Methods and apparatus for predicting glass properties

A method for identifying at least one material expected to have at least one desired η,T pair, where η is equilibrium viscosity and T is temperature, said method comprising:

• (A) selecting at least one candidate material comprising N viscosity-affecting components having selected concentrations, where N may be different for different candidate materials;
• (B) using a computer to obtain at least one η,T pair for the at least one candidate material of step (A) by evaluating an expression of the form
• log10 η(T,x)=C1+C2·(f1(x,FC1)/T)·exp([f2(x,FC2)−1]·[f1(x,FC1)/T−1])
• where
• C1 and C2 are constants,
• (ii) x={x1, x2, . . . xi . . . xN} are the concentrations of the N viscosity-affecting components,
• (iii) FC1={FC11, FC12 . . . FC1i . . . FC1N} is a first set of empirical, temperature-independent fitting coefficients, one coefficient for each of the N viscosity-affecting components, and
• (iv) FC2={FC21, FC22 . . . FC2i . . . FC2N} is a second set of empirical, temperature-independent fitting coefficients, one coefficient for each of the N viscosity-affecting components;
• (C) comparing the at least one η,T pair resulting from step (B) with the at least one desired η,T pair;
• and
• (D) repeating steps (A) to (C) as necessary until at least one candidate material is selected in step (A) which gives at least one η,T pair in step (B) which satisfies at least one selected criterion relative to the at least one desired η,T pair, said at least one candidate material being the at least one material expected to have the at least one desired η,T pair.

A method of determining a relationship between temperature T and viscosity η for a material that (i) is a glass or glass-forming liquid and (ii) comprises N viscosity-affecting components, said method comprising:

• (a) measuring the viscosity of a plurality of reference materials at a plurality of temperatures;
• and
• (b) using a programmed computer, fitting a function of the form
• log10 η(T,x)=C1+C2·(f1(x,FC1)/T)·exp([f2(x,FC2)−1]·[f1(x,FC1)/T−1])
• to the measured viscosities of step (a) to determine values for FC1 and FC2, where in said function:
• (i) C1 and C2 are constants,
• (ii) x={x1, x2, . . . xi . . . xN} are the concentrations of the N viscosity-affecting components,
• (iii) FC1={FC11, FC12 . . . FC1i . . . FC1N} is a first set of temperature-independent coefficients, one coefficient for each of the N viscosity-affecting components, and
• (iv) FC2={FC21, FC22 . . . FC2i . . . FC2N} is a second set of temperature-independent coefficients, one coefficient for each of the N viscosity-affecting components,
• said function and the values for FC1 and FC2 determined in step (b) constituting the relationship between viscosity and temperature for the material.

For a material that (a) is a glass or glass-forming liquid and (b) comprises N′ resistivity-affecting components, a method comprising

• (A) using a computer to evaluate an equation which relates resistivity p and temperature T and has the following form:
• log10 ρ(T,x)=Cρ1+Cρ2·(f1(x,FCρ1)/T)·exp([f2(x,FCρ2)−1]·[f1(x,FCρ1)/T−1])
• where
• Cρ1 and Cρ2 are constants,
• (ii) x={x1, x2, . . . xi . . . xN′} are the concentrations of the N′ resistivity-affecting components,
• (iii) FCρ1={FCρ1, FCρ2 . . . FCρi . . . FCρN′} is a first set of empirical, temperature-independent fitting coefficients, one coefficient for each of the N′ resistivity-affecting components, and
• (iv) FCρ2={FCρ1, FCρ2 . . . FCρi . . . FCρN′} is a second set of empirical, temperature-independent fitting coefficients, one coefficient for each of the N′ resistivity-affecting components, and
• (B) using the results of step (A) to provide at least one of:
• (i) a predicted resistivity ρ of the material at a temperature T, and (ii) a predicted temperature T at which the material has a resistivity ρ.

A method for identifying at least one material expected to have at least one desired ρ,T pair, where ρ is resistivity and T is temperature, said method comprising:

• (A) selecting at least one candidate material comprising N′ resistivity-affecting components having selected concentrations, where N′ may be different for different candidate materials;
• (B) using a computer to obtain at least one ρ,T pair for the at least one candidate material of step (A) by evaluating an expression of the form
• log10 ρ(T,x)=Cρ1+Cρ2·(f1(x,FCρ1)/T)·exp([f2(x,FCρ2)−1]·[f1(x,FCρ1)/T−1])
• where
• Cρ1 and Cρ2 are constants,
• (ii) x={x1, x2, . . . xi . . . xN′} are the concentrations of the N′ resistivity-affecting components,
• (iii) FCρ1={FCρ1, FCρ2 . . . FCρi . . . FCρN′} is a first set of empirical, temperature-independent fitting coefficients, one coefficient for each of the N′ resistivity-affecting components, and
• (iv) FCρ2={FCρ1, FCρ2 . . . FCρi . . . FCρN′} is a second set of empirical, temperature-independent fitting coefficients, one coefficient for each of the N′ resistivity-affecting components,
• (C) comparing the at least one ρ,T pair resulting from step (B) with the at least one desired ρ,T pair;
• and
• (D) repeating steps (A) to (C) as necessary until at least one candidate material is selected in step (A) which gives at least one ρ,T pair in step (B) which satisfies at least one selected criterion relative to the at least one desired ρ,T pair, said at least one candidate material being the at least one material expected to have the at least one desired ρ,T pair.

A method of determining a relationship between temperature T and resistivity ρ for a material that (i) is a glass or glass-forming liquid and (ii) comprises N′ resistivity-affecting components, said method comprising:

• (a) measuring the resistivity of a plurality of reference materials at a plurality of temperatures;
• and
• (b) using a programmed computer, fitting a function of the form
• log10 ρ(T,x)=Cρ1+Cρ2·(f1(x,FCρ1)/T)·exp([f2(x,FCρ2)−1]·[f1(x,FCρ1)/T−1])
• to the measured resistivities of step (a) to determine values for FCρ1 and FC92 2, where in said function:
• Cρ1 and Cρ2 are constants,
• (ii) x={x1, x2, . . . xi . . . xN′} are the concentrations of the N′ resistivity-affecting components,
• (iii) FCρ1={FCρ1, FCρ2 . . . FCρi . . . FCρN′} is a first set of temperature-independent coefficients, one coefficient for each of the N′ resistivity-affecting components, and
• (iv) FCρ2={FCρ1, FCρ2 . . . FCρi . . . FCρN′} is a second set of temperature-independent coefficients, one coefficient for each of the N′ resistivity-affecting components,
• said function and the values for FCρ1 and FCρ2 determined in step (b) constituting the relationship between resistivity and temperature for the material.