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The entropy associated with the magnetic transitions of the HCP rare earth metals
Scripta METALLURGICA
Vol. I, pp. 157-160, 1967 Printed in the United States
Pergamon Press, Inc.
THE ENTROPY ASSOCIATED WITH THE MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
David Smith
Department of Chemistry, Brooklyn College of the Clty University of New York, Brooklyn, New York
(Received August 31, 1967) The low temperature heat capacity results of the hexagonal close-packed metals from 20°K may be represented by Cp = Cq- + TT + (aCq)ST
Cq = 3D (e/T)
where D (x) represents the Debye function, TT the electronic contribution to the heat capacity, and (aCq)~T the difference between the heat capacity at constant pressure, Cp, and the heat capacity at constant volume.
The heat capacity data of zinc and cadmium can not be re-
presented by a single Debye function. than the other hcp metals.
Both zinc and cadmium have much higher c/a ratios
This explains the necessity of splitting the single Debye func-
tion with three degrees of freedom into two Debye functionsj one with two degrees of freedom and the other with one degree of freedom.
The heat capacity results of the twelve metals
listed in Table I can be represented by the above equations to within 0.i0 cal./deg.(g atom) between 20°K and 50°K and within 0.05 cal./deg.(atom) between 50°K and 300°K. A simple relation, due to Lindemann, relates the Debye characteristic temperature, e, with the melting point T of a metal.
If M Is the gram-atomic weight and V the gram-atomic
volume, then
FTm K is a constant. The values of 8 and "a" are determined from the heat capacity results below room temperature.
The values of y for the metals are taken from heat capacity results at liquid
helium temperatures (1)3 except for the metals La, Lu, Sc, and Y.
157
For these four metals
158
MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
Vol. 1, No. 3
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Vol. 1, No. 3
MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
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160
MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
Vol. 1, No. 3
the value of "a" was assumed to be equal to zero, since the dilation correction to the heat capacity is less than 0.05 cal./deg. (g atom) at 300°K. the heat capacity results between 20°K and 300@K.
The value of V is determined from
The values of ~ computed in this way are
somewhat lower than the values computed from the heat capacity results at liquid helium temperatures. Nine of the twelve hexagonal metals listed in Table I have values of K between 124 and 128.
By assuming that the rare earth metals which exhibit magnetic transitions have similar
values of K, it is possible to compute Cq, and subtractlng (Cq + VT) from the observed heat capacity, calculate the magnetic heat capacity.
In Table II are listed the values of the
Debye characteristic temperatures assuming a value of K of 127. La, Lu, Sc, and Y is 0.0018 eal./deg.S(g atom). netic rare earth metals, except for erbium.
The average value of V for
This is the value of V taken for the mag-
The value of V for erbium was chosen so that
the heat capacity associated with the magnetic transition would make no contribution to the observed heat capacity at 320°K.
The value of "a" for all the rare earth metals was assumed
to be equal to zero. For those metals in which the magnetic transition contributes to the heat capacity at room temperature, it is necessary to extrapolate the magnetic heat capacity to higher temperatures.
This may be done by assuming that the magnetic heat capacity above the N~el tem-
perature can be represented by AT -n, where A and n are constants. 2.2~ for Tin, 2.Oj for Tb, 1.8j and for Ho, 2.3.
The value of n for Dy is
The value of n for the other metals was as-
sumed to be equal to 2.0. In Table II the entropy associated with the magnetic transitions of the hcp rare earth metals are tabulated.
The values listed under the column heading S (T) @re the entropy values
at the highest temperature at which heat capacity measurements have been made with an adiabatic calorimeter.
Under the heading S (T = ~) the entropy computed by extrapolating the mag-
netic entropy are in excellent agreement with the expected values, except in the case of erbium.
This procedure has permitted an accurate determination of the heat capacity and entro-
py associated with the magnetic transitions of the hcp rare earth metals.
References 1.
R. O. Hultgren, R. L. Orr, P. D. Anderson and K. K Kelley, Selected Values of Thermodynamic Properties of Metals and Alloys, John Wiley & Sons, New York, (1963).
Vol. I, pp. 157-160, 1967 Printed in the United States
Pergamon Press, Inc.
THE ENTROPY ASSOCIATED WITH THE MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
David Smith
Department of Chemistry, Brooklyn College of the Clty University of New York, Brooklyn, New York
(Received August 31, 1967) The low temperature heat capacity results of the hexagonal close-packed metals from 20°K may be represented by Cp = Cq- + TT + (aCq)ST
Cq = 3D (e/T)
where D (x) represents the Debye function, TT the electronic contribution to the heat capacity, and (aCq)~T the difference between the heat capacity at constant pressure, Cp, and the heat capacity at constant volume.
The heat capacity data of zinc and cadmium can not be re-
presented by a single Debye function. than the other hcp metals.
Both zinc and cadmium have much higher c/a ratios
This explains the necessity of splitting the single Debye func-
tion with three degrees of freedom into two Debye functionsj one with two degrees of freedom and the other with one degree of freedom.
The heat capacity results of the twelve metals
listed in Table I can be represented by the above equations to within 0.i0 cal./deg.(g atom) between 20°K and 50°K and within 0.05 cal./deg.(atom) between 50°K and 300°K. A simple relation, due to Lindemann, relates the Debye characteristic temperature, e, with the melting point T of a metal.
If M Is the gram-atomic weight and V the gram-atomic
volume, then
FTm K is a constant. The values of 8 and "a" are determined from the heat capacity results below room temperature.
The values of y for the metals are taken from heat capacity results at liquid
helium temperatures (1)3 except for the metals La, Lu, Sc, and Y.
157
For these four metals
158
MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
Vol. 1, No. 3
!
¢II.
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0
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0
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v
gl
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0
G)
O 4~
-m
o~ ~,
~,
~.
~
~~
~.
~, .•
g.
~"~
~
o, ¢J
M
Vol. 1, No. 3
MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
8
o
Oh
II
°
K-
-I"
,-I Lrx
i"-I ~
~ ~1
~ kD
O r-I `%
11: 4~ r-4
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CO
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~
tf~
tY~
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O~
159
160
MAGNETIC TRANSITIONS OF THE HCP RARE EARTH METALS
Vol. 1, No. 3
the value of "a" was assumed to be equal to zero, since the dilation correction to the heat capacity is less than 0.05 cal./deg. (g atom) at 300°K. the heat capacity results between 20°K and 300@K.
The value of V is determined from
The values of ~ computed in this way are
somewhat lower than the values computed from the heat capacity results at liquid helium temperatures. Nine of the twelve hexagonal metals listed in Table I have values of K between 124 and 128.
By assuming that the rare earth metals which exhibit magnetic transitions have similar
values of K, it is possible to compute Cq, and subtractlng (Cq + VT) from the observed heat capacity, calculate the magnetic heat capacity.
In Table II are listed the values of the
Debye characteristic temperatures assuming a value of K of 127. La, Lu, Sc, and Y is 0.0018 eal./deg.S(g atom). netic rare earth metals, except for erbium.
The average value of V for
This is the value of V taken for the mag-
The value of V for erbium was chosen so that
the heat capacity associated with the magnetic transition would make no contribution to the observed heat capacity at 320°K.
The value of "a" for all the rare earth metals was assumed
to be equal to zero. For those metals in which the magnetic transition contributes to the heat capacity at room temperature, it is necessary to extrapolate the magnetic heat capacity to higher temperatures.
This may be done by assuming that the magnetic heat capacity above the N~el tem-
perature can be represented by AT -n, where A and n are constants. 2.2~ for Tin, 2.Oj for Tb, 1.8j and for Ho, 2.3.
The value of n for Dy is
The value of n for the other metals was as-
sumed to be equal to 2.0. In Table II the entropy associated with the magnetic transitions of the hcp rare earth metals are tabulated.
The values listed under the column heading S (T) @re the entropy values
at the highest temperature at which heat capacity measurements have been made with an adiabatic calorimeter.
Under the heading S (T = ~) the entropy computed by extrapolating the mag-
netic entropy are in excellent agreement with the expected values, except in the case of erbium.
This procedure has permitted an accurate determination of the heat capacity and entro-
py associated with the magnetic transitions of the hcp rare earth metals.
References 1.
R. O. Hultgren, R. L. Orr, P. D. Anderson and K. K Kelley, Selected Values of Thermodynamic Properties of Metals and Alloys, John Wiley & Sons, New York, (1963).