Abstract

Recent critical applications for ultralow expansion materials have required thermal expansion measurements with very high precision and accuracy. A Fizeau interferometer employing a helium–neon laser has given a precision of ±0.1 × 10−6 cm/cm. A second, more rapid method consists of a rod type vitreous silica dilatometer. A stirred water bath is used for specimen temperature control and a high output, linear variable differential transformer serves as the extensometer. Precision of this method is ±0.5 × 10−6 cm/cm. Calibration procedures and results for several low expansion materials are discussed.

© 1968 Optical Society of America

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References

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  1. J. B. Saunders, J. Res. Nat. Bur. Stand. 23, 179 (1939).
    [CrossRef]
  2. B. A. Lengyel, Lasers (John Wiley & Sons, Inc., New York, 1962), Sec. 17, pp. 91–99.
  3. K. D. Mielenz, R. B. Stephens, K. E. Gilliland, K. F. Nefflen, J. Opt. Soc. Amer. 56, 156 (1966).
    [CrossRef]
  4. ASTM Designation E228–66aT, “Tentative Method of Test for Linear Thermal Expansion of Rigid Solids with a Vitreous Silica Dilatometer,” ASTM Standards, Part 30, pp. 663–674, 1966.
  5. J. B. Austin, Physics 3, 240 (1932).
    [CrossRef]

1966 (1)

K. D. Mielenz, R. B. Stephens, K. E. Gilliland, K. F. Nefflen, J. Opt. Soc. Amer. 56, 156 (1966).
[CrossRef]

1939 (1)

J. B. Saunders, J. Res. Nat. Bur. Stand. 23, 179 (1939).
[CrossRef]

1932 (1)

J. B. Austin, Physics 3, 240 (1932).
[CrossRef]

Austin, J. B.

J. B. Austin, Physics 3, 240 (1932).
[CrossRef]

Gilliland, K. E.

K. D. Mielenz, R. B. Stephens, K. E. Gilliland, K. F. Nefflen, J. Opt. Soc. Amer. 56, 156 (1966).
[CrossRef]

Lengyel, B. A.

B. A. Lengyel, Lasers (John Wiley & Sons, Inc., New York, 1962), Sec. 17, pp. 91–99.

Mielenz, K. D.

K. D. Mielenz, R. B. Stephens, K. E. Gilliland, K. F. Nefflen, J. Opt. Soc. Amer. 56, 156 (1966).
[CrossRef]

Nefflen, K. F.

K. D. Mielenz, R. B. Stephens, K. E. Gilliland, K. F. Nefflen, J. Opt. Soc. Amer. 56, 156 (1966).
[CrossRef]

Saunders, J. B.

J. B. Saunders, J. Res. Nat. Bur. Stand. 23, 179 (1939).
[CrossRef]

Stephens, R. B.

K. D. Mielenz, R. B. Stephens, K. E. Gilliland, K. F. Nefflen, J. Opt. Soc. Amer. 56, 156 (1966).
[CrossRef]

J. Opt. Soc. Amer. (1)

K. D. Mielenz, R. B. Stephens, K. E. Gilliland, K. F. Nefflen, J. Opt. Soc. Amer. 56, 156 (1966).
[CrossRef]

J. Res. Nat. Bur. Stand. (1)

J. B. Saunders, J. Res. Nat. Bur. Stand. 23, 179 (1939).
[CrossRef]

Physics (1)

J. B. Austin, Physics 3, 240 (1932).
[CrossRef]

Other (2)

B. A. Lengyel, Lasers (John Wiley & Sons, Inc., New York, 1962), Sec. 17, pp. 91–99.

ASTM Designation E228–66aT, “Tentative Method of Test for Linear Thermal Expansion of Rigid Solids with a Vitreous Silica Dilatometer,” ASTM Standards, Part 30, pp. 663–674, 1966.

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Figures (9)

Fig. 1
Fig. 1

Environmental sample chamber for laser interferometric method.

Fig. 2
Fig. 2

Corning’s Code 7940 vitreous silica sample.

Fig. 3
Fig. 3

Linear thermal expansion of Code 7940 vitreous silica.

Fig. 4
Fig. 4

Linear thermal expansion coefficient of Code 7940 vitreous silica.

Fig. 5
Fig. 5

Linear thermal expansion of Code 9692 glass–ceramic.

Fig. 6
Fig. 6

High precision vitreous silica dilatometer.

Fig. 7
Fig. 7

Differential linear thermal expansion between standard Code 7940 vitreous silica and dilatometer vitreous silica.

Fig. 8
Fig. 8

Linear thermal expansion of Code 7971 low expansion vitreous silica. Code 7940 vitreous silica is shown by a dashed line.

Fig. 9
Fig. 9

Linear thermal expansion of Code 9623 clear glass-ceramic.

Tables (2)

Tables Icon

Table I Linear Thermal Expansion of Corning’s Code 7940 Vitreous Silica

Tables Icon

Table II Thermal Expansion of Code 9692 Glass-Ceramic

Equations (7)

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Δ L / L 0 = 4.40 × 10 - 7 T + 1.54 × 10 - 9 T 2 ,
α = d ( Δ L / L ) / d T = 4.40 × 10 - 7 + 0.0308 × 10 - 7 T .
19 A             Δ L / L = 0.00482 × 10 - 6 ( T - 12.54 ) 2 , σ = 0.098
19 B             Δ L / L = 0.00392 × 10 - 6 ( T - 14.41 ) 2 , σ = 0.147
23 A             Δ L / L = 0.00462 × 10 - 6 ( T - 15.24 ) 2 , σ = 0.150
23 B             Δ L / L = 0.00620 × 10 - 6 ( T - 11.96 ) 2 , σ = 0.082
Δ L L = ( V t - V 0 ) × 10 3 A L + B ( T t - T 0 ) ,

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