Crystals of hexagonal ice with (2 0 -2 3) Miller index faces explain exotic arcs in the Lascar halo display

Nicolas A. Lefaudeux

doi:10.1364/AO.50.00F121

Applied Optics
Vol. 50,
Issue 28,
pp. F121-F128
(2011)
•https://doi.org/10.1364/AO.50.00F121

Crystals of hexagonal ice with $(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$ Miller index faces explain exotic arcs in the Lascar halo display

Nicolas A. Lefaudeux

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Nicolas A. Lefaudeux, "Crystals of hexagonal ice with (2 0 -2 3) Miller index faces explain exotic arcs in the Lascar halo display," Appl. Opt. 50, F121-F128 (2011)

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Abstract

This article focuses on the 1997 Lascar halo display, during which very unusual arcs and halos were documented. Photographs have been analyzed with the aid of a specific image processing method developed by us. Using crystals of hexagonal ice with exotic $(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$ Miller index faces, it is possible to simulate all the features of the display with constant crystal populations and oriented crystals in plate orientation. The simulations perform better than the cubic ice explanation. The existence of $(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$ crystal faces is supported by a 1998 South Pole halo display.

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	Regular Pyramid	Exotic Pyramid	Mixed Pyramid
Crystal drawing
Miller index of pyramidal faces	$(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$	Top: $(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$ Bottom: $(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$
Face angle/C axis	$28.1 °$	$19.6 °$	$28.1 °$ and $19.6 °$

Halos from Basal Faces and $(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$ Pyramidal faces			Halos from Basal Faces and $(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$ Pyramidal Faces			Halos from $(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$ Faces on Bottom and $(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$ Faces on Top
Entry/exit faces	Interfacial angle	Halo angle	Entry/exit faces	Interfacial angle	Halo angle	Entry/exit faces	Interfacial angle	Halo angle
13-25	$52.3 °$	$18.2 °$	33-45	$56.2 °$	$20.0 °$
13-16 23-26	$56.2 °$	$20.0 °$ *	33-36 43-46	$39.2 °$	$12.9 °$ *
1-23 13-2	$61.9 °$	$22.8 °$ *	1-43 33-2	$70.4 °$	$27.7 °$ *
13-15 23-25	$80.4 °$	$35.0 °$ *	33-35 43-45	$70.7 °$	$27.8 °$ *
						33-26	$8.5 °$	$2.6 °$
						33-25	$55.0 °$	$19.4 °$

Crystal Type		Regular Pyramid		Mixed Pyramid	Exotic Pyramid
Population		I	II	III	IV	V	VI
Amount		5%	10%	25%	10%	18%	32%
Upper pyramid	type	$(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$	$(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$
Upper pyramid	height	0	0.7	0.5	0.15	0.3	0.6
Lower pyramid	type	$(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$	$(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$	$(\begin{matrix} 1 & 0 & \bar{\begin{matrix} 1 \end{matrix}} & 1 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$	$(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$
Lower pyramid	height	0.7	0.7	0.8	0.3	0.7	0.6
Habit		Hexagon	Hexagon	Intermediate	Hexagon	Triangle	Triangle
Orientation		Plate	Plate	Plate	Plate	Poor, Plate	Poor, Parry
Tilt		$3 °$	$6 °$	$3 °$	$8 °$	$30 °$	$15 °$ in rotation, $30 °$ in C-axis orientation
Drawing

Halo Family	Halo Type	Label	Main Responsible Population(s)	Entry/Exit Faces
Regular pyramidal arcs	$23 °$ plate arc, upper	23Pu	Pop I	1-23
	$23 °$ plate arc, lower	23Pl	Pop II, Pop III	13-2
	$20 °$ plate arc, upper	20Pu	Pop II	13-16
	$20 °$ plate arc, lower	20Pl	Pop I, II	23-26
	$18 °$ plate arc, side	18Ps	Pop II	13-25
	$35 °$ plate arc, upper side	35Pus	Pop II	13-15
Exotic pyramidal arcs	$28 °$ plate arc, upper	28ePu	Pop III	1-43
	$28 °$ plate arc, lower	28ePl	Pop III, IV	33-2
	$13 °$ plate arc, upper	13ePu	Pop III, IV	33-36
	$13 °$ plate arc, lower	13ePl	Pop IV	43-46
	$20 °$ plate arc, side	20ePs	Pop IV	33-45
	$28 °$ plate arc, upper side	28ePus	Pop III, Pop IV	33-35
	$28 °$ halo	28eH	Pop V, VI	33-35, 1-43
	$20 °$ halo	20eH	Pop V, VI	33-45
Mixed pyramidal arcs	$19 °$ plate arc, lower side	19mPls	Pop III	33-25
Mixed pyramidal arcs	$3 °$ plate arc, lower	3mPl	Pop III	33-26

Halos from Prism Faces on Bottom and $(\begin{matrix} 2 & 0 & \bar{\begin{matrix} 2 \end{matrix}} & 3 \end{matrix})$ Faces on Top
Entry/Exit Faces	Interfacial Angle	Halo Angle
33-6	$19.6 °$	$6.2 °$
33-5	$61.9 °$	$22.8 °$

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Applied Optics