In an XRD pattern using Cu Kα radiation, a certain cubic crystal shows peaks at 2θ...

In an XRD pattern using Cu Kα radiation, a certain cubic crystal shows peaks at 2θ values (in degrees) of 44.3, 64.4, 81.6, 98.0. It is known that the size of the cubic crystal is greater than 2.5 Angstroms. Based on this information and the location of the peaks, we conclude that the lattice of the crystal is

1. simple cubic 2. face centered cubic

3. body centered cubic 4. none of the other choices

Expert Solution

The Bragg's law of crystal diffraction gives

For an (hkl) plane in a cubic crystal,

Considering only n = 1 mode,

For each structure, the possible h,k,l values for diffraction is different.

To find the crystal structure, we have to make the following table.

2 theta	Theta	sin(theta)	sin^2(theta)	m = sin^2(theta)/sin^2(theta(min)	*2m**	*3m**
44.3	22.15	0.3768511	0.142016782	0.999999999	2	3
64.4	32.2	0.5326352	0.283700221	1.997652794	3.995306	5.992958
81.6	40.8	0.6531473	0.426601376	3.003880034	6.00776	9.01164
98	49	0.7544251	0.569157188	4.007675572	8.015351	12.02303

Once we make this table, if the row containing m appears as continuous counting numbers (approximately), the crystal structure is simple cubic

If the row 2*m is showing this property, the crystal is BCC and FCC for 3*m

Here, the periodic nature is there for m itself. So, the crystal structure is simple cubic.

genius_generous answered 1 year ago

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