We present an investigation of the optical spectra of 264 low-redshift (z < 0.2) Type Ia supernovae (SNe Ia) discovered by the Palomar Transient Factory, an untargeted transient survey. We focus on velocity and pseudo-equivalent width measurements of the Si II 4130, 5972, and 6355 A lines, as well those of the Ca II near-infrared (NIR) triplet, up to +5 days relative to the SN B-band maximum light. We find that a high-velocity component of the Ca II NIR triplet is needed to explain the spectrum in ~95 per cent of SNe Ia observed before -5 days, decreasing to ~80 per cent at maximum. The average velocity of the Ca II high-velocity component is ~8500 km/s higher than the photospheric component. We confirm previous results that SNe Ia around maximum light with a larger contribution from the high-velocity component relative to the photospheric component in their Ca II NIR feature have, on average, broader light curves and lower Ca II NIR photospheric velocities. We find that these relations are driven by both a stronger high-velocity component and a weaker contribution from the photospheric Ca II NIR component in broader light curve SNe Ia. We identify the presence of C II in very-early-time SN Ia spectra (before -10 days), finding that >40 per cent of SNe Ia observed at these phases show signs of unburnt material in their spectra, and that C II features are more likely to be found in SNe Ia having narrower light curves.
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