Comparison: metals vs alloys; composites ：練習問題

Pure gold (\( 24 \)-carat) has a density of \( 19.3 \text{ g cm}^{-3} \). When it is alloyed with copper (density \( 8.9 \text{ g cm}^{-3} \)) to create \( 18 \)-carat gold, how do the density and hardness of the resulting material compare to pure gold?

A composite material is engineered by embedding ceramic particles (density \( 3.50 \text{ g cm}^{-3} \)) into a polymer matrix (density \( 1.20 \text{ g cm}^{-3} \)). If the final composite consists of \( 40 \% \) ceramic and \( 60 \% \) polymer by volume, calculate the theoretical density of the composite material.

Which of the following statements best compares the malleability of a pure metal to that of an interstitial alloy formed from it?

When carbon is added to iron to form steel, an interstitial solid solution is formed. How does this addition typically affect the unit cell of the iron lattice?

In dental applications, composite resins are used for fillings. These composites usually consist of a polymer matrix (such as BIS-GMA) and inorganic fillers (like silica). Why is the volume fraction of the inorganic filler carefully controlled to be as high as possible?

Compare the melting point of an alloy like solder to its constituent metals, tin and lead, and explain this difference in terms of atomic structure and the regularity of the metallic lattice.

Analyze the difference between a substitutional alloy and an interstitial alloy regarding their atomic packing, and explain why the introduction of relatively small atoms into interstitial sites typically leads to a more significant reduction in ductility compared to substituting atoms of similar size.

Bronze is significantly less malleable than pure copper. State the structural reason for this change in property and explain how the presence of tin atoms affects the movement of atomic layers within the metallic lattice.

Iron exhibits different metallic crystal structures depending on environmental conditions. One common structure is the body-centered cubic (bcc) arrangement.
(a) Determine the coordination number of an iron atom in a bcc unit cell.
(b) Calculate the total number of iron atoms contained within a single bcc unit cell.
(c) Steel is an alloy produced by adding carbon to iron. Explain, in terms of the arrangement of atoms, why steel is typically harder and less malleable than pure iron.

A composite material consists of a matrix and a reinforcement.
(a) Using glass-reinforced plastic (GRP) as an example:
(i) Identify the matrix and the reinforcement.
(ii) Explain how the combination of these two components results in a material that is superior to the individual components in terms of strength-to-weight ratio and brittleness.
(b) Reinforced concrete is another common composite. Explain why it is important for the steel rods and the concrete to have similar coefficients of thermal expansion.