Abstract

Use of a photometer-equipped polarizing microscope permits the measurement of linear crystallization velocity in a flexible manner. Ease of sample preparation and manipulation compared with conventional methods for measuring crystallization velocity are among the advantages of the method reported here. A simple barrier layer silicon photodetector in short-circuit operation gives the fast response necessary to follow the moving solid–liquid interface. Sample results on the crystallization of α- and β-resorcinol illustrate the utility of this method.

© 1983 Optical Society of America

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References

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  1. D. Gernez, C.R. Acad. Sci. 95, 1278 (1982); C.R. Acad. Sci. 97, 1298, 1366, 1433 (1884).
  2. G. Tammann, States of Aggregation, translated by R. F. Mehl (Van Nostrand, Princeton, N.J., 1925).
  3. J. W. Cahn, W. B. Hillig, G. W. Sears, Acta Metall. 12, 1421 (1964).
    [CrossRef]
  4. R. F. Strickland-Constable, Kinetics and Mechanism of Crystallization (Academic, London, 1968), pp. 271–275.
  5. I. N. Fridlyander, in Growth of Crystals, Vol. 1, A. V. Shubnikov, N. N. Sheftal, Eds. (Consultants Bureau, New York, 1959), pp. 142–149.
  6. D. Kirtisinghe, Ph.D. Thesis, London U. (1964); see also Ref. 4.
  7. V. T. Borisov, in Growth of Crystals, Vol. 3, A. V. Shubnokov, N. N. Sheftal, Eds. (Consultants Bureau, New York, 1962), pp. 135–137.
  8. R. E. Powell, T. S. Gilman, J. H. Hildebrand, J. Am. Chem. Soc. 73, 2525 (1951).
    [CrossRef]
  9. J. B. Hudson, W. B. Hillig, R. M. Strong, J. Phys. Chem. 63, 1012 (1959).
    [CrossRef]
  10. W. B. Hillig, in Growth and Perfection of Crystals, R. H. Doremus, B. W. Roberts, D. Turnbull, Eds. (Wiley, New York, 1958), pp. 350–360.
  11. L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
    [CrossRef]
  12. L. J. Soltzberg, S. M. Cannon, C. A. Clarke, Y. W. Ho, Appl. Opt. 20, 670 (1981).
    [CrossRef] [PubMed]
  13. P. G. Witherell, M. E. Faulhaber, Appl. Opt. 9, 73 (1970).
    [CrossRef] [PubMed]
  14. The actual function is the area enclosed by a circle and its chord as the chord moves at a constant rate perpendicular to the normal diameter of the circle. That is,A(x)=∫−rx(r2−x2)1/2dx,where r is the radius of the circle (the microscope field) and x is the position of the moving interface. Then, A(x) = ½[x(r2 − x2)1/2 + r2sin−1(x/r)] + πr2/4.

1982 (1)

D. Gernez, C.R. Acad. Sci. 95, 1278 (1982); C.R. Acad. Sci. 97, 1298, 1366, 1433 (1884).

1981 (1)

1979 (1)

L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
[CrossRef]

1970 (1)

1964 (1)

J. W. Cahn, W. B. Hillig, G. W. Sears, Acta Metall. 12, 1421 (1964).
[CrossRef]

1959 (1)

J. B. Hudson, W. B. Hillig, R. M. Strong, J. Phys. Chem. 63, 1012 (1959).
[CrossRef]

1951 (1)

R. E. Powell, T. S. Gilman, J. H. Hildebrand, J. Am. Chem. Soc. 73, 2525 (1951).
[CrossRef]

Armstrong, E. C.

L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
[CrossRef]

Bobrowski, S. J.

L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
[CrossRef]

Borisov, V. T.

V. T. Borisov, in Growth of Crystals, Vol. 3, A. V. Shubnokov, N. N. Sheftal, Eds. (Consultants Bureau, New York, 1962), pp. 135–137.

Cahn, J. W.

J. W. Cahn, W. B. Hillig, G. W. Sears, Acta Metall. 12, 1421 (1964).
[CrossRef]

Cannon, S. M.

Clarke, C. A.

Cohn, V. E.

L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
[CrossRef]

Faulhaber, M. E.

Fridlyander, I. N.

I. N. Fridlyander, in Growth of Crystals, Vol. 1, A. V. Shubnikov, N. N. Sheftal, Eds. (Consultants Bureau, New York, 1959), pp. 142–149.

Gernez, D.

D. Gernez, C.R. Acad. Sci. 95, 1278 (1982); C.R. Acad. Sci. 97, 1298, 1366, 1433 (1884).

Gilman, T. S.

R. E. Powell, T. S. Gilman, J. H. Hildebrand, J. Am. Chem. Soc. 73, 2525 (1951).
[CrossRef]

Hildebrand, J. H.

R. E. Powell, T. S. Gilman, J. H. Hildebrand, J. Am. Chem. Soc. 73, 2525 (1951).
[CrossRef]

Hillig, W. B.

J. W. Cahn, W. B. Hillig, G. W. Sears, Acta Metall. 12, 1421 (1964).
[CrossRef]

J. B. Hudson, W. B. Hillig, R. M. Strong, J. Phys. Chem. 63, 1012 (1959).
[CrossRef]

W. B. Hillig, in Growth and Perfection of Crystals, R. H. Doremus, B. W. Roberts, D. Turnbull, Eds. (Wiley, New York, 1958), pp. 350–360.

Ho, Y. W.

Hudson, J. B.

J. B. Hudson, W. B. Hillig, R. M. Strong, J. Phys. Chem. 63, 1012 (1959).
[CrossRef]

Kirtisinghe, D.

D. Kirtisinghe, Ph.D. Thesis, London U. (1964); see also Ref. 4.

Parziale, P. A.

L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
[CrossRef]

Powell, R. E.

R. E. Powell, T. S. Gilman, J. H. Hildebrand, J. Am. Chem. Soc. 73, 2525 (1951).
[CrossRef]

Sears, G. W.

J. W. Cahn, W. B. Hillig, G. W. Sears, Acta Metall. 12, 1421 (1964).
[CrossRef]

Soltzberg, L. J.

L. J. Soltzberg, S. M. Cannon, C. A. Clarke, Y. W. Ho, Appl. Opt. 20, 670 (1981).
[CrossRef] [PubMed]

L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
[CrossRef]

Strickland-Constable, R. F.

R. F. Strickland-Constable, Kinetics and Mechanism of Crystallization (Academic, London, 1968), pp. 271–275.

Strong, R. M.

J. B. Hudson, W. B. Hillig, R. M. Strong, J. Phys. Chem. 63, 1012 (1959).
[CrossRef]

Tammann, G.

G. Tammann, States of Aggregation, translated by R. F. Mehl (Van Nostrand, Princeton, N.J., 1925).

Witherell, P. G.

Acta Metall. (1)

J. W. Cahn, W. B. Hillig, G. W. Sears, Acta Metall. 12, 1421 (1964).
[CrossRef]

Appl. Opt. (2)

C.R. Acad. Sci. (1)

D. Gernez, C.R. Acad. Sci. 95, 1278 (1982); C.R. Acad. Sci. 97, 1298, 1366, 1433 (1884).

J. Am. Chem. Soc. (1)

R. E. Powell, T. S. Gilman, J. H. Hildebrand, J. Am. Chem. Soc. 73, 2525 (1951).
[CrossRef]

J. Chem. Phys. (1)

L. J. Soltzberg, S. J. Bobrowski, P. A. Parziale, E. C. Armstrong, V. E. Cohn, J. Chem. Phys. 71, 1652 (1979).
[CrossRef]

J. Phys. Chem. (1)

J. B. Hudson, W. B. Hillig, R. M. Strong, J. Phys. Chem. 63, 1012 (1959).
[CrossRef]

Other (7)

W. B. Hillig, in Growth and Perfection of Crystals, R. H. Doremus, B. W. Roberts, D. Turnbull, Eds. (Wiley, New York, 1958), pp. 350–360.

G. Tammann, States of Aggregation, translated by R. F. Mehl (Van Nostrand, Princeton, N.J., 1925).

R. F. Strickland-Constable, Kinetics and Mechanism of Crystallization (Academic, London, 1968), pp. 271–275.

I. N. Fridlyander, in Growth of Crystals, Vol. 1, A. V. Shubnikov, N. N. Sheftal, Eds. (Consultants Bureau, New York, 1959), pp. 142–149.

D. Kirtisinghe, Ph.D. Thesis, London U. (1964); see also Ref. 4.

V. T. Borisov, in Growth of Crystals, Vol. 3, A. V. Shubnokov, N. N. Sheftal, Eds. (Consultants Bureau, New York, 1962), pp. 135–137.

The actual function is the area enclosed by a circle and its chord as the chord moves at a constant rate perpendicular to the normal diameter of the circle. That is,A(x)=∫−rx(r2−x2)1/2dx,where r is the radius of the circle (the microscope field) and x is the position of the moving interface. Then, A(x) = ½[x(r2 − x2)1/2 + r2sin−1(x/r)] + πr2/4.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of the photometer. The silicon photovoltaic cell is in short-circuit operation with the photocurrent converted to voltage by operational amplifier circuit. 0.001-mF capacitor is compromise between sufficient response speed and adequate noise filtering. 10K potentiometer allows for offset of output voltage.

Fig. 2
Fig. 2

Typical LCV data: photometer output vs time. Vertical axis is in raw ADC units on a scale of 0 to 4095 (0 to +5 V). Horizontal axis is time with each small division having a value dependent on ADC sampling rate; e.g., with sampling at 1 sample every 4 msec, each division corresponds to 20 msec. J labels on the time axis are index numbers for the sampled points, (a) Resorcinol crystallizing as α-polymorph at 60°C. Transit time is 320 msec. (b) Resorcinol crystallizing as β-polymorph at 60°C. Transit time is 195 msec.

Equations (1)

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A(x)=rx(r2x2)1/2dx,

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