Abstract

The composition, transparency, refractive index, and infrared reflectance of yttria-stabilized cubic hafnia (c-HfO2) single crystals were measured. The material is transparent from the ultraviolet to the mid-infrared and for 9.6-mol % Y2O3, the index is slightly smaller than for comparable cubic zirconia c-ZrO2 or for diamond, but the dispersion (nFnC = 0.02811) is larger than that of diamond. The index vs wavelength from 0.36 μm in the ultraviolet to 5.0 μm in the infrared is represented by a three-term Sellmeier formula to 1 × 10−4. The temperature dependence of refractive index is similar to that of c-ZrO2. The infrared reflectance spectrum is fitted in a classical dispersion analysis with seven oscillators derived from the transverse optical phonon as well as acoustic frequencies with splittings due to lowered symmetry derived from the randomly distributed stabilizer ions.

© 1990 Optical Society of America

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References

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  1. D. L. Wood, K. Nassau, “Refractive Index of Cubic Zirconia Stabilized with Yttira,” Appl. Opt. 21, 2978–2981 (1982).
    [CrossRef] [PubMed]
  2. D. L. Wood, K. Nassau, T. Y. Kometani, “Refractive Index Versus Composition for Y2O3-Stabilized Cubic Zirconia,” Appl. Opt., in press.
  3. K. Nassau, “Cubic Zirconia, the Latest Diamond Substitute,” Lapidary J. 31, 900–904, 922–926 (1977).
  4. D. L. Wood, J. W. Fleming, “Computerized Refractive Index Measurement for Bulk Materials in the Ultraviolet, Visible, and Infrared,” Rev. Sci. Instrum. 53, 43–47 (1982).
    [CrossRef]
  5. W. G. Driscoll, W. Vaughn, Eds., Handbook of Optics (McGraw-Hill, New York, 1978), p. 82.
  6. V. L. Aleksandrov, V.V. Osiko, A. M. Prokhorov, V. M. Tatarintsev, “Synthesis and Crystal Growth of Refractory Materials by RF Melting in a Cold Container,” in Current Topics in Materials, Vol. 1, E. Kaldis, Ed. (North-Holland, Amsterdam, 1978), Chap. 6, p. 453.
  7. V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).
  8. Y. Tsay, B. Bendow, S. S. Mitra, “Theory of the Temperature Derivatives of the Refractive Index in Transparent Crystals,” Phys. Rev. B 8, 2688–2696 (1973).
    [CrossRef]
  9. W. G. Spitzer, D. A. Kleinman, “Infrared Lattice Bands of Quartz,” Phys. Rev. 121, 1324–1335 (1961).
    [CrossRef]
  10. D. A. Kleinman, W. G. Spitzer, “Theory of the Optical Properties of Quartz in the Infrared,” Phys. Rev. 125, 16–30 (1962).
    [CrossRef]
  11. W. Kaiser, W. G. Spitzer, R. H. Kaiser, L. E. Howarth, “Infrared Properties of CaF2, SrF2 and BaF2,” Phys. Rev. 127, 1950–1954 (1962).
    [CrossRef]

1982 (2)

D. L. Wood, J. W. Fleming, “Computerized Refractive Index Measurement for Bulk Materials in the Ultraviolet, Visible, and Infrared,” Rev. Sci. Instrum. 53, 43–47 (1982).
[CrossRef]

D. L. Wood, K. Nassau, “Refractive Index of Cubic Zirconia Stabilized with Yttira,” Appl. Opt. 21, 2978–2981 (1982).
[CrossRef] [PubMed]

1977 (2)

K. Nassau, “Cubic Zirconia, the Latest Diamond Substitute,” Lapidary J. 31, 900–904, 922–926 (1977).

V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).

1973 (1)

Y. Tsay, B. Bendow, S. S. Mitra, “Theory of the Temperature Derivatives of the Refractive Index in Transparent Crystals,” Phys. Rev. B 8, 2688–2696 (1973).
[CrossRef]

1962 (2)

D. A. Kleinman, W. G. Spitzer, “Theory of the Optical Properties of Quartz in the Infrared,” Phys. Rev. 125, 16–30 (1962).
[CrossRef]

W. Kaiser, W. G. Spitzer, R. H. Kaiser, L. E. Howarth, “Infrared Properties of CaF2, SrF2 and BaF2,” Phys. Rev. 127, 1950–1954 (1962).
[CrossRef]

1961 (1)

W. G. Spitzer, D. A. Kleinman, “Infrared Lattice Bands of Quartz,” Phys. Rev. 121, 1324–1335 (1961).
[CrossRef]

Aleksandrov, V. I.

V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).

Aleksandrov, V. L.

V. L. Aleksandrov, V.V. Osiko, A. M. Prokhorov, V. M. Tatarintsev, “Synthesis and Crystal Growth of Refractory Materials by RF Melting in a Cold Container,” in Current Topics in Materials, Vol. 1, E. Kaldis, Ed. (North-Holland, Amsterdam, 1978), Chap. 6, p. 453.

Bendow, B.

Y. Tsay, B. Bendow, S. S. Mitra, “Theory of the Temperature Derivatives of the Refractive Index in Transparent Crystals,” Phys. Rev. B 8, 2688–2696 (1973).
[CrossRef]

Fleming, J. W.

D. L. Wood, J. W. Fleming, “Computerized Refractive Index Measurement for Bulk Materials in the Ultraviolet, Visible, and Infrared,” Rev. Sci. Instrum. 53, 43–47 (1982).
[CrossRef]

Howarth, L. E.

W. Kaiser, W. G. Spitzer, R. H. Kaiser, L. E. Howarth, “Infrared Properties of CaF2, SrF2 and BaF2,” Phys. Rev. 127, 1950–1954 (1962).
[CrossRef]

Kaiser, R. H.

W. Kaiser, W. G. Spitzer, R. H. Kaiser, L. E. Howarth, “Infrared Properties of CaF2, SrF2 and BaF2,” Phys. Rev. 127, 1950–1954 (1962).
[CrossRef]

Kaiser, W.

W. Kaiser, W. G. Spitzer, R. H. Kaiser, L. E. Howarth, “Infrared Properties of CaF2, SrF2 and BaF2,” Phys. Rev. 127, 1950–1954 (1962).
[CrossRef]

Kalabukhova, V. F.

V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).

Kleinman, D. A.

D. A. Kleinman, W. G. Spitzer, “Theory of the Optical Properties of Quartz in the Infrared,” Phys. Rev. 125, 16–30 (1962).
[CrossRef]

W. G. Spitzer, D. A. Kleinman, “Infrared Lattice Bands of Quartz,” Phys. Rev. 121, 1324–1335 (1961).
[CrossRef]

Kometani, T. Y.

D. L. Wood, K. Nassau, T. Y. Kometani, “Refractive Index Versus Composition for Y2O3-Stabilized Cubic Zirconia,” Appl. Opt., in press.

Lomonova, E. E.

V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).

Mitra, S. S.

Y. Tsay, B. Bendow, S. S. Mitra, “Theory of the Temperature Derivatives of the Refractive Index in Transparent Crystals,” Phys. Rev. B 8, 2688–2696 (1973).
[CrossRef]

Nassau, K.

D. L. Wood, K. Nassau, “Refractive Index of Cubic Zirconia Stabilized with Yttira,” Appl. Opt. 21, 2978–2981 (1982).
[CrossRef] [PubMed]

K. Nassau, “Cubic Zirconia, the Latest Diamond Substitute,” Lapidary J. 31, 900–904, 922–926 (1977).

D. L. Wood, K. Nassau, T. Y. Kometani, “Refractive Index Versus Composition for Y2O3-Stabilized Cubic Zirconia,” Appl. Opt., in press.

Osiko, V. V.

V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).

Osiko, V.V.

V. L. Aleksandrov, V.V. Osiko, A. M. Prokhorov, V. M. Tatarintsev, “Synthesis and Crystal Growth of Refractory Materials by RF Melting in a Cold Container,” in Current Topics in Materials, Vol. 1, E. Kaldis, Ed. (North-Holland, Amsterdam, 1978), Chap. 6, p. 453.

Prokhorov, A. M.

V. L. Aleksandrov, V.V. Osiko, A. M. Prokhorov, V. M. Tatarintsev, “Synthesis and Crystal Growth of Refractory Materials by RF Melting in a Cold Container,” in Current Topics in Materials, Vol. 1, E. Kaldis, Ed. (North-Holland, Amsterdam, 1978), Chap. 6, p. 453.

Spitzer, W. G.

D. A. Kleinman, W. G. Spitzer, “Theory of the Optical Properties of Quartz in the Infrared,” Phys. Rev. 125, 16–30 (1962).
[CrossRef]

W. Kaiser, W. G. Spitzer, R. H. Kaiser, L. E. Howarth, “Infrared Properties of CaF2, SrF2 and BaF2,” Phys. Rev. 127, 1950–1954 (1962).
[CrossRef]

W. G. Spitzer, D. A. Kleinman, “Infrared Lattice Bands of Quartz,” Phys. Rev. 121, 1324–1335 (1961).
[CrossRef]

Tatarintsev, V. I.

V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).

Tatarintsev, V. M.

V. L. Aleksandrov, V.V. Osiko, A. M. Prokhorov, V. M. Tatarintsev, “Synthesis and Crystal Growth of Refractory Materials by RF Melting in a Cold Container,” in Current Topics in Materials, Vol. 1, E. Kaldis, Ed. (North-Holland, Amsterdam, 1978), Chap. 6, p. 453.

Tsay, Y.

Y. Tsay, B. Bendow, S. S. Mitra, “Theory of the Temperature Derivatives of the Refractive Index in Transparent Crystals,” Phys. Rev. B 8, 2688–2696 (1973).
[CrossRef]

Wood, D. L.

D. L. Wood, J. W. Fleming, “Computerized Refractive Index Measurement for Bulk Materials in the Ultraviolet, Visible, and Infrared,” Rev. Sci. Instrum. 53, 43–47 (1982).
[CrossRef]

D. L. Wood, K. Nassau, “Refractive Index of Cubic Zirconia Stabilized with Yttira,” Appl. Opt. 21, 2978–2981 (1982).
[CrossRef] [PubMed]

D. L. Wood, K. Nassau, T. Y. Kometani, “Refractive Index Versus Composition for Y2O3-Stabilized Cubic Zirconia,” Appl. Opt., in press.

Appl. Opt. (1)

Inorg. Mater. (1)

V. I. Aleksandrov, V. F. Kalabukhova, E. E. Lomonova, V. V. Osiko, V. I. Tatarintsev, “Influence of Impurities and Annealing Conditions on the Optical Properties of Single Crystals of ZrO2 and HfO2,” Inorg. Mater. 13, 1747–1751 (1977).

Lapidary J. (1)

K. Nassau, “Cubic Zirconia, the Latest Diamond Substitute,” Lapidary J. 31, 900–904, 922–926 (1977).

Phys. Rev. (3)

W. G. Spitzer, D. A. Kleinman, “Infrared Lattice Bands of Quartz,” Phys. Rev. 121, 1324–1335 (1961).
[CrossRef]

D. A. Kleinman, W. G. Spitzer, “Theory of the Optical Properties of Quartz in the Infrared,” Phys. Rev. 125, 16–30 (1962).
[CrossRef]

W. Kaiser, W. G. Spitzer, R. H. Kaiser, L. E. Howarth, “Infrared Properties of CaF2, SrF2 and BaF2,” Phys. Rev. 127, 1950–1954 (1962).
[CrossRef]

Phys. Rev. B (1)

Y. Tsay, B. Bendow, S. S. Mitra, “Theory of the Temperature Derivatives of the Refractive Index in Transparent Crystals,” Phys. Rev. B 8, 2688–2696 (1973).
[CrossRef]

Rev. Sci. Instrum. (1)

D. L. Wood, J. W. Fleming, “Computerized Refractive Index Measurement for Bulk Materials in the Ultraviolet, Visible, and Infrared,” Rev. Sci. Instrum. 53, 43–47 (1982).
[CrossRef]

Other (3)

W. G. Driscoll, W. Vaughn, Eds., Handbook of Optics (McGraw-Hill, New York, 1978), p. 82.

V. L. Aleksandrov, V.V. Osiko, A. M. Prokhorov, V. M. Tatarintsev, “Synthesis and Crystal Growth of Refractory Materials by RF Melting in a Cold Container,” in Current Topics in Materials, Vol. 1, E. Kaldis, Ed. (North-Holland, Amsterdam, 1978), Chap. 6, p. 453.

D. L. Wood, K. Nassau, T. Y. Kometani, “Refractive Index Versus Composition for Y2O3-Stabilized Cubic Zirconia,” Appl. Opt., in press.

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Figures (4)

Fig. 1
Fig. 1

Refractive index vs wavelength for c-HfO2 stabilized with 9.6-mol % Y2O3.

Fig. 2
Fig. 2

Temperature dependence of refractive index for c-HfO2 as a function of wavelength expressed as the derivative index with respect to temperature for six mercury emission lines.

Fig. 3
Fig. 3

Transparency of single crystal c-HfO2.

Fig. 4
Fig. 4

Reflectivity at near normal incidence for single crystal c-HfO2 in the infrared. Full curve calculated using classical dispersion from Table IV; points are experimental values.

Tables (4)

Tables Icon

Table I Analyses of Cubic Hafnia

Tables Icon

Table II Optical Parameters for Cubic Hafnia

Tables Icon

Table III Temperature Coefficient of Refractive Index vs Wavelength for Cubic Hafniaa

Tables Icon

Table IV Characteristics of Classical Oscillators Required to Fit Reflectivity vs Wavelength for Cubic Hafnia in the Infrared (0 = 4.20)

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

n = [ 1 + i = 1 3 A i λ 2 / ( L i 2 - λ 2 ) ] 1 / 2 ,
α t = log 10 ( I 0 / I ) - 2 log 10 { 1 - [ ( n - 1 ) / ( n + 1 ) ] 2 } ,
n 2 - k 2 = 0 + j 4 π ρ j ν j 2 ( ν j 2 - ν 2 ) ( ν j 2 - ν 2 ) 2 + γ j 2 ν 2 ν j 2 ,
n k = j 2 π ρ j ν j 2 γ j ν ν j ( ν j 2 - ν 2 ) 2 + γ j 2 ν 2 ν j 2 ,
R = [ ( n - 1 ) 2 + k 2 ] / [ ( n + 1 ) 2 + k 2 ] ,
α = 4 π k / λ .

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