powder X-ray diffraction
Growing one flawless crystal is hard, so powder diffraction takes the opposite route: grind the sample to a fine powder of millions of tiny crystallites, each pointing a different random way. Now for any given family of atomic planes, there are always some crystallites turned to just the right angle to satisfy Bragg's law. Those planes fire diffracted rays out along a cone around the beam (a Debye-Scherrer cone), and a detector sweeping round records each cone as a peak.
The randomness has a beautiful consequence. A single crystal would give a full three-dimensional constellation of spots; averaging over every orientation collapses that 3D reciprocal lattice down to a simple one-dimensional list — just the set of plane spacings d, with no direction left. The detector scans the angle 2-theta, and each plane family with spacing d produces a peak whose position obeys Bragg's law, lambda = 2 d sin(theta). What you draw is intensity versus 2-theta: a row of peaks, the powder pattern.
Powder XRD is fast, cheap, needs no single crystal, and is the everyday tool for identifying which crystalline phases are present, measuring lattice parameters, estimating crystallite size from peak width, and — via Rietveld refinement — extracting full structural detail. Be honest about its main limitation: collapsing 3D to 1D throws information away, so different peaks can pile up on top of each other (overlap), and preferred orientation of non-spherical grains can distort the intensities. Solving a brand-new structure from powder alone is real work, not a readout.
Table salt (NaCl) powder in a Cu K-alpha beam gives its first strong peak near 2-theta = 31.7 degrees, from the (200) planes with d = 2.82 angstrom — the same pattern for any salt sample, which is why the pattern is a fingerprint.
Random crystallite orientations turn a 3D reciprocal lattice into a 1D list of peaks versus 2-theta.
Good powder data need many tiny, randomly oriented crystallites. Too few large grains give spotty, unreliable intensities; platy or needle-like grains lie down preferentially and skew the pattern.