Photoemission study on the valence bands of DMe-DCNQI derived charge-transfer salts

HAL Id: jpa-00246417

https://hal.archives-ouvertes.fr/jpa-00246417

Submitted on 1 Jan 1991

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Photoemission study on the valence bands of DMe-DCNQI derived charge-transfer salts

D. Schmeißer, A. Gonzales, J. von Schütz, H. Wachtel, H. Wolf

To cite this version:

D. Schmeißer, A. Gonzales, J. von Schütz, H. Wachtel, H. Wolf. Photoemission study on the valence

bands of DMe-DCNQI derived charge-transfer salts. Journal de Physique I, EDP Sciences, 1991, 1

(9), pp.1347-1354. �10.1051/jp1:1991110�. �jpa-00246417�

Classificafion

Physics

Abstracts

79.60 76.30

Photoendssion study

_on

the valence bands of DMe-DCNQI

derived charge-transfer salts

D. SchmeiBer

(2),

^{A. Gonzales}

('),

J. U. _von Schiitz

('),

H. Wachtel

(')

and

H. C. Wolf

(')

(')

3.

Physikalisches Institut, Pfaffienwaldring

57, 7000

Stuttgart, Germany

~2) Institut ffir

Physikalische

und Theoretische Chemie, Auf der

Morgenstelle

8, 7400

Tfibingen, Gennany

(Received18 February

1991, accepted in

final form

13 May

1991)

Abstract. -The electronic structure of

crystalline

needles of the

2,5-Dimethyl

substituted

(DCNQI)~M

(M ₌ Cu,

Rb, Cs)

radical-anion salts,

prepared

_u1situ, is determined

by photoelec-

tron spectroscopy

using synchrotron

radiation. The electronic structure at the top ^of the valence bands is determined to arise

mainly

from contributions of

C2p

and

N2p

states. In

particular,

the Cu3d atomic levels do not contribute

significantly

to the

density

of states next to the Fermi

energy. This

comparison

of salts with different central _atoms

gives

the first

experimental

evidence of _a

truely organic

metal with the uppermost

(conducting)

band

originating

from

C2p

and

N2p

derived _states.

In&oduction.

The

conducting organic

radical anion salts derived from the

Dicyanobenzoquinonediimines (DCNQI)

^show

extremely high

conductivities which _{range up to} 1000 S

cm-'

at 300 K

[I].

For

(DMe-DCNQI)~Cu (Me =CH~)

the

conductivity

increases _at lower

temperatures indicating

metallic

behaviour,

whereas for the

(Br, Cl)

substituted salts _a decrease of

conductivity

towards lower temperatures is found

[2-4].

The

crystal

structure for the

differently

substituted salts _was determined

by X-ray

diffraction

[1, 5, 6].

A chain of the metallic counterions is surrounded

by

^stacks of

organic DCNQI

molecules and is connected

by

cyano

(CN~

_groups of the anions in _a tetrahedral coordination

[5].

The distances between the Cu-atoms and the

nitrogen

atoms _are

remarkably

low

(0.198 nm)

and _are of the order of

chemical bonds. For the Rb salts the _structure is

similar,

however the metal-CN distances _are

increased,

and the coordination is 8-fold

[6].

In _a

previous study

_we have determined the oxidation state of the Cu counterion

[7].

^We found that there is almost _no satellite emission from the

Cu2+

_state within the

Cu2p

_spectra of the

(2,5-DMe-DCNQI)~Cu

salts and their Br and Cl derivatives when

prepared

in

N2

atmosphere. Significant emission, however,

is observed when the

samples

have been

kept

in air

prior

to the measurements. This

comparison

demonstrates the need for careful

sample

1348 JOURNAL DE

PHYSIQUE

I M 9

preparation

of these

organic

materials to separate extrinsic contributions from intrinsic behaviour. In that work _we also determined the valence band structure,

thereby

it became evident that the

(2,5-DMe-DCNQI)~Cu

^{salt is} a true

organic

metal _as it exhibits _a metallic

density

of states

(DOS)

at the Fermi energy.

The scope of this contribution is to elucidate the electronic structure in _more detail. We do

not restrict ourselves for the

DMe(DCNQI)2Cu

salt

only,

but compare the valence band

range ^to those of alkali salts. We _use in situ

preparation techniques

to allow

sample

preparation

at a

synchrotron

radiation

(SR) experimental setup

^without

influencing

the multiuser conditions in iJHV. The work focusses in

particular

_on the _appearance and width of

Cu3d states in the valence band _near the Fermi _energy.

Photon-energy dependent

photoemission

studies allow to determine the

partial

densities of _states in the valence band

region compared

with those derived from the

quinone ring system

^{and of the CN} groups.

Tl~ese detailed data enable _a

comparison

to the

theoretically

derived

partial

DOS. We find

good agreement

^with the

partial density

of states derived from _an extended Hiickel

calculation that

give

_a clear

separation

^{of the}

quinone

derived _gr

system

^from the bands

originating

from the cyanogroups and the Cu3d states. A further

approach

to separate ^the

DCNQI

derived bands from contributions of the central metal atoms is to prepare alkali based Cs- and

Rb-DCNQI

salts with _no metal derived states _near

E~

and to

investigate

their valence band structure under identical conditions. Such _a

comparison

^should correlate the differences in the valence band

regime

to the differences in the

conductivity

behaviour.

Expedmental.

Single crystalline

_copper salts of

N,N'-dicyano-2,5-dimethyl-I,4-benzoquinone-diirnines (2,5- DMe-DCNQI)2Cu

_are

prepared

_as

reported

elsewhere

[8].

We have grown the

crystals

in _a

glove

box under

catalytically

cleaned

nitrogen atmosphere,

in order to avoid surface oxidation and contamination

by hydrocarbons,

_as

required

for the studies in UHV

systems.

The

samples

were grown on a Cu foil and mounted within the

glove

box _{on a}

sample

stub.

They

_were then

transported

in

N2 atmosphere

to the fast entry lock of the UHV

system.

^{Details of the} UHV and the transfer systems are described elsewhere

[9]. Samples

_are also

prepared

in _a reaction vessel under

N2 atmosphere

and transferred

immediately

to the UHV system. ^The

reacting

agent ^{has been} filled under

N2 atmosphere.

Rb and Cs salts have been

prepared by

_a solid state diffusion

technique

described in _more details elsewhere

[10]. Alternating layers

of

DCNQI

and Rb

(Cs)

_are

evaporated

in stoichiometric ratios onto an oxidized Si wafer

(Au coated) kept

at 80 K at around 10-8 mbar. Diffusion is initiated

by continuously warming

the sandwich structures to _room

temperature

over 6-8 h.

Afterwards,

the films _are transferred from the

preparation

vessel to the

spectrometer.

The data have been taken at the TGM7 and TGM4 beam lines at

BESSY, Berlin,

where _a commercial VGADES400 _was installed. For all

systems investigated,

the spectra are

referred to the Fermi energy of _a clean Cu

single crystal.

The _use of the

sample preparation

under UHV _{or at} least inert gas conditions is essential for UPS studies _as the extreme surface

sensitivity

of that

technique requires

clean

sample

preparation.

Results.

In _an extended Hfickel

type

calculation for

(2,5-DMe-DCNQI)~Cu

the derived

partial density

of states

(Mulliken population analysis) suggested

that the metallic nature is _not correlated to the existence of Cu states _near the Fermi _energy

[11]. However, experimentally

_a metallic

conductivity

is found

only

for Cu salts.

Therefore,

the contribution of Cu3d electrons to the

density

of valence band states still is _{an open}

question

in the discussion of the electrical and

magnetic properties

of such

organic

^materials. In

general,

in

organic

materials the electronic

structure in the valence band _range is

composed

of

bonding

and _non

bonding

molecular

orbitals

(gr systems)

derived from

N2p

and

C2p

atomic levels. The ionization _cross sections of these _states

usually

have _no

significant

differences and _are very weak _at

high

_energy

excitation.

However,

the _energy

dependence

of the

photoionization

_cross sections of

2p

and 3d levels _can be used to determine the relative abundance of Cu3d states in the valence band

regime.

Characteristic valence band

spectra

of

(2,5-DMe-DCNQI)2Cu

taken at various excitation

energies

_are shown in

figure

I. In all spectra the strong contributions from the

N2p

and

C2p

levels _are observable around 7 eV.

However,

the _range around 4

eV,

which is

typical

for Cu3d levels

[19],

also shows

pronounced

emission. Its relative

intensity

varies with the excitation _energy and dominates in the spectra taken at

photon energies

around 75 eV.

IDM-DcNoi)

~ cu

b hwlev]

a

I

fi

85

75 41

Cu

12 8 4 O

Energy

below

E~ ievi

Fig.

I. -Valence band spectra of

(2,5-DMe-DCNQI)2Cu

taken at different excitation

energies.

In

figure

2 the valence band spectra of

DMe-DCNQI

salts of

Cu,

Cs and Rb _are

compared.

The data _are taken at

photon energies

around 40 eV at which the Cu3d contributions _are not enhanced. The emission from the

Rb4p, Cssp

levels _are

indicated, they

_are well below the main emission from the

DCNQI

at 7eV. These levels

certainly

do not contribute to the

conductivity

due to their

high binding energies (shallow

_core

levels).

The range above 7 eV

however,

is

remarkably

similar for the three salts

investigated.

At lower

binding energies

there _are distinct

peaks

around 4 eV and 2

eV, only

the Cu salt shows _a rather broad emission

pattem

in that

regime.

The _most

significant

difference in the

DOS, however,

is at the Fermi

JOURNAL DE PHYSIQUE I T I,M 9, SEPTEMBRE lwl 53

1350 JOURNAL DE

PHYSIQUE

I bt 9

(DCNtJI)~ ^salts

Hell(40.8 evl

-

41 eV

3

E

~

~Cu E~

E

W

Cs

~

3

C _Cs

5p

^'

C

Rb

4p

16 12 8 4 O

Energy

below

E~ [eV]

Fig.

2. -Valence band spectra ^of

(2,5-DMe-DCNQI)2

salts with

Cu(a), Cs(b)

and

Rb(c)

as central atoms.

energy. The alkali salts exhibit _a

pronounced

valence band maximum which is 0.9 eV and 0.65 eV below

E~.

This contrasts the metallic DOS which is observed for the Cu salts

only.

Discussion.

1. ATOMIC PARENTAGE OF THE VALENCE BANDS. the

conductivity

of the

(DCNQI)2Cu

radical-anion salts has been discussed in terms of mixed valence _states of the central Cu _atoms

[5, 7, 12].

^Its mixed

valency,

I-e- the contribution and admixture of the localized d-electrons to the

topmost

^molecular

orbitals, principally

reflects in the formal oxidation state which _can be derived from the relative satellite intensities determined in the XPS

spectra.

For

Cu,

the

Cu2+

_{state allows easy}

charge

transfer via the open

d9 shell, causing

the _appearance of

satellites in the _core level

spectra. However,

_our XPS data indicate that the oxidation _state of the central counterion Cu witlfin

preparative

and

experimental

_errors, is not above ₊

[7J.

On the other

hand,

in covalent

solids,

the interaction of the

high lying

valence orbitals

causes a

mixing

of molecular orbitals which reflects in the valence band formation. As _a

consequence, the contributions of the different orbitals _no

longer

_can be considered

independently,

_as all of them contribute _to the valence band. For the

(2,5-DMe-DCNQI)2Cu

salt _a

significant

contribution of Cu3d levels _to the

density

^of states near the Fermi _energy is

tentatively expected [5, 7].

In the

present study

_we

employ

two

approaches

to elucidate this

problem,

the variatiun of the

photon energies

in Cu salts should allow to

separate

^Cu3d states from

C,N2p levels,

and the variation of the central atoms without d-orbital _wave functions should show the

DCNQI

derived levels ~vithout _any contribution from d levels.

In

photoelectron spectroscopy

^the energy

dependent

^{variation of the}

partial

ionization

moss sections has been used for _a number of

systems

^{in the}

past

to separate contributions from d electrons from others. First it has been associated with the shake _up

occurring

about 8 eV below the N13d valence band

[13]. Regarding organic materials,

Koch _et al.

[14]

have demonstrated that resonant

photoemission

allows a

separation

of atomic d-states from the benzene-derived _gr bands

by comparing Phthalocyanine (CuPc

to

H2Pc)

valence band

spectra

taken _near the _resonance. For

DMe(DCNQI)~Cu,

the variation in the relative intensities for the

C,N2p

and the Cu3d emission reflects _an increase in the different ionization

probabilities

and is not a

typical

_resonance behaviour. The maximum Value is reached around 80 eV where

a resonance would be

expected

but the increase is not

sharp

at _a certain energy, it rises

smoothly

from about 40 eV to reach the maximum value.

However,

the relative intensities vary

significantly

with _a total diffierence of almost _a factor often- The

origin

of this increase is

a side effect of _an atomic _resonance and is believed to arise from the

Cu2p

electrons that _can

contribute when the

photon

_energy reaches 75eV

(Cu2p binding energies

at

77.3eV,

75. I

ev~.

Resonant

photoemission

is found _{to occur} with enhanced satellite intensities _as the result of _an interference between _an

Auger

_process and _a multielectron interaction

[13].

It also is associated with enhancement of valence

photoelectron

features

resulting

from the

coupling

of excitation and

decay

^mechanisms at _core electron

photoabsorption

onsets

[15, 16].

This _process is

expected

for atomic Cu states and it is affected

by

chemical interaction of the atom

investigated.

The maximum _{occurs at}

slightly

^different

photon energies, ranging

between 75.6 eV for Cu metal and 76.5 eV for

CU~O [15, 16].

For

DMe(DCNQI)~Cu,

the enhancement is not _as

pronounced, although

there exist reports on

systems

^{~vith almost} no

enhancement at all

[17J.

Enhancement of the relative ionization cross-section may also be

caused

by

molecular _resonances

(shape

or Fano

resonances). However,

such variations in

general

^contribute at lower ionization

energies

_or above _a certain atomic threshold.

Furthermore,

the radical anion

systems

are not

expected

to show such variations _{as even} in the NEXAFS

signals,

_a local

(molecular) probe,

the molecular _resonances smoothen and broaden _upon

charge

transfer

[18]. Consequently,

the observed enhancement allows _a clear

separation

of the different atomic contributions. Our results also demonstrate that there _are

no contributions from d-like states in the DOS in the _range next to

E~.

In

figure

I the _range of the 3d emission _can be

clearly distinguished

^from the emission from C and N derived states. It starts about 0.5 eV below

E~

and reaches _to

binding energies

around 4.5 eV. The low

density

of states and its

independence

_on the

photon

_energy

(Fig. I)

indicate that the DOS _near

EF

is determined

by C,N

derived bands. As _a consequence, in the electronic structure of the

(2,5-DMe-DCNQI)~Cu

salt the top-most band consists of _a

mixing

of

C2p

and

N2p

derived states without considerable contributions from Cu3d derived states

[19].

For _our second

approach,

the variation of the central atom

using

metals without d-

electrons,

valence band

spectra

^of the Rb and Cs salts _are

compared

to that of the Cu salt in

figure

2. Here _we notice that the alkali salts exhibit distinct emission

pattems

^{in the} range

near

EF. First,

this

comparison

is of

importance

_as it demonstrates that the

DCNQI

films indeed have molecular orbital bands in this

region. Secondly,

the atomic

origin

of these bands is not from levels of the central atom but has _to arise from the

DCNQI

molecule. An _even

more

precise assignment

_can be deduced from _gas

phase

studies and theoretical work. In _a recent theoretical

approach

to understand'the _metallic

properties

of this

organic

metal _a modified extended Hfickel formalism _was

applied [11].

The calculations _{use a} linear

arrangement

of two

DCNQI

molecules connected via the central copper atom and result in _a metallic behavior of the salt caused

by

_a

partly

filled band at the Fermi _energy, derived of

C,N

1352 JOURNAL DE

PHYSIQUE

I M 9

atomic _wave functions

only.

Our results do confirm these calculations. _From the

analysis

of CN

containing

molecules

by

molecular orbital

(M.O.)

calculations

[I1, 20]

and _gas

phase photoemission

studies it is known that the CN groups contribute to the uppermost M-O- almost

predominantly,

in

particular

in

larger

molecules

[21]. Thereby,

_{we are} able to

assign

the _upper band in _our

spectra

to arise from the CN _groups also.

2. METALLIC _AND SEMICONDUCTING DENSITY OF STATES. The valence band

spectra

ⁱⁿ

figures

I and 2 demonstrate the metallic nature of the Cu salt _as the

density

of states exhibits

no band _gap, but extends _up to the Fermi _energy. This observation is

remarkable,

_as hitherto

no Fermi

edge

has been observed for any

organic material, including conducting polymers [22-25]. Further,

the width of the ESR lines at

temperatures

^{above the}

phase

transition

points

towards _a multi-dimensional

spin

motion _as observed in metals.

However,

differences to pure

metals _are found in the

Knight

shift measurements _: in the

DMe(DCNQI)2Cu

salts the Cu

Knight

shift is

strongly temperature dependent

and exceeds the value of _{pure copper}

significantly

at low

temperatures.

The

interpretation

of the UPS

spectra

^{of the} non copper salts is _more difficult. We find _an energy gap which is much

larger

than the activation _energy determined

by

the

temperature dependence

of the

conductivity.

Such a controversy was found also earlier. The

temperature dependence

of the

conductivity

for the one-dimensional

organic

metals

TTF-TCNQ

and

(SN)~

is similar to that of

(DCNQI)~Cu, during

the discussions of their electronic structure it has been

reported

that there is _no

sharp

emission

edge

observable

[24, 26].

For

example,

valence band

spectra

^{of the}

TTF-TCNQ salts,

which _are I-dimensional metallic

conductors,

did not show _a finite DOS and _a gap of about 0.3 eV _was observed. As _an

explanation

_a

coupling

of _a

phonon

mode to the

outgoing

emitted

photoelectron

_was

suggested.

The

coupling strength

is

supposed

to be enhanced

by

the localized _wave functions of the _van der Waals bound molecules. In

this explanation

the localized _nature of the states _near

E~

is stressed.

By this,

^unlike the _case for

inorganic metals,

_a fast relaxation is not

possible

and the

outgoing photoelectron

leaves the ionized molecule in _a state exited with various molecular vibrations. The kinetic energy of the

photoelectron

is reduced and is left in bond vibrations

by

the

instability

of the one-dimensional metal bands

[24, 26].

These

findings, however,

_are in contrast to the

generally accepted

metallic behavior of the

microscopic

electronic _structure of _some

highly conducting organic

solids

[1-3, 7, 26]. However,

in contrast to the

(DCNQI)~Cu salts,

the

TTF-TCNQ spectra

^have no DOS _near

E~. Evidently,

_our

preparation technique,

which is

significantly improved

_over all hitherto

reported approaches,

allows _us to determine the DOS _near

E~

from _our valence band spectra

accurately. Using

_a

similar

procedure

_we also have observed _a metallic

density

of states for fJlms of

polypyrrole

after

doping [26].

The metallic nature observed

by

UPS is consistent with the electrical measurements

and/or

other

independent

manifestation of the metallic state. We therefore believe that _a vibrational

coupling

to the final _state does _not influence the

photoelectron spectra

as

long

_as the DOS is _a

truely

metallic _one. We like to mention that in low dimensional systems ^~vith a

high

correlation energy a metal _to semiconductor transition should be

observable also in the DOS. This

implies

that the _non-copper salts _are

semiconducting

_even

around _room

temperature [28].

3. STABILITY OF THE METALLIC STATE.

Having

established the

origin

of the bands which

cause a metallic state, we concentrate on the

experimental

conditions _necessary for its

stability.

For the

R,R'(DCNQI)~Cu

salts the metallic DOS is found to

depend

_on the

substituent,

_a I-dimensional

instability

is

reversibly

observed for the

Me,

Cl substituted Cu salt

[28]

whereas for the DMe substituted salts the metallic behaviour is maintained _upon

cooling

to 80 K.

Furthermore,

the temperature

dependence

of the valence band

spectra

^{of the}

Cl substituted salts in the DOS

clearly

indicates _a metal-semiconductor transition _near 100

K,

in

agreement

^{with the}

conductivity

measurements. The metallic DOS furthermore is demonstrated to be also

extremely dependent

_on the

cristallineity

of the films. For

amorphous

films _a gap of 0.3 eV is observed

[7].

^These

findings

_are not

only

valid for the

Cu-salts,

but also for the alkali salts. For the

latter,

the

position

of the

top

^band

depends

also _on the

quality

of the

films,

it is found to vary within the rust 8 h after the

preparation, reflecting changes

in the

stoichiometry during

the diffusion _process.

Thereby

it becomes evident that for the _upper

band in _our

spectra,

^{which in} theoretical and _gas

phase

^studies on isolated molecules arises from the CN groups,

slight changes

in the

geometric

structure _{can cause}

significant changes

in the electronic structure _as the orbital

overlap

is

severely

influenced. This close

relationship certainly

_causes the

disappearance

of the metallic

density

of states in the

amorphous (2,5-

DMe-DCNQI)2Cu

film

[7].

^{Our data} suggest, ^{that in} the DOS of all the

DCNQI

based salts the _upper band is of

purely

CN derived orbitals. We notice that the

binding

_energy of this

band and its

shape

decrease from Rb

(Ev E~

₌ I eV

)

to Cs

(Ev E~

= 0.6 eV

).

For the

Ag

salt _a value of

Ev E~

=

0.3 eV has been observed

[28].

For Cu it reaches the Fermi energy. It is this sequence derived from _our

systematic

studies which confirms _our

assignment

of the _upper band.

Accordingly,

the

only

influence of the central atom in the electronic structure of

DCNQI

salts is to shift the

position

of the

uppermost

^{band relative} to that of the Fermi energy, whereas the atomic

parentage

^is unaffected

by

the different central atoms and is of _cyano derived C and N atomic _wave functions. This

assignment

is in line with the Hiickel

results

[I I], however,

_our data _are not in line with the

finding

that the upper band is

always metallic,

I-e-

partially occupied, independent

_on the central atom. In contrast, the central

atom

sensitively

determines the

Ev E~ separation.

Summary.

Metallic

conductivity

of the

(2,5-DMe-DCNQI)~Cu

salt is observed

only

ⁱⁿ its

crystalline phase.

It is caused

by

contribution of

C2p,

and

N2p

molecular orbitals in the valence band.

We

find,

that the molecular orbital

overlap depends sensitively

_on

cristallineity,

and exhibits _a

significant dependence

_on temperature ^and pressure. We state, that the detailed molecular

structure and the

geometric

arrangement are reflected

extraordinarily sensitively

in the

physical properties

of these salts. In

particular,

_we have demonstrated that the

extremely high

values for the

conductivity

at room

temperature

can not be

explained by

admixture of Cu states to the valence levels. The

high conductivity

is caused

by

a pure

organic (CN derived)

band. Its width and

separation

from the Fermi _energy is influenced

by geometric parameters (ordering,

size of the central atom,

crystal field)

and not

by

the electronic contributions of the

central atom.

Acknowledgements.

We

highly acknowledge

the

stimulating

discussions _{with S.}

Hiinig

_as well _as his collaborators for

providing DCNQI.

We also like to thank K. Graf and W. Neu for their excellent technical

assistance in

optimizing

the

preparation techniques.

We thank R.

Dudde,

K. H.

Frank,

and E.E. Koch _as well _as Ch.Pettenkofer and

W.Jaegermann

for

using

their

experimental

setup.

^{This work is}

supported by

SFB 329.

1354 JOURNAL DE

PHYSIQUE

I M 9

References

[Ii

AUMULLER A., ERK P., KLEBE G., HUNIG S., voN SCHUTz J. U. and WERNER H.-P., Angew.

Chem. 98

(1986)

759 _; Angew. Chem. Int. Ed.

Engl.

25

(1986)

740.

[2] voN SCHUTz J. U., BAIR M., WERNER H.-P., WOLF H. C., AUMULLER A., ERK P. and HONIG

S.,

Nato ASI,

Workshop

Menorca, Nato ASI Series, Vol. _:

Organic

and

Inorganic

Low Dimensional

Crystalline

Materials

(1987),

P.Delhaes, M.Drillon Eds. ~Plenum Press,

1987)p.

297.

[3] voN SCHUTz J. U., BAIR M., GROSS H. J., LANGOHR U., WERNER H.-P., WOLF _H. C.,

SCHMEIBER D., GRAF K., GbPEL W., ERK P., MEIXNER H. and HUNIG S.,

Synth.

Met. 27

(1988)

B 249 ; and References within.

[4] voN SCHUTz J. U., WERNER H.-P., WOLF H. C., AUMULLER A., ERK P. and HUNIG S., Proc.

XXIII

Congress Ampere,

Ed.

Maraviglia (1986) p.158.

[5] KATO R., KOBAYASHI H., KOBAYASHI A., MORI T. and INOKUCHI H., Chem. Lett.

(1987)

_p.

1579.

[6] ERK P., MEIXNER H., METzENTHIN T., HONIG S., LANGOHR U., voN SCHUTz J. U., WOLF H. C., SCHAUMBURG G., BURKERT R. and HELBERG H. W., Adv. Mater., in _press.

[7] SCHMEIBER D., GRAF K., GbPEL W., voN SCHUTz J. U., ERK P. and HUNIG S., Chem.

Phys.

Lett.

148

(1988)

423.

[8] ERK P., HUNIG S., MEIXNER H., voN SCHOTz J. U., WERNER H.-P., Liebigs Ann. Chem. (1988) 157.

[9] RACER A., GOMPF B., DORSELEN L., MOCKERT H., SCHMEIBER D. and GOPEL W., J. Molec.

Electron. 5

(1989)

227.

[10] WACHTEL H., Thesis, Universitit

Stuttgart (1990)

_;

WACHTEL H., _voN SCHOTz J. U., WOLF H. C., ICSM 1990,

Synth.

Met. 42

(1991)

1789.

[I Ii

KOCH W. and SEELIG F. F., Z.

Naturjorsch

42a

(1987)

875.

[12] ^KOBAYASHI H., KATO R. and KOBAYASHI A., ICSM 1990, Synth. Met., ⁱⁿ press.

[13] IWAN M., HIMPSEL F. and EASTMAN D. E.,

Phys.

Rev. Lett. 43

(1979)

1829.

[14] IWAN M., KOCH E. E., CHIANG T. C., EASTMAN D. E. and HIMPSEL F. J., Solid State Commun. 34

(1980)

57.

[15] KURTz R. L., STOCKBAUER R. L., MUELLER D., SHIH A., TOTH L. E., OSOFSKY M. and WOLF S. A.,

Phys.

Rev. B 38

(1987)

8818.

[16] THULER M. R., BENBOW R. L. and HURYCH Z.,

Phys.

Rev. 826

(1982)

669.

[17J GHIHSEN J.,

Phys.

Rev. 842 (1990) 2268.

[18] GONzALES A., SCHMEIBER D., TABORSKI J., WOSTENHAGEN V., UMBACH E., _voN SCHOTz J. U., WOLF H. C. and GbPEL W.,

Synth.

Met. 41-43

(1991)

1809.

[19] SCHMEIBER D., JACOBI K. and KOLB D. M.,

Appl. Surf.

Sci. ll/12

(1982)

164.

[20] ERK P., Dissertation 1989, Universitit

Wfirzburg.

[21] TURNER D. W., BAKER C. and BRUNDLE C. R., Molecular Photoelectron

Spectroscopy ~wiley-

Interscience, New York,

1970).

[22] MOCKERT H., SCHMEIBER D. and GOPEL W., Sensors and Actuators 19

(1989)

159.

[23] JUGNET Y., TOURILLON G. and TARN MINH DUG,

Phys.

Rev. Lett. 56

(1986)

1862.

[24] GROBMAN W. D. and KOCH E. E., in Photoemission in Solids II, L.

Ley

and M. Cardona Eds.

(Springer,

Berlin,

1979)

_p. 261.

[25] PFLUGER P. and STREET G. B.,

Polym. Prepr. (Am.

^Chern.

Soc.,

Div.

Polyrn. Chem.)

23

(1982)

122.

[26] ^GROBMAN W. D., POLLAK R. A., EASTMAN D. E., ^{MAAS E.} T., Jr. and Scow B. A., Phys. Rev.

Lea. 32

(1974)

534.

[27J BATz P., SCHMEIBER D. and GOPEL W., Solid State Commun. 74

(1990)

461,

Phys.

Rev. B

(1991)

in press.

[28]

SCHMEIBER D., GbPEL W., LANGOHR U., voN SCHUTz J. U. and WOLF H. C.,

Synth.

Met. 42

(1991)

1805.

Statistical

physics

F. MANDL

(Second edition) (John Wiley

&

Sons) 1988,

385 pages, £ I1.95.

Mandl is _a standard second year text which has been

extensively

used in

England

for the last two decades for the

teaching

of

introductory

_course8 in

thermodynamics

and statistical mechanics _to

physics undergraduates.

The

major

drawback that I found when

using

the book _was the omission of _a treatment of systems with variable numbers of

particles.

This makes the derivation of the Ferrni-Dirac distribution, for

example, unnecessarily complicated.

In the second edition of the work Mandl has corrected this defect

through

the introduction of _a discussion of the Gibbs

grand

canonical distribution. This also allowed him to extend his treatment of chemical reactions. The other

significant

modification in this edition is _a useful clarification of the

thermodynamics

of

magnetic

_systems.

In my

experience

students like the clear

presentation

of the book. It is

fairly

self-contained _; it supposes

only

_a limited

prior knowledge

of quantum states and the kinetic

theory

of gases. The

problems following

each

chapter

_are discussed in _some detail at the end of the book.

Finally

it is at a

price

that

they

can afford

Cohn WILKIN.

Mkthodes

probabiJbtes

_pour Ies

kquatiolw

de la

physique Rddigd

_sous la direction de R. DAUTRAY

Collection CEA-Slrie

SynthJse (Eyrolles, Paris) 1989,

420 pages, 350 F.

L'objet

de cet ouvrage ^est le traitement

approfondi

de certaines

6quations

_aux ddrivdes

partielles (EDP)

et de leurs

solutions,

I l'aide de mdthodes issues de la Thdorie des Probabilitds.

L'objectif pratique

est de mettre en

correspondance

les versions discrdtisbes des EDP _avec les traitements Monte- Carlo des _processus de Markov associds.

L'esprit

de cette ddmarche, reliant

analyse

fondarnentale _et

solutions

numkriques

dlabordes _par Ies

ingdnieurs,

a

ddji

dtd

appliquk

_avec le succls _que l'on sait dans l'dlaboration du traitd de

physique mathdmatique Dautray-Lions

dditd dons la mdme collection.

Le texte peut dtre abordd _{par un} dtudiant de fin de

maitrise,

motivd _par des

d6veloppements

mathdrnatiques

cch6rents. Los concept8

probabilistes

sous lent forrne fonctionnelle sont introduits dan8

le texte. Une familiaritd _avec la th60rie des fonctions r6eIles est

cependant requise. L'ouvrage

est

structur6 _en 4

parties.

La

prernidre

introduit bridvement les notions

probabilistes

dans leur cadre fonctionnel, Ie concept ^{de chaine} de Markov, ainsi _que

I'dquation

de

Kolrnogorov

et ses variantes. Los solutions de contains

probldmes

stationnaires _sont alors

exprim6es

k I'aide de

l'espbrance

conditionnelle et de la chaine de Markov associ6es. La 2°

partie

^d6taille les relations entre processus

stochastiques

et

EDP, et

plus prdcisdment

entre processus de diffusion et EDP du 2° orate. Los processus de Wiener sont alors introduits _en relation _avec le

probldme

de Dirichlet, ainsi _que la notion de

semi-groupe

(celui de Feller

jouant

_un r61e

particulier).

La construction de certains processus

stochastiques

_comrne

solutions

d'6quations

diffiErentielles

stochastiques,

permet par

exemple, d'exprimer

la solution d'un

probldme

d'6volution _avec EDP

parabolique,

I-e-

Kolrnogorov r6trograde,

_{ou son} dual Fokker-Planck.

L'6tude des relations entre processus

stochastiques

et EDP est faite dans la 3C

partie,

^ccnsacr6e aux

probldmes

de transports ^formal1s6s sous

I'aspect

^diffusion

(neutrons

et

rayonnement).

Pour _ce faire, _on

1356 JOURNAL DE

PHYSIQUE

I M 9

y introduit Ies _processus k accroissements

indkpendants

et ceux de ccmptage. ^{La r6soIution}

num6rique

des

Equations

de transport est forte _par la m6thode de Monte-Carlo en

appendice.

Id, _{on a une}

pr6sentation

daire d'un certain

iombre

_de

prob16matiques neutroniques,

k l'aide de la forrnule de

Ka6,

et de la convergence d'un processus de transport avec libre parcours moyen fini _{vers sa} limite diffusion.

La

4°partie

^aborde des thdmes du mdme ordre _pour le traitement

stochastique

de

l'6quation

de

Schr~edinger

en

M6canique Quantique.

Los concepts centraux sont alors

l'analogie

_avec

l'dquation

de la chaleur _avec

potentiel ~processus

de diffusion _{et mouvement}

brownien),

et la fonnule de

Feynman-Ka6.

Ces aspects, bien que non triviaux sont

d6ji

familiers I de nombreux th60riciens. Un r61e

particulier

est

jou6

_par le

semi-groupe impliquant

l'hamiltonien. Los r6sultats de Lieb _concemant le spectre et la stabilit6

61ectrostatique

de la mafidre sont ainsi naturellement introduits.

Au total, on a un ouvrage r6alisant _une

synthdse

incontestablement r6ussie entre

Analyse

fonctionnelle _et

probldmes

fondamentaux _en Th60rie du

Transport

et

Mdcanique Quantique.

Bien _que

produit

_par 5 auteurs, le _{texte est} uniforrne d'un bout k l'autre. Ici aussi, le travafl de

synthdse

est une

incontestable rdussite. Los notations, les espaces fonctionnels utilisds, I'index

syntaxique

sont ddtai1l6s et d'une

grande

utilit6 _pour Ie ccmrnengant.

La

qualit6

de la

prEsentation

est k la hauteur des

produits d6jk dassiques

de _cette s6rie. Le

public

ccncem6 peut ^{inclure les} 6tudiants de DEA de

Math6matiques appliqu6es, Physique thdorique

et

math6matique.

Avec _{un peu}

d'assiduitd,

les

praticiens

nurn6riciens _en th60rie du transport, peuvent en

firer _un

grand

bdndfice.

C. DEUTSCH.

Mkcanique, points matkriels, sofides~

fluides J. Ph. P#REZ

2e

Edition,

Collecfion

Enseignement

dk la

Physique (Masson) 1989,

490 pages, 144 F.

Optique gkomktrique,

ondulatoire et

polarhation

J. Ph. PfREZ

3e

kdition,

Collection

Enseignement

dk la

Physique (Masson) 1991,

483 pages, 175 F.

Ces deux livres, comrne celui sur

l'61ectromagn6tisme

examin6 _{il y a peu} de temps,

appartiennent

I la collection Enseignement de la

Physique

destin6e _aux 6tudiants du Premier

Cycle

de l'Universit6 _{et aux} 61dves des classes

pr6paratoires.

Issus d'un

enseignement

_au DEUG A I Toulouse, ils sont

organisds

_en braves

legcns (dventuellement

destindes I servir de moddles _aux dtudiants

prdparant l'agrdgation).

D6butant _sur des

rappels

de calcul

vectoriel,

le livre de

mdcanique

consacre trds

dassiquement

_sa

premidre partie (14 legons)

k la

cindmatique

et la

dynamique

du

point rnatdriel,

de la

composition

des

mouvements au

probldme

de Kepler et au mouvement d'une

particule chargde

dans _un

champ 61ectrique

et

magndtique,

I l'oscillateur

harmonique libre,

arnorti _ou fores, etc. La seccnde

partie (12

legons) est d6dike I l'6tude des

systdmes

mat6riels, du solide

simple

et _ses mouvements _aux

systdmes

d'oscfllateurs

coup16s

et leurs modes _propres. Une troisidme

partie,

^brave et fort dense (3

legcns)

est consacrde _aux milieux continus fluides. Get ensemble est suivi d'annexes donnant

quelques

constantes utiles et

rappelant

des r6sultats

math6matiques

_sur les

coniques

et sun

l'analyse

vectorielle. Puts viennent

quelques

conseils _pour la rdsolution des

probldmes

de

mdcanique,

des 6nonc6s de

probldmes

dass6s _par

chapitres,

enfin leurs solutions. Une

bibliographie

somrnaire _{et un} index

compldtent

le _tout. Le

petit reproche

_que

je

ferai _conceme la trop

grande

fid61it6 _aux prograrnmes des _concours. J'aurais _en effiet

aims trouver une ouverture mdme trds limitde _{I la}

mdcanique analytique (une

ou deux le~ons hors-

programme auraient suffi !).

Quant _au livre

d'optique,

il

adopte

_une ddmarche

identique,

_{cours sous} fonne de _courtes legons

(32

au

total: 17

d'optique gdomdtrique,

13 sun

l'optique

ondulatoire _et 3 _sur la Iumidre

polaris%e)

avec

probldmes

et solutions. Ici les

probldmes

sont accolds _au

chapitre correspondant,

les solutions 6tant

toujours regroupbes

I la fin

aprds

les _annexes. Get ensemble de facture

pIut6t classique

reste

dgalement

trds fiddle _{au contenu}

requis

_pour Ies _concours I

option physique.

Ces programrnes ^sort

cependant

_assez

largement d6pass6s

dans Ie domaine de

I'optique

cohdrente, _ce

qui

n'est certes pas I

d6pIorer.

La

prdsentation

de cette 3° Edition de

l'ouvrage

est

grandement

am61ior6e _par rapport ^{I celle des 6ditions} ant6rieures, dont Ie Ewe

pr6cfident

est un

repr6sentant, puisque

Ie

style

znachine d dcrire _aux caractdres peu lisibles _a enfin 6t6 abandonn6 _au

profit

d'une

typographie plus

_«

professionnelle

».

Joints _au livre _sun

l'61ectromagn6tisme,

et

malgr6

leur ambition _{un peu} limitde, _ces volumes forrnent

un ensemble

homogdne digne

d'intdrdt _pour l'dtudiant de licence tout autant quo pour l'dldve de

pr6pa.

Paul MANNEVILLE.

Parallel

Algoridnns

in

Computational

Science

D. W. HEERMANN and A. N. BURKITr

Springer

Serie.v in

Information

Sciences

@. Kohonen, ed.),

Vol. 24

(Springer Verlag) 1991,

183 pp., DM 60

(Hardcover).

Computer

experts can be divided into _two groups those who _use computers as a tool _to

study

another

field,

like

physics,

and those for whom the computer ^is an

object

worth

studying

in itselL The first group may simulate for

example large Ising

models, and the second may

develop

new

compilers

or new computer

languages. Usually

eacb member of _{one group} holds the members of the other group in

low _esteem. The present team of experts, ^with

partial experience

in both _camps, tries to build a

bridge

by offering

_a treatment of

parallel computing algorithms

with

examples nearly

all from statistical

physics.

From this book _{we can} leam how _{to use a} computer ^with P different processors, ^{at a} combined

speed

of

hopefully nearly

P limes the

speed

of _a

single

_processor.

After _an introduction, one

chapter explains

for the computer expert ^{who knows} not much about

physics

the two basic simulation methods _: Monte Carlo and molecular

dynamics,

with

emphasis

_on

Ising

models and fluids,

respectively.

Then _we learn about

parallelism,

both from the

physics

and from the machine

point

of view _:

separation

of a lattice into sublattices, communication networks in

parallel

computers,

examples

of

special-purpose

computers.

The

simplest

case of

parallel algorithms, «replication»,

distribute, P different lattices _onto P different _processes,

simulating

them for

example

at P different temperatures. More

sophisticated,

and thus

explained

in much greater ^detail as the _core of the book, is «

geometric

_»

parallelization

where _a

large

lattice _or system ^is

separated

into P

big

chunks _; each such sublattice is dealt with

by

_one of the P processors who thus have to communicate the status of their border sites to the

neighboring

processors.

For the _case of

long-range interactions,

_as well _as for _some

polymers,

_a third type of _« data

parallel

_»

programming

h

explained,

where for

example

each of the P processors follows the _same

particles throughout

the simulation.

A final

long chapter

introduces _us to the

programming language

OCCAM, which is useful

particularly

for the most

widespread parallel

computer systems based _on

Transputers (formerly

T800, now

T9000).

In the

appendices,

_many

explicit

_{programs are} listed, and many further

examples

_are left for the

numerous exercises.

A

physicist

finds here an excellent introduction into the

mysteries

of

parallel computing

_; this reviewer believes that the supercomputers ^{for the} next century will be

massively parallel

and difficult to program computers. ^{The reader finds}

explicit plots

of

speed

_versus number of processors,

proving

the

bureaucratic

principle

than too many processors for _a small lattice _{are a} hindrance and not a

help.

The

examples

_are

problems

which the reader from

computational physics presumably

has

already programmed

before _{on a} normal computer _; ^whether readers from

chemistry, biology,

_or other sciences will find these

examples

also

interesting

is not so clear.

Personally

I

prefer

to read about

programming by looking

at

explicit

_propams. That would have been difficult here since the types ^of communication needed, and _even the

languages

used, are not yet dear.

Thus it _{was a}

good compromise

to write most of the book in rather

general

terms and to shift OCCAM examples to the very end

(after

_nasty remarks

against

FORTRAN in _an earlier

chapter).

I would have

1358 JOURNAL DE PHYSIQUE I M 9

liked _to read _more about the

programming simplifications

which _are

possible

if all _processors work

independently

but share the _{same memory ;} here _even

explicit

FORTRAN code

might

have

helped.

Also,

books in this

rapidly developing

field _must be

printed

^faster.

Dietrich STAUFFER.

In&oduction to the Mathematics of

Quasicrystals

Marko V. JARIC Ed.

(Acadenfic Press) 1989,

226 pages, £ 59.50.

Cet _ouvrage est le second d'une sdrie consacrde I

«Aperiodicity

and order _». Le

premier

volume,

« Introduction to

quasicrystals

»

prdsentait

six _{articles de revues}

sun les

sujets

suivants _: coordination

icosakdriques

clans les cristaux

mdtalliques,

ordre I _{courte et} I

longue

distance de type

icosaddrique

dans les cristaux, les _verres et les

quasicristaux,

m6tallurgie

des

quasicristaux, quasicristallographie,

stabflitk et dEforrnation dans les solides

quasicristallins,

syrndtrie,

dlasticitd _et

hydrodynamique

dans les structures

quasipbriodiques.

Le second volume, conforrndment k _son

titre,

_est sensiblement

plus

forrnel _que le

premier.

C'est

6galernent

une

compilation

de

cinq

articles de _{revue, ou} de

synthdses,

sur certains aspects

math6matiques

des

quasicristaux.

Le

premier

article, _par

Madorie

S6ndchal, traite du

probldme gdndral

du pavage de

l'espace.

Elle ddcrit les limitations des

syrndtries acceptdes

_par les pavages

pkriodiques

et montre que

plusieurs

mdthodes de construction existent pour paver

l'espace

de fa~on _non

pkriodique, quoiqu'en prdservant

un ordre k

grande

distance.

Le second article s'attache I tons les aspects ^des pavages de Penrose. En

particulier

les

probldmes

lids I la croissance d'amas infinis

parfaitement

ordonnds sort exarninds _en ddtail. L'auteur de _cette

partie

est

Roger Penrose lui-mdme.

Le troisidme article est dcrit _par P. Kramer et R. W. Haase. La thdorie des groupes

appliqude

_aux

quasicristaux icosaddriques

_y est

ddveloppbe

_{avec un} trds

grand

luxe de

rigueur mathdmatique.

Andrd Katz traite ensuite de certaines propridtds locales de rdseaux de Penrose I trois dimensions. Il ddcrit la m6thode de

projection,

dont il est l'auteur _avec Michel Duneau, d6finit les

propri6t6s d'isomorphisme

local, donne _une classification des types

d'arrangement

des cellules _{et propose} des

«

matching

rules _» pour rkaliser la croissance des r6seaux.

Le

cinquidme

et demier article, _par J.

Bohsung

et H. R. Trebin, s'attache I introduire la notion de d6fauts de r6seau darts les structures

quasip6riodiques.

Le

probldme

des dislocations, _{avec ce}

qui

les diffi6rencie nettement de leurs «sernblables» dans les cristaux

pbriodiques,

est en

particulier

bien illustrd.

Le troisidme volume de la

sdrie,

_« Extended Icosahedral Structures _»

ddji

_paru, est une

compilation

des dif§6rents moddles

qui

ont >t>

propos6s

_pour dbcrire la _structure des

phases icosa6driques expbrimentalement

observde.

Dans la

pr6face

du second volume, il est dcrit _que cette s6rie _est kditde I l'intention des ddbutants dans le domaine des

quasicristaux.

Cola apparait ainsi seulement en

partie.

II

s'agit

li, _par contre, d'une

excellente documentation de base pour les chercheurs de _ce domaine.

Chdstian JANOT.