Spin resonance method for conduction electron contribution to paramagnetic susceptibility of metallic sodiu

Vehse, W. E.

English

NASA Technical Reports Server

The Paramagnetic Susceptibility of 
Lithium and Sodium M e t a l  
* 
Research Project NASA -11-63 
CFSTI PRICE(S) $ 
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Microfiche (MF) 
ff 653 J u l y 6 5  
U. E. Vehse 
Department of Physics 
West Virginia University 
https://ntrs.nasa.gov/search.jsp?R=19660016969 2020-03-16T19:20:56+00:00Z
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The originall, proposal for t h i s  grant consisted of the following 
projects  : 
(a) Remeasurement of the  cmduction electron suscept ib i l i ty ,  YE, 
for l i thium m e t a l  chiefly at room temperat-. 
measllrements at 77%. 
Sane 
ib) Knight s h i f t  and suscept ib i l i ty  measurements in t h e  same 
sample of sodium a t  77%. 
(c) Relative suscept ibi l i ty  measurements i n  sodium as a function 
of sample preparation over t he  range 4% t o  77%. 
(d)  Extension of technique t o  previously unmeasured substances. 
(e) Effects of impurities on the suscept ib i l i ty .  kasurements 
w i l l  be ma& chief ly  in sodium at 77% with the poss ib i l i t y  
of some very l a w  temperature measurements also. 
These areas will be reviewed i n  detail. 
I. Summary of Experiments 
(a) Using a spin resonance technique f i r s t  devised by Schumacher 
and Slichter', t he  paramagnetic suscept ib i l i ty  of the  conductiun electrons 
of metallic lithium w a s  measured at r o o m  temperature. These results 
w e r e  reported i n  a paper at  the "March 1966" meeting of t he  American 
Physical Society2. 
It should be noted t h a t  the suscept ib i l i ty  has also been measured a t  4.2%. 
These results w e r e  a l so  reported i n  par t  of the same paper. 
ments w e r e  i n  agreement with previous results. 
res-dts were essent ia l ly  the same as predicted theoret ical ly .  
Copies of t h i s  paper are included with t h i s  report. 
The m e a s u r e -  
The low and high temperature 
- 2 -  
(b) Knight s h i f t  measurements wge made i n  samples of sodium 
p r e p m d  by t h e  same technique as was used for the suscept ib i l i ty  
measurements. 
cut  evidence t ha t  exis t ing calculations of the nature of the  wave 
€unctions describing the  electrons w e r e  incorrect. 
change Cri the !bight sh i f t  w a s  &served as a re su i t  o€ sampie preparation. 
The Knight shift measureuknts are =ported i n  an unpubllsfied masters 
t hes i s  of Hr. aohrt Jefferson4. 
The purpose of t h i s  experiment was t o  provide clear 
As expected no 
(c) Low temperature (4.2%) measurements of t h e  absolute 
suscept ib i l i ty  of the conduction electrons i n  sodium have been m a d e .  
These results are i n  good agreement with the  20% and 77% measurements 
of Schumacher and VehseS.  
seems a t  present that absolute measurements are more ccmvenimt. 
goal of these measurements is t o  determine whether or not a reported 
Knight shift anomaly might be due t o  a corresponding anmaly i n  t h e  
electron susceptibility‘. 
out any suscept ibi l i ty  change. 
No relative measurements w e n  made as it 
The 
Our precision is not yet  high enough t o  rule 
These law temperature results w i l l  be reported in a meeting of 
the  West Virginia Academy of Sciences in April 1966. 
t h i s  paper is included with t h i s  report. 
An abstract of 
(d) We have t r i e d  to measure t h e  suscept ib i l i ty  of metallic 
b e r y l l i m  by t h e  Schumacher-Slichter technique. 
reported an electron resonance in beryllium and give an approximate 
Feher and Kip” have 
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value f o r  $ W e  have searched under conditions such t ha t  w e  
should have been able t o  measure t he  suscept ib i l i ty ,  but have not 
been able t o  observe the resonance. 
successful i n  reproducing t h e  results of Fehere and Kip. 
t h i s  part of the project has been discontinued. 
Other  investigators have not been 
The work on 
( d  Q e )  The effect of impurities QT~. the susaqtibility has 
been investigated i n  metallic lithium. 
traces of magnesium and lithium. 
suscept ib i l i ty  upon alloying but the  research has not ye t  progressed 
t o  the point where we wish t o  publish o-ur findings. 
continued. 
We have m a d e  some alloys of 
There is an apparent decrease i n  the 
The work is being 
A report will be submitted t o  NSA yon completion. 
11. Evaluation of Results 
It is felt t h a t  our research has made two def in i t e  contributions 
t o  scientific knowledge. 
the  accuracy of previously reported measurements of the  conduction 
electron suscept ib i l i ty  of lithium. 
measur,-ncnts of this quantity i n  metallic sodium than have previously 
been made. 
kiterest t o  those studying the properties of metals. 
We have cleared up any existing doubts as to  
We have made better absolute 
Our r e su l t s  on t h e  Li-Mg alloys shouid be of d e f i n i t e  
111. P u b l i c a t i o n  Plans 
Already Published 
W. L. Shanholtzer and W. E. Vehse, Measuremeat of the Electron 
Spin Suseept ibi l i ty  of Metallic Lithium 
Bull. Am. Phys. Soa. Ser, 11 Vol. 11, 220, 1966. 
Planned Publication 
R .  L. Stenger and W. E .  Vehse, Conduction Electron Susceptibility of 
Metallic Sodium at 4.2%. 
of Sciences April 1966. 
To be presented at the W.Va. Academy 
*pa completion of this phase of the work, a review of all measurements 
to date w i l l  be submitted for publication, 
J. E. Kettler and W. E. Vehse. Conduction Fbectmn Siscept ib l l i ty  of 
Li-Mg Alloys ( t o  be presented for publication upon completion 
of the work) 
IV. Continuation of th i s  Research 
A proposal has been submitted to  the AEC for funds t o  continue 
this project. The reviews have been favorable. The proposal is being 
held for consideration when the budget for the next fiscal year is 
available. 
. .  
V. Expenditures. 
Salar ies  * 
Principle Investigator 
4 Assistant 
SOC. Sec. 
Workmen's Camp. T I M ,  
TOTAL 
Capital  Equipment . 
Centrifuge 
Frequency Meter 
VTVM 
Heat Gun 
Large Vacuum Pump 
Audio Oscillator 
Power Supply 
Vacuum Pump 
Isolator Lab 
D e w a r  Assembly 
Isotemp Oven 
Ultrasonic Probe 
TOTAL 
Coolants 
Nitrogen 
H e l i u m  - (including rentals)  
TOTAL 
$1200.00 
4888.88 
30.88 
$6119.76 
160.50 
79.50 
63.55 
38.83 
760.35 
332.90 
281.95 
147.29 
615.00 
230.00 
436.00 
890.00 
$4035.87 
65.00 
265.00 
$ 330.00 
Miscellaneous 
Hardware 
Electronic Par ts  
C h e m i c a l s  
Film 
TOTAL $1217.76 
Total Expenditures - $11703.39 
Total  Allocated $11,809.00 
Expenditures ll,703.39 
Unused Balance $ 105.61 
Note: S a x  iizvoices &-e is yet outstanding so that the above 
f igures  based on a few estimates may change by a f e w  dollars. 
A corrected tabulation of expenditures w i l l  be forwarded as 
soon as possible. 
FOOTNOTES 
1. R. T. Schumacher and C. P .  Slichter, Phys. Rev. 101, 58 (1956). -
2. W .  L. Shanholtzer and H, E. Vehse, Bull. Am, Phys. Soc. Ser U 
Vol. 11, 220 (1966) 
4. G. R. Jefferson, Thesis (unpublished) West Virginia University. 
5. R. T. Schumacher and H .  E .  Vehse, J.  Phys. Chem. Solids, 24, -
297, (1963). 
6. D. W. Feldman and W .  D. Knight, Private Communicat ion  to 
R. T. Schumacher. 
7. G. Feher and A. F. Kip, Phys. Rev. E, 337, (1955) .  
THE ELECTRON SPIN SUSCEPTIBILITY OF METALLIC LITHIUX 
W.L. Shanholtzer and W.E. Vehse 
West Virginia University 
I. INTRODUCTION AND MOTIVATION FOR PRESEhT RESEARCH 
Tbe static magnetic suscept ibi l i ty  "of a metal is mually s l i g h t l y  
paramagnetic. This is due t o  the paramagnetism of the conduction electran 
spin manents. The contribution of the  spin moments t o  the t o t a l  suscepti- 
b i l i t y  may be i so la ted  and measured for cer tain metals, including lithium, 
using a spin resonance techxiique first devised by Schmcher  and S l i c h t e d .  
The motivation for the  present research was to increase the pre- 
cision of the  or ig ina l  man temperature measurements of Schumacher and 
Sl ichter ,  which, because of the work of Schumacher and Vehse2, we felt 
might be in error by as much as twenty percent. 
extend the measurement to liquid helium tcmperatues, which we have recently 
completed. 
analysis of the integrated area under the elect- spin resonance absorption 
curve from which t h e  paramagnetic suscept ib i l i ty  is determiaed. 
In addition, we wished to 
We proposed t o  increase t h e  precisian by a more systematic 
IT. TECHNIQUE 
The technique that we use in the measurement involves the  observa- 
t ion  of the radio-frequency spin suscept ibi l i ty  for both the  nuclei  and the 
conduction electrons. 
frequency, changing only the applied magnetic f i e ld .  
The measurement is made i n  the  same sample a t  constant 
It is possible t o  show3 that  the paramagnetic suscept ib i l i ty  of 
e i t h e r  nuclei or electrons is re lated to the  integrated area under the 
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resop1aace absorption curve plotted as a function of the magnetic f i e l d ,  
i.e. ; 
where y is t h e  nuclear o r  electrmic gymmagnetic ratio, o the frequency 
of the  applied rf f i e ld ,  and 
plex magnetic suscept ib i l i ty .  
integrated area under the  electron resonance curve and by A, for the m a  
under the  nuclear resanance c m ,  w e  see t h a t  f o r  a given freauency we 
have : 
*' (Ho) t he  absorption component of the  com- 
If we designate t h e  in tegra ls  by & f o r  the 
which is our working equatiaa. The constants ye and yn are known and the  
nuclear suscept ib i l i ty  is given accurately by the  Langevin-Debye formula: 
where Nn is the  number of nuclei/unit volume, I the nuclear spin,  and 
fi,k,T all have t h e i r  usual meaning. Thus t h e  experiment ccmsists of a 
simple canparison of areas. 
The measurements were perfomred at  ordinary radio frequencies. 
Q-meter detection is employed. 
i n  reference 2. 
h e  experimental apparatus is described 
The samples w e r e  paraffin o i l  o r  paraff in  wax dispersions of l i t h i u m  
par t ic les .  
Pictures of the  electron and nuclear resonances are taken with 
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a Polaroid camera; projected and traced on graph paper. 
t he  curves is determined and the experimental integrat ion performed by 
A base l i n e  for 
counting squares. As w e  mentioned earlier, a new feature of our work is a 
more detai led analysis of t he  integrated area under an electron sp in  resonance 
absorption curve, Because the electron sp in  resonance curves have broad 
Lorentzian ta i l s ,  some P o r t i a  o f t h e  total area may be excluded when 
drawing in the experimental base l ine.  In our analysis of the  area w e  
compute the f rac t iona l  error i n  t h e  experimental integrat ion due t o  the  
displacement of the base f ine  f'mm its t r u e  value and correct t h e  measured 
area accordingly. Corrections of fran 5 - 20% consistently y i e ld  the same 
values of x,, giving us additional confidence in our correction procedure. 
Determination of a base l i n e  for the nuclear xesanance curves is no problem 
e 
for t he  low temperature measurements, since the  curves, which appear t o  be 
Gaussian, fall off very rapidly i n  the wings. 
the  room temperature measurements as t o  whether it might be desirable t o  
(There is some question about 
apply a small correction t o  the  nuclear msonance areas also.) 
111. RESULTS OF THIS MEASUREMENT 
The results t h a t  we report  f o r  the  conduction electron spin suscepti-  
b i l i t y  of metallic lithium are: 
at 3OO0K. ........ 2.09 k .06 X cgs volume units.  
a t  4.2OK. ........ 2.18 k .20 X cgs volume units. 
IV. COMPARISON WITH OTHER VALUES 
Comparison of Experimental and Theoretical Values of ')lp e 
Experimental: 
Schumacher and S l i c h t e s  2.08 ?r 0 . 1 . X  . 
Hecht' 1.96 3f Q41 X loTG 
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Theoretical: 
5 Pines 
shimizu6 
~ i l v e r s t e i n 7  
1-90 x 10-6 
2.3.2 x 
2.20 x 10-6 (0%)  
In addition t o  the above direct cqar i sms ,  one can obtain xF 
f r o m  re la ted  measurements. 
r e l a t ed  to YFthmugh  the equation 
The Knight shift of t he  nuclear resonance is 
where K is the Knight shift. 
B is a col lect ion of w e l l  knawn canstants 
PF is the electroa probabili ty density at the  nucleus averaged over 
the Fermi surface and 
PA is s i m i l a r  t o  PF except t h a t  the  average is for the  free atom. 
The Overhouser or “day’’ s h i f t ,  D, is given by a s i m i l a r  expression, 
Combining these one has, 
Using the published values of K and D, one can infer t h a t  
xF= (1.90 - 1-98) x 10-6 cgs vol. units .  
The Korringa relation given i n  modified form by Pines’ relates 
xF t o  the nuclear spin lattice relaxation t i m e , T i e ;  the  absolute temperature, 
T; the  Knight s h i f t ,  K; the  r a t i o  of the  spec i f i c  heat constant for a real 
metal t o  t h a t  of the  free electron model C/c s a n d  t h e  conduction electron 
) 
suscept ib i l i ty  of the  fme electron model,,$*e. % This r e l a t ion  is 
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One obtains a of 2 .3  X 
values for the experimental quantities. 
cgs vol. units using the best current 
v. coIscLusIoN 
We conclude that the measwments of re as  originally reported by 
Schumacher and Slichter a m  essential ly  correct and i n  agreement with our 
low temperature measurements. 
P 
VI. ACKNOWLEDGEMENTS 
The support of NASA is gratefully acknowledged. We also wish t o  
thank Mr. R. L. Stenger for the use of h i s  equipment i n  performing our 
low temperature measurements. 
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. 
FOOTNOTES 
1. R. T, Schumacher and C .  P.  S l i ch ter ,  Phys. Rev, 101, 58, (1956). -
2. R. T. Schunacher and W. E. Vehse, J, Phys. Chem. Solids, 24, -
297, (1963). 
3. R. T. Schmacher, T. R. Carver, and C. P. SZichter, Phys. Rev. - 95, 1089 ( W  (1954). 
4. R. H e c h t ,  Phys. Rev. 132 966, (1963). 
-7 
5. D. Pines,  Solid State Physics (Academic P r e s s ,  Ine. New York, --
(19561, ed, F. Seitz and D. T u r n b u l l ,  Vol. I, p. 367. 
6. M. Shimizu, J. Phys, SOC. Japan, 15, 2227, (1960). 
7. S. Silverstein, Wys. Rev. - 130, No. 5, 1703, (June 1963). 
Conduction Elect- Susceptibil ity of 
htall ic Sodium at 4%. 
by R.L. Stenger Jr. and U.E. Vehse 
Department of Physics 
West Virginia University 
ABSTRACT 
Using a spin resonance technique, the paramagnetic ccintri- 
buticn of the conduction electrons to the total susmptibi l i ty  of 
metallic sodium has been isolated and measured at 4%. A Robinson 
MHR spectrometer w a s  used to make these measurements. The results 
are in excellent agreement w i t h  measurements at 20% and 77%. The 
precision is not yet high enough to  ru le  out a change in the suscepti- 
bility a8 the cause cf a Knight shift anomaly at low temperatures 
however. 
F 


The Paramagnetic Susceptibility of Lithium and Sodium Metal Final Report

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