# Packaging Particles: Hexagonal vs. Cubic vs. Body Centred

• m0286
In summary, the hexagonal lattice has the least efficient arrangement of atoms, and the body-centred space lattice has the most efficient arrangement of atoms.
m0286
**see attached file for image**
Sorry to post again so soon but I am having troubles with a new question...
With hexagonal closest packaging, cubic closest packaging and body centred... which of these three types of packaging has the least efficient arrangement of atoms, and why?

Though I do not know forsure, since my book has literally taught me NOTHING on this subject.. by looking atthe pictures and volumes (if they were put into a tight box) I would say hexagonal is the least effieient, since it holds 13 atoms, as does cubic packaging... however the volume of the hexagonal packaging would be larger than the cubic packaging. (assuming 1 unit per sphere- hexagonal 27, and cubic- 18.75 (since not all spehere take up a full space of the sphere due to the pattern. The body-centred only holds 12, and has a smaller volume of 12. I am really confused about this topic, quite possibly I am going about this ALL wrong.. If anyone could help you'd be AWESOME! THANKS A LOT!

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Draw the 3d close-packed structures of the 3 bravais lattices. Assume the radius of the atom (sphere) is r and calculate the volume of the unit cell in terms of r. Divide this volume by the total volume of the number of atoms in a unit cell ($n \cdot (4/3)\pi r^3$). The inverse of the above ratio will be a number independent of r and is a number called the packing fraction or density and it tells you the effiiciency of close packing.

1 - (this number) = fraction of the volume that is unoccupied.

Calculate the packing density for the hexagonal, fcc and bcc structures and compare them. There's a little bit of tricky 3d geometry involved in the case of the hexagonal unit cell...but we'll cross that hurdle when we get to it.

Last edited:
doing the same experiment...i don't get it either:(

Are you actually doing an experiment, or are you trying to do a calculation? What exactly don't you get?

i don't get the questions they are asking:
- Which of these types of packing has the least efficient arrangement of atoms? Justify your answer

i think itz the body centered space lattice...buh i don't know why..coz maybe it seems to have more space

- How do the two more efficient forms of packing compare regarding volume?
totally confused on this one..

- State the co-ordination number of each of the type of paking, i.e., what is the number of neighbours touching each atom in an infinite array of space lattices?

don't know thsi one..

## 1. What are packaging particles and why are they important?

Packaging particles refer to the way atoms or molecules are arranged in a solid material. They play a critical role in determining the properties and behavior of the material, such as its strength, density, and melting point. Understanding the different types of packaging particles is important for various fields of science, including materials science, chemistry, and physics.

## 2. What is the difference between hexagonal, cubic, and body-centred packaging particles?

The main difference between these three types of packaging particles lies in the way the atoms or molecules are arranged in space. In hexagonal packaging, the particles are arranged in a hexagonal lattice structure, while in cubic packaging, they are arranged in a cubic lattice structure. In body-centred packaging, there is an additional atom or molecule at the center of the lattice, resulting in a more compact structure.

## 3. How do these different types of packaging particles affect the properties of a material?

The type of packaging particles greatly influences the properties of a material. For example, hexagonal packaging tends to result in a stronger and more dense material, while cubic packaging can lead to a more ductile material. Body-centred packaging can result in a combination of both strength and ductility. Additionally, the type of packaging particles can also affect the thermal and electrical conductivity of a material.

## 4. What are some real-world applications of hexagonal, cubic, and body-centred packaging particles?

Hexagonal packaging particles are commonly found in materials like graphite and some metals, making them useful for applications such as building materials, electronics, and batteries. Cubic packaging is often found in metals and ceramics, making it useful for structural applications in construction and engineering. Body-centred packaging is found in materials such as iron, which is used in the production of tools and machinery.

## 5. How can scientists control and manipulate the type of packaging particles in a material?

Scientists can manipulate the type of packaging particles in a material through various methods, such as changing the temperature or pressure during the material's formation, or by adding different elements or compounds to the material. They can also use advanced techniques such as crystal growth or thin film deposition to precisely control the arrangement of particles. Understanding and controlling the type of packaging particles is crucial for designing and creating new materials with desired properties for specific applications.

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