Transcript zone-refined NaCl

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Cherenkov light in
ice and salt
• zone-refined NaCl
• lab-grown ice
S. Pole ice, 1740 m
S. Pole ice, 1690 m
S. Pole ice, 900 m
South Pole ice is better
than zone-refined NaCl.
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Natural NaCl is probably
worse than zone-refined.
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Acoustic absorption in
ocean
Pure water absorbs due to
its viscosity.
water
+ B(OH)3
+ MgSO4
water +
MgSO4
water
Frequency [Hz]
In sea water, a pressure
wave shifts chemical
equilibrium between a
molecule and ions, taking
energy from wave:
B(OH)3 = B3+ + 3 OH(relaxation freq. ≈ 1 kHz)
MgSO4 = Mg2+ + SO42(relaxation freq. ≈ 100 kHz)
Conversion of ionization energy into acoustic energy
T (ºC)
<vL> [m s-1]
 [m3 m-3 K-1]
CP [J kg-1 K-1]
Peak frequency
ocean
15º
1530
25.5x10-5
3900
7.7 kHz
ice
-51º
3920
12.5x10-5
1720
20 kHz
NaCl
30º
4560
11.6x10-5
839
42 kHz
 = Grüneisen constant = figure of merit of the medium
= <vL>2/CP
0.153
1.12
2.87
Scattering of sound off of air bubbles in ice is negligible:
scattering coefficient [m-1]
bbub [m-1] = 2.68 x 10-10 (no/200 cm-3) (db/0.02 cm)6 (f/10 kHz)4
bub =100 km
bub =103 km
Speed of a
pressure wave in
a crystalline solid
depends on angle
with respect to caxis (symmetry
axis).
This leads to
scattering at grain
boundaries.
Scattering of acoustic wave at grain boundaries
Rayleigh regime (/4πa > 1)
Stochastic regime (0.5 < /4πa < 1)
Geometric regime (/4πa < 0.5)
(a = grain radius for a polycrystalline medium)
Acoustic properties depend on elastic constants, cij
Ice (hexagonal): c11, c12, c13, c33, c44
NaCl (cubic): c11, c12, c44
Scattering in Rayleigh regime for NaCl:
 scatt
5 



a 4 (c11  c12  2c44 )  3 v L 


k
1  
2

 2  v 

375
c11

S


4
3
3
2
3
4




a
f
4
 1.65  10 
  4  m 1
1cm  10 
Scattering in stochastic regime for NaCl:
4 c11  c12  2c 44  2

k a
2
525
c11
2
 scatt
2




a
f
1
 7.21  104 
m
 4 
1cm 10 
2f
where k 
; a  mean grain radius
vL
Analogous expressions for ice (hexagonal)
1
South Pole ice
In top 600 m, grain
diameter ≈ 0.2 cm

diam
0.4 cm 0.2 cm
• at 10 kHz, acoustic
scattering length
≈ 800 km!
• at 30 kHz, acoustic
scattering length
≈ 10 km
Acoustic wave loses energy by reorienting
molecules on ice lattice: protons move from one
bond site to another by motion of L and D defects
D
L
D = doppel; L = leer
Absorptivity of ice: lab measurements of decay of free oscillations
Calculated from
Kuroiwa’s lab
meas. of internal
friction of ice
Experiments on
mechanical relaxation
of ice as fn of T and f
predict a for -51ºC:
Schiller 1958: 5.7 km
Kuroiwa 1964: 8.6 km
Oguro 1982: 11.7 km
Measurements at
Byrd by Bentley et al.
(blue circle, -28ºC;
black triangle, -21ºC)
Tests of acoustic attenuation theory for ice
SCATTERING
Scattering off grain boundaries in titanium (hexagonal structure
like ice) agrees with theory to ± 3X. There are no
measurements of scattering in pure glacial ice at low
temperature.
ABSORPTION
Estimated a from lab experiments on internal friction of ice
and from seismic reflection shooting of Bentley.
Must measure a, s, and noise as function of frequency in 3
IceCube boreholes. Maybe hear stick-slip at bedrock.
Natural NaCl
Evaporite beds have high impurity content.
(water inclusions, beds of clay, silt, anhydrite,…)
Salt domes are purer and have longer absorption lengths.
Several mines are known to have >99% NaCl and have only 2
to 40 ppm water.
Grain sizes in salt domes (smaller is better)
Avery Island, LA
~7.5 mm
Bryan Mound, TX
2 - 40 mm; av. 8 mm
Big Hill, TX
3.7 - 60 mm
West Hackberry, LA
6 - 30 mm
Moss Bluff, TX
av 11 mm
Bayou Choctaw, LA
at 0 - 728 m: 10 - 20 mm
Zuidwending (Austria)
25% have 1-3 mm; 75% 3-10 mm
Liquid inclusions in salt domes scatter acoustic waves.
Section through polycrystalline halite from salt dome. Most grains
have recrystallized, and scattering can occur at their boundaries.
Scattering is negligible at subgrain boundaries.
Grain boundaries (up to 90º)
Subgrain boundaries (<1º)
s
a
103 km
104 km
105 km
phonon-phonon
absorption
expts a(f)  f 2
(weak fn of T)
Summary of predictions for ice and NaCl
scatt
104 Hz
3x104 Hz
Ice (D=0.2 cm)
1650 km 20 km
NaCl (D=0.75 cm) 120 km 1.4 km
abs
104 Hz
8-12 km
3x104 km
3x104 Hz
8-12 km
3300 km
1. Clay, liquid inclusions, and anhydrite in salt domes dominate
scattering and absorption.
2. Scattering in salt domes is worse than in South Pole ice
because grain size is larger (geometric rather than Rayleigh).
3. In ideal salt, absorptivity would be far lower than in ice; in real
salt it will be worsened by heterogeneities.
4. Must measure scatt and abs in South Pole ice and salt domes
-induced cascade
leads to a
pressure wave:
P   vL2/Cp
<f> ≈ vL/2d
Pice/Pwater ≈ 10
<f>ice/<f>water ≈ 2
Absorption and
Scattering in
Ice and Salt
P. B. Price
(see NIM A325, 346, 1993
for my initial work on
acoustic attenuation in ice)
Equations for optical and acoustic waves
are identical.
Test predictions: a ≈ 8.8 ± 3 km
s ≈ 10 km at 30 kHz, 200 m at 100 kHz, …
Deploy powerful acoustic transmitter in one
borehole and receiver in a borehole at various
distances.
NaCl
Jefferson Island salt dome, Louisiana
Acoustic absorption -- a “relaxation” phenomenon
For acoustic waves in ice at f < 105 Hz and T
below -10ºC, protons get reoriented.
1. Relaxation time:  = 0 exp (U/kT); (U ≈ 0.58 eV)
( = characteristic transition time between two
possible configurations)
2. Logarithmic decrement:  = max 4π f  /(1 + 4π2 f 2 2)
3. Absorptivity:
 [m-1] =  f / vT