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This shift results from the contributions of the index temperature change and the expansion coeficient and one has: (1/v)(dv/dT) = -(1/N)(dN/dT)-(1/a)(da/dT). At 300 K, the thermal frequency shift is negative, of the order of -2.5 MHz/mK. Although (dN/dT) is not well known at low T, the small positive thermal shift that we have measured at 6 K agrees with the expansion coefficient of silica which is known to vanish and change sign below 20 K.
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