Refrigerants for uhv-compatible adiabatic demagnetization refrigeration to very low temperatures

Abstract

The invention describes a process and a use of a substance from the class ABP2O7 as a refrigerant for cooling to temperatures below 100 mK, in particular for cooling to temperatures below 40 mK, wherein A is an alkali metal and B is selected from the group of rare earths.

Description

[0001] Cooling substances for UHV-compatible adiabatic demagnetization cooling to very low temperatures

[0002] The invention describes a method and a use of a substance of the class ABP2O7 as a cooling substance for cooling to temperatures below 100 mK, where A is an alkali metal and B comes from the group of rare earths.

[0003] background

[0004] Due to the lack of 3For several years now, there has been considerable interest in adiabatic demagnetization cooling for the generation and utilization of temperatures below 50 mK. Single-crystal paramagnetic salts with a very low ordering temperature have been used as cooling substances. In a multi-stage process, these are first pre-cooled to a temperature of approximately 2 K in a magnetic field of typically several Tesla. The thermal contact to the bath is then cut by pumping out the He gas or opening a thermal switch, and the cooling substance is demagnetized. In this adiabatic process, the already very low entropy of the cooling substance due to pre-cooling in the magnetic field requires that the temperature of the cooling substance be significantly reduced, ideally to below 50 mK. The decisive factor for the achievable final temperature is the lowest possible coupling of the magnetic moments.Typically, the final temperature is slightly above the ordering temperature caused by the coupling. The available entropy change per volume is a key parameter for the efficiency of the cooling substance [P. Wikus, E. Canavan, S. Trowbridge Heine, K. Matsumoto, T. Numazawa, Cryogenics 62 (2014), 150].

[0005] The paramagnetic salts used to date, such as CrK(SU4)2 I2H2O, contain water of crystallization. Only this allows the required low ordering temperature to be achieved. However, due to the high vapor pressure of the water of crystallization, encapsulated cooling units are necessary. Due to their low stability, these crystals cannot be heated. Therefore, applications in ultra-high vacuum are not possible, as the corresponding structures must first be heated before being evacuated and cooled. Furthermore, the paramagnetic salts must be grown as single crystals into a metal structure using a complex process to achieve sufficiently good thermal conductivity for coupling to the structure or experiment to be cooled.

[0006] The present invention is therefore based on the object of providing an improved method for cooling to low temperatures below 100 mK.

[0007] Summary of the invention

[0008] The solution to this problem consists in the use of a substance from the class ABP2O7 as a cooling substance for cooling to temperatures below 100 mK, in particular for cooling to temperatures below 40 mK, where A is an alkali metal and B comes from the group of rare earths. The alkali metals Li, Na, K, Rb, and Cs are preferably used. Mixtures of the alkali metals can also be used. The rare earths Gd, Yb, Dy, Tb, Ho, and Er are preferably used. Mixtures of rare earths can also be used here. Due to the octahedral crystal structure of these compounds and the triangular configuration of the magnetic moments and the associated geometric frustration, the use of ABP2O7 as a cooling substance is particularly advantageous. The cooling substance is easy to process.It can preferably be used in (commercial) cryogenic devices such as the widely used Physical Property Measurement System (PPMS) from Quantum Design, which achieves 2 K as standard. The cooling substance according to the invention is, on the one hand, a significantly cheaper alternative to a 3 He- 4 He application, and on the other hand, in comparison to other adiabatic cooling substances already used, i.e. paramagnetic salts such as CrK(SU4)2 I2H2O (CPA), in addition to the advantages mentioned above, it has at least a comparable achievable lowest temperature and service life.

[0009] In one embodiment, the structural formula for this substance is NaYbP2O7 or KYbP2O7. The use of KYbP2O7 allows for the achievement of a particularly low minimum temperature. NaYbP2O7 enables a particularly long service life below 2 K. In the case of NaGdP2O7, an extremely long warm-up time of over 54 hours is observed at a minimum temperature of 225 mK. Alternatively, the substance consists of a mixture of two alkali metals (Na, K)YbP2O7. Any mixing ratio between Na and K can be chosen. This structural disorder can further reduce the magnetic ordering temperature, thus allowing even lower temperatures to be achieved.

[0010] According to a preferred embodiment, the cooling substance is anhydrous. This eliminates the need for encapsulation for ultra-high vacuum applications.

[0011] According to one embodiment, the cooling substance exhibits no long-range magnetic order between room temperature and 600 mK, in particular wherein the cooling substance of the form AYbP2O? exhibits no long-range magnetic order between room temperature and 40 mK, further in particular wherein the cooling substance of the form AGdP2O7 exhibits no long-range magnetic order between room temperature and 570 mK. This allows a low cooling temperature to be achieved. For example, different cooling substances can be used for stepwise cooling.

[0012] According to another embodiment, the cooling substance can be heated to at least 600 °C without degradation. This makes the cooling substance stable during typical processes for evacuating vacuum equipment. Therefore, no encapsulation or other protection of the cooling substance is necessary.

[0013] According to one embodiment, the cooling substance is suitable for use in ultra-high vacuum (UHV), in particular at pressures below 10' 6 mbar. The cooling substance thus offers an advantage over previously known cooling substances, which often contain water of crystallization and are therefore not UHV-stable. The cooling substance according to the invention can therefore be used in a wide variety of applications. Furthermore, the cooling substance can be used directly for cooling and does not require encapsulation.

[0014] According to one embodiment, the cooling substance is in powder form and has a grain size of 0.1-500 pm, in particular 10-50 pm. Powder samples of this grain size can, for example, be pressed into pellets, allowing the cooling substance to be used directly.

[0015] In one embodiment, the cooling substance is used in the form of pressed pellets and / or in a form with admixed metallic powder, particularly silver powder. Using the cooling substance in pellet form eliminates the need for encapsulation. This allows a more compact and lightweight heat sink for use in cryogenic devices. Due to the lower manufacturing effort, the pellets are also advantageous in terms of production.

[0016] The addition of metallic powder improves the thermal conductivity and thermal contact of the cooling agent. The pellets can contain either the cooling agent or a mixture of the cooling agent and metallic powder.

[0017] A further aspect of the invention describes a method for cooling to temperatures below 100 mK, in particular below 40 mK. The method comprises the use of the cooling substance described above, generating an ultra-high vacuum, preferably below 10' 6 mbar, setting a starting temperature, preferably of 5-1 K, in particular of 2 K, generating a magnetic field, preferably of 5 T, demagnetizing to 0 T, preferably at a rate of 0.15 T / min, cooling, preferably to 1 - 0.01 K, preferably to less than 100 mK, in particular to less than 40 mK.

[0018] In one embodiment, the method further comprises the production of pellets from the cooling substance, in particular the production of pellets with the addition of metallic powder, for example, silver powder. Encapsulation of the cooling substance is not necessary if the cooling substance is used in pellet form. The production of the pellets is described in more detail below. By adding silver powder, very good thermal contact or thermal coupling can be achieved.

[0019] In one embodiment, the cooling substance in the form of a pressed pellet is mechanically post-processed. The post-processing of the pellets produced by pressing with admixed metal powder can be carried out, for example, by machining. Drilling or cutting, for example, is also possible. This is an advantage compared to previous cooling substances, which, due to their construction and material parameters, can only be processed with great effort. The shape of a pellet, consisting of the cooling substance and admixed metal powder, can thus be adapted to the desired application. In a preferred embodiment, the cooling substance can be used unencapsulated. This simplifies the use of the cooling substance and makes it more cost-effective.

[0020] A further aspect of the invention describes a substance of the substance class ABP2O7 as a cooling agent for achieving temperatures below 100 mK, in particular below 40 mK. In one embodiment, the substance is as defined above.

[0021] The invention is described in more detail below using several preferred embodiments.

[0022] It shows:

[0023] Fig. 1 a crystal structure of the cooling substances NaYbP2O? (left) and KYbP2O? (right);

[0024] Fig. 2 a crystal structure of the cooling substances NaYbP2O? (left) and KYbP2O? (right) with labeled YbOr, octahedra and PO4 tetrahedra;

[0025] Fig. 3 the isothermal magnetization of NaYbP2O? at 0.4 K and temperature-dependent magnetic susceptibility at T < 1.8 K;

[0026] Fig. 4 the isothermal magnetization of KYbP2O? at 0.4 K and temperature-dependent magnetic susceptibility at T < 1.8 K;

[0027] Fig. 5 the temperature dependence of the magnetic susceptibility for NaYbP2O? and KYbP2O7;

[0028] Fig. 6 the X-ray powder diffractograms of NaYbP2O? and KYbP2O?;

[0029] Fig. 7 the temperature dependence of the heat capacity of NaYbP2O?

[0030] Fig. 8 the temperature dependence of the heat capacity of KYbP2O?;

[0031] Fig. 9 the heat capacity and entropy of NaYbP2O? at different magnetic field strengths;

[0032] Fig. 10 shows the heat capacity and entropy of KYbP2O? at different magnetic field strengths;

[0033] Fig. 11 is a flow diagram of a process for cooling below 100 mK;

[0034] Fig. 12 the magnetization of K¥bP2O?at different temperatures;

[0035] Fig. 13 Cooling and warm-up curves for pellets of NaYbP2O? and KYbP2O? during demagnetization. The following definitions serve to clarify certain terms or symbols and to describe particular embodiments of the invention. In the embodiments of the invention mentioned above and below, individual, several, or all terms or symbols may be replaced by more specific definitions, resulting in particular embodiments of the invention.

[0036] Room temperature is understood to mean a temperature in the range of 20 ± 2 °C, in particular 20 ± 0.5 °C.

[0037] Wherever “(Na,K)YbP2O7” is mentioned, this always means NaYbP2O?, KYbP2O? or a substance containing a mixture of Na and K as the alkali metal of the compound.

[0038] Particle sizes and particle size distributions can be determined using conventional methods (sieve analysis, laser diffraction, image analysis, etc.).

[0039] Figure 1 shows the monoclinic crystal structure of substances from the class of alkali metal rare earth diphosphates ABP2O7 (NaYbP2O7 in 1a and KYbP2O7 in 1b). A can be Li, Na, K, Rb, or Cs. B can be Gd, Yb, Dy, Tb, Ho, or Er. Particularly preferred are the compounds shown, KYbP2O7 and NaYbP2O7, which crystallize in a monoclinic lattice, space group P 2i / c (No. 14). Characteristic of the crystal structure is a nearly undistorted triangular lattice arrangement of the rare earth atoms, which carry magnetic moments. Thus, this class of materials exhibits a geometric frustration of magnetic moments. Mixed compounds are also possible.

[0040] Figure 2 shows the crystal structure of NaYbP2O7 in 2a and KYbP2O7 in 2b. The highlighted YbOe octahedra are linked via PO4 tetrahedra and span a slightly distorted triangular lattice. The geometric frustration of magnetic moments on the triangular lattices of the materials allows for a high density of magnetic moments (entropy density) with a very low ordering temperature. This combination is desirable, but has so far been very rare for anhydrous cooling substances. The data show no magnetic ordering down to 37 mK. At an ambient temperature of the standard achievable 2 K in a Dynacool PPMS with approximately 2.5 g of the cooling substance, the operating time below 2 K is approximately one hour, depending on the insulation of the cooling substance. Figures 3 and 4 show the isothermal magnetization of NaYbP2O? and KYbP2O? at 0.4 K. The temperature-dependent magnetic susceptibilities at low temperatures T < 1.8 K are shown as an embedded sub-image.

[0041] It has been found that ABP2O7 compounds have the advantage over paramagnetic salts in that they can be heated to temperatures of at least 600 °C in a vacuum without degradation. Paramagnetic salts contain water of crystallization, which would escape under these conditions. Paramagnetic salts containing water of crystallization must therefore be encapsulated and must not be heated. However, especially in high-vacuum applications, heat must be applied during the evacuation process (bake-out). This makes known paramagnetic salts unsuitable for high-vacuum applications.

[0042] The cooling substance according to the invention is suitable for high vacuums – it neither contaminates the vacuum nor is it damaged by the vacuum. In particular, the cooling substance in pellet form (see below for pellet production) is suitable for pressures between atmosphere and 5x10" 9 mbar stable.

[0043] Magnetic susceptibility measurements (Figure 5) down to 0.4 K show independently fluctuating Yb 3+ Magnetic moments that are polarizable in the applied magnetic field. A Quantum Design MPMS3 with the helium-3 option (iQuantum He3) was used for the susceptibility and magnetization measurements.

[0044] Furthermore, no long-range magnetic order is observed down to at least 0.4 K. The magnetic order resulting from the unit cell volume of 669.52 Å 3 (KYbP2O?) or 601.81 Ä 3 (NaYbP2O?) calculated entropy densities are 57.1 mJ / K^cm' 3 (KYBP2O7) or 63.6 mJ / K^cm' 3 (NaYBP2O7).

[0045] A particular embodiment relates to such a cooling substance, which is prepared by a process briefly outlined below. The following example serves to illustrate the invention without limiting its scope. Synthesis

[0046] Polycrystalline samples of (Na,K)YbP2O? suitable for the present invention were prepared by solid-state reaction of a stoichiometric mixture of Na2CCh / IGCCh (99.99%), Yb2O3 (99.99%) and NH4H2PO4 (99.99%) in an alumina boat.

[0047] For the preparation of NaYbP2O?, the stoichiometric mixture was ground for 2 hours using an agate mortar and pestle, and the powder was then preheated at 500 °C for 12 hours to allow the resulting CO2, H2O, and NH3 to escape. The powder was ground again for 2 hours, pelletized, and heated once at 600 °C for 24 hours and then twice at 650 °C for 24 hours, each time with intermediate grinding and pelletizing, to obtain the pure phase. The phase purity of the samples was determined by powder diffraction (XRD, PANa) using a nanoparticle chromatography (NPC) with Cu K. a Radiation, k a\c = 1.54182 Å) at room temperature was verified at each intermediate step. Figure 6 shows powder diffractograms of NaYbP2O? and KYbP2O?. A Bragg-Brentano configuration with a rotating sample carrier was used. The phase purity of the final product was confirmed by Rietveld refinement. Rietveld refinement was performed using the FullProf package (https: / / www.ill.eu / sites / fullprof / php / programs.html).

[0048] To prepare KYbP2O?, the stoichiometric mixture was thoroughly mixed with a spatula and preheated at 500 °C for 12 hours to evaporate the resulting CO2, H2O, and NH3. The powder was then thoroughly ground for 2 hours using an agate mortar and pestle, pelletized, and heated once at 550 °C for 24 hours and then twice at 600 °C for 24 hours, each time with intermediate grinding and pelletizing, to obtain the pure phase. The XRD pattern of the powder was checked at each intermediate step (as above). The phase purity of the final product was confirmed by Rietveld refinement (as above).

[0049] Due to the hygroscopic nature of K2CO3, some of the NH4H2PO4 dissolved in moisture can be lost, which can be reflected as a uniform impurity peak of Yb2O3 in the XRD powder pattern. To account for this, some additional NH4H2PO4 may need to be added, depending on the intensity of the observed Yb2O3 peak. Figures 7 and 8 show measurements of the temperature dependence of the heat capacity of NaYbP2O? and KYbP2O?. Heat capacity measurements at different magnetic field strengths (Figures 9 and 10) show a magnetic entropy of Rln2 in the low-temperature range below 10 K, as expected for a magnet with effective spin L> moments. A quantum-design PPMS "Physical Property Measurement System" Dynacool was used for the heat capacity measurement. This time with the “Helium 3 Option” extension, also from Quantum Design, and the heat capacity measurement extension – also from Quantum Design.The heat capacity was determined up to 400 mK.

[0050] According to the invention, powder samples of potassium or sodium ytterbium diphosphate with a grain diameter of 0.1 to 500 pm were produced. In particular, powder samples with a grain diameter of 10 to 50 pm can be used. This can be achieved by pulverizing in a mortar. Alternatively, sieve towers can be used, in which the maximum grain diameter can be limited by staggering increasingly finer sieves. Optical microscopy or laser diffraction can be used to verify the grain size. For grain size determination by laser diffraction, the particles are placed in a suspension and irradiated with a laser. By analyzing the diffracted radiation, a statement can be made about the particle size distribution and the shape of the particles.

[0051] In one embodiment of the invention, the potassium or sodium ytterbium diphosphate powder, or the powder mixture of potassium or sodium ytterbium diphosphate and silver powder, is pressed into pellets in a press mold having, for example, a diameter of 15 mm and a height of 5 mm.

[0052] Production of the pellets

[0053] The synthesis product was pulverized in a mortar and weighed. An identical mass of silver powder was mixed into the phosphate powder with a spatula. The mixture can alternatively contain between 10% and 90% of the cooling agent. The silver powder preferably has a grain size of 0.1 to 500 μm, preferably less than 20 μm, and is highly pure. Alternatively, other metallic powders, such as copper or gold, or mixtures of metallic powders can be used. The prerequisite is that no superconducting transition occurs. The mixture was reweighed and placed in a cylindrical compression mold with a nominal diameter of 15 mm. This compression mold was then loaded with 70 kN using a hydraulic press. After the compression process, the pellet was removed from the mold, cleaned of excess material, and measured and weighed.

[0054] Mechanically, pressing with silver powder is significantly simpler than previous production methods for paramagnetic salts. These are embedded in extremely fine silver / gold wire mesh, which is time-consuming and results in a fragile product. Because the powder pellets are well mixed, no wear is noticeable between use cycles—thermal or magnetic expansion or contraction does not damage the pellets. The pressed powder pellets can also be mechanically processed, for example, by machining.

[0055] In an alternative embodiment, a suspension of the phosphate powder can be produced in a molten metal. The molten metal preferably contains a metal or alloy with a melting temperature below 600 °C and does not undergo superconducting transition at low temperatures down to approximately 1 mK. This method allows for any casting shape.

[0056] In another alternative embodiment, single crystals of the diphosphates can be produced and used directly as a cooling substance.

[0057] Use of the cooling substance

[0058] Pellets made from the cooling substance were used in a process according to Figure 11 for cooling to low temperatures below 40 mK. The process was carried out in a Physical Property Measurement System (Dynacool PPMS) from Quantum Design.

[0059] The pellet is placed on an upper platform of the experimental setup, held in place by three hooks. A ruthenium oxide resistance thermometer is bonded to the top of the pellet using GE #7031 adhesive. The thermometer is connected to a circuit board located below the pellet using superconducting NbTi wires. From there, a four-wire measurement is formed using manganin wires to the PPMS resistance puck. The experimental setup is sealed with a brass cap as a thermal shield and inserted into the Dynacool PPMS. A LakeShore Model 372 AC Resistance Bridge is used to measure the thermometer's resistance, connected via an electrical filter to the Dynacool PPMS's expansion port (grey Lemo). This device is configured to a maximum resistance of 63.2 kOhm and an excitation current of 1 nA to limit the thermometer's heating.

[0060] At 300 K, the atmosphere of the sample volume is pumped out five times using a rotary vane pump and replaced with 5.0 helium. The setup is then cooled to 2 K (rate: 10 K / min) and simultaneously a 5 T field is established (rate: 100 Oe / s). After a waiting time of one hour at 2 K, the helium remaining in the chamber is pumped out first using a rotary vane pump and then using a cryopump. After another waiting time of 30 minutes, the field is driven to 0 T at a rate of 25 Oe / s. During this time, the resistance of the thermometer is continuously measured, from which the temperature can be determined.

[0061] After reaching the initial 2 K mark, the cryopump was isolated from the chamber and the setup was heated to 300 K. After stabilizing the temperature, the sample volume was flooded with helium and then vented.

[0062] Higher and lower initial temperatures, preferably between 1 and 5 K, are conceivable. The temperature ranges also depend on the rare earth and alkali metals used. Gadolinium offers the longest holding times at low temperatures, while ytterbium achieves the lowest temperature. The cooling material can be adapted to the requirements using different mixtures of rare earth or alkali metal sites.

[0063] Figure 12 shows the magnetization of K¥bP2O?at different temperatures.

[0064] Figure 13 shows the cooling and heating curves for pellets made of NaYbP2O? and KYbP2O? during demagnetization from 5 T to 0 T at a rate of 0.15 T / min. This allows the minimum temperature to be read off, but also the duration of the temperature stay below 2 K to be determined. This time is also referred to as the dwell time or holding time. Due to the external heat input (and from the thermometer), the sample slowly heats up after cooling. The rate of heating depends on the heat flow and the heat capacity of the sample (in zero field). The heat capacity and entropy density are interdependent, which is why a high entropy density S / V should be achieved to achieve the slowest possible heating. At the same time, the heat flow into the pellet must be limited. For this purpose, the experimental setup is constructed from materials with poor thermal conductivity.

[0065] In another example, cooling can be carried out in stages. For this purpose, several cooling substances, each with a different heat capacity or minimum temperature, are used. The cooling substances can first be cooled using a conventional cooling system, for example, a pulse tube cooler. Subsequently, cooling is carried out using a pre-cooling substance in a pre-cooling stage. Preferably, a cooling substance of the compound AGdP2O7 is used for this purpose. The actual cooling objective is then achieved using a cooling substance with the lowest possible minimum temperature, preferably a cooling substance of the compound AYbP2O?.

[0066] Staged cooling allows for a longer service life. This is primarily due to the greater heat capacity of the pre-cooling substance. Furthermore, a lower minimum temperature can be achieved than with a single-stage cooler. This is primarily due to the lower temperature of the surrounding shields and connections, which have already been cooled by the pre-cooling stage.

Claims

1. Use of a substance of class ABP2O7 as a cooling substance for cooling to temperatures below 100 mK, in particular for cooling to temperatures below 40 mK, where A is an alkali metal and B is from the group of rare earths.

2. Use according to claim 1, wherein the substance is NaYbP2O7 or KYbP2O7 or (Na,K)YbP2O7.

3. Use according to any one of the preceding claims, wherein the cooling substance is anhydrous.

4. Use according to one of the preceding claims, wherein the cooling substance has no long-range magnetic order between room temperature and 600 mK, in particular wherein the cooling substance of the form AYbP2O7 has no long-range magnetic order between room temperature and 40 mK, further in particular wherein the cooling substance of the form AGdP2O7 has no long-range magnetic order between room temperature and 570 mK 5. Use according to any one of the preceding claims, wherein the cooling substance can be heated to at least 600 °C without degradation.

6. Use according to one of the preceding claims, wherein the cooling substance is suitable for use in ultra-high vacuum, in particular at pressures below 10' 6 mbar, is suitable.

7. Use according to one of the preceding claims, wherein the cooling substance is in powder form and has a grain size of 0.1-500 pm.

8. Use according to one of the preceding claims, wherein the cooling substance is used in the form of pressed pellets and / or wherein the cooling substance is used in a Form with added metallic powder, especially silver powder.

9. Use according to one of the preceding claims, wherein the cooling substance is mechanically post-processed in the form of a pressed pellet.

10. Use according to one of the preceding claims, wherein the cooling is carried out by means of adiabatic demagnetization.

11. A method for cooling to temperatures below 100 mK, in particular below 40 mK, the method comprising: Use of a cooling substance according to any one of claims 1-10; Setting a starting temperature, preferably 5 - 1 K, in particular 2 K; Generating a magnetic field, preferably of 5 T; Creating an ultra-high vacuum, preferably below 10' 6 mbar; demagnetize to 0 T, preferably at a rate of 0.15 T / min; Cooling, preferably to 1 - 0.01 K, preferably to less than 100 mK, in particular to less than 40 mK.

12. A method of cooling according to claim 11, the method further comprising: Production of pellets from the cooling substance, in particular production of pellets with the addition of metallic powders, for example silver powder.

13. The method according to claim 11 or 12, wherein the cooling substance is used unencapsulated.

14. Substance of class ABP2O7 used as a cooling agent to achieve temperatures below 100 mK, in particular below 40 mK.

15. A substance according to claim 14, wherein the substance is as defined in any one of claims 1-10.

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