Soil material used in this study was sampled from a Podzol developed on granitic parent material under spruce forest in central Germany (Schrumpf et al., 2013, 2021). This soil was selected because it was already known to have large differences in 14C content between density fractions (Schrumpf et al., 2021) and because of strong depth-dependent differences in stabilization processes in Podzol A and B horizons (De Coninck, 1980). Surface (0–10 cm) and subsoil (30–50 cm) samples were subjected to laboratory fractionations described in detail by Schrumpf et al. (2013). Briefly, soils first underwent density separation using dense sodium polytungstate solution (SPT) (1.6 g cm-3). Suspended OM was separated from denser material that did not float using centrifugation. The floating free particulate OM (FPOM) fraction was collected and rinsed to remove remaining SPT solution. The sinking fraction was dispersed again in 1.6 g cm-3 solution, sonicated to disrupt aggregates, and then centrifuged. After centrifugation, floating material from the supernatant was collected, rinsed, and designated as occluded particulate organic matter (OPOM). The remaining dense material in the sediment was repeatedly rinsed to remove SPT solution and is designated mineral-associated organic matter (MOM).

Two chemical fractionations were performed in parallel on the MOM fraction, as described by Schrumpf et al. (2021). The first subsample was extracted with NaF–NaOH to solubilize and remove all potentially desorbable SOM complexed with minerals through pH increase and competition with OH and F anions (Kaiser et al., 2007; Mikutta and Kaiser, 2011). Briefly, 125 mL of a NaF–NaOH solution was added to 25 g MOM material, agitated overnight, and centrifuged. The supernatant was extracted, and an additional 125 mL of NaF–NaOH was added to repeat this process four times in total. Then, each extraction was filtered through glass fiber filters and combined. The remaining soil material was washed with deionized water and freeze-dried.

The second chemically treated MOM underwent strong oxidation in heated hydrogen peroxide (H2O2) to isolate the most resistant and oldest OM (Helfrich et al., 2007; Jagadamma et al., 2010). In this procedure, 60 mL H2O2 was added to a mixture of 2 g MOM and 20 mL deionized water. Samples were then heated and periodically stirred in a 50 ∘C water bath for a total of 120 h. Samples were then centrifuged, washed with deionized water, freeze-dried, and homogenized with a ceramic ball mill.

Oxidative thermal fractionation of bulk SOM and physically and chemically separated fractions was performed using an Elementar soli TOC cube carbon analyzer. Samples were not analyzed under pyrolytic conditions, as pyrolysis can produce charring artifacts, and 14C distributions have been shown to be comparable between operational modes (Williams et al., 2014; Grant et al., 2019). The design of the instrument used is very similar to those used in previous thermal fractionation publications (Rosenheim and Galy, 2012; Bianchi et al., 2015). Primarily, it consists of two ovens in sequence, a mechanical arm to hold and manipulate the sample container, and a non-dispersive infrared analyzer (NDIR) to measure the CO2 concentration in the gas exiting the ovens. The sample is introduced to the first oven, which is heated at a constant rate under a constant flow of carrier gas supplied through the sampler arm (78 % N2, 22 % O2). The second oven contains a Pt catalyst held at 800 ∘C that ensures all C released from the sample is oxidized to CO2. The carrier gas then passes through a glass tube filled with brass wire at 20 ∘C to remove HCl from acidified samples (note that no samples were acidified in this experiment) followed by a glass tube containing magnesium perchlorate to remove water vapor. Finally, the CO2 concentration in the gas mixture is measured by the NDIR (DIN 19539).

Several additional procedures were required to adapt the use of the commercial device for the collection of C released by thermal fractionation. Due to the relatively large sample size (> 1g of dried soil or fraction) required to collect small thermal fractions with sufficient C for radiocarbon measurement, as well as the high flow rate of carrier gas in this instrument, samples with high C content (such as standards or FPOM/OPOM fractions) were diluted to ∼ 2 % (by weight) C with pre-combusted sand (1000 ∘C for 10 h) to prevent ignition and charring during heating. An artificial soil standard was analyzed with different sand dilutions to ensure that thermograms were not altered by dilution with sand (Fig. S1). Further, the sample oven was designed for rapid heating (up to 110 ∘C min-1), and temperatures were observed to be less stable at slower heating rates. To reduce the cycles of on/off oven cycling while ensuring thermogram consistency (with sand dilution), samples were heated at 15 ∘C per minute.

To collect CO2 for isotope analysis, a custom collection manifold was attached to the instrument outflow port (Figs. S2–S4). The manifold consists of parallel glass CO2 traps submerged in LN2 under vacuum. Exhaust gas released within a desired temperature range (thermal fraction) flows through a cold trap until the desired upper temperature is reached. Then, the trap is closed and the next opened to collect the next CO2 fraction. This process is repeated for each thermal fraction (F1 (first thermal fraction) - Fmax (highest temperature thermal fraction); see Supplement Tables S1 and S2). A vacuum pump together with a capillary restriction upstream of the manifold was used to reduce the overall pressure in the manifold system to < 6 mbar to improve cryotrapping efficiency and to prevent condensation of O2 in the LN2 traps.

Traps with CO2 samples were subsequently transferred to a vacuum line where the CO2 was further purified (see below) and measured volumetrically for comparison (calibration) of the NDIR CO2 analysis. An aliquot was taken for analysis of δ13C using a modified GasBench inlet to a continuous flow isotope ratio mass spectrometer (IRMS; Wendeberg et al., 2013). In addition to CO2, we noticed that nitrogen oxide gasses (including N2O3, which is dark blue when frozen) were visibly trapped. These gasses are produced by the reaction of N2 and O2 at high temperatures. As these, as well as S oxides that also freeze with CO2 at liquid nitrogen temperatures, can cause graphitization failure, we used an additional purification procedure to remove them. An amount of sample CO2 representing approximately 0.5 mg C was transferred cryogenically and then sealed under vacuum in a pre-combusted borosilicate tube containing ∼ 50 mg CuO and ∼ 10 mg Ag (Hemingway et al., 2017) and baked at 525 ∘C for 1 h. Purified CO2 released after breaking this tube was graphitized using zinc reduction (Xu et al., 2007) and measured at the Keck AMS lab at the University of California Irvine. Resulting radiocarbon data are expressed as fraction modern (Fm).

Thermograms and activation energy (Ea) were analyzed using the open-source “rampedpyrox” Python package (Hemingway, 2017; Hemingway et al., 2017). For each thermogram, a distributed Ea model derived from time–temperature C-release data is solved inversely to produce a continuous distribution of Ea (in kJ mol-1). It assumes a finite set of n components (thermal fractions) in order of increasing temperature, referred to as F1-Fmax, where Fmax is thermal Fn, the highest temperature range collected (Supplement Tables S1 and S2) in superposition to construct the bulk soil E distribution. Each of these components can thus be mathematically assigned a mean Ea (μE) and standard deviation (σE). Here, standard deviation describes the variance of distribution of E or the heterogeneity of the bonding environment within a thermal fraction or sample rather than data variance. Thus, direct comparisons can be made between the E distribution within a thermal fraction and its isotopic composition. However, it should be noted that such Ea descriptors derived from thermograms are not necessarily comparable to other methods of measuring Ea (Feng and Simpson, 2008; Hemingway et al., 2019).

We compared the thermograms and the isotopic (14C and 13C) signatures of CO2 released as a function of temperature for each physical and chemical fraction individually and then compared the summed contribution of each physical and chemical fraction to the bulk soil (for density fractions) or MOM (for chemical fractions) to assess (1) the behavior of each of the different fractions and (2) how much each fraction contributes to the bulk thermogram at different temperature intervals.

All density and chemical fractions and bulk soil released 90 %–98 % of their total C between 150 and 500 ∘C. No fraction had a unique thermal signature (Fig. 1a, b), and the thermograms mostly overlapped, with some C released across the whole temperature range of combustion. However, differences were observed among density fraction thermograms. For particulate fractions (FPOM and OPOM), C release displayed one or two muted peaks and most of the C was oxidized between 250 and 450 ∘C. MOM and chemical residues released most of their C between 250 and 350 ∘C but also released more C at temperatures > 500 ∘C compared to FPOM and OPOM fractions. Since most bulk soil C is in the MOM fraction (Table 1), thermograms for the bulk soil resemble those of the MOM fractions in both depths (Fig. 1a).

Mean activation energy (μE) estimated from thermograms of bulk soil and fractions ranged from 133.5 to 137.8 kJ mol-1 in surface soil and 137.9 to 144.3 kJ mol-1 in subsoil (Table 1, Supplement Figs. S1 and S2, Tables S1 and S2). Between depths, μE was greater in subsoil than surface soil on average by 5.2 kJ mol-1 (p=0.01, paired t test) for all samples except NaF extraction residues, which showed no difference. In subsoil, particulate fractions FPOM and OPOM μE values were ∼ 3–6 kJ mol-1 greater than bulk soil and MOM but showed little difference in surface soils. The standard deviation of E (σE), a metric of bond strength heterogeneity, only varied with depth among chemical fraction residues which were ∼ 5–6 kJ mol-1 greater in subsoil, suggesting greater diversity of bonds in the subsoil fractions (Hemingway et al., 2017). Thus, despite large differences in the chemistry and relationship to mineral surfaces, the Ea range was similar across all chemical and physical fractions. It is puzzling that NaF and H2O2 residues had lower activation energies than might be expected given that they represent the most “recalcitrant” C resistant to harsh chemical treatments.

The mean radiocarbon (14C, expressed as Fm) differed for each density or chemical residue fraction (Table 1). For a given soil depth, the FPOM had the highest 14C content, consisting mostly of C fixed since the 1960s (Fm > 1.0), while the lowest 14C was in the residue after H2O2 treatment of the MOM. The 14C of the bulk soil and each fraction decreased from the 0–10 to 30–50 cm depth, and the overall pattern of Fm for the different physical and chemical fractions (FPOM > OPOM > MOM> NaF residue > H2O2 residue) remained the same.

Within all fractions, the Fm of released CO2 stayed similar or declined as the temperature increased (Fig. 2; temperatures of combustion are converted to Ea in Fig. 3). In both Figs. 2 and 3, the large differences in 14C between the other FPOM density and chemical fractions far exceed the range of Fm released across temperatures during combustion of the individual fractions. Indeed, as reported by Schrumpf et al. (2021), much of the combusted C from MOM fractions had very similar 14C signatures (small range of Fm), except for the highest Ea fractions of MOM and bulk soil.

For the bulk soil and MOM fraction in the surface sample and FPOM fractions at both depths, the C oxidized at the lowest temperature had Fm > 1, indicating that a portion of the C in the fraction was fixed mostly in the last 60 years. For the FPOM fractions with Fm > 1, 14C values are not as simply related to the “age” of the C. For example, the most recently fixed C could have lower values than the mean but so could older C if that is a mixture of pre- and post-bomb C. For all samples other than FPOM, the decline in Fm 14C indicates a clear trend of increasing age (decreasing Fm, indicating more time for radioactive decay of 14C) especially at temperatures above that where most C was released (Fig. 2). The highest-temperature thermal fractions (Fmax, mostly 450–800 ∘C; Supplement Tables S1 and S2) of surface bulk soil and MOM were similarly depleted in 14C and much older than any other values measured (Fig. 2).

In subsoils (30–50 cm), bomb 14C was found only in the FPOM fractions, so the decline in 14C with energy was determined mostly by the much lower 14C of C released at high temperatures (Fig. 3). All fractions except the NaF residue (NAF Res.) increased in Fm from the C collected in F1 and F2 (and F3 in bulk soil) temperature ranges (140–375 ∘C), followed by decreases at increasingly higher temperatures. Excluding FPOM and OPOM, all fractions decreased significantly in Fm in Fmax compared to the temperature range previous.

The chemical fractionation residues contained C with lower Fm than the unextracted MOM at all temperature ranges except in the highest temperature range collected. However, the highest temperature fraction collected for the MOM was greater (505–750 ∘C) because insufficient C evolved from the chemical fraction residues in this range (Fig. 3). Thermograms for the chemical residues follow a similar pattern to those of MOM, with a small amount of younger but chemically resistant C released at low temperatures and much older C released in Fmax. As noted above, although the chemical residues contained less than 30 % of the total MOM C (Table 1), their thermograms were very similar. The very old Fmax thermal fractions in the chemical residues represent only a small amount (1 %–4 %) of the total bulk soil C (Supplement Tables S1 and S2).

The δ13C of CO2 released from SOM generally increased with temperature in bulk soil and all fractions. The range of δ13C values from F1 to Fmax was the greatest (increasing by 4 ‰–5 ‰) for the chemical residues and smaller (3 ‰–4 ‰) for the density fractions. Across density fractions, the range of values and the differences in δ13C between different fractions was greater in the deeper soil layer. Interestingly, the FPOM at 30–50 cm was more enriched in 13C than OPOM. At high temperatures subsoil δ13C was generally more enriched than surface soil.

Thermograms (Fig. 1) demonstrate that C released by the bulk sample at all temperatures contains C contributed from all physical and chemical fractions. For example, of the bulk C released in the temperature range where most C was released (250 to 325 ∘C), FPOM and OPOM contributed 9 % and 6 %, respectively, of total C released in surface soil and 16 % and 8 % in subsoil (Table 1, Fig. 1a). However, at higher temperature ranges, while the total C released was small (< 5 % of the total C) the proportional contribution from FPOM and OPOM fractions increased to ∼ 40 % in surface soil and 30 % in subsoil (Fig. 1c).

Thus, each thermal fraction from a combusted bulk soil contains C with a broad range of Fm and 13C, with variable contributions from the different physically fractionated components. Figure 5 summarizes the Fm distribution of C across the density and thermal fractions and emphasizes that the difference in Fm between density fractions (especially FPOM versus MOM) is greater than the range of Fm within any individual density fraction (excluding a small amount of very old MOM) released as a function of temperature or Ea (Fig. 5).

The measured distribution of 14C for C released with increasing temperature from the bulk soil clearly does not capture the contribution of FPOM with high Fm because its young C is released across the same temperature ranges as other density and chemical fractions (Figs. 1a, 1c, 3, 4). Thus, the surface soil age distribution misses the ∼ 9 % of total C in FPOM that has a much higher 14C signature than bulk soil; instead, its contributions skew the bulk soil thermal 14C (Fig. 5, wide bars in the middle of the distribution) higher than the separated MOM thermal fractions (green). This difference is even more pronounced in the subsoil.

With a sufficient number of thermal fractions at high temperatures, thermal analysis of the bulk soil C captured the small percentage of C with very depleted 14C signatures better than the chemical fractions that still mixed younger and older constituents. In surface soil, bulk soil Fmax 14C values (Fm 0.75) were comparable to Fmax fractions of NaF Res. and H2O2 Res. (Fm 0.76 and 0.78, respectively) and represented similar amounts of C (2.6 %, 2.7 %, and 3.0 % of total C, respectively) (Supplement Table S1). Bulk subsoil Fmax isolated older C (Fm 0.32, 5 % of total C) than Fmax values of NaF and H2O2 residues (Fm 0.56, 8.1 % total C and Fm 0.41, 3.8 % total C, respectively), but high-temperature samples were not collected for these fractions because of low C yield (Supplement Table S2).

Thermal fractionation of bulk soils and component physically and chemically separated SOM fractions demonstrate that increased thermal stability (i.e., higher Ea) is associated with lower radiocarbon (14C) content (i.e., older C ages; Fig. 3) and more enriched 13C content (i.e., more microbially processed; Fig. 4). This supports the general assumptions of thermal analysis, which is that older and more microbially processed/degraded C will be released with increasing temperatures, even among fractions like FPOM that are not associated with minerals (Plante et al., 2009). Because there are large differences in Fm between the physically and chemically separated fractions, C released with similar activation energies (i.e., in a given thermal fraction of bulk soil) therefore can mix C with a very different chemistry and 14C age.

For example, particulate fractions FPOM and OPOM that contain fresh plant material, as well as microbial residues (Castanha et al., 2008; Angst et al., 2021), release C across a similar temperature range as MOM. While presumably “labile”, FPOM releases C between 300–500 ∘C, reflecting the temperatures required to oxidize molecules like cellulose that make up plant material (Dahiya and Rana, 2004; Plante et al., 2009). Despite a range of activation energies, δ13C signatures (Fig. 4), and high σE (Table 1) all suggesting chemical diversity, FPOM in this soil is all recent in origin (post-bomb, Fm > 1.0; Fig. 3) and typically breaks down within decades. Because of the temporal dynamics of the bomb spike, an increase or decrease in Fm is more difficult to associate directly to specific age for FPOM, and it is difficult to associate Ea directly to 14C values.

Mineral-associated organic matter (MOM) fractions demonstrated larger though mostly overlapping ranges of Ea but released 14C-depleted and 13C-enriched C above 165 kJ mol-1 (Figs. 2–4). For most MOM thermal fractions, Fm less than 1.0 reflects the loss of 14C due to radioactive decay and therefore indicates an increase in age. Thus, within a given fraction there are predictable patterns of increasing age and δ13C with Ea. However, as found in other studies (Leifeld and von Lützow, 2014; Williams et al., 2018; Hemingway et al., 2019), these patterns do not allow the prediction of age from Ea alone, highlighting fundamental differences in the processes controlling Ea, 14C content, and age in each fraction. While Ea can either increase or decrease over time as C transforms with decomposition and recycling, the age of the involved C atoms can only increase.

Both chemical and thermal fractionation methods for MOM indicate the presence of two distinct components with very different Fm, one representing > 95 % of the C and having Fm similar to that of the bulk MOM but decreasing in 14C with increasing Ea, as well as a small amount (< 5 %) of much older C. In this Podzol, the main stabilization mechanisms are likely the interactions between percolating dissolved organic matter and pedogenic (oxy-)hydroxides that could explain the large amount of relatively younger C (decades to centuries) removed by NaF and H2O2 (Fig. 1b) that represents the largest thermal fraction of the MOM (F2). As shown by Schrumpf et al. (2021), the chemical extraction and oxidation of MOM using NaF and H2O2, respectively, removed C that was slightly higher in 14C concentration than the MOM overall, leaving smaller but much older residues that resist destabilization. The majority of MOM C removed through chemical fractionation had similar, younger ages that could reflect SOM more weakly associated with mineral surfaces, while the small proportion remaining could have been trapped within the mineral structure (e.g., in clays on formation) or represent elemental C. Both methods support the idea put forward by Schrumpf et al. (2021) that much of the MOM was cycling on decadal timescales, while a small amount (< 10 %) was much older (Fm 0.628). However, thermal methods demonstrate that the 3 % of subsoil MOM oxidized at temperatures greater than 505 ∘C was even older (Fm 0.23; Fig. 3, Table A1).

While NaF and H2O2 treatments removed younger C, combustion of the residues showed that they still contained C with a range of activation energies and ages. The chemical methods used here are believed to only remove sorbed C that likely has higher Fm (i.e., is younger) than the residue (Kaiser et al., 2007; Mikutta and Kaiser, 2011). These results are somewhat puzzling, as particularly the H2O2 treatment is expected to remove all easily oxidizable C, leaving behind C that is either isolated or highly “recalcitrant”. We therefore expected that the H2O2 residue would not only be older but also on average have higher Ea. On the contrary, there was actually proportionally less C in Fmax for both residues compared to the unextracted MOM (Figs. 1, 3) such that the oldest C in the residues was likely mixed with younger C. The observation that H2O2 residues had a range of activation energies and 14C ages could indicate incomplete chemical oxidation or interaction of the OM associated with dissolved pedogenic phases with the remaining mineral phases. Alternatively, the presence of low Ea material with very low 14C could reflect the incorporation of sedimentary shale parent material C into microbial food webs with long-term stabilization of microbial residues (Seifert et al., 2013).

Understanding the nature of the small amount of very old C found in MOM and bulk soil and explaining the age and δ13C structure of the NaF and H2O2 residue thermal fractions require additional information. One possibility is that the oldest C persists in the form of charcoal (Cusack et al., 2012; Sanderman et al., 2016) or is derived from the shale parent material of the Wetzstein site (Schrumpf et al., 2011; Grant et al., 2023). Unpublished 14C data collected from the surface of rock fragments found in the soil indicate a Fm of 0.27, similar to values calculated for subsoil MOM Fmax fractions (Table 1). The thermal alteration of sedimentary parent material during metamorphosis could also explain the chemical recalcitrance, heavier δ13C, and higher activation energies of this very old C. A second possibility is the presence of non-crystalline minerals that are often correlated with the amount of very old C found in soil (Huang et al., 2016; Khomo et al., 2017; Heckman et al., 2018a). The investigated soils have moderate oxalate extractable Fe contents of 9.2 (0–10 cm) and 17.4 (30–50 cm) g kg-1 (Schrumpf et al., 2021). Dithionite extractable Fe concentrations (including both crystalline and non-crystalline components) were 17 and 27.4 g kg-1, respectively. However, quantifying such effects would require investigation of soils with varying amounts of non-crystalline minerals. A third explanation of long SOM persistence is the stochastic nature of the decomposition process. Available C is not uniformly decomposed, and some substrate may persist in soil on much longer timescales (Bolin and Rodhe, 1973; Bosatta and Ågren, 1985; Sierra et al., 2018). Through random chance associated with biological, chemical, and physical processes, a small portion of total SOM remains in soil for centuries to millennia. Such persistent C may be associated with the high activation energies measured here.

The goal of any fractionation scheme for 14C analysis is to provide clearer delineation of C ages in soil, which integrates multiple types of SOM and stabilization mechanisms. Combining operationally defined fractionation methods can further isolate distinct pools of C with varying 14C ages. Such age distributions can be used to constrain models of SOM dynamics (Sierra et al., 2014; Metzler et al., 2018; Chanca et al., 2022) and test hypotheses linking stabilization mechanisms with rates of C cycling. Overall, Fig. 5 demonstrates that density fractionation alone cannot quantify the age structure of bulk SOM, especially of MOM, while thermal fractionation of bulk SOM fails to capture the youngest part of the age distribution. This is because the youngest component of the soil C, the low-density FPOM, releases C across nearly the entire range of combustion temperatures (Fig. 1c), making the C released from bulk soil at the lowest temperature reflect 14C ages that are too old and the C released at higher temperatures too young. At the highest temperatures, however, thermal oxidation methods can isolate C even older than what can be found via aggressive chemical extractions (Fig. 3). At the very highest temperatures, the contributions of C from oxidation of FPOM and OPOM are relatively small (Figs. 1c, 2) but may skew data with much younger C.

In order to best capture the age distribution of C in SOM, we therefore recommend first separating the low-density fraction, then applying thermal fractionation of the heavy fraction with attention to C liberated at very high temperatures to constrain and describe the age structure of MOM. As removal of the FPOM can also be accomplished using size separation, density separation may not be necessary if the main goal is to remove relatively fresh plant material (Castanha et al., 2008; Lavallee et al., 2020). However, the presence of charcoal that would be removed by density but not size could complicate the interpretation of thermal fractions, and further work is needed to resolve this special circumstance.

Describing the distribution of ages in SOM is a powerful tool for testing hypotheses about the timescales of different C stabilization mechanisms in soils and for comparison with age distributions produced by multi-compartment models (Metzler et al., 2018; Chanca et al., 2022). Our results are for a single soil, a Podzol that likely has one major mechanism for stabilizing C on mineral surfaces: interaction with pedogenic oxides. To explore other mineral stabilization mechanisms and timescales, it would be useful to compare thermograms and age distributions for soils with different mineral composition – e.g., allophane, 2:1 clays, 1:1 clays, sands, and mixed mineralogy soils. Additionally, a comparison with temperature-resolved spectra (e.g., py-GC/MS; Sanderman and Grandy, 2020; DRIFTS; Nkwain et al., 2018) that associate SOM chemistry with thermal stability may help in determining the roles that OM chemistry and mineralogy play in controlling C age and persistence in soil.