We present a systematic temporal and spectral study of all Swift-XRT observations of GRB afterglows discovered between 2005 January and 2007 December. After constructing and fitting all light curves and spectra to power-law models, we classify the components of each afterglow in terms of the canonical X-ray afterglow and test them against the closure relations of the forward shock models for a variety of parameter combinations. The closure relations are used to identify potential jet breaks with characteristics including the uniform jet model with and without lateral spreading and energy injection, and a power-law structured jet model, all with a range of parameters. With this technique, we survey the X-ray afterglows with strong evidence for jet breaks (~12% of our sample), and reveal cases of potential jet breaks that do not appear plainly from the light curve alone (another ~30%), leading to insight into the missing jet break problem. Those X-ray light curves that do not show breaks or have breaks that are not consistent with one of the jet models are explored to place limits on the times of unseen jet breaks. The distribution of jet break times ranges from a few hours to a few weeks with a median of ~1 day, similar to what was found pre-Swift. On average Swift GRBs have lower isotropic equivalent gamma-ray energies, which in turn results in lower collimation corrected gamma-ray energies than those of pre-Swift GRBs. Finally, we explore the implications for GRB jet geometry and energetics.
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