Amphibole-only and Amphibole-Liquid¶

This workbook demonstrates how to use the various amphibole-only, and amphibole-liquid functions

You need to install Thermobar once on your machine, if you haven't done this yet, uncomment the line below (remove the #)

In [1]:

#!pip install Thermobar

Load python things¶

In [2]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import Thermobar as pt
pd.options.display.max_columns = None

Load data¶

In [3]:

out=pt.import_excel('Amphibole_Liquids.xlsx', sheet_name="Amp-Liq")
my_input=out['my_input']
Amps=out['Amps']
Liqs=out['Liqs']

Checking data read in correctly (check no columns are full of zeros that you think you inputted)¶

In [4]:

display(Amps.head())
display(Liqs.head())

	SiO2_Amp	TiO2_Amp	Al2O3_Amp	FeOt_Amp	MnO_Amp	MgO_Amp	CaO_Amp	Na2O_Amp	K2O_Amp	Cr2O3_Amp	Sample_ID_Amp
0	40.57	2.45	12.82	13.11	0.26	13.02	11.63	2.20	0.92	0.00	probe1
1	39.45	1.88	10.80	11.85	0.00	11.32	10.94	2.04	0.75	0.00	probe2
2	42.88	3.46	14.28	15.99	0.54	14.25	12.12	2.43	1.18	0.03	probe3
3	42.20	2.75	11.10	13.10	0.39	13.55	11.07	2.27	0.95	0.01	probe4
4	40.37	2.28	10.06	11.76	0.19	12.41	10.40	2.09	0.82	0.00	probe5

	SiO2_Liq	TiO2_Liq	Al2O3_Liq	FeOt_Liq	MnO_Liq	MgO_Liq	CaO_Liq	Na2O_Liq	K2O_Liq	P2O5_Liq	H2O_Liq	Sample_ID_Liq
0	62.317403	0.592583	17.015042	5.578974	0.147384	1.493784	5.199067	3.799517	3.840125	0.320967	5	probe_s2_1
1	63.410655	0.567627	16.682223	5.211648	0.139473	1.343074	4.680291	3.797226	4.118336	0.320854	5	probe_s2_2
2	64.978351	0.531840	16.204967	4.684912	0.128130	1.126960	3.936379	3.793940	4.517285	0.320691	5	probe_s2_3
3	60.953715	0.623712	17.430191	6.037164	0.157251	1.681775	5.846172	3.802375	3.493093	0.321109	5	probe_s2_4
4	60.188394	0.641183	17.663178	6.294307	0.162789	1.787278	6.209337	3.803979	3.298333	0.321189	5	probe_s2_5

Example 1 - Amphibole-only pressure¶

can use help to see equation options

In [5]:

help(pt.calculate_amp_only_press)

Help on function calculate_amp_only_press in module Thermobar.amphibole:

calculate_amp_only_press(amp_comps=None, equationP=None, T=None, deltaNNO=None, classification=False, Ridolfi_Filter=True)
    Amphibole-only barometry, returns pressure in kbar.
    
    Parameters
    -----------
    
    amp_comps: pandas.DataFrame
        Amphibole compositions with column headings SiO2_Amp, MgO_Amp etc.
    
    
    EquationP: str
        | P_Mutch2016 (T-independent)
        | P_Ridolfi2012_1a (T-independent)
        | P_Ridolfi2012_1b (T-independent)
        | P_Ridolfi2012_1c (T-independent)
        | P_Ridolfi2012_1d (T-independent)
        | P_Ridolfi2012_1e (T-independent)
        | P_Ridolfi2021 - (T-independent)- Uses new algorithm in 2021 paper to
        select pressures from equations 1a-e.
    
        | P_Ridolfi2010  (T-independent)
        | P_Hammarstrom1986_eq1  (T-independent)
        | P_Hammarstrom1986_eq2 (T-independent)
        | P_Hammarstrom1986_eq3 (T-independent)
        | P_Hollister1987 (T-independent)
        | P_Johnson1989 (T-independent)
        | P_Blundy1990 (T-independent)
        | P_Schmidt1992 (T-independent)
        | P_Anderson1995 (*T-dependent*)
    
    T: float, int, pandas.Series, str  ("Solve")
        Temperature in Kelvin
        Only needed for T-sensitive barometers.
        If enter T="Solve", returns a partial function
        Else, enter an integer, float, or panda series
    
    Returns
    -------
    pandas series
       Pressure in kbar

Ridolfi 2021 - Minerals - algorithm¶

here, we specify equationP="P_Ridolfi2021", which combines equations 1a-1e from Ridolfi 2012 and chooses the "correct" equation using a number of filters (see Ridolfi 2021, Minerals)
The output dataframe shows the calulated pressure, as well as the equation selected
The code also prints a warning that some of the rows have oxide sums <90, so a Nan is returned for these following Ridolfi 2021 supplement

In [6]:

P_Ridolfi2021=pt.calculate_amp_only_press(amp_comps=Amps, equationP="P_Ridolfi2021")
P_Ridolfi2021.head()

Out[6]:

	P_kbar_calc	Input_Check	Fail Msg	classification	equation	H2O_calc	Fe2O3_calc	FeO_calc	Total_recalc	Sum_input	SiO2_Amp_cat_prop	MgO_Amp_cat_prop	FeOt_Amp_cat_prop	CaO_Amp_cat_prop	Al2O3_Amp_cat_prop	Na2O_Amp_cat_prop	K2O_Amp_cat_prop	MnO_Amp_cat_prop	TiO2_Amp_cat_prop	Cr2O3_Amp_cat_prop	Si_Amp_13_cat	Mg_Amp_13_cat	Fet_Amp_13_cat	Ca_Amp_13_cat	Al_Amp_13_cat	Na_Amp_13_cat	K_Amp_13_cat	Mn_Amp_13_cat	Ti_Amp_13_cat	Cr_Amp_13_cat	cation_sum_Si_Mg	Si_T	Al_IV_T	Ti_T	Cr_C	Fe3_C	Mg_C	Fe2_C	Mn_C	Ca_B	Na_B	Na_A	K_A	Al_VI_C	Ti_C	Charge	Fe3_calc	Fe2_calc	O=F,Cl	Total	Mgno_Fe2	Mgno_FeT	Na_calc	B_Sum	A_Sum	class	APE
0	4.572174	True		Mg-hastingsite	(1b+1c)/2	1.917780	7.000433	6.810921	99.599134	96.98	0.675221	0.323045	0.182474	0.207386	0.251469	0.070992	0.019534	0.003665	0.030664	0.000000	5.985442	2.863604	1.617522	1.838356	2.229123	0.629301	0.173157	0.032490	0.271819	0.000000	1.466538	5.985442	2.014558	0.000000	0.000000	0.777185	2.863604	0.840337	0.032490	1.838356	0.161644	0.467656	0.173157	0.214565	0.271819	45.222815	0.777185	0.840337	-0.0	NaN	0.773124	0.639037	0.161644	2.0	0.640813	N/A	28.333126
1	NaN	False	Recalc Total<98.5	Pargasite	1b	0.000000	0.000000	10.836615	88.016615	89.03	0.656581	0.280865	0.164936	0.195082	0.211846	0.065829	0.015924	0.000000	0.023530	0.000000	6.380489	2.729380	1.602808	1.895758	2.058664	0.639707	0.154749	0.000000	0.228659	0.000000	1.337758	6.380489	1.619511	0.000000	0.000000	0.137068	2.729380	1.465740	0.000000	1.895758	0.104242	0.535465	0.154749	0.439153	0.228659	45.862932	0.137068	1.465740	0.0	0.0	0.650608	0.630023	0.104242	2.0	0.690215	N/A	NaN
2	NaN	False	Recalc Total>102	Mg-hastingsite	1c+1d	2.120043	13.095088	4.206872	110.592004	107.16	0.713668	0.353563	0.222559	0.216124	0.280107	0.078414	0.025054	0.007612	0.043305	0.000395	5.722690	2.835117	1.784638	1.733032	2.246096	0.628776	0.200904	0.061042	0.347252	0.003165	1.621209	5.722690	2.246096	0.031214	0.003165	1.315111	2.835117	0.469527	0.061042	1.733032	0.266968	0.361808	0.200904	0.000000	0.316038	44.684889	1.315111	0.469527	-0.0	NaN	0.857919	0.613694	0.266968	2.0	0.562712	N/A	53.674852
3	NaN	False	APE >60	Mg-hastingsite	1b	1.933630	7.604246	6.257602	100.085478	97.39	0.702350	0.336195	0.182334	0.197400	0.217730	0.073251	0.020171	0.005498	0.034419	0.000132	6.174890	2.955744	1.603040	1.735493	1.914232	0.644002	0.177338	0.048336	0.302602	0.001157	1.478658	6.174890	1.825110	0.000000	0.001157	0.837300	2.955744	0.765739	0.048336	1.735493	0.264507	0.379495	0.177338	0.089122	0.302602	45.162700	0.837300	0.765739	-0.0	NaN	0.794238	0.648362	0.264507	2.0	0.556833	N/A	60.173092
4	NaN	False	Recalc Total<98.5	Mg-hastingsite	1b	1.794195	4.540852	7.674083	92.629130	90.38	0.671893	0.307910	0.163683	0.185453	0.197330	0.067442	0.017411	0.002678	0.028536	0.000000	6.366185	2.917447	1.550901	1.757165	1.869706	0.639015	0.164966	0.025378	0.270382	0.000000	1.372031	6.366185	1.633815	0.000000	0.000000	0.538848	2.917447	1.012053	0.025378	1.757165	0.242835	0.396180	0.164966	0.235891	0.270382	45.461152	0.538848	1.012053	-0.0	NaN	0.742447	0.652914	0.242835	2.0	0.561146	N/A	36.692839

Without quality filters¶

If you want to use the pressures which yield "input errors", you can specify "Ridolfi_Filter=False"
This is more for looking at what ones it has discarded, we don't necessarily recomend this, we just have it as a feature you can use at your peril.

In [7]:

P_Ridolfi2021=pt.calculate_amp_only_press(amp_comps=Amps, equationP="P_Ridolfi2021", 
                                          Ridolfi_Filter=False)
P_Ridolfi2021.head()

Out[7]:

	P_kbar_calc	Input_Check	Fail Msg	classification	equation	H2O_calc	Fe2O3_calc	FeO_calc	Total_recalc	Sum_input	SiO2_Amp_cat_prop	MgO_Amp_cat_prop	FeOt_Amp_cat_prop	CaO_Amp_cat_prop	Al2O3_Amp_cat_prop	Na2O_Amp_cat_prop	K2O_Amp_cat_prop	MnO_Amp_cat_prop	TiO2_Amp_cat_prop	Cr2O3_Amp_cat_prop	Si_Amp_13_cat	Mg_Amp_13_cat	Fet_Amp_13_cat	Ca_Amp_13_cat	Al_Amp_13_cat	Na_Amp_13_cat	K_Amp_13_cat	Mn_Amp_13_cat	Ti_Amp_13_cat	Cr_Amp_13_cat	cation_sum_Si_Mg	Si_T	Al_IV_T	Ti_T	Cr_C	Fe3_C	Mg_C	Fe2_C	Mn_C	Ca_B	Na_B	Na_A	K_A	Al_VI_C	Ti_C	Charge	Fe3_calc	Fe2_calc	O=F,Cl	Total	Mgno_Fe2	Mgno_FeT	Na_calc	B_Sum	A_Sum	class	APE
0	4.572174	True		Mg-hastingsite	(1b+1c)/2	1.917780	7.000433	6.810921	99.599134	96.98	0.675221	0.323045	0.182474	0.207386	0.251469	0.070992	0.019534	0.003665	0.030664	0.000000	5.985442	2.863604	1.617522	1.838356	2.229123	0.629301	0.173157	0.032490	0.271819	0.000000	1.466538	5.985442	2.014558	0.000000	0.000000	0.777185	2.863604	0.840337	0.032490	1.838356	0.161644	0.467656	0.173157	0.214565	0.271819	45.222815	0.777185	0.840337	-0.0	NaN	0.773124	0.639037	0.161644	2.0	0.640813	N/A	28.333126
1	NaN	False	Recalc Total<98.5	Pargasite	1b	0.000000	0.000000	10.836615	88.016615	89.03	0.656581	0.280865	0.164936	0.195082	0.211846	0.065829	0.015924	0.000000	0.023530	0.000000	6.380489	2.729380	1.602808	1.895758	2.058664	0.639707	0.154749	0.000000	0.228659	0.000000	1.337758	6.380489	1.619511	0.000000	0.000000	0.137068	2.729380	1.465740	0.000000	1.895758	0.104242	0.535465	0.154749	0.439153	0.228659	45.862932	0.137068	1.465740	0.0	0.0	0.650608	0.630023	0.104242	2.0	0.690215	N/A	NaN
2	6.203253	False	Recalc Total>102	Mg-hastingsite	1c+1d	2.120043	13.095088	4.206872	110.592004	107.16	0.713668	0.353563	0.222559	0.216124	0.280107	0.078414	0.025054	0.007612	0.043305	0.000395	5.722690	2.835117	1.784638	1.733032	2.246096	0.628776	0.200904	0.061042	0.347252	0.003165	1.621209	5.722690	2.246096	0.031214	0.003165	1.315111	2.835117	0.469527	0.061042	1.733032	0.266968	0.361808	0.200904	0.000000	0.316038	44.684889	1.315111	0.469527	-0.0	NaN	0.857919	0.613694	0.266968	2.0	0.562712	N/A	53.674852
3	3.228704	False	APE >60	Mg-hastingsite	1b	1.933630	7.604246	6.257602	100.085478	97.39	0.702350	0.336195	0.182334	0.197400	0.217730	0.073251	0.020171	0.005498	0.034419	0.000132	6.174890	2.955744	1.603040	1.735493	1.914232	0.644002	0.177338	0.048336	0.302602	0.001157	1.478658	6.174890	1.825110	0.000000	0.001157	0.837300	2.955744	0.765739	0.048336	1.735493	0.264507	0.379495	0.177338	0.089122	0.302602	45.162700	0.837300	0.765739	-0.0	NaN	0.794238	0.648362	0.264507	2.0	0.556833	N/A	60.173092
4	2.761702	False	Recalc Total<98.5	Mg-hastingsite	1b	1.794195	4.540852	7.674083	92.629130	90.38	0.671893	0.307910	0.163683	0.185453	0.197330	0.067442	0.017411	0.002678	0.028536	0.000000	6.366185	2.917447	1.550901	1.757165	1.869706	0.639015	0.164966	0.025378	0.270382	0.000000	1.372031	6.366185	1.633815	0.000000	0.000000	0.538848	2.917447	1.012053	0.025378	1.757165	0.242835	0.396180	0.164966	0.235891	0.270382	45.461152	0.538848	1.012053	-0.0	NaN	0.742447	0.652914	0.242835	2.0	0.561146	N/A	36.692839

Mutch et al. (2016)¶

In [8]:

P_Mutch2016=pt.calculate_amp_only_press(amp_comps=Amps, equationP="P_Mutch2016")
P_Mutch2016.head()

Out[8]:

	P_kbar_calc	Si_T	Al_T	Al_C	Ti_C	Mg_C	Fe3_C	Fe2_C	Mn_C	Cr_C	Fe2_B	Mn_B	Na_B	Ca_B	Na_A	K_A	Al_tot
0	6.252577	6.025054	1.974946	0.268940	0.273685	2.882541	0.477503	1.097331	0.000000e+00	0.00000	0.053392	0.032705	0.063319	1.850584	0.570150	0.174302	2.243886
1	5.416489	6.393160	1.606840	0.455922	0.229169	2.734787	0.045632	1.534490	0.000000e+00	0.00000	0.025869	0.000000	0.074545	1.899586	0.566437	0.155056	2.062763
2	6.380755	5.784745	2.215255	0.055209	0.351103	2.865846	0.830090	0.894551	0.000000e+00	0.00320	0.079348	0.061703	0.107065	1.751884	0.528533	0.203081	2.270464
3	4.867111	6.242718	1.757282	0.177987	0.306001	2.988196	0.340790	1.185856	-8.881784e-16	0.00117	0.094001	0.048866	0.102516	1.754616	0.548564	0.179285	1.935268
4	4.662231	6.420595	1.579405	0.306290	0.272760	2.942367	0.149918	1.328664	0.000000e+00	0.00000	0.085573	0.025595	0.116590	1.772242	0.527891	0.166375	1.885695

Example 2 - Amphibole-only temperatures¶

Unlike pressures, some thermometers are sensitive to P
here, we calculate tempeatures for P=5 kbar

In [9]:

P_Put2016_5kbar=pt.calculate_amp_only_temp(amp_comps=Amps, equationT="T_Put2016_eq6", P=5)
P_Put2016_5kbar.head()

Out[9]:

0    1222.719936
1    1182.392756
2    1243.702036
3    1205.288448
4    1186.384118
dtype: float64

Example 3 - Iterating P and T¶

We can also iterate pressure and temperature - most barometers are actually T-insensitive, so it isn't actually iterating, but instead calculates the pressure first, then uses this to calculate the temperature (which does depend on P).

In [10]:

PT_Mutch=pt.calculate_amp_only_press_temp(amp_comps=Amps, equationT="T_Put2016_eq6", 
                                          equationP="P_Mutch2016")
PT_Mutch.head()

Out[10]:

	P_kbar_calc	T_K_calc	SiO2_Amp	TiO2_Amp	Al2O3_Amp	FeOt_Amp	MnO_Amp	MgO_Amp	CaO_Amp	Na2O_Amp	K2O_Amp	Cr2O3_Amp	Sample_ID_Amp
0	6.252577	1225.530720	40.57	2.45	12.82	13.11	0.26	13.02	11.63	2.20	0.92	0.00	probe1
1	5.416489	1183.327357	39.45	1.88	10.80	11.85	0.00	11.32	10.94	2.04	0.75	0.00	probe2
2	6.380755	1246.800450	42.88	3.46	14.28	15.99	0.54	14.25	12.12	2.43	1.18	0.03	probe3
3	4.867111	1204.990244	42.20	2.75	11.10	13.10	0.39	13.55	11.07	2.27	0.95	0.01	probe4
4	4.662231	1185.626165	40.37	2.28	10.06	11.76	0.19	12.41	10.40	2.09	0.82	0.00	probe5

In [11]:

PT_Ridolfi=pt.calculate_amp_only_press_temp(amp_comps=Amps, equationT="T_Ridolfi2012", 
                                            equationP="P_Ridolfi2021")
PT_Ridolfi.head()

Out[11]:

	P_kbar_calc	T_K_calc	Input_Check	Fail Msg	classification	equation	SiO2_Amp	TiO2_Amp	Al2O3_Amp	FeOt_Amp	MnO_Amp	MgO_Amp	CaO_Amp	Na2O_Amp	K2O_Amp	Cr2O3_Amp	Sample_ID_Amp
0	4.572174	1214.531361	True		Mg-hastingsite	(1b+1c)/2	40.57	2.45	12.82	13.11	0.26	13.02	11.63	2.20	0.92	0.00	probe1
1	NaN	NaN	False	Recalc Total<98.5	Pargasite	1b	39.45	1.88	10.80	11.85	0.00	11.32	10.94	2.04	0.75	0.00	probe2
2	NaN	NaN	False	Recalc Total>102	Mg-hastingsite	1c+1d	42.88	3.46	14.28	15.99	0.54	14.25	12.12	2.43	1.18	0.03	probe3
3	NaN	NaN	False	APE >60	Mg-hastingsite	1b	42.20	2.75	11.10	13.10	0.39	13.55	11.07	2.27	0.95	0.01	probe4
4	NaN	NaN	False	Recalc Total<98.5	Mg-hastingsite	1b	40.37	2.28	10.06	11.76	0.19	12.41	10.40	2.09	0.82	0.00	probe5

In [12]:

PT_Ridolfi=pt.calculate_amp_only_press_temp(amp_comps=Amps, equationT="T_Ridolfi2012", 
                                            equationP="P_Ridolfi2021", Ridolfi_Filter=False)
PT_Ridolfi.head()

Out[12]:

	P_kbar_calc	T_K_calc	Input_Check	Fail Msg	classification	equation	SiO2_Amp	TiO2_Amp	Al2O3_Amp	FeOt_Amp	MnO_Amp	MgO_Amp	CaO_Amp	Na2O_Amp	K2O_Amp	Cr2O3_Amp	Sample_ID_Amp
0	4.572174	1214.531361	True		Mg-hastingsite	(1b+1c)/2	40.57	2.45	12.82	13.11	0.26	13.02	11.63	2.20	0.92	0.00	probe1
1	NaN	NaN	False	Recalc Total<98.5	Pargasite	1b	39.45	1.88	10.80	11.85	0.00	11.32	10.94	2.04	0.75	0.00	probe2
2	6.203253	1289.245454	False	Recalc Total>102	Mg-hastingsite	1c+1d	42.88	3.46	14.28	15.99	0.54	14.25	12.12	2.43	1.18	0.03	probe3
3	3.228704	1212.306099	False	APE >60	Mg-hastingsite	1b	42.20	2.75	11.10	13.10	0.39	13.55	11.07	2.27	0.95	0.01	probe4
4	2.761702	1165.913034	False	Recalc Total<98.5	Mg-hastingsite	1b	40.37	2.28	10.06	11.76	0.19	12.41	10.40	2.09	0.82	0.00	probe5

Example 4 - Amphibole-liquid thermometry¶

as for Amp-only, except also specify liquid composition
help function details your options

In [13]:

help(pt.calculate_amp_liq_temp)

Help on function calculate_amp_liq_temp in module Thermobar.amphibole:

calculate_amp_liq_temp(*, amp_comps=None, liq_comps=None, meltmatch=None, equationT=None, P=None, H2O_Liq=None, eq_tests=False)
     Amphibole-liquid thermometers. Returns temperature in Kelvin.
    
    Parameters
     -------
    
     amp_comps: pandas DataFrame
         amphibole compositions (SiO2_Amp, TiO2_Amp etc.)
    
     liq_comps: pandas DataFrame
         liquid compositions (SiO2_Liq, TiO2_Liq etc.)
    
     equationT: str
         T_Put2016_eq4a_amp_sat (P-independent, H2O-dep through hydrous fractions)
         T_Put2016_eq4b (P-independent, H2O-dep)
         T_Put2016_eq9 (P-independent, H2O-dep through hydrous fractions)
    
     P: float, int, pandas.Series, str  ("Solve")
         Pressure in kbar
         Only needed for P-sensitive thermometers.
         If enter P="Solve", returns a partial function
         Else, enter an integer, float, or panda series
    
     eq_tests: bool. Default False
         If True, also calcualtes Kd Fe-Mg, which Putirka (2016) suggest
         as an equilibrium test.
    
    
     Returns
     -------
     pandas.core.series.Series
         Temperature in Kelvin

Using T_Put2016_eq4a_amp_sat.¶

Note, this calculates the temperature at which a liquid is saturated in amphibole, not the temperature of the liquid

In [14]:

eq4a_T=pt.calculate_amp_liq_temp(liq_comps=Liqs, amp_comps=Amps, equationT="T_Put2016_eq4a_amp_sat")
eq4a_T.head()

Out[14]:

0    1228.795223
1    1226.300156
2    1221.844038
3    1233.595436
4    1233.106477
dtype: float64

eq_tests=True¶

As for other functions, you can also specify eq_tests=True, to get the Kd Fe-Mg value Putirka suggest may be a useful equilibrium test (+0.28+-0.11)

In [15]:

eq4a_T_EqTest=pt.calculate_amp_liq_temp(liq_comps=Liqs, amp_comps=Amps, equationT="T_Put2016_eq4a_amp_sat", 
                                        eq_tests=True)
eq4a_T_EqTest.head()

Out[15]:

	T_K_calc	Kd-Fe-Mg	Eq Putirka 2016?
0	1228.795223	0.269594	Y
1	1226.300156	0.269763	Y
2	1221.844038	0.269914	Y
3	1233.595436	0.269310	Y
4	1233.106477	0.269070	Y

Overwriting H2O_Liq.¶

These equations are a little sensitive to melt H2O, because they are parameterized in terms of hydrous fractions, and some contain a separate T term too. You can overwrite the H2O_Liq value in the entered spreadsheet

In [16]:

eq4a_T_1H2O=pt.calculate_amp_liq_temp(liq_comps=Liqs, amp_comps=Amps, equationT="T_Put2016_eq4a_amp_sat", H2O_Liq=1)
eq4a_T_1H2O.head()

Out[16]:

0    1229.395340
1    1229.204834
2    1228.025620
3    1231.299927
4    1229.196688
dtype: float64

Example 5 - Amphibole-Liquid barometry¶

In [17]:

eq7a_T_1H2O=pt.calculate_amp_liq_press(liq_comps=Liqs, amp_comps=Amps, equationP="P_Put2016_eq7a", H2O_Liq=1)
eq7a_T_1H2O.head()

Out[17]:

0    4.328014
1    2.960536
2    5.182170
3    3.167717
4    2.728212
dtype: float64

Example 6 - Iterating equations for Pressure and temperature for amphibole liquid¶

The function prints to tell you actually you selected 2 functions independent of P and T, so only 1 iterative step is being done.

In [18]:

eq7a_eq4b=pt.calculate_amp_liq_press_temp(liq_comps=Liqs, amp_comps=Amps, equationP="P_Put2016_eq7a", 
                                          equationT="T_Put2016_eq4b")
eq7a_eq4b.head()

Youve selected a P-independent function
Youve selected a T-independent function

Out[18]:

	P_kbar_calc	T_K_calc
0	6.168027	1202.507284
1	4.801223	1189.376371
2	7.023825	1185.097051
3	5.006890	1216.975219
4	4.566914	1219.944334

Both are actually pretty sensitive to water.¶

In [19]:

eq7a_eq4b_1H2O=pt.calculate_amp_liq_press_temp(liq_comps=Liqs, amp_comps=Amps, equationP="P_Put2016_eq7a", 
                                               equationT="T_Put2016_eq4b", H2O_Liq=1)
eq7a_eq4b_1H2O.head()

Youve selected a P-independent function
Youve selected a T-independent function

Out[19]:

	P_kbar_calc	T_K_calc
0	4.328014	1192.934086
1	2.960536	1180.068037
2	5.182170	1175.871630
3	3.167717	1207.106379
4	2.728212	1210.015416

can also specify eq_tests=True, and it calculates Kd Fe-Mg, and then classifies within this is within the suggested range of Putirka (2008)¶

In [20]:

eq7a_eq4b_1H2O_EqTests=pt.calculate_amp_liq_press_temp(liq_comps=Liqs, amp_comps=Amps, equationP="P_Put2016_eq7a", 
                                                       equationT="T_Put2016_eq4b", H2O_Liq=1, eq_tests=True)
eq7a_eq4b_1H2O_EqTests.head()

Youve selected a P-independent function
Youve selected a T-independent function

Out[20]:

	P_kbar_calc	T_K_calc	Kd-Fe-Mg	Eq Putirka 2016?
0	4.328014	1192.934086	0.269594	Y
1	2.960536	1180.068037	0.269763	Y
2	5.182170	1175.871630	0.269914	Y
3	3.167717	1207.106379	0.269310	Y
4	2.728212	1210.015416	0.269070	Y

Example 8 - Calculating melt compositions from amphibole compositions.¶

You need to specify amphibole compositions.
For some equations, e.g., equation 3 and 5 from Zhang, Putirka (2016) SiO2 content you also need to specify temperature.
If you don't, it returns a warning telling you that you won't get results for 3 equations unless you enter a T.

In [21]:

Melt_Comps=pt.calculate_amp_only_melt_comps(amp_comps=Amps)
Melt_Comps.head()

c:\users\penny\onedrive - oregon state university\postdoc\pymme\mybarometers\thermobar_outer\src\Thermobar\amphibole.py:229: UserWarning: You must enter a value for T in Kelvin to get results from equation3 and 5 from Zhang, and SiO2 from Putrka (2016)
  w.warn('You must enter a value for T in Kelvin to get results from equation3 and 5 from Zhang, and SiO2 from Putrka (2016)')

Out[21]:

	SiO2_Eq1_Zhang17	SiO2_Eq2_Zhang17	SiO2_Eq4_Zhang17	TiO2_Eq6_Zhang17	FeO_Eq7_Zhang17	MgO_Eq9_Zhang17	CaO_Eq10_Zhang17	CaO_Eq11_Zhang17	K2O_Eq12_Zhang17	K2O_Eq13_Zhang17	Al2O3_Eq14_Zhang17	H2O_Ridolfi21	deltaNNO_Ridolfi21	Si_Amp_cat_23ox	Mg_Amp_cat_23ox	Fet_Amp_cat_23ox	Ca_Amp_cat_23ox	Al_Amp_cat_23ox	Na_Amp_cat_23ox	K_Amp_cat_23ox	Mn_Amp_cat_23ox	Ti_Amp_cat_23ox	Cr_Amp_cat_23ox	cation_sum_Si_Mg	cation_sum_Si_Ca	cation_sum_All	Mgno_Amp	Si_T	Al_T	Al_C	Ti_C	Mg_C	Fe_C	Cr_C	Fe_B	Mn_B	Na_B	Ca_B	Na_A	K_A	Sum_T	Sum_C	Sum_B	Sum_A	factor_8SiAl	factor_15eK	factor_13eCNK	All ferric	8Si_Min	16CAT_Min	15eNK_Min	Min_MinFactor	Min_factor	Max_factor	Av_factor	Si_T_ideal	Al_IV_T_ideal	Al_VI_C_ideal	Ti_C_ideal	Cr_C_ideal	Fe3_C_ideal	Mg_C_ideal	Fe2_C_ideal	Mn_C_ideal	Fe2_B_ideal	Mn_B_ideal	Ca_B_ideal	Na_B_ideal	Na_A_ideal	K_A_ideal	FeO_Eq8_Zhang17
0	59.333654	60.645146	56.117080	0.685874	5.586412	2.128936	6.437242	4.935349	2.378780	2.334718	17.886312	6.221705	2.781062	6.088253	2.912777	1.645305	1.869995	2.267423	0.640114	0.176130	0.033048	0.276556	0.000000	13.223362	15.093357	15.909602	0.639036	6.088253	1.911747	0.355676	0.276556	2.912777	1.454991	0.000000	0.190314	0.033048	0.000000	1.869995	0.640114	0.176130	8.0	4.723444	2.093357	0.816245	0.957433	0.953381	0.861306	0.965468	1.314006	1.005682	0.993815	0.993815	0.993815	0.965468	0.979641	5.964303	2.035697	0.185564	0.270926	0.000000	0.936506	2.853476	0.675302	0.032375	0.00000	0.000000	1.831924	0.168076	0.459007	0.172544	5.949181
1	70.902522	70.515408	66.223315	0.273132	2.250664	0.846023	3.285068	3.603327	1.974113	2.730521	17.962779	9.282463	1.956064	6.399508	2.737503	1.607585	1.901472	2.064811	0.641619	0.155210	0.000000	0.229397	0.000000	13.038803	14.940276	15.737104	0.630022	6.399508	1.600492	0.464319	0.229397	2.737503	1.568782	0.000000	0.038803	0.000000	0.059724	1.901472	0.581894	0.155210	8.0	4.770603	2.000000	0.737104	0.945144	0.962656	0.870131	0.966233	1.250096	1.016705	1.003998	1.003998	1.000000	0.966233	0.983116	6.291461	1.708539	0.321410	0.225524	0.000000	0.776650	2.691284	0.803792	0.000000	0.00000	0.000000	1.869369	0.130631	0.500154	0.152589	2.686836
2	51.363763	52.107144	50.932554	1.245742	11.372546	3.023436	7.405270	5.178338	2.916734	2.438641	17.480366	4.148120	2.869497	5.891052	2.918512	1.837141	1.784078	2.312188	0.647279	0.206813	0.062837	0.357556	0.003258	13.382545	15.166623	16.020715	0.613693	5.891052	2.108948	0.203240	0.357556	2.918512	1.517434	0.003258	0.319708	0.062837	0.000000	1.784078	0.647279	0.206813	8.0	4.642444	2.166623	0.854092	0.975224	0.948533	0.857145	0.961596	1.357992	0.998707	0.989014	0.989014	0.989014	0.975224	0.982119	5.785715	2.214285	0.056559	0.351162	0.003200	0.822521	2.866326	0.900231	0.000000	0.08154	0.061714	1.752177	0.104570	0.531135	0.203115	9.665180
3	60.687647	62.268993	61.703644	0.690791	4.614921	1.239917	5.309611	3.706322	3.330558	2.619149	16.370036	4.303575	2.046019	6.289313	3.010500	1.632744	1.767712	1.949713	0.655939	0.180623	0.049231	0.308285	0.001178	13.240963	15.008675	15.845238	0.648361	6.289313	1.710687	0.239025	0.308285	3.010500	1.441011	0.001178	0.191732	0.049231	0.000000	1.767712	0.655939	0.180623	8.0	4.691715	2.008675	0.836562	0.970989	0.957572	0.866166	0.965722	1.271999	1.009767	0.999422	0.999422	0.999422	0.970989	0.985205	6.196264	1.803736	0.117131	0.303724	0.001161	0.680556	2.965960	0.928032	0.003435	0.00000	0.045067	1.741559	0.213373	0.432862	0.177951	4.298402
4	66.494122	68.100781	65.870371	0.454822	2.915419	0.863156	4.323992	3.348260	2.908677	2.620235	16.658488	5.642425	1.799559	6.441589	2.951988	1.569270	1.778037	1.891861	0.646588	0.166919	0.025679	0.273652	0.000000	13.154038	14.932075	15.745582	0.652913	6.441589	1.558411	0.333450	0.273652	2.951988	1.440910	0.000000	0.128359	0.025679	0.067925	1.778037	0.578663	0.166919	8.0	4.726348	2.000000	0.745582	0.959987	0.962855	0.870609	0.967011	1.241930	1.016158	1.004549	1.004549	1.000000	0.967011	0.983505	6.335338	1.664662	0.195993	0.269138	0.000000	0.758750	2.903296	0.784635	0.025255	0.00000	0.000000	1.748709	0.251291	0.384632	0.164166	3.109003

Calculations at a fixed temperature

In [22]:

Melt_Comps2=pt.calculate_amp_only_melt_comps(amp_comps=Amps, T=1300)
Melt_Comps2.head()

Out[22]:

	SiO2_Eq10_Put2016	SiO2_Eq1_Zhang17	SiO2_Eq2_Zhang17	SiO2_Eq4_Zhang17	TiO2_Eq6_Zhang17	SiO2_Eq3_Zhang17	FeO_Eq7_Zhang17	TiO2_Eq5_Zhang17	MgO_Eq9_Zhang17	CaO_Eq10_Zhang17	CaO_Eq11_Zhang17	K2O_Eq12_Zhang17	K2O_Eq13_Zhang17	Al2O3_Eq14_Zhang17	H2O_Ridolfi21	deltaNNO_Ridolfi21	Si_Amp_cat_23ox	Mg_Amp_cat_23ox	Fet_Amp_cat_23ox	Ca_Amp_cat_23ox	Al_Amp_cat_23ox	Na_Amp_cat_23ox	K_Amp_cat_23ox	Mn_Amp_cat_23ox	Ti_Amp_cat_23ox	Cr_Amp_cat_23ox	cation_sum_Si_Mg	cation_sum_Si_Ca	cation_sum_All	Mgno_Amp	Si_T	Al_T	Al_C	Ti_C	Mg_C	Fe_C	Cr_C	Fe_B	Mn_B	Na_B	Ca_B	Na_A	K_A	Sum_T	Sum_C	Sum_B	Sum_A	factor_8SiAl	factor_15eK	factor_13eCNK	All ferric	8Si_Min	16CAT_Min	15eNK_Min	Min_MinFactor	Min_factor	Max_factor	Av_factor	Si_T_ideal	Al_IV_T_ideal	Al_VI_C_ideal	Ti_C_ideal	Cr_C_ideal	Fe3_C_ideal	Mg_C_ideal	Fe2_C_ideal	Mn_C_ideal	Fe2_B_ideal	Mn_B_ideal	Ca_B_ideal	Na_B_ideal	Na_A_ideal	K_A_ideal	FeO_Eq8_Zhang17
0	49.655108	59.333654	60.645146	56.117080	0.685874	56.992424	5.586412	0.649426	2.128936	6.437242	4.935349	2.378780	2.334718	17.886312	6.221705	2.781062	6.088253	2.912777	1.645305	1.869995	2.267423	0.640114	0.176130	0.033048	0.276556	0.000000	13.223362	15.093357	15.909602	0.639036	6.088253	1.911747	0.355676	0.276556	2.912777	1.454991	0.000000	0.190314	0.033048	0.000000	1.869995	0.640114	0.176130	8.0	4.723444	2.093357	0.816245	0.957433	0.953381	0.861306	0.965468	1.314006	1.005682	0.993815	0.993815	0.993815	0.965468	0.979641	5.964303	2.035697	0.185564	0.270926	0.000000	0.936506	2.853476	0.675302	0.032375	0.00000	0.000000	1.831924	0.168076	0.459007	0.172544	5.949181
1	51.515902	70.902522	70.515408	66.223315	0.273132	66.974467	2.250664	0.246485	0.846023	3.285068	3.603327	1.974113	2.730521	17.962779	9.282463	1.956064	6.399508	2.737503	1.607585	1.901472	2.064811	0.641619	0.155210	0.000000	0.229397	0.000000	13.038803	14.940276	15.737104	0.630022	6.399508	1.600492	0.464319	0.229397	2.737503	1.568782	0.000000	0.038803	0.000000	0.059724	1.901472	0.581894	0.155210	8.0	4.770603	2.000000	0.737104	0.945144	0.962656	0.870131	0.966233	1.250096	1.016705	1.003998	1.003998	1.000000	0.966233	0.983116	6.291461	1.708539	0.321410	0.225524	0.000000	0.776650	2.691284	0.803792	0.000000	0.00000	0.000000	1.869369	0.130631	0.500154	0.152589	2.686836
2	49.243987	51.363763	52.107144	50.932554	1.245742	51.883607	11.372546	1.191996	3.023436	7.405270	5.178338	2.916734	2.438641	17.480366	4.148120	2.869497	5.891052	2.918512	1.837141	1.784078	2.312188	0.647279	0.206813	0.062837	0.357556	0.003258	13.382545	15.166623	16.020715	0.613693	5.891052	2.108948	0.203240	0.357556	2.918512	1.517434	0.003258	0.319708	0.062837	0.000000	1.784078	0.647279	0.206813	8.0	4.642444	2.166623	0.854092	0.975224	0.948533	0.857145	0.961596	1.357992	0.998707	0.989014	0.989014	0.989014	0.975224	0.982119	5.785715	2.214285	0.056559	0.351162	0.003200	0.822521	2.866326	0.900231	0.000000	0.08154	0.061714	1.752177	0.104570	0.531135	0.203115	9.665180
3	52.572962	60.687647	62.268993	61.703644	0.690791	62.475868	4.614921	0.652253	1.239917	5.309611	3.706322	3.330558	2.619149	16.370036	4.303575	2.046019	6.289313	3.010500	1.632744	1.767712	1.949713	0.655939	0.180623	0.049231	0.308285	0.001178	13.240963	15.008675	15.845238	0.648361	6.289313	1.710687	0.239025	0.308285	3.010500	1.441011	0.001178	0.191732	0.049231	0.000000	1.767712	0.655939	0.180623	8.0	4.691715	2.008675	0.836562	0.970989	0.957572	0.866166	0.965722	1.271999	1.009767	0.999422	0.999422	0.999422	0.970989	0.985205	6.196264	1.803736	0.117131	0.303724	0.001161	0.680556	2.965960	0.928032	0.003435	0.00000	0.045067	1.741559	0.213373	0.432862	0.177951	4.298402
4	53.104275	66.494122	68.100781	65.870371	0.454822	66.590674	2.915419	0.428619	0.863156	4.323992	3.348260	2.908677	2.620235	16.658488	5.642425	1.799559	6.441589	2.951988	1.569270	1.778037	1.891861	0.646588	0.166919	0.025679	0.273652	0.000000	13.154038	14.932075	15.745582	0.652913	6.441589	1.558411	0.333450	0.273652	2.951988	1.440910	0.000000	0.128359	0.025679	0.067925	1.778037	0.578663	0.166919	8.0	4.726348	2.000000	0.745582	0.959987	0.962855	0.870609	0.967011	1.241930	1.016158	1.004549	1.004549	1.000000	0.967011	0.983505	6.335338	1.664662	0.195993	0.269138	0.000000	0.758750	2.903296	0.784635	0.025255	0.00000	0.000000	1.748709	0.251291	0.384632	0.164166	3.109003

Calculations using amphibole only thermobarometers to get temperature, to then feed into this function

In [23]:

PT_Rid=pt.calculate_amp_only_press_temp(amp_comps=Amps, equationP="P_Ridolfi2021", 
                                        equationT="T_Ridolfi2012", Ridolfi_Filter=False)
Melt_Comps3=pt.calculate_amp_only_melt_comps(amp_comps=Amps, T=PT_Rid['T_K_calc'])
Melt_Comps3.head()

Out[23]:

	SiO2_Eq10_Put2016	SiO2_Eq1_Zhang17	SiO2_Eq2_Zhang17	SiO2_Eq4_Zhang17	TiO2_Eq6_Zhang17	SiO2_Eq3_Zhang17	FeO_Eq7_Zhang17	TiO2_Eq5_Zhang17	MgO_Eq9_Zhang17	CaO_Eq10_Zhang17	CaO_Eq11_Zhang17	K2O_Eq12_Zhang17	K2O_Eq13_Zhang17	Al2O3_Eq14_Zhang17	H2O_Ridolfi21	deltaNNO_Ridolfi21	Si_Amp_cat_23ox	Mg_Amp_cat_23ox	Fet_Amp_cat_23ox	Ca_Amp_cat_23ox	Al_Amp_cat_23ox	Na_Amp_cat_23ox	K_Amp_cat_23ox	Mn_Amp_cat_23ox	Ti_Amp_cat_23ox	Cr_Amp_cat_23ox	cation_sum_Si_Mg	cation_sum_Si_Ca	cation_sum_All	Mgno_Amp	Si_T	Al_T	Al_C	Ti_C	Mg_C	Fe_C	Cr_C	Fe_B	Mn_B	Na_B	Ca_B	Na_A	K_A	Sum_T	Sum_C	Sum_B	Sum_A	factor_8SiAl	factor_15eK	factor_13eCNK	All ferric	8Si_Min	16CAT_Min	15eNK_Min	Min_MinFactor	Min_factor	Max_factor	Av_factor	Si_T_ideal	Al_IV_T_ideal	Al_VI_C_ideal	Ti_C_ideal	Cr_C_ideal	Fe3_C_ideal	Mg_C_ideal	Fe2_C_ideal	Mn_C_ideal	Fe2_B_ideal	Mn_B_ideal	Ca_B_ideal	Na_B_ideal	Na_A_ideal	K_A_ideal	FeO_Eq8_Zhang17
0	59.262728	59.333654	60.645146	56.117080	0.685874	56.082183	5.586412	0.713445	2.128936	6.437242	4.935349	2.378780	2.334718	17.886312	6.221705	2.781062	6.088253	2.912777	1.645305	1.869995	2.267423	0.640114	0.176130	0.033048	0.276556	0.000000	13.223362	15.093357	15.909602	0.639036	6.088253	1.911747	0.355676	0.276556	2.912777	1.454991	0.000000	0.190314	0.033048	0.000000	1.869995	0.640114	0.176130	8.0	4.723444	2.093357	0.816245	0.957433	0.953381	0.861306	0.965468	1.314006	1.005682	0.993815	0.993815	0.993815	0.965468	0.979641	5.964303	2.035697	0.185564	0.270926	0.000000	0.936506	2.853476	0.675302	0.032375	0.00000	0.000000	1.831924	0.168076	0.459007	0.172544	5.949181
1	NaN	70.902522	70.515408	66.223315	0.273132	NaN	2.250664	NaN	0.846023	3.285068	3.603327	1.974113	2.730521	17.962779	9.282463	1.956064	6.399508	2.737503	1.607585	1.901472	2.064811	0.641619	0.155210	0.000000	0.229397	0.000000	13.038803	14.940276	15.737104	0.630022	6.399508	1.600492	0.464319	0.229397	2.737503	1.568782	0.000000	0.038803	0.000000	0.059724	1.901472	0.581894	0.155210	8.0	4.770603	2.000000	0.737104	0.945144	0.962656	0.870131	0.966233	1.250096	1.016705	1.003998	1.003998	1.000000	0.966233	0.983116	6.291461	1.708539	0.321410	0.225524	0.000000	0.776650	2.691284	0.803792	0.000000	0.00000	0.000000	1.869369	0.130631	0.500154	0.152589	2.686836
2	50.680338	51.363763	52.107144	50.932554	1.245742	51.769071	11.372546	1.206181	3.023436	7.405270	5.178338	2.916734	2.438641	17.480366	4.148120	2.869497	5.891052	2.918512	1.837141	1.784078	2.312188	0.647279	0.206813	0.062837	0.357556	0.003258	13.382545	15.166623	16.020715	0.613693	5.891052	2.108948	0.203240	0.357556	2.918512	1.517434	0.003258	0.319708	0.062837	0.000000	1.784078	0.647279	0.206813	8.0	4.642444	2.166623	0.854092	0.975224	0.948533	0.857145	0.961596	1.357992	0.998707	0.989014	0.989014	0.989014	0.975224	0.982119	5.785715	2.214285	0.056559	0.351162	0.003200	0.822521	2.866326	0.900231	0.000000	0.08154	0.061714	1.752177	0.104570	0.531135	0.203115	9.665180
3	62.370970	60.687647	62.268993	61.703644	0.690791	61.541928	4.614921	0.718307	1.239917	5.309611	3.706322	3.330558	2.619149	16.370036	4.303575	2.046019	6.289313	3.010500	1.632744	1.767712	1.949713	0.655939	0.180623	0.049231	0.308285	0.001178	13.240963	15.008675	15.845238	0.648361	6.289313	1.710687	0.239025	0.308285	3.010500	1.441011	0.001178	0.191732	0.049231	0.000000	1.767712	0.655939	0.180623	8.0	4.691715	2.008675	0.836562	0.970989	0.957572	0.866166	0.965722	1.271999	1.009767	0.999422	0.999422	0.999422	0.970989	0.985205	6.196264	1.803736	0.117131	0.303724	0.001161	0.680556	2.965960	0.928032	0.003435	0.00000	0.045067	1.741559	0.213373	0.432862	0.177951	4.298402
4	66.077116	66.494122	68.100781	65.870371	0.454822	65.162647	2.915419	0.496739	0.863156	4.323992	3.348260	2.908677	2.620235	16.658488	5.642425	1.799559	6.441589	2.951988	1.569270	1.778037	1.891861	0.646588	0.166919	0.025679	0.273652	0.000000	13.154038	14.932075	15.745582	0.652913	6.441589	1.558411	0.333450	0.273652	2.951988	1.440910	0.000000	0.128359	0.025679	0.067925	1.778037	0.578663	0.166919	8.0	4.726348	2.000000	0.745582	0.959987	0.962855	0.870609	0.967011	1.241930	1.016158	1.004549	1.004549	1.000000	0.967011	0.983505	6.335338	1.664662	0.195993	0.269138	0.000000	0.758750	2.903296	0.784635	0.025255	0.00000	0.000000	1.748709	0.251291	0.384632	0.164166	3.109003

In [24]:

PT_Rid.head()

Out[24]:

	P_kbar_calc	T_K_calc	Input_Check	Fail Msg	classification	equation	SiO2_Amp	TiO2_Amp	Al2O3_Amp	FeOt_Amp	MnO_Amp	MgO_Amp	CaO_Amp	Na2O_Amp	K2O_Amp	Cr2O3_Amp	Sample_ID_Amp
0	4.572174	1214.531361	True		Mg-hastingsite	(1b+1c)/2	40.57	2.45	12.82	13.11	0.26	13.02	11.63	2.20	0.92	0.00	probe1
1	NaN	NaN	False	Recalc Total<98.5	Pargasite	1b	39.45	1.88	10.80	11.85	0.00	11.32	10.94	2.04	0.75	0.00	probe2
2	6.203253	1289.245454	False	Recalc Total>102	Mg-hastingsite	1c+1d	42.88	3.46	14.28	15.99	0.54	14.25	12.12	2.43	1.18	0.03	probe3
3	3.228704	1212.306099	False	APE >60	Mg-hastingsite	1b	42.20	2.75	11.10	13.10	0.39	13.55	11.07	2.27	0.95	0.01	probe4
4	2.761702	1165.913034	False	Recalc Total<98.5	Mg-hastingsite	1b	40.37	2.28	10.06	11.76	0.19	12.41	10.40	2.09	0.82	0.00	probe5

Comparing calculated melts from different equations¶

In [26]:

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10,5))
ax1.plot(Melt_Comps3['SiO2_Eq1_Zhang17'], Melt_Comps3['SiO2_Eq10_Put2016'], 'ok')
ax1.set_xlabel('SiO$_2$ wt% Eq 1 Zhang17')
ax1.set_ylabel('SiO$_2$ wt% Eq 10 Putirka 2016')

ax2.plot(Melt_Comps3['SiO2_Eq1_Zhang17'], Melt_Comps3['TiO2_Eq6_Zhang17'], 'ok')
ax2.set_xlabel('SiO$_2$ wt% Eq 1 Zhang17')
ax2.set_ylabel('TiO$_2$ wt% Eq 6 Zhang17')

ax1.plot([50, 85], [50, 85], '-r')

Out[26]:

[<matplotlib.lines.Line2D at 0x292b1c59f70>]

In [ ]: