 447 (1931).
[CrossRef]

1930

M. Czerny, Z. Phys. 56, 600 (1930).

1909

E. Madelung, Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 100 (1909); Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 43 (1910).

Aronson, J. R.

J. R. Aronson, H. G. McLinden, spectral measurements, A. D. Little, Inc. Reports on AFCRL Contract No. AF19-(604)-8504 (1961/65).

Barker, A. S.

A. S. Barker, Phys. Rev. 132, 1474 (1963).
[CrossRef]

Barnes, R. B.

R. B. Barnes, Z. Phys. 75, 723 (1932).
[CrossRef]

R. B. Barnes, M. Czerny, Z. Phys. 72, 447 (1931).
[CrossRef]

Berreman, D. W.

D. W. Berreman, Phys. Rev. 130, 2193 (1963).
[CrossRef]

Boutin, H.

H. Boutin, H. Prask, Surface Sci. 2, 261 (1964).
[CrossRef]

Brafman, O.

O. Brafman et al., Solid State Commun. 6, 523 (1968).
[CrossRef]

O. Brafman, S. S. Mitra, Phys. Rev. 171, 931 (1968).
[CrossRef]

Buyers, W. J. L.

W. J. L. Buyers, Phys. Rev. 153, 923 (1967).
[CrossRef]

Czerny, M.

R. B. Barnes, M. Czerny, Z. Phys. 72, 447 (1931).
[CrossRef]

M. Czerny, Z. Phys. 56, 600 (1930).

de Klerk, J.

J. de Klerk, Rev. Sci. Instrum. 36, 1540 (1965).
[CrossRef]

Dolling, G.

G. Dolling et al., Phys. Rev. 168, 972 (1968).
[CrossRef]

Ferguson, J.

G. R. Hunt, C. H. Perry, J. Ferguson, Phys. Rev. 134, A688 (1964).
[CrossRef]

Fujita, S.

A. Mitsuishi, H. Yoshinaga, S. Fujita, J. Phys. Soc. Japan 14, 110 (1959).
[CrossRef]

Gielisse, P. J.

J. N. Plendl, P. J. Gielisse, Phys. Stat. Sol. 35, K151 (1969).
[CrossRef]

P. J. Gielisse et al., Phys. Rev. 155, 1039 (1967).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Appl. Opt. 4, 853 (1965).
[CrossRef]

P. J. Gielisse et al., J. Appl. Phys. 36, 2446 (1965).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Appl. Opt. 3, 943 (1964).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Z. Kristal. 118, 404 (1963).
[CrossRef]

J. N. Plendl, P. J. Gielisse, AFCRL-69-0429, Phys. Sci. Res. Papers #395; also being published in Phys. Chem. Sol. 31, 874 (1970).

Hadni, A.

A. Hadni et al., in Quantum Electronics 3, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964).

A. Hadni, spectral measurements, Univ. de Nancy Reports on AFCRL Contract No. AF61(052)-518 and AF61(052)-957 (1961/69).

Hill, D.

B. Stone, D. Hill, Phys. Rev. Lett. 4, 282 (1960).
[CrossRef]

Hiller, J. E.

J. E. Hiller, Kristallchemie (W. De Gruyter Verlag, Berlin, 1952).

Hunt, G. R.

G. R. Hunt, C. H. Perry, J. Ferguson, Phys. Rev. 134, A688 (1964).
[CrossRef]

Jasperse, J. R.

J. R. Jasperse et al., Phys. Rev. 146, 526 (1966).
[CrossRef]

J. R. Jasperse, spectral measurements, A. D. Little, Inc. Reports on AFCRL Contract No. AF19(628)-4351 (1964/65).

Landolt-Boernstein,

Landolt-Boernstein, Atom und Molekularphysik (Springer Verlag, Berlin, 1955), Vol. 4/I

Lynch, D. W.

C. R. Renneke, D. W. Lynch, Phys. Rev. 138, A530 (1965).
[CrossRef]

Madelung, E.

E. Madelung, Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 100 (1909); Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 43 (1910).

Mason, W. P.

W. P. Mason, in Lattice Dynamics (Academic Press, New York, 1965), Vol. III/B.

McLinden, H. G.

J. R. Aronson, H. G. McLinden, spectral measurements, A. D. Little, Inc. Reports on AFCRL Contract No. AF19-(604)-8504 (1961/65).

Mitra, S. S.

O. Brafman, S. S. Mitra, Phys. Rev. 171, 931 (1968).
[CrossRef]

Mitsuishi, A.

A. Mitsuishi, H. Yoshinaga, S. Fujita, J. Phys. Soc. Japan 14, 110 (1959).
[CrossRef]

Moeller, K. D.

K. D. Moeller, S. T. Varma, spectral measurements, Fairleigh Dickinson Univ. Reports on AFCRL Contract No. AF19(628)-4084 (1964/69).

Mooij, J. E.

J. E. Mooij, Phys. Lett. 24A, 249, (1967).

Oetjen, R. A.

H. Yoshinaga, R. A. Oetjen, J. Opt. Soc. Amer. 45, 1085 (1955).
[CrossRef]

Perry, C. H.

G. R. Hunt, C. H. Perry, J. Ferguson, Phys. Rev. 134, A688 (1964).
[CrossRef]

C. H. Perry, Diss., Queen Mary College, London1960; and spectral measurements, MIT Reports on AFCRL Contract No. AF19(628)-6066 (1966/68).
[PubMed]

Pickar, P. B.

J. S. Ziomek, P. B. Pickar, Phys. Stat. Sol. 21, 271 (1967).
[CrossRef]

Picus, G.

G. Picus, in Advan. Electronics and Electron Phys., 7, 24 (1955), E. Burstein, P. E. Egli, Eds.

Plendl, J. N.

J. N. Plendl et al., Solid State Comm. 7, 109 (1969).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Phys. Stat. Sol. 35, K151 (1969).
[CrossRef]

J. N. Plendl et al., Appl. Opt. 5, 397 (1966).
[CrossRef] [PubMed]

J. N. Plendl, P. J. Gielisse, Appl. Opt. 4, 853 (1965).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Appl. Opt. 3, 943 (1964).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Z. Kristal. 118, 404 (1963).
[CrossRef]

J. N. Plendl, Phys. Rev. 123, 1172 (1961).
[CrossRef]

J. N. Plendl, “New Concepts in the Physics of Solids,” Monograph, Spec. AFCRL Report No. 52 (1966).

J. N. Plendl, P. J. Gielisse, AFCRL-69-0429, Phys. Sci. Res. Papers #395; also being published in Phys. Chem. Sol. 31, 874 (1970).

J. N. Plendl, AFCRL-69-0353, Phys. Sci. Res. Paper No. 393 (1969).

J. N. Plendl, “Resonance Vibrations of the Ionic Lattice from the Mechanical Aspect,” presented at the European Conference of Molecular Spectroscopists” at Freiburg (Br.), Germany, 1957.

Pohl, R. W.

R. W. Pohl, Optik (Springer Verlag, Berlin, 1940), p. 43.

Prask, H.

H. Boutin, H. Prask, Surface Sci. 2, 261 (1964).
[CrossRef]

Renneke, C. R.

C. R. Renneke, D. W. Lynch, Phys. Rev. 138, A530 (1965).
[CrossRef]

Schmunk, R. E.

R. E. Schmunk, Bull. Amer. Phys. Soc. 12, 281 (1967).

Shapiro, S. M.

S. M. Shapiro et al., Phys. Rev. Lett. 19, 361 (1967).
[CrossRef]

Simmons, G.

G. Simmons, J. Graduate Res. Center, Dallas, Texas, Vol. 34, Nos. 1 and 2 (March1965).

Spitzer, W. G.

W. G. Spitzer et al., Silicon Carbide (Pergamon Press, Oxford, 1960), p. 347.

Stone, B.

B. Stone, D. Hill, Phys. Rev. Lett. 4, 282 (1960).
[CrossRef]

Tarte, P.

P. Tarte, Acad. Roy. Belgique, Memoirs 35 (1965).

P. Tarte, Rev. Silicates Industriels, 7–8, 1 (1963).

P. Tarte, spectral measurements, Univ. de Liège Reports on AFCRL Contract No. AF61(052)-917 (1966/69).

Varma, S. T.

K. D. Moeller, S. T. Varma, spectral measurements, Fairleigh Dickinson Univ. Reports on AFCRL Contract No. AF19(628)-4084 (1964/69).

Woods, A. D. B.

A. D. B. Woods et al., Phys. Rev. 131, 1025 (1963).
[CrossRef]

Yoshinaga, H.

A. Mitsuishi, H. Yoshinaga, S. Fujita, J. Phys. Soc. Japan 14, 110 (1959).
[CrossRef]

H. Yoshinaga, R. A. Oetjen, J. Opt. Soc. Amer. 45, 1085 (1955).
[CrossRef]

Ziomek, J. S.

J. S. Ziomek, P. B. Pickar, Phys. Stat. Sol. 21, 271 (1967).
[CrossRef]

Acad. Roy. Belgique, Memoirs

P. Tarte, Acad. Roy. Belgique, Memoirs 35 (1965).

Appl. Opt.

Bull. Amer. Phys. Soc.

R. E. Schmunk, Bull. Amer. Phys. Soc. 12, 281 (1967).

J. Appl. Phys.

P. J. Gielisse et al., J. Appl. Phys. 36, 2446 (1965).
[CrossRef]

J. Graduate Res. Center, Dallas, Texas

G. Simmons, J. Graduate Res. Center, Dallas, Texas, Vol. 34, Nos. 1 and 2 (March1965).

J. Opt. Soc. Amer.

H. Yoshinaga, R. A. Oetjen, J. Opt. Soc. Amer. 45, 1085 (1955).
[CrossRef]

J. Phys. Soc. Japan

A. Mitsuishi, H. Yoshinaga, S. Fujita, J. Phys. Soc. Japan 14, 110 (1959).
[CrossRef]

Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.)

E. Madelung, Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 100 (1909); Nachr. Ges. Wiss. Goettingen (Math. Phys. Kl.) 43 (1910).

Phys. Lett.

J. E. Mooij, Phys. Lett. 24A, 249, (1967).

Phys. Rev.

D. W. Berreman, Phys. Rev. 130, 2193 (1963).
[CrossRef]

G. Dolling et al., Phys. Rev. 168, 972 (1968).
[CrossRef]

P. J. Gielisse et al., Phys. Rev. 155, 1039 (1967).
[CrossRef]

W. J. L. Buyers, Phys. Rev. 153, 923 (1967).
[CrossRef]

O. Brafman, S. S. Mitra, Phys. Rev. 171, 931 (1968).
[CrossRef]

J. R. Jasperse et al., Phys. Rev. 146, 526 (1966).
[CrossRef]

A. D. B. Woods et al., Phys. Rev. 131, 1025 (1963).
[CrossRef]

A. S. Barker, Phys. Rev. 132, 1474 (1963).
[CrossRef]

C. R. Renneke, D. W. Lynch, Phys. Rev. 138, A530 (1965).
[CrossRef]

J. N. Plendl, Phys. Rev. 123, 1172 (1961).
[CrossRef]

G. R. Hunt, C. H. Perry, J. Ferguson, Phys. Rev. 134, A688 (1964).
[CrossRef]

Phys. Rev. Lett.

S. M. Shapiro et al., Phys. Rev. Lett. 19, 361 (1967).
[CrossRef]

B. Stone, D. Hill, Phys. Rev. Lett. 4, 282 (1960).
[CrossRef]

Phys. Stat. Sol.

J. S. Ziomek, P. B. Pickar, Phys. Stat. Sol. 21, 271 (1967).
[CrossRef]

J. N. Plendl, P. J. Gielisse, Phys. Stat. Sol. 35, K151 (1969).
[CrossRef]

Rev. Sci. Instrum.

J. de Klerk, Rev. Sci. Instrum. 36, 1540 (1965).
[CrossRef]

Rev. Silicates Industriels

P. Tarte, Rev. Silicates Industriels, 7–8, 1 (1963).

Solid State Comm.

J. N. Plendl et al., Solid State Comm. 7, 109 (1969).
[CrossRef]

Solid State Commun.

O. Brafman et al., Solid State Commun. 6, 523 (1968).
[CrossRef]

Surface Sci.

H. Boutin, H. Prask, Surface Sci. 2, 261 (1964).
[CrossRef]

Z. Kristal.

J. N. Plendl, P. J. Gielisse, Z. Kristal. 118, 404 (1963).
[CrossRef]

Z. Phys.

R. B. Barnes, M. Czerny, Z. Phys. 72, 447 (1931).
[CrossRef]

M. Czerny, Z. Phys. 56, 600 (1930).

R. B. Barnes, Z. Phys. 75, 723 (1932).
[CrossRef]

Other

J. R. Aronson, H. G. McLinden, spectral measurements, A. D. Little, Inc. Reports on AFCRL Contract No. AF19-(604)-8504 (1961/65).

C. H. Perry, Diss., Queen Mary College, London1960; and spectral measurements, MIT Reports on AFCRL Contract No. AF19(628)-6066 (1966/68).
[PubMed]

J. N. Plendl, AFCRL-69-0353, Phys. Sci. Res. Paper No. 393 (1969).

A. Hadni, spectral measurements, Univ. de Nancy Reports on AFCRL Contract No. AF61(052)-518 and AF61(052)-957 (1961/69).

W. P. Mason, in Lattice Dynamics (Academic Press, New York, 1965), Vol. III/B.

R. W. Pohl, Optik (Springer Verlag, Berlin, 1940), p. 43.

J. N. Plendl, “Resonance Vibrations of the Ionic Lattice from the Mechanical Aspect,” presented at the European Conference of Molecular Spectroscopists” at Freiburg (Br.), Germany, 1957.

P. Tarte, spectral measurements, Univ. de Liège Reports on AFCRL Contract No. AF61(052)-917 (1966/69).

J. R. Jasperse, spectral measurements, A. D. Little, Inc. Reports on AFCRL Contract No. AF19(628)-4351 (1964/65).

K. D. Moeller, S. T. Varma, spectral measurements, Fairleigh Dickinson Univ. Reports on AFCRL Contract No. AF19(628)-4084 (1964/69).

A. Hadni et al., in Quantum Electronics 3, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964).

W. G. Spitzer et al., Silicon Carbide (Pergamon Press, Oxford, 1960), p. 347.

G. Picus, in Advan. Electronics and Electron Phys., 7, 24 (1955), E. Burstein, P. E. Egli, Eds.

J. N. Plendl, “New Concepts in the Physics of Solids,” Monograph, Spec. AFCRL Report No. 52 (1966).

J. N. Plendl, P. J. Gielisse, AFCRL-69-0429, Phys. Sci. Res. Papers #395; also being published in Phys. Chem. Sol. 31, 874 (1970).

J. E. Hiller, Kristallchemie (W. De Gruyter Verlag, Berlin, 1952).

Landolt-Boernstein, Atom und Molekularphysik (Springer Verlag, Berlin, 1955), Vol. 4/I

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Figures (46)

Fig. 1
Fig. 1

Schematic presentation of energy distribution of incoming radiation for single crystal model (A) and film model (B), as proposed in text.

Fig. 2
Fig. 2

Transmission data of NaCl for various thicknesses, after Barnes and Czerny (1931).2

Fig. 3
Fig. 3

(a) Reflectivity, transmission and sum value as a function of wavelength for NaCl. Experimental data from Barnes and Czerny (1931)2 and Czery (1930)3; (b) evaluation of energy absorption in NaCl from data of using the method of this paper.

Fig. 4
Fig. 4

Energy absorption spectrum of NaCl for four thicknesses (μ); crystal model.

Fig. 5
Fig. 5

Energy absorption spectrum of NaCl for four layer thicknesses (μ); film model.

Fig. 6
Fig. 6

Reflectivity data for different angles of incidence (12 deg and 52 deg) of three alkali halides, after Mitsuishi et al. (1959).4

Fig. 7
Fig. 7

Transmission TL(νr), reflection RL(νr), absorption AL(νr), absorption function F[AL(νr)], damping Δν/νr, and parameter X as a function of layer thickness d for an evaporated film of NaCl.

Fig. 8
Fig. 8

Absorption function F[AC(νr)] and specific absorption function d · F[AC(νr)] vs layer thickness for NaCl (single crystal model).

Fig. 9
Fig. 9

Increase of specific energy absorption in percent with penetration depth for the two TO modes of NaCl.

Fig. 10
Fig. 10

Energy absorption spectrum of NaCl according to a film and a crystal model, based on transmission data2 and reflection data.4

Fig. 11
Fig. 11

Energy absorption spectrum of KCl according to a film and a crystal model, based on transmission data2,11 and reflection data.4

Fig. 12
Fig. 12

Energy absorption spectrum of LiF according to a film and a crystal model, based on transmission data12 and reflection data.13

Fig. 13
Fig. 13

Comparison of energy absorption spectrum and k spectrum for LiF, based on k data.14 For references to other data, see Fig. 12.

Fig. 14
Fig. 14

Comparison of energy absorption spectrum and k spectrum for MgO, based on transmission,15 reflection, and k data.14

Fig. 15
Fig. 15

Comparison of spectra of emission (E) at 339 K, cold neutron (N) at 90 K, ir energy absorption spectrum (ir) at 295 K, and calculated elastic (↑) at 295 K for KBr, based on transmission,11 reflection,4 cold neutron,16 and emission.17

Fig. 16
Fig. 16

Comparison of cold neutron spectra (dashed line) and the energy absorption spectrum (solid line) for LiF, the high frequency extension of which is based on transmission18 and reflection data,13 cold neutron data.19

Fig. 17
Fig. 17

Comparison of cold neutron spectra (dashed lines) for two orientations of NaI and its energy absorption spectrum (solid line), based on transmission and reflection data11 and cold neutron data.16 Neutron spectra at 100 K, absorption at 295 K.

Fig. 18
Fig. 18

Comparison of cold neutron spectrum20 (solid line) and energy absorption spectrum (dashed line) for Al2O3. The cold neutron spectrum has been measured much further out in the low frequency range than the ir data.

Fig. 19
Fig. 19

Equality between fundamental frequencies from three types of experimental spectra and those calculated from elastic constant data.

Fig. 20
Fig. 20

Laser-Raman line and correspond energy absorption line for cubic BP, based on transmission,23 reflection,24 and laser–Raman data.25

Fig. 21
Fig. 21

Laser–Raman line and corresponding energy absorption line for α-quartz (vibrations between Si–O4 tetrahedra), based on transmission,26 reflection,27 and laser–Raman data.28

Fig. 22
Fig. 22

Laser–Raman line and corresponding energy absorption line for ZnS (sphalerite type), based on transmission,29 reflection,30 and laser–Raman data.31

Fig. 23
Fig. 23

Laser-Raman lines and corresponding energy absorption line for cubic SiC, based on transmission and reflection data,32 and laser–Raman data.33

Fig. 24
Fig. 24

Characteristic energy absorption spectra of selected potassium salts, based on transmission data of KI,11 KBr,11 KCl,2,11 and reflection data of KI,11 KBr, and KCl.4 Low frequency evaluation of the three salts based on special transmission and reflection data.34

Fig. 25
Fig. 25

Characteristic energy absorption spectra comparing related chlorides, based on transmission and reflection data of CsCl,11 RbCl,11 KC,2,4 NaCl.2,4

Fig. 26
Fig. 26

Characteristic energy absorption spectra comparing related bromides, based on transmission and reflection data of TlBr,11 CsBr,11 RbBr,11 KBr11,4 and NaBr.11

Fig. 27
Fig. 27

Characteristic energy absorption spectra comparing related iodides, based on transmission and reflection data of TlI,11 CsI,35 RbI,11 KI,11 CuI.36

Fig. 28
Fig. 28

Characteristic energy absorption spectra of selected metal oxides, based on transmission data of NiO26 and reflection data of NiO,37 MgO,15,14 and MnO.15,38.

Fig. 29
Fig. 29

Influence of particle size on characteristic energy absorption spectra for MnO, based on transmission15,26 and reflection data.39 Curve A (very fine) and curve B (fine particle) size. Exact size not known.

Fig. 30
Fig. 30

Characteristic energy absorption spectra of Al2O3 and Cr2O3, based on transmission data of Al2O3 and Cr2O3,39 and reflection data of Al2O440 and Cr2O3.41 Both spectra for EC axis; numbers refer to mode frequencies. For cold neutron spectrum of Al2O3 see Fig. 18.

Fig. 31
Fig. 31

Equality between TO mode frequencies from characteristic energy absorption spectra and those calculated from respective elastic constants.

Fig. 32
Fig. 32

Equality between LO mode frequencies from characteristic energy absorption spectra and those calculated from respective elastic constants.

Fig. 33
Fig. 33

Equality between center frequencies from ir spectra (reflectivity and absorption)42,43 and those calculated from respective elastic constants.44

Fig. 34
Fig. 34

Schematic presentation of different types of anharmonic force characteristics.42

Fig. 35
Fig. 35

Differentiation between anharmonic soft and hard force characteristic in the energy absorption curve.42 For a and b values see text.

Fig. 36
Fig. 36

Differentiation between hard and soft core solids based on anharmonicity values (Xm−1/p).42 Changeover takes place at NaF (neon configuration).45,46 Xm−1/p is calculated value of Ψ(A).

Fig. 37
Fig. 37

Relation between modified TO mode frequencies and interatomic distances of solids. The Z parameter refers to the valency of the compound.

Fig. 38
Fig. 38

Relationship between the shear moduli and interatomic distances of solids, corresponding to the relation of Fig. 37.

Fig. 39
Fig. 39

Damping versus radius ratio for structures with distinctly different coordination numbers: zincblende or wurtzite (CN = 4), rocksalt (CN = 6) and cesium chloride (CN = 8) (upper curve).47

Fig. 40
Fig. 40

Influence of structure on the specific absorption function.

Fig. 41
Fig. 41

Influence of structure on the incline of the specific energy absorption as the number of atomic layers increases: (a) rocksalt structure; (b) cesium chloride structure.

Fig. 42
Fig. 42

Characteristic energy absorption spectra of some selected solids on normalized scale for absorption. For SiO2 (α-quartz) and Al2O3 (corundum) the spectra are almost complete, whereas for LiF, MgO, and SiC(c) only the main absorption is shown.

Fig. 43
Fig. 43

Portion of characteristic energy absorption spectrum of α-quartz for vibrations within the Si–O4 tetrahedra for EC and EC axis, based on transmission48 and reflection data.27

Fig. 44
Fig. 44

Characteristic energy absorption spectrum of MgF2 (rutile structure), based on transmission and reflection data.50 Numerical values refer to the triplets of the two TO modes that result from three different lengths of the deformed octahedral Mg–F edges in the crystalline structure.51

Fig. 45
Fig. 45

Frequency spectrum of the fundamental modes and center frequency of LiF as a function of temperatures from absolute zero to the melting point. Note the crossover between TO100 and LO100 at 900 K.

Fig. 46
Fig. 46

Frequency spectrum of the fundamental modes and center frequency of KBr as a function of temperatures from absolute zero to the melting point. Note the anomaly of the LO110 and center frequency at 350 K which corresponds to a point of inflection in the curve of thermal expansion.

Tables (2)

Tables Icon

Table I Characteristic Absorption Frequencies of Fifteen Solids, as Calculated from Elastic Constants (Simmons10) and as Determined from Characteristic Energy Absorption Spectra and/or Cold Neutron Scattering Data

Tables Icon

Table II Dependence of the Specific Absorption on the Number of Atomic Layers for Rocksalt and Cesium Chloride Structures

Equations (14)

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Σ R L j ( ν ) + Σ T L j ( ν ) + Σ A L j ( ν ) = 1
R L ( ν ) + T L ( ν ) + A L ( ν ) = 1 ,
R C ( ν ) + T L ( ν ) + A L ( ν ) = X ,
A L ( ν ) = X - [ R C ( ν ) + T L ( ν ) ] .
F [ A C ( ν ) ] = { X - [ R C ( ν ) + T L ( ν ) ] } / [ 1 - R C ( ν ) ] .
F [ A L ( ν ) ] = { X - [ R C ( ν ) + T L ( ν ) ] } / [ X - R C ( ν ) ] .
( 100 ) { ν LO = ( c 11 / ρ ) 1 2 / 2 r 0 c ( cm - 1 ) ν TO = ( c 44 / ρ ) 1 2 / 2 r 0 c ( cm - 1 ) ;
( 110 ) { ν LO = [ ( c 11 + c 12 + 2 c 44 ) / 2 ρ ] 1 2 / 2 r 0 c ( cm - 1 ) ν TO = [ ( c 11 - c 12 ) / 2 ρ ] 1 2 / 2 r 0 c ( cm - 1 ) ;
( 111 ) { ν LO = [ ( c 11 + 2 c 12 + 4 c 44 ) / 3 ρ ] 1 2 / 2 r 0 c ( cm - 1 ) c 11 = [ ( c 11 - c 12 + c 44 ) / 3 ρ ] 1 2 / 2 r 0 c ( cm - 1 ) degenerate ;
ν ctr = [ ( c 11 + 2 c 12 ) / 3 ρ ] 1 2 / 2 r 0 c ( cm - 1 ) .
Ψ ( A ) = 1 + ( 1 / π ) [ 1 - ( b / a ) ] ,
( 1 2 ) m r v i j 2 = U 0 / N ,
( 1 2 ) m r v i j 2 = 11.75 × 10 - 12 ( ergs / molecule ) .
U 0 / N = ( 1 / N ) × 169 ( kcal / mole ) = 11.7 × 10 - 12             ( ergs / molecule ) .

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