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1 Sample - Fe-Mg equilibrium in ol-hosted MIs

• This notebook shows how to assess Fe-Mg equilibrium between olivines and melt inclusions, and between melt inclusions and co-erupted matrix glasses to let you assess Fe-Mg diffusion and post-entrapment crystallization

• In this example, we have just 1 sample in our spreadsheet, so we dont have to segment by sample name

• You can download the spreadsheet here: https://github.com/PennyWieser/Thermobar/blob/main/docs/Examples/Melt_Inclusion_FeMg_Equilibrium/2018_MIs_Glasses.xlsx

## Install Thermobar if you haven't already (remove the # and press run!)

#!pip install Thermobar

# Loading various python things
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import Thermobar as pt

Loading a dataset

• This dataset is from Wieser et al. (2021) - https://doi.org/10.1029/2020GC009364

• It shows olivine-hosted melt inclusions from Fissure 8, which have undergone extensive and variable amonuts of PEC.

• We load in measured melt inclusion compositions (e.g. before PEC correction), and host olivines, as well as the composition of the co-erupted matrix glass

• You can download the spreadsheet here - https://github.com/PennyWieser/Thermobar/blob/main/docs/Examples/Melt_Inclusion_FeMg_Equilibrium/2018_MIs_Glasses.xlsx

Load in the matrix glasses

# We dont have to add _Liq as its all liquids,
# just specify the _Liq in the import
MG_input=pt.import_excel('2018_MIs_Glasses.xlsx',
                         sheet_name='LL4_MGs', suffix="_Liq")
MG_all=MG_input['my_input'] ## All columns
MG_Liqs=MG_input['Liqs'] ## Just Liquid columns
MG_Liqs.head()

	SiO2_Liq	TiO2_Liq	Al2O3_Liq	FeOt_Liq	MnO_Liq	MgO_Liq	CaO_Liq	Na2O_Liq	K2O_Liq	Cr2O3_Liq	P2O5_Liq	H2O_Liq	Fe3Fet_Liq	NiO_Liq	CoO_Liq	CO2_Liq	Sample_ID_Liq
0	50.6243	2.8773	13.0360	11.8288	0.1830	5.8471	10.2471	2.5120	0.5234	0.0	0.2689	0.0	0.0	0.0	0.0	0.0	0
1	50.0975	2.8840	12.8885	11.2897	0.1769	5.8521	9.9658	2.4681	0.5305	0.0	0.2652	0.0	0.0	0.0	0.0	0.0	1
2	50.1346	2.8741	12.8953	11.8696	0.1814	5.8682	10.2012	2.4618	0.5778	0.0	0.2875	0.0	0.0	0.0	0.0	0.0	2
3	50.5233	2.8765	12.9818	11.3536	0.1454	5.8673	10.1806	2.6206	0.5206	0.0	0.2759	0.0	0.0	0.0	0.0	0.0	3
4	51.5840	2.9055	13.3290	11.5014	0.2286	5.8450	10.0408	2.1722	0.5565	0.0	0.2693	0.0	0.0	0.0	0.0	0.0	4

Load in the melt inclusion data and the olivines

• As they are in the same sheet, we have to make sure we have _Liq after the melt inclusion oxide, and _Ol after the olivine

MIs_in=pt.import_excel('2018_MIs_Glasses.xlsx',
                         sheet_name='LL4_MIs')
MIs_Ol=MIs_in['Ols']
MIs_Liqs=MIs_in['Liqs']
MIs_input=MIs_in['my_input']

Workflow 1: Assess if the olivines are in equilibrium with the co-erupted matrix glass

1. Calculate Mg# for liquids

Liq_Mgno_calc=pt.calculate_liq_mgno(liq_comps=MG_Liqs, Fe3Fet_Liq=0.15)
Liq_Mgno_calc.head()
# Calculate mean value to plot
Liq_Mgno_calc_mean=np.mean(Liq_Mgno_calc)

2. Calculate Olivine Fo contents

Ol_Fo_Calc=pt.calculate_ol_fo(ol_comps=MIs_Ol)

3. Calculate fields you want to plot on a Rhodes diagram

Rhodes=pt.calculate_ol_rhodes_diagram_lines(Min_Mgno=0.5, Max_Mgno=0.7)
Rhodes.head()

	Mg#_Liq	Eq_Ol_Fo_Roeder (Kd=0.3)	Eq_Ol_Fo_Roeder (Kd=0.27)	Eq_Ol_Fo_Roeder (Kd=0.33)	Eq_Ol_Fo_Matzen (Kd=0.34)	Eq_Ol_Fo_Matzen (Kd=0.328)	Eq_Ol_Fo_Matzen (Kd=0.352)
0	0.500000	0.769231	0.787402	0.751880	0.746269	0.753012	0.739645
1	0.502020	0.770662	0.788751	0.753384	0.747796	0.754512	0.741198
2	0.504040	0.772087	0.790095	0.754883	0.749317	0.756006	0.742745
3	0.506061	0.773506	0.791432	0.756375	0.750832	0.757493	0.744286
4	0.508081	0.774919	0.792763	0.757861	0.752341	0.758975	0.745822

4. Plot the Kd model you want, along with the olivine and glass Mg

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))

# Plotting for Roeder and Emslie
ax1.set_title('Roeder and Emslie, 1970')
# Plotting equilibrium lines
ax1.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Roeder (Kd=0.27)'], ':k')
ax1.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Roeder (Kd=0.33)'], ':k')
ax1.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Roeder (Kd=0.3)'], '-k')

# Plotting data
ax1.plot(Ol_Fo_Calc*0+Liq_Mgno_calc_mean, Ol_Fo_Calc, 'ok', mfc='red')

ax2.set_title('Matzen (2011)')
# Plotting equilibrium lines
ax2.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Matzen (Kd=0.328)'], ':k')
ax2.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Matzen (Kd=0.352)'], ':k')
ax2.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Matzen (Kd=0.34)'], '-k')
# Plotting data
ax2.plot(Ol_Fo_Calc*0+Liq_Mgno_calc_mean, Ol_Fo_Calc, 'ok', mfc='red')
ax1.set_ylabel('Ol Fo content')
ax1.set_xlabel('Glass Mg#')
ax2.set_xlabel('Glass Mg#')
ax1.set_ylim([0.74, 0.92])
ax2.set_ylim([0.74, 0.92])
ax1.set_xlim([0.5, 0.7])
ax2.set_xlim([0.5, 0.7])

(0.5, 0.7)

• We can see that a lot of the olivines are way to primitive to be in equilibrium with the co-erupted liquid, regardless of what Kd model we use. This is the first sign that the olivines have undergone extensive post-entrapment cooling and crystallization.

Workflow 2: Assess if the olivines and their melt inclusions are in equilibrium

• If post entrapment crystallization occurs, then the crystals erupt immediatly, the melt inclusion and host olivine will be out of Mg-Fe equilibirum. -However, as Danysuhevsky et al. show in a series of papers if sufficient time passes between the cooling event driving PEC and eruption, Fe-Mg will re-equilbrate, Fe will be lost from the inclusion, and the melt inclusion will re-approach equilibrium with its host olivine

1. Calculate melt inclusion Mg

MI_Mgno_calc=pt.calculate_liq_mgno(liq_comps=MIs_Liqs, Fe3Fet_Liq=0.15)
MI_Mgno_calc.head()
# Calculate mean value to plot
MI_Mgno_calc_mean=np.mean(MI_Mgno_calc)

2. Plot on a rhodes diagram

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))

# Plotting for Roeder and Emslie
ax1.set_title('Roeder and Emslie, 1970')
# Plotting equilibrium lines
ax1.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Roeder (Kd=0.27)'], ':k')
ax1.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Roeder (Kd=0.33)'], ':k')
ax1.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Roeder (Kd=0.3)'], '-k')

# Plotting data
ax1.plot(MI_Mgno_calc, Ol_Fo_Calc, 'ok', mfc='red')

ax2.set_title('Matzen (2011)')
# Plotting equilibrium lines
ax2.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Matzen (Kd=0.328)'], ':k')
ax2.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Matzen (Kd=0.352)'], ':k')
ax2.plot(Rhodes['Mg#_Liq'], Rhodes['Eq_Ol_Fo_Matzen (Kd=0.34)'], '-k')
# Plotting data
ax2.plot(MI_Mgno_calc, Ol_Fo_Calc, 'ok', mfc='red')
ax1.set_ylabel('Ol Fo content')
ax1.set_xlabel('Melt inclusion Mg#')
ax2.set_xlabel('Melt inclusion Mg#')
ax1.set_ylim([0.74, 0.92])
ax2.set_ylim([0.74, 0.92])
ax1.set_xlim([0.5, 0.7])
ax2.set_xlim([0.5, 0.7])

(0.5, 0.7)

• We can see using the Roeder and Emslie model, the melt inclusions are perfectly in line with the equilibrium field. Combined with the extensive olivine-matrix glass Fe-Mg disequilibrium, this shows extensive PEC, followed by diffusive re-equilibration

• Another line of evidence comes from plotting matrix glass and melt inclusoins in MgO-FeO space, its clear MI have lost abundant Fe

plt.plot(MIs_Liqs['MgO_Liq'], MIs_Liqs['FeOt_Liq'], 'ok', mfc='red', label='MIs')
plt.plot(MG_Liqs['MgO_Liq'], MG_Liqs['FeOt_Liq'], '^k', mfc='k', label='MG')
plt.xlabel('MgO Glass (wt%)')
plt.ylabel('FeOt Glass(wt%)')
plt.legend()

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