Hydroxyapatite (HAp) is the premier building block for biomineralized tissues. I

Question

Hydroxyapatite (HAp) is the premier building block for biomineralized tissues. It comes in many sizes, shapes, and flavors based on how it was made (synthesis conditions) and what its intended purpose is (structural reinforcement, mineral storage bank, etc). In order to better understand its vital role in hard tissue (bone and teeth) as well as an additional assortment of biologically relevant subjects such as cancer metastasis, biological activity and adsorption phenomena related to extracellular matrix (ECM) proteins and pathological calcification, it is imperative to be able to measure fundamental properties related to its chemical and physical properties. It is also important to be able to navigate within its time and space domain to unravel the intricacies and mysteries of its structure and purpose. Imagine that you partner with Antman and you co-develop a machine that allows you to shrink to atomic scale dimensions and you are able to move within a single crystal of HAp. Imagine what you would be able to see and experience as you navigate throughout the crystal and measure the boundaries of the crystal?

Please answer the following questions regarding hydroxyapatite. Please show all work.

How many atoms are in the unit cell for Hap?

What are the unit cell parameters? Please use the attached diagram to determine.

Calculate the unit cell volume for HAp.

Calculate the density for HAp.

Calculate the packing factor for HAp.

Derive an equation for calculating the specific surface area for hydroxyapatite particles consisting of unit cell dimension particles. Calculate the value for the specific surface area of these particles in meters squared per gram (m^2/g). What is interesting about the magnitude of this number?

How would you differentiate between a polycrystalline, a single crystalline, and a nanocrystalline sample of HAp?

Explanation / Answer

As you have not provided the figure, I am giving the general solution to solve this question.

Suppose that the unit cell length is denoted by a.

Ca5(PO4)3(OH) is the molecular formula for HAp, but the unit cell contains 2 units of HAp, so unit cell is generally represented by Ca10(PO4)6(OH)2.

Thus the unit cell contains total (10+6+24+4) = 44 atoms

MW of HAp is 1004.6 g/mol

So mass contained in a unit cell = m = 1004.6*2/NA grams ,where NA is avogadro's number.

So the density is mass per unit volume = m/a3

HAp crystallizes in a HCP structure so it should have a packing fraction of 0.74, but experimental results show that it crystallizes with a packing fraction of 0.67

I have looked for the data and am providing you the answers below :

Density = 3.15 g/cm3

Specific surface area = 18.3 m2/g

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