Tutorial

The microstructural analysis is a powerful, but underused tool of petrostructural analysis. Except acquirement of common statistical parameters, this technique can significantly improve understanding of processes of grain nucleation and grain growth, can bring insights on the role of surface energies or quantify duration of metamorphic and magmatic cooling events as long as appropriate thermodynamical data for studied mineral exist. This technique also allows systematic evaluation of degree of preferred orientations of grain boundaries in conjunction with their frequencies. This may help to better understand the mobility of grain boundaries and precipitations or removal of different mineral phases.

We introduce a new platform, object-oriented Python package PolyLX providing several core routines for data exchange, visualization and analysis of microstructural data, which can be run on any platform supported by Scientific Python environment.

Grains objects

To start working with PolyLX we need to import the polylx package. For our convinience, we can import PolyLX into actual namespace:

from polylx import *

To read example data, we can use example method. Note that we create new Grains object, which store all imported Grain features.

g = Grains.example()

To visualize grain objects from shape file, we can use plot method of Grains object:

g.show()

or we can just select Grains by its class name:

g['qtz'].show()

The dot notation is used to access individual properties commonly returning values for individual Grain as numpy array.

g['qtz'].ar

array([1.46370088, 3.55371458, 1.43641139, 1.26293055, 2.10676277,
       1.45200805, 1.98973326, 1.97308557, 2.13420187, 1.76682269,
       1.70083897, 1.38205897, 1.88811465, 1.59948827, 2.50452919,
       1.60296389, 1.4918233 , 2.15318719, 1.27665794, 1.38714959,
       1.67235338, 2.33179583, 1.30609967, 2.73148246, 1.02760669,
       1.33627299, 2.65451284, 1.29069569, 1.73051094, 1.25763409,
       1.90027316, 2.56110638, 1.78555385, 2.40926108, 2.26741705,
       1.71957235, 1.79168709, 1.04770164, 1.293186  , 1.29420065,
       1.48331817, 2.15510614, 2.21246419, 1.57101091, 2.01989715,
       1.1428675 , 2.02888455, 4.07405108, 1.47968881, 1.24770095,
       1.4750185 , 1.37946472, 1.49048108, 1.56668345, 1.43717521,
       1.59756777, 1.58948843, 2.12557437, 2.54316052, 1.98917177,
       1.29809155, 1.70022052, 1.40121941, 1.24674038, 1.50255058,
       1.42880415, 1.73447054, 2.3548111 , 1.52891827, 3.26773221,
       1.33011244, 2.26173396, 3.2151532 , 2.15638456, 1.61602624,
       1.13898611, 2.91625233, 1.94275485, 2.68487563, 1.12446842,
       1.48814907, 1.79425743, 1.19512385, 1.28301942, 1.39853133,
       1.59860483, 3.80709622, 1.75016693, 1.59940152, 1.43972155,
       1.09439109, 2.00023212, 1.87470191, 1.04157011, 1.48561371,
       1.14172901, 1.48211332, 1.52569202, 1.59357336, 1.58054224,
       1.86890813, 1.84729576, 1.45085424, 1.4400654 , 2.6284034 ,
       1.62077026, 1.35218688, 1.69040095, 1.2829313 , 2.7380623 ,
       1.55901231, 1.72569674, 1.18396915, 1.67864861, 2.40971617,
       2.08496427, 2.12907657, 1.20981316, 1.46045276, 1.55428179,
       4.73482949, 2.32570855, 1.95106722, 1.81174297, 4.08295286,
       2.04530043, 1.56215221, 1.42587721, 1.70016792, 1.78887212,
       2.17273986, 2.47995119, 4.59660941, 3.43961286, 3.04193405,
       2.91162332, 2.98790473, 2.55352686, 1.33076709, 7.09385883,
       1.91715238, 1.47161362, 2.39020581, 1.51938795, 1.87839843,
       1.9946499 , 2.27873759, 4.50321651, 5.78162231, 6.9806063 ,
       1.3177092 , 2.33701528, 1.86371784, 1.26166336, 1.28322623])

or we can collect any properties to pandas.DataFrame using df method:

g.df('la', 'sa', 'lao', 'sao', 'area', 'length', 'ead', 'ar').head(10)

	la	sa	lao	sao	area	length	ead	ar
fid
0	0.066027	0.045110	70.596636	160.596636	0.002286	0.186196	0.053956	1.463701
1	0.099033	0.057029	70.983857	160.983857	0.004409	0.258753	0.074922	1.736522
2	0.074248	0.020893	61.438248	151.438248	0.001123	0.175821	0.037813	3.553715
3	0.045232	0.031489	85.088587	175.088587	0.001005	0.134427	0.035779	1.436411
4	0.136445	0.108038	170.839835	80.839835	0.011489	0.398558	0.120948	1.262931
5	0.073578	0.044938	123.223347	33.223347	0.002471	0.201258	0.056090	1.637319
6	0.103567	0.065119	149.397514	59.397514	0.005213	0.283110	0.081474	1.590441
7	0.103189	0.077988	23.758847	113.758847	0.005951	0.318774	0.087048	1.323142
8	0.187049	0.036611	82.108720	172.108720	0.004407	0.404066	0.074904	5.109041
9	0.270513	0.128402	76.193288	166.193288	0.024576	0.729051	0.176894	2.106763

g.df('ead').describe()

	ead
count	701.000000
mean	0.072812
std	0.056812
min	0.000350
25%	0.037140
50%	0.058338
75%	0.093503
max	0.638144

To visualize orientations of objects, we can use rose method:

g.rose()

or for just single class:

g['ksp'].rose()

To aggregate and summarize multiple properties by different functions according to defined classification (name by default) we can use agg method. Note that cirstat provides functions to calculate various circular statistics.

g.agg(
    N=['name', 'count'],
    area=['area', 'sum'],
    mean_ead=['ead', 'mean'],
    mean_or=['lao', circstat.mean],
    spo=['vec', circstat.ot_ar]
)

	N	area	mean_ead	mean_or	spo
class
ksp	254	2.443733	0.089710	76.875488	2.125597
pl	292	1.083516	0.060629	94.197847	1.815966
qtz	155	1.166097	0.068071	74.320337	6.113376

The groups method return Pandas GroupBy object which allows any pandas-style manipulation

g.groups('ead', 'area', 'la', 'sa').describe().T

	class	ksp	pl	qtz
ead	count	2.540000e+02	292.000000	1.550000e+02
	mean	8.970974e-02	0.060629	6.807125e-02
	std	6.495077e-02	0.032438	7.054971e-02
	min	6.641998e-04	0.001850	3.501464e-04
	25%	4.133005e-02	0.038226	2.970151e-02
	50%	7.403298e-02	0.053984	4.794577e-02
	75%	1.191733e-01	0.077308	7.892656e-02
	max	4.105520e-01	0.190210	6.381439e-01
area	count	2.540000e+02	292.000000	1.550000e+02
	mean	9.620995e-03	0.003711	7.523208e-03
	std	1.548182e-02	0.004170	2.778736e-02
	min	3.464873e-07	0.000003	9.629176e-08
	25%	1.341681e-03	0.001148	6.930225e-04
	50%	4.304819e-03	0.002289	1.805471e-03
	75%	1.115444e-02	0.004694	4.892680e-03
	max	1.323812e-01	0.028416	3.198359e-01
la	count	2.540000e+02	292.000000	1.550000e+02
	mean	1.295772e-01	0.086681	1.019395e-01
	std	1.053259e-01	0.053220	1.366152e-01
	min	1.013949e-03	0.006461	1.017291e-03
	25%	5.439610e-02	0.050202	4.314167e-02
	50%	9.871911e-02	0.072777	7.151284e-02
	75%	1.793952e-01	0.106761	1.206513e-01
	max	8.097226e-01	0.279398	1.437277e+00
sa	count	2.540000e+02	292.000000	1.550000e+02
	mean	7.545538e-02	0.049585	5.255111e-02
	std	5.428555e-02	0.027663	4.632415e-02
	min	3.648908e-04	0.000583	1.457310e-04
	25%	3.370683e-02	0.031980	2.183093e-02
	50%	6.643814e-02	0.043545	3.640605e-02
	75%	1.021515e-01	0.063468	6.490102e-02
	max	3.252086e-01	0.166726	3.035541e-01

The method classify could be used to define new classification, based on any property and using variety of rules, e.g. 'quantile':

g.classify('ar', rule='quantile', k=6)
df = g.df('class', 'name', 'area')
df.head()

	class	name	area
fid
0	1.45-1.63	qtz	0.002286
1	1.63-1.89	pl	0.004409
2	2.36-12.16	qtz	0.001123
3	1.28-1.45	qtz	0.001005
4	1.02-1.28	qtz	0.011489

To summarize results for individual phases per class we can use pandas pivot table:

pd.pivot_table(df,index=['class'], columns=['name'], aggfunc='sum')

	area
name	ksp	pl	qtz
class
1.02-1.28	0.348379	0.158328	0.079026
1.28-1.45	0.366220	0.176028	0.106734
1.45-1.63	0.424773	0.163026	0.192027
1.63-1.89	0.325575	0.157087	0.067631
1.89-2.36	0.362103	0.226971	0.168503
2.36-12.16	0.616684	0.202075	0.552178

or we can directly plot it..

pd.pivot_table(df,index=['class'], columns=['name'], aggfunc='sum').plot(kind='bar');

g.classify('ar', rule='jenks', k=6)

g.show()

g[132].show()

Boundaries objects

The map of grain boundaries could be created from topologically correct grains using boundaries method:

b = g.boundaries()

b.show()

df = b.groups('length').sum()
df['percents']= 100 * df['length'] / df['length'].sum()
df

	length	percents
class
ksp-ksp	23.383974	21.384276
ksp-pl	38.592227	35.291983
ksp-qtz	17.920424	16.387946
pl-pl	11.302490	10.335949
pl-qtz	11.535006	10.548581
qtz-qtz	6.617133	6.051264

b.rose(weights=b.length, scaled=False)