Abstract

Magnetically induced extinction and birefringence of systems containing a mixture of ultramicroscopic particles with different optical and magnetic properties have been theoretically investigated. It is shown that the effects may exhibit an extremum and an inversion in sign with increasing applied field strength if the system contains diamagnetic as well as ferromagnetic particles. The field strengths at which the effects exhibit the extremum and the inversion in sign are found to depend on the relative number distribution of the two types of particles and on the wavelength of the incident radiation. Experimental results from systems containing particles of bentonite and chromium ferrite in different proportions are also discussed.

© 1980 Optical Society of America

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  1. Y. G. Naik, J. N. Desai, Indian J. Pure Appl. Phys. 3, 27 (1965).
  2. H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 282 (1968).
  3. M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).
  4. J. N. Desai, Y. G. Naik, R. V. Mehta, M. J. Dave, Indian J. Pure Appl. Phys. 7, 534 (1969).
  5. M. J. Shah, D. C. Thompson, C. M. Hart, J. Phys. Chem. 67, 1170 (1963).
    [CrossRef]
  6. M. J. Shah, J. Phys. Chem. 67, 2215 (1963).
    [CrossRef]
  7. W. Heller, Nouvelles recherches sur les propriétés magnétooptiques des solutions colloidales, Monograph 806 in Actualités Scientifiques et Industrielles (Hermann, Paris, 1939).
  8. W. Heller, G. Quimfe, Y. Ta, Phys. Rev. 62, 479 (1942).
    [CrossRef]
  9. R. V. Mehta, H. S. Shah, J. B. Bhagat, D. M. Bhagat, IEEE Trans. Magn., TM-16, (in press).
  10. C. T. O’Konski, K. Yoshioka, W. H. Orttung, J. Phys. Chem. 63, 1558 (1959).
    [CrossRef]
  11. R. V. Mehta, D. M. Bhagat, IEEE Trans. Magn. MAG-16, 258 (1980).
    [CrossRef]
  12. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1955).
  13. R. V. Mehta, in Thermomechanics of Magnetic Fluids, B. Berkovsky, Ed. (Hemisphere, Washington, D.C., 1978), pp. 139–148.
  14. R. V. Mehta, H. S. Shah, J. Phys. D. 7, 2483 (1974).
    [CrossRef]
  15. R. V. Mehta, J. Colloid Interface Sci. 42, 165 (1973).
    [CrossRef]
  16. R. V. Mehta, H. S. Shah, M. J. Dave, J. Colloid Interface Sci. 35, 41 (1971).
    [CrossRef]

1980

R. V. Mehta, D. M. Bhagat, IEEE Trans. Magn. MAG-16, 258 (1980).
[CrossRef]

1974

R. V. Mehta, H. S. Shah, J. Phys. D. 7, 2483 (1974).
[CrossRef]

1973

R. V. Mehta, J. Colloid Interface Sci. 42, 165 (1973).
[CrossRef]

1971

R. V. Mehta, H. S. Shah, M. J. Dave, J. Colloid Interface Sci. 35, 41 (1971).
[CrossRef]

1969

J. N. Desai, Y. G. Naik, R. V. Mehta, M. J. Dave, Indian J. Pure Appl. Phys. 7, 534 (1969).

1968

H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 282 (1968).

M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).

1965

Y. G. Naik, J. N. Desai, Indian J. Pure Appl. Phys. 3, 27 (1965).

1963

M. J. Shah, D. C. Thompson, C. M. Hart, J. Phys. Chem. 67, 1170 (1963).
[CrossRef]

M. J. Shah, J. Phys. Chem. 67, 2215 (1963).
[CrossRef]

1959

C. T. O’Konski, K. Yoshioka, W. H. Orttung, J. Phys. Chem. 63, 1558 (1959).
[CrossRef]

1942

W. Heller, G. Quimfe, Y. Ta, Phys. Rev. 62, 479 (1942).
[CrossRef]

Bhagat, D. M.

R. V. Mehta, D. M. Bhagat, IEEE Trans. Magn. MAG-16, 258 (1980).
[CrossRef]

R. V. Mehta, H. S. Shah, J. B. Bhagat, D. M. Bhagat, IEEE Trans. Magn., TM-16, (in press).

Bhagat, J. B.

R. V. Mehta, H. S. Shah, J. B. Bhagat, D. M. Bhagat, IEEE Trans. Magn., TM-16, (in press).

Dave, M. J.

R. V. Mehta, H. S. Shah, M. J. Dave, J. Colloid Interface Sci. 35, 41 (1971).
[CrossRef]

J. N. Desai, Y. G. Naik, R. V. Mehta, M. J. Dave, Indian J. Pure Appl. Phys. 7, 534 (1969).

M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).

Desai, J. N.

J. N. Desai, Y. G. Naik, R. V. Mehta, M. J. Dave, Indian J. Pure Appl. Phys. 7, 534 (1969).

M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).

H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 282 (1968).

Y. G. Naik, J. N. Desai, Indian J. Pure Appl. Phys. 3, 27 (1965).

Hart, C. M.

M. J. Shah, D. C. Thompson, C. M. Hart, J. Phys. Chem. 67, 1170 (1963).
[CrossRef]

Heller, W.

W. Heller, G. Quimfe, Y. Ta, Phys. Rev. 62, 479 (1942).
[CrossRef]

W. Heller, Nouvelles recherches sur les propriétés magnétooptiques des solutions colloidales, Monograph 806 in Actualités Scientifiques et Industrielles (Hermann, Paris, 1939).

Mehta, R. V.

R. V. Mehta, D. M. Bhagat, IEEE Trans. Magn. MAG-16, 258 (1980).
[CrossRef]

R. V. Mehta, H. S. Shah, J. Phys. D. 7, 2483 (1974).
[CrossRef]

R. V. Mehta, J. Colloid Interface Sci. 42, 165 (1973).
[CrossRef]

R. V. Mehta, H. S. Shah, M. J. Dave, J. Colloid Interface Sci. 35, 41 (1971).
[CrossRef]

J. N. Desai, Y. G. Naik, R. V. Mehta, M. J. Dave, Indian J. Pure Appl. Phys. 7, 534 (1969).

M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).

R. V. Mehta, H. S. Shah, J. B. Bhagat, D. M. Bhagat, IEEE Trans. Magn., TM-16, (in press).

R. V. Mehta, in Thermomechanics of Magnetic Fluids, B. Berkovsky, Ed. (Hemisphere, Washington, D.C., 1978), pp. 139–148.

Naik, Y. G.

J. N. Desai, Y. G. Naik, R. V. Mehta, M. J. Dave, Indian J. Pure Appl. Phys. 7, 534 (1969).

M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).

H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 282 (1968).

Y. G. Naik, J. N. Desai, Indian J. Pure Appl. Phys. 3, 27 (1965).

O’Konski, C. T.

C. T. O’Konski, K. Yoshioka, W. H. Orttung, J. Phys. Chem. 63, 1558 (1959).
[CrossRef]

Orttung, W. H.

C. T. O’Konski, K. Yoshioka, W. H. Orttung, J. Phys. Chem. 63, 1558 (1959).
[CrossRef]

Quimfe, G.

W. Heller, G. Quimfe, Y. Ta, Phys. Rev. 62, 479 (1942).
[CrossRef]

Shah, H. S.

R. V. Mehta, H. S. Shah, J. Phys. D. 7, 2483 (1974).
[CrossRef]

R. V. Mehta, H. S. Shah, M. J. Dave, J. Colloid Interface Sci. 35, 41 (1971).
[CrossRef]

H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 282 (1968).

M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).

R. V. Mehta, H. S. Shah, J. B. Bhagat, D. M. Bhagat, IEEE Trans. Magn., TM-16, (in press).

Shah, M. J.

M. J. Shah, J. Phys. Chem. 67, 2215 (1963).
[CrossRef]

M. J. Shah, D. C. Thompson, C. M. Hart, J. Phys. Chem. 67, 1170 (1963).
[CrossRef]

Ta, Y.

W. Heller, G. Quimfe, Y. Ta, Phys. Rev. 62, 479 (1942).
[CrossRef]

Thompson, D. C.

M. J. Shah, D. C. Thompson, C. M. Hart, J. Phys. Chem. 67, 1170 (1963).
[CrossRef]

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1955).

Yoshioka, K.

C. T. O’Konski, K. Yoshioka, W. H. Orttung, J. Phys. Chem. 63, 1558 (1959).
[CrossRef]

IEEE Trans. Magn.

R. V. Mehta, D. M. Bhagat, IEEE Trans. Magn. MAG-16, 258 (1980).
[CrossRef]

Indian J. Pure Appl. Phys.

Y. G. Naik, J. N. Desai, Indian J. Pure Appl. Phys. 3, 27 (1965).

H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 282 (1968).

M. J. Dave, R. V. Mehta, H. S. Shah, J. N. Desai, Y. G. Naik, Indian J. Pure Appl. Phys. 6, 364 (1968).

J. N. Desai, Y. G. Naik, R. V. Mehta, M. J. Dave, Indian J. Pure Appl. Phys. 7, 534 (1969).

J. Colloid Interface Sci.

R. V. Mehta, J. Colloid Interface Sci. 42, 165 (1973).
[CrossRef]

R. V. Mehta, H. S. Shah, M. J. Dave, J. Colloid Interface Sci. 35, 41 (1971).
[CrossRef]

J. Phys. Chem.

C. T. O’Konski, K. Yoshioka, W. H. Orttung, J. Phys. Chem. 63, 1558 (1959).
[CrossRef]

M. J. Shah, D. C. Thompson, C. M. Hart, J. Phys. Chem. 67, 1170 (1963).
[CrossRef]

M. J. Shah, J. Phys. Chem. 67, 2215 (1963).
[CrossRef]

J. Phys. D.

R. V. Mehta, H. S. Shah, J. Phys. D. 7, 2483 (1974).
[CrossRef]

Phys. Rev.

W. Heller, G. Quimfe, Y. Ta, Phys. Rev. 62, 479 (1942).
[CrossRef]

Other

R. V. Mehta, H. S. Shah, J. B. Bhagat, D. M. Bhagat, IEEE Trans. Magn., TM-16, (in press).

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1955).

R. V. Mehta, in Thermomechanics of Magnetic Fluids, B. Berkovsky, Ed. (Hemisphere, Washington, D.C., 1978), pp. 139–148.

W. Heller, Nouvelles recherches sur les propriétés magnétooptiques des solutions colloidales, Monograph 806 in Actualités Scientifiques et Industrielles (Hermann, Paris, 1939).

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Figures (5)

Fig. 1
Fig. 1

Plot of ϕ(h) vs h for different values of R.

Fig. 2
Fig. 2

Extinction parameter vs field strength for bentonite (dotted curves) and chromium ferrite (—). ○ and ● denote observed values of Q, and Δ and ▲ denote those of Q.

Fig. 3
Fig. 3

Induced phase retardation for bentonite Δ and chromium ferrite ○.

Fig. 4
Fig. 4

Induced phase retardation for mixed systems for different ratios w of weight concentrations of chromium ferrite to that of bentonite. Curves B and C represent phase retardation for bentonite and chromium ferrite, respectively.

Fig. 5
Fig. 5

Induced phase retardation for λ = 546.1 nm Δ and λ = 589.3 nm ○. Extinction parameter for λ = 546.1 nm for the same sample (□, Q and ∇, Q).

Equations (25)

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C = 8 π 2 N λ [ Im β o + Im ( β e β o ) ϕ ( h ) ] ,
C = 8 π 2 N λ [ Im β e + β o 2 Im β e β o 2 ϕ ( h ) ] ,
C l = C ,
β j = α j 8 π 2 i λ | α j | 2 .
α j = V 4 π [ m j 2 1 ( m j 2 1 ) L j 1 ] .
ϕ ( h ) d = 1 2 h 2 [ 1 h exp ( h 2 ) E h ] ,
h 2 = ( χ o χ e ) V H 2 2 k T ,
E h = 0 h exp ( x 2 ) d x .
ϕ ( h ) f = 1 2 h ( coth h 1 h ) ,
h = ( m H ) / ( k T ) ,
[ C ext ] mixture = [ C ext ] diamagnetic + [ C ext ] ferromagnetic ,
[ C ext ] M = 8 π 2 λ { N [ Im β o + IM ( β e β o ) ϕ ( h ) d ] + N [ Im β o + Im ( β e β o ϕ ( h ) f ] } ,
[ C ext ] M = 8 π 2 λ { N [ Im β e + β o 2 Im β e β o 2 ϕ ( h ) d ] + N [ Im β e + β o 2 Im β e β o 2 ϕ ( h ) f ] } ,
[ C ext ] M L = [ C ext ] M .
C 0 = 8 π 2 3 λ [ N ( β e + 2 β o ) + N ( β e + 2 β o ) ] .
Q = 1 B { 3 ( Im β o + N N Im β o ) + [ Im ( β e β o ) + N N Im ( β e β o ) ] ϕ ( h ) } ,
Q = 1 2 B { 3 [ Im ( β e + β o ) + N N Im ( β e + β [ Im ( β e β o ) + N N Im ( β e β o ) ] ϕ ( h ) } ,
Q L = Q ,
B = Im ( β e + 2 β o ) + N N Im ( β e + 2 β o ) .
ϕ ( h ) = 3 1 + R [ ϕ ( h ) d + R ϕ ( h ) f ] ,
R = N N Im β e β o β e β o .
Δ n = 2 π n 0 N Re β e β o 2 [ 3 ϕ ( h ) d , f 1 ] ,
[ Δ n ] M = Δ n d + Δ n f = 2 π n 0 { N Re β e β o 2 [ 3 ϕ ( h ) d 1 ] + N Re β e β o 2 ( 3 ϕ ( h ) f 1 ) } = 2 π n 0 N ( β e β o ) [ ϕ ( h ) 1 ] .
ϕ ( h ) = 3 { ϕ ( h ) d + R [ ϕ ( h ) f 1 3 ] }
R = N N Re β e β o β e β o .

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