Introduction

The kinetics of crystal nucleation and growth are fundamental for the interpretation of rock textures in terms of thermal history of a magma during its ascent to the surface and to constrain timescales of magmatic processes. Crystallization kinetics has been investigated in lunar and terrestrial basalts (Dowty et al. 1974; Lofgren 1974, 1983; Grove and Walker 1977; Grove and Raudsepp 1978; Walker et al. 1978; Lesher et al. 1999) and in silicic hydrous systems (Lofgren 1980; Kirkpatrick et al. 1981; Hammer and Rutherford 2002; Hammer 2006; Zieg and Lofgren 2006; Pupier et al. 2008). However, there are relatively few investigations of alkaline compositions (e.g. Conte et al. 2006; Agostini et al. 2013; Arzilli et al. 2015).

Clinopyroxene (Cpx) is a common phenocryst in basaltic systems and, due to its wide crystallization range, it may contain the most complete record of evolutionary history of a magma. To date, experimental studies of Cpx crystallization kinetics (e.g. crystal growth rate) in primitive alkaline compositions are few and limited to low pressure conditions (≤ 0.5 GPa; e.g. Orlando et al. 2008; Arzilli and Carroll 2013; Pontesilli et al. 2019). To constrain clinopyroxene crystallization kinetics at high pressure, we experimentally investigated the growth rate of clinopyroxene in an alkaline basalt (APR16 sample; Bonechi et al. 2017) representative of the least-evolved rocks of the whole Campi Flegrei Volcanic District (CFVD). Both anhydrous and hydrous experiments were conducted at a pressure of ~ 0.8 GPa that is representative of the crustal-mantle boundary (~ 25 km of depth; Di Stefano et al. 2011) in the Phlegraean area, and the location of a possible crystallization zone, hypothesized on the basis of melt inclusion studies (Mormone et al. 2011; Moretti et al. 2013), seismic data (Di Stefano et al. 1999; Piochi et al. 2005a, b; Chiarabba et al. 2008) and gravimetric and petrological modelling (Fedi et al. 2018). Moreover, Perinelli et al. (2019) demonstrated that early magmatic storage and crystallization at high pressure (i.e. at the local crust base) contributed to the differentiation of primitive magmas of the Campania Province. For these reasons, the experimental data on high-pressure clinopyroxene growth kinetic will be useful for constraining timescales of magmatic processes in this area. In particular, the estimation of the magma ascent rate in the CFVD is of paramount significance in terms of volcanic hazard. Indeed, deep-level ascent rates may be the key to understand the triggering mechanisms of volcanic eruptions, and are essential for understanding the rates at which magmas are supplied to volcanic complexes (Armienti et al. 2013; Perinelli et al. 2018). Thus, to investigate the CFVD magmas transport at Moho-lower crust depth and provide an estimate of magma recharge of the deep reservoirs, we assessed the cooling rate and the deep-level ascent rates of K-basaltic magmas by combining the clinopyroxene growth rate determined by high-pressure crystallization experiments with data from crystal size distribution analyses and thermobarometry of clinopyroxenes occurring in the most primitive scoria clasts of the CFVD.

Experimental and analytical techniques

Starting material

The starting material used in this work is an anhydrous glass (APR16GL; Table 1) prepared by melting the APR16 natural powder in a gas-mixing furnace at 1400 °C and atmospheric pressure for 15 min to reduce all Fe3+ to Fe2+ using a CO/CO2 gas mixture at the Bayerisches Geoinstitut (Bayreuth, Germany). The starting material did not contain crystalline phases, as analysed by both microprobe and image analyses. The APR16 sample (Table 1) is a primitive alkaline basalt found as scoria clast in the deposits of the Solchiaro hydromagmatic centre located in Procida island (Campi Flegrei, Italy). It is characterized by 12 vol.% of forsteritic olivine and diopsidic clinopyroxene phenocrysts in a groundmass of olivine, clinopyroxene, plagioclase, Ti-magnetite, alkali feldspar and glass (D’Antonio et al. 1999; De Astis et al. 2004).

Table 1 Composition (wt.%) of APR16 rock sample, APR16GL starting material, SCE and SOG rock samples
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Experimental technique

Experiments were performed, at the isobaric pressure of 0.8 GPa, as function of temperature, water content and time by using the ½ inch end loaded piston cylinder apparatus at the HP-HT Laboratory of the Earth Sciences Department (Sapienza University, Rome, Italy). The assembly consists of an outer CaF2 cell, graphite furnace and MgO crushable spacers. Firstly, the APR16GL glass was crushed and ground in an agate mortar under acetone to a grain size ≤ 10 μm. Then this glassy powder (40–50 mg) was dried at 110 °C for at least 2 h to remove the moisture before being loaded and pressed into Au75Pd25 capsules, along with distilled water for hydrous experiments, and then welded. For each experiment, the capsule was placed in the MgO crushable spacers and surrounded by powder of alumina (for no water added experiments) or pyrophyllite (for water added ones). Temperature was measured using a type D W3Re97-W25Re75 thermocouple and maintained with an uncertainty of ± 5 °C. The experimental assembly was first pressurized to the target pressure by a piston-out procedure (Johannes et al. 1971; Presnall et al. 1978) that applies an overpressure of ~ 10% of the run pressure and then gradually increases the temperature to the working temperature, while correcting for pressure drops due to stress relaxation within the assembly during heating. The heating rate was imposed at 150 °C/min. The sample was maintained at the pressure and temperature for a given duration (nominal duration), and then quenched by turning off the power. The temperature dropped to below 500 °C within < 5 s (average cooling rate of 150 °C/s). All the runs were self-buffered; we estimated fO2 through the equation of Kress and Carmichael (1991) using the liquid Fe3+/Fetot mole ratios from KD Fe-Mg ol/liq calculated following Toplis (2005). This procedure yielded fO2 values of ΔNNO + 0.12 to + 2, in agreement with those estimated for similar furnace assemblages (Conte et al. 2009; Weaver et al. 2013). We performed a total of 24 experiments, whose experimental conditions are reported in Table 2. The experiments were divided into three series based on the amount of water added to the starting material. All series were run at a constant pressure and at four different dwell times (0.25, 3, 6 and 9 h). Experiments of Series 1 (i.e. APR16-C1) were run at anhydrous conditions (no water added to the starting material, NWA) and at temperatures of 1200 °C (subseries APR16-C1A) and 1250 °C (subseries APR16-C1B). Experiments of Series 2 (i.e. APR16-C2) were run at hydrous conditions (2 wt.% H2O added to the starting material), and at temperatures of 1170 °C (subseries APR16-C2A) and 1220 °C (subseries APR16-C2B). Experiments of Series 3 (i.e. APR16-C3) were run at hydrous conditions (4 wt.% H2O added to the starting material), and at temperatures of 1080 °C (subseries APR16-C3A) and 1030 °C (subseries APR16-C3B). Initial water contents and experimental temperatures were chosen on the basis of the melt inclusion studies (Moretti et al. 2013) and phase data were taken from high-pressure anhydrous/hydrous experiments on Procida alkaline basalt magmas as reported in Perinelli et al. (2019).

Table 2 Experimental run conditions, calculated water contents, phase assemblages and proportions in run products
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Finally, because undercooling (ΔT = Tliquidus − Texperiment) is one of the critical parameters that influences the kinetics of magma crystallization, we determined the effective undercooling (ΔTeff) for each sample. This is defined as the difference between the equilibrium clinopyroxene liquidus temperature (TCpxL) and the experimental temperature (Hammer and Rutherford 2002). The TCpxL values used to calculate ΔTeff for each experiment were taken from Procida K-basalt experimental data (Perinelli et al. 2019) and from calculations using MELTS software (Ghiorso and Sack 1995; Asimow and Ghiorso 1998). Resulting TCpxL and ΔTeff are listed in Table 2.

Analytical techniques

The recovered samples were mounted in epoxy resin, ground flat and polished. Textural aspects of the recovered samples were analysed by Scanning Electron Microscopy (SEM) using a FEI Quanta-400 equipped for microanalysis with an EDAX Genesis system at the Earth Sciences Department (Sapienza University, Rome, Italy). A minimum of eight backscattered electron (BSE) images were acquired for each experimental sample in order to accurately measure the nucleation of clinopyroxene and other crystallized mineral phases (e.g. Clarke et al. 2007; Couch 2003; Hammer et al. 2000). Phase compositions were analysed at the CNR-Istituto di Geologia Ambientale e Geoingegneria (Rome), with a Cameca SX50 electron microprobe equipped with five wavelength dispersive spectrometers (WDS). Quantitative compositional analyses were performed using 15 kV accelerating voltage and 15 nA beam current. As standards we employed metals for Mn and Cr, jadeite for Na, wollastonite for Si and Ca, orthoclase for K, corundum for Al, magnetite for Fe, rutile for Ti and periclase for Mg. Counting times were 20 s for elements and 10 s for backgrounds. Light elements were counted first to prevent loss by volatilization. The PAP correction method (Pouchou and Pichoir 1991) was used. Minerals were analysed using a beam diameter of 1 μm while for glasses a defocused electron beam of 10 to 15 μm was used. From chemical analyses, the water contents of experimental glasses were estimated according to the by-difference method (Devine et al. 1995). We are aware that this method may result in significant errors in the estimates of H2O contents in the melts, particularly for H2O-poor glasses (uncertainty of ~ 0.5 wt.% for H2Omelt ≤ 1 wt.%; Devine et al. 1995). However, the obtained H2O values are close to those determined by micro-Raman spectroscopy measurements on residual melts of equilibrium experiments performed on the same composition, at the same P, T and initial hydrous conditions (see Perinelli et al. 2019, for details). Therefore, the H2O calculated using the by-difference method, with EPM analyses, can be considered to be reliable estimates of water contents of experimental melts.

Finally, phase proportions were calculated using bulk and experimental phase compositions and the least squares regression routine implemented in EXCEL®. Image analysis conducted with ImageJ software was used to estimate the fraction of total solids in each experiment. Estimates of crystal fraction obtained by the latter approach did not produce good results for all samples due to the difficulty in clearly distinguishing the minor phases from glass by applying the thresholding process to backscattered images. However, due to the strong dominance of clinopyroxene in almost all experiments, it is reasonable to assume that the clinopyroxene crystal fraction (Cpx-ϕ) is representative of the crystallinity of each experiment. Figure S1 in Online Resource 1 displays the comparison of Cpx-ϕ values obtained by the two methods.

Growth rate calculation

In the SEM images, crystal dimensions were measured using the measure tool in the ImageJ® software. The maximum growth rate (GL) values were calculated using a common method reported in literature (Burkhard 2002; Hammer and Rutherford 2002; Couch et al. 2003; Baker 2008; Iezzi et al. 2011):

$$ {G}_L=\frac{(L.W)^{0.5}}{t\ast 2} $$
(1)

where L and W are the mean length and width, respectively, of the ten largest crystals for each BSE image (Fig. 1) and t is the duration of the experiments (s). As also shown in the literature, the main growth event often occurs at the beginning of the experiment, since diffusion- or interface-controlled growth normally display lower incremental growth rates as the system approaches equilibrium (e.g. Arzilli et al. 2015; Couch et al. 2003; Orlando et al. 2008). Consequently, long-lasting experiments could show an apparent decrease in GL as time increases.

Fig. 1
figure 1

Backscattered SEM image of a typical experimental result. L and W are the dimensions (i.e. length and width, respectively) that were measured to calculate the growth rate

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Crystal size distribution analysis

For textural analyses, we used ImageJ® software (Abramoff et al. 2004; Schneider et al. 2012) on BSE images from which binary images of each mineral were constructed following the procedure described by Philpotts and Ague (2009). Manual reconstruction of edges of overlapping crystals was necessary before conversion into binary images. Subsequently, the data were transferred to the CSDcorrections® software (v. 1.62018; Higgins 2000, 2002) to perform the 2D to 3D conversion and the calculation of CSD plots for each mineral type. Following Higgins (1994), a clinopyroxene aspect ratio of 1:2:2 and a roundness factor of 0.1 were used, and crystals were assumed to have a uniform shape. Indeed, most of the clinopyroxene crystals have an aspect ratio (A, long/short dimension) ranging from one to four with equant habit, while only few crystals have higher aspect ratios (A ~ 8) with elongate habits, as shown in Fig. 2 and Fig. S2 in Online Resource 1. The APR16-C1A runs reported in Fig. 2 suggest that crystals tend to start anisotropic (e.g. APR16-C1Aa, APR16-C1Ab) and then become more equant with time (e.g. APR16-C1Ad); this is visible in all the runs (Fig. S2 in Online Resource 1).

Fig. 2
figure 2

Length vs. aspect ratio for APR16-C1A runs. We also give the width vs aspect ratio plot (lower inset) and aspect ratio histogram (upper inset)

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The CSD theory (Randolph and Larson 1971; Cashman and Marsh 1988; Marsh 1988) assumes that a steady crystal population grows with a growth rate G (cm·s−1) producing a number of crystals n(L) with length L per unit volume. The total number of crystals is:

$$ N(L)={\int}_0^Ln(L) dL $$
(2)

With a characteristic crystal residence time S, the growth rate is:

$$ G=L/\mathrm{S} $$
(3)

and the steady variation of population per size interval dL is:

$$ dn(L)/ dL=\hbox{--} n/G $$
(4)

where n is the number density of crystals.

The integration of Eq. (4) provides:

$$ n={n}_0\ \mathit{\exp}\left(-L/ GS\right)\kern0.5em $$
(5)

that taking the natural logarithm, the relation is:

$$ \ln \kern0.2em (n)=\ln \kern0.15em \left({n}_0\right)--L/ GS $$
(6)

where n0 is the number of nuclei at the time of consideration, which is represented here by the time at isothermal conditions. On a plot ln(n) versus L the continuous crystallization ideally provides a linear relation with a slope of − 1/GS, from which G may be evaluated if S is known, or vice versa. In the same plot, the intercept provides the nucleation density, ln(n0). The nucleation rate J can now be derived from:

$$ J={n}_0G $$
(7)

When the natural logarithm of the population density of crystals varies linearly with the crystal length, CSDs can provide insight into time scales of magmatic processes (e.g. Mangan 1990; Piochi et al. 2005b; Brugger and Hammer 2010a).

Experimental results

BSE images allowed us to identify differences in texture, crystal dimensions and phase abundances as well as to calculate the growth rates of the crystallized phases in each of the experimental Series and determine the Crystal Size Distribution (CSD) formed during the experiments.

Phase relations and crystallinity

The experimental products consist of glass and microlites of clinopyroxene (Cpx) ± olivine (Ol) ± plagioclase (Plg) ± oxide (Ox) ± amphibole (Amph). Small bubbles dispersed within the residual glasses or grouped along the capsule walls are frequently observed in the experiments at H2O-undersaturated conditions, that for the Procida K-basalt magmas occur when water content in the melt is < 8 wt.% (Perinelli et al. 2019). These bubbles were probably trapped within the glassy powder during the experimental charge preparation, and served as nucleation sites, as testified by the crystal clusters around them.

Phase relations obtained from the three experimental Series are shown in the diagram T vs water content in the residual glasses (H2Of; Fig. 3). The mineral assemblage as well as the phase abundances obtained in the long experiments (6 and 9 h) generally matches those obtained from equilibrium experiments reported by Perinelli et al. (2019; see Table S1 in Online Resource 2).

Fig. 3
figure 3

Phase relation data from this experimental study plotted in the diagram of temperature vs. water content in the melt phase (H2Of). The diagram reports experimental saturation curves (dashed when estimated), phase assemblages and stability fields at 0.8 GPa, for K-basaltic scoria clasts of the Solchiaro deposit and APR16GL (modified after Perinelli et al. 2019). Black stars are the experiments in which the crystallized mineral assemblage matches that obtained in the equilibrium experiments of Perinelli et al. (2019). Phase abbreviations are Liq: liquid; Cpx: clinopyroxene; Ol: olivine; Ox: oxide; Plg: plagioclase; Opx: orthopyroxene and Amph: amphibole

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For our study, mass balance calculations indicate variable crystallization degrees within each subseries of experiments showing, as a general rule, crystallinity increasing with time (Table 2). Exceptions are the APR16-C1A (NWA, 1250 °C runs) and APR16-C2A (H2Oi = 2 wt.%, 1220 °C runs) subseries, in which the initial increase of crystal fraction is followed by a significant decline in mineral abundance (i.e. runs at 9 h of dwell time; Table 2). In contrast, crystallization data determined from backscattered image analyses indicate higher degrees of crystallization than those determined by mass balance calculations and a similar crystallinity between runs of 3, 6 and 9 h for both the APR16-C1A and APR16-C2A subseries (Fig. S1 in Online Resource 1). Image analysis also shows a good correspondence between the mass balance versus image analyses for Cpx-ϕ values of the APR16-C1B (NWA, 1200 °C runs) and APR16-C2B (H2Oi = 2 wt.%, 1170 °C runs) subseries (Fig. S1 in Online Resource 1). This is probably related to the high undercooling (ΔTeff ~ 100 °C) for both the APR16-C1B and APR16-C2B experimental subseries, which drives the melt towards a crystallization degree approaching that of equilibrium conditions (Lesher et al. 1999; Conte et al. 2006; Hammer 2008). Concerning the APR16-C1A and APR16-C2A subseries experiments, several lines of evidence suggest that heterogeneous nucleation is the general rule in all experiments (i.e. preferential nucleation of clinopyroxenes along the capsule surfaces or around small bubbles, Fig. S3 in Online Resource 1). In heterogeneous nucleation, the nuclei growing on pre-existing surfaces in the liquid require less energy to reach the critical size than that required for homogeneous nucleation (Cashman 1993), where the appearance of new crystals is promoted. Thus, for the APR16-C1A and APR16-C2A experimental subseries, the variation in crystallization degree and phase relations can be explained by heterogeneous nucleation that promoted crystallization of a specific mineral phase at the expense of the others, or influenced the crystal-melt distribution along the wall of sample holder producing chemical inhomogeneities of residual glass that were not completely equilibrated.

Textural features of the experimental runs

Experimental textures of the three Series show limited variations mainly linked to the increase of crystal abundance in the charge. In general, relatively large pools of residual glass (≥ 50 × 50 μm in size; Fig. S3-S4 in Online Resource 1) are confined to the boundary of sample holder and crystal aggregation is observed (Fig. S4-S5 in Online Resource 1).

Series 1

In the runs of the subseries APR16-C1A (1250 °C, NWA; Fig. S3a in Online Resource 1), the dominant phase is Cpx while olivine (Ol) crystallizes only in the APR16-C1Ac run at 6 h (Table 2). The habit and sizes of Cpx vary with time: subhedral grains with sizes of 5 μm occur in the shortest run (APR16-C1Aa; 0.25 h), while those that are euhedral in shape and up to 15 μm in size appear in the run with longest duration (APR16-C1Ad; 9 h). Olivine is euhedral with well-faceted faces and sizes of ~ 10 μm (Fig. 4).

Fig. 4
figure 4

Backscattered SEM image of an olivine crystal showing a euhedral habit with well-faceted faces from run APR16-C1Ac of Series 1

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The runs of the subseries APR16-C1B (1200 °C, NWA; Fig. S3b in Online Resource 1) show a higher degree of crystallization than those of the APR16-C1A subseries and the mineral assemblage consists of Cpx + Ol + Plg + Ox. In the run with shortest duration (APR16-C1Ba; 0.25 h), Cpx is present as subhedral crystals, sometimes forming aggregates. With increasing duration, Cpx develops euhedral habits with sizes up to 20 μm. Similarly, Plg forms large tabular crystals (up to ~ 100 μm in length and ~ 30 μm in width) in the run with longest duration (APR16-C1Bd; 9 h). Olivine and Ox (present only in the runs at 6 and 9 h) have euhedral habits with sizes of ~ 25 and 15 μm, respectively. Some Ox crystals are characterized by a Cr-rich core.

Series 2

The mineral phases crystallized in subseries APR16-C2A (1220 °C, 2 wt.% H2Oi; Fig. S4a in Online Resource 1) are the same as those that crystallized in subseries APR16-C1B. Clinopyroxene and Ol are ubiquitous in these runs, whereas Plg is present only in the runs at 3 and 6 h and Ox is absent in the run at 6 h. Clinopyroxene shows a subhedral habit in the run with shortest duration and is euhedral in the other runs, with sizes between ~ 10 and 20 μm. Olivine crystals are well-faceted with sizes of ~ 15 μm; occasionally they contain embayments. Plg is euhedral with sizes up to ~ 40 μm.

The runs of the subseries APR16-C2B (1170 °C, 2 wt.% H2Oi) show a higher degree of crystallization (Fig. S4b in Online Resource 1) and the mineral assemblage is Cpx + Ol + Plg ± Ox (Table 2). Clinopyroxene, Ol and Plg crystallize in all the runs, while Ox occurs only in the longest run (APR16-C2Bd; 9 h). Textural features are very similar to subseries APR16-C1B.

Series 3

In the runs of subseries APR16-C3A (1080 °C, 4 wt.% H2Oi; Fig. S5a in Online Resource 1) and APR16-C3B (1030 °C, 4 wt.% H2Oi; Fig. S5b in Online Resource 1), the main phase is Amph, which is ubiquitous. The runs with the shortest durations (APR16-C3Aa, APR16-C3Ba and APR16-C3Ab, APR16-C3Bb; 0.25 and 3 h, respectively) are characterized by an extensive distribution of tiny crystals, most of them smaller than 10 μm in size, frequently occurring in crystalline aggregates (Fig. S5 in Online Resource 1). Small plugs of glass occasionally occur at the edge of these aggregates, but they are too small to be accurately analysed. The runs with the longest duration (APR16-C3Ad and APR16-C3Bd, 9 h) are characterized by the crystallization of Amph, Cpx and Ox. Clinopyroxene crystals are euhedral, up to ~ 5 μm in size, and sometimes constitute the core of Amph crystals (Fig. 5). Amphibole and Ox show euhedral habits with sizes up to ~ 60 and 40 μm, respectively.

Fig. 5
figure 5

Backscattered SEM images of Cpx crystals constituting the core of Amph from run APR16-C3Ad of Series 3

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An interesting feature concerns Ol crystals, which has a morphology that can be described as polyhedral, according to the classification of Faure et al. (2003). Polyhedral Ol crystals contain embayments or cavities, formed during multiple growth steps (Faure and Schiano 2005); these polyhedral habits were found in several experimental runs (e.g. APR16-C2Bb, APR16-C2Bc, APR16-C2Bd). In particular, it was possible to recognize (i) melt inclusions isolated inside their host crystals, with sizes between 1 and 3 μm, and shapes that can be spherical, sub-spherical or ovoid, up to irregular but still curvilinear (Fig. 6a); and (ii) open melt inclusions (embayments) extending to the crystal rim through a narrow or wide neck (Fig. 6b). This type of texture is sometimes interpreted as resulting from processes unrelated to the growth of the host crystal (e.g. chemical resorption due to crystal-melt disequilibria or thermal erosion at the crystal-liquid interface associated with transport in the magma conduit; Helz and Wright 1992; Thornber 2001; Pan and Batiza 2002). However, in our experiments, as found by Faure and Schiano (2005), this embayed texture was formed during olivine crystal growth under near-equilibrium conditions.

Fig. 6
figure 6

Backscattered SEM images of polyhedral Ol crystals containing embayments formed in run APR16-C2Bc of Series 2. a Closed melt inclusion isolated inside their host crystals. b Open melt inclusions extending to the crystal rim through a narrow or wide neck

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Clinopyroxene composition and approach to equilibrium

Chemical compositions of clinopyroxene and glass are given in Table S2 in Online Resource 2. Clinopyroxene crystals are augitic (Wo42-En41-Fs18) and diopsidic (Wo47-En43-Fs10) in composition according to the classification scheme of Morimoto et al. (1998). Overall, the Mg# of Cpx (calculated as the molar MgO/(MgO + FeOtot) ratio) varies between 0.76 and 0.88, while the Mg# of glass lies between 0.52 and 0.77. The Fe–Mg distribution coefficients between clinopyroxene and melt (KD(Fe-Mg)Cpx-liq = FeCpx × Mgliq/MgCpx × Feliq, calculated assuming all Fe as Fe2+ in both phases) varies between 0.39 ± 0.05 and 0.30 ± 0.05 for APR16-C1A runs, 1.00 ± 0.10 and 0.29 ± 0.01 for APR16-C1B runs, 0.43 ± 0.06 and 0.31 ± 0.06 for APR16-C2A runs, and 0.57 ± 0.06 and 0.34 ± 0.04 for APR16-C2B runs. As shown in Fig. 7, all the shortest experiments, and in particular those of the subseries APR16-C1B and APR16-C2B, show significant deviation from the equilibrium range (KD(Fe-Mg)Cpx-liq = 0.28 ± 0.08 according to Putirka (2008)), while runs of 3 h or more increasingly reach equilibrium conditions.

Fig. 7
figure 7

Relation between KD(Fe-Mg)Cpx-liq and time. The duration of each run is indicated with different symbols: circles for 0.25 h runs, triangles for 3 h runs, diamonds for 6 h runs and squares for 9 h runs. Series are indicated with different colours: red for APR16-C1, light blue for APR16-C2. Within each series, subseries are indicated with full (runs at lower temperature) and empty (runs at higher temperature) symbols. The green field represents the equilibrium range according to Putirka (2008), while the dotted line represents the average KD value for Cpx (0.28 ± 0.08; Putirka (2008))

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Crystal growth rates

Maximum growth rates determined for clinopyroxene are reported in Table 3, and Fig. 8 shows the relationships between (a) crystal size (L) and experimental duration, and (b) crystal growth rate (GL) and experiment duration. In Series 1, we observed an increase in crystal size with increasing experiment duration. Moreover, Cpx in APR16-C1A runs at 1250 °C are smaller than in APR16-C1B runs at 1200 °C. As regards crystal growth rates, the obtained values decrease by about an order of magnitude with increasing duration of the experiments, decreasing from 10−7 to 10−8 cm·s−1 as duration increases from 0.25 to 9 h. Within each series, GL calculated from experiments at higher temperatures are slightly lower than those obtained from experiments at lower temperatures (Fig. 8b). Growth rates calculated for other phases are in Table 4. As seen for clinopyroxene, the calculated growth rates of all other phases decrease with increasing time. For both Ol (Fig. 9a) and Plg (Fig. 9b), GL decreases from about 10−6 to 10−8 cm·s−1 (Table 4) as time increases from 0.25 to 9 h. For Amph and Ox, we were able to calculate the growth rates only for the runs with duration ≥ 3 h, and these had values of ~ 10−8 cm·s−1 (Table 4).

Table 3 Calculated growth rate values for clinopyroxene
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Fig. 8
figure 8

Relation between a Cpx size (L) and experimental duration, and b Cpx growth rate (GL) and experimental duration (t). The duration of the runs is indicated with different symbols: circle for 0.25 h runs, triangle for 3 h runs, diamond for 6 h runs and square for 9 h runs. Series are indicated with different colours: red for APR16-C1, light blue for APR16-C2 and green for APR16-C3. Within each series, each subseries is indicated with full (runs at lower temperature) and empty (runs at higher temperature) symbols. In Fig. 8b, the error bars are not shown since they are inside the symbols

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Table 4 Calculated growth rate values for olivine, plagioclase, amphibole and oxide
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Fig. 9
figure 9

Relation between the growth rate (GL) and the experiment duration (t) for olivine (a) and plagioclase (b). Symbols are as in Fig. 8. Error bars in Fig. 9b are not shown since they are inside the symbols

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Crystal size distribution analysis

The CSDs calculated for the APR16GL runs of Series 1 and 2 are shown in Fig. 10a–d. For the runs of Series 3, it was not possible to perform CSD analysis due to the small size of the Cpx (which was below the detection limit). CSD theory predicts that steady-state conditions of continuous nucleation and growth will produce a linear CSD plot with a negative slope, while deviations from linearity suggest the involvement of other processes (Cashman and Marsh 1988; Marsh 1988, 1998; Lentz and Mcsween 2000). For instance, a turnover at the smallest grain sizes may be due to (i) a complete cessation of nucleation with continued growth that favours the growth of the smallest grains in the next largest bin sizes, but with no replacements produced by nucleation (Lentz and Mcsween 2000); (ii) annealing that causes absorption of small grains with balancing growth of larger ones (Lentz and Mcsween 2000); and/or (iii) a limitation to the imaging technique (Marsh 1988). Another possible deviation from linearity is an increase of the largest grain sizes that implies an excess of large grains compared with smaller sizes; this may be due to accumulation or addition of large phenocrysts (Marsh 1988). All runs suitable for CSD analysis show similar curves. In the longest runs (6–9 h), in particular, CSDs yield two best-fit lines with different slopes: a gentler slope for coarser crystals and a steeper slope for the smallest crystals (< 8 μm in size). Moreover, a reduction in both slope and intercept leads to a counter-clockwise rotation of the CSD with time (Fig. 10a–d), which indicates an absence of new nucleation (Ni et al. 2014). Small crystals may also partly or completely dissolve due to their higher surface energies, which causes their population density to fall below the log-linear CSD curve (Ni et al. 2014). Moreover, by using the growth rates calculated in this work for the APR16 runs, we estimated nucleation rates J (J = n0GL) of 105 and 103 mm-3·s-1 in the run with the shortest (0.25 h) and the longest (9 h) durations, respectively (Table S3 in Online Resource 2).

Fig. 10
figure 10

CSD relation between the natural logarithm of the population density of crystals (ln(L)) and the crystal length (L) for the APR16-C1A (a), APR16-C1B (b), APR16-C2A (c) and APR16-C2B (d) subseries

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Discussion

Chemical and crystal fraction equilibrium of experimental clinopyroxene

Putirka (1999) and Putirka et al. (2003) have demonstrated that Fe–Mg exchange between clinopyroxene and the melt (KD(Fe-Mg)Cpx-liq = FeCpx × Mgliq/MgCpx × Feliq) can be extremely useful for the assessment of equilibrium conditions. The KD(Fe-Mg)Cpx-liq calculated for our experimental runs show that chemical equilibrium was reached at between 3 and 6 h. In order to observe if the crystal fraction equilibrium is achieved in the same amount of time as the chemical equilibrium, we plotted clinopyroxene fraction and against experimental dwell time (Fig. 11). In Fig. 11a, we observed a rapid increase in Cpx-ϕ, and increase that occurs in the first 15 min, after which Cpx-ϕ remains approximately constant. In the APR16-C1A and APR16-C2A experiments, however, Cpx-ϕ increases for up to 3 h before approaching a constant value, suggesting an approach to crystal fraction equilibrium conditions (Fig. 11a). This trend is similar to those obtained in previous studies (Melnik and Sparks 2005; Polacci et al. 2018), in which the crystal content initially increases rapidly, and then increases less slowly, but linearly, until it reaches equilibrium. Moreover, evolution towards equilibrium is also testified by the decrease in the crystallization rate with time (Fig. 11b). Thus, our experiments show that for Procida K-basalt magmas, independently of ΔTeff and for H2Oi ≤ 2 wt.%, the approach to clinopyroxene equilibrium (both chemical and crystal fraction) occurs after 3 h of dwell time.

Fig. 11
figure 11

Relation between a crystal fraction (Cpx-Ф) and time, and b crystallization rate and time. Symbols are as in Fig. 7

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Growth rate dependence on time

As observed in previous studies (e.g. Hammer and Rutherford 2002; Couch 2003; Arzilli and Carroll 2013; Arzilli et al. 2015), time plays a key role in the crystallization processes of silicate melts. The effective Cpx growth rate calculated in this work varies by an order of magnitude between the runs with the shortest and those with the longest durations (Fig. 8b). In particular, starting from a dwell time of ≥ 3 h, the runs begin to achieve conditions close to the textural equilibrium, at which point kinetic processes (i.e. growth and nucleation) begin to slow down. In detail, as shown in Fig. 11a, Cpx crystallization is negligible after 15 min for the two samples with ΔTeff ~ 100 °C but continues for up to 3 h for the two samples with ΔTeff ~ 50 °C. Concerning the sizes of Cpx, instead, for all considered undercoolings, they show a general increase increasing the dwell time only up to 6 h runs (Fig. 8a), remaining approximately constant for longer experimental times. All that suggests that the GL values determined for long-lasting (> 6 h) experiments are apparent and that, at this point, we are approaching conditions near to the textural equilibrium (Fig. 11; Arzilli et al. 2015). The influence of time on crystal growth rate thus appears to be strictly related to the equilibration time of the growing phases, as observed by previous studies (e.g. Couch 2003; Couch et al. 2003; Orlando et al. 2008; Arzilli et al. 2015). These authors, indeed, noted that the growth of some mineral phases, such as plagioclase and clinopyroxene, require different times to reach the equilibrium conditions. For instance, time has no resolvable influence on plagioclase at experimental durations longer than 1–2 h, a time which appears to be sufficient for the Plg-melt system to approach a near-equilibrium state (Couch 2003; Couch et al. 2003; Arzilli et al. 2015). Clinopyroxene may also require longer times (of the order of 20 h; Orlando et al. 2008).

Differences of clinopyroxene growth rate

There are several studies of clinopyroxene growth (e.g. Baker 2008; Burkhard 2002, 2005; Orlando et al. 2008), although they are completely absent for high-pressure conditions (> 0.5 GPa). There is, though a difference between the pressure values of our study and those available in literature (e.g. Baker 2008; Burkhard 2002, 2005; Orlando et al. 2008; Oze and Winter 2005; Pontesilli et al. 2019; Shea and Hammer 2013; Simakin et al. 2003; Table S3). However, the Cpx growth rates (10−5–10−9 cm·s−1) appear to be comparable, since they show similar trends in the growth rate vs dwell time diagram (Fig. 12). In particular, our data combined with literature data outline three parallel trends. The first is an upper trend which includes single-step cooling and decompression experiments on a basaltic-andesite (dwell times of 12–48 h at 995–1025 °C and 65–150 MPa) as reported by Shea and Hammer (2013). It also includes the dynamic isothermal time-series experiments on a trachybasaltic composition (dwell times of 0.5–24 h at 1100 °C and 400 MPa) reported by Pontesilli et al. (2019), and is characterized by high growth rates. The second is a low end-member trend that includes the CSD analyses performed by Burkhard (2002) on re-heated Hawaiian basalts (crystal residence times of ~ 0.01–7 h) and by Oze and Winter (2005) on natural basalts (crystal residence times of ~ 0.04–9 h). It also includes the static experiments of Burkhard (2005) on re-heated anhydrous basaltic glasses (dwell times of 22–576 h at 930–990 °C and 1 atm) and is characterized by low growth rate values. The third is a middle trend which includes our static experiments on the APR16 alkaline basalt and the experiments (dwell times of 3–40 h at 1170 °C and 1 atm) on a K-trachybasalt from Mt. Etna by Orlando et al. (2008). It is characterized by growth rate values between the two end-members. All of the above experiments were performed at different temperature conditions and H2O contents (Table S4 in Online Resource 2), which are two key factors controlling the viscosity of magmas (e.g. Pinkerton and Stevenson 1992; Dingwell et al. 1993; Giordano et al. 2004). Notably, variations in melt viscosity deeply affect the kinetics of the crystallization process and then the value of GL (Orlando et al. 2008; Vona and Romano 2013). Therefore, differences in melt viscosity appear to be the main factor in explaining the differences between the three trends observed in Fig. 12. For example, the runs of Shea and Hammer (2013) that fall in the upper trend (Fig. 12) were performed under saturation conditions. Hence, the high amount of water, reducing the viscosity and increasing element diffusivity in the melt, explains high growth rate values in respect to the runs that are undersaturated. Regarding the runs of the middle and the lower trends (Fig. 12), instead, the different growth rate values can be explained by taking into account the effect of chemical composition and temperature on the viscosity. The runs of the lower trend, indeed, were performed using a tholeiitic basalt as starting material. This is characterized by higher SiO2 and lower Σalkali contents than the APR16-basalt of this study and the Mt. Etna trachybasalt of Orlando et al. (2008), making the tholeiitic melts of the lower trend more viscous than the alkaline ones of the middle trend (see below and Fig. S6 of Online Resource 1). This, consequently, determines the low growth rate values observed for such tholeiitic basaltic composition (~ 10−9 cm·s−1), with respect to the GL values (~ 10−8 cm·s−1) obtained for the alkaline basalts of the middle trend (Fig. 12). Furthermore, the runs of the lower trend were carried out at lower temperatures (~ 900 °C) with respect to those of the middle trend (~ 1100–1250 °C). The high temperature, as well as the water content, will affect the crystal growth rate due to its depolymerizing effect, reducing viscosity and increasing element diffusivity in the melt (Ni et al. 2015).

Fig. 12
figure 12

Relation between crystal growth rate (GL) and experimental duration (t) for this and previous studies on clinopyroxenes. Literature experimental data are from Burkhard (2002, 2005), Orlando et al. (2008), Oze and Winter (2005), Pontesilli et al. (2019) and Shea and Hammer (2013). The coloured fields represent: the upper trend in green, the middle trend in dark orange and the lower trend in light blue. Coloured fields correspond to different viscosity values (see Fig. S6 in Online Resource 1) that tend to increase from the upper to the lower trend, as shown by the coloured arrow on the right. The runs of Pontesilli et al. (2019), which should fall in the middle trend based on viscosity, fall instead in the upper one due to the higher undercooling and cooling rate

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To verify this hypothesis, we calculated the viscosity of all compositions reported in Fig. 12 at atmospheric pressure using the EXCEL® spreadsheet of Giordano et al. (2008). As seen in Fig. S6 in Online Resource 1, at the temperatures considered here (900–1200 °C), the samples have viscosity values that confirm our inference, since they match the distribution observed for the growth rates in the diagram of Fig. 12. However, the growth rates calculated by Pontesilli et al. (2019) for a trachybasaltic composition (10−6–10−8 cm·s−1) show values higher than those of the middle trend defined here in Fig. 12. We expect them to fall in this trend since they have a composition very close to the K-trachybasalt of Orlando et al. (2008) which is that plotted here. For this case viscosity cannot explain the different growth rate values between these two trachybasalts, since they show the same viscosity variation trend with temperature (Fig. S6 in Online Resource 1). Instead, we suggest that the difference in GL is a function of the undercooling and the cooling rate (e.g. Lesher et al. 1999; Conte et al. 2006; Arzilli et al. 2015). The experiments performed by Pontesilli et al. (2019), indeed, are characterized by a cooling rate of 80 °C/min and higher degrees of undercooling (80–120 °C) with respect to the static low undercooling (ΔT = 20 °C) experiments of Orlando et al. (2008).

Considering, also, the influence of water content on crystal growth rate, due to its depolymerizing effect that reduces viscosity and increases element diffusivity in the melt (Hess and Dingwell 1996; Ni et al. 2015), in our experiments the calculated growth rates at different water contents remain in the same (order of magnitude) field (Fig. 13). In particular, we note that growth rates of runs with H2Of (i.e. water dissolved in the melt) between 2 and 4 wt.% are slightly higher than those with H2Of < 2 wt.%, and similar to those observed by Pontesilli et al. (2019). The very minor influence of water on crystal growth rate, and consequently on viscosity of our results, and those of Pontesilli et al. (2019), is probably due to the composition used in the experiments; being alkaline in both cases. Alkaline magmas are more depolymerized than calc-alkaline compositions, due to the presence of alkalis that act as “modifier networks” (Hess et al. 1995). This difference has been noted in the literature, where the model accounting for non-Arrhenian variation of viscosity in calc-alkaline magmas has been proved to not apply to alkaline magmas (Giordano et al. 2006).

Fig. 13
figure 13

Relation between Cpx growth rate (GL) and water content dissolved in the melt (H2Of). Diamonds represent APR16 runs while triangles are the results of Pontesilli et al. (2019). Colours indicate different amounts of water content dissolved in the melt: H2Of ≤ 2 wt.% in light blue, 4 wt.% < H2Of > 2 wt.% in green, H2Of > 5 wt.% in yellow

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Moreover, growth rates calculated in runs with high-water contents in the melt (> 5 wt.%) are lower than those obtained for runs with lower water contents (1–3 wt.%). As observed by Bonechi et al. (2019), this is probably due to the dominance on crystallization of the hydrous phase, amphibole, which grows at the expense of Cpx that, indeed, never exceeds a size of ~ 10 μm in our experiments (Fig. 8a).

Magma refilling of the deep reservoir of the Campi Flegrei Volcanic District

Measurements of CSD, when combined with experimental growth rate data, can provide useful information to better constrain the time of magma crystallization (Cashman and Marsh 1988; Marsh 1988; Piochi et al. 2005b; Armienti et al. 2007; Brugger and Hammer 2010b; Arzilli et al. 2016). To date, there is limited kinetic data (crystal growth rate) on alkaline products and most of them concern feldspar minerals (e.g. Orlando et al. 2008; Agostini et al. 2013; Arzilli et al. 2015). Here we focused on Cpx growth rate, since (i) as demonstrated by Perinelli et al. (2019), clinopyroxene is the liquidus phase of the APR16 composition at high pressure (0.8 GPa), and (ii) thermobarometric estimates obtained from natural less-evolved samples of CFVD indicate an initial stage of clinopyroxene crystallization near the Moho (~ 25 km depth; Di Stefano et al. 2011). Moreover, Cpx growth rate data combined with thermobarometric data provide an estimate of deep-level ascent rate for CFVD primitive magmas (Armienti et al. 2013). We assume that a deep episode of magmatic crystallization takes place at low undercooling, a condition that produces slow crystal growth rates. This condition has been verified, here, by CSD investigations for clinopyroxene growth of natural samples. Cpx-CSDs were measured for two K-basaltic scoria clasts (SCE and SOG samples) collected in the deposit of the Solchiaro tuff ring (of Procida island). Both SCE and SOG have chemical compositions very close to that of APR16 sample (Table 1, Table S5 in Online Resource 2 and Online Resource 3). Note that, parameters used for the CSD analysis of natural samples were the same as those used for the experimental runs applied here.

CSD results for these two scoria clasts show an upward curvature (Fig. 14). This indicates the possible involvement of a number of processes, including changes in the magma cooling rate, crystal aggregation, magma mixing, or textural coarsening, during the crystallization history of these samples (Armienti et al. 1994; Higgins 1998, 2002; Higgins and Roberge 2003; Marsh 1998; Zieg and Marsh 2002). We recognize three populations of clinopyroxenes, each of which has an almost linear distribution (Fig. 14). The first population is of larger phenocrysts with size > 0.32 mm that can be interpreted as early-formed phenocrysts. The second is of smaller phenocrysts with sizes between 0.04 and 0.32 mm. The third involves microlites with L < 0.04 mm. The portion of the CSD plot relative to the larger phenocrysts shows that, on the basis of their composition and thermobarometric data (see Online Resource 3), they formed during a crystallization stage at a deep (20–25 km) level. This is apparent from an almost horizontal slope and a low intercept, which suggests that these crystals formed at low and almost constant undercooling and growth rates (Armienti et al. 1994). Using the growth rate value obtained here of 2.2·10−8 cm·s−1 (i.e. the average of GL values that on the basis of KD(Fe-Mg)Cpx-liq fall in the field representing equilibrium conditions; Fig. S7 in Online Resource 1), it is possible to evaluate the minimum growth time. Using this value, a minimum residence time of the largest SCE and SOG clinopyroxenes can be obtained (Cashman and Marsh 1988; Armienti et al. 1994). This value is estimated as ~ 5 months for a Cpx growth of ~ 3 mm. Moreover, the ascent rate of primitive CFVD magmas can be assessed by combining data on Cpx growth rate with thermobarometric data of natural clinopyroxenes (Armienti et al. 2013). The range of temperatures and pressures of crystallization estimated for the larger population of clinopyroxenes obtained here are 1141–1178 °C and 0.7–0.9 GPa (which converts to a 20–25 km depth assuming an average crustal density of 2.8 g·cm−3). According to the approach of Armienti et al. (2013), for a ΔT of 37 °C (ΔT = 1178–1141 °C), a ΔL of ~ 0.3 cm (based on the magnitude of deep growth of clinopyroxene from CSD analyses; Fig. 14) and a growth rate of 2.2·10−8 cm·s−1, as estimated by our experiments, the cooling rate during the ascent of CFVD K-basaltic magmas can be estimated to be 0.3·10−5 °C/s. This value, combined with the dP/dT from thermobarometry (see Online Resource 3), provides a deep-level ascent velocity of ~ 0.5·10−4 m·s−1, which is comparable with the average magma transport rate of 3.6·10−4 m·s−1 estimated for Mt. Etna for depth > 6 km (Armienti et al. 2013). Nevertheless, the olivine/clinopyroxene ratio (~ 1) of the SCE and SOG scoriae indicates, according to the experimental phase relations at 0.2–0.8 GPa (Granati 2016), that the most primitive magmas of CFVD pond at relatively shallow levels before eruption. This is confirmed by barometric estimates based on the smaller phenocrysts, whose crystallization onset occurred at 0.3–0.5 GPa (8–14 km depth; see Online Resource 3). Consequently, the calculated residence time of the larger Cpx population (i.e. 5 months at least) multiplied by the magma volume erupted from the CFVD tuff ring (0.1–1 km3; Mastrolorenzo et al. 2017) could represent the minimum recharge rate of the large magmatic reservoir, whose top has been located in the CFVD at a depth of about 8 km (e.g. Rapolla et al. 1989; Cecchetti et al. 2001; Auger et al. 2001; Zollo et al. 2008; Esposito et al. 2011; Pappalardo and Mastrolorenzo 2012; Fanara et al. 2015; Fedi et al. 2018).

Fig. 14
figure 14

Relation between population density (ln(N)) and length (L) of clinopyroxenes for SCE (a) and SOG (b) natural samples. Coloured rectangles indicate three different Cpx populations: in orange larger phenocrysts (L > 0.32 mm); in green smaller phenocrysts (0.04 < L < 0.32 mm); in light blue microlites (L < 0.04 mm)

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Conclusions

Through this work, we have improved knowledge of crystallization kinetics of clinopyroxene in alkaline basaltic melts, providing new crystal growth rate data under high-pressure conditions. At the investigated conditions, clinopyroxene growth rate (GL) is strongly affected by time, with values that vary from 10−7 to 10−8 cm·s−1 from the shortest (0.25 h) to the longer-lasting (6–9 h) experiments. By comparing our clinopyroxene growth rate data with those available in the literature, we observe that viscosity, and the parameters that control it (temperature, water content and chemical composition), undercooling and cooling rate are the factors that most affect crystal growth rate. This is a result of their control over element diffusivity in the melt. On the other hand, pressure appears to have no influence on crystal growth rate. The experimental Cpx growth rate combined with data from CSD and thermobarometry of CFVD clinopyroxenes suggests that recharge by primitive magmas in the deep CFVD reservoirs occurs with a relatively high ascent rate (~ 0.5·10−4 m·s−1).