What is the mathematical definition of the surface density (SV) of a set of interfaces in a reference space?
Refer to equation (6.1) to see the relationship between area and volume.
What are the simplified dimensions of surface density (SV)?
Think about the relationship between a unit of area in the numerator and a unit of volume in the denominator.
In the equation Sv = 2⋅I/L, what does the term I/L represent?
This term combines an event count with a measurement of the probe’s length.
What condition must be met for the estimator Sv = 2⋅I/L to be unbiased?
Think about the concept of random orientation in three-dimensional space.
In the ‘Fakir’s bed’ analogy, why does the number of holes change if you flatten a ball of putty before dropping it?
Consider which geometric property of the object is altered by stretching or squashing.
Why does a uniform distribution of longitude (ϕ) and colatitude (θ) not result in an isotropic distribution of directions on a sphere?
Imagine the segments of an orange and how their width varies from the top to the middle.
What is the distinctive feature of the ‘Vertical Uniform Random’ (VUR) sections in relation to the chosen vertical axis?
Consider the relationship between the cutting plane, the vertical axis and the horizontal reference plane.
When using vertical sections (VUR), why are cycloid grids used rather than straight lines?
Identify the relationship between the shape of the curve and the weighting required for 3D isotropy.
In practice, how should a cycloid grid be aligned on a micrograph taken from a VUR section?
The text mentions a specific axis of the rectangle enclosing the cycloid arc, which must be aligned with the vertical.
If you have an estimate of the surface density Sv and you know the volume of the reference space V, how do you work out the total surface area S?
Refer to equation (6.2) to see the relationship between density and total quantity.
