Glass Viscosity (Vogel-Fulcher-Tammann)
Computes the viscosity of a glass with the Vogel-Fulcher-Tammann equation, log₁₀η = A + B ÷ (T − T₀), that is, η = 10^(A + B/(T − T₀)), where A, B and T₀ are the three constants fitted for each composition and T is the working temperature. The answer comes out in poise (1 P = 1 dPa·s) provided coefficient A was fitted in poise, the unit in which the glass industry pins its reference points; fits published in Pa·s need 1 added to A: 10⁴ P is the working point, 10^7.6 P is the Littleton softening point and 10^13 P is the annealing point. Since the denominator goes to zero as T approaches the Vogel temperature T₀, viscosity blows up and the equation loses meaning below it — which is why the page rejects T at or below T₀. Enter the constants A, B and T₀ and the glass temperature.
Result
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Glass viscosity with the Vogel-Fulcher-Tammann fit
A supplier data sheet hands over three temperatures and nothing in between: working point, softening point, annealing point. Anyone running a furnace, tuning a feeder or setting the temperature of a forehearth needs viscosity at an arbitrary temperature, and straight-line interpolation between fixed points misses by orders of magnitude — glass viscosity spans thirteen decades over little more than five hundred degrees. The Vogel-Fulcher-Tammann equation covers that whole span with three fitted constants.
log₁₀η = A + B ÷ (T − T₀), so η = 10^(A + B/(T − T₀)). A is the logarithm of the viscosity the liquid would have at infinite temperature, B sets how fast viscosity climbs on cooling, and T₀, the Vogel temperature, marks where the curve would blow up. With the page defaults — A = −2.4, B = 4000 °C, T₀ = 250 °C and T = 1000 °C — the denominator gives 750, the quotient 5.3333, the sum 2.9333 and the answer 857.70 P. Check it by inversion: the working point sits at 10⁴ P, which demands T = T₀ + B ÷ (4 − A) = 250 + 4000 ÷ 6.4 = 875 °C. Type 875 and the page returns 10000.00 P.
VFT is an empirical fit and holds only across the range it was fitted over, in practice between the annealing point and the working point, roughly 10¹³ down to 10² P. Extrapolating above the liquidus or below the glass transition misses badly, and the equation knows nothing of devitrification, thermal history or non-Newtonian behaviour at high shear rates. Near T₀ the exponent overflows: with the defaults, 251 °C prints Infinity, and any T at or below T₀ gets rejected with a warning. Mind the unit as well — the number lands in poise only if A was fitted in poise.
Frequently asked questions
Does the answer come out in poise or in pascal-seconds?
Where do I get A, B and T₀ for my own composition?
Can I get the temperature of a fixed point instead of the viscosity?
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