30 Questions
What is the significance of 'magic numbers' in nanometric crystals?
They represent clusters with higher stability than others.
What is the general trend regarding the binding energy (Eb) in a given structure?
It can be estimated based on the packing of spheres into certain shapes.
Why should a structure minimize its surface contribution when considering surface and volume contributions?
To achieve a spherical shape similar to an icosahedron.
What happens to the volume contribution compared to the surface energy as the size of a nanocluster grows?
Volume contribution increases faster than surface energy.
What kind of nanoclusters are likely to become abundant based on their evaporation rates or binding energies?
Clusters with low evaporation rates or strong binding energies.
Which sizes are more abundant among nanoclusters according to the text?
$N=8, 20, 40, 58, 92$
What determines the stability, reactivity, and electronic properties of atoms?
Energy gap between the highest occupied and lowest unoccupied orbital
What is the minimum number of atoms required for icosahedral structures with fivefold symmetry to appear in clusters?
13 atoms
In clusters of atoms, where are the electrons distributed?
Along the bonds formed by the atoms
What defines whether a crystal is semiconducting or insulating?
Overlap between discrete energy levels
Which metal clusters exhibit fivefold symmetry even in clusters with as few as 6 atoms?
Gold (Au)
What type of bonding arises when electrons are delocalized and energy gaps at the Fermi level disappear?
Metallic bonding
What is unique about gold clusters compared to other coinage group metals?
They are chemically inert
At what number of atoms do Au clusters assume a cage structure according to Dr. Bozeya?
14–18 atoms
Which model for a cluster assumes uniform distribution of positive charge and electronic shells for valence electrons?
Jellium model
What type of functions are the wave functions of electrons in a spherical potential well according to the text?
Bessel Functions
What is the distinctive feature of Au20 cluster structure?
(111) surface mimicry
What effect is attributed to the sharp departure of Au cluster geometries from other monovalent simple metal atoms?
Relativistic effects on electronic structure
What type of structure is formed by Au clusters containing 14–18 atoms?
Hollow cage structures
What structure do Al clusters show during growth?
Icosahedric growth
At what size do Au clusters switch from a planar structure to a hollow cage structure?
20 atoms
How do the properties of Al clusters compare to those of Au clusters?
Al clusters exhibit icosahedric growth, while Au clusters show pyramidal growth
When does the Si crystal structure mimic the cage structures discussed?
Around 70 atoms
What is a common characteristic of heteroatomic clusters involving two metals like Au and Al?
Behaving as simple metals
What is the total spin angular momentum, S, for an individual iron atom?
3/2
What is the typical material size for the ferromagnetic to para-magnet phase transition to occur in nanocrystals?
3-50 nm
What happens to the ferromagnetic material when its size is reduced significantly?
It becomes paramagnetic
What is the valence electron configuration of iron in the bcc structure?
3d^7 4s^1
What happens to the spin moments of neighboring atoms in the bcc structure of iron metal?
All of the above
Which of the following materials are used to create monodisperse semiconductor nanocrystals?
Sufides and Selenides of cadmium
Test your knowledge on equilibrium shapes, structural magic numbers, and packing of spheres in nanometric crystals. Explore concepts like icosahedron, octahedron, truncated octahedron, and decahedron structures.
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