The absorption features of sulfate (gypsum and anhydrite) and phosphate (apatite) result from vibrations of the S-O and P-O bonds in the sulfate and phosphate anions, respectively. The strong ionic bonding of the chlorides inhibits independent vibration between the individual diatomic pairs (e.g., Na and Cl) but rather requires the entire crystal lattice to vibrate as a whole.
This figure is from Lane, M.D. and P.R. Christensen, Thermal infrared emission spectroscopy of salt minerals predicted for Mars, Icarus, 135, 528-536, 1998.
CLICK ON IMAGE TO ENLARGE --SOURCE: Arizona State University website: www.mars.asu.edu/~lane/sulfphoschl.html
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