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 silvermanganese and silver-tin-manganese alloys. J. Phys. Radium, 1962, 23 (10), pp.685-691.
<10.1051/jphysrad:019620023010068501>. <jpa-00236662>
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Submitted on 1 Jan 1962
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685
Les résultats qui viennent
Remerciements.
d’être décrits ont été obtenus grâce à la collaboration 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 électriques 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.
LE JOURNAL DE
PHYSIQUE
[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.
ET LE RADIUM
TOME
23,
OCTOBRE
1962,
THE PARAMAGNETIC SUSCEPTIBILITY
OF FACE-CENTRED CUBIC SILVER-MANGANESE AND SILVER-TIN-MANGANESE ALLOYS
B. HENDERSON
Department
Résumé.
of
(1)
Physical Metallurgy
and
G. V.
of the
RAYNOR
University of Birmingham.
La variation thermique de la susceptibilité paramagnétique des systèmes Ag-Mn
Ag-Sn-Mn a été étudiée. Entre 300 et 700 °K, et pour les concentrations en manganèse inférieures à 17 %, on trouve une loi de Curie-Weiss. Les valeurs expérimentales du moment magnétique 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 conduction, 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
2014
et
en
moments localisés.
Abstract.
The variation with temperature of the paramagnetic susceptibility of 24 alloys
silver-manganese and silver-tin-manganese systems has been investigated, and shown to
relationship in the temperature range 300 to 700 °K for compositions less
a Curie-Weiss
to 18 atomic per cent manganese. The changes in the experimentally derived values
than 17
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.
2014
of the
obey
Introduction.
The present investigation forms
of
a
general
part
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
686
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 silvertin-manganese (-phase, ternary compositions having the same electron : atom ratio as a certain
silver-tin (-phase alloy are established ; assuming
silver and tin to be respectively mono- and quadrivalent, the contribution of the manganese atoms to
the conduction band may be derived. The results [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 composition 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 effective 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 therefore been sought from magnetic data.
The paramagnetic properties of the solid solutions 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 temperature dependent paramagnetism, and the susceptibility obeys the Curie-Weiss relationship
C/T - 0, where x is the paramagnetic susx
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 effective Bohr magneton number by the relationship
g(S(S + 1)]1/2, where g (= 2) is the Landé
pex
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 described above for close-packed hexagonal alloys, are
discussed.
Materials and experimental methods.
The
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
-
single-phase alloys
weight by melting together accurately weighed
quantities of the component metals sealed in thinwalled 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 homogenized at 4800 C in sealed pyrex capsules containing approximately 1/3 atmosphere of argon, and
quenched into cold water. After metallographic
examination and the removal of an X-ray specimen, the remainder of each ingot was ground, using
a silicon carbide grinding wheel, into cylindrical
specimens of radius 0.095 ins. weighing approximately 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 displacement, as measured by an optical lever system,
was then proportional to the mass and susceptibility of the specimen and to the field characteristics 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 resistance 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 copperconstantan thermocouple placed very near to the
687
specimen holder, but not in actual contact with it. known [13] ; the data were checked using Analar
The field characteristics, and particularly the MnS04.4HE0. Previously reported room -temvalue of H dhldx, given by a constant current of perature susceptibilities of certain salts [14, 15] are
8 A, were determined using a pure tantalum speci- compared with values obtained using the present
men, for which the susceptibility is accurately apparatus in Table I. The reliability of the baTABLE 1
lance over the temperature range 2900 to 700 DK
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
was
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 constant 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 measurements of lattice spacings, which were made, after
cooling, for comparison with those previously re-
ported [10].
The measured mass susceptibilities were converted into gm. atomic susceptibilities, and corrected 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 susceptibility measurements for selected alloys are
shown, in figures 1, 2 and 3, as graphs of the reciprocal of the gm. atomic susceptibility of the alloys,
corrected for diamagnetism, plotted against absolute 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 silvermanganese alloys.
-
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-
alloy containing
688J
FIG. 2.
Reciprocal of corrected gm. atomic susceptibility
plotted against absolute temperature for silver-tin-manganese alloys with constant tin content of 2 atomic per
-
cent.
FIG. 4.
-
Variation with
composition of peff, C and P
binary silver-manganese alloys.
Present results : 0 ; van Itterbeek [5]
and Williams [7] : fb ; Gustafsson [4] : .
ton numbers
for
: D; Morris
plotted against alloy composition
binary silver-manganese alloxs, and compared 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 valotilization of manganese, similar to that reported by
Morris and Williams [7] for the binary silvermanganese alloys, though no trouble was experienced in the present work on binary alloys from
FIG. 3.
atomic
of
corrected
gm.
susceptibility
Reciprocal
plotted against absolute temperature for silver-tin-man- this cause.
The changes in C and 0 of silver-manganese
ganese_alloys with constant tin content of 4 atomic per
cent.
alloys produced by additions of tin are small ; differences become apparent only when pefi is plotted
turated silver-manganese alloys containing up to as a function of alloy composition, as shown for the
38 atomic per cent manganese.
ternary alloys in figure 5, in which peff is given as a
In figure 4, the values of the Curie constant, function of atomic per cent manganese at constant
Weiss temperature and the effective Bohr magne- tin contents, and of atomic per cen tin at constant
for the
-
are
689
TABLE III
FIG. 5.
Variations of peff with composition in the silvermanganese 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, together with calculated values of C, 0 and pefr, are
given in Table III.
Figures 6 and 7 show the gm. atomic susceptibilities plotted as functions of manganese content
at selected constant temperatures for binary silvermanganese 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 wûrkers, the susceptibility falls at compositions exceeding the upper limit of this range.
.
FIG. 6.
Gram. atomic susceptibility plotted as a function
of manganese content at selected temperatures for silvermanganese alloys. 300 OK : ob ; 400 OK : 0 ; 500 oK :
-
690
neighbourhood of the introduced atom, and corresponding 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 ; manganese 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 occupancy 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 manganese 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-manganese face-centred cubic solid solutions as the
FIG. 7.
Gram. atomic susceptibility plotted as a function 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.
-
ternary
Discussion.
In both binary and
alloys
of the systems studied, the effective Bohr magneton
number decreases with increasing manganese content. 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 containing manganese and either copper and germanium, silver and tin, or gold and tin, it has been
suggested that the effective valency of manganese,
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 transformed, by resonance with states in the conduction
band, into a series of states localized in space to the
in 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 manganese 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 decrease 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
691
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 electrons of the manganese atoms. The work of
Kouvel emphasizes the dependence of such interactions on composition, since it was -shown that, in
binary copper-manganese and silver-manganese pri
mary solid solutions, the temperature of the paramagnetic anti-ferromagnetic transition increases
with increasing manganese content. This suggests
d interractions may assume imthat direct d
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 containing 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 manganese 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 facecentred cubic solid solution alloys are mainly associated 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, leading to a decrease in peff from the value characteristic 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 considered.
The authors wish to express their thanks to
Dr. S. G. Glover for helpful advice in the construction of the magnetic balance used ; grateful
acknowledgement is also made to the Royal
Society, the Department of Scientific and Industrial Research and Imperial Chemical Industries
Ltd., for financial support of the general programme of which this work forms a part.
REFERENCES
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[3] FRIEDEL (J.), Canad. J. Phys., 1956, 34, 1190.
[4] GUSTAFSSON (G.). Amm. Phys. Lpz., 1936, 25, 545.
[5] MYERS (H. P.), Canad. J. Phys., 1956, 34, 527.
[6] OWEN (J.), BROWNE (M. E.), ARP (V.) and KIP (A. F.),
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[7] MORRIS (D. P.) and WILLIAMS (I.), Proc. Phys. Soc.,
London, 1959, 73, 422.
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(F.), Applied Scientific Research, 1960, B 8, 337.
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