Proton mobility in molybdenum bronzes

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Proton mobility in molybdenum bronzes

A. Cirillo, J.J. Fripiat

To cite this version:

A. Cirillo, J.J. Fripiat. Proton mobility in molybdenum bronzes. Journal de Physique, 1978, 39 (3),

pp.247-255. �10.1051/jphys:01978003903024700�. �jpa-00208760�

PROTON MOBILITY IN MOLYBDENUM BRONZES

A. CIRILLO and J. J. FRIPIAT

C.R.S.O.C.I.,

^{C.N.R.S. rue de la}

Férollerie,

^{45045 Orléans}

Cedex,

^France

(Reçu

^{le 18}

juillet 1977,

^{révisé le 24 octobre}

1977, accepté

^{le 6 décembre}

1977)

Résumé. ²⁰¹⁴ Des bronzes de molybdène ^sont

préparés

^en exposant ^à

l’hydrogène

gazeux des micro- cristaux de

MoO3

dont la surface est recouverte de petites

particules

^de

platine.

^{L’étude en résonance}

magnétique protonique pulsée

^{a été effectuée} pour des bronzes de

composition H1,6MoO3

^{entre 160}

et 320 K à 90, 40 ^et 15 MHz. Ces bronzes semblent se comporter ^comme des conducteurs

métalliques

et du point ^{de vue} relaxation, les résultats sont

comparables

^{à ceux} qui ^ont été relatés pour les hydrures

métalliques.

La vitesse de relaxation

spin-réseau (1/T1)-1

^est constituée

principalement

^{de trois} contributions dues

respectivement

^à l’interaction avec les électrons de conduction

(1/T1)-1e

^{et à} l’interaction

dipo-

laire proton-proton

(1/T1)-1d

^et proton-centre

paramagnétique (1/T1)-1ed.

Ces deux dernières sont modulées _{par les} mouvements du proton dans le réseau de

l’oxyde.

T1 ^{a été} analysé par la théorie de Torrey modifiée par Krüger. ^Le rapport ^du

déplacement quadratique

moyen du proton ^à la distance minimale

d’approche

^{de deux} protons ^{semble ~} 1, ^ce

qui implique

^{un mouve-}

ment de diffusion.

L’énergie

d’activation, déduite de la variation du temps ^de corrélation en fonction de la température ^{est ~} 0,3 ^eV.

La raie est

asymétrique

^{et elle est}

déplacée

par rapport à celle de l’eau absorbée par l’oxyde ^ou

à celle du néopentane. ^Le

déplacement

^est faible, ^ce

qui

serait à relier à un affaiblissement de la densité

électronique

^au

voisinage

du noyau

provoqué

par la diffusion.

Abstract. ²⁰¹⁴ Molybdenum ^{bronzes were} prepared by exposing

microcrystalline

MoO3, ^covered

with small

particles

^of Pt, ^to gaseous

hydrogen.

^A

pulsed

proton

magnetic

^resonance study ^was

made of

H1.6MoO3

^{bronzes between} 160 and 320 K at 90, 40 and 15 Mhz. The bronzes behave as

metallic conductors and, ^{from the}

point

^{of view of} relaxation, ^are

comparable

^{to metallic} hydrides.

The

longitudinal

relaxation rate

(T1)-1

has three main contributions : one from the interaction between protons and conduction electrons

(T1)-1e,

and the others from the proton-proton

dipolar (T1)-1d

^and proton-paramagnetic ^centre interactions

(T1)-1ed.

T1e ^and T1d ^{are modulated} by ^the proton mobility in the oxide lattice, and T1 ^{has been treated} using

the

theory

^of Torrey, ^modified by Krüger. The ratio of the mean square displacement ^to the square of the distance of closest

approach

^{is much} greater ^than 1, ^which implies diffusion. The activation energy derived from the variation of the correlation time with temperature is about 0.3 eV.

The NMR line is

asymmetric

^{and is}

displaced

^{from that of water absorbed on} the oxide. The dis-

placement is very small due ^to the small electron

density

^seen by the nucleus as a result of diffusion.

Classification Physics ^Abstracts

76.60

1. Introduction. ^- Powdered

molybdenum

^trioxide

in the _presence of

finely dispersed platinum

^{metal will}

react with

hydrogen

^via

hydrogen spillover

^{to form}

hydrogen molybdenum ^bronze, HxMo03,

^at tempera-

tures between 50 °C and 120 OC. In these

compounds

^x

has a maximum value around 1.7 in violation of the range of

compositions usually accepted

for bronzes.

The formation of the

hydrogen molybdenum

^bronze

can be visualized as

occurring

^{in three} steps :

first,

dissociative

chemisorption

of molecular

hydrogen

^on

the surface of

platinum ; second,

transfer of the

hydro-

gen

species

^{formed to the oxide - a} process aided

by

^a

carrier ;

^and

third,

the invasion of the oxide lattice.

Water has been shown to be an efficient carrier for the

second

step [1],

^{and we note that even when}

working

with

dry hydrogen

gas it can be assumed that the surface

hydration produces

^{a small amount of water}

which could act as a carrier.

Other

possible products

of this reaction are lower

oxides,

^{such as}

Mo20s,

^and

oxyhydroxides,

^such

as

Mo03-x(OH)x.

Sermon and Bond

[2]

^{have shown}

by gravimetric

measurements and differential thermal

analysis

that lower oxide formation does not occur

below 200 °C. Our volumetric measurements of water released

during

the bronze formation confirm this

results

^{and NMR} results show that there is no noti- ceable formation of a

hydrated

lower oxide such

as

Mo205 . H20. ^Also,

^{the observed}

proton magnetic

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01978003903024700

248

resonance is far too narrow to be due to any oxy-

hydroxide species,

which would

typically

^exhibit

resonance lines of the order of several gauss.

In order to avoid reduction and the formation of water, the ^NMR measurements were never per- formed at temperatures

higher

^{than 50 °C.}

It has been

suggested by

Sermon and Bond that upon

adsorption,

^the

hydrogen

^{atom donates an}

electron to the conduction band of the bronze-

forming

^{oxide. We} have noted that when a

sample

^of

the bronze is

placed

^{within an EPR}

cavity,

^it

produces

the same effects as would be

produced by

^{a metallic}

powder,

^that

is,

^{the resonance}

frequency

^{of the}

cavity

is

shifted, the Q

^{of the}

cavity

is reduced and

tuning

^is

extremely

difficult. Therefore in the relaxation ^ana-

lysis

^to

follow,

it will be assumed that the conduction band is

occupied

^and the behaviour of the

protons

^is

comparable

^to that observed in metal

hydrides [3].

This means that the

longitudinal

relaxation rate should contain a contribution due to the interaction of the protons with the conduction electrons as well as a

dipolar

contribution modulated

by

^the proton ^motion.

The proton

mobility

in the similar

hydrogen tungsten

bronze has been studied

by

^Dickens

[4],

Nishimura

[5]

and Vannice et al.

[6]

^with

seemingly contradictory

^{results. In}

relatively large crystals,

Dickens asserts that the

protons

^{are not mobile at room} temperature, ^{whereas the} other authors show that in

W03

^made from thinner

crystals,

^the protons ^are mobile in this temperature range.

Pure

Mo03

^{has an} orthorhombic

crystal

^structure

[7]

with a ⁼ 13.85

Á,

^{b = 3.696}

Á,

^{and c = 3.966}

^Á.

From a structural

viewpoint,

^the formation of a

bronze with a

stoichiometry

^{such as}

Hl.6MO03

^must

lead to an

expansion

of the lattice. We estimate the distance between protons ^{in a}

doubly-occupied

^inter-

stice to be about 2.5

Á

or less. This situation would lead to

extremely strong

electrostatic

repulsion.

^One

way ^to stabilize this

configuration might

be the for- mation of ^an associated

pair

^of

hydrogens

^{in the form}

of the

H 2

molecule-ion. This could occur

by

^the

combination of two protons

receiving

^an electron from the conduction band. The

H’

^{would rotate in the}

interstices but would not diffuse

readily.

^{An increase}

in

temperature might

^{reverse this} process

allowing proton

^{diffusion to} occur more

readily.

2.

Experimental.

^{- 2} .1 SAMPLE PREPARATION. ^-

The

platinum

^was

dispersed

within the

powdered molybdenum

^trioxide

(anhydrous, analytically

pure

reagent) by impregnation

^{with the}

appropriate

^volume

of ^a 0.1 M solution of

hexachloroplatinic ^acid,

followed

by evaporation

^{and air}

drying

^{at 120 OC for}

at least two hours

[8].

^The

hydrogen molybdenum

bronze was

prepared by exposing

^the

molybdenum

trioxide

containing

either 0.5

%

^{or 2.0}

% platinum (by weight)

^{to an initial} pressure of 600 torr of

dry hydrogen

gas ^at either 60 °C or 120 OC for _up to three hours. The

specific

^{surface area of the}

Mo03 powder

was 4

M’/g (BET),

^{and the} average

particle

^size

around

10 g (TEM).

The

stoichiometry

^was calculated from the

uptake

of

hydrogen

^{which was measured}

volumetrically.

^The

Pt/MO03

^was

outgassed

^at the reduction temperature

prior

^{to the formation} of the bronze.

2.2 NMR MEASUREMENTS. ^-- Sealed _pyrex tubes

(10

^mm

o.d.) containing

^about 2 grams of the bronze

were used for the measurements, with ^an

equilibrium

pressure

of H2 (100 torr) remaining

^{above the}

sample.

The proton

magnetic

^resonance spectra ^{were obtained} from the Fourier Transform of the FID

(free

^induction

decay) signal using

^a Bruker SXP

pulse Spectrometer equipped

with the usual variable

temperature

^acces- sories. The

longitudinal (or spin-lattice)

^relaxation

time, Tl,

^was obtained from a 180-T-90

pulse

sequence and the

resulting signal

^was accumulated 20 times to

improve

^the

signal

^to noise characteristics. It should be

emphasized

^that

only

^one

Tl

^was measured in all ^cases

reported

^{here. The} transverse

(or spin-spin)

^relaxation

time, T2,

^was measured from the

spin-echo produced by

^{a 90-i-180} sequence. Below 200

K,

^the

signal

broadens so

rapidly

^{that the}

rigid

lattice line width ^was not measurable.

Measurements were also

performed

^{on a}

similarly prepared Dj.rM003

^bronze

using

the Bruker SXP Pulse

Spectrometer

^{as well as a} Varian DP-60

Spec-

trometer. These failed to detect _any

2 H

resonance

signal despite

extensive accumulation and a careful search for

extremely

^broad resonances. The

inability

to detect the

2H species

^{in the} bronze will be discussed below.

3. Results and discussion. ^- 3 .1 LINESHAPE. ^- The temperature variation of the proton ^{NMR line for}

a bronze with x ⁼ 1.53 and 0.5

%

^Pt

(w/w)

^{is shown}

in

figure

^1. This behaviour is

typical

of all the bronzes studied so

far,

^{and does not}

change

^{if the}

platinum

content is raised to 2.0

%.

The line is

asymmetric

^at

temperatures

between 210 K and 333

K ;

^below

that,

^it

slowly

becomes Lorentzian and broadens

rapidly.

^It

should be noted that the centre of the low

temperature symmetric

line is located

exactly

^{at the}

position

^{of the}

centre of

gravity

^{of the}

asymmetric

line. There is a

slight

shift of the proton ^{resonance which is constant}

over the

region

^of

temperature

studied. The

magnitude

of the shift is _very

small, 7,3

±

0,7

^x

10-4 %

^as

measured with respect ^{to a} n-pentane ^standard contained within a small

capillary

in the bronze

sample. Figure

^{2 shows the room}

temperature proton

resonance of the same bronze taken for two different values of the field. The increase in linewidth with

increasing

field is characteristic of

anisotropic

magne- tic

broadening.

^{At room} temperature ^{the distance}

between v, and vl,

for this line is 0.6 G at 90 MHz.

(v

Il

-

vi)

^{should be}

proportional

^{to the}

frequency

^but

the

uncertainty

^{in the}

positions

^{of the} V.1

and v

Il

components

^{at 15 MHz}

precludes

any definite conclu- sion in this respect.

FIG. l. - The temperature dependence ^{of the} proton ^resonance line for the H1,53MOO3 ^{bronze formed at 120 OC.}

FIG. 2. - The room temperature proton ^{resonance line of} H1.53MoO3 is shown for two values of the applied field. The _asym- metric shape and the increase in linewidth with increasing ^{field are}

characteristic of anisotropic magnetic broadening.

As

previously

^{mentioned we were unable to observe}

the

2H

resonance in an

analogous D1.66Mo03

^bronze.

This is

unexpected

since the

2H species

^{has been}

observed in various metal

hydride

systems

[9, 10]

where both

strong quadrupolar

interactions and interactions with conduction electrons are known to exist. If the deuterium atoms are in a non-cubic

environment,

^{the electric}

quadrupole

interaction would be _very strong ^{and the resonance would be} both broadened and weakened. The asymmetry ^{of the}

proton signal

indicates that such a case exists.

Thus,

we conclude that the extreme width of the

2H

reso- nance,

coupled

with the lower

sensitivity

^{of NMR for}

the

2H species,

makes the deuterium resonance

unobservable in the deuterium

molybdenum

^bronze.

The observed

temperature dependence

of the line-

shape

^{is one that is not}

normally

encountered. For most systems, ^{the NMR} line becomes more

symmetric

as the temperature ^{increases due to motional}

averaging of any anisotropic

environment. The

anisotropy

^{of the}

pure

Mo03 crystal

^structure has been described

[11]

and _may lead to field

gradients

^{in the}

hydrogen molyb-

denum bronze. There is also the

possibility

^{of non-}

uniform distribution of conduction electrons in ^an oxide such as

H,,MO03.

^{For these reasons the ani-}

sotropy

of the NMR line is not

surprising

^but

they

^fail

to

explain

^the temperature

dependence

of the line-

shape

which will be treated in Section 3.4. The eventual

tendency

^{toward a} Lorentzian line

shape

^at

low

temperatures suggests

that motion still exists in the system. This could be due to rotational motion since the modified

Torrey theory

^to be described in

Section

3.2 does not

distinguish

between translation and rotation for the

limiting

^cases.

It should be noted that _any attempt ^to

produce

^a

bronze of

Ho.5Mo03 composition using

^{a limited}

amount of

H2

gas ^{or a} mixture of

H2

^{and He} gases leads to a

heterogeneous product consisting

^{of violet}

regions

^{that are most}

probably

the bronze with x = 1.6 and _gray

regions

^that

obviously

^{remain as}

Pt/Mo03.

This suggests that the bronzes are formed

grain-by- grain,

^that

is,

^{once a}

particle

^of

Pt/Mo03

^{has been}

converted to the

bronze,

it increases the

probability

of bronze formation within

adjacent particles.

We have formed a bronze at 60 °C from a gaseous mixture

of 70 % D2

^and

30 % H2 (atom percent)

^which

has a total x ⁼ 1.66. If we assume that the same

percentage ^of

hydrogen

and deuterium exists in the bronze as in the _gas

phase,

^we would have a system

composed

^of

Ho.5MO03

⁺

D1.IMo03. Also,

^{there is}

no reason to assume the

segregation

^of

hydrogen

^and

deuterium,

^{so we} _expect the

hydrogen

^{to be}

evenly dispersed throughout

^the

homogeneous

bronze. This bronze will be referred to as

(H

⁺

D)1.66MoO3.

The

temperature dependence

^{of the}

lineshape

^for

the

(H

⁺

D)1.66Mo03

^{is shown in}

figure

^{3. It is}

striking

that the addition of

2H

atoms in such a

large

ratio has no effect whatsoever on the

asymmetric

lineshape

^{of the}

^bronze, although

^the

intensity

^{of the}

250

FIG. 3. - The temperature dependence ^{of the} proton ^resonance line for the (H ⁺ D)1.66MoO3 bronze formed at 60°C. In this

sample, H/Mo ^{= 0.56 and} D/Mo ^{= 1.10.}

line is decreased due to the smaller number of ’H nuclei.

Using

^the

H1,64Mo03

^{as a} standard for _compa- rison

of integrated

^areas normalized

by

^{the amount of}

sample

in the NMR

probe,

we calculate x ⁼

0.56:t

^0.05 for the

bronze containing

^both

hydrogen

^{and deute-}

rium. This _agrees with the

previous assumption

^{that the}

percentage ^{of atoms} in the bronze follows that of the gas

phase.

The similar behavior of the

’H

resonance in the two

samples

confirms the fact that the structure of the two bronzes is the same

(as expected)

^{and that the}

important

contributions to the line

shape

^{in the}

high temperature

range do not come from the nearest-

neighbour

interaction of the proton. This evidence does not

discount, however,

the fact that associated

pairs might

^{exist at lower}

temperatures, perhaps

^evi-

denced

by

^the

slightly larger

linewidth of the deute-

rium-containing

^{bronze at} very low

temperatures.

The

2H

resonance was not observable in the

(H

⁺

D)1.66MoO3

^bronze.

3.2 LONGITUDINAL RELAXATION TIME. ^- Since most of the measurements have been carried out in the

temperature region

^where

T2 is temperature dependent

and thus where motional

narrowing

^{occurs the}

spin-

diffusion contribution _may be

neglected

^with respect

to the

proton self-diffusion,

ⁱⁿ agreement ^{with Roinel} and Winter

[12].

The

longitudinal

relaxation ^rate in the

hydrogen molybdenum

^{bronzes therefore} consists of three contributions. The first arises from the interaction between nuclear

spins

and conduction

electrons,

^the second from the interaction between nuclear

spins

^and

paramagnetic

^centres

(e.g. M05 +),

and the third from

dipolar spin-spin

interaction. The second and third

contributions are modulated

by

^the proton ^motions in the solid.

Torrey’s theory [13]

and its modification

by Krüger [14] permit

the calculation of the Power Function for

oscillatory

motion and translational diffusion. Thus we can write :

where

(Tl)e

describes the first contribution mentioned

above, (Tl)ed

^the

second,

^and

(Tl)d

the third. Accord-

ing

^to

Abragam [15], (Tle)

^{T is}

temperature indepen-

dent. For an

isotropic Knight

^shift

(K), Korringa’s relationship

indicates that

Korringa’s equation

^{could not be}

applied

^{as such in}

our case since the

protons

^are mobile. Indeed Fert and Averbuch

[16]

show that the effect of a

proton

^vibra- tion is to decrease the observed

Knight

^shift

by

^a factor which

depends

upon the mean square

amplitude

of the vibrational motion. Since the latter is tempera-

ture

dependent,

the shift becomes

temperature depen-

dent. The small

magnitude

of the shift indicates ^a small

amplitude

of the electron ^wave function at the

proton

nucleus. The

T1e

contribution in

equation (1)

^was

estimated

graphically.

^The

experimental

limitations in the

high

^{and low}

temperature

ranges,

already mentioned,

^{do not}

permit

^{a better} accuracy.

Concerning ( 1 / Tl )d

^and

(1/T1)ed,

^{we can use the}

Torrey relationship

^modified

by Krüger

^{for a}

thermally

activated diffusion _process and write :

and also :

where yl,s ⁼ úJ¡,S ’l’co

The constants are defined as :

in which N is the number of

spins

per

cm3, d

^{= H-H}

distance, Jpc

⁼

H-parâmagnetic

^centre

distance,

^and

the other

quantities

have their usual values. The

intensity

function for translation is

given

^{as :}

where :

w + ww

and : -.

v

The parameter ^a is defined ^{as :}

where ( r2 )

^{is the mean} square

jump

distance and d is the distance of closest

approach

^{between two interact-}

ing spins.

^{In this}

theory

the functions _g, and _g2

give

the

relationships

between the relaxation rates and the correlation

time,

where D is the diffusion constant.

We can evaluate

roughly

the contributions from like and unlike

spins by calculating

^{the constants defined}

in

equation (8). Assuming

^the

density

of the bronze to be 4.5

g/cm3,

^{we calculate}

NI

^{= 3.0 x}

1022 protons

per

cm3. Taking

^{d = 2.5}

Á,

^we then calculate

Kt,like =

^2.48.

Similarly,

^{we assume}

Ns

^{= 1 x}

¹⁰¹⁹ spins

per

cm 3

and

dpc

⁼

10 A. Thus, Kt,unlike

^{= 3.61. In this case,}

dpc

^{has been}

arbitrarily

^{taken as 10}

^Á

to account for the

boundary

outside of which the protons ^{are not} shifted from resonance under the influence of para-

magnetic

^centres

(e.g. ^{Mo5 +}

^or

impurities). If dpc

^were

smaller

by

^a factor of two,

Kt,unlike

^{would be much}

more efficient for relaxation than

Kt,like,

^{but as a first}

approximation they

may be considered ^as almost

equal.

^{To assume that}

Ns

^{= 1 x}

¹⁰¹⁹ spins

per

cm3

is

surely

^a

rough approximation

^and

nothing

^{is known}

conceming

^the

position

^{of the centres relative to that}

of the

protons.

Should these

paramagnetic

^{centres be}

concentrated on the

surface,

their influence would be less

important.

Conceming

the functions 9l,like and g 1,unlike’ ^the numerical values calculated

by Krüger

show interest-

ing

^{features. For the}

dipolar

^case

(like),

gl,like goes ^{to a} maximum which is scattered about _W’Cc ⁼ 1. For WT. «

1, gl,like is approximately independent

^{of the}

value of _a, whereas in the

region cor,, »

^{1 the}

depen-

dence _upon a becomes

strong.

^We recall that ^a is the

ratio of the mean square

jump

^{distance to} the distance of closest

approach

^{between two}

interacting spins.

^For

the case in which the

paramagnetic

^{centre is}

interacting

with the

proton (unlike),

the results are

approximately

the same, except for the absolute value of the maximum which is

lower,

^{and a second maximum} appears in the

region

^where cos Te ⁼ 1. This maximum is much less

pronounced (it

appears ^{as a} shoulder*in the monotonic decrease of gl,u.lik, ^with respect ^to

úJ’tc).

^{As a conse-}

quence of this

superposition

^{of the two}

maxima,

^the

relaxation rate rises more

slowly

than the correlation time in the

region co-r,, «

cos ’tc.

Therefore,

^the appa- rent energy of activation derived from the correlation time is greater ^{than that} derived from the

slope

^{of the}

variation of the

spin-lattice

relaxation time with temperature.

Since it is

impossible,

^{in the} present

situation,

^to

distinguish

^between

(l/7B)d

^and

(l/7B)ed?

^the

experi-

mental results will be treated in two ways

depending

upon the

assumption

^of

dipolar

interaction or that with

paramagnetic

^centres. Calculations will be made such that the

experimentally

observed maximum in the

plot

^of

(llT1)obs

^versus

1 IT

^divided

by

g 1

yields

^an

observed

Kt.

This so-called

KobS

will be used to cal- culate the variation of

Tl

^with

respect

^to

1/7B

^{This will}

allow us to

approximate

the value of ^a to obtain the activation _energy of the

proton

motion and

ultimately

the variation

ofïc

^with

1/T.

As we are also interested in the

frequency depen-

dence of

Tl,

it should be

emphasized

that the overall correlation time used in the above treatment results from two contributions :

where _rs is the

longitudinal

relaxation time of the

paramagnetic

^{centre. Navon}

[17]

has shown that _Te is

frequency dependent

because of the contribution of the electron

spin-lattice

relaxation

timers.

3.3 ANALYSIS OF THE LONGITUDINAL RELAXATION RATE. ^- The contribution to the

longitudinal

^relaxa-

tion rate due to interaction with conduction electrons

was removed

using equation (1)

and the data shown in

figure

^{4 for a}

Hl.-13MO03

bronze formed at 120 °C.

It is assumed that in the

high

^{and low} temperature

regions

the motion of the protons will be either too

rapid

^{or too slow to} contribute

efficiently

^{to the}

relaxation. Thus we may write :

The

slope

taken from the

(Ti)obs

^versus

1/Tcurve gives

the constant

(Ti)e T,

which for this system ^was about 63 ± ^{5 s K. To} obtain better _accuracy for

(T1)e T,

it would be desirable to

perform Tl

^measure-

ments at lower and

higher temperature,

outside the range ^were

they

^{are not affected}

by

the motion.

Unfortunately

^{this was}

impossible

^for

experimental

reasons : above 60°-100

OC,

reduction of the bronze to lower oxides starts

slowly

^{whereas at low}

temperature

the NMR

signal

^broadens

beyond

^detection.

252

FIG. 4. ^- The temperature dependence of the observed longitu-

dinal relaxation time at 90 Mhz (e) and 40 Mhz (.). ^{The value}

of (T 1)e ^T in s K is taken from the slope of the line.

Once the

Tle

contribution has been removed from the total observed relaxation rate, ^the

theory of Torrey

modified

by Krüger

^{can be used to treat the}

remaining

components. ^{From the} maximum relaxation rate,

Kobs

^was calculated for a ⁼ oo and this value used to obtain the ratio

(N/d) assuming

^{first the} pure

dipolar

interaction and then interaction with

paramagnetic

centres

only.

^The proton ^content of the bronze cal- culated from the volumetric measurements of the

hydrogen uptake

^{was 2.9 x}

¹⁰²²

protons per

cm3.

In the

dipolar

^case, the closest distance of

approach

was 1.3

A ;

^{for the case} with interaction between proton ^and

paramagnetic

^centre

only, assuming NS

^{= 1 x}

1019, gives dpc

^{= 4.6}

^A.

^{With a surface}

area of 4

m2/g

^and 2 grams of

sample,

^we estimate the maximum number of surface

hydroxyls

^{to be of the}

order of 1 ^x

1019.

Since there is no measurable water

given

^off

during

bronze formation below 50

OC,

we would estimate that this number

corresponds

to the number of

M05 + species

formed. It should be noted that Sermon and Bond

[2]

^{measure much}

less than this

by

^EPR.

Adding

^{to this a maximum}

of 100 _ppm of other

magnetic impurities,

^{we arrive}

at 1.5 x

1019 spins jcm3

^{as an} estimate of the

highest possible

^{content of}

paramagnetic

^{centres in} the bronze.

If the number of

paramagnetic

^centres is much less than

this,

^their average distance from the proton ^would be so

large

that their effective contribution could come

only through

^a

spin-diffusion

mechanism. The _pro- nounced temperature

dependence

^{allows us to discard}

this

hypothesis. Therefore,

^{it seems} reasonable to assume that the

greater

contribution is from the

dipolar interaction,

^{and we have a} system that behaves in a manner similar to that of the transition metal

hydrides. However,

the distance of closest

approach

calculated above is smaller than the

probable

^diameter

of the

interstices, although

it is of the same order as the intemuclear distance in

H’

Figure

^{5 shows a}

plot

of the correlation time

’rd ^versus

IIT

^{for a = oo. Thé} activation _energy

FIG. 5. ^- The temperature dependence ^of Td, the correlation time calculated from (Tl)d using equation (6), assuming ^{a = oo. These}

data were taken from the Hl,s3Mo03 ^{bronze at 90 Mhz} (o), ^{40 Mhz} (Â) and 15 Mhz (a).

FIG. 6. ^- The temperature dependence of (Tl)d ^{for the} Hl,s3Mo03 bronze shown for three values of the applied field. The solid lines represent the theoretical values predicted by the modified Torrey

theory if Ea ^{= 7.23} kcal/mole ^{and a = oo.}

is 7.2

kcal/mole.

^{A similar}

plot

^{for a = 0}

gives Ea

^{= 11.2}

kcal/mole.

^The

assumption

^{of a = oo}

gives

the best linear fit to the data and the more reasonable value for d.

Figure

^{6 shows a}

plot

^of

(Tl)d

^versus

1/T

^{for the}

data taken at

90,

^{40 and 15 MHz} in which the solid lines

represent

the theoretical values

predicted using

a ⁼ oo and

Ea

^{= 7.2}

kcal/mole.

^In view of the

approximations

made in the calculation

(for

^{instance :} correction for the contribution from the conduction

electrons, etc...)

the fit is

acceptable. Using

^{a = 0 and}

Ea

^{= 11.2}

kcal/mole gives

very poor agreement. ^The

experimental

and theoretical data are summarized in table I. The

relatively large

deviation in the 40 MHz data could be due to a contribution from

(TI)ed if,

^as

Navon has

shown,

^{this term is}

frequency dependent (see equation (9)).

Similar data taken for

H1,64MOO3

bronze formed at 60°C are shown in

figure

^7. The value of

(TI)e T

is ^N 72 s K. The minima are broader than in the

previous

^case

indicating

^a

greater

distribution of

FIG. 7. ^- The temperature dependence ^of (Tl)d ^at different values of the field for the H 1.64Mo03 bronze formed at 60 °C. Also shown is the transverse relaxation time, obtained from spin-echo

measurements at 90 Mhz.

correlation times. The correlation times have been calculated in the manner

previously

described and are

shown in

figure

⁸

plotted

^{as a function of}

1/T for

^both

=

a ⁼ oo and a ⁼ 0. The values of the activation

energies

taken from this

plot

^{are 6.9}

kcal/mole

^and

11.3 kcal/mole respectively.

The correlation time rd calculated for ^{a =} oo is in

good

agreement ^{with that} obtained for the

Hl.s3Mo03

^bronze.

FIG. 8. - A plot ^of Td ^versus 1000/Temp ^{for the} H1.64Mo03

bronze assuming ^{a = oo} (0) ^{and oc = 0} (,9,). Also shown is the

same plot ^{for the} (H ⁺ D)1,66MOO3 ^bronze assuming ^{ce = oo} (.) .

A

comparison

^of

Ti

^and

T2

data taken for the

Hl.1,4MO03

^and

(H

⁺

D)1.66MO03

bronzes formed at 60 °C is shown in

figure

^{9. The}

spin-lattice

^relaxation

times for the two

samples

^are identical above room

température ^but the shift in the minimum and the steeper

slope

^{in the}

region

^{where cor » 1 for the}

bronze

with lower

hydrogen

^{content indicates a}

higher

activation _energy

for

motion. For this

sample, (Tl)e

^{T ri 241 s}

K,

e.g. much

higher

than in the two

previous hydrogen

bronzes. This

unexplained

^increase

would mean that the conduction electron contribution to the observed relaxation rate is much smaller

(by

^a

.

TABLE 1

Data

taken from

^{the minima}

of (Tl)d

^versus

1/T for H1.53Mo03formed

^{at 120 °C}

254

FIG. 9. ^- A comparison ^{of the} longitudinal ^and transverse relaxa- tion times for the H1,64MOO3 (e) ^and (H ⁺ D)1.66MoD3 (a)

bronzes formed at 60°C. The data were taken at 90 Mhz.

factor of ~

4)

than those found for the

hydrogen

bronzes even

though

^the

Knight

shifts do not vary, within the limits of the measurements. A

plot

^of ’rd versus

IIT

^for

(H

⁺

D)1.66Mo03

is included in

figure 8,

where the activation _energy is found to be 9.5

kcal/mole.

^A summary of the data for the two bronzes with x 1.6 is

given

^{in table II.}

From the data taken for the two bronzes formed at 60 °C we can

attempt

^to evaluate the relative

magnitudes

^{of the}

(Tl)d 1

^and

(T,),dl

contributions to

(T1)obs-1.

^{We assume} that the dilution of the bronze with deuterium does not

change

^the

(Tl)edl

compo- nent, since it has no effect on the concentration or

relative

position

^{of the}

paramagnetic

centres,

although

we have seen that the contribution from the interaction with conduction electrons was reduced

by

^{a factor - 4}

which is

roughly equal

^to the ratio of the

hydrogen

contents of the two bronzes. The

only

other effect that dilution with deuterium should have is to increase d and thus weaken the

dipolar

interaction.

Any

^inter-

actions with

species

^{such as}

^95Mo

^and

y’Mo,

^or

¹⁷⁰

are

easily

^{shown to be}

negligible.

After

removing

the electronic contribution

(T1)e -1

from the observed relaxation rate

using equation (1)

and the data

given

^{in table}

II,

^{we have for the}

H 1.64MOO3

^{bronze at 90 MHz at the}

Tl

^{minimum :}

where

and

Similarly,

^{for the}

(H

⁺

D)1.66Mo03

^{bronze :}

where

and

(Tl)éd’

^{is the same as in}

equation (11).

The factor 1.43 in the denominator of

(Tl)d 1

^comes

from the

assumption

that all the nearest

neighbours

^of

the proton ^{lie on} the surface of a

sphere

^{of radius}

d,

and that

decreasing

^the

density

^of protons

by

^{a factor}

(0.56/1.64)

would increase the distance between nearest

neighbours by

the factor

(1.64/0.56)1/3

If we use the

assumptions given

above and solve

equations (11)

^and

(12) simultaneously,

^{we find that}

the proton-proton distance is about 2.9

Á,

^{and that}

the distance between protons ^and

paramagnetic

centres is about 6.7

Á.

It should be noted that these distances are not

necessarily

^{accurate but}

only suggestive,

within the model that has been

proposed

above. For

example,

^{if we assume}

Ns

^{to be 1 x}

¹⁰¹⁹

and

Jpc

of the order of 10

Á,

^the

dipolar

contribution becomes more

important

^and d is about 1.6

Á.

3. 4 ANALYSIS OF THE TRANSVERSE RELAXATION TIME.

-

Figure

^{9 shows a}

plateau

in the values of

T2 (measured by

^the

spin-echo technique)

^{which occurs}

in the same

temperature region

^as the minimum in the

Tl

^curve. The correlation time for the motion has been shown in

figure

^{8 to be 8 x}

^10-10

^{s at 274 K}

for a ⁼ _oo, so

the jump frequency (z) r 1

^{= 1.25 x 10 9}

TABLE II

Data

taken from

^{the minima}

of (Tl)d

^versus

1/T for samples formed

^{at 60 °C}