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SQU  Journal For  Science, 11 (2006) 95-101 
 © 2006 Sultan Qaboos University  

95  

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

K.A. Mohammed  

Department of Physics, College of Science, Sultan Qaboos University, P.O.Box 
36, Al Khod 123, Muscat, Sultanate of Oman, Email: kadhimm@squ.edu.om.   

   في درجات الحرارة الواطئة   Dy.40 Cu.37 Y.23يكة  الحرارة النوعية للسب

    كاظم احمد محمد   

تم في هذا البحث دراسة الحرارة النوعية في درجات الحرارة الواطئة للسبيكة العشوائية المغناطيسية   :خالصة 
Dy0.40Cu0.37Y0.23 2  في مدى درجات الحرارة K 50 إلى K .ة في الحرارة إذ تم حساب المساهمة المغناطيسي

النوعية وتغيرات االنتروبي المغناطيسي ودرجة حرارة التحول في الطور المغناطيسي والعزم المغناطيسي 
 K 28 مساوية تقريبا إلى Tmأظهرت الحرارة النوعية المغناطيسية قمة عريضة مرتكزة عند درجة حرارة، .المؤثر

كانت .   والمقاسة من التأثرية المغناطيسيةK 23.5المساوية إلى  وTf أعلى من قيمة Tmإن قيمة . متبوعة بتأثير شوتكي
 من قيمة االنتروبي المغناطيسي 84 % مساوية تقريبا إلى Tm إلى K 0قيم االنتروبي المغناطيسي المحسوبة بين 

عناصر تتفق تصرفات هذه السبيكة العشوائية مع تصرفات السبائك العشوائية المكثفة لل. العظمى المحسوبة نظريا
  .األرضية النادرة

  
ABSTRACT: 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. 

 
KEYWORDS:  Specific Heat, Amorphous Alloys, Dysprosium Amorphous Alloys. 

1.   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 



K.A. MOHAMMED 

  96

temperature, Tf, which is a function of the magnetic element, a broad maximum in the specific heat at a 
temperature, Tm, 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 Pr21Ag79, Sm21Ag79 and Lu21Ag79 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 Tf and Tm 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 Tf and Tm. The specific heat and ac susceptibility of the amorphous 
GdxCu0.37Y0.63-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 Dy0.40Cu0.37Y0.23 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 RE0.33Cu0.67, RE0.33Al0.67 and RE0.33Ag0.67 amorphous 
alloys have been reported (Mohammed et al., 1994). Spin glass like behavior and low temperature specific heat 
have been investigated for bulk amorphous ErxNi1-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). 

2.    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. 



SPECIFIC HEAT OF  Dy.40 Cu.37 Y.23 AMORPHOUS ALLOY   

  97

 
Figure 1. The ac susceptibility, χ versus temperature, T [Reference 5]. 

 
 
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 180o 
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). 

3.   Results and discussion 

The total specific heat results, Cp, of the magnetic Dy0.40Cu0.37Y0.23 amorphous alloy are shown in Figure 2 
as Cp versus temperature, T. Figure 2 also includes specific heat results of the non-magnetic Lu0.40Cu0.37Y0.23 
amorphous alloy for comparison (Mohammed et al., 1987). It is clear that there is no sharp transition in Cp at the 
ordering temperature, as observed in crystalline Dy metal and alloys (Lounassma et al.,1966). 

 



K.A. MOHAMMED 

  98

 
 

Figure 2. The specific heat Cp versus temperature, T. 
 
 
The total specific heat Cp of the amorphous magnetic alloys can be written as ;  
 

p e L mC = C +C +C                                                                          (1) 
       
where Ce, CL and Cm represent the electronic, lattice and magnetic terms respectively. Cm forms the major part of 
Cp for magnetic materials below their critical temperatures. An acceptable method to estimate values of the non-
magnetic terms  Ce and CL 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 Lu0.40Cu0.37Y0.23 amorphous 
alloy can be considered to be the best alloy to represent the non-magnetic terms in the specific heat of the 
magnetic Dy0.40Cu0.37Y0.23 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 Lu0.40Cu0.37Y0.23 amorphous alloy from the total specific heat Cp of the amorphous 
Dy0.40Cu0.37Y0.23 alloy, i.e.; 
                   

( ) ( )m p Dy-Cu-Y Lu-Cu-YC =C C p−                                                                                       (2) 
          



SPECIFIC HEAT OF  Dy.40 Cu.37 Y.23 AMORPHOUS ALLOY   

  99

 
Figure 3. The magnetic specific heat, Cm versus temperature, T. 

 
Figure 4. Cm / T versus temperature, T. 

 
 



K.A. MOHAMMED 

  100

Values of Cm for this alloy are shown in Figure 3 as Cm versus T. This excess specific heats have been 
attributed to the magnetic effects in this magnetic alloy. It is clear that Cm shows clearly broad maximum 
centered at Tm=28±1 K. The value of Tm is about 1.1 times higher than the value of Tsg(=23.5 K)_ obtained from 
the low field ac susceptibility results (del Moral et al.,1986). Values of Cm/T versus T are shown in Figure 4. 

The magnetic entropy changes, Sm, in the magnetic systems are usually related to the magnetic specific 
heat, Cm, through the following relation. 

m
m

C
S c dT

T
= ∫                                                                         (3) 

where c represents the molar fraction of the magnetic metal in the alloy. The magnetic entropy changes, Sm(Tm), 
in the alloy between 0 K and Tm  have been determined by integrating the smooth Cm results between 0 K and Tm 
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  

( )ln 2 1mS R J= +                                                                     (4) 
 where R is the gas constant. The numerically estimated values of the magnetic entropy changes, Sm(Tm), 
between 0 K and Tm 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 Sm(Tm)/Sm(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 Tf and Tm. This is very similar to the results of 
(Hattori et al.,1995) for the magnetic amorphous ErxNi1-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. 

The results of the low temperature specific heat of the amorphous Dy-Cu-Y alloy agree quite well with 
reported results for other magnetic amorphous systems such as Pr21Ag79, Sm21Ag79 and Lu21Ag79 amorphous 
alloys (Garoche et al.,1980), Gd-Y-Cu (Mohammed et al., 1986), Tb-Y-Ni (Mohammed,1998), Er-Ni (Hattori et 
al., 1995), Gd-Cu (Mohammed, 2002) and Er-Cu-Y and Ho-Cu-Y (Mohammed, to be published). 
 

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

Dy.40Cu.37Y.23 Calculated 
Parameters 

Value Ref. 
Tf  (K) 23.5  [del Moral, 1986] 
Tm  (K) 28 ± 1  
Tm / Tf 1.1 
Sm (Tm) (J/mol,K) 19.5 ± 1 
Spin (J) 15/2 
Effective Spin 6.3 
Sm(max) = Rℓn (2J+1) 23.56 
Sm(Tm) / Sm(max)  % 84 ± 2 

 
 
 

This 
Study 

4.   Conclusion 

The specific heat of the magnetic Dy0.40Cu0.37Y0.23 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, 
Tf, of the phase transition but the magnetic specific heat exhibits broad anomaly centered at Tm of about 28±1 K. 
The value of Tm is 1.1 higher than Tf determined from susceptibility measurements for the same alloy. The 
maximum magnetic entropy changes expected theoretically, Sm(max), is calculated using the relation R ln(2J+1) 



SPECIFIC HEAT OF  Dy.40 Cu.37 Y.23 AMORPHOUS ALLOY   

  101

for the spin value, J = 15/2 for a mole of Dy ions. The ratio of Sm(Tm)/Sm(max) is equal to about 84 %. This gives  
an effective spin value equal to about 6.3 rather than 15/2. 

5.    Acknowledgment  

The experimental part has been done at the Physics Department Southampton University (U.K.) The author 
would like to thank the magnetism group at Southampton for their help with these measurements. 

6.    References   

COEY J. M.D. 1978. Amorphous Magnetic Order. J. Appl. Phys.49: 1646-1652. 
DEL MORAL A., ARNAUDAS J.J. and MOHAMMED K.A. 1986. Spin Glass Parameter of RE-Cu-Y Alloys 

(RE=Rare Earth). Solid State Commun.58: 395-398. 
GAROCHE P., FERT A., VEYSSIE J.J. and BOUCHER B. 1980. Specific Heat of Rare Earth Amorphous 

Alloys. J. Magn. Magn. Mater. Vol. 15-18:1397-1398.  
HARRIS R., PLISCHKE M. and ZUCKERMANN M.J. 1979. New Model for Amorphous Magnetism. Phys. 

Rev. Lett. 31: 160-162.  
HATTORI H., FUKAMICHI K., SUZUKI K., ARUGA-KATORI H. and GOTO T. 1995. Spin-glass-like 

Behaviour and Low-temperature Specific Heat of Amorphous ErxNi1-x Random Magnetic Anisotropy 
System. J. Phys. : Condens. Matter. 7: 4193-4205. 

LANCHESTER P.C. and MOHAMMED K.A. 1985. Apparatus For Heat Capacity Measurements of Amorphous 
Metals. J. Phys. E : Sci. Instrum.18: 581. 

LIEBERMANN H. and GRAHAM, C., Jr 1976. Production of Amorphous Alloy Ribbons and Effect Apparatus 
Parameters on Ribbon Dimensions. IEEE Trans. Magn. 12: 921-923. 

LOUNASMAA O.V. and SUNDSTROM L.J. 1966. Specific Heat of Gadolinium, Terbium, Dysprosium, 
Holmium and Thulium Metals between 3 and 25 K.  Phys. Rev. 150: 399-412. 

MOHAMMED K.A. and LANCHESTER P.C. 1986. The Low Temperature Specific Heat of Gd-Cu-Y Metallic 
Glasses. J. Magn. Magn. Mater. 60: 275-284. 

MOHAMMED K.A. and LANCHESTER P.C. 1987. The Low Temperature Specific Heat of Lu-Cu-Y Metallic 
Glasses. J. Magn. Magn. Mater. 65: 15-20. 

MOHAMMED K.A. 1994. The Low Temperature Specific Heat and Spin Glass Ordering Temperature of 
RExCu1-x, RExAg1-x AND RExA11-x Metallic Glasses. J. Edu. and Sci. 22: 57-63. 

MOHAMMED K.A. 1998. The Specific Heat and AC Susceptibility of Tb- Metallic Glasses. Raf. Jour. Sci. 9: 
84-89. 

MOHAMMED K.A. 2002. THE Specific Heat and ac Susceptibility of Gd.33Cu.67 Metallic Glass. J. Abhath AL-
Yarmouk : “Pure Sci. & Eng.” 11: 183-191. 

RAINFORD B.D., SAMADIAN V., BEGUM R.J., LEE E.W. and BURKE S.K. 1982. Crystal Field Splittings in 
Dilute Amorphous Rare Earth Alloys. J. Appl. Phys. 53: 7725-7727. 

 
 
 
Received   17 October 2004          
Accepted   28 February 2006