Kubo et al.
Progress in Earth and Planetary Science(2022) 9:21
https://doi.org/10.1186/s40645-022-00480-9

Progress in Earth andPlanetary Science

Open Access

RESEARCH ARTICLE

Back‑transformation processes
in high‑pressure minerals: implications
for planetary collisions and diamondtransportation from the deep Earth
Tomoaki Kubo1*, Ko Kamura2, Masahiro Imamura2, Yoshinori Tange3, Yuji Higo3 and Masaaki Miyahara4

Abstract
We conducted back-transformation experiments in ringwoodite, bridgmanite, and lingunite at 0.47–8.1 GPa and
310–920 °C by in situ X-ray observation method. Ringwoodite back-transformed to olivine by grain-boundary nucleation and growth mechanism. The site saturation occurred at the early stage under the conditions far from the equilibrium boundary, and we observed the growth-controlled back-transformation kinetics in ringwoodite. The growth
kinetics determined in the present study is largely different from that in the previous study (Reynard et al. in Am Min
81:585–594, 1996), which may be due to the effects of water. Bridgmanite did not directly back-transform to thestable phase orthoenstatite at ~ 1–4 GPa, but first becomes amorphous with increasing temperatures. We observed
kinetics of the orthoenstatite crystallization from amorphous bridgmanite that was controlled by both nucleation andgrowth processes. The temperature range in the amorphous state became narrow with increasing pressures, and the
direct back-transformation to high-P clinoenstatite without amorphization eventually occurred at 8 GPa. Amorphization was also observed in lingunite when increasing temperature at ~ 1.5 GPa; however, the plagioclase crystallization
proceeded before the complete amorphization. The back-transformation in ringwoodite variedly occurs in shocked
meteorites depending on the degree of the post-shock annealing, which can be reasonably interpreted based on thegrowth kinetics. On the other hand, the presence of hydrous ringwoodite in diamond inclusions cannot be explained
without the help of residual stress. The present study also indicates that complete amorphization or the back-transformation to enstatite is unavoidable in bridgmanite during the post-shock annealing. This is inconsistent with thepresence of crystalline bridgmanite in shocked meteorites, still requiring further investigations of kinetic behaviors inshorter timescales.
Keywords: High-pressure mineral, Shocked meteorite, Diamond inclusion, Back-transformation, Synchrotron
radiation, High-pressure experiment, Transformation kinetics, Amorphization
1 Introduction
High-pressure minerals stable at deep mantle pressures
have been naturally found on Earth such as in shocked
meteorites and diamond inclusions, which provides*Correspondence: kubotomo@geo.kyushu-u.ac.jp
1
Department of Earth and Planetary Sciences, Faculty of Sciences, Kyushu
University, Fukuoka 819‑0395, Japan
Full list of author information is available at the end of the article

important constraints on detailed processes of planetary
collisions and deep mantle dynamics. Because the timescales are limited in these dynamic processes, the reactions often remain incomplete and/or metastable state.
The back-transformation also occurs during the transportation to the surface of the Earth, which complicatesthe interpretation. Therefore, considering the reaction
kinetics is potentially important to deduce the P–T–t history of these dynamic processes.

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Kubo et al. Progress in Earth and Planetary Science(2022) 9:21

In shocked meteorites, experimentally determinedkinetics on the forward (prograde) reactions have been
widely used to investigate shock history including shock
duration and size of the impactor (e.g., Ohtani et al. 2004;
Xie and Sharp 2007; Kubo et al. 2010, 2015; Miyahara
et al. 2010). The forward kinetics have also been discussed to understand dynamics of subducting oceanic
plates (e.g., Rubie and Ross 1994; Kubo et al. 2009).
On the other hand, the importance of the backward(retrograde) reactions for the dynamic processes has notbeen extensively focused. There have been some reportson the back-transformation of high-pressure phases suchas ringwoodite, majoritic garnet, and lingunite originallyproduced in or near shock melt veins of a chondrite during atmospheric entry (Kimura et al. 2004; Fukimoto et al.
2020). They observed back-transformation texture gradually changed with the distance from the fusion crust, andproposed the mechanisms of the back-transformation.
In addition to the atmospheric passage event, the postshock annealing can also cause the back-transformation(e.g., Walton 2013). Hu and Sharp (2017) have discussed
post-shock thermal history on the basis of the texturalobservations combined with thermal models of shock
melt cooling and reaction kinetics. They proposed strong
shock events can erase high-pressure signatures by thecomplete back-transformation in post-shock annealing.
Survival of high-pressure minerals in diamond inclusions is thought to be more difficult because of thelonger timescales for the diamond transportation. The
low-pressure polymorphs with having distinct chemicalcompositions and phase assemblages are often used as
the evidence for the presence of the former high-pressure
phases such as bridgmanite (e.g., Hayman et al. 2005).
Majoritic garnet have been commonly found in diamond
avoiding the back-transformation (Moore and Gurney
1985; Tappert et al. 2005) probably due to the slow kinetics of the decompositional back-transformation (Nishi
et al. 2010). Recent new findings of ringwoodite (Pearson et al. 2014) and davemaoite (Tschauner et al. 2021)
in diamond are enigmatic because the polymorphic backtransformation rate is thought to be faster, in which theresidual stress in the host diamond may be important forthe preservation of high-pressure phases.
In spite of the important information from survival ofhigh-pressure phases in shocked meteorites and diamondinclusions, experimental data on mechanisms and kinetics of the back-transformation have not been investigatedadequately so far. Most previous data were obtained atambient pressure, and the pressure and temperaturedependences on the kinetics have been poorly known.
Here we report experimental results on the polymorphic back-transformation in ringwoodite, bridgmanite,and lingunite at high pressures and temperatures. In situ

Page 2 of 16

X-ray observations with synchrotron radiation enable
us to catch the detailed reaction processes and kinetics.
Based on the results obtained, we briefly discussed survival of high-pressure minerals in shocked meteorites
and diamond inclusions.

2 Experimental procedure
We used three kinds of starting materials, polycrystalline ringwoodite, bridgmanite, and lingunite, for the
back-transformation experiments. These high-pressure minerals were synthesized using a KAWAI-type
multi-anvil (MA) apparatus (QDES) at Kyushu University, from San Carlos olivine single crystal, San Carlos
orthopyroxene ­(En89.4Fs8.6Wo2.0) powder, and natural
oligoclase ­(Ab72.6An23.0Or4.4) powder, respectively. The
sample assembly was the same as that used in the previous study (Kubo et al. 2017). The synthesis conditions
for ringwoodite and bridgmanite were 22 GPa, 1400 °C
for 180 min, and 25 GPa, 1800 °C for 60 min, respectively. Lingunite was synthesized as a metastable phaseat 20 GPa, 1160 °C for 5 min heating (Kubo et al. 2017).
The synthesized polycrystalline high-pressure phases
were cut into the disks with ~ 800–1000 µm in diameter and ~ 350–750 µm in height, and used as the starting material for the back-transformation experiments.
Unpolarized infrared absorption spectra of the synthesized ringwoodite were obtained in air using Fouriertransform infrared spectrometer. The broad absorption
peak was observed at ~ 3400 ­cm−1. The water content wasestimated to be ~ 1400 wt. ppm ­H2O by integrating thebroad absorption band based on the calibration by Paterson (1982). The observed absorption spectra are almost
consistent with those for ringwoodite containing similar
amounts of water (Kawazoe et al. 2016). A small amountof stishovite were contained in the bridgmanite sample.
Majorite was also confirmed in one of the starting materials of bridgmanite (Run M2715).
We performed the back-transformation experiments
by in situ X-ray observations at the synchrotron radiation
facilities of the Photon Factory (AR-NE5C) and SPring-8(BL04B1) using the DIA-type apparatuses MAX-80 andSPEED1500 Mk-II, respectively. A MA6-6-type assembly
was used to generate pressures (Nishiyama et al. 2008).
The truncated edge length (TEL) of the second-stage
anvils is 4 or 6 mm. The sample assembly was composedof boron-epoxy pressure medium, a cylindrical graphite heater, a Cu electrode, and a hBN sample capsule(Fig. 1a). Temperature was measured at the center of thesample assembly with W3%Re–W25%Re thermocouples. The temperature fluctuation during heating was lessthan ± 5 °C. We put a mixture of NaCl and hBN powders
into the hBN capsule, and then the disk-shaped starting
material was embedded in the powder mixture. In someKubo et al. Progress in Earth and Planetary Science(2022) 9:21

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Fig. 1 Sample assembly used in the back-transformation experiments (TEL6 system). a Cross section of the sample assembly. b Its radiography
image around the sample at a load of 5 ton (Run M2621)

experiments, we put two kinds of starting materials in a
capsule above and below the thermocouples. For the runat the lowest pressure of ~ 0.5 GPa (Run M2932), only
hBN powder was used to avoid melting of NaCl.
White X-rays from synchrotron radiation were used as
the incident X-ray beam in most of runs. We monitored
thermocouples and samples in a capsule by radiography image to locate the position for the measurement of
X-ray diffraction (XRD) pattern (Fig. 1b). The diffracted
beam was measured in the vertical or horizontal direction between the second-stage anvils by the energydispersive method using a Ge solid-state detector. The
glancing angle (2θ) of the solid-state detector was fixed at
5.0°. A conical slotted anvil was used at the downstreamside to measure XRD patterns in the horizontal direction. The sample was first compressed at room temperature and then heated in 100–300 K steps at ~ 3.3–8.3 °C/s
with a constant load. The temperature was held constantat each step during the collection of diffraction patterns
every 10 to 500 s.
In one experiment for ringwoodite (Run M2096),
monochromatic X-ray of 50 keV was used as an incident
X-ray beam and two-dimensional X-ray diffraction (2DXRD) patterns were measured by CCD detector. The
obtained 2D-XRD pattern was converted to 1D-XRD pattern to analyze kinetic data in the same way as in otherruns. The sample assembly was almost the same as thatshown in Fig. 1 except that the starting ringwoodite was
directly put into the MgO capsule instead of the hBN
capsule without using the NaCl + hBN powder, and sandwiched between two A­ l2O3 rods instead of MgO rods.

Temperature was measured at the bottom of the sample
by the thermocouples. Although the different experimental method was applied in this run, we analyzed the
kinetic data together with all runs as the quality of thedata was similar.
The pressure was calculated from the unit-cell volume
of NaCl (Brown 1999) in most of runs. For the runs without using NaCl powder for sample medium, the unit-cellvolume of ringwoodite was used for the pressure calculation (Nishihara et al. 2004). The pressure uncertainties are estimated to be less than ± 0.1 GPa in most ofruns from the errors of the volume calculation. Reaction
microstructures in some recovered samples were investigated using a field emission scanning electron microscope (FE-SEM, JEOL JSM-70001F) with an electron
back-scattered diffraction (EBSD) system.

3 Results and discussion
3.1 In situ X‑ray and SEM observationsof the back‑transformation processes

Eight experiments were conducted using ringwoodite at
0.47–7.5 GPa and 455–920 °C. We observed the backtransformation of ringwoodite to olivine at higher temperature than 650–700 °C as summarized in Fig. 2 andTable 1. The back-transformation temperatures slightly
increase with pressures. Figure 3 shows an example
of changes of XRD patterns from ringwoodite to olivine at 4.1 GPa and 820 °C. We did not observe formation of metastable phase and amorphization during theback-transformation of ringwoodite in our experimental
conditions.

Kubo et al. Progress in Earth and Planetary Science(2022) 9:21

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Fig. 2 P–T conditions for the back-transformation in ringwoodite. The
back-transformation to olivine occurred at higher than ~ 600–700 °C(red circles)

Polycrystalline microstructure of the starting material is shown in Fig. 4a. The starting ringwoodite
exhibits equiangular texture, and the grain size wasestimated to be 8.9 µm by intercept method from several SEM images. Figure 4b shows the reaction microstructure of the partially back-transformed sample at
1.2 GPa and 645 °C (Run M2893). In this image, thedarker regions are present between the brighter grains
with several microns in size. The EBSD analysis indicates that the brighter grains are ringwoodite. The final
transformed fraction and the growth distance of olivine

Fig. 3 Changes of XRD patterns during the back-transformation in
ringwoodite. Ringwoodite (Rw) directly transforms to olivine (Ol) at
4.1 GPa and 820 °C (Run M2620)

Table 1 P–T–t conditions and estimated values of kinetic parameters for the back-transformation from ringwoodite to olivine
Run No.

Pressure (GPa)Temperature
(°C)

M2932

0.5

715

360

M2716

1.1

615

1620

1.1

765

1225

1.2

510

1055

1.2

645

18,340

M2614

1.3

920

135

M2714

1.9

455

3920

1.7

715

2720

4.1

510

445

4.1

820

230

M2717

7.4

515

435

M2096

7.5

700

415

6.6

800

2590

M2893

M2620

1

The uncertainties in growth rate are listed in parentheses

Duration (s)∆Gr (J/mol)

n

ln k

Growth ­rate1 (m/s)− 45,101

0.67− 4.36

3.0 (0.1) × ­10–9− 43,039

0.64− 1.965.7 (0.4) × ­10–8− 9.103.8 (0.1) × ­10–11− 6.747.2 (0.1) × ­10–10− 3.505.8 (0.4) × ­10–8− 5.632.9 (0.2) × ­10–9− 41,382− 39,817

No transformation
No transformation− 41,283

0.85− 36,326

No transformation− 28,161

No transformation− 16,122

No transformation− 21,536

0.91− 43,924

Completed within 10 s

− 39,917

0.89− 31,202− 17,412

1.11
No transformation

Kubo et al. Progress in Earth and Planetary Science(2022) 9:21

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Fig. 4 Back-scattered electron (BSE) images showing back-transformation microstructures in ringwoodite. a Polycrystalline microstructure of thestarting material (ringwoodite). b Fine-grained olivine (darker regions indicated by white arrows) forms reaction rims along grain boundaries ofparental ringwoodite grains in the partially back-transformed sample recovered at 1.2 GPa and 645 °C (Run M2893). c Polycrystalline olivine after thecompletion of the back-transformation at 6.6 GPa and 800 °C (Run M2096)

are estimated to be ~ 34 vol% and ~ 0.7 µm, respectively, from analysis of kinetic data in this run. Theseobservations suggest that the darker region between
the brighter ringwoodite grains consists of newly transformed fine-grained olivine although the phase identification by EBSD was difficult due to the small grain
size. We do not have any evidences for intra-crystalline
nucleation such as lamellar texture, and therefore theback-transformation of ringwoodite proceeds by grainboundary nucleation and growth. This is consistent
with that observed in shocked meteorites (Fukimoto
et al. 2020). The olivine texture after the completionof the back-transformation at higher temperature of
800 °C and 6.6 GPa (Run M2096) is shown in Fig. 4c.
The grain size becomes much larger (a few microns),
which may result from the grain growth following theback-transformation.
We conducted eight experiments on bridgmanite
at 1.1–8.1 GPa and 310–920 °C (Fig. 5 and Table 2).
At ~ 1 GPa, we observed disappearance of diffraction
peaks in bridgmanite and increase in halo pattern withtemperatures from 310 to 615 °C (Fig. 6a), suggestingthat the thermal-induced amorphization occurred inbridgmanite. The amorphization quickly progressed
when increasing temperature, but hardly with time
when keeping the temperature constant. As a result,diffraction peaks in bridgmanite were still present andthe sample was in the partially amorphous state in thetemperature range 410–510 °C. The complete amorphization was observed at 615–715 °C, and then crystallization of orthoenstatite occurs with disappearance ofthe halo pattern at 770 °C (Fig. 6b). These results are
summarized in Fig. 5 and Table 2.
The amorphization temperature increases with pressures. At ~ 4 GPa, the bridgmanite amorphization
did not start until the temperature reached 720 °C. It

completed at 820 °C in 30 s, followed by the orthoenstatite crystallization (Fig. 6c). These observations indicate that bridgmanite does not directly back-transformto the stable phase orthoenstatite at ~ 1–4 GPa, but first
becomes amorphous with increasing temperatures. The
temperature range in the amorphous state becomesnarrow with increasing pressures because the pressure dependence of the amorphization temperature ismuch greater than that of the crystallization temperature (Fig. 5). The amorphous state eventually vanishesat ~ 8 GPa, and bridgmanite directly back-transforms tohigh-P clinoenstatite at 820 °C without amorphization(Fig. 6d). Thus, the amorphization behavior in bridgmanite largely changes with pressures. Microstructures in the amorphized bridgmanite and crystallized
orthoenstatite were not clear in the FE-SEM images.
Figure 7 shows microstructures of partially back-transformed bridgmanite to high-P clinoenstatite at 7.9
GPa and 820 °C (Run M2715). High-P clinoenstatite is
expected to further transform to low-P clinoenstatite
during decompression to ambient pressure (Angel et al.
1992; Akashi et al 2009). We infer that the brighter
phase is the relict bridgmanite and the darker phase is
the low-pressure phase in this image. The grain size ofparental bridgmanite is not clear but roughly estimatedto be ~ 10–20 µm. Figure 7 suggests that the backtransformation proceeds by both inter- and intra-crystalline processes, resulting in a crazing texture of relict
bridgmanite. The back-transformation may also occur
in cracks that might be produced in bridgmanite grains
when decompression and recompression stages atroom temperature. Further investigations of these samples using TEM will be required for understanding thedetailed process of amorphization and crystallization.
We conducted one experiments on lingunite at ~ 1.5–
1.8 GPa and up to 820 °C (Fig. 8). The amorphization ofKubo et al. Progress in Earth and Planetary Science(2022) 9:21

Page 6 of 16

The obtained n values in the back-transformation fromringwoodite to olivine are nearly 1 (~ 0.9–1.1) althoughruns M2716 and M2932 show relatively small n values ~ 0.7 probably due to the lack of the kinetic data at
the initial stage. This suggests that the site saturation
occurs at the early stage of the transformation under theconditions far from the equilibrium boundary (i.e., large
free energy differences), followed by one-dimensional
interface-controlled growth (e.g., Cahn 1956; Rubie et al.
1990). This is consistent with the back-transformation
microstructures observed in Fig. 4b. In this case, thegrowth rate ẋ can be deduced from the rate constant kwith the n value of 1 using the following equation:

kn=1 = 2S ẋ,Fig. 5 P–T conditions for the back-transformation in bridgmanite.
Bridgmanite (Brg, black circles) becomes amorphous (partially, blue
diamonds; completely, blue circles), followed by orthoenstatite
crystallization (OEn, red squares) with increasing temperaturesat ~ 1–4 GPa, and directly back-transforms to high-P clinoenstatite (HPCEn) at ~ 8 GPa. A double-headed arrow indicates the temperature
condition for partially amorphization observed in Durben and Wolf
(1992)

lingunite proceeded at 610–720 °C, which was confirmedby the decrease in peak intensity in lingunite and theincrease in amorphous halo (Fig. 9a). However, before
completing the amorphization, the plagioclase crystallization started at ~ 720–820 °C with decreasing the halo
(Fig. 9b). The diffraction peaks in lingunite eventuallydisappeared in ~ 7 min at 820 °C.
3.2 Analysis of kinetic data

In the back-transformation experiments of ringwoodite,
we measured transformed volume fraction as a function of time at six different P–T conditions as shown in
Fig. 10a,b. The transformed fraction was estimated basedon the integrated intensities of several diffraction peaks.
The kinetic data were analyzed by using the Avrami rateequation as follows:
V = 1−exp −kt n(1)where V is transformed volume fraction, k and n are constants, and t is time. Kinetic parameters in the rate Eq. (1)were estimated from nonlinear least-squares fitting. The
obtained k and n values are listed in Table 1. Plots of ln
ln {1/(1 − V)} against ln (t) are also shown in Fig. 10c, inwhich the intercept and the slope are corresponding to
the values of ln k and n, respectively.

(2)

where S is the grain-boundary area per unit volume. S
can be expressed 3.35/d, where d is the grain size of theparental phase (8.9 µm). The estimated growth rate islisted in Table 1.
In the back-transformation experiments of bridgmanite, amorphization first occurs before crystallization oforthoenstatite at least up to ~ 4 GPa. We could not obtainthe kinetic data on the amorphization, but succeeded
to measure the crystallization kinetics of enstatite from
amorphous bridgmanite at 3 different P–T conditions.
We also obtained kinetic data of the direct back-transformation from bridgmanite to high-P clinoenstatite at
7.9 GPa and 820 °C. These kinetic data were analyzed byusing the rate Eq. (1) in a similar way to the case of ringwoodite, as summarized in Fig. 11 and Table 2.
In contrast to the olivine formation from ringwoodite,the n value for the orthoenstatite crystallization from
amorphous bridgmanite is larger (~ 1.8–2.0), implyingthat not only the growth but also the nucleation processcontrols the overall reaction rate. In the ringwoodite toolivine back-transformation, the change in the chemical
free energy is very large under low-pressure conditions.
This enhances the nucleation process by the decreasein the activation energy for nucleation, thus leading to
the site saturation at the early stage (i.e., growth-controlled transformation). The difference in the chemical free energy is also thought to be very large between
bridgmanite and orthoenstatite; however, the presenceof the intermediate amorphous phase would reduce thedifference available for the orthoenstatite nucleation.
The interfacial energy between the enstatite crystal andamorphous phase may also affect the nucleation kinetics.
Owing to these reasons, the bridgmanite amorphization
possibly inhibited the enstatite nucleation, resulting in
the increase in n values for overall reaction kinetics.
On the other hand, the kinetics of the direct backtransformation from bridgmanite to high-P clinoenstatite
without amorphization is rather different as shown inKubo et al. Progress in Earth and Planetary Science(2022) 9:21

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Table 2 P–T–t conditions and estimated values of kinetic parameters for the back-transformation in bridgmanite
Run No.

Pressure (GPa)Temperature (°C) Duration (s)Phase1nln k

ln k for the
averaged n­value2

2.02− 13.9− 13.1 (0.07)

1.89− 5.90− 5.76 (0.22)

OEn formation from amorphous bridgmanite
M2718

M2619

M2621

backtra11

backtra12

M2618

1.0

330

410

Brg

1.1

615

620

Complete amo

1.1

765

1655

OEn

1.3

310

290

Brg

1.2

410

410

Partial amo

1.2

510

700

Partial amo

1.2

615

1560

Complete amo

1.4

310

265

Brg

1.3

410

425

Partial amo

1.4

510

375

Partial amo

1.3

615

450

Complete amo

1.2

820

485

OEn

1.5

310

560

Brg

1.5

510

2050

Partial amo

1.5

715

1620

Complete amo

1.8

310

510

Brg

1.6

410

460

Brg

1.7

510

470

Partial amo

1.6

615

1250

Partial amo

1.6

715

1400

Complete amo

1.6

820

720

OEn

1.4

920

840

OEn

4.2

410

130

Brg

4.1

510

460

Brg

4.0

615

305

Brg

4.2

720

465

Partial amo

3.9

820

30

Complete amo

4.0

820

690

OEn

7.7

410

440

Brg

7.8

514

485

Brg

8.0

617

420

Brg

7.9

720

265

Brg

7.8

515

1165

Brg

8.1

620

1560

Brg

7.9

820

2515

HP CEn− 18.4#

No kinetic data obtained

1.79− 9.100.40− 2.18Bridgmanite to HP-CEn transformation
M2613

M2715

1

Brg, bridgmanite; amo, amorphization; OEn, orthoenstatite; HP CEn, high-P clinoenstatite2

The uncertainties in rate constant are listed in parentheses#

The maximum k value was estimated (see text)− 9.61 (0.08)(See figure on next page.)
Fig. 6 Changes of XRD patterns during the back-transformation in bridgmanite. a Amorphization of bridgmanite with increasing temperaturesfrom 410 to 610 °C at ~ 1.2 GPa (Run M2619). b Crystallization of orthoenstatite from amorphous bridgmanite at 1.1 GPa and 770 °C (RunM2718). c Amorphization of bridgmanite occurred in 30 s, followed by orthoenstatite crystallization at 4.0 GPa and 820 °C (Run M2618). d Directback-transformation from bridgmanite to high-P clinoenstatite without amorphization at 7.9 GPa and 820 °C (Run M2715). St: stishovite, Mj:
majorite, *: unknown

Kubo et al. Progress in Earth and Planetary ScienceFig. 6 (See legend on previous page.)(2022) 9:21

Page 8 of 16

Kubo et al. Progress in Earth and Planetary Science(2022) 9:21

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Fig. 7 BSE images showing back-transformation microstructures from bridgmanite to high-P clinoenstatite. a The back-transformation occurred indarker regions by both inter- and intra-crystalline processes at 7.9 GPa and 820 °C (Run M2715). b A high-magnification image of a white-coloredbox in a

Fig. 11. The n value is very small (~ 0.5), suggesting thatthe nucleation is thought to be very fast relative to thegrowth process in this reaction. This indirectly supports
the interpretation that the enstatite nucleation is inhibited due to the formation of the intermediate amorphous
phase.
3.3 Pressure and temperature dependencesof the back‑transformation rate

The growth rate data for the back-transformation in ringwoodite were analyzed by using the rate equation for theinterface-controlled growth as follows:




Gr
H∗
1 − exp −ẋ = AT exp −
(3)
RT
RT
where A is constant, H* is activation enthalpy, Gr is thefree energy change of the transformation, R is gas constant, and T is absolute temperature (Turnbull 1956). The
activation enthalpy is described as H* = E* + PV*, where
E* is activation energy, P is pressure, and V* is activation
volume. For calculation of Gr , the thermodynamic dataof Kojitani et al. (2017) for M­ g2SiO4, and Akaogi et al.
(1989) and Fabrichnaya et al. (2004) for ­Fe2SiO4 wereused. We applied symmetric regular solution model byusing nonideal parameters of Kojitani and Akaogi (1994)
for olivine and Akaogi et al. (1989) for ringwoodite. Calculated values of Gr are listed in Table 1. This rate equation was fitted to the growth rate data listed in Table 1
by a least-squares procedure, which yields E* = 456 kJ/
mol and V* = 6.9 ­cm3/mol. The results of the fitting aresummarized in Fig. 12a and Table 3. Based on thesekinetic parameters with Eqs. (1)–(3), we can estimate
the growth-controlled back-transformation rate in ringwoodite at a given P, T, and grain size condition.

The n = 1 kinetics has also been reported in the backtransformation of ­Mg2SiO4 wadsleyite in air, fromwhich the growth rate can be deduced based on theparental grain size of ~ 1 µm (Reynard et al. 1996; Hu
and Sharp 2017). We analyzed these data based on the
Eq. (3) assuming the same activation volume determined in this study (Fig. 12, Table 3). Gr was estimated from PV , where P is the pressure difference
from the equilibrium boundary, and V is molar volume change of the reaction. For calculation of P , weused the equilibrium olivine-wadsleyite phase boundary in ­Mg2SiO4 (Morishima et al. 1994). Figure 12 indicates that, although the temperature dependence isFig. 8 P–T conditions for the back-transformation in lingunite.
Partial amorphization and plagioclase crystallization proceeded withincreasing temperatures (Run backtra12)

Kubo et al. Progress in Earth and Planetary Science(2022) 9:21

Page 10 of 16

Fig. 9 Changes of XRD patterns during the back-transformation in lingunite (Run backtra12, Lgn: lingunite, Pl: plagioclase). The arrows indicate
the change of the peak intensity with temperature or time. a Lingunite amorphization occurred with increasing temperature at ~ 1.7 GPa and
610–820 °C, and plagioclase crystallization started before its completion. b Crystallization of plagioclase proceeded with decreasing amorphous
halo at ~ 1.6 GPa and 820 °C

similar, the growth rate in the present study is about 4
orders of magnitude lager than those obtained in Reynard et al. (1996) even considering the pressure effect.
Interface mobility is thought to be similar between theolivine-wadsleyite and the olivine-ringwoodite interphase boundary. It is unlikely that differences in ironcontent have such large effects on the growth kinetics.
The reason for the large difference in the growth rate
may be originated from water contained in the starting
ringwoodite (~ 1400 wt. ppm ­H2O). Effects of water on
the interface kinetics are significant as reported in previous studies (Hosoya et al. 2005; Nishihara et al. 2006).
Hosoya et al. (2005) have shown that the growth ratein the olivine–wadsleyite transformation is proportional to OH content to the power of 3.2. Considering
this water dependent kinetics, the large differences ingrowth rates can be explained assuming that the sample
of Reynard et al. (1996) is relatively dry ~ 70 wt. ppm­H2O (Fig. 12).
We also examined pressure and temperature dependences of the rate constant k for orthoenstatite crystallization from amorphous bridgmanite by the following
Arrhenius type equation:k = k0 exp −H ∗ /RT(4)
where k0 is constant. We obtained the k data at three different P–T conditions (1.1–4.0 GPa and 765–820 °C)
with the averaged n value of 1.9 (Table 2). Additionally,
we also preliminarily observed that the orthoenstatite

crystallization did not start in 27 min at 1.5 GPa and715 °C (Run backtra 11). We estimated the maximum kvalue of this run assuming the n = 1.9 kinetics (Table 2).
Thus, a total of four data points were used to estimate
kinetic parameters in Eq. (4) as summarized in Fig. 12b
and Table 3. The activation energy for the orthoenstatite
crystallization from amorphous bridgmanite is muchlarger than that for the olivine formation from ringwoodite. This is probably because the rate constant k for theorthoenstatite crystallization involves both nucleationand growth processes as discussed above.
Knittle and Jeanloz (1987) reported much fasterkinetics with smaller activation energy of ~ 70 kJ/mol
for the back-transformation of bridgmanite to enstatite
at ambient pressure. They did not obtain time-dependent kinetic data in most of runs. Although the n = 3
kinetics was obtained in a limited condition, it was
not enough to estimate the quantitative temperaturedependence of the k value. The back-transformation
to enstatite was observed at much lower temperaturesof ~ 520–610 °C in 6–24 h in their experiment. Extrapolations of our kinetic data (Fig. 12b) to their condition(0 GPa and 600 °C) indicate that more than 1000 h arenecessary for the 10% enstatite crystallization. Additionally, they observed bridgmanite even at ~ 550 °C for
6 h and no glass in any samples, which is inconsistent
with the amorphization behavior observed in previous
studies (Durben and Wolf 1992; Wang et al. 1992) andthis study (Fig. 5). Durben and Wolf (1992) showed that

Kubo et al. Progress in Earth and Planetary Science(2022) 9:21

Page 11 of 16

Fig. 10 Back-transformation kinetics from ringwoodite to olivine. a, b Transformation-time data at six different P–T conditions. Curves obtainedby least-squares fits of the kinetic data to Eq. (1) are also shown. Note that Run M2893 lasted 18,340 s until the transformed fraction reached ~ 34
vol% although kinetic data with t > 8000 s is not shown. c Plots of ln ln {1/(1 − V)} against ln (t). The intercept and the slope are corresponding to thevalues of ln k and n, respectively

thermally induced vitrification of bridgmanite begins
near 130 °C and is complete by ~ 480 °C on the basis ofa Raman spectroscopic study, which is in good agreement with extrapolations of our results on the amorphization temperatures to ambient pressure condition(Fig. 5). Knittle and Jeanloz (1987) synthesized thestarting bridgmanite in a diamond-anvil cell, whereas a
KAWAI-type apparatus was used in Durben and Wolf
(1992) and our study, which may affect the back-transformation behaviors through the differences in grain
size and/or crystallinity.

3.4 Back‑transformations during the post‑shock stage
in shocked meteorites

In the present study, the back-transformation kinetics was examined in the timescale from several tens ofseconds to a few hours (Figs. 10, 11). In order to discuss different timescales in planetary collision and diamond transportation, the obtained kinetic parameters
were used to estimate pressure and temperature kinetic
boundaries in a given timescale appropriate for each
event.
P–T history during the shock event have been discussed in some shocked meteorites based on thermalKubo et al. Progress in Earth and Planetary Science(2022) 9:21

Page 12 of 16

Fig. 11 Back-transformation kinetics in bridgmanite. a Transformation-time data for orthoenstatite crystallization from amorphous bridgmanite(red, black, and blue circles), and for direct back-transformation from bridgmanite to high-P clinoenstatite (green circles). b Plots of ln ln {1/(1 − V)}against ln (t). The n values (slope) are different depending on the reaction

Fig. 12 Analysis of pressure and temperature dependences of the back-transformation rate. For plotting purposes, the data are plotted after
corrections to the pressure of 1 GPa using the activation volume determined in this study. Obtained kinetic parameters are summarized inTable 3. a Fits of the growth rate data in the ringwoodite-olivine (black circles; this study) and in the wadsleyite-olivine (red triangles; Reynard
et al. 1996; Hu and Sharp 2017) back-transformations to Eq. (3). Large discrepancies between these growth rate data correspond to the differencein water contents by about 20 times (red and blue triangles) considering the water content exponent of 3.2 (see text). b Fits of the k data in theorthoenstatite crystallization from amorphous bridgmanite to Eq. (4)modelling considering the distributions of high-pressure phases in shock vein and host rock. Duration of
the pressure pulse experienced in shocked meteorites

has been estimated to be ~ 0.01 s to a few seconds (e.g.,
Ohtani et al. 2004; Beck et al. 2005; Xie and Sharp 2007).
After the shock pulse release, pressure and temperatureKubo et al. Progress in Earth and Planetary Science(2022) 9:21

Table 3 P and T dependences of the rate constant k and growth
rate
Reaction

ln k0

E* (kJ/mol)V* ­(cm3/mol)Ringwoodite to ­olivine1

29.6 (4.1)

456 (34)

6.9 (1.0)

Wadsleyite to ­olivine2

17.2 (2.5)

431 (22)6.9 (fixed)

Brg glass to ­OEn3

108 (10)1025 (88)10.7 (3.4)

The uncertainties in kinetic parameters are listed in parentheses
1

Equation (3) was fitted to the growth rate data obtained in this study

2Equation (3) was fitted to the growth rate data obtained in Reynard et al. (1996)
and Hu and Sharp (2017) assuming the same activation volume as that of the
ringwoodite to olivine transformation

3

Equation (4) was fitted to the rate constant k data obtained in this study

suddenly drop by the adiabatic decompression, followedby the cooling at ambient pressure in longer timescales(~ ­100–102 s) by thermal conduction in the post-shockannealing stage (e.g., Ohtani et al. 2004; Hu and Sharp2017). Ringwoodite is present in fragments in shock veinand host rock in the vicinity of shock vein with having
granular and lamellar textures (e.g., Tomioka and Miyahara 2017). The grain sizes and lamellar widths of ringwoodite are ~ 0.5–2 µm (e.g., Ohtani et al. 2004; Xie andSharp 2007; Miyahara et al. 2008). Our experiments suggested that the back-transformation from ringwoodite toolivine is growth-controlled process. To discuss the backtransformation of ringwoodite considering these points,
we estimated kinetic boundaries for the 1 µm growth ofolivine from ringwoodite in the timescale of 0.1–100 s(Fig. 13a).
The back-transformation rate in shocked meteorites
may be influenced by water; however, previous studies on water contents of nominally anhydrous minerals in shocked meteorites have been limited. Hallis et al.
(2017) have reported that ringwoodite grains in Tissint
Martian meteorite contain up to 1132 wt. ppm ­H2O. Thiswater content is similar to that in our starting material.
It is thought that constituent minerals in L5/6 ordinarychondrites are relatively dry compared to those in Tissint
Martian meteorite. Therefore, we plotted two kinetic
boundaries based on the parameters deduced from ourexperiments and Reynard et al. (1996) (Table 3), which
may represent wet and dry conditions in shocked meteorites, respectively.
To avoid the back-transformation, the P–T path should
be below the kinetic boundary during both the adiabatic
decompression and the post-shock annealing stages. The
temperature–time history during the post-shock stage
depends on several factors such as the post-shock temperature, the shock melt vein thickness, and the distancefrom the vein. We plotted typical three thermal models(A–C) proposed in previous studies (Ohtani et al. 2004;
Hu and Sharp 2017) in Fig. 13a, suggesting possible

Page 13 of 16

variations of the back-transformation of ringwoodite inshocked meteorites. Ringwoodite at 20 µm in the hostfrom a shock vein of 0.8–1.0 mm thickness (case A, Hu
and Sharp 2017) can survive over the post-shock annealing stage if it is under dry condition, whereas ringwoodite at 100 µm in the host from a shock vein of 2.0 mm
thickness (case B, Ohtani et al. 2004) can survive evenunder wet condition like Tissint Martian meteorite. The
back-transformation cannot be avoided along the temperature–time path expected in fragments in shock veinsof 0.8–1.0 mm thickness (case C, Hu and Sharp 2017).
Thus, thermal history of shock events including thepost-shock stage can be uniquely constrained by considering both forward and backward olivine-ringwoodite
transformations.
Figure 13b shows the back-transformation processes
expected in bridgmanite from our experimental data.
Crystalline bridgmanite have been found in the clast in
the shock vein and host rock in L5–6 ordinary chondrites, usually coexisting with amorphous bridgmanite(Tomioka and Fujino 1997; Tschauner et al. 2014). Sharp
et al. (1997) have reported the presence of amorphousbridgmanite in the shock vein matrix. In Martian meteorites, crystalline and amorphous bridgmanite have beenfound in the post-spinel decompositional assemblage(Miyahara et al. 2011), and the back-transformation to
enstatite have also been reported (Miyahara et al. 2019).
For the preservation of crystalline bridgmanite during
adiabatic decompression to ambient pressure, it is necessary to avoid complete amorphization and the directback-transformation to high-P clinoenstatite.
If we adopt thermal models (A–C) discussed above to
Fig. 13b, it turns out that the preservation of crystalline
bridgmanite during the post-shock stage is rather difficult. Complete amorphization is unavoidable in bridgmanite by the post-shock annealing at ~ 700 °C for 100 sin the case B. The higher temperature paths of case A
and C would result in the back-transformation to highP clinoenstatite (and to low-P clinoenstatite). However,kinetic behaviors in shorter timescales than 10 s remains
unclear for both processes as we could not determine
quantitative kinetics yet. Additionally, it has been suggested that volume expansion associated with amorphization produces transformation stress in the residual
crystalline bridgmanite (Durben and Wolf 1992). Theyobserved residual Raman shift in crystalline bridgmanitethat is comparable to a hydrostatic pressure of ~ 1.3 GPa.
This effect may avoid the complete amorphization during
the post-shock annealing stage.
Lingunite, that is a hollandite-type high-pressure polymorph of N
­ aAlSi3O8-rich plagioclase, has been foundin shock veins in ordinary chondrites (e.g., Tomioka
et al. 2000; Gillet et al. 2000). Amorphous plagioclase isKubo et al. Progress in Earth and Planetary Science(2022) 9:21

Page 14 of 16

Fig. 13 Back-transformations in timescales of 0.1–100 s and 10–100 days expected in shocked meteorites and diamond inclusions, respectively.
a Kinetic boundaries for the 1 µm and 20 µm growth of olivine from ringwoodite including effects of water. b Amorphization conditions inbridgmanite and kinetic boundaries for 10% and 90% crystallization of orthoenstatite from amorphous bridgmanite. Typical three thermal models(A–C) during the post-shock annealing stage are shown in bold dashed lines. (A) 20 µm inside the host with vein thickness of 0.8–1 mm, Pmax ~ 15
GPa and post-shock T ~ 1500 K (Hu and Sharp 2017). (B) 100 µm inside the host with vein thickness of 2 mm, Pmax ~ 20 GPa and post-shock T ~ 1240 K(Ohtani et al. 2004). (C) 200 µm clast in the shock vein of 0.8–1 mm thickness, Pmax ~ 15 GPa and post-shock T > 2000 K (Hu and Sharp 2017)present in the vicinity of lingunite; however, there havebeen no reports on the fine-grained plagioclase that may
be back-transformed from lingunite. Although the stability field of the hollandite-type phase in this chemicalcomposition has not been confirmed by phase equilibrium studies, it has been suggested that the metastableformation from amorphous plagioclase is a possible origin of lingunite in shocked chondritic meteorites (Kuboet al. 2017). The present study showed that re-amorphization of lingunite proceeds at slightly higher temperatures (~ 600–700 °C) compared to the bridgmanite case.
Plagioclase crystallization, that occurs at ~ 700–800 °C inseveral minutes, requires higher temperatures in shortertime scales of shock event. Formation and survival of lingunite in shocked meteorites would give another important constraint on shock history although quantitative
kinetics are needed to discuss further details.
3.5 Back‑transformations during the diamondtransportation from the deep Earth

The timescale of transportation of deep diamonds frommantle transition zone to the surface of the Earth is still
unclear. Until the kimberlite eruption has brought diamonds at the final stage, they might be transferred tothe upper mantle by the long-time mantle flow (Harte
and Cayzer 2007), or the rapid kimberlite ascent mightbring them directly from deeper mantle (Ringwood et al.
1992). Nishi et al. (2010) compared the back-transformation textures in majoritic garnet observed in diamondinclusion with those in laboratory kinetics experiments
and suggested that diamonds have been transported
directly from deep mantle by the rapid kimberlite magmain ~ 190–2000 h at 1200–1400 °C. We discuss survival ofhigh-pressure minerals during the diamond transportation considering this timescale in Fig. 13.
There has been only one report on the ringwoodite inclusion in diamond (Pearson et al. 2014). It contains ~ 14,000–15,000 wt. ppm H­ 2O, and its grain sizeis ~ 40 µm. We plotted kinetic boundaries for the 20 µm
growth of olivine from ringwoodite in the timescalesof 10–100 days (Fig. 13a). Assuming the water content exponent of 3.2 for the growth rate (Hosoya et al.
2005), kinetic boundaries with different water contents­(COH = 1400 and 10,000 wt. ppm H­ 2O) are shown. Figure 13a indicates that preservation of ~ 40 µm hydrous
ringwoodite during the kimberlite magma ascent is quitedifficult. It requires lower temperatures than ~ 600 °C.
Because it is unlikely that such low temperatures wererealized when erupting kimberlite magma, the internalpressure in the diamond must be high enough to preventthe hydrous ringwoodite from the back-transformation.
Majoritic garnet can be survived to the Earth surface bykimberlite eruption due to the slow back-transformation
kinetics as shown in Nishi et al. (2010), but ringwoodite cannot be preserved in diamond without the help ofresidual stress.
On the other hand, (Mg, Fe)SiO3 bridgmanite has
not been found in diamond so far. Several studies have

Kubo et al. Progress in Earth and Planetary Science(2022) 9:21

suggested super-deep diamonds that include the lowermantle assemblage of ferropericlase and enstatite
inverted from the former bridgmanite (e.g., Hayman
et al. 2005). Our study clearly shows that both crystalline
and amorphous bridgmanite cannot be preserved, but
the back-transformation to high-P clinoenstatite likely
occurs along P–T–t paths expected for the transportation of diamond by kimberlite magma. Even if bridgmanite is amorphized during the diamond ascent, it seems tohave enough time to crystallize to enstatite at higher than
600 °C (Fig. 13b). This is in agreement with the presenceof enstatite instead of the amorphous phase as the former
bridgmanite in super-deep diamonds.

4 Summary
Survival of high-pressure minerals in shocked meteorites
and diamond inclusions provide important constraints
on the P–T–t history of planetary collisions and diamond transportation by considering the back-transformation kinetics. High-pressure in situ X-ray observations
revealed that ringwoodite directly back-transforms toolivine by grain-boundary nucleation and growth mechanisms. The obtained kinetics can explain the varieties ofthe back-transformation along the possible P–T–t pathsin the post-shock stage of shocked meteorites considering the water effects. Preservation of the hydrous ringwoodite during diamond transportation from the deep
Earth is quite difficult without the help of residual stress.
Bridgmanite first becomes amorphous state followedby crystallization of orthoenstatite at ~ 1–4 GPa, anddirectly back-transforms to high-P clinoenstatite at ~ 8
GPa. The amorphization also occurs in lingunite at ~ 1.5
GPa, and plagioclase crystallization starts before thecomplete amorphization. Our results are consistent withthe presence of enstatite instead of the amorphous phaseas the former bridgmanite in super-deep diamonds, however cannot explain the presence of crystalline bridgmanite in shocked meteorites. It is necessary to investigate
detailed processes of amorphization in much shorter
timescale to assess this issue.
Acknowledgements
This paper is dedicated to late Prof. Ahmed El Goresy who made a great
contribution to the field of meteoritical sciences. We deeply appreciate forhis interest and helpful comments on our experimental studies. We thank K.
Shimada, S. Yamanouchi, D. Wakabayashi, and M. Ikehara for their assistancewith experiments, M. Nishi and Y. Tsubokawa for helpful discussion, and H.
Kojitani for the calculation of thermodynamic properties. X-ray diffraction
experiments using synchrotron radiation were carried out at AR-NE5C of the
Photon Factory (proposal no. 2016G598) and at BL04B1 of SPring-8 (proposal
nos. 2016B1358, 2018B1363 and 2019A1487).
Author contributions
TK and MM proposed the topic, and TK and KK conceived and designed thestudy. TK, KK, MI, YT, and YH carried out the experimental study. TK, KK, andMM analyzed the data and helped in their interpretation. TK wrote the manuscript. All authors read and approved the final manuscript.

Page 15 of 16

Funding
This work was partially supported by MEXT/JSPS KAKENHI Grant Numbers
JP18H01269 and JP18H05232.
Availability of data and materials
The datasets supporting the conclusions of this article are included within thearticle.

Declarations
Ethical approval
This article does not contain any studies with human participant or animals
performed by any of the authors.
Competing interests
The authors declare that they have no competing interests.
Author details
1
Department of Earth and Planetary Sciences, Faculty of Sciences, Kyushu
University, Fukuoka 819‑0395, Japan. 2 Department of Earth and Planetary
Sciences, Graduate School of Sciences, Kyushu University, Fukuoka 819‑0395,
Japan. 3 Japan Synchrotron Radiation Research Institute, Hyogo 679‑5198,
Japan. 4 Graduate School of Advanced Science and Engineering, Hiroshima
University, Higashi‑Hiroshima 739‑8526, Japan.
Received: 31 October 2021 Accepted: 1 April 2022

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