Abstract

This paper describes analyses and confirming experiments on the optimum temperature for fast response in nematic liquid crystal (LC) modulators. It is demonstrated that the LCs or LC mixtures with higher nematic–isotropic phase transition temperatures have higher optimum temperatures and greater potential for improving the figure of merit. Also discussed is the performance of the LC mixture exhibiting optimum temperature at around room temperature.

© 1987 Optical Society of America

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References

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  1. For example, see L. M. Blinov, Electro-optical and Magneto-optical Effects of Liquid Crystals (Wiley, New York, 1983).
  2. For an overview, see S. T. Wu, “Infrared Properties of Liquid Crystals: an Overview,” Opt. Eng. 26, 120 (1987).
    [CrossRef]
  3. E. Jackman, E. P. Raynes, “Electro-Optic Response Times in Liquid Crystals,” Phys. Lett. A 39, 69 (1972).
    [CrossRef]
  4. S. T. Wu, U. Efron, “Optical Properties of Thin Nematic Liquid Crystal Cells,” Appl. Phys. Lett. 48, 624 (1986).
    [CrossRef]
  5. H. K. Bucher, R. T. Klingbiel, J. P. VanMeter, “Frequency-Addressed Liquid Crystal Field Effect,” Appl. Phys. Lett. 25, 186 (1974).
    [CrossRef]
  6. M. Schadt, “Low-Frequency Dielectric Relaxation in Nematics and Dual-Frequency Addressing of Field Effects,” Mol. Cryst. Liq. Cryst. 89, 77 (1982).
    [CrossRef]
  7. D. J. Channin, D. E. Carlson, “Rapid Turn-off in Triode Optical Gate Liquid Crystal Devices,” Appl. Phys. Lett. 28, 300 (1976).
    [CrossRef]
  8. H. J. Deuling, E. Guyon, P. Pieranski, “Deformation of Nematic Layers in Crossed Electric and Magnetic Fields,” Solid State Commun. 15, 277 (1974).
    [CrossRef]
  9. S. T. Wu, “Dual Field Effect on Liquid Crystal Relaxation,” J. Appl. Phys. 58, 1419 (1985).
    [CrossRef]
  10. P. G. DeGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).
  11. E. M. Averyanov, V. F. Shabanov, “Structural and Optical Anisotropy of Liquid Crystals,” Sov. Phys. Crystallogr. 23, 177 (1978).
  12. S. T. Wu, “Birefringence Dispersions of Liquid Crystals,” Phys. Rev. A 30, 1270 (1986).
    [CrossRef]
  13. V. V. Belyaev, S. A. Ivanov, M. F. Gorebenkin, “Temperature Dependence of Rotational Viscosity of Nematic Liquid Crystals,” Sov. Phys. Crystallogr. 30, 674 (1985).
  14. A. Saupe, “Temperature-Dependence and Magnitudes of Deformation Constants in Strained Liquids,” Z. Naturforsch. Teil A 15, 810 (1960).
  15. M. J. Bradshaw, D. G. McDonnell, E. P. Raynes, “Physical Properties of Nematic Materials Containing Different Ring Systems,” Mol. Cryst. Liq. Cryst. 70, 289 (1981).
    [CrossRef]
  16. H. Imura, K. Okano, “Temperature Dependence of the Viscosity Coefficients of Liquid Crystals,” Jpn. J. Appl. Phys. 11, 1440(1972).
    [CrossRef]
  17. I. Haller, “Thermodynamic and Static Properties of Liquid Crystals,” Prog. Solid State Chem. 10, 103 (1975).
    [CrossRef]
  18. S.-T. Wu, “Ir Markers for Determining the Order Parameters of Uniaxial Liquid Crystals,” Appl. Opt. 26, 3434 (1987).
    [CrossRef] [PubMed]
  19. BDH Chemical Ltd., Poole Dorset, England BH12 4NN.
  20. S. T. Wu, U. Efron, L. D. Hess, “Birefringence Measurements of Liquid Crystals,” Appl. Opt. 23, 3911 (1984).
    [CrossRef] [PubMed]
  21. S. T. Wu, “Phase Retardation Dependent Optical Response Time of Parallel-Aligned Liquid Crystals,” J. Appl. Phys. 60, 1836 (1986).
    [CrossRef]
  22. M. Schadt, F. Muller, “Physical Properties of New Liquid Crystal Mixtures and Electrooptical Performance in Twisted Nematic Displays,” IEEE Trans. Electron Devices ED-25, 1125 (1978).
    [CrossRef]
  23. U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
    [CrossRef]
  24. S. T. Wu, A. M. Lackner, W. H. Smith, U. Efron, “Guidelines for Selecting and Synthesizing Nematic Liquid Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 684, 69 (1986).

1987

For an overview, see S. T. Wu, “Infrared Properties of Liquid Crystals: an Overview,” Opt. Eng. 26, 120 (1987).
[CrossRef]

S.-T. Wu, “Ir Markers for Determining the Order Parameters of Uniaxial Liquid Crystals,” Appl. Opt. 26, 3434 (1987).
[CrossRef] [PubMed]

1986

S. T. Wu, A. M. Lackner, W. H. Smith, U. Efron, “Guidelines for Selecting and Synthesizing Nematic Liquid Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 684, 69 (1986).

S. T. Wu, U. Efron, “Optical Properties of Thin Nematic Liquid Crystal Cells,” Appl. Phys. Lett. 48, 624 (1986).
[CrossRef]

S. T. Wu, “Birefringence Dispersions of Liquid Crystals,” Phys. Rev. A 30, 1270 (1986).
[CrossRef]

S. T. Wu, “Phase Retardation Dependent Optical Response Time of Parallel-Aligned Liquid Crystals,” J. Appl. Phys. 60, 1836 (1986).
[CrossRef]

1985

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

V. V. Belyaev, S. A. Ivanov, M. F. Gorebenkin, “Temperature Dependence of Rotational Viscosity of Nematic Liquid Crystals,” Sov. Phys. Crystallogr. 30, 674 (1985).

S. T. Wu, “Dual Field Effect on Liquid Crystal Relaxation,” J. Appl. Phys. 58, 1419 (1985).
[CrossRef]

1984

1982

M. Schadt, “Low-Frequency Dielectric Relaxation in Nematics and Dual-Frequency Addressing of Field Effects,” Mol. Cryst. Liq. Cryst. 89, 77 (1982).
[CrossRef]

1981

M. J. Bradshaw, D. G. McDonnell, E. P. Raynes, “Physical Properties of Nematic Materials Containing Different Ring Systems,” Mol. Cryst. Liq. Cryst. 70, 289 (1981).
[CrossRef]

1978

M. Schadt, F. Muller, “Physical Properties of New Liquid Crystal Mixtures and Electrooptical Performance in Twisted Nematic Displays,” IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

E. M. Averyanov, V. F. Shabanov, “Structural and Optical Anisotropy of Liquid Crystals,” Sov. Phys. Crystallogr. 23, 177 (1978).

1976

D. J. Channin, D. E. Carlson, “Rapid Turn-off in Triode Optical Gate Liquid Crystal Devices,” Appl. Phys. Lett. 28, 300 (1976).
[CrossRef]

1975

I. Haller, “Thermodynamic and Static Properties of Liquid Crystals,” Prog. Solid State Chem. 10, 103 (1975).
[CrossRef]

1974

H. J. Deuling, E. Guyon, P. Pieranski, “Deformation of Nematic Layers in Crossed Electric and Magnetic Fields,” Solid State Commun. 15, 277 (1974).
[CrossRef]

H. K. Bucher, R. T. Klingbiel, J. P. VanMeter, “Frequency-Addressed Liquid Crystal Field Effect,” Appl. Phys. Lett. 25, 186 (1974).
[CrossRef]

1972

E. Jackman, E. P. Raynes, “Electro-Optic Response Times in Liquid Crystals,” Phys. Lett. A 39, 69 (1972).
[CrossRef]

H. Imura, K. Okano, “Temperature Dependence of the Viscosity Coefficients of Liquid Crystals,” Jpn. J. Appl. Phys. 11, 1440(1972).
[CrossRef]

1960

A. Saupe, “Temperature-Dependence and Magnitudes of Deformation Constants in Strained Liquids,” Z. Naturforsch. Teil A 15, 810 (1960).

Averyanov, E. M.

E. M. Averyanov, V. F. Shabanov, “Structural and Optical Anisotropy of Liquid Crystals,” Sov. Phys. Crystallogr. 23, 177 (1978).

Belyaev, V. V.

V. V. Belyaev, S. A. Ivanov, M. F. Gorebenkin, “Temperature Dependence of Rotational Viscosity of Nematic Liquid Crystals,” Sov. Phys. Crystallogr. 30, 674 (1985).

Blinov, L. M.

For example, see L. M. Blinov, Electro-optical and Magneto-optical Effects of Liquid Crystals (Wiley, New York, 1983).

Braatz, P.O.

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

Bradshaw, M. J.

M. J. Bradshaw, D. G. McDonnell, E. P. Raynes, “Physical Properties of Nematic Materials Containing Different Ring Systems,” Mol. Cryst. Liq. Cryst. 70, 289 (1981).
[CrossRef]

Bucher, H. K.

H. K. Bucher, R. T. Klingbiel, J. P. VanMeter, “Frequency-Addressed Liquid Crystal Field Effect,” Appl. Phys. Lett. 25, 186 (1974).
[CrossRef]

Carlson, D. E.

D. J. Channin, D. E. Carlson, “Rapid Turn-off in Triode Optical Gate Liquid Crystal Devices,” Appl. Phys. Lett. 28, 300 (1976).
[CrossRef]

Channin, D. J.

D. J. Channin, D. E. Carlson, “Rapid Turn-off in Triode Optical Gate Liquid Crystal Devices,” Appl. Phys. Lett. 28, 300 (1976).
[CrossRef]

DeGennes, P. G.

P. G. DeGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

Deuling, H. J.

H. J. Deuling, E. Guyon, P. Pieranski, “Deformation of Nematic Layers in Crossed Electric and Magnetic Fields,” Solid State Commun. 15, 277 (1974).
[CrossRef]

Efron, U.

S. T. Wu, U. Efron, “Optical Properties of Thin Nematic Liquid Crystal Cells,” Appl. Phys. Lett. 48, 624 (1986).
[CrossRef]

S. T. Wu, A. M. Lackner, W. H. Smith, U. Efron, “Guidelines for Selecting and Synthesizing Nematic Liquid Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 684, 69 (1986).

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, “Birefringence Measurements of Liquid Crystals,” Appl. Opt. 23, 3911 (1984).
[CrossRef] [PubMed]

Gorebenkin, M. F.

V. V. Belyaev, S. A. Ivanov, M. F. Gorebenkin, “Temperature Dependence of Rotational Viscosity of Nematic Liquid Crystals,” Sov. Phys. Crystallogr. 30, 674 (1985).

Grinberg, J.

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

Guyon, E.

H. J. Deuling, E. Guyon, P. Pieranski, “Deformation of Nematic Layers in Crossed Electric and Magnetic Fields,” Solid State Commun. 15, 277 (1974).
[CrossRef]

Haller, I.

I. Haller, “Thermodynamic and Static Properties of Liquid Crystals,” Prog. Solid State Chem. 10, 103 (1975).
[CrossRef]

Hess, L. D.

Imura, H.

H. Imura, K. Okano, “Temperature Dependence of the Viscosity Coefficients of Liquid Crystals,” Jpn. J. Appl. Phys. 11, 1440(1972).
[CrossRef]

Ivanov, S. A.

V. V. Belyaev, S. A. Ivanov, M. F. Gorebenkin, “Temperature Dependence of Rotational Viscosity of Nematic Liquid Crystals,” Sov. Phys. Crystallogr. 30, 674 (1985).

Jackman, E.

E. Jackman, E. P. Raynes, “Electro-Optic Response Times in Liquid Crystals,” Phys. Lett. A 39, 69 (1972).
[CrossRef]

Klingbiel, R. T.

H. K. Bucher, R. T. Klingbiel, J. P. VanMeter, “Frequency-Addressed Liquid Crystal Field Effect,” Appl. Phys. Lett. 25, 186 (1974).
[CrossRef]

Lackner, A. M.

S. T. Wu, A. M. Lackner, W. H. Smith, U. Efron, “Guidelines for Selecting and Synthesizing Nematic Liquid Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 684, 69 (1986).

Little, M. J.

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

McDonnell, D. G.

M. J. Bradshaw, D. G. McDonnell, E. P. Raynes, “Physical Properties of Nematic Materials Containing Different Ring Systems,” Mol. Cryst. Liq. Cryst. 70, 289 (1981).
[CrossRef]

Muller, F.

M. Schadt, F. Muller, “Physical Properties of New Liquid Crystal Mixtures and Electrooptical Performance in Twisted Nematic Displays,” IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

Okano, K.

H. Imura, K. Okano, “Temperature Dependence of the Viscosity Coefficients of Liquid Crystals,” Jpn. J. Appl. Phys. 11, 1440(1972).
[CrossRef]

Pieranski, P.

H. J. Deuling, E. Guyon, P. Pieranski, “Deformation of Nematic Layers in Crossed Electric and Magnetic Fields,” Solid State Commun. 15, 277 (1974).
[CrossRef]

Raynes, E. P.

M. J. Bradshaw, D. G. McDonnell, E. P. Raynes, “Physical Properties of Nematic Materials Containing Different Ring Systems,” Mol. Cryst. Liq. Cryst. 70, 289 (1981).
[CrossRef]

E. Jackman, E. P. Raynes, “Electro-Optic Response Times in Liquid Crystals,” Phys. Lett. A 39, 69 (1972).
[CrossRef]

Reif, P. G.

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

Saupe, A.

A. Saupe, “Temperature-Dependence and Magnitudes of Deformation Constants in Strained Liquids,” Z. Naturforsch. Teil A 15, 810 (1960).

Schadt, M.

M. Schadt, “Low-Frequency Dielectric Relaxation in Nematics and Dual-Frequency Addressing of Field Effects,” Mol. Cryst. Liq. Cryst. 89, 77 (1982).
[CrossRef]

M. Schadt, F. Muller, “Physical Properties of New Liquid Crystal Mixtures and Electrooptical Performance in Twisted Nematic Displays,” IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

Schwartz, R. N.

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

Shabanov, V. F.

E. M. Averyanov, V. F. Shabanov, “Structural and Optical Anisotropy of Liquid Crystals,” Sov. Phys. Crystallogr. 23, 177 (1978).

Smith, W. H.

S. T. Wu, A. M. Lackner, W. H. Smith, U. Efron, “Guidelines for Selecting and Synthesizing Nematic Liquid Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 684, 69 (1986).

VanMeter, J. P.

H. K. Bucher, R. T. Klingbiel, J. P. VanMeter, “Frequency-Addressed Liquid Crystal Field Effect,” Appl. Phys. Lett. 25, 186 (1974).
[CrossRef]

Wu, S. T.

For an overview, see S. T. Wu, “Infrared Properties of Liquid Crystals: an Overview,” Opt. Eng. 26, 120 (1987).
[CrossRef]

S. T. Wu, U. Efron, “Optical Properties of Thin Nematic Liquid Crystal Cells,” Appl. Phys. Lett. 48, 624 (1986).
[CrossRef]

S. T. Wu, “Birefringence Dispersions of Liquid Crystals,” Phys. Rev. A 30, 1270 (1986).
[CrossRef]

S. T. Wu, A. M. Lackner, W. H. Smith, U. Efron, “Guidelines for Selecting and Synthesizing Nematic Liquid Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 684, 69 (1986).

S. T. Wu, “Phase Retardation Dependent Optical Response Time of Parallel-Aligned Liquid Crystals,” J. Appl. Phys. 60, 1836 (1986).
[CrossRef]

S. T. Wu, “Dual Field Effect on Liquid Crystal Relaxation,” J. Appl. Phys. 58, 1419 (1985).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, “Birefringence Measurements of Liquid Crystals,” Appl. Opt. 23, 3911 (1984).
[CrossRef] [PubMed]

Wu, S.-T.

Appl. Opt.

Appl. Phys. Lett.

S. T. Wu, U. Efron, “Optical Properties of Thin Nematic Liquid Crystal Cells,” Appl. Phys. Lett. 48, 624 (1986).
[CrossRef]

H. K. Bucher, R. T. Klingbiel, J. P. VanMeter, “Frequency-Addressed Liquid Crystal Field Effect,” Appl. Phys. Lett. 25, 186 (1974).
[CrossRef]

D. J. Channin, D. E. Carlson, “Rapid Turn-off in Triode Optical Gate Liquid Crystal Devices,” Appl. Phys. Lett. 28, 300 (1976).
[CrossRef]

IEEE Trans. Electron Devices

M. Schadt, F. Muller, “Physical Properties of New Liquid Crystal Mixtures and Electrooptical Performance in Twisted Nematic Displays,” IEEE Trans. Electron Devices ED-25, 1125 (1978).
[CrossRef]

J. Appl. Phys.

U. Efron, J. Grinberg, P.O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, “The Silicon Liquid Crystal Light Valve,” J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

S. T. Wu, “Dual Field Effect on Liquid Crystal Relaxation,” J. Appl. Phys. 58, 1419 (1985).
[CrossRef]

S. T. Wu, “Phase Retardation Dependent Optical Response Time of Parallel-Aligned Liquid Crystals,” J. Appl. Phys. 60, 1836 (1986).
[CrossRef]

Jpn. J. Appl. Phys.

H. Imura, K. Okano, “Temperature Dependence of the Viscosity Coefficients of Liquid Crystals,” Jpn. J. Appl. Phys. 11, 1440(1972).
[CrossRef]

Mol. Cryst. Liq. Cryst.

M. J. Bradshaw, D. G. McDonnell, E. P. Raynes, “Physical Properties of Nematic Materials Containing Different Ring Systems,” Mol. Cryst. Liq. Cryst. 70, 289 (1981).
[CrossRef]

M. Schadt, “Low-Frequency Dielectric Relaxation in Nematics and Dual-Frequency Addressing of Field Effects,” Mol. Cryst. Liq. Cryst. 89, 77 (1982).
[CrossRef]

Opt. Eng.

For an overview, see S. T. Wu, “Infrared Properties of Liquid Crystals: an Overview,” Opt. Eng. 26, 120 (1987).
[CrossRef]

Phys. Lett. A

E. Jackman, E. P. Raynes, “Electro-Optic Response Times in Liquid Crystals,” Phys. Lett. A 39, 69 (1972).
[CrossRef]

Phys. Rev. A

S. T. Wu, “Birefringence Dispersions of Liquid Crystals,” Phys. Rev. A 30, 1270 (1986).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

S. T. Wu, A. M. Lackner, W. H. Smith, U. Efron, “Guidelines for Selecting and Synthesizing Nematic Liquid Crystals,” Proc. Soc. Photo-Opt. Instrum. Eng. 684, 69 (1986).

Prog. Solid State Chem.

I. Haller, “Thermodynamic and Static Properties of Liquid Crystals,” Prog. Solid State Chem. 10, 103 (1975).
[CrossRef]

Solid State Commun.

H. J. Deuling, E. Guyon, P. Pieranski, “Deformation of Nematic Layers in Crossed Electric and Magnetic Fields,” Solid State Commun. 15, 277 (1974).
[CrossRef]

Sov. Phys. Crystallogr.

V. V. Belyaev, S. A. Ivanov, M. F. Gorebenkin, “Temperature Dependence of Rotational Viscosity of Nematic Liquid Crystals,” Sov. Phys. Crystallogr. 30, 674 (1985).

E. M. Averyanov, V. F. Shabanov, “Structural and Optical Anisotropy of Liquid Crystals,” Sov. Phys. Crystallogr. 23, 177 (1978).

Z. Naturforsch. Teil A

A. Saupe, “Temperature-Dependence and Magnitudes of Deformation Constants in Strained Liquids,” Z. Naturforsch. Teil A 15, 810 (1960).

Other

For example, see L. M. Blinov, Electro-optical and Magneto-optical Effects of Liquid Crystals (Wiley, New York, 1983).

P. G. DeGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

BDH Chemical Ltd., Poole Dorset, England BH12 4NN.

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Figures (4)

Fig. 1
Fig. 1

Temperature-dependent birefringence of E-7 (dots) and E-44 (triangles) LC mixtures. The wavelength used in these measurements is λ = 0.633 μm. The TNI for E-7 and E-44 is 60 and 100° C, respectively.

Fig. 2
Fig. 2

Temperature-dependent viscoelastic coefficient of E-7 (dots) and E-44 (triangles) LC mixtures.

Fig. 3
Fig. 3

Temperature-dependent normalized figure of merit for the E-7 LC mixture. Dots represent the normalized experimental results, and the solid line represents the theoretical calculations using Eq. (8). The parameters used for calculation are E = 0.45 eV, β = 0.17, and TNI = 333 K.

Fig. 4
Fig. 4

Temperature-dependent normalized figure of merit for the E-44 LC mixture. Dots represent the normalized experimental results, and the solid line represents the theoretical calculations using Eq. (8). The parameters used for calculation are E = 0.45 eV, β = 0.17, and TNI = 373 K.

Tables (1)

Tables Icon

Table I Comparison of the Merit Factor for the HRL-7P6 LC and Some Commercially Available LCs at Room Temperature

Equations (13)

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

τ = γ 1 d 2 K 11 π 2 .
δ = 2 π d Δ n / λ ,
F . M . = K Δ n 2 / γ 1
Δ n ρ S ;
γ 1 = a 1 S exp ( E 1 / k T ) + a 2 S 2 exp ( E 2 / k T ) ;
K S 2 ,
γ 1 S exp ( E / k T ) .
S = ( 1 T / T NI ) β ,
F . M . ( 1 T / T NI ) 3 β exp ( E / k T ) ,
T op = E 6 β k [ ( 1 + 12 β k T NI / E ) 1 / 2 1 ] .
T op T NI ( 1 3 β k T NI / E + ) .
G = ( T NI T op T NI T ) 3 β exp ( E k T op T T op · T )
Δ n ( T , λ ) = G ( T ) λ 2 λ * 2 λ 2 λ * 2 ,

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