Specific Heat of Dy . 40 Cu . 37 Y . 23 Amorphous Alloy at Low Temperatures

The low temperature specific heat of the magnetic Dy0.40Cu0.37Y0.23 amorphous alloy have been investigated in the temperature range 2 to 50 K. The magnetic contributions to the specific heat, magnetic entropy changes, ordering temperatures and the effective magnetic spin have been estimated for this magnetic amorphous alloy. The magnetic specific heat show broad anomaly at a certain temperature, Tm of about 28 K. The value of Tm is higher than Tf (=23.5 K) determined from low field ac susceptibility measurements. The magnetic entropy changes between 0 K and Tm are estimated to be 84 % of the maximum theoretical value. The behaviors of this amorphous alloy agree quit well with those of condensed rare earth amorphous systems.


Introduction
rystal field effects are likely to be well-defined in amorphous rare earth (RE) alloys.The topological disorder in this amorphous alloy results in a competition in sign exchange interactions together with random uniaxial crystal fields with the local easy axis of magnetic anisotropy varying from site to site (Coey, 1978;Harris et al., 1979).The low temperature specific heat of rare earth magnetic amorphous alloys appears to posses intrinsic features such as the well defined sharp anomaly in the low field ac susceptibility at a certain C temperature, T f , which is a function of the magnetic element, a broad maximum in the specific heat at a temperature, T m , and specific heat linear term in T at low temperatures.Moreover, characteristics contributions to the specific heat are expected in the paramagnetic phase resulting from the crystal field excitations.The low temperature specific heat results of some rare earth metals and alloys show another contribution to the specific heat arising from the hyperfine nuclear magnetic effects (Garoche et al., 1980).
Measurements of the specific heat of Pr 21 Ag 79 , Sm 21 Ag 79 and Lu 21 Ag 79 amorphous alloys reported by (Garoche et al., 1980) are characterized by a large and nearly temperature independent term down to very low temperatures.These behaviors have been attributed to the low energy crystal field excitations associated with the distribution of the asymmetry parameter of the crystalline electric field effects.
Values of the magnetic entropy changes, which have been usually estimated between 0 K and T f and T m are usually less than the maximum magnetic entropy expected theoretically.This means that effective spin value is less than the maximum value expected for pure metals and there is still considerable amount of magnetic order even at temperatures higher than T f and T m .The specific heat and ac susceptibility of the amorphous Gd x Cu 0.37 Y 0.63-x (0<x<0.63)have been studied at low temperature (Mohammed et al., 1986).This investigation showed the spin glass nature for x<0.35 for Gd.The magnetic amorphous Dy 0.40 Cu 0.37 Y 0.23 alloy exhibits low cusp in its low field ac susceptibility as shown in Figure 1, indicating spin glass phase transition to the paramagnetic phase (del Moral et al.,1986).Theoretical calculations of Debye temperature, lattice specific heat and the spin glass ordering temperatures in the magnetic RE 0.33 Cu 0.67 , RE 0.33 Al 0.67 and RE 0.33 Ag 0.67 amorphous alloys have been reported (Mohammed et al., 1994).Spin glass like behavior and low temperature specific heat have been investigated for bulk amorphous Er x Ni 1-x (x=0.33,0.50 and 0.80) alloys prepared by high rate direct current sputtering (Hattori et al., 1995).The specific heat parameters of the magnetic Er-Cu-Y and Ho-Cu-Y amorphous alloys had been investigated in the temperature range 0 K to 50 K (Mohammed K. A. to be published).

Experimental procedure
The phase diagram of the crystalline binary Cu-Y alloys shows that the deepest eutectic point occurs at about 33 at % Cu.It has been reported (Rainford et al., 1982).that a 37 at % Cu is marginally better for glass formation than 33 at % Cu.Accordingly, copper proportion was fixed at 37 at % in this sample.Prior to preparing ribbons in the amorphous state polycrystalline alloys were prepared by melting together appropriate quantities of Dy, Cu and Y of 99.99% nominal purity, which were supplied by rare earth products Ltd.The alloys were prepared in an arc furnace in a high purity (99.999%) reduced argon atmosphere.The alloy was turned and remelted many times to promote homogeneity.The loss in the total mass after alloying was less than 0.1 %.The production of the amorphous ribbons method was the well tried melt spinning technique, which is quite similar to that described by Liebermann et al. (1976).In this method typically about half a gram of an alloy is melted by rf induction in a quartz crucible and immediately expelled under pressure onto a rapidly rotating massive copper wheel, which cools the melt sufficiently rapidly for amorphous samples to be produced.The crucible was about 5 to 10 cm long and 9 to 10 mm in diameter with an orifice of about 1mm diameter at its bottom end.High purity (5N) argon gas at pressure of 5 to 10 psi was used to force the molten stream through the hole in the bottom of the tube.The space between the orifice and the surface of the copper wheel was between 1 and 3mm.The diameter of the copper wheel was 15 cm and the optimum speed of rotation was found to be approximately 4000 to 6000 rpm.The amorphous nature of the ribbons was checked by studying the x-ray diffraction using CuKα radiation.Normally no evidence of crystallite was observed.On the matter of testing samples for amorphicity, it is perhaps of interest to point out that we have found that in nearly every case an amorphous ribbon can sustain a sharp 180 o bend without fracture whereas the same operation will break ribbons with any trace of crystalline.This has been used to test the amorphicity of the very long length of ribbon required to form a satisfactory sample for heat capacity measurement.The heat capacity was measured using a modified adiabatic continues heating technique from 4.2 K to 50 K while the heat pulse technique has been used in the temperature range 1.5 K to 7 K.The accuracy of the measured temperature and the heat capacity were better than ± 3 mK and 1 % respectively (Lanchester et al.,1987).

Results and discussion
The total specific heat results, C p , of the magnetic Dy 0.40 Cu 0.37 Y 0.23 amorphous alloy are shown in Figure 2 as C p versus temperature, T. Figure 2 also includes specific heat results of the non-magnetic Lu 0.40 Cu 0.37 Y 0.23 amorphous alloy for comparison (Mohammed et al., 1987).It is clear that there is no sharp transition in C p at the ordering temperature, as observed in crystalline Dy metal and alloys (Lounassma et al.,1966).where C e , C L and C m represent the electronic, lattice and magnetic terms respectively.C m forms the major part of C p for magnetic materials below their critical temperatures.An acceptable method to estimate values of the nonmagnetic terms C e and C L is to use experimentally measured specific heat results of a similar but non-magnetic material (Lounassma et al.,1966).Therefore, the specific heat of the non-magnetic Lu 0.40 Cu 0.37 Y 0.23 amorphous alloy can be considered to be the best alloy to represent the non-magnetic terms in the specific heat of the magnetic Dy 0.40 Cu 0.37 Y 0.23 amorphous alloy.Fortunately, the experimental results of the reference materials do not need to be corrected for the atomic mass difference between the magnetic and non magnetic crystalline alloys because the average atomic weights are very similar and the difference does not affect the accuracy of such calculations.
The magnetic contribution to the specific heat can now be obtained simply by subtracting the specific heat of the non-magnetic Lu 0.40 Cu 0.37 Y 0.23 amorphous alloy from the total specific heat C p of the amorphous Dy 0.40 Cu 0.37 Y 0.23 alloy, i.e.;  Values of C m for this alloy are shown in Figure 3 as C m versus T. This excess specific heats have been attributed to the magnetic effects in this magnetic alloy.It is clear that C m shows clearly broad maximum centered at T m =28±1 K.The value of T m is about 1.1 times higher than the value of T sg (=23.5 K) _ obtained from the low field ac susceptibility results (del Moral et al.,1986).Values of C m /T versus T are shown in Figure 4.
The magnetic entropy changes, S m , in the magnetic systems are usually related to the magnetic specific heat, C m , through the following relation.where c represents the molar fraction of the magnetic metal in the alloy.The magnetic entropy changes, S m (T m ), in the alloy between 0 K and T m have been determined by integrating the smooth C m results between 0 K and T m respectively.Moreover, the magnetic entropy changes (per mole) are theoretically related to the magnetic spin, J, of the magnetic element in the magnetic systems through another relation, which is ( ) where R is the gas constant.The numerically estimated values of the magnetic entropy changes, S m (T m ), between 0 K and T m are shown in Table 1 together with the expected maximum entropy values obtained from equation (4) for J=15/2 for Dy ions.The ratio S m (T m )/S m (max) is equal to about 84 % .This indicates that the effective spin value is equal to about 6.3 rather than 15/2 in this alloy and the that there is still a considerable amount of magnetic order even at temperatures higher than T f and T m .This is very similar to the results of (Hattori et al.,1995) for the magnetic amorphous Er x Ni 1-x system, which shows magnetic entropy changes of about 45 % to 60 % of the theoretical maximum values with an effective spin value less than the 15/2 expected for Er ions.

Conclusion
The specific heat of the magnetic Dy 0.40 Cu 0.37 Y 0.23 amorphous alloy has been investigated in the temperature range 2 to 50 K.The total specific heat does not show any clear changes at the ordering temperature, T f , of the phase transition but the magnetic specific heat exhibits broad anomaly centered at T m of about 28±1 K.The value of T m is 1.1 higher than T f determined from susceptibility measurements for the same alloy.The maximum magnetic entropy changes expected theoretically, S m (max), is calculated using the relation R ln(2J+1)

Figure 2 .
Figure 2. The specific heat C p versus temperature, T.

Figure 3 .
Figure 3.The magnetic specific heat, C m versus temperature, T.

Table 1 .
Specific heat parameters of the magnetic Dy .40Cu .37Y .23 amorphous alloy.