HEAT CAPACITY MEASUREMENTS ON THE DILUTED ISING SYSTEM Cs3CopZn1-pCl5

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HEAT CAPACITY MEASUREMENTS ON THE DILUTED ISING SYSTEM Cs3CopZn1-pCl5

E. Lagendijk, W. Huiskamp, P. Bongers

To cite this version:

E. Lagendijk, W. Huiskamp, P. Bongers. HEAT CAPACITY MEASUREMENTS ON THE DILUTED

ISING SYSTEM Cs3CopZn1-pCl5. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1008-C1-

1009. �10.1051/jphyscol:19711359�. �jpa-00214395�

JOURNAL DE PHYSIQUE Colloque C 1, supplkment au no 2-3, Tome 32, F'e'vrier-Mars 1971, page C 1 - 1008

HEAT CAPACITY MEASUREMENTS

ON THE DILUTED ISING SYSTEM Cs3CopZn,-,CIS

E. LAGENDIJK and W. J. HUISKAMP Kamerlingh Onnes Laboratory, Leiden, The Netherlands

and P. F. BONGERS

Philips Research Laboratories, Eindhoven, The Netherlands

R6sum6. - Des mesures de la chaleur spkcifique sur le systkme Cs3Co,Zn1-,Cls montrent que TN dbpend de p d'une manikre qui correspond nettement avec les calculs sur le modkle d'Ising pour un rBseau cubique simple et pour une dilution au hasard des ions magnktiques.

Abstract. - Heat capacity measurements on the system Cs3Co,Zn1,Cls show a dependence of TN on p which agrees with calculations on the randomly diluted simple cubic (s. c.) Ising model.

Low temperature measurements on the magnetic heat capacity C, have been performed on a series of compounds Cs,Co,Zn, -,C15 with p = 1 .O, 0.9, 0.8, 0.7, 0.5 respectively.

The system C S , C O , Z ~ ~ - , C ~ ~ is a favorable one for comparison with theories [I, 2, 31 on the influence of dilution on the critical point behaviour of an anti- ferromagnet with experiment because : a) the undiluted compound Cs,CoCl, represents nicely a three dimen- sional s. c. Ising system [4], b) the lattice parameters for p = 1 and p = 0 differ only 0.5 %, c) the exchange interaction is approximately the same for the undiluted and the very diluted case 141.

The mixed compositions were prepared from Cs,CoCl, and Cs,ZnCl, by melting in a platinum crucible contained in an evacuated silica ampoule at 700 OC. X-ray powder patterns showed the samples to have the Cs3CoC1, structure ; no second phase could

.

$a) molecular field (b) lsing s.c. (c) lsing sq,

s = f Y

FIG. 1. - Measured specific heat curves together with some theoretical predictions.

be detected. Cs3ZnC1, and Cs,CoCl, have the same crystal structure with nearly identical lattice para- meters 151, a = 9.25 A, c = 14.50 A and a = 9.22 A, c ⁼ 14.55 A respectively. Therefore the occurrence of completely mixed crystals could not be deduced unambiguously from the X-ray data, the width of the reflection lines being comparable to the separation of the lines f o r p = 0 a n d p = 1.

The component Cs3CoC1, (Co content 10.6 + ^{0.5 %,}

theor. 9.3) was obtained from an aqueous solution containing excess of CsC1. Cs,ZnCl, (Zn content 10.6 + ^{0.3 %} theor. 10.2) was prepared by heating CsCl with carefully dried Cs,ZnCI, which was obtai- ned from an aqueous solution of CsCl and ZnC1,.

The apparatus and the use of carbon resistance ther- mometry have been described before [6]. We have measured a series of peaks at Tm = 0.513, 0.450, 0.404, 0.343, 0.228 OK for decreasing p-values, Tm being the temperature at which the maximum in the specific heat is attained. The measured specific heat curves for p = 1.0, p = 0.7 and p = 0.5 are shown in figure 1, together with the theoretical predictions

FIG. 2. - Reduced critical temperature of the system CssCo,Zn

1,Cls as a function of p compared with theoretical calculations line : a. Smart 121, BPW, z

6 ; b. Heap [3], S. C. Ising ; c.

Heap [3], S. C. Heisenberg ; see text.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711359

HEAT CAPACITY MEASUREMENTS ON THE DILUTED ISING SYSTEM C 1 - 1009

for the three-dimensional s. c. Ising model, the two- dimensional square Ising model and the molecular field. For comparison the experimental points have been multiplied by l/p in the vertical scale (not all points measured are shown in the figure). I t is remarka- ble that the heat capacity peaks remain sharp at low p-values, showing a pronounced critical behaviour and little impurity broadening even at high dilution.

The entropy values measured and the high tempera- ture dependence of the specific heat on p are in good agreement with the expected proportionality with p.

The short range ordering entropy is approximately constant for a wide range of p-values, so the ratio of short range to long range ordering entropy is increasing, which suggest a transition to lower dimensionality

in the ordering process as predicted by Oguchi [I].

I n figure 2, T,(p)/T,,,(I) is plotted versus p and compared to various theoretical calculations. Line a shows the result of B. P. W. calculations of Smart [2]

with coordination number z = 6 , line b is the result for the s. c. Ising model obtained by Heap [3] by the method of series expansion of the susceptibility, line c shows his result for the s. c. Heisenberg model in the high p region. The vertical arrow shows the cal- culated critical concentration by Sykes et al. 171.

It is clear from the figure that more data on the low p-side are necessary to make a distinction between case a and case b. Results of measurements on more diluted samples and a more detailed analysis of the data will be published elsewhere.

References

[I] OGUCHI (T.), J. Phys. Soc. Japan, 1969, 26, 580. [5] VAN STAPELE (R. P.), BELJERS (H. G.), BONGERS (P. F.) [2] SMART (J. S.), J. Phys. Chem. Sol., 1960, 16, 169. and ZIJLSTRA (H.), J. Chem. Phys., 1966, 44, [3] HEAP (B. R.), PYOC. Phys. Soc., 1963, 82,252. 3719.

[4] WIELINGA (R. F.), BLOTE (H. W. J.), ROEST (J. A.) and 161 MESS (K. W.), thesis, Leiden University 1969 and HUISKAMP (W. J.), Physica, 1967,33, 555. LAGENDIJK (E.), to be published.

[7] S Y K E ~ (M. F.) and ESSAM (J. W.), Phys. Rev., 1964,

133, A 310.