Si + Al Mg Fe + Mn +Ni Ca rim Ca p.f.u

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1 .6.5. y = -.4x +.8 R =.9574 y = - x +.14 R =.9788 y = -.4 x +.7 R =.9896 Si + Al Fe + Mn +Ni y =.55 x.36 R = core rim =.6 ±.6 4 =.6 ± p.f.u y = -3.9 x R = distance [ m] Supplementary Figure 1 Fitted profile of clinopyroxene compositional boundary. The composition of a clinopyroxene has been measured along the red dots profile in Fig. a to evaluate the variation and contribution of each element to the backscatter coefficient 1, (ETA), i.e. to the brightness of BSE image. a. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions. b. ETA value of each spot analysis versus and the relative c. ETA value versus distance [μm] compositional profile, along the red dots traverse of the clinopyroxene shown in Fig. a. The red line is the best fitting of the compositional profile and the value of the fitting parameter 4 is given. d. Compositional profile of cations (a.p.f.u.) versus distance [μm], along the red dots traverse of the clinopyroxene shown in Fig. a. The red line is the best fitting of the compositional profile and the value of the fitting parameter 4 is given. Error bars ( standard deviation) represent uncertainties of electron microprobe analyses (), and error propagation uncertainties of electron microprobe analyses (ETA).

$148 Supplementary Figure - Electron microprobe compositional data of CPX1. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions.$

2 Y=-.474x+.783 R =.9373 CPX1 1 Y=-.749x R =.981 Y=.568x-.357 R =.995 Y=-.3896x+.7 R =.97. Y=-3.68x R = Supplementary Figure - Electron microprobe compositional data of CPX1. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions. d. ETA value of each spot analysis versus and the relative

$149 Supplementary Figure 3 - Electron microprobe compositional data of CPX. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions.$

3 Y=-.467x+.783 R = CPX Y=-.795x+.144 R =.957 Y=.5343x R =.996 Y=-.47x+.76 R =.961. Y=-3.73x R = Supplementary Figure 3 - Electron microprobe compositional data of CPX. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions. d. ETA value of each spot analysis versus and the relative

$15 Supplementary Figure 4 - Electron microprobe compositional data of CPX3. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions.$

4 1 Y=.671x-.371 R =.993 Y= -.866x+.841 R =.958 Y= x R =.96. CPX3 Y= -.963x+.565 R =.955 Y= x R = Supplementary Figure 4 - Electron microprobe compositional data of CPX3. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions. d. ETA value of each spot analysis versus and the relative

$15 Supplementary Figure 5 - Electron microprobe compositional data of CPX4. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions.$

5 CPX4 1 Y=.374x-.315 R =.991 Y= -.4x+.748 R =.955 Y= x+.173 R =.841 Y= x+.773 R =.98. Y= -8.81x R = Supplementary Figure 5 - Electron microprobe compositional data of CPX4. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions. d. ETA value of each spot analysis versus and the relative

$b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions. d. ETA value of each spot analysis versus and the relative$

6 11 Y= -.473x+.757 R =.816 Y= -.199x+.78 R =.5341 Y= x+.148 R =.81 Y=.61853x R =.964. CPX5 Y= x R = Supplementary Figure 6 - Electron microprobe compositional data of CPX5. b. versus distance [ µ m] along the analysed compositional boundary. c. ETA value of each spot analysis versus ETA fraction of,,, and along with their relative linear regressions. d. ETA value of each spot analysis versus and the relative

7 Supplementary Table 1. Electron microprobe analyses of the compositional boundary layer of the clinopyroxene in Fig. Major Elements Distance (µm) SiO TiO Al O 3 Cr O 3 Fe O 3 FeO MnO NiO O O Na O sum (rim) (core) Distance (µm) Atomic proportion on the basis of 4 cations and Fe 3+ from stoichiometry Si IV Al VI Al Ti Cr Fe 3+ Ni Fe + Mn Na sd (rim) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± (core) ± 6 and elemental ETA fraction per formula unit Distance (µm) Si Al Ti Cr Fe Ni Mn Na Ox ETA sd ETA 15keV (rim) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± (core) ±.9 Core- rim ETA fraction variation of the major constituents grouped according to their similar atomic weights Fe+Mn+ Ni Ox absolute percentage 3.% - 111% 14.6% 9.% 1.7% footnote: Major element composition of the clinopyroxene in Fig. a, measured along the red dots profile ( µm: rim, 5 µm: core). For each spot analysis we have calculated the number of cations per formula unit, the backscatter coefficient (ETA, Ref. 1, ), and the contribution of each element to the ETA value. The backscatter coefficient has been calculated from the formula unit weight [g mol -1 ], the weight of each element [g mol -1 ], and the elemental backscatter coefficient at 15 kev (Ref. ). The core-rim ETA fraction variation (absolute and percentage) of the major constituents of the clinopyroxene composition is also reported. These major constituents are grouped according to their similar atomic weights (Si + Al,,, Fe + Ni + Mn, Ox). [/(+Fe) at.] and ETA uncertainties ( standard deviation) represent error propagation of electron microprobe analyses.

8 Supplementary References 1. Reed, S.J.B. Electron microprobe analysis. mbridge Univ. Press, pp.399 (1975).. Hunger, H.J. & Küchler L. Measurements of the electron backscattering coefficient for quantitative EPMA in the energy range 4 to 4 kev. IPSSa, 56, K45-K48 (1979).

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