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Chemistry 4000/5000/6000

Chemical Crystallography

Part 3 - Introduction to X-rays, their generation and interactionwith matter

Multiplicity of powder lineso Thed spacing formulae involve squares of the Miller indices. This has a consequence for the

observedmultiplicityof lines with identicald values. Consider first thecubic crystal system.h k l multiplicity h k l multiplicity h k l multiplicity h k l multiplicity

1 0 0 1 1 0 1 1 1

0 1 0 0 1 1 1 1

0 0 1 1 0 1 1 2 1

2 0 0 2 1 0 1 1 2

0 2 0 1 2 0 2 2 1

0 0 2 2 2 0 2 1 2

{ 1 0 0 } 6 0 2 1 1 2 2

0 2 2 { 1 1 1 } 8

2 0 1

1 0 2

2 0 2

{ 1 1 0 } 12

Sample problem1. Calculate andd values forthe first eight linesin the X-ray powder pattern, using CuK

radiation (1.54184 ), of a primitive cubic substance witha = 5.00. What is the multiplicity ofeach line? Also, calculate the value of (h2 +k2 +l2) for each reflection.

Sample problem1. Calculate andd values forthe first eight linesin the X-ray powder pattern, using CuK radiation

(1.54184 ), of a primitive cubic substance witha = 5.00. What is the multiplicity of each line? Also,calculate the value of (h2 +k2 +l2) for each reflection.

2 2 2

2 2

12 sin 5.00

h k ld a

d a

+ += = =

Miller h2+k2+l2 D() multiplicity{100} 1 5.00 8.87 6{110} 2 3.54 12.6 12{111} 3 2.87 15.5 8{200} 4 2.50 17.6 6210} 5 2.24 20.2 12{211} 6 2.04 22.2 8{220} 8 1.79 25.5 12{221} 9 1.67 27.5 8{300} 9 1.67 27.5 6{310} 10 1.58 29.2 12

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Powder X-ray Diffractometers 1):Systematic Absences

o Instead of a strip of film to collect the diffraction data, a radiation counter is used.o The counter may be of the scintillation counter type, in which the impinging X-ray causes a

photon emission at a phosphor, which is then detected optically this type must be movedwith 2 (located on a suitable mechanical arm)

o Alternatively a fixed area detector is used (measures the whole diffraction pattern in one go.)o Thegeometryis highly reminiscent of the Debye-Scherrercamera, with the sample

contained in a glass or quartz capillary at the middle of the device.o The detectors collectboth geometric and intensity data under computer data collection

control. Output is to a file of 2 vs. intensity or on older instruments to a strip chartrecorder.

Powder Diffractometer with Scintillation Detector

Xray source

Sample mount

Detector

A typical modern powder diffractomter (PANalytical brand)

Detail view of similar instrument

Powder Diffractometer with Area Detector

Detector

Sample mount

Xray source

Probably a sample heating (or cooli ng) device

The Powder Pattern

o The result is a printout of intensity versusangle.

o The example is that of metallic nickel, which isface centred cubic witha = 3.524 .

o This powder pattern can be compared to thefilm produced from an equivalent measurementperformed with a Debye-Scherrer camera,shown below.

o For each line in the film, there is a peak in theprintout.

o Theintensityof the peaks is much easier todiscern than would be the case by comparingfaint and bright lines in the photographic film.

o The hump at the origin is leakage past thebeam stop that is used to collect the directbeam and prevent this strong X-ray beam fromdestroying the highly sensitive counter.

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The International Tables list the conditions for reflectionsto be presentratherthan to be absent. This sort of makes sense because we use the Tables onlyafter we find out what the space group is and we can check the presences.

These are thegeneral conditions for reflections to be present forany crystal ins space group. s st ncu es wt n t t e con t ons or an - att ce

Theseextra conditions for reflections to be present when there are atomsincluded in the special locations. These apply only to atoms which are located inthe special Wyckoff positions.

Thus if onlsome of the atomsare on a special Wyckoffpositions the extra conditionsapply only to thecontributionof those atoms to the totalscattering. Ifallatoms in thelattice are at such positions,then these conditions apply

completely.