Temperature Dependence of the K Absorption Edge of Lithium

Physics and Astronomy Publications

Physics and Astronomy

12-1974

Temperature Dependence of the K Absorption

Edge of Lithium

C. Kunz

Deutsches Elektronen-Synchrotron

H. Petersen

Deutsches Elektronen-Synchrotron

David W. Lynch

Iowa State University, [email protected]

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Temperature Dependence of the K Absorption Edge of Lithium

Abstract

The shape of the K absorption edge of Li has been measured at 293, 373, 443, and

∼

480 K (liquid) by

photoyield methods. Unpublished transmission data on the shape of the edge at and below room temperature

have been reanalyzed. There is a marked increase of the width of the edge with increasing temperature above

293 K, indicating that the lattice plays a major role in the broadening of the edge.

Keywords

photoyield, emission edge, Ames Laboratory

Disciplines

Atomic, Molecular and Optical Physics | Physics

Comments

VOLUME 33,NUMBER 26

PHYSICAL

REVIEW

LETTERS

23DECEMBER 1974

Temperature

Dependence

of

the

E

Absorption

Edge

of

Lithium

C.Kunz and H. Petersen

Deutsches Elektxonen-Synchrotron, 2000Hamburg 5Z, Gem+any

D. W. Lynch

Ames Laboratory USA—E_{C, and Department of Physics,} Iowa State University, Ames, Iowa 50010, *and II.Institut fu~ ExpemmentalPhysik, Unive~sitat Hamburg, 2000Hamburg 50, Germany

(Received 21October 1974)

The shape oftheKabsorption edge of

I i

has been measured at293, 378, 443, and

480K (l.iquid) by photoyield methods. Unpublished transmission data on the shape of the edge at and below room temperature have been reanalyzed. There is amarked in-crease ofthe width ofthe edge with increasing temperature above 298 K, indicating that the lattice plays a major role in the broadening ofthe edge,

The explanation of the shapes of the K

absorp-tion and emission edges in

Li

(and L edges in

several other light metals)

is

a subject of

con-siderable recent controversy. The apparent

de-pression from the expected relatively sharp

Fer-mi step has been explained

as a

many-body

ef-fect'

in which adepression

is

expected for

s-p

transitions in absorption,

e.

g., the

Li

Kedge, and an enhancement

("spike")

expected for ab-sorptive

p-

s transitions,

e.

g., the Na,

I.

»

edge.

Dow and co-workers' 4_{have disagreed with the}

many-body explanation for the Li

K

edge,

pro-posing that a simpler model explains the round-ing of the edge. While

earlier

attempts' to calcu-late the broadening ofthe initial

1s

electron level

by a

direct

interaction mith the phonons in

its

most sophisticated version yielded small values

at room temperature (~

0.

1 eV), Dow, Robinson,

and

Carver'

propose a stronger indirect

interac-tion mediated by the 2s electrons, which in a

first

rough estimate appeared to confirm the

ex-perimental edge width

(-0.

5 eV). Another

possi-ble source of the edge broadening

is

the lifetime

of the

1s

hole due to Auger transitions. 4

The many-body theory

is

an essentially

temper-ature-independent mechnaism; the Auger

broad-ening has

a

temperature-independent base width4

at zero temperature and could possibly contain

also atemperature-dependent term' from the

os-cillating 2s wave-function amplitude atthe hole

site.

Ifthe

direct' or

the indirect' interaction of the

core

hole with phonons was responsible for

the edge width a strong temperature dependence

is

expected to show up. Therefore measurements of the edge width as a function oftemperature

are

clearly important. Such measurements

are

reported herein.

In addition tothe published7 values at —77 K,

unpublished absorption measurements at and be-low 300Kwere made in this laboratory.

'

A 2-m

Rowland-mount monochromator and the synchro-tron radiation from DESYwere used.

'

The

reso-lution at 50 eVwas

0.

03 eV. The

pressure

in the sample chamber was about 10

'

Torr

during evaporation and measurements. The samples mere surrounded by a radiation shield which

served to protect the films from water molecules,

which enhance the

rate

of oxidation. The

temper-ature of the sample mount was measured with a

thermocouple to be

4.

2 and 77 K, but the film

temperatures were probably some

5-10

K higher.

The transmission spectra were converted to

ab-sorption coefficient

spectra.

The data taken at 300Kwere on films in various states of oxida-tion and

are

the

least

representative of

clear

Li.

En this

case

a superposition ofmetal and oxide

spectra was observed. Therefore from these

da-ta no accurate edge width could be obtained.

The present measurements at and above 293 K

were of the photoyield of massive specimens of

Li.

The photoyield has been shown to be

propor-tional to the absorption coefficient, except for

the shape of the smoothly varying background.

'"

The light source was DESYand a recently

de-signed monochromator especially suited to such

a source.

"

The resolution was &0.15 at 50 eV.

The calibration mas accurate to

+0.

2 eV. The

photoemitted electrons were passed through a

re-tarding field and a spherical-plate energy

analy-zer.

"

The 2-eV resolution of the analyzer does

not affect our measurements, for only the

inelas-tically scattered electrons

are

measured, which

are

taken a,

s

representative of the yield. Scans of the yield spectrum were made at several

VOLUME 337NUMBER 26

PH

YSICAL

RK

VIE%~

LETTERS

23DECEMBER1974

v)]0 I—

I I t I

I I I I I

I I I I l I I

1.0 CQ CL O Q UJ N LL LL LLI O O ~V) ~CO Ih 0 54

I I I i

ABS.COEFF.)

I I I I I I I I I I I I

55 hv (eVj

x

O uJ C) UJ -I I MP

FIG.

1.

Ii Xedge at different temperatures. The curve at4 K was obtained by absorption measurements, the other curves by yield spectroscopy. The 50%values ofthe edges oftwo curves not drawn at 77 (absorption)

and at 373 K {yield) are 54.87and 55.03 eV,

respective-ly. The curves are scaled tothe same amplitudes. All the yield curves coincide with the dashed curve below

54,5eV.

I

200

T(K)

600

FIG.

2.

LiKedge width 4$"versus temperature, MP isthe melting point (452 K). Open circles from Ref. 13,closed circles this experiment.

ues of the retarding potential to permit removal of the structure due to the unscattered electrons

directly emitted from the K level. The samples

were pieces of solid

Li

placed on a Ta

strip.

A

thermocouple was inserted into the melt under

Ar protection before evacuating the system.

Af-ter

bakeout and cryopumping, when the pressure

was in the

(1-8)

X10 '0

Torr

range, the sample was melted, then scraped and

stirred

with a W

brush. This moved macroscopic pieces of oxide

aside

or

made them sink into the melt. Clean

liquid Li, once obtained, could be maintained for

several hours. The solid Liwas cleaned by

scraping with the W brush. At a measured

pres-sure of

1.

3

x10

'

Torr

the

Li

remained

free

of oxide for about 2 h. Thereafter indications of

ox-ide could be observed. The oxidation was

moni-tored by measuring the ratio of the edge

discon-tinuity with

respect

to the signal below the edge

(4.

5:1

was our best value;

it

decreases

with

oxi-dation). Another indication of oxide

is

a.peak emerging at 58 eV.

Figure 1 shows the absorption edge. The edge

at

77K has been published previously,

'

but a

re-measurement' gives the edge as shown in Fig. 1,

shifted with

respect

to the older measurements to higher energy (by

0.

16 eV). The 50%position of the edge at 77 and at 4 K

is

54.86~

0.

15 eV.

The shape ofthe absorption spectrum above the edge has been published elsewhere.

"'

The

yield-spectroscopy data show a shift of the edge to

high-er

energies by

0.

06 eV between 293 and 443 K.

There

is

a further shift of

0.

12eV upon melting. The shift between 4 and 293 K

is

also to higher

energies, but difficult to estimate because two

different monochromators were used.

The 10to 90%width of the edge (b, W)

as

a

func-tion oftemperature

is

plotted in

Fig.

2. Below

room temperature we

are

in disagreement with

a value obtained with an energy-loss technique

by Ritsko, Schnatterly, and Gibbons.

"

In

con-trast

to Ritsko, Schnatterly, and Gibbons" we did not attempt to make

a

deconvolution of our measurements since we believe that the accuracy

of such a procedure

is

usually low. In

order

to

be consistent we used their raw-data value of the

edge widths at both temperatures.

It is clear

that there

is

a large,

temperature-dependent broadening of the edge. The

theoreti-cal estimate by Dow, Robinson, and

Carver'

of

the phonon broadening of the

1s

levels gives the width of the edge as proportional to the rms

lat-tice

displacements, which have been measured

by Smith

et

al.

'4 A plot of the measured width of

the

Li

K edge versus rms displacement

is

shown

in

_Fig.

3.

The yield data fall on a reasonably

good straight line. The width of the

Fermi

VOLUME 3

),

NUMBER 26

PHYSICAL

REVIEW

LETTERS

23DECEMBER1974

1.0

443K

than previously believed.

We wish to acknowledge many lively

discus-sions with

J.

D. Dow. One ofus (D.W.

L.

)wishes

to thank the

II.

Institut fGr Experimentalphysik, Universitat Hamburg, for financial support.

0. 5-T

C5 4K

I I

0.1 0.2

I I

0.3 0.4

6R(ki

I

0.5 0.6

FIG.

3.

Li

E

edge width 4Wversus rms lattice dis-placement {Ref.14)t5R. The straight line is an

inter-polation ofthe high-amplitude values.

broadening,

for

other models involving phonons

will have a similar dependence. 4

Figure 3 does,

homever, demonstrate that phonons

are

involved in the broadening mechanism. Ifphonon coupling to the

1s

electrons

is

the sole broadening

mecha-nism, the slope of the line in Fig. 3,

1.

3 eV/A,

is a

measure of the coupling constant. This must

be viewed with caution,

for

the displacements used for

Fig.

3

are

total displacements, involv-ing phonons from all branches, while the

1s

elec-tron will couple to different phonon branches with different weights. The generally

looser

struc-ture ofthe liquid ought to account for the

discon-tinuity ofthe width at the melting point. We

are

not aware ofany measurements of the mean square displacement in liquid

Li.

Our measurements have demonstrated that

there

is

a temperature dependence ofthe width

of the Kabsorption edge in Li, one that varies

roughly as the rms lattice displacement. A

pos-sible explanation of the temperature dependence

is

the phonon-broadening model ofDow, Robin-sin, and

Carver'.

One also must examine the

ef-fect

oflattice vibrations on the Auger width of

the

1s

hole.

'

The many-body calculation has not

been

carried

out extensively at finite tempera-ture, but

it

has been

estimated"

as being approx-imately independent oftemperature.

It

seems

clear

from

Fig.

3 tha,

t

at 0 K, zero-point lattice

vibrations account

for

at

least

part of the width, making the role ofmany-body effects smaller

*Permanent address.

G. D.Mahan, Phys. Rev. 153, 882 {1967),and 163, 612 (1967),and in "Solid State Physics,

"

edited by

F.

Seitz, D.Turnbull, and H. Ehrenreich (Academic,

New York, tobe published), Vol.29;

P.

Nozieres and

C.

T.

de Dominicis, Phys. Bev. 178, 1097 (1967);

J. J.

Hopfield, Comments Solid State Phys. 2, 40 (1969).

J,

D.Dow, Phys. Bev. Lett. 31,1132 (1973).

3J.D.Dow,

J.

E.

Robinson, and

T.

R.

Carver, Phys. Rev. Lett. 31, 759(1973).

4J. D.Dow and D.R.Franceschetti,

J.

Phys.

F:

Met-al Phys. 4, L151 (1974).

Adirect phonon mechanism was suggested by A. W. Overhauser. See A.

J.

McAlister, Phys. Bev. 186, 595 (1969). Later work is reported by B,Bergersen,

B.

McMullen, and

J.

P.

Carbotte, Can,

J.

Phys. 49, 3155(1971).

~J. D.Dow, private communication.

C.Kunz,

J.

Phys. (Paris) Colloq. 32, C4-181(1971);

B,

Haensel, G,Keitel,

B.

Sonntag, C.Kunz, and

P.

Schreiber, Phys, Status Solidi (a) 2, 85 (1970); C.Kunz,

B.

Haensel, G.Keitel,

P.

Schreiber, and

B.

Sonntag, inEtectxonic Density ofStates, edited by

L.

H.Bennett, U, S,National Bureau ofStandards Special Publication No. 329 (U.S.GPO, Washington, DoC o 1 7

B,

Haensel, C.Kunz, U. Nielsen, and

B.

Sonntag, unpublished.

W.Gudat and C.Kunz, Phys. Rev. Lett. 29, 169 {1972).

'_{W.Gudat and C.Kunz, in Proceedings ofthe Fou&k}

Intensational Conference on Vacuum Uttxaviolet

Itadia-tion Physics, Hamburg, 1974, edited by E,

E.

Koch,

R.Haensel, and C.Kunz (Pergamon, New York, 1974), p. 392.

~H.Dietrich and C.Kunz, Rev, Sci,Instrum. 43, 434 (1972).

H. Petersen and C.Kunz, in PxoceeChngs ofthe Pougth Intentional Conference on Vacuum Uttxaviolet Radiation Physics, Hanibuxg, 1974, edited by E,

E.

Koch, R.Haensel, and C.Kunz (Pergamon, New York, 1974), p. 587.

~3J.

_J,

_{Ritsko, S.}

_E.

_{Schnatterly, and}

_P.

_C,Gibbons, Phys, Rev, B(tobe published).

4H._{G.Smith, G.Dolling,}

_B.

_M.Nicklow,

_{P. B.}

Vija-yaraghavan, and M.K.Wilkinson, in Proceedings ofthe E'ou&h JAEA _Symposium on Ãeutxon Inelastic

Scatter-ing, Copenhagen, Denmark, 19680:nternationa1 Atomic Energy Agency, Vienna, Austria, 1968), p.149.

B.

A.Ferrell, Phys. Rev. 186, 399{1969).