The paramagnetic susceptibility of face-centred cubic silver-manganese and silver-tin-manganese alloys

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The paramagnetic susceptibility of face-centred cubic silver-manganese and silver-tin-manganese alloys

B. Henderson, G.V. Raynor

To cite this version:

B. Henderson, G.V. Raynor. The paramagnetic susceptibility of face-centred cubic silver-manganese

and silver-tin-manganese alloys. J. Phys. Radium, 1962, 23 (10), pp.685-691. �10.1051/jphys-

rad:019620023010068501�. �jpa-00236662�

Remerciements.

Les résultats qui ^viennent

d’être décrits ont été obtenus grâce ^à la collabo- ration dévouée de plusieurs chercheurs de notre

laboratoire, que je ^suis heureux de remercier ici. La

préparation ^{des lames et} l’étude de leurs facteurs de

réflexion dans l’infra-rouge ^{ont été faites} par M. Burtin, ^{les autres mesures} optiques ^{et élec-} triques ^étant dues à Mme Mertz et à Mlle Leslourdy,

Mme Gandais a pris ^{tous leâ} diagrammes ^de

rayons X.

BIBLIOGRAPHIE

[1] DOMENICALI (C. A.) ^et CHRISTENSON (E. L.), ^J. Appl.

Physics, 1961, 32, ^2450.

[2] SONDHEIMER (E. H.), ^{Adv. in} Physics, 1952, 1, 1.

[3] ^LINDE (J. O.), Thèse, Lund, ^1939.

[4] ^HASS (G.), Amer. Inst. Phys. ^Handbook.

[5] ^SEGALL (B.), Phys. Rev., 1962, 125, 109.

[6] ^MOTT (N. F.) ^{et JONES} (H.), Properties of metals and

alloys, ^Oxford University Press, 1936, p.112.

[7] ^ABELÈS (F.), C. R. Acad. Sc., 1961, 253, ^2213.

THE PARAMAGNETIC SUSCEPTIBILITY

OF FACE-CENTRED CUBIC SILVER-MANGANESE AND SILVER-TIN-MANGANESE ALLOYS

B. HENDERSON (1) ^and G. V. RAYNOR Department ^of Physical Metallurgy ^{of the} University ^of Birmingham.

Résumé.

La variation thermique ^{de la} susceptibilité paramagnétique ^des systèmes Ag-Mn

et Ag-Sn-Mn ^a été étudiée. Entre 300 et 700 °K, ^et pour les concentrations ^en manganèse ^infé- rieures à 17 %, ^{on trouve une} loi de Curie-Weiss. Les valeurs expérimentales ^{du moment magné-} tique ^{et de la} température ^{de Curie} paramagnétique sont liées au nombre d’électrons présents ^et

aux distances interatomiques. ^{Dans les} alliages ternaires, ^{on trouve un} maximum du moment

magnétique, ^en fonction de la concentration en étain, qui correspond ^{à une} concentration fixe en

manganèse. ^Ceci paraît résulter de la superposition de deux effets contraires : a) ^{Si on} augmente

le nombre d’électrons par atome, ^on augmente l’oecupation du niveau virtuel 3d et on diminue le moment magnétique. b) ^La dilatation du réseau déplace des électrons 3d vers la bande de con-

duction, ^ce qui augmente le moment. On évoque aussi brièvement l’effet possible des interactions directes dd entre manganèses ^dans les solutions pas trop diluées et les limitations de la description

en moments localisés.

Abstract.

The variation with temperature ^{of the} paramagnetic susceptibility ^{of 24} alloys

of the silver-manganese ^and silver-tin-manganese systems ^{has been} investigated, ^{and shown to}

obey a Curie-Weiss relationship ^{in the} temperature range ³⁰⁰ to 700 °K for compositions ^less

than 17 to 18 atomic per ^cent manganese. The changes ^{in the} experimentally derived values of the Bohr magneton number and the Weiss constant 03B8 as the manganese concentration is increased

are discussed in terms of the effects of variation in electron concentration and lattice spacings ^on

the electronic configuration of manganese in solid solution. It is suggested that the observed maxima in the curves of _peff against atomic per ^cent tin along lines of constant maganese content in the ternary system ^{result from two} competing effects, ^{in which} increasing ^electron concentration reduces the magnetic ^moment per manganese atom ^{as a} consequence of increased occupancy of 3d virtual bound states, while lattice expansion ^causes electron transfer from 3d states to the conduction band, resulting ^{in an} increase in the Bohr magneton ^number. Possible effects of an

increase in the number of direct d-d interactions between nearest neighbour manganese atoms ^as their concentration increases, ^{and the} limitations of the localized electron treatment ^as applied

to alloys ^rich in manganese, ^are briefly ^discussed.

LE JOURNAL DE PHYSIQUE ET LE RADIUM TOME 23, ^OCTOBRE 1962,

Introduction.

The present investigation ^forms part ^{of a} general programme of research into the effective electronic constitutions of transition metals in solid solution in noble metals, ^or alloys

based on them. Previous work has shown that, ⁱⁿ

the close-packed hexagonal 3/2 ^électron compounds ((-phases) ^{found in} ternary systems ^formed by

(ij Now at A. E. R. E., Harwell, England.

copper, silver or gold ^{with two elements of the B} sub-groups ^{of the Periodic} Table, ^the axial ratio remains constant at a constant value of the electron concentration. As pointed out by Cockayne ^and Raynor [1] and Henderson and Raynor [2], ^this

observation allows an assessment of the effective electronic constitution of a transition metal in solid solution in a binary (-phase, ^{such as that formed} by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:019620023010068501

copper ^and germanium ^or silver and tin. The variacion of axial ratio with composition ^{in the} ternary (-phase ^is determined experimentally ; ^it

is then reasonable to assume that a ternary alloy

of given ^axial ratio has an electron : atom ratio identical with that of the binary alloy ^{of the same}

axial ratio. For example, ^{in the case of the silver-} tin-manganese (-phase, ternary compositions ^ha- ving ^{the same} electron : atom ratio as a certain silver-tin (-phase alloy ^are established ; assuming

silver and tin to be respectively ^{mono- and} quadri- valent, ^the contribution of the manganese ^{atoms to} the conduction band may be derived. The ^re- sults [2] ^are consistent with fractional effective

valencies, for manganese in solid solution in binary

§-phases, ^{of between 1 and} 2, depending upon the electron concentration and the lattice spacing.

The variation of effective valency ^with alloy ^com- position may be attributed to exchange of electrons between the partially filled virtual bound 3-d states associated with the manganese ^atoms [3]

and the conduction band of the alloy. ^{The effec-}

tive valency of manganese in the face-centred cubic

primary ^solid solution in the silver-tin-manganese systems, however, ^{cannot be estimated in the}

manner described above. Information has there- fore been sought ^from magnetic ^data.

The paramagnetic properties of the solid solu- tions formed by ^{the noble} metals with manganese have received considerable attention [4-9], ^{and are}

of interest on account of the low temperature paramagnetic antiferromagnetic transition, ^and

the uncertainty in the electronic constitution of manganese when present ^{in a} non-transition metal solvent. Above 1000K, alloys containing ^less

than 20 atomic per ^cent manganese exhibit ^{a tem-}

perature dependent paramagnetism, ^{and the sus-} ceptibility obeys ^the Curie-Weiss relationship

x

C/T - 0, where x ^{is the} paramagnetic ^sus- ceptibility ^{in e. m. u. per gm. atom of} alloy, ^{C is}

the Curie constant and 0 is the Weiss temperature.

The Cmie constant, derived from the slope ^{of the}

curve of 1 /x against temperature, may then be related to the effective Bohr magneton ^{number for}

the manganese ^atoms by ^the equation

where x is the atom fraction of manganèse in the

alloy ^under examination. The total spin quantum number S maybe calculated from the derived effec- tive Bohr magneton ^number by ^the relationship

pex

g(S(S + 1)]1/2, where g (= 2) is the Landé

splitting factor, and it is assumed that the orbital momenta ^are completely quenched. Information with regard ^to the electronic constitution of the transition metal in solid solution may therefore be derived directly ^{from the} temperature dependence

of the paramagnetic susceptibility.

In the present paper measurements of the ma-

gnetic susceptibility ^of silver-manganese ^and silver"

tin-manganese face-centred cubic alloys ^are repor-

.ted, ^{and the} suggested variations ^{in the effective} valency of manganese, analogous ^to those des- cribed above for close-packed hexagonal alloys, ^are

discussed.

Materials and experimental ^methods.

^The single-phase alloys used in the present ^{work were}

those for which lattice spacing values have been

recently reported by ^{the authors} [10], ^{and were} prepared ^from spectrographically standardised metals obtained from Messrs. Johnson, Matthey

and Co., ^{Ltd. The} impurity ^{contents were less}

than 10, ^{9 and 13} parts per million in the silver,

tin and maganese samples respectively. Alloys

were made in quantities ^not exceeding ^{5 g. in} weight by melting together accurately weighed quantities ^{of the} component metals sealed in thin- walled silica capsules ^{under a reduced} pressure ^of clean argon. After thorough mixing by vigorous shaking, ^the capsules ^were quenched ^{into ice-cold}

water to minimize ségrégation ^{in the solid} ingot, ^and

the resulting specimen ^was reweighed. Normally weight ^{losses on} melting ^were negligible, ^{and the} synthetic compositions ^{of the} alloys ^were accepted, previous experience with similar alloys having

s how chis procédure tobejutified.Anyall0Ys showing

abnormal weight ^loss were rej ected. Ingots ^{were ho-} mogenized at 4800 C in sealed pyrex capsules ^contai- ning approximately 1/3 atmosphere ^of argon, and

quenched ^{into cold water. After} metallographic

examination and the removal of an X-ray speci-

men, the remainder of each ingot ^was ground, using

a silicon carbide grinding wheel, ^into cylindrical specimens of radius 0.095 ins. weighing approxi- mately 0. 5 g. ^{for use in the} magnetic susceptibility apparatus.

Magnetic measurements were made between 3000 and 700 °K using ^a modified Sucksmith ring

balance in which the force exerted on the specimen

in an inhomogeneous region ^{of the} magnetic ^field displaced ^the specimen vertically. ^The displa- cement, ^{as measured} by ^an optical ^lever system,

was then proportional ^{to the mass and} suscepti- bility ^{of the} specimen ^{and to the field charac-}

teristics between pole pieces, ^{of the} type ^described by ^Sucksmith [11,12], ^{of an} electromagnet supplied

with a stabilized D. C. output controlled to within

+0.5 % ^{of the current selected.} Specimens ^were suspended between the pole pieces by ^{means of a}

super pure aluminium ^rod bearing ^a specimen

holder of the same material, and heated by ^{a resis-}

tance furnace. The furnace was wound onto the pyrex tube which formed ^an integral part ^{of the}

vacuum system, ^{and was attached to the base of}

the balance by ^a ground-glass ^cone joint. ^The

specimen temperature ^{was measured} by ^a copper-

constantan thermocouple placed very ^{near to} the

687

specimen ^{holder, but not in actual contact with it.}

The field characteristics, ^and particularly ^the

value of H dhldx, given by ^a constant current of 8 A, ^were determined using ^a pure tantalum speci-

men, for which the susceptibility ^is accurately

known [13] ; ^{the data were checked} using ^Analar MnS04.4HE0. Previously reported ^{room -tem-} perature susceptibilities of certain salts [14, 15] ^are compared ^with values obtained using ^the present apparatus ^{in Table I. The} reliability ^{of the ba-}

TABLE 1

lance ^over the temperature range 2900 ^to 700 DK

was tested with Analar MnS04,4H20, ^{and the}

values of C, 0, and peff determined ^are given ⁱⁿ

Table II ; this Table contains also values given by

TABLE II

Bates [14], ^and satisfactory agreement ^{is shown.}

At each temperature, corrections were made for the deflection corresponding to ^the empty specimen

holder. Measurements for the ternary alloys ^were

made after holding ^the specimen temperature ^cons-

tant for periods ^of approximately ^{15 minutes at} regular ^intervals during heating ^and cooling. ^No

evidence was obtained for precipitation ^{of other} phases ^{from the} binary ^{solid solution} alloys, ⁱⁿ

either the magnetic measurements, ^{or the measu-}

rements of lattice spacings, ^{which were} made, ^after cooling, ^for comparison with those previously ^re- ported [10].

The measured mass susceptibilities ^{were con-}

verted into gm. atomic susceptibilities, ^{and correc-}

ted for the core diamagnetism ^{of silver and} tin,

assumed to be respectively -19. 56 and - 29. 7

e. m. u./gm. ^atom.

Expérimental ^results.

^The results of the ^sus-

ceptibility measurements for selected alloys ^are shown, ⁱⁿ figures 1, ^{2 and} 3, ^as graphs of the reci-

procal of the gm. atomic susceptibility ^{of the} alloys,

corrected for diamagnetism, plotted against ^abso-

lute temperature. ^For alloys containing ^{less than}

18 atomic per ^cent manganese, the Curie-Weiss

relationship ^is accurately obeyed. ^The binary

FIG. 1.

Reciprocal of corrected gm. atomic susceptibility plotted against ^absolute temperature ^for binary ^silver-

manganese alloys.

alloy containing 19 atomic per ^cent manganese, and the ternary alloy ^with 4 atomic per ^cent tin and 18 atomic per ^cent manganese, deviate from the relationship, ⁱⁿ agreement ^{with the} previous

results of Morris and Williams [7] for supersa-

688J

FIG. 2.

Reciprocal ^of corrected gm. atomic susceptibility plotted against ^absolute temperature for silver-tin-man- ganese alloys with constant tin content of 2 atomic per cent.

FIG. 3.

Reciprocal of corrected gm. atomic susceptibility plotted against ^absolute temperature for silver-tin-man-

ganese_alloys with constant tin content of 4 atomic per

cent.

turated silver-manganese alloys containing up ^to 38 atomic per ^cent manganese.

In figure 4, the values of the Curie constant, Weiss temperature ^{and the effective} Bohr magne-

FIG. 4.

Variation with composition ^of peff, C ^and P for

binary silver-manganese alloys.

Present results : 0 ; ^van Itterbeek [5] : D; ^Morris

and Williams [7] : fb ; Gustafsson [4] : .

ton numbers are plotted against alloy composition

for the binary silver-manganese alloxs, ^{and com-} pared ^{with the} previously reported results of Gustafsson [4], ^{Owen et al.} [6], ^{Morris and}

Williams [7] ^{and van Itterbeek et al.} [8]. ^Good agreement i5 shown, particularly ^{with the work of}

Morris and Williams [7]. ^{For the} ternary alloys

rich in manganese, ^curves of 1 Jx against ^{To A}

showed a slight ^{deviation from} linearity ^above

6000 C ; ^{this was most} probably ^{due to valotili-}

zation of manganese, similar ^to that reported by

Morris and Williams [7] ^{for the} binary ^silver-

manganese alloys, though ^{no trouble was} expe- rienced in the present ^{work on} binary alloys ^from

this cause.

The changes in C and 0 of silver-manganese alloys produced by additions of tin are small ; ^diffe-

rences become apparent only ^when pefi ^is plotted

as a function ^of alloy composition, ^as shown for the ternary alloys ⁱⁿ figure 5, ⁱⁿ which peff is given ^{as a}

function of atomic per ^cent manganese at constant

tin contents, ^{and of atomic} per ^cen tin at constant

FIG. 5.

Variations of _peff with composition in the silver- manganese system.

(a) At constant atomic percentages ^{of tin} equal ^to

2: .; 4:: 0 ; 8 : D ; "and 10:.. The broken line refers to 0 atomic per ^cent tin.

(b) At constant atomic percentages of manganese

equal ^{to 2 :} 0 ; ^{5 :} 0 ; ^{10 :} ; and ^{15 :} Q.

manganese ^contents. The addition of tin increases the value of peft ^{to a} maximum at 4-5 atomic _per cent tin, while further additions cause it to decrease.

The compositions ^{of the} alloys investigated, toge-

ther with calculated values of C, 0 and pefr, are

given in Table III.

Figures ^{6 and} 7 show the gm. atomic suscepti-

bilities plotted ^{as functions} of manganese ^content at selected constant temperatures ^for binary ^silver-

manganese alloys ^{and for} ternary alloys containing

2 atomic per ^cent tin ; essentially similar results

were obtained for ternary alloys ^with 4, ^{8 and}

10 atomic per ^cent tin. The susceptibility ^increases uniformly up ^to 10-12 atomic _per cent manganese, and subsequently, increases less rapidly. ^{This is}

consistent with the observation of Morris and Williams [7] ^{that the} susceptibility ^{for the} binary alloys ^is approximately ^{constant from} 20-32 atomic per ^cent manganese ; according ^{to the same wûr-} kers, ^the susceptibility ^{falls at} compositions ^excee- ding the upper limit of this range.

TABLE III

FIG. 6.

Gram. atomic susceptibility plotted ^{as a function}

of manganese content at selected temperatures ^{for silver-}

manganese alloys. 300 OK : ob ; 400 OK : 0 ; 500 oK :

FIG. 7.

Gram. atomic susceptibility plotted ^{as a func-}

tion of manganese content at selected temperatures ^for silver-tin-manganese alloys containing ² atomic per cent tin. 300 oK : . ; ^{400 oK :} 0 ; 500 oK :. ; ^{600 oR :} D.

Discussion.

In both binary ^and ternary ^alloys

of the systems studied, ^{the effective Bohr} magneton number decreases with increasing manganese ^con- tent. For five unpaired electrons, corresponding

to the 3d5.4s2 configuration in the manganese

atoms, pen = 5. 91 ; ^{for the 3d6 .4S1} configuration, only four electrons remain unpaired, and peff is reduced to 4.9. As shown in figures ^{4 and} 5, ^the

value of _pefr at infinite dilution (zero manganese

content) lies between 5: 7 and 5.8, and ^{is therefore}

consistent with the 3d5.4s2 configuration ^{for the}

manganese ^atoms.

From the results of earlier work [1, 2], ^{based on}

the measurement and analysis ^{of lattice} spacings ⁱⁿ close-packed hexagonal ternary (-phases ^con- taining manganese ^and either copper and germa-

nium, silver and tin, ^or gold ^and tin, ^{it has been} suggested ^{that the effective} valency of manganese, in the sense of the number of electrons per atom contributed ^{to the} conduction band of the alloys,

decreased ^from a value close to 2 at the solute-poor phase boundary ^{towards a value of} unity ^{at the}

solute-rich phase boundary. The observed value at

any given composition depended upon the électron : atom ratio and thé lattice spacing. ^{These effects}

were interpreted ^{in terms of the concept of virtual}

bound states [3], according ^{to which the 3d states}

of the introduced _manganese atoms become trans-

formed, by ^{resonance with} states in the conduction

band, ^{into a series of states} localized in _space to the

neighbourhood ^{of the} introduced atom, ^{and corres-}

ponding ^{to an} energy range overlapping that of the conduction band. In silver-manganese alloys, ^the magnetic interactions are sufficiently strong ^to

differentiate the virtual bound states into two groups, of opposite spin, ^{one of} which lies below the Fermi surface and is fully occupied. by ^.five

electrons per manganese atom, and the other of which lies slightly above the Fermi surface ; ^man-

ganese in solid solution max therefore ^{exert an} effective valency ^{of 2} by contributing 2 electrons to the conduction band. The decrease in effective

valency with increase in electron : atom ratio may then be interpreted ^{as due to the} raising ^{of the}

energy of the Fermi surface until it overlaps ^the

upper group of virtual bound states, allowing ^occu-

pancy of these by ^{electrons whicb do not therefore}

enter the conduction band. A further deduction from the earlier work ^was that decrease in lattice spacing (i.e. contraction of the environment of the manga-

nese atoms) encouraged s ^{-+ d} transitions, ^and

vice versa.

The present work, ^{in which it is} shown that _pefr decreases in silver-manganese ^and silver-tin-man- ganese face-centred cubic solid solutions as the manganese ^content increases, reaching ^{a value of}

about 5.1 at 18 atomic percent manganese, suggest

that the behaviour of manganese in these cubic

alloys is very similar ^to that in the close-packed hexagonal (-phases ^as outlined above. At all man-

ganese ^contents the lower group ^of virtual bound states appears ^{to be} filled, giving ^{rise to} conformity

with the Curie-Weiss relationship, ^{while at low}

manganese contents the upper group of virtual bound states contains very few electrons derived from the 3d states of the manganese atom, ^so

that peff approaches the value for 5 unpaired spins.

As the energy of the Fermi surface is raised by alloying with manganese of effective valency ^close

to 2, it may be supposed that the upper group of virtual bound states is further overlapped, ^and progressively occupied by electrons, ^{which are of} opposite spin to those in the totally occupied ^lower

group and hence lead to a decrease _{in pet.}

In figure 5, ^{the curves} of paft against atomic per cent tin at various constant maganese ^{contents rise} to maximum values at approximately ⁴ atomic per ent tin. In terms of the above interpretation

this may be due ^{to the} balance of two opposing

effects. Increase in Fermi energy caused by ^the

solution of tin allows occupancy ^{of the} upper group of virtual bound 3d states, ^thus tending ^{to de-}

crease pff ; ^at the same time, ^{the solution of tin} markedly ^{increases the lattices} pacing ^{of a} given silver-manganese alloy [10], ^thus leading ^{to an} expanded environment for the manganese ^atoms and encouraging ^{d - s} transitions from the upper group of virtual bound states to the conduction

band, which tends to increase _put. The resultant

effect on peff is in any ^case small (fis. 5) ^{and the}

existence ^{of a} shallow maximum is not inconsistent with these considerations.

It must be recognised ^that considerations other than those referred to above probably also affect the observed value of the effective Bohr magneton numbers. In the alloys of manganese with copper, silver and gold ^as solvents, it is known that there is

a transition to anti-f erromagnetic properties ^{at low} temperatures, ^{which has} been discussed by ^Owen

et al. [6] ^and by ^Kouvel [9], and which directs attention ^to direct interactions between the a elec- trons of the manganese ^atoms. The work of Kouvel emphasizes ^the dependence ^{of such inter-}

actions on composition, ^{since it was -shown} that, ⁱⁿ binary copper-manganese and silver-manganese pri

mary ^solid solutions, ^the temperature of the para-

magnetic anti-ferromagnetic transition increases with increasing manganese ^content. This suggests

that direct ^d

^d interractions _may assume im- portance ^{in the} alloys co nsidered in this paper ^as the manganese ^content increases, ^{and this will tend}

to contribute to the observed decrease in pefi. It may be noted that the change ^{in the measured}

value of 0 with tin concentration for alloys ^contain- ing ^{a constant} percentage of manganese is almost

negligible ; since 03B8 depends upon ^{the nature of the} interaction between atoms with resultant magnetic moment, ^{this behaviour} implies ^{that the} degree

of d

d interaction is aff ected only by changes ⁱⁿ

the manganese ^content of the alloys.

The concept of virtual bound 3d states associated with the dissolved _manganese atoms [3] ^is strictly applicable only ^{in thé} absence of direct interactions

betw,een the manganese atoms, and discussion of the observed eff ects according ^to this model is justi-

fied only ^at relatively low manganese contents.

At relatively high concentrations, ^{it is} probable

that the 3d electrons associated with the manga-

nese atoms should not be considered as effectively

localized. The magnetic susceptibilities ^of alloys containing ^{more than} approximately ^{20 atomic} per cent manganese do ^not in fact conform to the Curie-Weiss relationship, ^{and it is} probable ^that

this composition ^{marks a} transition from localized virtual bound 3d states to a condition in which ^a collective electron treatment of the 3d electrons is

more appropriate.

The experiments reported in this paper suggests

that the changes ^{in the} magnetic susceptibility ^of silver-manganese ^and silver-tin-manganese ^face-

centred cubic solid solution alloys ^are mainly ^asso-

ciated with changes in the electronic structure of the dissolved manganese ^atoms brought ^about by

increases in the electron : atom ratio and the lattice spacing. The effect of increasing ^{electron :}

atom ratio is to encourage s ^-+ d transitions, ^lea- ding ^{to a} decrease in peff from the value charac- teristic of 5 unpaired spins per manganese atom, while increasing ^lattice spacing ^{has the reverse}

effect. The possible ^{influence of direct} interaction between the 3d electrons of the manganese ^{atoms as} their concentration increases should also be consi- dered.

The authors wish to express ^{their thanks to}

Dr. S. G. Glover for helpful ^{advice in the cons-}

truction of the magnetic ^balance used ; grateful acknowledgement is also made to the Royal Society, ^the Department ^of Scientific and Indus- trial Research and Imperial ^Chemical Industries Ltd., ^{for financial} support ^{of the} general pro- gramme of which this work forms a part.

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