Electrochemical

In [1]:

from PASCal.app import fit
import numpy as np

from PASCal.app import fit import numpy as np

In [2]:

# Define example data from the app
data = np.loadtxt((line for line in """
#Variable electrochemical Data for NMC-811 
#Data published in Märker et al., Chem. Mater. 2019, 31, 7, 2545–2554 
#https://pubs.acs.org/doi/10.1021/acs.chemmater.9b00140 
0.00	0.01	2.8704	2.8704	14.1918	90.0	90.0	120.0
3.11	0.01	2.8704	2.8704	14.1918	90.0	90.0	120.0
6.22	0.01	2.8701	2.8701	14.1932	90.0	90.0	120.0
9.32	0.01	2.8695	2.8695	14.1958	90.0	90.0	120.0
12.43	0.01	2.8689	2.8689	14.1984	90.0	90.0	120.0
15.54	0.01	2.8683	2.8683	14.2012	90.0	90.0	120.0
18.65	0.01	2.8677	2.8677	14.2039	90.0	90.0	120.0
21.75	0.01	2.8671	2.8671	14.2066	90.0	90.0	120.0
24.86	0.01	2.8665	2.8665	14.2094	90.0	90.0	120.0
27.97	0.01	2.8658	2.8658	14.2124	90.0	90.0	120.0
31.08	0.01	2.865	2.865	14.2157	90.0	90.0	120.0
34.19	0.01	2.8641	2.8641	14.2196	90.0	90.0	120.0
37.29	0.01	2.863	2.863	14.2244	90.0	90.0	120.0
40.40	0.01	2.8616	2.8616	14.2309	90.0	90.0	120.0
43.51	0.01	2.86	2.86	14.238	90.0	90.0	120.0
46.62	0.01	2.8587	2.8587	14.2444	90.0	90.0	120.0
49.72	0.01	2.8576	2.8576	14.2499	90.0	90.0	120.0
52.83	0.01	2.8567	2.8567	14.255	90.0	90.0	120.0
55.94	0.01	2.8558	2.8558	14.2595	90.0	90.0	120.0
59.05	0.01	2.8551	2.8551	14.2638	90.0	90.0	120.0
62.15	0.01	2.8543	2.8543	14.2682	90.0	90.0	120.0
65.26	0.01	2.8536	2.8536	14.2726	90.0	90.0	120.0
68.37	0.01	2.8529	2.8529	14.277	90.0	90.0	120.0
71.48	0.01	2.8522	2.8522	14.2818	90.0	90.0	120.0
74.59	0.01	2.8514	2.8514	14.2868	90.0	90.0	120.0
77.69	0.01	2.8507	2.8507	14.2921	90.0	90.0	120.0
80.80	0.01	2.8499	2.8499	14.2977	90.0	90.0	120.0
83.91	0.01	2.8491	2.8491	14.3038	90.0	90.0	120.0
87.02	0.01	2.8482	2.8482	14.3108	90.0	90.0	120.0
90.12	0.01	2.8474	2.8474	14.3172	90.0	90.0	120.0
93.23	0.01	2.8464	2.8464	14.325	90.0	90.0	120.0
96.34	0.01	2.8454	2.8454	14.3326	90.0	90.0	120.0
99.45	0.01	2.8444	2.8444	14.3406	90.0	90.0	120.0
102.56	0.01	2.8434	2.8434	14.3487	90.0	90.0	120.0
105.66	0.01	2.8423	2.8423	14.3569	90.0	90.0	120.0
108.77	0.01	2.8412	2.8412	14.3652	90.0	90.0	120.0
111.88	0.01	2.8401	2.8401	14.3734	90.0	90.0	120.0
114.99	0.01	2.839	2.839	14.3815	90.0	90.0	120.0
118.09	0.01	2.8378	2.8378	14.3895	90.0	90.0	120.0
121.20	0.01	2.8367	2.8367	14.3971	90.0	90.0	120.0
124.31	0.01	2.8355	2.8355	14.404	90.0	90.0	120.0
127.42	0.01	2.8344	2.8344	14.4107	90.0	90.0	120.0
130.53	0.01	2.8332	2.8332	14.4171	90.0	90.0	120.0
133.63	0.01	2.8321	2.8321	14.4231	90.0	90.0	120.0
136.74	0.01	2.831	2.831	14.4286	90.0	90.0	120.0
139.85	0.01	2.8299	2.8299	14.4338	90.0	90.0	120.0
142.96	0.01	2.8289	2.8289	14.4387	90.0	90.0	120.0
146.06	0.01	2.8279	2.8279	14.4435	90.0	90.0	120.0
149.17	0.01	2.8269	2.8269	14.4483	90.0	90.0	120.0
152.28	0.01	2.8259	2.8259	14.4534	90.0	90.0	120.0
155.39	0.01	2.8248	2.8248	14.4591	90.0	90.0	120.0
158.49	0.01	2.8237	2.8237	14.4665	90.0	90.0	120.0
161.60	0.01	2.8225	2.8225	14.4734	90.0	90.0	120.0
164.71	0.01	2.8216	2.8216	14.4781	90.0	90.0	120.0
167.82	0.01	2.8211	2.8211	14.48	90.0	90.0	120.0
170.93	0.01	2.8201	2.8201	14.483	90.0	90.0	120.0
174.03	0.01	2.8201	2.8201	14.483	90.0	90.0	120.0
177.14	0.01	2.8188	2.8188	14.4834	90.0	90.0	120.0
180.25	0.01	2.8188	2.8188	14.4834	90.0	90.0	120.0
183.36	0.01	2.8176	2.8176	14.4792	90.0	90.0	120.0
186.46	0.01	2.8176	2.8176	14.4792	90.0	90.0	120.0
189.57	0.01	2.8166	2.8166	14.4716	90.0	90.0	120.0
192.68	0.01	2.8161	2.8161	14.4652	90.0	90.0	120.0
195.79	0.01	2.8157	2.8157	14.4579	90.0	90.0	120.0
198.90	0.01	2.8153	2.8153	14.4488	90.0	90.0	120.0
202.00	0.01	2.8151	2.8151	14.4363	90.0	90.0	120.0
205.11	0.01	2.815	2.815	14.4202	90.0	90.0	120.0
208.22	0.01	2.815	2.815	14.4021	90.0	90.0	120.0
211.33	0.01	2.8147	2.8147	14.3846	90.0	90.0	120.0
214.43	0.01	2.8143	2.8143	14.3647	90.0	90.0	120.0
217.54	0.01	2.8139	2.8139	14.3427	90.0	90.0	120.0
220.65	0.01	2.8134	2.8134	14.3159	90.0	90.0	120.0
223.76	0.01	2.813	2.813	14.2823	90.0	90.0	120.0
226.87	0.01	2.8127	2.8127	14.2396	90.0	90.0	120.0
229.97	0.01	2.8125	2.8125	14.191	90.0	90.0	120.0
233.08	0.01	2.8122	2.8122	14.1469	90.0	90.0	120.0
236.19	0.01	2.8119	2.8119	14.1034	90.0	90.0	120.0
239.30	0.01	2.8118	2.8118	14.0538	90.0	90.0	120.0
242.40	0.01	2.8117	2.8117	14.0078	90.0	90.0	120.0
""".splitlines()))

# Define example data from the app data = np.loadtxt((line for line in """ #Variable electrochemical Data for NMC-811 #Data published in Märker et al., Chem. Mater. 2019, 31, 7, 2545–2554 #https://pubs.acs.org/doi/10.1021/acs.chemmater.9b00140 0.00 0.01 2.8704 2.8704 14.1918 90.0 90.0 120.0 3.11 0.01 2.8704 2.8704 14.1918 90.0 90.0 120.0 6.22 0.01 2.8701 2.8701 14.1932 90.0 90.0 120.0 9.32 0.01 2.8695 2.8695 14.1958 90.0 90.0 120.0 12.43 0.01 2.8689 2.8689 14.1984 90.0 90.0 120.0 15.54 0.01 2.8683 2.8683 14.2012 90.0 90.0 120.0 18.65 0.01 2.8677 2.8677 14.2039 90.0 90.0 120.0 21.75 0.01 2.8671 2.8671 14.2066 90.0 90.0 120.0 24.86 0.01 2.8665 2.8665 14.2094 90.0 90.0 120.0 27.97 0.01 2.8658 2.8658 14.2124 90.0 90.0 120.0 31.08 0.01 2.865 2.865 14.2157 90.0 90.0 120.0 34.19 0.01 2.8641 2.8641 14.2196 90.0 90.0 120.0 37.29 0.01 2.863 2.863 14.2244 90.0 90.0 120.0 40.40 0.01 2.8616 2.8616 14.2309 90.0 90.0 120.0 43.51 0.01 2.86 2.86 14.238 90.0 90.0 120.0 46.62 0.01 2.8587 2.8587 14.2444 90.0 90.0 120.0 49.72 0.01 2.8576 2.8576 14.2499 90.0 90.0 120.0 52.83 0.01 2.8567 2.8567 14.255 90.0 90.0 120.0 55.94 0.01 2.8558 2.8558 14.2595 90.0 90.0 120.0 59.05 0.01 2.8551 2.8551 14.2638 90.0 90.0 120.0 62.15 0.01 2.8543 2.8543 14.2682 90.0 90.0 120.0 65.26 0.01 2.8536 2.8536 14.2726 90.0 90.0 120.0 68.37 0.01 2.8529 2.8529 14.277 90.0 90.0 120.0 71.48 0.01 2.8522 2.8522 14.2818 90.0 90.0 120.0 74.59 0.01 2.8514 2.8514 14.2868 90.0 90.0 120.0 77.69 0.01 2.8507 2.8507 14.2921 90.0 90.0 120.0 80.80 0.01 2.8499 2.8499 14.2977 90.0 90.0 120.0 83.91 0.01 2.8491 2.8491 14.3038 90.0 90.0 120.0 87.02 0.01 2.8482 2.8482 14.3108 90.0 90.0 120.0 90.12 0.01 2.8474 2.8474 14.3172 90.0 90.0 120.0 93.23 0.01 2.8464 2.8464 14.325 90.0 90.0 120.0 96.34 0.01 2.8454 2.8454 14.3326 90.0 90.0 120.0 99.45 0.01 2.8444 2.8444 14.3406 90.0 90.0 120.0 102.56 0.01 2.8434 2.8434 14.3487 90.0 90.0 120.0 105.66 0.01 2.8423 2.8423 14.3569 90.0 90.0 120.0 108.77 0.01 2.8412 2.8412 14.3652 90.0 90.0 120.0 111.88 0.01 2.8401 2.8401 14.3734 90.0 90.0 120.0 114.99 0.01 2.839 2.839 14.3815 90.0 90.0 120.0 118.09 0.01 2.8378 2.8378 14.3895 90.0 90.0 120.0 121.20 0.01 2.8367 2.8367 14.3971 90.0 90.0 120.0 124.31 0.01 2.8355 2.8355 14.404 90.0 90.0 120.0 127.42 0.01 2.8344 2.8344 14.4107 90.0 90.0 120.0 130.53 0.01 2.8332 2.8332 14.4171 90.0 90.0 120.0 133.63 0.01 2.8321 2.8321 14.4231 90.0 90.0 120.0 136.74 0.01 2.831 2.831 14.4286 90.0 90.0 120.0 139.85 0.01 2.8299 2.8299 14.4338 90.0 90.0 120.0 142.96 0.01 2.8289 2.8289 14.4387 90.0 90.0 120.0 146.06 0.01 2.8279 2.8279 14.4435 90.0 90.0 120.0 149.17 0.01 2.8269 2.8269 14.4483 90.0 90.0 120.0 152.28 0.01 2.8259 2.8259 14.4534 90.0 90.0 120.0 155.39 0.01 2.8248 2.8248 14.4591 90.0 90.0 120.0 158.49 0.01 2.8237 2.8237 14.4665 90.0 90.0 120.0 161.60 0.01 2.8225 2.8225 14.4734 90.0 90.0 120.0 164.71 0.01 2.8216 2.8216 14.4781 90.0 90.0 120.0 167.82 0.01 2.8211 2.8211 14.48 90.0 90.0 120.0 170.93 0.01 2.8201 2.8201 14.483 90.0 90.0 120.0 174.03 0.01 2.8201 2.8201 14.483 90.0 90.0 120.0 177.14 0.01 2.8188 2.8188 14.4834 90.0 90.0 120.0 180.25 0.01 2.8188 2.8188 14.4834 90.0 90.0 120.0 183.36 0.01 2.8176 2.8176 14.4792 90.0 90.0 120.0 186.46 0.01 2.8176 2.8176 14.4792 90.0 90.0 120.0 189.57 0.01 2.8166 2.8166 14.4716 90.0 90.0 120.0 192.68 0.01 2.8161 2.8161 14.4652 90.0 90.0 120.0 195.79 0.01 2.8157 2.8157 14.4579 90.0 90.0 120.0 198.90 0.01 2.8153 2.8153 14.4488 90.0 90.0 120.0 202.00 0.01 2.8151 2.8151 14.4363 90.0 90.0 120.0 205.11 0.01 2.815 2.815 14.4202 90.0 90.0 120.0 208.22 0.01 2.815 2.815 14.4021 90.0 90.0 120.0 211.33 0.01 2.8147 2.8147 14.3846 90.0 90.0 120.0 214.43 0.01 2.8143 2.8143 14.3647 90.0 90.0 120.0 217.54 0.01 2.8139 2.8139 14.3427 90.0 90.0 120.0 220.65 0.01 2.8134 2.8134 14.3159 90.0 90.0 120.0 223.76 0.01 2.813 2.813 14.2823 90.0 90.0 120.0 226.87 0.01 2.8127 2.8127 14.2396 90.0 90.0 120.0 229.97 0.01 2.8125 2.8125 14.191 90.0 90.0 120.0 233.08 0.01 2.8122 2.8122 14.1469 90.0 90.0 120.0 236.19 0.01 2.8119 2.8119 14.1034 90.0 90.0 120.0 239.30 0.01 2.8118 2.8118 14.0538 90.0 90.0 120.0 242.40 0.01 2.8117 2.8117 14.0078 90.0 90.0 120.0 """.splitlines()))

In [3]:

x = data[:, 0]
x_error = data[:, 1]
unit_cells = data[:, 2:]

x = data[:, 0] x_error = data[:, 1] unit_cells = data[:, 2:]

In [4]:

fit_results = fit(x, x_error, unit_cells, {"data_type": "electrochemical"})

fit_results = fit(x, x_error, unit_cells, {"data_type": "electrochemical"})

Performing fit with options=Options(data_type=<PASCalDataType.ELECTROCHEMICAL: 'Electrochemical'>, eulerian_strain=True, finite_strain=True, use_pc=False, pc_val=None, deg_poly_strain=5, deg_poly_vol=5)

In [5]:

fit_results.plot_strain()

fit_results.plot_strain()

In [6]:

fit_results.plot_charge_derivative()

fit_results.plot_charge_derivative()

In [7]:

fit_results.plot_volume()

fit_results.plot_volume()

In [8]:

fit_results.plot_residual()

fit_results.plot_residual()

In [9]:

fit_results.plot_indicatrix(plot_size=600)

fit_results.plot_indicatrix(plot_size=600)

In [10]:

import pprint
pprint.pprint(fit_results.named_coefficients)

import pprint pprint.pprint(fit_results.named_coefficients)

{'Deriv': array([[ -106.30860481,  -102.01597303,   -98.36861968,   -95.3338365 ,
          -92.85160516,   -90.89313964,   -89.41994057,   -88.3971522 ,
          -87.78182238,   -87.54252286,   -87.64485082,   -88.05542837,
          -88.73928684,   -89.66959249,   -90.81425967,   -92.14400703,
          -93.62557625,   -95.24136569,   -96.96062371,   -98.75816555,
         -100.60381567,  -102.48640694,  -104.37794689,  -106.25734729,
         -108.10454485,  -109.8948281 ,  -111.62178048,  -113.26254297,
         -114.80114884,  -116.21828834,  -117.50922312,  -118.65629068,
         -119.64762085,  -120.47236842,  -121.11892077,  -121.58267582,
         -121.85348573,  -121.92460184,  -121.79106675,  -121.44733115,
         -120.88981568,  -120.11586823,  -119.12386163,  -117.91743677,
         -116.48923023,  -114.84422656,  -112.98489514,  -110.92172013,
         -108.64589629,  -106.16928318,  -103.49844673,  -100.65045603,
          -97.61552808,   -94.41219175,   -91.05110952,   -87.54396884,
          -83.91538719,   -80.1556533 ,   -76.29102397,   -72.33728319,
          -68.32428254,   -64.24391619,   -60.12787788,   -55.99604815,
          -51.86933252,   -47.78277612,   -43.7329064 ,   -39.75693831,
          -35.87987391,   -32.13957617,   -28.53889203,   -25.1181756 ,
          -21.90652548,   -18.93406523,   -16.24016461,   -13.83952931,
          -11.77449595,   -10.07928466,    -8.79260134],
       [    5.95096829,    19.63282312,    31.94811292,    42.97679518,
           52.89847459,    61.77946862,    69.71872424,    76.78874611,
           83.12405942,    88.78480039,    93.8503238 ,    98.39508247,
          102.47611753,   106.18424181,   109.56536358,   112.67434347,
          115.55216449,   118.26233707,   120.8354164 ,   123.30667092,
          125.6988367 ,   128.05275118,   130.38117589,   132.69978705,
          135.0193589 ,   137.33826997,   139.67245649,   142.01053495,
          144.34368737,   146.65080008,   148.92819347,   151.14487848,
          153.27244494,   155.27758071,   157.11644291,   158.75790235,
          160.14774495,   161.23306635,   161.95438169,   162.25381207,
          162.06082151,   161.30291347,   159.90268939,   157.78593398,
          154.85202959,   151.01450564,   146.17637137,   140.25671522,
          133.11084495,   124.64434725,   114.74063916,   103.31772375,
           90.17586418,    75.21806349,    58.30814657,    39.30503627,
           18.13480467,    -5.4895996 ,   -31.65933176,   -60.53506114,
          -92.17549536,  -126.95477519,  -164.95090037,  -206.34413241,
         -251.31963482,  -299.90447564,  -352.60654298,  -409.47513263,
         -470.71500028,  -536.31659246,  -606.91712252,  -682.5318961 ,
         -763.38526112,  -849.70646745,  -941.42438107, -1039.3691363 ,
        -1143.49810218, -1254.0601208 , -1370.92093991],
       [ -106.30860481,  -102.01597303,   -98.36861968,   -95.3338365 ,
          -92.85160516,   -90.89313964,   -89.41994057,   -88.3971522 ,
          -87.78182238,   -87.54252286,   -87.64485082,   -88.05542837,
          -88.73928684,   -89.66959249,   -90.81425967,   -92.14400703,
          -93.62557625,   -95.24136569,   -96.96062371,   -98.75816555,
         -100.60381567,  -102.48640694,  -104.37794689,  -106.25734729,
         -108.10454485,  -109.8948281 ,  -111.62178048,  -113.26254297,
         -114.80114884,  -116.21828834,  -117.50922312,  -118.65629068,
         -119.64762085,  -120.47236842,  -121.11892077,  -121.58267582,
         -121.85348573,  -121.92460184,  -121.79106675,  -121.44733115,
         -120.88981568,  -120.11586823,  -119.12386163,  -117.91743677,
         -116.48923023,  -114.84422656,  -112.98489514,  -110.92172013,
         -108.64589629,  -106.16928318,  -103.49844673,  -100.65045603,
          -97.61552808,   -94.41219175,   -91.05110952,   -87.54396884,
          -83.91538719,   -80.1556533 ,   -76.29102397,   -72.33728319,
          -68.32428254,   -64.24391619,   -60.12787788,   -55.99604815,
          -51.86933252,   -47.78277612,   -43.7329064 ,   -39.75693831,
          -35.87987391,   -32.13957617,   -28.53889203,   -25.1181756 ,
          -21.90652548,   -18.93406523,   -16.24016461,   -13.83952931,
          -11.77449595,   -10.07928466,    -8.79260134]]),
 'VolCheb': array([101.3776913 , 101.31817056, 101.26480491, 101.2169916 ,
       101.1737316 , 101.13454963, 101.09886048, 101.06623056,
       101.03596447, 101.00773219, 100.98113837, 100.95583004,
       100.93157156, 100.90793271, 100.88475491, 100.86183408,
       100.83907171, 100.81617942, 100.79311674, 100.76979572,
       100.74622893, 100.72222225, 100.69782878, 100.67304392,
       100.64787879, 100.6224408 , 100.59660216, 100.57049036,
       100.54415892, 100.51775222, 100.49116214, 100.46453746,
       100.43794132, 100.41143414, 100.38515606, 100.35898627,
       100.33304978, 100.30737568, 100.28206129, 100.25694441,
       100.23209123, 100.20746673, 100.1830147 , 100.15873403,
       100.13436369, 100.10985021, 100.08503231, 100.05979973,
       100.03376419, 100.00674462,  99.9784419 ,  99.94861651,
        99.91669672,  99.88235199,  99.84511256,  99.80446092,
        99.75998017,  99.71076578,  99.65628141,  99.59579794,
        99.52875624,  99.45387888,  99.3704615 ,  99.27753065,
        99.1740466 ,  99.05929148,  98.9313498 ,  98.78932181,
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