Chapter 4: Problem 7
Which of the following systems (i.e., pair of metals) would you expect to exhibit complete solid solubility? Explain your answers. (a) \(\mathrm{Cr}-\mathrm{V}\) (b) \(\mathrm{Mg}-\mathrm{Zn}\) (c) \(\mathrm{Al}-\mathrm{Zr}\) (d) \(\mathrm{Ag}-\mathrm{Au}\) (e) \(\mathrm{Pb}-\mathrm{Pt}\)
Short Answer
Expert verified
Answer: (a) Cr-V and (d) Ag-Au
Step by step solution
01
Analyze Cr-V system
For Cr and V, both having a similar atomic radii and both being elements found in the same group in the periodic table, they have the same crystal structure (BCC). Also, the difference in atomic radii is less than 15%, and the electronegativity difference is small. Thus, we can expect the Cr-V system to exhibit complete solid solubility.
02
Analyze Mg-Zn system
Mg and Zn have different crystal structures (Mg: HCP, Zn: HCP) and a difference in atomic radii greater than 15%. Moreover, the electronegativity difference is relatively large. Hence, the Mg-Zn system would not exhibit complete solid solubility.
03
Analyze Al-Zr system
Al and Zr have different crystal structures (Al: FCC, Zr: HCP) and a difference in atomic radii greater than 15%. The electronegativity difference is also relatively large. Thus, the Al-Zr system would not exhibit complete solid solubility.
04
Analyze Ag-Au system
Ag and Au share the same crystal structure (FCC), have a difference in atomic radii less than 15%, and have a small electronegativity difference. Therefore, we can expect the Ag-Au system to exhibit complete solid solubility.
05
Analyze Pb-Pt system
Pb and Pt share the same crystal structure (FCC), but the difference in atomic radii is greater than 15%. Moreover, the electronegativity difference is relatively large. Hence, the Pb-Pt system would not exhibit complete solid solubility.
Based on the analysis of the different systems, we can conclude that the following systems would exhibit complete solid solubility:
(a) Cr-V
(d) Ag-Au
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Atomic Radii
Understanding atomic radii is crucial when discussing the solubility of different metals in each other. The atomic radius is roughly the distance from the atomic nucleus to the outer perimeter of the electron cloud.
When two metals have similar atomic radii, they can more easily fit into each other's crystal lattice without causing distortion. This is particularly important in solid solutions, where the atoms of one metal must occupy positions in the crystal lattice of another.
When two metals have similar atomic radii, they can more easily fit into each other's crystal lattice without causing distortion. This is particularly important in solid solutions, where the atoms of one metal must occupy positions in the crystal lattice of another.
Importance in Metal Solubility
One of the Hume-Rothery rules for complete solid solubility is that the atomic radii difference between the two metal species should not exceed 15%. This rule arises because significant size differences lead to distortions that can cause strains within the crystal lattice and result in a limited solubility.- In the case of the Cr-V system, the similar atomic radii suggest a high probability for complete solid solubility.
- Conversely, in systems such as Mg-Zn or Al-Zr, where the atomic radii differ significantly, complete solid solubility is not typically observed.
Crystal Structures of Metals
The crystal structure of a metal refers to the arrangement of atoms in a crystalline lattice. Common structures include Face-Centered Cubic (FCC), Body-Centered Cubic (BCC), and Hexagonal Close-Packed (HCP).
Impact on Solubility
The similarity in crystal structures between two metals is pivotal for solid solubility. If two metals are to form a homogeneous solid solution, their atoms must seamlessly integrate into each other's lattice without disrupting the overall structure.- The Ag-Au pair shares an FCC crystal structure, promoting a favorable interaction between their lattices.
- In contrast, the Mg-Zn pair, despite both having an HCP structure, fail to exhibit complete solubility due to other factors that interfere, such as atomic radii discrepancy and electronegativity differences.
Hume-Rothery Rules
The Hume-Rothery rules are a set of guidelines used to predict whether two metals will be completely soluble in each other in the solid state. These rules are based on certain key factors:
It's noteworthy that these rules, while helpful, are not absolute. There are exceptions due to the complexity of metallic bonding and crystal formation. Yet, they are instrumental in predicting solubility trends, which is essential for alloy design and materials science applications.
- Atomic Size Factor: The atomic radius should not differ by more than 15%.
- Crystal Structure: The participating metals should have the same crystal structure.
- Electronegativity: The difference in electronegativity between the metals should be minimal to avoid compound formation.
- Valency: The metals should preferably have the same valency to maintain a uniform distribution of electrons in the structure.
Application
By applying the Hume-Rothery rules, we can better comprehend why certain metal systems, like Ag-Au and Cr-V, allow for complete solid solubility. These systems conform to the rules and thus do not introduce significant lattice strain or form intermetallic compounds, which would otherwise limit solubility.It's noteworthy that these rules, while helpful, are not absolute. There are exceptions due to the complexity of metallic bonding and crystal formation. Yet, they are instrumental in predicting solubility trends, which is essential for alloy design and materials science applications.