Step 1: Understanding the Question:
The question asks to select the specific scientific instrumentation technique employed to investigate, solve, and accurately determine the internal atomic crystal lattices of a solid substance.
Step 2: Detailed Explanation:
Let us review the primary functions of each analytical option provided:
Scanning electron microscope (SEM): Primarily captures high-resolution topographic images of a specimen's surface morphology rather than mapping internal atomic spacing.
FTIR spectrophotometer (Fourier-Transform Infrared): Used to scan vibrational modes within chemical groups to identify functional bonds and molecular structures.
X-ray diffractometer (XRD): Operates directly on the fundamental principles of Bragg's Law:
$$ 2d\sin(\theta) = n\lambda $$
When a highly coherent beam of monochromatic X-rays hits a crystalline solid grid, the neatly spaced atomic planes scatter the waves, creating distinctive constructive interference arrays. Measuring these distinct diffraction patterns allows researchers to precisely measure interplanar distances ($d$) and reconstruct the entire three-dimensional crystal architecture.
Transmission electron microscope (TEM): Passes electron streams through ultra-thin samples to capture exceptional microstructural and internal morphological views, but it is not the baseline instrument dedicated to structural crystallographic matrix determinations.
Therefore, an X-ray diffractometer is the dedicated instrument for determining crystal structures.
Step 3: Final Answer:
The proper instrument configuration matches option (C).