Potassium isotope anomalies in meteorites inherited from the protosolar molecular cloud

Potassium, a moderately volatile element, shows presolar isotopic heterogeneity in meteorites.

Abstract

Potassium (K) and other moderately volatile elements are depleted in many solar system bodies relative to CI chondrites, which closely match the composition of the Sun. These depletions and associated isotopic fractionations were initially believed to result from thermal processing in the protoplanetary disk, but so far, no correlation between the K depletion and its isotopic composition has been found. Our new high-precision K isotope data correlate with other neutron-rich nuclides (e.g., ⁶⁴Ni and ⁵⁴Cr) and suggest that the observed ⁴¹K variations have a nucleosynthetic origin. We propose that K isotope anomalies are inherited from an isotopically heterogeneous protosolar molecular cloud, and were preserved in bulk primitive meteorites. Thus, the heterogeneous distribution of both refractory and moderately volatile elements in chondritic meteorites points to a limited radial mixing in the protoplanetary disk.

INTRODUCTION

Thermal processing in the solar nebula is believed to have depleted solar system bodies in moderately volatile elements (MVEs) (1) and fractionated their isotopes by partial condensation of the nebular gas (2, 3) and/or evaporation during planetesimal collisions (4). Among the moderately volatile and relatively abundant elements, only potassium (K) has more than one stable isotope (³⁹K and ⁴¹K), with ⁴¹K being primarily the decay product of the short-lived ⁴¹Ca [t_1/2 ~ 0.1 million years (Ma) (5)]. These characteristics make K a good candidate for studying the history of nucleosynthetic components and thermal processing in the early solar system.

Many planetary bodies show variable depletions in K, often quantified by the K/U ratio. One advantage of this ratio is that it can be measured remotely by a γ-ray survey (6). For chondritic and planetary samples, Ca/K is a better indicator of K depletions because Ca is one of the refractory major elements, with well-defined and relatively constant concentrations in different solar system bodies. Early work on K isotopes in solar system bodies found no differences within an uncertainty of ~0.5‰ (2). Recent higher-precision (~ 0.1‰) K isotope data show K isotopic fractionation of ~0.4‰ between the Earth and the Moon (7), interpreted as a result of incomplete vapor condensation during Moon formation. More recently, observed K isotope variations among planetary bodies and chondrites (8–11) were interpreted to result from potential K loss from their parent bodies. If the thermal processing (evaporation/condensation) that depleted K has also fractionated K isotopes, a correlation between K isotopic compositions and K depletions is expected. However, no clear correlation has been found so far. Apparently, the processes that depleted K in the solar system bodies did not fractionate K isotopes to an observable degree.

Stellar nucleosynthetic processes (e.g., p-, s-, and r-processes) can also result in K isotope variations, because ⁴¹Ca, the source of most ⁴¹K, is mainly produced by an s-process (12). These variations are likely preserved in chondritic meteorites because they are thought to have accreted in the accretionary disk from materials that formed in the solar nebula and/or were inherited from the presolar molecular cloud. Small isotopic anomalies have been found in chondrites for many neutron-rich isotopes (13–17). While the causes of these anomalies remain uncertain, an incomplete mixing of materials from different stellar sources is a leading explanation. If the observed ⁴¹K variations are of nucleosynthetic origin, correlations between ⁴¹K and other neutron-rich nuclides in chondrites are expected.

To constrain the astrophysical environment and understand the thermal events that occurred a few million years before and after the formation of the solar system, we carried out high-precision [~30 parts per million (ppm); fig. S2A] K isotope measurements of samples from a number of solar system objects. We studied both chondrites of different petrologic types and samples of differentiated planetary bodies, aiming to evaluate the contributions of stellar nucleosynthetic processes and mass-dependent fractionations to the observed ⁴¹K variations. K isotopic compositions were measured using the multicollector inductively coupled plasma mass spectrometry (ICP-MS) Nu Sapphire and are expressed relative to our laboratory standard, Merck Suprapur: δ⁴¹K (‰) = ((⁴¹K/³⁹K)_sample/(⁴¹K/³⁹K)_standard – 1) × 10³. Uncertainties are reported at the two-sigma level (2SE). For a convenient conversion, other commonly used standards were also measured relative to Suprapur: Seawater and NIST SRM-3141a yielded δ⁴¹K = +0.215 ± 0.024‰ and +0.047 ± 0.003‰, respectively (fig. S5 and table S1). The δ⁴¹K notation and K isotopic standards are described in detail in section S1.

RESULTS

We found well-resolved δ⁴¹K differences among different planetary bodies, including Mars, Earth, and Vesta, as well as between ordinary (O), enstatite (E), and carbonaceous (C) chondrites (Fig. 1 and Table 1). The samples of the same chondritic meteorites from different sources yield similar δ⁴¹K values, suggesting the homogeneity of the samples and robustness of the measurements.

Fig. 1. Chemical and isotopic variations of K among chondrites and planetary bodies.

Each data point is the group mean calculated using available samples within each group. The corresponding uncertainties on the group means are larger than the analytical uncertainty because of the heterogeneity among different meteorites within groups (details in Table 1). Note that evaporation/condensation cannot explain our K isotopic data. The K and Ca concentrations in each group are taken from the literature (32, 45–47). The group mean and uncertainties (2SE) for the CI group in this study are based on Orgueil.

Table 1. K isotopic composition of each sample in this study.

The interior portion and fusion crust of Holbrook-1 were powdered independently; the fusion crust, Holbrook-1 (c), is not included in calculating the group mean. NIST SRM-3141-a was measured with respect to Suprapur = +0.047 ± 0.003‰. The group mean and the corresponding 2SE are calculated on the basis of different meteorites. Details are in Materials and Methods. N, numbers of independent analytical runs; n, total number of the bracketed δ⁴¹K values from N days; ANSMET, Antarctica Meteorite Collection (NASA); ASU, Center for Meteorite Studies, Arizona State University; Caltech (JW), Caltech Jerry Wasserburg; HMNH, Harvard Museum of Natural History; Harvard (CL), Harvard University (Charlie Langmuir); MNHN, Museum national d’Histoire naturelle; NEMS, New England Meteoritical Services; SAO (JW), Smithsonian Astrophysical Observatory (John Wood); SAO (UM), Smithsonian Astrophysical Observatory (Ursula Marvin); USNM3529, Smithsonian USNM3529, 4-kg Allende powder.

Group	Sample	Find/Fall	Type	δ41K Suprapur (‰)	±2SE*	N	n	Group mean	±2SE	Crushed powder (g)	Sources	δ41K SRM- 3141a (‰)
CI	Orgueil-2a	Fall	CI1	−0.125	0.030	5	21			0.11	SAO (JW)	−0.172
	Orgueil-2b			−0.192	0.030	5	26					−0.239
	Orgueil-3	Fall	CI1	−0.107	0.038	3	14	−0.133†	0.051	1024	MNHN	−0.154
CM	Murray-1a	Fall	CM2	0.205	0.033	4	19			0.29	SAO (JW)	0.158
	Murray-1b			0.241	0.046	2	9					0.194
	Mighei-1a	Fall	CM2	−0.255	0.046	2	10			1.94	SAO (JW)	−0.302
	Mighei-1b			−0.246	0.046	2	9					−0.293
	Murchison-1a	Fall	CM2	−0.112	0.030	10	50			10.00	SAO (UM)	−0.159
	Murchison-1b			−0.155	0.065	1	5	−0.054	0.285			−0.202
CO	Ornans-1	Fall	CO3.4	−0.012	0.029	5	24			0.88	SAO (JW)	−0.059
	Ornans-2	Fall	CO3.4	−0.057	0.038	3	14			6.45	MNHN	−0.104
	DaG 749	Find	CO3	−0.216	0.038	3	17			1.75	ASU	−0.263
	NWA7916	Find	CO3	0.136	0.033	4	21			1.60	ASU	0.089
	Kainsaz	Fall	CO3.2	−0.165	0.038	3	14	−0.070	0.157	1.70	NEMS	−0.212
CV	Allende-1a	Fall	CV3	−0.187	0.030	10	50			34	SAO (UM)	−0.234
	Allende-1b			−0.197	0.030	9	46					−0.244
	Allende-2	Fall	CV3	−0.035	0.033	4	19			4000	USNM3529	−0.082
	Vigarano-1a	Fall	CV3	−0.237	0.033	4	19			0.67	SAO (JW)	−0.284
	Vigarano-1b			−0.270	0.046	2	9	−0.184	0.140			−0.317
CK	NWA6254	Find	CK4	−0.255	0.046	2	12			2.22	ASU	−0.302
EH	Abee-1a	Fall	EH4	−0.293	0.025	7	36			1.00	NEMS	−0.340
	Abee-1b			−0.292	0.046	2	9					−0.339
	Indarch-1a	Fall	EH4	−0.119	0.038	3	15			1.82	NEMS	−0.166
	Indarch-1b			−0.160	0.033	4	22					−0.207
	Indarch-2	Fall	EH4	−0.333	0.038	3	15	−0.264	0.056	0.23	HMNH	−0.380
EL	MacHill 88481	Find	EL3	−0.556	0.038	3	15			0.44	ANSMET	−0.603
	Eagle	Fall	EL6	0.082	0.046	2	9			0.69	NEMS	0.035
LL	Tuxuac-1a	Fall	LL5	−0.609	0.046	2	11			2.46	NEMS	−0.656
	Tuxuac-1b			−0.543	0.038	3	14					−0.590
	Parnallee	Fall	LL3	−0.917	0.038	3	17			1.34	ASU	−0.964
	Vicencia	Fall	LL3	−0.759	0.038	3	17			1.32	ASU	−0.806
	Chainpur	Fall	LL3.4	−0.708	0.046	2	10	−0.740	0.141	0.99	SAO (JW)	−0.755
L	Marion Iowa	Fall	L6	−0.679	0.030	5	22			2.00	HMNH	−0.726
	Homestead	Fall	L5	−0.725	0.030	6	29			2.00	HMNH	−0.772
	Bruderheim	Fall	L6	−0.672	0.038	3	15			70	SAO (UM)	−0.719
	Peace River-1	Fall	L6	−0.632	0.038	3	15			190	SAO (UM)	−0.679
	Peace River-2	Fall	L6	−0.672	0.033	4	22			0.12	Caltech (JW)	−0.719
	Holbrook-1	Fall	L6	−0.636	0.038	3	25			0.93	SAO (JW)	−0.683
	Holbrook-1 (c)	Fall		−0.621	0.038	3	25			0.60		−0.668
	Holbrook-2	Fall	L6	−0.658	0.046	2	10	−0.675	0.028	3.07	HMNH	−0.705
H	Kernouve	Fall	H6	−0.628	0.030	5	23			2.00	HMNH	−0.675
	Dresden	Fall	H6	−0.681	0.030	5	24			2.00	HMNH	−0.728
	Forest City	Fall	H5	−0.724	0.030	6	27			2.00	HMNH	−0.771
	Grady	Find	H3	−0.710	0.038	3	15			70	Caltech (JW)	−0.757
	Guareña	Fall	H6	−0.681	0.038	3	15			53.40	Caltech (JW)	−0.728
	Estacado	Find	H6	−0.609	0.038	3	15	−0.672	0.037	2.80	NEMS	−0.656
Mars	Nakhla-1	Fall	Nakhla	−0.193	0.029	5	27			0.25	SAO (JW)	−0.240
	Nakhla-2	Fall	Nakhla	−0.164	0.029	5	25			0.23	SAO (JW)	−0.211
	QUE94201.55	Find	Shergottite	−0.152	0.038	3	15			0.10	ANSMET	−0.199
	Zagami-1	Fall	Shergottite	−0.279	0.038	3	15			0.11	NEMS	−0.326
	Zagami-2	Fall	Shergottite	−0.120	0.038	3	14	−0.177	0.027	0.94	ASU	−0.167
Vesta	Stannern	Fall	Eucrite	0.503	0.038	3	9			0.26	SAO (JW)	0.456
	Bouvante	Find	Eucrite	0.270	0.038	3	12			0.13	SAO (JW)	0.223
	Sioux County	Fall	Eucrite	0.202	0.038	3	16			0.20	SAO (JW)	0.155
	Juvinas	Fall	Eucrite	0.712	0.046	2	10	0.422	0.232	0.14	SAO (JW)	0.665
Earth	BHVO-2		Basalt	−0.333	0.030	9	46				USGS	−0.380
	BCR-2		Basalt	−0.370	0.030	9	46				USGS	−0.417
	CHEPR		Basalt	−0.538	0.033	4	18	−0.414	0.126		Harvard (CL)	−0.585
			Internal uncertainty = 30 ppm

*The uncertainty (2SE) is 2SD (65 ppm)/$\sqrt{N}$ (fig. S2) and was replaced with 30 ppm if less than 30 ppm. Additional uncertainty is negligible when converting Suprapur to SRM-3141a.

†The meteorite group means and 2SE are based on small numbers (numbers of different meteorites); CI group is based on two chunks of one meteorite, Orgueil.

The Orgueil δ⁴¹K value

Two individual pieces of CI chondrite analyzed in this work, Orgueil-2 and Orgueil-3, were obtained from different sources to establish the δ⁴¹K value of CI meteorites, which are considered the best representation of the starting material in the solar system. The mean δ⁴¹K value of −0.133‰ for the CI group is calculated on the basis of these two samples. The original δ⁴¹K value for CI chondrites that was published in (7) and that has been widely used in the literature [e.g., (11)] is indistinguishable from the bulk silicate earth (18). In this study, we analyzed the same material from (7) and found that this sample contains nearly 8 weight % (wt %) Earth crustal materials, based on major and trace element compositions. This implies that most of its K is terrestrial, not meteoritic. This issue is discussed in detail in section S2 and in figs. S3 and S4.

The δ⁴¹K of chondrites

The group mean δ⁴¹K and the corresponding 2SE are calculated on the basis of different meteorites (described in Materials and Methods). The mean δ⁴¹K value is −0.054‰ for CM chondrites, −0.070‰ for CO chondrites, −0.184‰ for CV chondrites, −0.255‰ for one CK chondrite, −0.264‰ for EH chondrites, and −0.696‰ for the main cluster of the ordinary chondrites (H, L, and LL). The ordinary chondrites have the lightest δ⁴¹K among all samples analyzed. The H and L chondrite δ⁴¹K values form a single cluster in the δ⁴¹K-Ca/K ratio diagram (Fig. 1), but one LL chondrite, Parnallee, has a substantially lighter δ⁴¹K value of −0.917‰ (Table 1). We have analyzed interior materials (Holbrook-1) and the fusion crust [Holbrook-1(c)] of the same meteorite and found indistinguishable δ⁴¹K values. There are small variations of δ⁴¹K in carbonaceous chondrites, but the mean δ⁴¹K value (CM, CO, and CV) is indistinguishable from CI chondrites. Enstatite chondrites (EH), which are enriched in K, have a lighter δ⁴¹K value relative to CI chondrites. The mean of EL chondrites is not included because the two samples analyzed have very different δ⁴¹K values (Table 1 and section S1).

The δ⁴¹K of achondrites

The samples of differentiated planetary bodies show differences in K isotopic compositions, with the mean δ⁴¹K values being −0.177‰ for Mars and +0.422‰ for the eucrite parent body, which generally agree with (9). Mars might have a unique bulk composition in the inner solar system, intermediate between carbonaceous chondrites and Earth. The eucrite parent body, Vesta, is strongly volatile-depleted and shows an enrichment in ⁴¹K compared to other meteorites and Earth. The bulk mean Earth, which is depleted in K relative to both carbonaceous and ordinary chondrites, has an intermediate δ⁴¹K value of −0.414‰. The mean value is determined on the basis of three samples—BCR-2, BHVO-2, and CHEPR (mid-ocean ridge basalt)—to be consistent with the previous work (18).

Our results are generally consistent with previously published δ⁴¹K values after correcting for different standards (fig. S5), except for one CI δ⁴¹K derived from a contaminated sample (7, 11). Some inconsistencies and larger δ⁴¹K variations observed in previous studies (8, 11) are likely due to the use of nonrepresentative samples (~0.1 g), and the substantial use of meteorite finds. Samples studied here, on the other hand, were mostly meteorite falls powdered from more than 2 g of whole rock (up to 200 g). In addition, many meteorites were obtained from multiple sources to overcome the possible heterogeneity of individual pieces. Despite a general agreement in the mean δ⁴¹K values for each meteorite group between this study and (11), we favor discussion and interpretation of the data based on samples studied here (see section S3).

DISCUSSION

Mass-dependent fractionation of K isotopes during evaporation/condensation

Variations in δ⁴¹K are often explained by evaporation/condensation processes, which could occur under kinetic or equilibrium conditions. In the case of equilibrium (P_i/P_i,sat = 1, where P_i,sat is the saturation pressure for species i), the isotopic composition of the condensed phase must be heavier than the bulk system, but the magnitude of fractionation (the horizontal dotted line in Fig. 1) is expected to be smaller than the current analytical uncertainty. Under P_i/P_i,sat < 1, evaporation of K from a condensed phase would enrich the residue in ⁴¹K. The magnitude of fractionation increases from a near-equilibrium value to 22‰ (19) as the P_i/P_i,sat ratio decreases to ~0 (Fig. 1 and section S4). If P_i/P_i,sat > 1, the condensate is expected to be depleted in ⁴¹K, with the magnitude of fractionation decreasing to ~0‰ as condensation continues in a closed system. Thus, if CI chondrites were the starting material for the solar nebula, then the observed magnitude of K isotopic fractionation in K-depleted samples cannot be explained by the loss of K during evaporation or condensation. Therefore, single-stage nebular thermal processing cannot account for the observed nebula-wide δ⁴¹K variations.

While other MVEs such as Zn and Cu (20) also show depletion in planetary bodies, K behaves very differently from them. For example, Zn and Cu are more easily fractionated during impact vaporization (21–23), but no K isotopic fractionation was found in tektites (24). A lack of correlations between δ⁴¹K and δ⁶⁶Zn and δ⁶⁵Cu (fig. S6) (11) further suggests incoherent behaviors among MVEs during nebula thermal processes and planetary formation (25). We have also considered parent body processes (i.e., aqueous alteration) and conclude that these processes cannot explain the overall K isotope variations in chondrites. A constant K-Rb ratio has been found for different meteorite groups studied here and the bulk Earth (fig. S7). In addition, we found that δ⁴¹K versus Al/K, Cr/K, Fe/K, and Ni/K in different chondrite groups and Earth show the same pattern, regardless of whether the element that K is compared to is mobile or immobile (fig. S7). The observed δ⁴¹K variations could be due to a heterogeneous distribution of either anomalous presolar grains or local aqueous alteration products. We have minimized these effects by using large samples (up to 200 g) whenever possible and using group means for each meteorite class based on multiple samples. Thus, we argue that the mean δ⁴¹K of each group should minimize these effects of small-scale sample heterogeneity.

Evidence supporting the type II supernova injection

Alternatively, the observed variations of δ⁴¹K in meteorites may reflect a heterogeneous distribution of ⁴¹Ca in the solar nebula. The presence of extinct ⁴¹Ca (now ⁴¹K) found in Ca-Al–rich inclusions (CAIs) (26) could result from either in situ irradiation, through the ⁴²Ca(p, pn)⁴¹Ca reaction, or injection by a recent supernova explosion. Thus, the observed ⁴¹K variations could potentially reflect varying proportions of Ca-rich (CAIs) and Ca-poor (chondrules and matrix) components of chondrites. Using available literature data and mass-balance calculations, we found that the contribution of ⁴¹K from CAIs to the total ⁴¹K balance is not sufficient to explain the observed K isotope variations in meteorites (details can be found in section S6).

Therefore, ⁴¹K (decay product of ⁴¹Ca) must have been heterogeneously distributed in the protosolar molecular cloud; such heterogeneity was preserved in the solar nebula and recorded in the primitive meteorites. The inhomogeneous distribution of ⁴¹K could be caused by one or more injections of ⁴¹K from a nearby stellar source into the presolar molecular cloud. ⁴¹Ca is primarily formed via neutron capture from abundant and stable ⁴⁰Ca and may be continuously ejected from massive stars during their Wolf-Rayet phase or ejected by final explosions of supernovae (27, 28). The main sources of presolar ⁴¹K (⁴¹Ca) are still debated, but it is almost certain that when a massive star explodes in a supernova, neutron-rich isotopes are ejected into the molecular cloud, which become part of the solar nebula materials (29, 30). Neutron capture extinct radionuclides (e.g., ⁴¹Ca, ¹²⁹I) and neutron-rich isotopes, especially the ones in the Fe peak (e.g., ⁴⁸Ca, ⁵⁰Ti, ⁵⁴Cr, and ⁶⁴Ni), are likely formed by nuclear reactions in stars shortly before the solar system formation (31). Because most ⁴¹Ca has decayed to ⁴¹K due to its half-life of ~0.1 Ma, massive stellar winds and supernova ejecta would add abundant ⁴¹K and little ⁴¹Ca to the solar nebula materials.

To evaluate whether K isotopic variations could result from an injection of ⁴¹K, we compare δ⁴¹K to ε⁶⁴Ni and ε⁵⁴Cr (Fig. 2). The mass-independent anomalies in ⁶⁴Ni and ⁵⁴Cr (expressed in ε-notation) are generally thought to reflect the heterogeneous distribution of distinct nucleosynthetic components in the solar system (13–15). We found positive correlations between ⁴¹K, ⁶⁴Ni, and ⁵⁴Cr, suggesting that ⁴¹Ca (the precursor of ⁴¹K) was probably produced in a type II supernova shell (15). This implies that the observed K isotopic variations reflect the heterogeneous distribution of presolar nuclides in the solar system. Earth, which is usually an end member in many nucleosynthetic isotope anomaly plots, such as μ¹⁴²Nd* and ε⁹²Mo (fig. S9), has an intermediate value between the carbonaceous and ordinary chondrites in δ⁴¹K, ε⁶⁴Ni, and ε⁵⁴Cr. The varying sequence of objects in each diagram (Fig. 2 and fig. S9) suggests that the correlations of δ⁴¹K with other isotopes cannot simply be due to a mixing between two end members, CM (or CI) and ordinary chondrites. Instead, possibly more than two nucleosynthetic components were present to explain the overall solar system anomalies observed in neutron-rich isotopes.

Fig. 2. Variations of δ⁴¹K, ε⁵⁴Cr, and ε⁶⁴Ni in bulk samples.

The concentrations of each element are from (32, 45), and mean ε⁵⁴Cr and ε⁶⁴Ni data for each group are from (17) (see fig. S8 for complete references). The gray regions show the three-component mixing model [modified from (32)] of chondrules, matrix, and CAIs. The chondrule and matrix components are estimated by the average ordinary and CI chondrites, respectively. The correlations between δ⁴¹K, ε⁵⁴Cr, and ε⁶⁴Ni suggest that these anomalies are primarily caused by nucleosynthetic processes and cannot be generated by a multicomponent mixing model between major chondrite components. The correlations also cannot be explained by the mixing of two isotopically distinct reservoirs, such as CM (or CI) and ordinary chondrites. This is because mixing between two end members would yield straight lines in δ⁴¹K-Ca/K plots (Fig. 1, and similar plots in fig. S7B), which is not observed. In addition, mixing the two end members’ compositions is unlikely to reproduce both volatile-depleted Earth and volatile-enriched enstatite chondrites that both have intermediate values of δ⁴¹K, ε⁶⁴Ni, and ε⁵⁴Cr. pptt, parts per ten thousand.

Testing a multicomponent mixing model

The chemical and isotopic compositions of chondrites result from mixing several components formed under different physicochemical conditions. For example, Alexander (32) used a four-component mixing model to successfully reproduce the K concentrations in six carbonaceous chondrite groups. These components are as follows: (i) CAIs, (ii) matrix of the CI composition, (iii) chondrules compositionally similar to the volatile-depleted CI chondrites, and (iv) H₂O-rich ices. Bloom et al. (11) used a similar model to explain the δ⁴¹K variations observed in carbonaceous chondrites by the mixing of chondrules and matrix. The matrix δ⁴¹K was approximated by the bulk CI δ⁴¹K value of −0.53‰, while the chondrule δ⁴¹K value ranging from −0.28 to 2.08‰ was calculated assuming fractional evaporative K loss (1 to 10%) from initial CI composition described by the Rayleigh fractionation law. However, because the initial CI δ⁴¹K value of −0.53‰ measured in the contaminated Orgueil sample is incorrect, both modeled δ⁴¹K values are also incorrect. Once the wrong initial CI δ⁴¹K value of −0.53‰ is replaced with the correct one of −0.133‰, the mixing model fails to account for the observed δ⁴¹K variations in both carbonaceous and ordinary chondrites. Thus, mixing of different components that experienced various degrees of thermal processing in the solar nebula is an unlikely explanation for the overall K isotope variations found in chondrites.

Let us now evaluate whether the four-component mixing model of (32) can reproduce the observed δ⁴¹K- ε⁶⁴Ni and δ⁴¹K-ε⁵⁴Cr correlations. Because ices are supposed to contain no K, Ni, and Cr, such a model reduces to three components with unknown δ⁴¹K values. Following (32), we approximate matrix with the bulk CI δ⁴¹K value of −0.133‰. The limited data on individual chondrules from Hamlet, an LL4-brecciated chondrite (33), show a very wide δ⁴¹K range, with the most chondrules having lighter δ⁴¹K than the bulk CI chondrites. This result is inconsistent with the fractional evaporative loss of K assumed by (11) but is in line with the observed addition of SiO₂ to crystallizing chondrule melts from the ambient gas (34–36). Because no reliable δ⁴¹K value for chondrules is currently available, we approximate it by the δ⁴¹K value of −0.692‰ from the bulk ordinary chondrites, which are known to contain up to 80 volume % chondrules (37). The δ⁴¹K value of 0.249‰ for CAIs is calculated on the basis of the assumption that all ⁴¹K is the product of ⁴¹Ca decay (section S6.1), and the ε⁶⁴Ni and ε⁵⁴Cr values are from (13, 38). The results of a three-component mixing are shown in Fig. 2. Because of the large positive anomalies of ε⁶⁴Ni and ε⁵⁴Cr in CAIs, the calculated mixing region is enriched in these nuclides and shifts away from the observed arrays, regardless of the δ⁴¹K values in CAIs (Fig. 2 and fig. S8). Hence, our data cannot be explained by the mixing of major chondrite components.

The most likely interpretation for the correlations of δ⁴¹K with ε⁶⁴Ni and ε⁵⁴Cr in bulk chondrites is presolar anomalies. As ⁴¹Ca could also be partially produced by s-processes, the ⁴¹K anomalies could arise from a combination of s-processes in other stars and a type II supernova explosion (consistent with ⁶⁴Ni). There is, however, not much evidence, so far, supporting an s-process origin, and our data thus preferentially suggest the type II supernova as the main source of presolar ⁴¹K heterogeneity.

Implications for an isotopically heterogenous molecular cloud

Out of many scenarios regarding the formation of an isotopically heterogeneous protoplanetary disk, three are illustrated in Fig. 3. The first scenario assumes that isotopically homogeneous materials infalling from the molecular cloud experienced nebula-wide thermal processing, resulting in the formation of an isotopically heterogeneous inner disk depleted in MVEs (Fig. 3A). The partial evaporation of thermally unstable phases would fractionate nuclides of different origins to the same degree (e.g., ⁴⁶Ti and ⁵⁰Ti) (39). If so, the isotopic composition of an element should correlate with its MVE depletion, which is not observed for K (Fig. 1). We thus rule out this model.

Fig. 3. Models explaining the observed isotopic heterogeneity and MVE depletions in the solar protoplanetary disk.

(A) A nebular thermal processing of infalling, isotopically homogeneous material from the molecular cloud results in both isotopic heterogeneity (for ε⁴⁶Ti and ε⁵⁰Ti) and variable depletions in MVEs in the disk (39). An expected correlation between isotope compositions and depletion of MVEs is not observed for K, ruling out this model. (B) Isotopic heterogeneity (for μ⁴⁸Ca and others) in the inner disk (depleted in n-rich isotopes) results from thermal processing of a homogeneous molecular cloud material. The inner disk gradually mixes with materials from the outer disk, making the isotopic composition of solid bodies in the inner solar system a function of time (increasing n-rich isotopes with time) (16). This would produce correlations among isotope compositions, MVE depletions, and sizes of planetary bodies in the inner solar system, which is not observed for K, ruling out this model too. (C) Isotopic heterogeneity inherited from an isotopically heterogeneous molecular cloud. Thermal processing in the disk produces the MVE depletions in the solid objects of the inner disk. No correlation between isotope compositions and MVE depletions is expected as long as mixing in the disk occurs on a local scale only, but the correlation between MVEs (δ⁴¹K) and other n-rich refractory nuclides (ε⁶⁴Ni, ε⁵⁴Cr) can be preserved. This is the model favored by our K isotope data.

In the second scenario (Fig. 3B), the degree of heterogeneity is time-dependent and reflects mixing between isotopically different materials from the inner and outer disk. Like in the first scenario, the protosolar disk forms from a homogeneous molecular cloud, but only the inner disk becomes depleted in neutron-rich isotopes during thermal processing. As the inner disk gradually mixes with the outer disk, the degree of isotopic heterogeneity changes with time. A special case of this scenario (16) predicts that larger, later-formed bodies like Earth would have heavier μ⁴⁸Ca than smaller, earlier-formed ones such as Mars and Vesta due to continuous admixing of isotopically heavier materials from the outer disk (i.e., carbonaceous chondrites). However, this case cannot explain the fact that Earth has lighter δ⁴¹K than Mars. The lack of correlation between K depletion and δ⁴¹K rules out thermal processing as the main cause for the inner-outer isotopic differences.

In the third scenario (Fig. 3C), isotopic heterogeneity in the protosolar disk was inherited from an isotopically heterogeneous molecular cloud. If so, the isotopic heterogeneity of both moderately volatile (⁴¹K) and refractory (⁵⁴Cr and ⁶⁴Ni) nuclides preserved in meteorites can only be explained by a limited mixing of nucleosynthetic materials. The depletion in MVEs, caused by thermal processing, does not need to correlate with the isotopic composition as long as mixing in the disk occurs only on a local scale. It also implies that the feeding zones of planetesimals and planets are relatively narrow and do not mix with one another. The correlations between δ⁴¹K and other neutron-rich refractory nuclide (ε⁶⁴Ni, ε⁵⁴Cr) anomalies can be preserved in this scenario. Thus, such a model is favored by our K data.

The survival of K isotopic heterogeneity implies a limited mixing among formation regions of the various planetary and chondrite parent bodies. Perhaps, any gaps in the protoplanetary disk [e.g., from early formation of planets (40–42)] can further segregate the presolar (pre-CAI formation) isotopically distinct reservoirs and serve as barriers against radial mixing. Such local isotopic heterogeneity can survive through later disk-wide disturbances [e.g., Grand Tack (43)] and would be preserved in the compositionally diverse asteroid belt where the most primitive meteorites might have come from (44). The isotopic anomalies, now, observed for both refractory and moderately volatile elements in primitive meteorites are inherited from the heterogeneous protosolar molecular cloud, which is likely associated with type II supernova injection before the solar system formed.

MATERIALS AND METHODS

We studied 15 ordinary (H, L, and LL), 11 carbonaceous (CI, CM, CV, CO, and CK), and 4 enstatite chondrites (EL and EH) of different petrologic types, both finds and falls, and 12 samples of differentiated planetary bodies, including 3 Martian meteorites, 4 eucrites, and 3 terrestrial samples. Whole-rock powders of four ordinary chondrites (Peace River-1, Bruderheim, Guareña, and Grady) were prepared by crushing and powdering >50 g of each meteorite. An additional 0.12-g powder aliquot of Peace River from a different source (Peace River-2 prepared from >5 g) was also analyzed to compare with a larger sample to test the sample representativeness of ordinary chondrites. Samples of other chondrites were prepared from >2 g rocks, which is sufficient to represent the bulk composition, with very few exceptions of carbonaceous chondrites. Samples weighing <5 g were crushed gently using high-purity aluminum oxide mortars and pestles to minimize possible metal contamination.

Samples of some meteorites were obtained from multiple sources to test homogeneity of these meteorites by repeated measurements; they are distinguished by Arabic numerals (Allende-1, Allende-2, etc.). In addition, we have tested the homogeneity of the sample powder by dissolving multiple aliquots of many samples. The separately dissolved aliquots of the same powdered sample have also passed through different columns to test the reproducibility of our column processing; such aliquots are marked by characters a and b (Allende-1-a, Allende-1-b, etc.) in Table 1.

Acid dissolution and chemical purification of potassium

Aliquots (50 to 150 mg) of the whole-rock powders were dissolved in multiple steps using mixtures of HF, HCl, and HNO₃. Samples were heated to 210°C in the CEM MARS 6 microwave digestion system repeatedly. After complete digestion, aliquots were redissolved in 0.5 N HNO₃ for K ion exchange column chemistry. The solutions were loaded on the 13-ml Bio-Rad AG50W-X8 cation-exchange resin (100 to 200 mesh) chromatography columns and processed with our established procedure (18), except less sample was loaded (~10 mg of whole rock). Solutions were passed through the columns twice to purify the K-cuts (>99% yield) and redissolved in dilute HNO₃ (~0.32 N) for ICP-MS analysis.

Mass spectrometry

The K isotopes were measured at Harvard University with the multicollector ICP-MS Nu Sapphire (serial no. SP001). We used the low-energy ion path and a hexapole collision cell to eliminate mass interferences from Ar-bearing ions such as ArH⁺, Ar⁺, and ArO⁺. Solutions containing ~250 ppb (parts per billion) of K yield ~4 nA ³⁹K signal. Samples and standard were matched for ³⁹K intensity within 1%. A single analytical sample-standard bracketing run (about five repeats) consumes ~4 ml of the solution, equivalent to ~1 μg of K. We reported the measured K isotope values relative to our laboratory standard Merck Suprapur KNO₃ of 99.995% purity.

Because K analytical solutions could be contaminated with small amounts of Ca, we also measured mass 40 (for Ca) to monitor the possible formation of ⁴⁰CaH⁺ (mass 41 interferes with ⁴¹K) in both analytical samples and standards. The contribution of ⁴⁰CaH⁺ to the mass 41 peak was calculated from the analysis of K standard solution spiked with Ca. The δ⁴¹K values of all samples of a particular run were corrected for ⁴⁰CaH⁺ interference, typically less than 0.02‰. In addition, we monitored the quality of each analytical run by analyzing an extra standard solution with up to 20% concentration mismatch. Runs were considered acceptable only when the δ⁴¹K difference between the “normal” and “mismatching” standard is less than 0.05‰ (an example is shown in fig. S1).

Accuracy and analytical uncertainties

High-precision isotope ratio measurements require repeated measurements to evaluate the uncertainty of a sample’s mean value. The uncertainty was calculated and reported as doubled SE of the mean (2σ_SE). Error estimates need to be verified by comparing external reproducibility and internal uncertainty. Therefore, we have taken into account (i) within-run uncertainties, (ii) instrument day-to-day variability, and (iii) column chemistry and dissolution uncertainties. The first quantity is the internal uncertainty, while the second and third quantities are defined here as external reproducibility.

The within-run uncertainty is the calculated SE of a sample that was repeatedly measured within an analytical run, given by

$$2\cdot {\mathrm{\sigma }}_{\text{SE}}=2\cdot \frac{{\mathrm{\sigma }}_{\text{SD}}}{\sqrt{n}}$$

where n is the bracketing repeats for a sample within a run (typically n = 5). The SD could be estimated by the self-bracketing on a standard within an analytical run (typically 2SD = 65 ppm). The internal uncertainty (2SE) was, thus, calculated as 30 ppm for a sample (fig. S2A). Uncertainties reported in Table 1 were replaced with 30 ppm if less than that value.

The external reproducibility takes into account the instrumental day-to-day variability and uncertainties of column processing and sample dissolution. The instrumental day-to-day variability was estimated by measuring one aliquot repeatedly on different days. We calculated the variations (2SD) of δ⁴¹K values of a single aliquot, BHVO-2, which was measured for 9 days, to be 27 ppm. We reported this as our external reproducibility for a single measurement (fig. S2B). The consistency between internal (within-run) uncertainty (30 ppm) and external reproducibility (27 ppm) implies that there is no additional variability added to the data.

Figure S2C shows that the uncertainties of column chemistry and dissolution processes are negligible, even if the uncertainties from dissolution processes for meteorites may be larger than typical terrestrial samples due to materials (SiC, graphite, etc.) that are hard to dissolve. We compare the mean δ⁴¹K values for two aliquots (a and b) from the same samples that were dissolved independently and analyzed on multiple days.

Calculating the group mean (Table 1)

The group mean and the corresponding 2SE are calculated on the basis of different meteorites. That is to say, if a meteorite was analyzed more than once, we first calculated the mean of these two or more analyses and then considered the calculated value as a single data point for the calculation of the group mean.

Most of the samples in this study were acquired from different sources, and some of them were dissolved and analyzed more than once. For instance, Allende was obtained from two different sources (Allende-1 and Allende-2), and Allende-1 was dissolved twice independently. The CV group mean should, however, consider Allende and Vigarano meteorites equally. We first calculate the mean δ⁴¹K for Allende by averaging [mean (Allende-1a, Allende-1b), Allende-2]. Then, we calculate the mean for Vigarano-1 from averaging Vigarano-1a and Vigarano-1b. Last, the group mean for CV chondrites is the mean value of Allende (both Allende-1 and Allende-2) and Vigarano-1, which is −0.184.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/41/eabd0511/DC1