3. THERMAL PROPERTIES UNDER HIGH PRESSURE 1 General survey
3.2 Experimental measurements at high pressure .1 Specific heat
Figure 28 shows the schematic drawing of a miniature piston-cylinder pressure cell designed for the adiabatic method. The dimensions of the CuBe cylinder are 8.8 and 2.7 mm in outer and inner diameters,
respectively, and the cylinder is 21 mm long. ZrO2is used for the piston and the piston-backup. Gold-plated Cu is used for sample cell. Teflon may also be used for the sample cell, but its heat capacity exhibits strong pressure dependence, which increases the uncertainty of the background.
The cell can be attached to a cryostat for specific heat measurement, and the same cell can be loaded into a Magnetic Property Measurement System (MPMS) in order to calibrate pressure at low temperature for the magnetization measurements, as also shown inFigure 28. For the mea- surements of specific heat, the thermometer and heater are fixed on the opposite swivels. These swivels are suspended from cold plate of 3He cryostat or mixing chamber of dilution refrigerator to an adiabatic space.
The upper lock nut is installed on the upper swivel, and the lower swivel is fixed to the lower lock nut with a small screw as inFigure 28.
During the measurements of the heat capacity under pressure, changes in the heat capacity of the pressure media must be accounted for. For example, the change in the specific heat of Fluorinert 70/77 is large at low pressures, and it becomes smaller pressure increases. The data below 5 K have been fitted using the following equation: C(P)¼ gglass(P)Tþb(P)T3 because Fluorinert 70/77 becomes glass-like solid under pressure at low temperatures. These results and those fitted using
Lifting thread Swivel
Swivel Setscrew
8.8
21mm
For heat capacity
Piston backup
Piston backup
For SQUID Magnetometer Piston
Piston Cu—cell Cu—cap Upper
lock nut
Lower lock nut Cylinder
(CuBe)
FIGURE 28 Schematic of the miniature piston-cylinder pressure cell (Uwatoko et al., 2005).
the asymptotic function f(P)¼a/(Pþb)þc in order to represent the specific heat of Fluorinert 70/77 at any pressure, where a,b, and c are the constants (Tomioka et al., 2008), show reasonable approximation of the heat capacity of this pressure-transmitting medium.
To avoid complications arising from the pressure variations of the background specific heat, it is possible to use solid AgCl as a pressure- transmitting medium. The pressure dependence of the specific heat of AgCl is negligibly small. However, liquid medium such as Fluorinert 70/77 is preferred for better hydrostaticity of the applied pressure.
To evaluate the performance of the described micro-pressure cell system in the temperature range from 0.7 to 5 K at pressure up to about 1.5 GPa, specific heat measurements of CeRhSi3, which has a non-centro- symmetric tetragonal BaNiSn3 structure, were carried out. This com- pound has a significantly enhanced electronic specific heat coefficient g of about 120 mJ/mol K2. Antiferromagnetic ordering temperatureTNhas been reported to be 1.6 K and the magnetic entropy released is only 12% of Rln 2 belowTN(Muro et al., 1998). The SC appears above about 1 GPa where the antiferromagnetic transition vanishes (Kimura et al., 2005).
Single crystal of CeRhSi3, Fluorinert 70/77, and Pb with mass of about 37, 25, and 0.18 mg were loaded into the Cu sample cell. To maintain the hydrostaticity of pressure, the volume of CeRhSi3was about 40% of that of sample cell. The specific heat of CeRhSi3was measured at high pres- sure and will be described in detail in the following section.Figure 29 shows the temperature dependence of specific heat of the pressure cell, Fluorinert 70/77, and sample at ambient pressure. These are about 87%,
Pressure cell 0.00
C (mJ/mol K) 0.5
1.0 1.5
1 2
T (K)
3 4
CeRhSi3 Fluorinert
Whole heat capacity
FIGURE 29 Temperature dependence of specific heat of the pressure cell, Fluorinert 70/77 and CeRhSi3sample at ambient pressure (Tomioka et al., 2008).
6%, and 7% of the total value at 2.5 K, respectively. One can see that the heat capacity of the pressure medium is a smooth function of temperature and a peak due to AFM transition is clearly observed at 1.6 K. Another conventional method to measure heat capacity under pressure, that is, temperature-modulated method (or AC method) can also be employed.
This method has achieved a remarkable progress during the past decade (Sullivan and Seidel, 1968). Several laboratories have shown its applica- bility using majority of pressure generators, namely: piston cylinder (Tateiwa et al., 2005; Hashimoto et al., 2006), Bridgman anvils (Bouquet et al., 2000; Demuer et al., 2002), diamond anvils (Salce et al., 2000), and cubic anvils (Matsubayashi et al., 2010a).
3.2.2 Thermal expansion
The basic principle in experimental investigation in condensed matter physics is to detect a response of a physical quantity to an external force such as temperature (T), pressure (P), electric field (E), and/or magnetic field (H). In the high-pressure work until now, almost all of the measure- ments have been done with varyingT, that is, changing only two of the external parameters (T,P). Developing a high-pressure apparatus suitable for high-pressure, high magnetic field, and low-temperature measure- ments should lead to highly quality data and result in better understand- ing of the electronic properties of condensed matter.
Here, we describe an apparatus which was designed to measure physical properties of condensed matter as function of T, P, and H (Honda et al., 2002; Oomi et al., 1993a). This apparatus is similar to that described bySwenson (1955)with some improvements, that is, taking the thermal expansion of the compression rod into account and possibility of use in high magnetic field. The ranges ofT,H, andP, respectively, are 1.3T 350 K, 0H11 T and 0P4 GPa at hydrostatic condition.
Figure 30shows a schematic cross-section of the high-pressure appa- ratus. Here, (1) is the pressure amplifier which generates loads up to 30 ton with an automatic control by a hydraulic pump; (2) is a piston made of SUS304; the He chamber is sealed by an O-ring; (3) the generated load is transmitted through the compression members; (4) and (5) to the high-pressure cell; (4) is an alternating pile of fiber-reinforced plastic (FRP) discs; and (5) is made from SUS304; in the present case, a piston- cylinder-type apparatus is shown, in which the tungsten carbide piston (8) and CuBe or NiCoCrMo(MP35N) alloy cylinders (9) are used; super- conducting magnet (10) is made of a NbTi superconducting coil located around (9); (6) is the thermal radiation shield; and (7) is a cryostat. The load is always kept constant automatically with less than 1% error.
(4) has a role not only as a compression member but also as a thermal insulator, which is a very important role when liquid He is used.
The maximum magnetic field is 9 T at 4.2 K (11 T at 2.2 K), and it is produced by an Oxford superconducting magnet, (10). The sample is placed inside the Teflon capsule, whose sample space is 4.5 mm in diameter and 20 mm in height. We usually employ a mixture of Fluorinert FC70 and FC77 or Daphne 7373 as the pressure-transmitting medium. The cylinder is made of MP35N alloy with HRC hardness of50 achieved after appropriate heat treatment. The outer and inner diameters are about 17.5 and 6 mm, respectively. The cylinder is tightened by insertion in a CuBe jacket with the thickness of 5 mm subjected to a force of about 10 ton, in order to increase the strength.
This high-pressure apparatus has been used for several different kinds of measurements such as electrical resistance, magnetic properties (mag- netic susceptibility and magnetization), and thermal expansion (Honda et al., 2002). The thermal expansion at high pressure and high magnetic
Hydraulic pump (1)
(2) (3)
(4)
(5)
(6)
(7)
(9) (8)
(10)
FIGURE 30 Schematic cross-section of the high-pressure apparatus. See the text for the details (Honda et al., 2002).
field measurements have been carried out by using strain gages and a conventional active-dummy method (Sakai et al., 1999).