Diamonds are witnesses of processes that have operated in Earth's mantle over more than 3 b.y. Essential to our understanding of these processes is the determination of diamond crystallization ages. These cannot be directly determined on diamond, but they can be calculated using radiogenic isotopic systematics of suitable minerals included in a diamond. This method relies on the assumption that the mineral inclusions were in isotopic equilibrium with the diamond-forming medium. We evaluated the validity of Sm-Nd ages yielded by clinopyroxene inclusions by combining crystallographic orientation analyses and Nd diffusion modeling at the relevant conditions for Earth's cratonic mantle. We investigated the crystallographic orientation relationships (CORs) for 54 clinopyroxene inclusions within 18 diamonds from South Africa and Siberia. Clinopyroxene inclusions in some diamonds showed specific CORs with their hosts, indicating possible syngenesis. Other samples had clusters of clinopyroxene inclusions sharing the same orientation but no specific orientation relative to their hosts, indicating that the inclusions are older than the diamond (i.e., they are protogenetic). Diffusion modeling in the temperature range typical for lithospheric diamonds (900–1400 °C) showed that resetting of the Sm-Nd isotopic system in clinopyroxene grains larger than 0.05 mm requires geologically long interaction with the diamond-forming fluid/melt (>3.5 m.y. at average temperature of ~1150 °C). Depending on inclusion size and temperature regime, protogenetic clinopyroxene inclusions may not fully reequilibrate during diamond-formation events. We suggest that small clinopyroxene inclusions (<0.2 mm) that equilibrated at temperatures higher than 1050–1080 °C may be the most suitable for age determinations.Diamonds and their inclusions are samples of Earth's interior and provide information about the geological processes that have operated over much of our planet's existence (Howell et al., 2020). The temporal significance of information derived from inclusions in diamonds depends on whether the inclusions and diamonds formed simultaneously (syngenesis) or if the inclusions were entrapped as preexisting grains (protogenesis) during diamond growth and failed to reach isotopic equilibrium upon entrapment. However, even protogenetic mineral grains can yield accurate diamond formation ages if their isotopic composition was re-equilibrated upon inclusion in diamond—these are termed synchronous inclusions (Nestola et al., 2019; Pamato et al., 2021).Distinguishing between proto- and syngenetic inclusions can be challenging. The traditional proof for syngenesis, apart from epitaxial relationships between inclusion and host (e.g., Jacob et al., 2016), has been the imposition of the diamond's morphology on the inclusion. However, this criterion has been disputed by Nestola et al. (2014), who found evidence of protogenesis for some olivine inclusions with diamond-imposed shape. The argument for protogenesis was the finding of clusters of olivine inclusions that are iso-oriented relative to one another but randomly oriented with respect to the diamond hosts. These clusters were interpreted as remnants of original olivine single crystals that were partially dissolved during the formation of the host diamond.Since these findings, many studies have been carried out to study the crystallographic orientation relationships (CORs) between diamond and its inclusions and explore their significance in terms of syn- versus protogenesis (e.g., Neuser et al., 2015; Milani et al., 2016; Davies et al., 2018; Nimis et al., 2018, 2019; Nestola et al., 2019; Sobolev et al., 2020; Pamato et al., 2021). Clinopyroxenes represent ~12% of all inclusions in lithospheric diamonds (Stachel and Harris, 2008), but a statistically significant COR data set for clinopyroxene inclusions is still lacking.Knowing the temporal relationships between inclusions and diamonds is crucial for the correct interpretation of diamond ages. These are determined by applying radiogenic isotope systematics to mineral inclusions under the assumption of synchronicity. The most used radiogenic isotope chronometers are Re-Os on sulfides and Sm-Nd on garnet and clinopyroxene (e.g., Richardson et al., 1984, 1990, 1993; Pearson et al., 1998; Koornneef et al., 2017; Timmerman et al., 2017; Gress et al., 2021). If inclusions predate the diamond host, obtaining valid isotopic ages from these protogenetic inclusions requires the inclusions to have reequilibrated isotopically at the time of diamond formation. Diffusive reequilibration is mainly a function of temperature and grain size. Several examples in the literature show that reequilibrated protogenetic inclusions in diamond can indeed yield valid diamond ages (Westerlund et al., 2004; Smit et al., 2016, 2019; Aulbach et al., 2018).Recent numerical modeling of Os diffusion in sulfides showed that the Re-Os system can rapidly reequilibrate at the relevant conditions for diamond formation (Pamato et al., 2021). Similar results were also obtained for the Sm-Nd method in protogenetic garnet inclusions, except for uncommon diamond formation conditions, e.g., at low temperature (900–1000 °C), as well as for large inclusion sizes (>0.2 mm) (Nestola et al., 2019). Clinopyroxenes coexisting with garnets in the same diamond host allow a two-mineral Sm-Nd isochron approach, which is likely more accurate than diamond model ages based on one mineral alone (e.g., Richardson, 1986; Richardson et al., 1993; for an extensive review, see Pearson and Shirey, 1999). It is therefore crucial to know whether clinopy-roxene inclusions in diamond are protogenetic and, if they are, whether they are likely to have been in diffusive equilibrium with the diamond-forming medium.We investigated the CORs of 54 clinopyroxene inclusions in 18 diamonds and provide evidence that the inclusions are protogenetic in several cases. Based on diffusion modeling of Nd in clinopyroxene at conditions typical for lithospheric diamonds, we provide boundary conditions for the reliability of the Sm-Nd method on clinopyroxene for dating diamonds.The crystallographic orientations of 54 clinopyroxene (cpx) inclusions within 18 diamonds from three kimberlites were studied by single-crystal X-ray diffraction (for details on data collection and processing, see the Supplemental Material1). More specifically, we studied 46 cpx (8 eclogitic, 27 websteritic, 3 peridotitic/websteritic, and 8 peridotitic) in 13 diamonds (3 eclogitic, 5 websteritic, 2 peridotitic/websteritic, 3 peridotitic) from Voorspoed, South Africa; 5 cpx (3 eclogitic, 2 peridotitic) in 2 diamonds (1 eclogitic, 1 peridotitic) from Cullinan, South Africa; and 3 cpx (1 eclogitic, 2 peridotitic) in 3 diamonds (1 eclogitic, 2 peridotitic) from Udachnaya, Siberian Russia (Table S1 in the Supplemental Material). A representative diamond studied in this work is shown in Figure 1.The relative crystallographic orientations between cpx inclusions and their diamond hosts are shown in Figure 2A. Fourteen (14) out of 54 cpx inclusions (~26%, all from Voorspoed) showed a specific COR, according to the terminology defined by Griffiths et al. (2016) for inclusion-host systems. In particular, for all these inclusions, the cpx (100) and (111) planes coincided within 4° with the diamond (111) and (001) planes, respectively (Fig. 2B; Table S1). More detail about the statistical method we used for determining and interpreting these specific CORs is reported in the Supplemental Material.In all other cases, the cpx showed no special COR with the diamond. Nonetheless, pairs of nearby inclusions located less than 0.5 mm from each other and showing nearly identical orientations (within 4°) were found in diamonds L22S36 and L41S1 from Voorspoed and diamond PR4 from Cullinan (Figs. 1 and 2C). The other inclusions in the same three diamonds were randomly oriented.The presence of clusters of multiple inclusions with similar crystallographic orientations but unrelated to their hosts may be explained if the diamond-forming fluid/melt forced the selective partial dissolution of mantle minerals, and the remaining portions of a preexisting cpx were encapsulated upon diamond growth. A very similar interpretation was proposed for 12 similar clusters of iso-oriented inclusions in diamonds worldwide (Nestola et al., 2014; Milani et al., 2016; Nestola et al., 2019; Nimis et al., 2019; Pamato et al., 2021), as well as for two iso-oriented cpx grains: one enclosed within and one external to a diamond in a diamondiferous xenolith from Finsch, South Africa (Nestola et al., 2017). The orientation patterns observed for cpx inclusions in diamonds L22S36, L41S1, and PR4 thus support a protogenetic relationship between at least these specific inclusions and their diamond hosts.Dating methods using radiogenic isotope systems record the time of the last diffusive equilibration, namely, the point in time when the mineral was effectively isolated from diffusional interaction with its surroundings. This can be achieved by cooling below the system-specific closure temperature (Ganguly and Tirone, 1999), at which diffusive exchange becomes inefficient, and/or when a mineral is entrapped by its diamond host and thus effectively is shielded from further interaction with Earth's mantle. Since diffusional reequilibration rates for a specific element in a mineral grain mainly depend on temperature and grain size, protogenetic minerals may not entirely reequilibrate at the time of diamond formation. Depending on the degree of reequilibration, isochrons and model ages obtained from such protogenetic inclusions can vary from providing no valid time information to presenting significant scatter and high uncertainty on the isotopic age if they experienced partial isotopic reequilibration (Nestola et al., 2019; Pamato et al., 2021).We modeled the diffusion of Nd in cpx between 800 °C and 1600 °C and 2 and 12 GPa. This range includes the typical pressure-temperature conditions for diamond formation in the cratonic mantle; i.e., 900–1400 °C and 4–7 GPa (Stachel and Harris, 2008). The average diamond formation temperatures were estimated to be 1160 ± 110 °C (±1σ; n = 164) for peridotitic and 1170 ± 110 °C (n = 144) for eclogitic diamonds based on geothermobarometry of various types of mineral inclusions in diamonds worldwide (Stachel and Harris, 2008; Stachel and Luth, 2015). Average residence temperatures based on the nitrogen-aggregation state of diamonds were also very similar, i.e., 1146 ± 50 °C (n = 399) for peridotitic and 1141 ± 48 °C (n = 256) for eclogitic diamonds, assuming a mantle residence of 3 b.y. (Stachel and Harris, 2008). In comparison, diamond formation at temperatures above 1300 °C is very rare for cratonic diamonds, and temperatures above 1400 °C are even rarer, since these temperatures exceed the mantle adiabat (Stachel and Harris, 2008). The typical temperature range for cratonic diamond formation includes temperatures that may be either below or above the closure temperature for the Sm-Nd system in cpx of 1000–1150 °C (Van Orman et al., 2002). At temperatures above the closure temperature, diffusive equilibration is efficient, depending on grain sizes and potential pressure effects, which are small for Nd in cpx (see the Supplemental Material).Typical grain sizes for inclusions in diamonds are between 0.05 and 0.2 mm, and 0.1 mm is the typical average size, whereas larger grains of ~0.2 mm are rare, and sizes of 0.5 mm are exceptional (Stachel et al., 2005). Modeling results for the diffusivity of Nd in cpx for these grain sizes are shown in Figure 3 (see the Supplemental Material for a detailed description of the diffusion model). For a typical cratonic geotherm of 40 mW m-2 (Hasterok and Chapman, 2011) (Fig. 3B) and at 1160 °C, a 0.05 mm cpx grain would require reequilibration with the diamond-forming fluid for around 3.5 m.y. to reset the isotopic clock and accurately record the age of diamond formation once included in the diamond. For larger grain sizes, the model predicts ~14 m.y. for 0.1 mm, 56 m.y. for 0.2 mm, and ~350 m.y. for a 0.5 mm inclusion (Fig. 3A).At higher temperatures, the calculated equilibration times for cpx are shorter. For instance, at 1300–1400 °C (near the upper limit for lithospheric diamond formation), the equilibration times range from tens of thousands of years for a 0.05 mm grain, to hundreds of thousands of years for a 0.1 mm grain, and to a few million years for a 0.5 mm grain. Nevertheless, these times are an order of magnitude longer than for similarly sized garnets (Nestola et al., 2019). At lower temperatures of 900–1000 °C (near the lower end for cratonic diamonds), the equilibration times are significantly longer, ranging from 450 m.y. at 1000°C to 20 b.y. at 900°C for even the smallest grain size of 0.05 mm, reflecting the inefficiency of Nd diffusivity at such low temperatures (Van Orman et al., 2002). These time spans are geologically significant or even unrealistic. Therefore, cpx inclusions in diamonds from such temperature regimes are unlikely to yield statistically meaningful isochrons nor valid model ages.Our model considered the ideal cases of perfectly crystallized cpx grains in diffusional exchange with a rare earth element–rich fluid. In reality, lattice defects in minerals may significantly accelerate diffusion, and partial dissolution/reprecipitation may further enhance chemical reequilibration. Therefore, the calculated equilibration times should be intended as the maximum possible times required for a specific cpx grain to reset its isotopic clock by interaction with the diamond-forming medium, before the grain is fully enclosed in the diamond.The closure temperature of the Sm-Nd system in cpx is significantly higher than that in garnet (1000–1150°C versus 750–900°C; Ganguly and Tirone, 1999; Van Orman et al., 2001, 2002) and closer to the average temperature of diamond formation in the cratonic upper mantle (1150°C). The time spans required for efficient isotopic equilibration of a protogenetic cpx with the diamond-forming fluid before encapsulation in the diamond host (namely, during any specific diamond growth episode) are orders of magnitude longer for cpx than for garnet, depending on the grain size. While our diffusion model used ideal scenarios, it did place realistic limits on the suitability of cpx inclusions to date their host diamonds. It raises awareness to the fact that, when dealing with protogenetic grains, cpx may be a less reliable timekeeper for diamond formation than garnet. More generally, among the most widely used methods for dating diamonds, Re-Os dating of sulfide inclusions stands out for being least affected by the proto- versus syngenetic nature of the inclusions (e.g., Smit et al., 2016, 2019; Aulbach et al., 2018; Pamato et al., 2021), whereas Sm-Nd dating of cpx inclusions appears to be the least robust to inclusion-host timing relationships. Therefore, careful selection of suitable cpx samples (i.e., small grain size and/or higher equilibration temperatures) would always be desirable. Single-cpx thermometry of peridotitic cpx (Nimis and Taylor, 2000) may help to discard excessively low-temperature samples in advance of isotopic analyses.We thank the European Research Council for support provided to F. Nestola (grant 307322) and the European Union's Horizon 2020 research for support to M.G. Pamato (Marie Skłodowska-Curie grant 796755). D.E. Jacob was supported by the Australian Research Council (CE110001017). We thank Matteo Chinellato for the photos in Figure 1. An anonymous reviewer, S. Mikhail, and particularly K. Smit are also thanked for constructive comments that strongly improved this work.

中文翻译：

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钻石中的原生单斜辉石包裹体和 Nd 扩散模型——对钻石测年的启示

钻石见证了地幔中超过 3 年的过程，我们了解这些过程的关键是确定钻石的结晶年龄。这些不能直接在钻石上确定，但可以使用钻石中包含的合适矿物的放射性同位素系统学来计算。该方法依赖于矿物包裹体与金刚石形成介质处于同位素平衡的假设。我们通过在地球克拉通地幔的相关条件下结合晶体取向分析和 Nd 扩散模型来评估由单斜辉石包裹体产生的 Sm-Nd 年龄的有效性。我们调查了来自南非和西伯利亚的 18 颗钻石中 54 种单斜辉石包裹体的晶体取向关系 (COR)。一些钻石中的单斜辉石内含物与它们的宿主显示出特定的 COR，这表明可能是同源的。其他样品有成簇的单斜辉石包裹体，它们具有相同的方向，但相对于它们的宿主没有特定的方向，表明这些包裹体比钻石更古老（即它们是原生的）。岩石圈钻石典型温度范围 (900–1400 °C) 的扩散模型表明，在大于 0.05 mm 的单斜辉石晶粒中重置 Sm-Nd 同位素系统需要与金刚石形成流体/熔体（>3.5 my平均温度约为 1150 °C）。根据包裹体尺寸和温度状况，原生单斜辉石包裹体可能不会在钻石形成事件期间完全重新平衡。我们建议小单斜辉石包裹体 (<0. 2 毫米）在高于 1050–1080 °C 的温度下达到平衡可能最适合确定年龄。钻石及其内含物是地球内部的样本，并提供了有关在我们星球的大部分存在过程中运行的地质过程的信息（豪厄尔等人，2020）。从钻石中的内含物获得的信息的时间意义取决于内含物和钻石是否同时形成（同生），或者内含物是否在钻石生长过程中作为预先存在的晶粒被截留（原生）并且在截留时未能达到同位素平衡。然而，即使是原生矿物颗粒，如果它们的同位素组成在包含在金刚石中时得到重新平衡，也可以得出准确的金刚石形成年龄——这些被称为同步夹杂物（Nestola 等人，2019；Pamato et al., 2021)。区分原生包裹体和同源包裹体可能具有挑战性。除了内含物和宿主之间的外延关系（例如，Jacob 等人，2016 年）之外，同源的传统证明是将钻石的形态强加于内含物上。然而，Nestola 等人对这一标准提出了质疑。(2014)，他发现了一些具有钻石形状的橄榄石内含物的原生形成证据。原生发生的论据是发现了橄榄石内含物簇，这些内含物相对于彼此是等向的，但相对于钻石主体是随机定向的。这些簇被解释为原始橄榄石单晶的残余物，在主体金刚石的形成过程中部分溶解。由于这些发现，已经进行了许多研究来研究钻石与其内含物之间的晶体取向关系 (CORs)，并探讨它们在同源性与原生质发生方面的意义（例如，Neuser 等人，2015；Milani 等人，2016；Davies 等人） al., 2018; Nimis et al., 2018, 2019; Nestola et al., 2019; Sobolev et al., 2020; Pamato et al., 2021)。单斜辉石占岩石圈钻石中所有包裹体的约 12%（Stachel 和 Harris，2008 年），但仍然缺乏具有统计意义的单斜辉石包裹体 COR 数据集。了解包裹体与钻石之间的时间关系对于正确解释钻石年龄至关重要. 这些是通过在假设同步性下将放射性同位素系统学应用于矿物包裹体来确定的。最常用的放射性同位素天文钟是硫化物上的 Re-Os 和石榴石和单斜辉石上的 Sm-Nd（例如，Richardson 等人，1984、1990、1993；Pearson 等人，1998；Koornneef 等人，2017；Timmerman 等人）等人，2017 年；Gress 等人，2021 年）。如果包裹体早于钻石宿主，则从这些原生包裹体中获得有效的同位素年龄需要包裹体在钻石形成时已经重新平衡同位素。扩散再平衡主要是温度和晶粒尺寸的函数。文献中的几个例子表明，钻石中重新平衡的原生内含物确实可以产生有效的钻石年龄（Westerlund 等人，2004 年；Smit 等人，2016 年，2019 年；Aulbach 等人，2018 年）。最近对硫化物中 Os 扩散的数值模拟表明，Re-Os 系统可以在金刚石形成的相关条件下快速重新平衡（Pamato 等人，2021 年）。对于原生石榴石包裹体的 Sm-Nd 方法也获得了类似的结果，除了不常见的金刚石形成条件，例如在低温 (900–1000 °C) 以及大尺寸包裹体 (>0.2 mm) (Nestola等人，2019）。单斜辉石与石榴石共存于同一钻石主体中，允许采用两种矿物 Sm-Nd 等时线方法，这可能比仅基于一种矿物的钻石模型年龄更准确（例如，Richardson，1986；Richardson 等，1993；对于广泛的评论，见 Pearson 和 Shirey，1999）。因此，了解钻石中的单斜辉石包裹体是否是原生的至关重要，如果是，它们是否可能与钻石形成介质处于扩散平衡状态。我们研究了 18 颗钻石中 54 个单斜辉石包裹体的 CORs，并提供了一些证据表明这些包裹体是原生的。基于岩石圈钻石典型条件下单斜辉石中 Nd 的扩散模型，我们为单斜辉石测年钻石的 Sm-Nd 方法的可靠性提供了边界条件。 来自三个金伯利岩的 18 颗钻石中 54 个单斜辉石 (cpx) 包裹体的晶体取向通过单晶 X 射线衍射进行了研究（有关数据收集和处理的详细信息，请参阅补充材料 1）。更具体地说，我们研究了 13 颗钻石（3 颗榴辉岩、5 颗橄榄岩、2 个橄榄岩/websteritic，3 个橄榄岩）来自南非 Voorspoed；来自南非库里南的 2 颗钻石（1 颗榴辉岩，1 颗橄榄岩）中的 5 cpx（3 颗榴辉岩，2 颗橄榄岩）；和来自俄罗斯西伯利亚乌达赫纳亚的 3 颗钻石（1 颗榴辉岩，2 颗橄榄岩）中的 3 cpx（1 颗榴辉岩，2 颗橄榄岩）（补充材料中的表 S1）。在这项工作中研究的具有代表性的金刚石如图 1 所示。cpx 夹杂物与其金刚石主体之间的相对晶体取向如图 2A 所示。根据 Griffiths 等人定义的术语，54 个 cpx 夹杂物中的十四 (14) 个（约 26%，全部来自 Voorspoed）显示出特定的 COR。（2016）用于包含主机系统。特别是对于所有这些夹杂物，cpx（100）和（111）平面分别与金刚石（111）和（001）平面重合在4°以内（图2B；表 S1)。有关我们用于确定和解释这些特定 COR 的统计方法的更多详细信息，请参见补充材料。在所有其他情况下，cpx 显示钻石没有特殊的 COR。尽管如此，在来自 Voorspoed 的钻石 L22S36 和 L41S1 以及来自 Cullinan 的钻石 PR4 中发现了彼此相距不到 0.5 毫米并且显示几乎相同的方向（4° 以内）的成对的附近包裹体（图 1 和 2C）。相同的三颗钻石中的其他包裹体是随机取向的。如果金刚石形成流体/熔体迫使地幔矿物选择性部分溶解，则可以解释具有相似晶体取向但与其宿主无关的多个包裹体簇的存在，并且先前存在的 cpx 的剩余部分在金刚石生长时被封装。对全球钻石中 12 个类似的等向内含物簇提出了非常相似的解释（Nestola 等人，2014；Milani 等人，2016；Nestola 等人，2019；Nimis 等人，2019；Pamato 等人） ., 2021)，以及两个等向 cpx 晶粒：一个封闭在来自南非 Finsch 的含金刚石捕虏体中的金刚石内部和一个外部（Nestola 等人，2017 年）。因此，在钻石 L22S36、L41S1 和 PR4 中观察到的 cpx 内含物的取向模式支持了至少这些特定内含物与其钻石宿主之间的原生关系。使用放射性同位素系统的测年方法记录了最后一次扩散平衡的时间，即点在矿物与周围环境的扩散相互作用有效隔离的时候。这可以通过冷却到系统特定的闭合温度以下来实现（Ganguly 和 Tirone，1999 年），此时扩散交换变得低效，和/或当矿物被其金刚石主体截留并因此有效地屏蔽了与地球的进一步相互作用时地幔。由于矿物晶粒中特定元素的扩散再平衡速率主要取决于温度和晶粒尺寸，因此原生矿物在金刚石形成时可能不会完全再平衡。根据再平衡的程度，从这些原生包裹体中获得的等时线和模型年龄可能会有所不同，从不提供有效时间信息到在经历部分同位素再平衡时，同位素年龄呈现显着分散和高度不确定性（Nestola 等人，2019 年；Pamato等人，2021）。我们在 800 °C 和 1600 °C 以及 2 和 12 GPa 之间模拟了 Nd 在 cpx 中的扩散。该范围包括克拉通地幔中钻石形成的典型压力-温度条件；即 900–1400 °C 和 4–7 GPa (Stachel and Harris, 2008)。根据全球钻石中各类矿物包裹体的地温气压测量，橄榄岩的平均钻石形成温度估计为 1160 ± 110 °C (±1σ；n = 164)，榴辉岩钻石的平均钻石形成温度估计为 1170 ± 110 °C (n = 144) （斯塔切尔和哈里斯，2008 年；斯塔切尔和卢斯，2015 年）。基于金刚石的氮聚集状态的平均停留温度也非常相似，即橄榄岩为 1146 ± 50 °C (n = 399)，榴辉岩金刚石为 1141 ± 48 °C (n = 256)，假设地幔居住3 （斯塔切尔和哈里斯，2008 年）。相比下，对于克拉通钻石来说，在 1300 °C 以上的温度下形成钻石是非常罕见的，而 1400 °C 以上的温度则更为罕见，因为这些温度超过了地幔的绝热温度（Stachel 和 Harris，2008 年）。克拉通金刚石形成的典型温度范围包括可能低于或高于 Sm-Nd 系统的闭合温度（以 cpx 为单位）的温度，即 1000-1150 °C（Van Orman 等人，2002 年）。在高于闭合温度的温度下，扩散平衡是有效的，具体取决于晶粒尺寸和潜在压力效应，这对于 cpx 中的 Nd 来说很小（参见补充材料）。金刚石中夹杂物的典型晶粒尺寸在 0.05 和 0.2 毫米之间，并且0.1 毫米是典型的平均尺寸，而约 0.2 毫米的较大晶粒很少见，而 0.5 毫米的尺寸是例外的（Stachel 等人，2005 年）。对于这些晶粒尺寸，cpx 中 Nd 扩散率的建模结果如图 3 所示（有关扩散模型的详细描述，请参见补充材料）。对于 40 mW m-2 的典型克拉通地热（Hasterok 和 Chapman，2011）（图 3B），在 1160 °C 下，0.05 mm cpx 晶粒需要与金刚石形成流体重新平衡约 3.5 my 才能重置同位素钟，准确记录钻石一旦包含在钻石中的形成年龄。对于较大的晶粒尺寸，该模型预测 0.1 mm 为 ~14 my，0.2 mm 为 56 my，0.5 mm 夹杂物为 ~350 my（图 3A）。在较高温度下，计算的 cpx 平衡时间更短。例如，在 1300-1400 °C（接近岩石圈金刚石形成的上限），0.0 的平衡时间范围为数万年。05 毫米晶粒，0.1 毫米晶粒到数十万年，0.5 毫米晶粒到几百万年。然而，这些时间比类似尺寸的石榴石长一个数量级（Nestola 等人，2019 年）。在 900–1000 °C 的较低温度下（接近克拉通钻石的下限），平衡时间明显更长，从 1000°C 时的 450 到 900°C 时的 20 微米，即使是最小的晶粒尺寸 0.05 毫米，反映了在如此低的温度下 Nd 扩散率的低效率（Van Orman 等人，2002 年）。这些时间跨度具有地质意义，甚至是不切实际的。因此，来自这种温度状态的钻石中的 cpx 夹杂物不太可能产生具有统计学意义的等时线，也不太可能产生有效的模型年龄。我们的模型考虑了完美结晶的 cpx 晶粒与富含稀土元素的流体进行扩散交换的理想情况。实际上，矿物中的晶格缺陷可能会显着加速扩散，部分溶解/再沉淀可能会进一步增强化学再平衡。因此，计算的平衡时间应为特定 cpx 颗粒在颗粒完全包裹在金刚石中之前通过与金刚石形成介质相互作用重置其同位素时钟所需的最大可能时间。 Sm 的闭合温度-cpx 中的 Nd 系统显着高于石榴石中的（1000–1150°C 对 750–900°C；Ganguly 和 Tirone，1999；Van Orman 等人，2001，2002）并且更接近金刚石形成的平均温度在克拉通上地幔（1150°C）。在包裹在金刚石主体中之前（即在任何特定的金刚石生长过程中），原始 cpx 与金刚石形成流体的有效同位素平衡所需的时间跨度对于 cpx 比石榴石长几个数量级，具体取决于粒度. 虽然我们的扩散模型使用了理想的场景，但它确实对 cpx 内含物与它们的主钻石约会的适用性设置了现实限制。它提高了人们对这样一个事实的认识，即在处理原生颗粒时，cpx 在钻石形成方面可能不如石榴石可靠。更一般地说，在最广泛使用的钻石定年方法中，硫化物包裹体的 Re-Os 测年因受包裹体的原始与同生性质的影响最小（例如，Smit 等人，2016 年，2019 年；Aulbach 等人）等人，2018；帕马托等人，2021），而 cpx 夹杂物的 Sm-Nd 测年似乎对夹杂物-宿主时间关系最不稳健。因此，始终需要仔细选择合适的 cpx 样品（即小晶粒尺寸和/或更高的平衡温度）。橄榄岩 cpx 的单 cpx 测温法（Nimis 和 Taylor，2000）可能有助于在同位素分析之前丢弃温度过低的样品。我们感谢欧洲研究委员会对 F. Nestola（赠款 307322）和欧盟的支持支持 MG Pamato 的 Horizo​​n 2020 研究（Marie Skłodowska-Curie 赠款 796755）。DE Jacob 得到了澳大利亚研究委员会 (CE110001017) 的支持。我们感谢 Matteo Chinellato 提供图 1 中的照片。匿名审稿人 S. Mikhail，特别是 K.