Reflectance measurements of mid‐ and far‐infrared spectroscopy
for crystalline olivine○Takahiro Naoi1, Hiroshi Suto2
1. National Astronomical Observatory of Japan, ALMA (E‐mail: taka.naoi@nao.ac.jp)
2. National Astronomical Observatory of Japan, Subaru Telescope

Abstract
We have measured reflectance for crystalline olivine ((Mg92Fe8)2SiO4). The measurements were conducted in 2007 and 2008 with FT‐IR spectrometer (BrukerIFS120HRX) at BL43IR beam line of SPring‐8. Temperature range was 300, 250, 200, 150, 100, and 60 K and wavelength range is 2000‐100 cm‐1 (5‐100 micron).
Reflection spectra were measured for each surface by using polarized infrared beam parallel to a, b, and c axes because crystal structure of olivine was theorthorhombic which had distinct three surfaces. When the temperature decreases, we confirmed the spectral features that; shift to shorter wavelength,
increase intensity, and become sharp. Olivine crystal belongs to the space group Pnma (D162h), and there are 35 IR active optical modes (9 91u, 13 B2u, 13 B3u)
expected from symmetry analysis. We have observed 8 in the axis c (B1u), 12 in the axis b (B2u), and 11 in the axis a (B3u) features. The dielectric constants ofthe crystal have also derived by fitting the reflection spectra with dispersion formula of damped oscillators. Our measured spectra of crystalline olivine areuseful for analysis of astronomical studies of low temperature environment.
Introduction
Crystalline silicate materials such as olivine and pyroxene were confirmed incomets, circumstellar environment, and young stellar objects based on thespectral identifications from ISO and ground‐based telescope infraredobservations (e.g., Waelkens et al. 1996; Waters et al. 1996; 1998; Malfait et al.
1998; Molster et al. 1999; Honda et al. 2003). Laboratory works wereconducted to investigate the temperature dependence of crystalline silicates
and the absorption spectra of silicate particles was measure in lowtemperatures (e.g., Koike et al. 2006) because simple spectral fits suggests thatmuch of the optically thin silicate emissions occurs at temperatures in 50‐100 K
range (e.g., Bowey et al 2002).
Absorption measurement of powder samples in laboratory is a conventional
way to look into the thermal behavior of the infrared features of solids, but theabsorption spectra by powder depend on the shape distribution, the sizedistribution and the coagulation degree of samples, which are difficult to beregulated. It is also difficult to know which optical axis an absorption feature
belongs to. On the other hand, if we are able to obtain a single crystalline
sample with good quality and reasonable size, its reflection measurements at
infrared region provide with little ambiguity the dielectric or optical constantsof crystal’s each optical axis, which is vital for accounting the radiation
characters of crystalline dust.
Measurement
Reflectance for crystalline olivine((Mg92Fe8)2SiO4) were measured
with FT‐IR spectrometer (BrukerIFS120HRX) at BL43IR beam lineof SPring‐8 in 2007 and 2008
(Figure 1). Ohmic heaters andsilicon diode temperature sensors
were on the sample stage in theFigure 1.
cryostat, and the sample
Optical systems of FT‐IR
temperature was controlled by aspectrometer in Spring‐8. A sample
Lakeshore temperature controller.
stage were installed in a chamber.
The cryostat was kept vacuumwith pressure less than 10‐4 Torr.
Spectral resolutions 1cm‐1 was used, and 0.5, 0.25, and 0.125 cm‐1 when weneeded to resolve narrow features.
Olivine single crystal was produced in Kohistan (Figure 2). Three pieces of afew millimeter size crystal were prepared from a large single crystal, andcrystalline axes were determined by the X‐ray precession method. Three pieces
were polished to make the (100), (010), and (001) surfaces.
Reflection spectra for the infrared beam polarized parallel to the axis a wasmeasured on (100) surface, the axis b on both (100) and (001), and the axis c on
both (100) and (010). Infrared spectra have been obtained at the temperatureof 300, 200, 100, and 50 K using a reflectance module of 10 degree incident
angle. A beam splitter and wire grid polarizer in the PE substrate (~400‐50 cm‐1)
and Thallium Bromo‐Iodide (KRS5) substrate (2000‐~400) were employed. A
customized optical module was used to derive the spectrometer beam to andfrom the sample compartment through the window on the cryostat wall. The
reflectance of the sample was calibrated with a gold‐coated silicon substratemirror that was also on the sample stage and inserted to the spectrometerbeam path in the sample way of the olivine sample. 100 percent reflectance for
all wavelength was assumed for the gold mirror.
Figure 2.
Measured millimeter size
sample of the clistalline
olivine and the samplestage.

Results
Figure 3 shows the measured reflectance for crystalline olivine of each axis as
a function of wave number. When the temperature decreased from 300 to 60
K, the intensity of reflectance changes drastic in linger wavelength (<~700 cm‐1). Olivine crystal belongs to the space group Pnma (D16 ) and there are 35 IR
2hactive optical modes (9 91u, 13 B2u, 13 B3u) expected from symmetry analysis(Ishii 1978). 8 in the axis c (B1u), 12 in the axis b (B2u), and 11 in the axis a(B3u) features have been clearly observed in our measurements.

Figure 3.
Reflectances for crystalline olivine of the a axis (left), b axis (center) ,and c axis (right) as a function of wave number [cm‐1]. The colors show
the differences of the temperatures for the crystal.
Discussion
The Dielectric constants are derived from the reflection spectra by adopting
the classical dispersion model of dumped oscillator (Bohren and Huffman1983). The dispersion relation is expressed as,

where ε0 is the dielectric constant at the short wavelength limit, ωpj2, ωj2, andγj are the oscillator strength, transverse optical wavelength, and dumping
factor, respectively. The reflectance R is calculated from ε(ω),

where θ is the beam incident angle to a surface of the crystal (10 degree). We
use the least‐square method to fit the parameters from reflectance. The resultsof the oscillator parameters are shown in Table.
Table.
Oscillator parameters for each axis at 300K. We assumed 11, 12, and 8features for a, b, and c axes respectively from results of the reflectances.
a‐axis (B3u): ε0=2.77
ω2pi/ω2i
γi/ωi
ωi
9.764E+02
9.580E+02
8.409E+02
6.040E+02
5.017E+02
4.023E+02
3.792E+02
3.196E+02
2.942E+02
2.748E+02
2.009E+02

6.718E+00
3.649E+00
8.427E+00
1.261E+01
1.284E+01
5.593E+00
5.511E+00
2.785E+00
3.454E+00
2.694E+00
2.459E+00

3.131E+05
1.486E+052.850E+03
8.008E+04
8.753E+04
2.473E+05
1.410E+05
8.486E+03
2.808E+04
3.982E+03
1.029E+03

b‐axis (B2u): ε0=2.70
ω2pi/ω2iγi/ωi
ωi

c‐axis (B1u): ε0=2.71
ω2pi/ω2iγi/ωi
ωi

9.842E+02 5.059E+00 7.006E+03
8.718E+02 2.794E+00 2.921E+05
8.378E+02 9.471E+00 9.026E+04
5.269E+02 1.250E+01 4.914E+04
5.060E+02 6.315E+00 1.120E+04
4.559E+02 8.902E+00 3.883E+04
4.168E+02 5.410E+00 4.806E+04
3.951E+02 5.337E+00 7.208E+04
3.487E+02 5.488E+00 1.471E+05
2.891E+02 4.421E+00 1.361E+05
2.768E+02 2.528E+00 6.413E+03
1.434E+02 2.078E+00 1.603E+03

8.741E+02 5.383E+00 4.681E+05
5.029E+02 9.920E+00 1.097E+05
4.762E+02 8.033E+00 3.457E+04
4.151E+02 5.624E+00 1.614E+05
4.084E+02 5.645E+00 8.116E+04
3.045E+02 4.644E+00 2.680E+03
2.911E+02 2.951E+00 1.046E+05
2.761E+02 2.627E+00 6.119E+03

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