Nuclear magnetic resonance in chromium-vanadium
alloys
L.E. Drain
To cite this version:
L.E. Drain. Nuclear magnetic resonance in chromium-vanadium alloys. J. Phys. Radium,
1962, 23 (10), pp.745-749. <10.1051/jphysrad:019620023010074500>. <jpa-00236675>
HAL Id: jpa-00236675
https://hal.archives-ouvertes.fr/jpa-00236675
Submitted on 1 Jan 1962
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TOME
LE JOURNAL DE PHYSIQUE ET LE RADIUM
NUCLEAR MAGNETIC RESONANCE IN
By
Solid State
L. E.
Physics Division,
23,
OCTOBRE
1962,
745.
CHROMIUM-YANADIUM ALLOYS
DRAIN,
A. E. R. E.
Harwell, England.,
Des observations de la variation de résonance magnétique et de largeurs de raie
Résumé.
de 51V ont été faites sur des solutions solides de chrome-vanadium sur un large domaine de concentration.
Le déplacement de Knight varie considérablement avec la composition atteignant une valeur
maximale de 0,687 % pour un alliage contenant 62 % de chrome. Ceci peut être rattaché à l’apparition de moments magnétiques sur les atomes Cr. On trouve une légère dépendence du déplacement
avec le champ magnétique qui est attribué aux effets quadrupolaires du second ordre. La largeur
de raie décroît jusqu’à environ 1,5 gauss quand la concentration en chrome augmente, à cause de la
réduction de l’élargissement dipolaire. On donne une discussion de la dépendence avec le champ
de la largeur de raie. Pour des concentrations de vanadium inférieures à 5 % des transitions larges
apparaissent pour lesquelles l’intensité du signal de résonance décroît. Ceci est attribué à l’apparition d’antiferromagnétisme.
2014
Observations have been made of the 51V magnetic resonance shift and line width
Abstract.
in chromium-vanadium solid solutions over a wide composition range. The Knight shift varies
considerably with composition reaching a maximum value of 0.687 % for an alloy containing 62 %
chromium. This may be connected with the appearance of magnetic moments on the Cr atoms.
A slight dependence of shift on magnetic field is found and is attributed to second order quadrupole
effects. The line width decreases to a value of about 1.5 gauss as the concentration of chromium
increases due to the reduction dipolar broadening. A discussion of the field dependence of the
line width is given. For vanadium concentrations less than 5 % broad transitions appear at which
the intensity of the resonance signal decreases. This is attributed to the appearance of antiferro2014
magnetism.
Introduction.
In the study of the electronic
metal alloys, vanadium is a
of
transition
properties
as it forms considerable
metal
useful
particularly
ranges of solid solution with the other metals of the
first transition series. In particular the binary
alloys of chromium and vanadium are body centred
cubic solid solutions over the entire composition
range. The high magnetic moment (5.139 nuclear
magnetons) of 61V makes this nucleus particularly
suitable for nuclear magnetic resonance investigations. Although the spin is 7 /2, electric quadrupole interactions are generally small [1] and the
resonance is not easily obscured by electric field
gradients in non-cubic or disordered crystals.
Measurements of the 51V magnetic resonance shift
and line width are here reported for the complete
range of vanadium-chromium alloys.
The low temperature specific heat [2] and magnetic susceptibility [3] of this system have been
studied. These properties are related to the density of states at the Fermi surface for all the conduction electrons including those having wave
functions related to atomic 4s and 3d types. The
Knight shift in nuclear magnetic resonance is however affected differently by " s " and " d " electrons.
We may thus expect somewhat different information from Knight shift measurements.
The s electron contribution arises from the con-
tact interaction between the conduction electron
and nucleus and can be written as follows [4] :
where v + Av and v are the resonance frequencies
in the metal and non-metallic reference respectively, in the same applied field. X, is the mass
susceptibility for Pauli spin paramagnetism for
the s electrons and M, the atomic mass. ity(0)12
represents the average probability density at the
nucleus for electronic states on the Fermi surface.
The wave function, F, is assumed to be normalized
over an atomic volume.
Since for d electrons,
03C8(0) 0, there is no contact interaction with the
nucleus. Nevertheless, in ferromagnetic iron for
example, d electrons are known to produce a field
of 340 kilogauss at the iron nuclei, in a direction
opposite to that of the electronic magnetization [5].
Several mechanism can contribute to this interaction [6]. Only one, core polarization [7], can
=
give a negative contribution and so must presumably be dominant in the example given.
Although the resulting electron-nucleus interaction is an order of magnitude less than that for s
electrons, the spin polarization of d electrons in a
transition metal is much greater due to the high
density of states in the
d band. Tube result is that
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:019620023010074500
746
the contributions of s and d electrons to the
shift are of comparable magnitude.
Experimental.
Knight
The alloys investigated were
prepared from high purity elements by argon arc
melting in a water cooled copper hearth. The
vanadium was supplied by the U. S. Bureau of
Mines. An analysis of impurities has been given
previously (C 2 of reference 8). The chromium
(99.99 % pure) was supplied by the Fulmer
Research Institute. This material had been hydrogen reduced to lower its oxygen content to 0.003
weight %. All the alloys used were made with
the above materials with three exceptions, those
containing 19. 7 and 24.6 at % Cr which were
made from Johnson Matthey spectroscopically
pure materials and the 5.1 at % V alloy which was
obtained from the Aero‘nautical Research Labo-
5.1 % alloy, the 51V resonance still has its full
intensity at 24 OK. A detailed study of these transitions is being made and the results will be repor-
ted elsewhere.
ratories, Melbourne.
,
To secure adequate penetration of the R. F. field
into the specimens, the alloy ingots were powdered
by grinding on an " Aloxite " eutting-off wheel
using paraffin as a lubricant. The grindings were
dried and passed through a 400 mesh (37 y) sieve.
Nuclear magnetic resonance was observed with
a Varian 6" electromagnet with a 11/4" gap and a
crossed coil type of spectro meter with an electrical
method of balancing previously described [9].
Measurements on all sarrples were made at a least
two frequencies 10.3 Mc/s and 4.4 Mc/s corresponding to magnetic fields of 9.15 and 3.90 kilogauss respectively. The signals wore recorded by
the A. F. field modulation technique at 40 c/s using
an A. F. phase sensitive detector which gives an
output proportional to the derivative of the resonance curve.
Modulation amplitudes were kept as
small as possible consistent with having an adequate signal and in any case peak to peak amplitudes where less than half the line width.
The transition teinperature of the 51V nuclear
resonance in chromium-vanadium alloys as a
function of composition.
-
magnetic
from the
of these transitions,
alloys appeared to be
insensitive to temperature. Measurements at
liquid nitrogen temperature at 10.3 Mc/s on alloys
containing 5.1, 15.3, 30.4, 35.5, 50.5, 70.4 and
100.0 at % V gave the same results for shift and
line width as at room temperature within experimental error. All other results reported in this
paper refer to room temperature approximately
Apart
the 51V
resonance
occurrence
in all the
296 oK..
’
The Knight shift. - The Knight shift Av/ v is
as a function of composition in figure 2.
plotted
should
The transition point.
be remarked
It
that in chromium rich alloys the occurrence of an
antiferromagnetic structure at low temperatures
has a profond influence on the nuélear magnetic
resonance.
In pure chromium the Néel point
occurs at 311 OK.
Neutron diffraction measurements [10] have shown that in the antiferromagnetic state, magnetic moments of 0.4 yB are
associated with the Cr atoms. These moments
would be expected to produce static magnetic fields
at the nuclei of dissolved V atoms leading to the
disappearance of the normal nuclear resonance in
an applied field.
It is in fact found that at low
temperatures, the amplitude of the 51V resonance
diminishes over a transition range of about 50 OK.
A similar transition in the 53Cr resonance has been
found in pure chromium [11]. The temperature
of the transition falls very rapidly as the concentration of vanadium is increased (fig. 1). In the
--
FIG. 1.
The Knight shift of the 51V magnetic resonance
FIG. 2.
in vanadium-chromium alloys relative to NaV03 solu-
tion, measured at
10.3JMc/s.
747
The référence is
an
aqueous solution of sodium
metavanadate, NaVO3. The shift was found to
be slightly depend ent on field (or frequency of mea-
sûrement). The différences found were just’outside experimental error. A detailed study of the
field dependence for alloys .containing 5.1 and
15.2 at % V is given in figure 3. In general, thé
FIG. 3.
-
The field dependence of Knight shift of the 51V
in alloys of chromium with 5.1 and 15.2 ato-
resonance
mic
percent vanadium.
value of shift obtained at 4.4 Mc/s is slighly less
than that at 10. 3 Mc/s, the maximum différence
being 0.01.8 % at 50.5 at % V. The difference is
most marked at the centre of the composition
range. Since this is the region of maximum disord er, it seems probable that the field dependence
of shift can be attributed to 2nd order quadrupole
effects. If this is so, the shift should vary linearly
with Ho 2 where Ho is the field at which resonance
is observed. The curves in figure 3 have been
drawn on this basis. In any case it appears that
at the higher frequency of 10.3 Mc/s, the correction required to the observed shifts on account of
this effect is negligible. It should be noted that
the effect on the line width of second order quadrupole interactions of the magnitude suggested
would not be easily detected even air the lowest
field used.
It will be seen from figure 2 that the Knight
shift reaches a maximum of 0. 687 % for an alloy
composition of 62 % chromium. There is at present no satisfactory explanation of this. The
increase in shift from 0 to 60 % Cr can be explained
by the decrease in the density of states of electrons
in the d band. There is strong evidence for this
from specific heat [2] and susceptibility measurements [3] and as discussed in the introduction,
it is quite probable that the d electrons give rise to
If we make
a negative contribution to the shift.
the assumption that over the range 0 to 60 % Cr
the shift is roughly a linear function of the density
of states- in the d band as determined by Chêng,
Wei and Beck [2], we may deduce that the d elec-
trons reduce the shift from
a value of about 0.77 %
due to other sources.
It is of interest to note that adding titanium to
vanadium decreases the Knight shift. This is consistent with the above interpretation. A value of
0.560 0/,, -L 0.003 % was found for a 75 % V25 % Ti alloy at 10. 3 Mc/s.
The rapid fall in Knight shift for chromium concentrations beyond 65 % présents a difficult problem
for this occurs in a region where the conduction
electron density of state appears to be relatively
constant. One suggestion is that there is a connection with the appearance of localized magnetic
moments on the chromium atoms, mo nents that
are known to exist in the antiferromagnetic state.
If between 60 and 100 % Cr, the extra electrons
available form these localized moments instead of
filling up the band structure, it would explain why
the density of states for conduction électrons is
constant in this range and give pure Cr the observed
moment of 0. 4 03BCB. In any case there is some evi.den.ce that the composition 62 % Cr corresponding
to an electron/atom ratio of 5.62 is a critical one
for the d band structure. In the analogous System
Nb-Mo, Jones, Pessel and McQuillan [12] have
found that the solubility of hydrogen beco nes insignificant for Mo concentrations greater than 60 %.
It is suggested that the d band is split, the lower
sub-band being filled at the electron/atom ration 5.6
It would interesting to determine whether the V-Cr
system behaves in a similar way.
The line width.
The results of the measuline width in the alloys
are shown in figure 4.
Line width is defined in the
usual way, i.e. it is the separation of the maximum
and minimum points of the derivative of the
absorption curve. There is a fairly marked dependence of line width on field. This is shown in
It is convemore detail for two alloys in figure 5.
nient to discuss separately, the field dependent and
field independent contributions to the line width.
There was a marked assymmetry in the resonance
curves at some compositions particularly around
50 % and 85 % Cr. Since the effect was very
much smaller at low fields, it is evidently associated
with the field dependent contribution to the, line
width.
The diminution of the field independent line
width increasing chromium concentration is a consequence of the decreasing concentration of 51V
nuclei since the main contribution to the width
cornes from dipole interactions between neighbouring 51V nuclei. The contribution from chromium nuclei is small since the only isotope with a
nuclear spin is 53Cr and this has a comparatively
small moment of 0.473 nuclear magnetons and a
natural abundance of only 9.5 %. The theore-
rements. of 51V
tical
dipolar
-
resonance
contribution to the line width is
748
some quadrupole
plotted in figure 4, The mean square width was satellite lines which still havethe
line widths for
For
of
Vleck
formula
Van
the
calculated by
consistency,
[13], broadening.
in
4 refer to the
vanadium
into
taken
in
the
lattice
figure
plotted
pure
parameter being
changes
account, and the line width deduced by assuming U. S. Bureau of Mines Material but as regards the
that the resonance curve has a gaussian shape. comparison of line width with most of the alloys,
the less pure Johnson Matthey material is perhaps
FIG. 4.
-
Line width of the 51V
vanadium-chromium alloys
as a
magnetic
function of
resonance
in
composition.
The fact that experimental values for the line
width for 5.1 and 10.2 at % alloys fall slightly
below the theoretical dipole values probably reflects
the inaccuracy of this assumption. The theoretical line width for infinite dilution of V in Cr is
0.22 gauss.
The field dependence of 51V resonance line width
Fi G. 5.
in alloys of chromium with 5.1 and 15.2 atomic percent
vanadium.
-
The sharp increàse in line width at the extreme
vanadium rich end of the composition range is due
ton the appearance of the first order quadrupole
more suitable as the 51V resonance from this contains only a small amount of satellite intensity [1].
The line widths for this material are 11.4 :L 0.2
gauss and 10.5 + 0.3 gauss at 10.3 Mc/s and
4.4 Mc/s respectively.
The field dependent contributions to the line
width can arise in several ways. All give contributions proportional to the applied field except
second order quadrupole interactions which were
discussed in connection with the Knight shift and
have been shown to be insignificant.
The first field dependent line width contribution
arises from magnetic field inhomogeneities produced by the bulk magnetism of the alloy particles.
This is a consequence of the experimental technique and has been demonstrated for nuclear magnetic resonance in platinum [14]. The estimated
line widths from this source are approximately 1.0
and 1.6 gauss for Cr and V respectively for an
applied field of 10 kilogauss. Secondly, the variation of Knight shift with atomic surroundings can
give a field dependent line width for in a disordered
alloy the situations of the V atoms. are not identical
and it is quite possib’e that the field at a vanadium
nucleus depends cn its immediate surroundings.
Lastly there may be a line width contribution
from the anisotropic shift of vanadium nuclei not
in cubic field.
In view of the strong dependence of shift on
composition in the range 70-100 % Cr, it is surprising that the field dependence of line width is
so small.
If in this region, the shift of a nucleus
were d epende’1f solely on the relative numbers of V
and Cr atoms forming the eight nearest neighbours,
the line width for a random alloy containing 15 %V
would be about 10 gauss at 10 kilogauss applied
field,. The observed field dependent contribution
is less than 3 gauss (at 10 kilogauss).
Thus the Knight shift in this region is certainly
not a function of nearest neighbours cnly. It is
dependent on longer range effects, probably the
band structure of the métal as a whole. ln the
composition range 0-50 % Cr howeven, a greater
field dependent line width is associated with a
smaller composition dependence of shift and a
similar conclusion cannot be drawn.
The author wishes to
Acknowledgements.
thank the Metallurgy Division, A. E. R. E. Harwell
for the preparation of the alloy ingots, Mr. B. Lent
for help with the specimen preparation and experimental work and Mr. J. Butterworth, Dr. w, Gardner, Dr. M. Lomer and Mr. A. D. Le Claire four
-
.
useful discussions,
749
REFERENCES
[1] DRAIN (L. E.), Bulletin Ampère 9e année, fasc. spécial 425, 1960.
[2] CHENG (C. H.), WEI (C. T.) and BECK (P. A.), Phys.
Rev., 1960, 120, 426.
[3] CHILDS (B. G.), GARDNER (W. E.) and PENFOLD (J.),
Phil. Mag., 1960, 5, 1267.
[4] TOWNES (C. H.), HERRING (C.) and KNIGHT (W. D.),
Phys. Rev., 1950, 77, 852.
[5] HANNA (S. S.), HEBERLE (J.), PERLOW (G. J.), PRESTON (J. S.) and VINCENT (D. H.), Phys. Rev. Letters,
1960, 4, 513.
[6] MARSHALL (W.), Phys. Rev., 1958, 110, 1280.
LE JOURNAL DE
PHYSIQUE
ET LE
RADIUM
[7] GOODINGS (D. A.) and HEINE (V.), Phys. Rev. Letters,
1960, 5, 370.
[8] CHILDS (B. G.), GARDNER (W. E.) and PENFOLD (J.),
Phil. Mag., 1959, 4, 1126.
[9] DRAIN (L. E.), Faraday Society Discussions, 1955, 19,
200.
[10] BACON (G.), Acta Crystallographica, 1960, 14, 823.
[11] BARNES (R. G.) and GRAHAM (T. P.), Phys. Rev.
Letters, 1962, 8, 248.
[12] JONES (D. W.), PESSALL (N.) and MCQUILLAN (A. D.),
Phil. Mag., 1961, 6, 455.
[13] VAN-VLECK (J. H.), Phys. Rev., 1948, 74, 1168.
[14] DRAIN (L. E.), To be published.
il
TOME
SOME ASPECTS OF SHORT-RANGE ORDER
By
J. B. COHEN and M. E. FINE
23,
OCTOBRE
1962,
(*)
(**),
Les aspects de l’ordre à courte distance* qui sont discutés ici sont :
Résumé.
a) problèmes expérimentaux rencontrés dans la détermination de l’ordre à courte distance ;
b) nature de l’ordre à courte distance ;
c) cinétique et mécanisme de l’augmentation de l’ordre a courte distance à basse température
dans les échantillons trempés ;
d) destruction de l’ordre à courte distance par déformation plastique, obtention de l’équation
2014
.
fondamentale pour le durcissement dû à l’ordre à courte distance et
les résultats expérimentaux.
sens
de la
comparaison
avec
The aspects of short-range order discussed are : a) Experimental problems involAbstract.
ved in determination of short-range order ; b) Nature of short-range order ; c) Kinetics and
mechanism for increase in short-range order at low temperatures in quenched specimens ; d) Destruction of short-range order by plastic deformation, derivation of the fundamental equation for
short-range order strengthening, and significance of the comparison with experimental results.
2014
deformation.
that in a random solution. In the absence of longrange order, the probability for an unlike atom pair
tends to the random value for large interatomic
distances, 20 to 50 A or so. Short-range order
results in broad, diffuse x-ray scattering in the
regions where super-structure peaks would appear
with long-range order if it occurs. Warren [6] has
expressed this diffuse intensity in terms of a single
Fourier series whose coefficients are the shortrange order parameter
I. The nature and détermination of short-range
order.
In an alloy, local order exists if the number of short-range unlike atom pairs is greater than
Pau is the probability that
Introduction.
Several excellent reviews [1-5]
have been written which deal with local atomic
arrangements in solid solutions. In this paper we
shall consider primarily developments since these
and topics that have not been previously dealt
with in reviews. We shall discuss progress ,in
experimental methods, some recent data, and particularly the role of local order in changes in properties at ambient temperatures and in plastic
-
-
(*)
This research
was
supported by
the United States
Ofiice of Naval Research and the Advanced Research Projects Agency of the Department of Defense, through the
Northwestern Materials Research Center.
(**) J. B. Cohen and M. E. Fine are Associate Professor
and Professor, respectively, in the Department of Materials
Science, The Technological Institute, Northwestern Uni-
versity, Evanston, Illinois, U. S. A.
a b atom is in the ith
shell around an a atom, mb and ma are the mole
fractions, i.e. the random probabilities, and Ci is
the coordination number of the ith shell. These
are probabilities averaged over time and position
in the sample.
(XI mb Ci is the average excess
over the random number of b atoms in the ith
shell around an a. As with all intensity measur-