BSTJ 30: 4. October 1951: Frequency Dependence of Elastic Constants and Losses in Nickel. (Bozorth, R.M.; Mason, W.P.; McSkimin, H.J.)

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ELASTIC CONSTANTS AND LOSSES IN’ NICKEL 987

2.5 X 10, and use of equation (2) with this and other appropr
indicates that the domain size is

1 = 0.035 mm, (2a)

as reported above.
‘A check on this value can be obtained from the frequency, fu corre-
sponding to the maximum of the vs f curve. If we use equation (16),

Pifa/R = 0.13, @)

with f= 1.5 X 10* (Fig. 11), we find /~ 0.045 mm, in reasonable agreement.
‘An actual photograph of domains in a single crystal of nickel, taken by H.
J. Williams and reproduced in Fig. 13, shows the presence of domains of
various sizes ranging from about 0.01 to 0.2 mm, Any such range in domain
sizes will naturally tend to flatten the maximum of the 6 vs f curve and,
on account of the form of the & vs f function, will push the maximum to a
higher frequency than that corresponding to the initial slope, and wi
4 lower maximum value to the decrement frequency curve.

‘The average domain size derived from our experiments is somewhat larger
than that previously obtained in 68 Permalloy.* This may be expectes
for nickel has a very high magnetostriction and the movement of domai
boundaries by stress will be relatively large, possibly so large that the re-
gions swept over by the domain walls will correspond to whole domains of
the original domain structure, when the stresses are equal to those used in
‘our experiments. The domain size which we have determined is based on
this interpretation,

APPENDIX
METHOD OF MEASUREMENT—FORMULAE

From transmission line theory (see reference of footnote 12) the ratio
of outputs, r, defined in the text and applicable to the circuit of Fig. 9 is
given by

1(Z1 4%
rm cosh ah +3 (2 + 2) sion oy
where @ = A ++ JB = propagation constant
iSo0_ characteris impedance of rod
At jB ped a

resistive terminating impedance provided by crystals
area of rod

‘This expression may be expanded into real and imaginary parts and the
latter term set to zero in accordance with the condition of phase balance,
U8 TE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951

B
‘Assuming that | Ze |>>Zrand that Q => 4 > 10, the ratio which is now a

real number determines the attenuation 4 in accordance with equation (13)
of the text.

Ti the crystal resonance frequency fis slightly diferent from the balance
frequency f, obtained with the rod specimen in place, correction may be
rade by considering a new terminating resistance Z formed by the crystal
driver and a small section of the rod sufficient to make the combined reso-
nance equal to fe. A slightly diferent length, f, of rod is then used to
compute velocities and attenuation. Also a different mass AI’, and rat
result. The equation applicable provided fa= Je is

id (= cosh At)

sinh AZ = “Pee (25)

lle

where

(26)

In the above a sufficiently accurate value of @ is ordinarily obtained by
assuming f, = fz. Further accuracy, if needed, can be obtained by recal-
culation, using the corrected value of Q.

We are glad to acknowledge the cooperation of Mr. J. G. Walker in grow-
ing and processing the single crystals used,? and in preparing also the poly-
crystalline specimen

Rerenences

4, EE Meshinin 1 eo Sie Amer 2 18 (98, patty mato K-

2. RM. Boson Valker, Piss. Res, 75, 1984
‘asis)

43. Sommavied by (0), Becker and W. Ding, Pevomenetignws, Srnge, Hein
i find by () Re M. Honor, Feconagnen, Van Nosttanl, New York

Nason, Ply Rex 83, 683 (1951).
sand R. M, Hosorth, Plye. Ren, 59,039 (1941), and reference 3,
‘Williams and J. G. Walker, Pi. Rev. 83, 634 (1951).
ELASTIC CONSTANTS AND LOSSES IN NICKEL 989

1.4.0, War J. Wins nd RM, onthe Se ramet 2,947 (90)
snd rlereice 2.

8. WP Mason, Pls, Re. 82,715, 1981.

5 W.'p. Maoog, Bisoelece Civatals and Their Application to Ultrasonics, Van
‘Nowranc, New York (1930.

10, K Honda dnt V. Srakava, Nippon Kinsoku Gakkat Si (Mt, fut, Mets, Japan)
“ADU 9ST, and Sc. Rep, Re Pay, Tohoku Univ. f, 9 (9).

11, Manama at aly aan 8, S382 aod Pl ec 7, $0 (950.

12 Thiel nthod a madicatio sf one deeb In *Elcromechanial Trance
and'ave Fitene We Fawn, D-Vay Neand (OED age 2407. For
FRequeples ove 20 ke, 45°Y2cu ammonium eydeogen phosphate crystals were
SoolBeloy 30 ke the iytale were comentedon are ras rods which were
Fitce at the ens ofthe mekel rv in place ofthe pesoelecee crystals alone

13, w! Daring, 2° Path 114,819 (99)