Abstract

This work represents the first stress-optical study of strontium titanate (SrTiO3). The report includes a brief review of previous stress-optical work on crystals, a brief review of synthetic SrTiO3, and a brief review of stress-optical theory. The remainder of the paper is divided into two parts: Part I describes the piezobirefringence experimental apparatus and experimental procedure, sources of error and corrections, the measured values of the piezobirefringence constants (q2211q1111) and 2q1212 for the spectral range 4200–7700 A in steps of 100 A, an investigation of the linearity of the stress-optical relationship up to “moderate” pressures, and an investigation of stress-optical hysteresis up to “moderate” pressures. Part II covers the following: the problem of measuring the absolute values of stress-optical constants q1111 and q2211, apparatus and procedure, sources of error, the measured values of the stress-optical constants at 5400 A, the theoretical change in index of refraction under an hydrostatic stress, and confirmation of the linearity of the stress-optical relationship up to “moderate” pressures.

Strontium titanate has been found to become an optically negative uniaxial crystal when stressed along a crystallographic axis and an optically negative biaxial crystal when under a crystallographic diagonal stress.

© 1957 Optical Society of America

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References

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  1. D. Brewster, Phil. Trans. 60(1815).
  2. G. Wertheim, Compt. rend. 33, 576 (1851).
  3. G. Wertheim, Ann. chim. phys. 40,Ser. III, 156 (1854).
  4. E. Coker and L. Filon, A Treatise on Photoelasticity (Cambridge University Press, New York, 1931).
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  6. W. Voigt, Handbuch der Kristallphysik (Teubner, Leipzig, 1910).
  7. C. Schramm, Ann. phys. 25, 309 (1935).
  8. H. Mueller, Z. Krist. A99, 122 (1938).
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    [CrossRef]
  10. S. Bhagavantam and D. Suryanarayana, Proc. Indian Acad. Sci. 25, 97 (1947).
  11. G. Ramachandran, Proc. Indian Acad. Sci. 32, 171 (1950).
  12. E. Burstein and P. Smith, Phys. Rev. 74, 229 (1948).
    [CrossRef]
  13. E. Burstein and P. Smith, Phys. Rev. 74, 1880 (1948).
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  14. C. West and J. Makas, J. Chem. Phys. 16, 427 (1948).
    [CrossRef]
  15. C. West and J. Makas, Am. Mineralogist 35, 130 (1950).
  16. P. Grodzinski, Brit. J. Appl. Phys. 1, 246 (1950).
  17. K. Iyengar, Nature 176, 1119 (1955).
    [CrossRef]
  18. E. Poindexter, Am. Mineralogist 40, 1032 (1955).
  19. H. Mueller, Phys. Rev. 47, 947 (1935).
    [CrossRef]
  20. F. Pockels, Weid. Ann. phys. 37, 151 (1889).
  21. Palache, Berman, and Frondel, Dana’s System of Mineralogy (John Wiley and Sons, Inc., New York, 1944), seventh edition, Vol. I.
  22. L. Merker and L. Lynd, U. S. Pat.2,628,156, February10, 1953.
  23. L. Merker, Mining Eng. 645(1955); Trans. Am. Inst. Mining Met. Eng. 202(1955).
  24. Naray-Szabo, Naturwissenschaften 31, 203 (1943).
  25. Levin, Field, Plock, and Merker, J. Opt. Soc. Am. 45, 737 (1955).
    [CrossRef]
  26. S. Levin (personal communication).
  27. S. Bhagavantam, Proc. Indian Acad. Sci. 15, 97 (1942).
  28. F. Fumi, Acta Cryst. 5, 44 (1952).
    [CrossRef]
  29. F. Fumi, Nuovo cimento 9, No. 9, 1 (1952).
  30. A. Brown and V. Hickson, Brit. J. Appl. Phys. 1, 39 (1950).
    [CrossRef]

1955 (4)

K. Iyengar, Nature 176, 1119 (1955).
[CrossRef]

E. Poindexter, Am. Mineralogist 40, 1032 (1955).

L. Merker, Mining Eng. 645(1955); Trans. Am. Inst. Mining Met. Eng. 202(1955).

Levin, Field, Plock, and Merker, J. Opt. Soc. Am. 45, 737 (1955).
[CrossRef]

1952 (2)

F. Fumi, Acta Cryst. 5, 44 (1952).
[CrossRef]

F. Fumi, Nuovo cimento 9, No. 9, 1 (1952).

1950 (4)

A. Brown and V. Hickson, Brit. J. Appl. Phys. 1, 39 (1950).
[CrossRef]

C. West and J. Makas, Am. Mineralogist 35, 130 (1950).

P. Grodzinski, Brit. J. Appl. Phys. 1, 246 (1950).

G. Ramachandran, Proc. Indian Acad. Sci. 32, 171 (1950).

1948 (3)

E. Burstein and P. Smith, Phys. Rev. 74, 229 (1948).
[CrossRef]

E. Burstein and P. Smith, Phys. Rev. 74, 1880 (1948).
[CrossRef]

C. West and J. Makas, J. Chem. Phys. 16, 427 (1948).
[CrossRef]

1947 (1)

S. Bhagavantam and D. Suryanarayana, Proc. Indian Acad. Sci. 25, 97 (1947).

1943 (1)

Naray-Szabo, Naturwissenschaften 31, 203 (1943).

1942 (1)

S. Bhagavantam, Proc. Indian Acad. Sci. 15, 97 (1942).

1938 (1)

H. Mueller, Z. Krist. A99, 122 (1938).

1935 (2)

H. Mueller, Phys. Rev. 47, 947 (1935).
[CrossRef]

C. Schramm, Ann. phys. 25, 309 (1935).

1933 (1)

K. Herzfeld and R. Lee, Phys. Rev. 44, 625 (1933).
[CrossRef]

1889 (1)

F. Pockels, Weid. Ann. phys. 37, 151 (1889).

1854 (1)

G. Wertheim, Ann. chim. phys. 40,Ser. III, 156 (1854).

1851 (1)

G. Wertheim, Compt. rend. 33, 576 (1851).

1815 (1)

D. Brewster, Phil. Trans. 60(1815).

Berman,

Palache, Berman, and Frondel, Dana’s System of Mineralogy (John Wiley and Sons, Inc., New York, 1944), seventh edition, Vol. I.

Bhagavantam, S.

S. Bhagavantam and D. Suryanarayana, Proc. Indian Acad. Sci. 25, 97 (1947).

S. Bhagavantam, Proc. Indian Acad. Sci. 15, 97 (1942).

Brewster, D.

D. Brewster, Phil. Trans. 60(1815).

Brown, A.

A. Brown and V. Hickson, Brit. J. Appl. Phys. 1, 39 (1950).
[CrossRef]

Burstein, E.

E. Burstein and P. Smith, Phys. Rev. 74, 229 (1948).
[CrossRef]

E. Burstein and P. Smith, Phys. Rev. 74, 1880 (1948).
[CrossRef]

Coker, E.

E. Coker and L. Filon, A Treatise on Photoelasticity (Cambridge University Press, New York, 1931).

Field,

Filon, L.

E. Coker and L. Filon, A Treatise on Photoelasticity (Cambridge University Press, New York, 1931).

Frondel,

Palache, Berman, and Frondel, Dana’s System of Mineralogy (John Wiley and Sons, Inc., New York, 1944), seventh edition, Vol. I.

Fumi, F.

F. Fumi, Acta Cryst. 5, 44 (1952).
[CrossRef]

F. Fumi, Nuovo cimento 9, No. 9, 1 (1952).

Grodzinski, P.

P. Grodzinski, Brit. J. Appl. Phys. 1, 246 (1950).

Herzfeld, K.

K. Herzfeld and R. Lee, Phys. Rev. 44, 625 (1933).
[CrossRef]

Hickson, V.

A. Brown and V. Hickson, Brit. J. Appl. Phys. 1, 39 (1950).
[CrossRef]

Iyengar, K.

K. Iyengar, Nature 176, 1119 (1955).
[CrossRef]

Lee, R.

K. Herzfeld and R. Lee, Phys. Rev. 44, 625 (1933).
[CrossRef]

Levin,

Levin, S.

S. Levin (personal communication).

Lynd, L.

L. Merker and L. Lynd, U. S. Pat.2,628,156, February10, 1953.

Makas, J.

C. West and J. Makas, Am. Mineralogist 35, 130 (1950).

C. West and J. Makas, J. Chem. Phys. 16, 427 (1948).
[CrossRef]

Merker,

Merker, L.

L. Merker, Mining Eng. 645(1955); Trans. Am. Inst. Mining Met. Eng. 202(1955).

L. Merker and L. Lynd, U. S. Pat.2,628,156, February10, 1953.

Mueller, H.

H. Mueller, Z. Krist. A99, 122 (1938).

H. Mueller, Phys. Rev. 47, 947 (1935).
[CrossRef]

Naray-Szabo,

Naray-Szabo, Naturwissenschaften 31, 203 (1943).

Palache,

Palache, Berman, and Frondel, Dana’s System of Mineralogy (John Wiley and Sons, Inc., New York, 1944), seventh edition, Vol. I.

Plock,

Pockels, F.

F. Pockels, Weid. Ann. phys. 37, 151 (1889).

F. Pockels, Lehrbuch der Kristalloptik (Leipzig-Berlin, 1906).

Poindexter, E.

E. Poindexter, Am. Mineralogist 40, 1032 (1955).

Ramachandran, G.

G. Ramachandran, Proc. Indian Acad. Sci. 32, 171 (1950).

Schramm, C.

C. Schramm, Ann. phys. 25, 309 (1935).

Smith, P.

E. Burstein and P. Smith, Phys. Rev. 74, 229 (1948).
[CrossRef]

E. Burstein and P. Smith, Phys. Rev. 74, 1880 (1948).
[CrossRef]

Suryanarayana, D.

S. Bhagavantam and D. Suryanarayana, Proc. Indian Acad. Sci. 25, 97 (1947).

Voigt, W.

W. Voigt, Handbuch der Kristallphysik (Teubner, Leipzig, 1910).

Wertheim, G.

G. Wertheim, Ann. chim. phys. 40,Ser. III, 156 (1854).

G. Wertheim, Compt. rend. 33, 576 (1851).

West, C.

C. West and J. Makas, Am. Mineralogist 35, 130 (1950).

C. West and J. Makas, J. Chem. Phys. 16, 427 (1948).
[CrossRef]

Acta Cryst. (1)

F. Fumi, Acta Cryst. 5, 44 (1952).
[CrossRef]

Am. Mineralogist (2)

C. West and J. Makas, Am. Mineralogist 35, 130 (1950).

E. Poindexter, Am. Mineralogist 40, 1032 (1955).

Ann. chim. phys. (1)

G. Wertheim, Ann. chim. phys. 40,Ser. III, 156 (1854).

Ann. phys. (1)

C. Schramm, Ann. phys. 25, 309 (1935).

Brit. J. Appl. Phys. (2)

P. Grodzinski, Brit. J. Appl. Phys. 1, 246 (1950).

A. Brown and V. Hickson, Brit. J. Appl. Phys. 1, 39 (1950).
[CrossRef]

Compt. rend. (1)

G. Wertheim, Compt. rend. 33, 576 (1851).

J. Chem. Phys. (1)

C. West and J. Makas, J. Chem. Phys. 16, 427 (1948).
[CrossRef]

J. Opt. Soc. Am. (1)

Mining Eng. (1)

L. Merker, Mining Eng. 645(1955); Trans. Am. Inst. Mining Met. Eng. 202(1955).

Nature (1)

K. Iyengar, Nature 176, 1119 (1955).
[CrossRef]

Naturwissenschaften (1)

Naray-Szabo, Naturwissenschaften 31, 203 (1943).

Nuovo cimento (1)

F. Fumi, Nuovo cimento 9, No. 9, 1 (1952).

Phil. Trans. (1)

D. Brewster, Phil. Trans. 60(1815).

Phys. Rev. (4)

H. Mueller, Phys. Rev. 47, 947 (1935).
[CrossRef]

K. Herzfeld and R. Lee, Phys. Rev. 44, 625 (1933).
[CrossRef]

E. Burstein and P. Smith, Phys. Rev. 74, 229 (1948).
[CrossRef]

E. Burstein and P. Smith, Phys. Rev. 74, 1880 (1948).
[CrossRef]

Proc. Indian Acad. Sci. (3)

S. Bhagavantam and D. Suryanarayana, Proc. Indian Acad. Sci. 25, 97 (1947).

G. Ramachandran, Proc. Indian Acad. Sci. 32, 171 (1950).

S. Bhagavantam, Proc. Indian Acad. Sci. 15, 97 (1942).

Weid. Ann. phys. (1)

F. Pockels, Weid. Ann. phys. 37, 151 (1889).

Z. Krist. (1)

H. Mueller, Z. Krist. A99, 122 (1938).

Other (6)

E. Coker and L. Filon, A Treatise on Photoelasticity (Cambridge University Press, New York, 1931).

F. Pockels, Lehrbuch der Kristalloptik (Leipzig-Berlin, 1906).

W. Voigt, Handbuch der Kristallphysik (Teubner, Leipzig, 1910).

Palache, Berman, and Frondel, Dana’s System of Mineralogy (John Wiley and Sons, Inc., New York, 1944), seventh edition, Vol. I.

L. Merker and L. Lynd, U. S. Pat.2,628,156, February10, 1953.

S. Levin (personal communication).

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Figures (8)

Fig. 1
Fig. 1

The “ideal” perovskite type cubic structure.

Fig. 2
Fig. 2

Stress transformation of m3m to 4/mmm for SrTiO3.

Fig. 3
Fig. 3

Stress transformation of m3m to mmm for SrTiO3.

Fig. 4
Fig. 4

Orthodox (a) and unorthodox (b) orientations used for SrTiO3 and (c) their angular relationship.

Fig. 5
Fig. 5

An over-all view of the piezobirefringence experimental apparatus.

Fig. 6
Fig. 6

View of the crystal compressor with a SrTiO3 specimen in place.

Fig. 7
Fig. 7

Measured piezobirefringence constants of SrTiO3 at 27°C±1° for the spectral range 4200–7700 A.

Fig. 8
Fig. 8

Schematic diagram of the experimental apparatus used to determine the values of stress-optical constants q2211 and q1111 for SrTiO3.

Tables (6)

Tables Icon

Table I The index of refraction of single crystal samples of strontium titanate at 21°C26.

Tables Icon

Table II Graphically derived indexes of refraction for SrTiO3 at 21°C for 4200–7700 A in steps of 100 A.

Tables Icon

Table III Piezobirefringence constant (q2211q1111) of strontium titanate for the spectral range 4200–7700 A at 27°C±1°.

Tables Icon

Table IV Piezobirefringence constant 2q1212 of strontium titanate for the spectral range 4200–7700 A at 27°C±1°.

Tables Icon

Table V Experimental values of Δn for 5400 A light vibrating parallel to X2 X ¯ 2 under an applied stress of 182.2×106 dynes/cm2 directed along X1 X ¯ 1.a

Tables Icon

Table VI Experimental values of Δn for 5400 A light vibrating 2 parallel to X1 X ¯ 1 under an applied stress of 182.2×106 dynes/cm2 directed along X1 X ¯ 1.a

Equations (14)

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Δ a i j = q i j k l T k l ,
q 1111 = q 2222 = q 3333
q 1122 = q 2233 = q 3311 = q 2211 = q 3322 = q 1133
q 1212 = q 1221 = q 2112 = q 2121 = q 2323 = q 3223 = q 2332 = q 3232 = q 1313 = q 3113 = q 1331 = q 3131 .
q 1111 = 1 2 q 1111 + 1 2 q 2211 + q 1212 .
q 2211 = 1 2 q 1111 + 1 2 q 2211 - q 1212 .
q = 2 h λ / n 0 3 T d ,
q i j k l = 2 Δ n i j n 0 3 T k l .
n = sin 1 2 ( A + D ) sin 1 2 A .
Δ n = cos 1 2 ( A + D ) 1 2 Δ D sin 1 2 A
D = i + arcsin [ n sin ( A - arcsin sin i / n ) ] - A ,
q 2211 = 3 × 10 - 14 cm 2 / dyne q 1111 = - 8 × 10 - 14 cm 2 / dyne .
q 2211 - q 1111 = 11 × 10 - 14 ( q 2211 - q 1111 ) = 9.68 × 10 - 14 .
q ( hydrostatic ) = q 1111 + 2 q 2211 = - 2 × 10 - 14 cm 2 / dyne .