Final answer:
The pair that can be considered to have the same phase is a piece of copper and a piece of nickel, both with face-centered cubic (FCC) structure, as both metals have the same lattice arrangement. Correct option is a. a piece of copper and a piece of nickel, both with fcc structure
Step-by-step explanation:
When considering phases in materials science, we refer to a physically distinct and homogeneous state of matter. Two samples that are in the same phase will have identical structural arrangements or, in the case of metals and crystals, the same lattice structure. In the context of your question, the pairs that can be considered to have the same phase are those that have equivalent crystalline structures.
A face-centered cubic (FCC) structure is one where atoms are arranged in a cubic lattice with atoms at all the corners and at the centers of each face. This closely packed structure is also known as cubic closest packing (CCP) and is found in many metals, including copper and nickel. If both a piece of copper and a piece of nickel have an FCC structure, then they can be considered to have the same phase.
Body-centered cubic (BCC) structures, on the other hand, have atoms at the cube's corners and an additional atom in the center of the cube. Iron at room temperature is known to crystallize in a BCC arrangement, and if two samples of iron one with BCC and one with an FCC structure would not have the same phase.
For grains in a polycrystalline material, such as aluminum, assuming they are both in the same BCC structure, they could be considered the same phase.
In the case of water and ice in a cup, they are not the same phase. Water is in the liquid phase and ice is in the solid phase, despite being chemically identical.
Finally, amorphous silicon dioxide (glass) and crystalline silicon dioxide (quartz) are not the same phase. Glass is amorphous, meaning its constituent particles are not arranged in a defined lattice pattern, whereas quartz has a defined crystalline structure.
Therefore, the pair that can be considered to have the same phase is: a piece of copper and a piece of nickel, both with FCC structure.