Explain why silicate glasses tend to form amorphous glasses, however, metallic melts typically crystallize easily.

Assume that instead of asphericalnucleus, we have a nucleus in the form of a cube of length $x$. Calculate the critical dimension $x^*$ of the cube necessary for nucleation. Write an equation similar to Equation 9-1 for a cubical nucleus, and derive an expression for $x^*$ similar to Equation 9-2.

A $5-\mathrm{cm}$-diameter sphere solidifies in $1050 \mathrm{~s}$. Calculate the solidification time for a $0.3 \mathrm{~cm} \times 10 \mathrm{~cm} \times 20 \mathrm{~cm}$ plate cast under the same conditions. Assume that $n=2$

What is a spherulite?

Define the following terms: nucleation, embryo, heterogeneous nucleation, and homogeneous nucleation.

A 2-in. cube solidifies in $4.6 \mathrm{~min}$. Assume $n=2$. Calculate (a) the mold constant in Chvorinov's rule; and (b) the solidification time for a $0.5$ in. $\times$ $0.5$ in. $\times 6$ in. bar cast under the same conditions.

Why do most plastics contain amorphous and crystalline regions?

Find the mold constant $\mathrm{B}$ and exponent $n$ in Chvorinov's rule using the following data and a $\log -\log$ plot:Determine (a) the time at which solidification begins at the surface and (b) the time at which the entire casting is expected to be solid. (c) Suppose the center of the casting actually solidified in $720 \mathrm{~s}$. Explain why this time might differ from the time calculated in part (b).

Explain the role of nucleation and growth in growing single crystals

Write down Chvorinov’s rule and explain the meaning of each term.

Define the term directional solidification.

Using Equation $9-2$, demonstrate that interfacial energy $\left(\sigma_{s l}\right)$ has units of $\mathrm{J} / \mathrm{m}^2$ in SI.

Consider the tensile stress strain curves in Figure 8-20 labeled 1 and 2 and answer the following questions. These diagrams are typical of metals. Consider each part as a separate question that has no relationship to previous parts of the question.(a) Which of the two materials represented by samples 1 and 2 can be cold rolled to a greater extent? How do you know? (b) Samples 1 and 2 have the same composition and were processed identically, except that one of them was cold worked more than the other. The stress strain curves were obtained after the samples were cold worked. Which sample has the lower recrystallization temperature: 1 or 2 ? How do you know? (c) Samples 1 and 2 are identical except that they were annealed at different temperatures for the same period of time. Which sample was annealed at the higher temperature: 1 or 2 ? How do you know? (d) Samples 1 and 2 are identical except that they were annealed at the same temperature for different periods of time. Which sample was annealed for the shorter period of time: 1 or 2 ? How do you know?

Analysis of a nickel casting suggests that $28 \%$ of the solidification process occurred in a dendritic manner. Calculate the temperature at which nucleation occurred. The specific heat of nickel is $4.1 \mathrm{~J} /\left(\mathrm{cm}^3,{ }^{\circ} \mathrm{C}\right)$