Chapter 1: Problem 16
Which one of the following is not a close packed arrangement? (a) bcc (b) \(\mathrm{ccp}\) (c) hcp (d) All of these
Short Answer
Expert verified
Choice (a) bcc is not a close packed arrangement.
Step by step solution
01
Understanding Close Packing in Crystals
Close packing in crystals refers to the efficient arrangement of atoms within a solid material. The term 'close packed' implies that the atoms are packed together as closely as possible. The two most common types of close packing are face-centered cubic (fcc) or cubic close-packed (ccp) and hexagonal close-packed (hcp).
02
Analyze Choice (a) - bcc
Body-centered cubic (bcc) structure has atoms at each corner of a cube and a single atom at the center of the cube. This arrangement does not allow for the atoms to be packed as efficiently as possible, as there are fewer atoms per unit cell compared to ccp and hcp structures.
03
Analyze Choices (b) and (c) - ccp and hcp
The ccp or fcc and hcp structures are both types of close-packed structures. In ccp, atoms are arranged in a sequence of layers of a three-dimensional pattern (ABCABC...). Similarly, in hcp structures, atoms are arranged in a pattern (ABAB...), which also represents close-packed layers.
04
Identify the Non-close Packed Arrangement
Due to the layer arrangement and the number of atoms per unit cell, both ccp and hcp are considered as close-packed structures, while bcc, with less efficient packing, is not considered close packed. Hence, bcc is the correct choice for a non-close packed arrangement.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Body-Centered Cubic (BCC)
The body-centered cubic (bcc) arrangement in crystals distinguishes itself from close-packed structures by the unique position of its atoms. Imagine a cube where each corner has an atom, and there is a single atom positioned right in the center of the cube. This setup creates a type of lattice that is not as tightly packed as others, reducing the overall efficiency of the arrangement.
A key point to remember is that the bcc structure has a coordination number of 8, meaning each central atom is in direct contact with 8 surrounding atoms, versus the 12 atoms in close-packed structures. This factor contributes to the bcc not being as dense as its ccp or hcp counterparts.
In practical terms, the bcc structure is common among metals such as iron at certain temperatures, which explains the metal's properties in its alpha phase. Despite being an important crystal arrangement in the world of materials science, bcc falls short in the race for maximum packing efficiency.
A key point to remember is that the bcc structure has a coordination number of 8, meaning each central atom is in direct contact with 8 surrounding atoms, versus the 12 atoms in close-packed structures. This factor contributes to the bcc not being as dense as its ccp or hcp counterparts.
In practical terms, the bcc structure is common among metals such as iron at certain temperatures, which explains the metal's properties in its alpha phase. Despite being an important crystal arrangement in the world of materials science, bcc falls short in the race for maximum packing efficiency.
Cubic Close-Packed (CCP)
Cubic close-packed (ccp), often interchangeable with the term face-centered cubic (fcc), represents one of the most ideally packed structures in crystallography. Atoms in ccp configurations are arrayed in consecutive layers, following a repeat pattern often denoted as ABCABC... This implies that the third layer is a direct copy of the first, creating a three-dimensional, tessellating pattern of atoms.
Each atom in a ccp lattice is surrounded by 12 other atoms, which marks a coordination number of 12—the highest for any elemental crystal structure. This high coordination number clarifies why ccp is considered highly efficient in terms of packing.
Common materials with ccp structure include metals like copper, aluminum, and silver, which are known for their good electrical and thermal conductivity. These properties are in part due to the close-packing and symmetry of the ccp structure, which allows for easier movement of electrons.
Each atom in a ccp lattice is surrounded by 12 other atoms, which marks a coordination number of 12—the highest for any elemental crystal structure. This high coordination number clarifies why ccp is considered highly efficient in terms of packing.
Common materials with ccp structure include metals like copper, aluminum, and silver, which are known for their good electrical and thermal conductivity. These properties are in part due to the close-packing and symmetry of the ccp structure, which allows for easier movement of electrons.
Hexagonal Close-Packed (HCP)
In a hexagonal close-packed (hcp) structure, atoms are arranged in a way that might remind us of a sandwich pattern—where layers labeled 'A' and 'B' alternateback and forth (ABAB...). Just like ccp, hcp is a model of efficiency in atomic packing, with each atom surrounded by 12 neighbors, maintaining that high coordination number that signifies close packing.
A distinct feature of hcp is its two-layer repeat pattern, which creates a hexagonal symmetry when viewed down the c-axis. This means that unlike cubic structures, hcp has an anisotropic characteristic—meaning its properties can vary depending on the direction of measurement.
Metals like magnesium, titanium, and zinc crystallize in the hcp structure, and their mechanical properties, such as high strength-to-weight ratios, can often be attributed to the nature of this close-packed arrangement.
A distinct feature of hcp is its two-layer repeat pattern, which creates a hexagonal symmetry when viewed down the c-axis. This means that unlike cubic structures, hcp has an anisotropic characteristic—meaning its properties can vary depending on the direction of measurement.
Metals like magnesium, titanium, and zinc crystallize in the hcp structure, and their mechanical properties, such as high strength-to-weight ratios, can often be attributed to the nature of this close-packed arrangement.