Low Energy Optical Absorption Peak in Aluminum and Al Mg Alloys

Physics and Astronomy Publications

Physics and Astronomy

7-1970

Low-Energy Optical Absorption Peak in

Aluminum and Al-Mg Alloys

L. W. Bos

Iowa State University

David W. Lynch

Iowa State University, dlynch@iastate.edu

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Low-Energy Optical Absorption Peak in Aluminum and Al-Mg Alloys

Abstract

Measurements of the absorptivity of Al and dilute Al-Mg alloys were made at 4.2 K in the 0.2- to 5-eV energy

region by a calorimetric technique. In addition to the well-known conductivity peak around 1.6 eV, another

peak has been found near 0.5 eV. These peaks are present in the alloys, broadened, but unshifted, as well as in

Al. The peaks are at about 2|V200|and 2|V111|, respectively, where the V's are Fourier coefficients of the

pseudopotential.

Keywords

pseudopotential, conductivity, Ames Laboratory

Disciplines

Atomic, Molecular and Optical Physics | Physics

Comments

VQLUME 2$,NUMBER $

PHYSICAL

REVIEW LETTERS

20Jvr.v 1970 LOW-ENERGY OPTICAL ABSORPTION PEAK IN ALUMINUM AND Al-Mg ALLOYS*

L.

W. Bos1' and D. W. Lynch

Department of Physics and Institute for Atomic Research, Iowa State University, Ames, Iowa 50010 (Received 14May 1970)

Measurements ofthe absorptivity ofAl and dilute Al-Mg alloys were made at

4.

2 K in the 0.2-to 5-eV energy region by a calorimetric technique. In addition to the well-known conductivity peak around

1.

6eV, another peak has been found near

0.

5eV. These peaks are present inthe alloys, broadened, but unshifted, as well as in Al. The peaks are at

about 2''200( and 2k~~ql~ respectively, where the V's are Fourier coefficients ofthe

pseu-dopotential.

The optical absorption ofaluminum

is

rather featureless in the region of interband absorption. The only reported structure'

is

a

ref

lectivity minimum at

1.

5 eV, although suspicions of an absorption peak at lower energy have been

re-ported in some experimental work.

'

'

The strength of the

1.

5-eV absorption peak was once a contro-versial subject,

'

but recent calculations agree well with experiment.

'

"

This peak was original-ly attributed to transitions near

~

in the

Bril-louin zone,

"

but now it appears to be the result oftransitions occurring in

a larger

volume of the zone, near, but not including W.

Harrison" first

pointed out that for many polyvalent metals, a pseudopotential approach leads to parallel bands, partly empty, partly occupied, throughout ap-preciable regions ofk space. Such bands lead to

a

sharp edge in the conductivity at

a

photon en-ergy of 2~Vs~, where Vo

is a

Fourier coefficient

of the pseudopotential. At higher energy, each edge is followed by

a

decaying

tail.

Golovashkin, Kopeliovich, and Motulevich"

carried

out similar calculations. Any pseudopotential calculation of the band structure for Al should give bands that will yield roughly the above results when the

op-tical

properties

are

calculated from them.

Re-cent calculations,

'

"

including calculated dipole matrix elements, predict two absorption peaks, corresponding to 2~V»,~

(-1.

5 eV) and 2I V»&l

(-0.

5eV). The lower energy peak has not been reported previously. The high-energy peak has recently been remeasured.

'

%e have measured the absorptivity of Al and several alloys of Al with Mg at

4.

2 K using

a

calorimetric method.

'

'

' _{The aluminum was}

a

99.

999% pure Cominco polycrystalline ba.

r.

The alloys were produced by

arc

melting. The samples were spark cut, mechanically polished, electropolished, annealed in Ar at 550 C

for

at

least

100h, then electropolished again just

be-fore use. The samples were exposed to

air

for

less

than 2 h, and within another 3h were at a pressure of 10

'

Torr

or

less.

Data were taken

by

a

method similar to that of Biondi,

'

""

but with higher sensitivity and resolution. A prism double monochromator was used to ensure high spectral purity in the infrared. Since structure in the

1.5-eV

absorptivity peak has been report-ed' for pure Al, points were taken every 0,02 eV (the spectral bandpass) in that region. The

er-rors

in the measurements of the absorptivity are estimated to be 2~/~ in the

0.

5-

to

3-eV

region, rising to 10% at

0.

2 eV, not including any

errors

due to imperfect sample

surfaces.

Figure 1shows the absorptivities of Al and three alloys of Al with Mg. The absolute values of the absorptivities in this figure are difficult to guarantee. Several samples with noticeably poorer electropolished surfaces yielded absorp-tivity spectra like those shown in Fig. 1, but shifted upward by about

0.01

in the infrared and

0.

02 around 3eV. The structure near

0.

5eV was

still

discernible in these samples.

Better

surfaces might yield still lower absorptivities in the infrared. However, the absorptivities for pure Al shown in Fig. 1

are

lower than any

re-ported to date, 4_{indicating somewhat better}

sur-faces on our samples.

A Kramers-Kronig inversion of the absorptivity was made to obtain the optical conductivity. Above 5 eV, published

data"

for

Al were used, while for the alloys above 3 eV, we used the Al data multiplied by a

factor

between

0.

8 and 1to make a smooth fitwith the alloy data at 3 eV. From 0 to

0.05

eV the absorptivity of a free

elec-tron gas was used, and asmooth monotonic curve was drawn between

0.05

and

0.

2 eV to connect to the data. Changes in the low-energy extrapola-tion had little effect on the computed conductivity, but changes in the high-energy extrapolation had a large effect on the magnitude, but not the shape, ofthe conductivity between

0.

2 and 3 eV. The alloy data are particularly sensitive here because their poorer surfaces produced

errors

in the ab-sorptivity. The conductivity

spectra

have only qualitative significance for the alloys, but that

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for

pure Al

is

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for

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and both peaks

persist

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ti

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VoLUME 25,NUM@Em $

PHYSI

CAI

REVIEW

LETTERS

20 JU~v 1970

a

Drude term has been subtracted from the total

conductivity. Because interband absorption con-tributes everywhere in our data range and

be-cause ofthe anomalous skin effect, there is no

way to obtain the Drude parameters from our data.

For

both samples we used k~~ =_{12.7 eV.}

For

Al we used _(~~T)

'

=y=

0.

0035and

0.

0030,

while

for

the alloy, y ranges from

0.

0062 to

0.008,

the former value being that expected from the dc conductivity.

"

It

is clear

that the main peak in Al seems structure

free

except for possible slope changes at

1.

40 and

1.

65 eV (better detected on plots with different

scales).

A recent

set

ofmeasurements' by an ac technique" reports structure on the low-energy side of the

1.

6-eV

peak, structure large enough to be discernible in our data, but which

is

not found. The reason for the disagreement is not

clear.

It

is

either an

artifact

of the ac method

or

apparatus,

or

the result of inferior surfaces in our measurements.

The new peak at

0.

50eV has been predicted

a

number oftimes,

'

"

but not observed before. According to Harrison's model, there should be sharp

rises

in the conductivity at Nv= 2iVo

i.

Ashcroft's

values"

of iVoi, which yield a Fermi

surface in substantial agreement with

experi-ment, give 21 V2oo1=1 52 eVand 21ViiiI

=_{0 485}

eV. The conductivity should then fall offas

'(kv-2i

Voi)

"'

beyond the sharp

rise.

"

Dresselhaus' and

Brust'"

have recently calcu-lated the conductivity more realistically, using the above pseudopotential coefficients. Their peak values of the conductivity are in substantial agreement with those of

Fig.

2. They point out that the low-energy peak does not

rise

at 2i

V»,

i

but begins at zero photon energy,

a

result ofthe crossing of two bands at the Fermi level on

cer-tain planes in the Brillouin zone. This low-en-ergy absorption must be considered when obtain-ing the electron effective mass from infrared data on Al, as recognized by Golovashkin, Motu-levich, and Shubin' and by Gurzhi and Motulevich.

'

Adding Mg, which simply. lowers the Fermi en-ergy according to

a

rigid-band model, has little effect on the positions of the peaks. The peaks simply broaden and become lower, an effect of the increased scattering in the alloys. Thus, the two values of iVoi change very little. A shift

in the Fermi level

is

not expected to alter the position ofthe conductivity peak, because

a

low-er Flow-ermi

level only makes the regions in &

space where transitions occur at a particular

photon energy move slightly. Since the bands are nearly parallel in both regions, no appreci-able change in the conductivity results.

Measurements further into the infrared

are

in progress, and a more detailed separation of the absorptivity into

free-carrier

and interband terms will be reported

later.

We wish to acknow-ledge profitable discussions and correspondence with Dr. D. Brust, Dr. G. Dresselhaus, and

Pro-fessor

K.

I.

Kliewer, and the sample preparation by H. H. Baker and

F.

A. Schmidt,

*Work performed atthe Ames Laboratory ofthe U.

S.

Atomic Energy Commission.

)Present address: Western Electric Company, Engineering Research Center, Box 900, Princeton,

N.

J.

08540.

H.

E.

Bennett, M.Silver, and

E.

J.

Ashley,

J.

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Soc.Amer. 53, 1089 (1963).

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I.

Golovashkin, G.

P.

Motulevich, and A.A.

Shubin, Zh. Eksp. Teor. Fiz.38, 51 (1960)ISov. Phys. JZTP 11,38 (1960)].

R.N. Gurzhi and G.

P.

Motulevich, Zh. Eksp. Teor. Fiz. 51, 1220 (1966) [Sov. Phys. JZTP 24, 818(1967)].

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I.

Guobadia, Phys. Bev. 166, 667 (1968).

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J.

Powell,

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C.Phillips, Solid State Phys. 18, 55 (1966). 'A.

_J.

Hughes, D. Jones, and A. H. Lettington,

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Phillipp, and

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_{K.G.Bamanthan, Proc. Phys. Soc.London, Sect.A} 65, 532 (1952).

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Madden,

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Canfield, and G.Hass,

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