The spatial distribution and accessibility of organic matter (OM) to soil microbes in aggregates – determined by the fine-scale, 3-D distribution of OM, pores and mineral phases – may be an important control on the magnitude of soil heterotrophic respiration (SHR). Attempts to model SHR on fine scales requires data on the transition probabilities between adjacent pore space and soil OM, a measure of microbial accessibility to the latter. We used a combination of osmium staining and synchrotron X-ray computed tomography (CT) to determine the 3-D (voxel) distribution of these three phases (scale 6.6 µm) throughout nine aggregates taken from a single soil core (range of organic carbon (OC) concentrations: 4.2–7.7 %). Prior to the synchrotron analyses we had measured the magnitude of SHR for each aggregate over 24 h under controlled conditions (moisture content and temperature). We test the hypothesis that larger magnitudes of SHR will be observed in aggregates with (i) shorter length scales of OM variation (more aerobic microsites) and (ii) larger transition probabilities between OM and pore voxels.

After scaling to their OC concentrations, there was a 6-fold variation in the magnitude of SHR for the nine aggregates. The distribution of pore diameters and tortuosity index values for pore branches was similar for each of the nine aggregates. The Pearson correlation between aggregate surface area (normalized by aggregate volume) and normalized headspace C gas concentration was both positive and reasonably large (r  =  0.44), suggesting that the former may be a factor that influences SHR. The overall transition probabilities between OM and pore voxels were between 0.07 and 0.17, smaller than those used in previous simulation studies. We computed the length scales over which OM, pore and mineral phases vary within each aggregate using 3-D indicator variograms. The median range of models fitted to variograms of OM varied between 38 and 175 µm and was generally larger than the other two phases within each aggregate, but in general variogram models had ranges  <  250 µm. There was no evidence to support the hypotheses concerning scales of variation in OM and magnitude of SHR; the linear correlation was 0.01. There was weak evidence to suggest a statistical relationship between voxel-based OM–pore transition probabilities and the magnitudes of aggregate SHR (r  =  0.12). We discuss how our analyses could be extended and suggest improvements to the approach we used.