The present invention relates to an adiabatic coolant for cooling below 7 K, a method of producing the adiabatic coolant, a use of the adiabatic coolant as well as an adiabatic cooling device.

The ability to generate and stabilise low temperatures is a key technology in mod ern societies. Nowadays, temperatures below 4 K or -269.15°C are indispensable for academic basic research, e.g., in solid state physics, astrophysics, particle or high energy physics as well as metrology. In addition, entire branches of industry are concerned with the utilization of superconductivity, e.g., in clinical MRI scan ners or in power cables, and other quantum technologies, e.g., quantum infor mation technology, quantum computers, quantum cryptography, quantum commu nication and quantum simulation. Only extreme cooling can weaken disturbing thermal effects enough so that quantum physical laws can be applied to commer cial products, e.g., sensitive amplifiers. Also large parts of our population already benefit indirectly from cryogenics. For example, improvements in particularly sen sitive sensors, detectors and telescopes, both earth-bound and in space pro grammes, lead to a steady increase in the informative value of remote sensing, earth observation, weather forecasts and military operations.

Generation of temperatures much below 4 K can be achieved nowadays by three different methods, namely ⁴ He- and ³ He-evaporation cooling, ³ He- ⁴ He-dilution cooling and magnetic cooling by adiabatic demagnetisation.

Cooling systems that use the noble gas Helium (He) are used almost exclusively. It is possible, with the aid of complicated apparatuses, to cool down to tempera- tures of about 1 .4 K (corresponds to -271 75°C) with naturally occurring helium, which consists of 99.999863% ⁴ He and only 0.000137 % ³ He. To generate lower temperatures down to 5 mK, the extremely rare helium isotope ³ He must be used. He dilution refrigerators are well-established beyond developmental stage and commercially available. They provide reliable cooling to below 100 mK if the sys tem is properly designed, manufactured, maintained and handled. However, the gas handling system is often cumbersome, e.g. due to blockages occurring with unavoidable contaminations inside the He system, which require the whole system to be warmed up and cooled down again after removal of the blockage, thereby wasting precious resources.

The main source of ³ He is currently the decay of tritium. Tritium in turn is mainly used for nuclear weapons and is therefore fortunately produced less and less fre quently due to international disarmament treaties. Thus, gaseous ³ He is extremely rare and outrageously expensive and in the future, the price will continue to rise steadily. Also, the finite and scarce amount of ³ He will ultimately limit mass produc tion of dilution refrigerators as the platform for, e.g., next-generation quantum technologies. The application of He dilution refrigeration is further limited, as un desirable vibrations caused by pumping liquid or gaseous helium through the cool ing system might impair sensitive setups. Another limitation of dilution refrigerators is that they require calm gravity, which makes them hard to implement for mobile use and problematic for space applications.

Suitable alternatives to He-cooling exist in the form of magnetic cooling systems. Magnetic cooling is based on the temperature dependence of the entropy of the magnetic moments in the applied cooling material. Because of the so-called mag netocaloric effect (MCE) certain materials undergo a temperature increase when placed into a strong magnetic field. If the MCE is reversed, this leads to a tem perature decrease when the magnetic field is removed. The effect can be based on electronic magnetic moments as well as nuclear magnetic moments. The MCE is being exploited in the so-called adiabatic demagnetisation refrigerator (ADR) since nearly a century ago.

The method of magnetic cooling to sub-Kelvin temperatures by adiabatic demag netisation was independently proposed by P. Debye and W. F. Giauque (Debye, Annalen der Physik, 368 (1926) 1154-1160) using paramagnetic salts or para magnetic garnet minerals, delivering temperatures in the region of 20 mK. In fact, most traditional ADRs for the temperature range between 40 mK < T < 2 K use hydrated paramagnetic salts or garnets as cooling agents. This group of popular cooling materials includes, e.g., Cerium Magnesium Nitrate for the 10 to 40 mK temperature range, Chromic Potassium Alum, Cesium Chromic Alum and Ferric Ammonium Alum (FAA) for the 40 to 100 mK temperature range, Manganese Ammonium Sulfate for temperatures above 0.3 K and Dysprosium Gallium Garnet, Gadolinium Gallium Garnet (GGG) or Dysprosium Aluminum Garnet for tempera tures below 1 K. Although these materials are commonly used in adiabatic cooling, they are impractical and extremely sensitive. Flydrated paramagnetic salts degen erate or melt already at moderate temperatures, e.g., at 40°C for FAA, and are prone to dehydration when exposed to environmental influences. This often im poses significant restrictions on equipment design due to the need for hermetic sealing of these insulating materials and their weak thermal conductivity requiring an extra wire harness for assuring good thermal contact.

Despite these drawbacks of the paramagnetic salts and garnets, research and development concerning novel adiabatic substances was neglected since the 1970s because at that time, due to the adequately available and favourably priced ³ He, the advantages of ³ He- or ³ He- ⁴ He-refrigerators which provided continuous cooling prevailed. Even though promising applications like zero gravity cryostats for magnetic cooling systems emerged, until 2014 no further promising material classes have been proposed besides the known paramagnetic salts and garnets. More recent developments show that certain metallic materials provide attractive alternatives as coolants in ADRs, e.g., Ce4Pti2Sn25 and CeNi8 _. 9Coo _. 1Ge4, YbCu4 _.6 Auo.4 and YbCLuNi (Sereni, Philosophical Magazine (2020), 1-15). YbPt2Sn was shown to work as a magnetocaloric material. YbPt2Sn crystallizes in a hexag onal structure and features a high Yb density featuring an unusually weak magnet ic Yb-Yb interaction. It has a magnetic ordering temperature To ^s 240 mK and en ables adiabatic demagnetisation cooling from 2 K down to T _f = 0.16 K (Jang et al. , Nature Commun., 6, (2015) 8680; Gruner et al., J. Phys.: Condes. Matter, 26 (2014) 485002)). However YbPt2Sn is synthesised from very expensive raw mate rials.

It is an object of the present invention to improve cooling down to very low tem peratures and make it more economical.

The object is accomplished by an adiabatic coolant for cooling below 7 K with the features of claim 1 , a method of producing the adiabatic coolant, use of the adia batic coolant as well as an adiabatic cooling device. In particular, an adiabatic coolant for cooling below 7 K according to the present invention comprises a com pound according to formula (1):

(Ybi-xAx)a(Nii- _y By)b(C)c (1 ) wherein A is one or more members selected from rare earth elements other than Yb;

B is one or more members selected from the group of members consisting of Al, Ga, Ge, Fe, Mn, V, Co, Cu, Rh, Pd, Ag, Ir, Pt, and Au;

C is one or more members selected from the group of members consisting of Sn, In, Tl, Pb, and Bi; x is in the range of 0 to 0.9; y is in the range of 0 to 1 when B is one or more selected from the group consist ing of Al, Ga, Ge, Fe, Mn, V, Co, Cu, Rh, Ag, Ir, and Au; y is in the range of 0 to less than 1 when B is Pd or Pt; and wherein a, b and c satisfy the following conditions: a = c and 0.25a < b < 4a, wherein the value of a is not equal to 0.

Formula (1) describes a family of intermetallic alloys which can be used as refrig eration material in solid state cooling systems like ADRs. The family of intermetal lic alloys according to the invention comprises compounds with metallic behaviour, offering a high density of stable trivalent Yb ³⁺ with weakly coupled electronic Yb ³⁺ magnetic moments. They do not exhibit a magnetic order above a material-specific magnetic ordering temperature To, e.g. 0.1 K. This provides the magnetic entropy for use in adiabatic cooling.

The adiabatic coolant is made of cost-efficient raw materials, e.g., by using Ni in the compound. Also, raw materials of lower quality, i.e. , purity, can be sufficient for compound synthesis, which helps keeping the material cost even more reasona ble. The combination of Yb and Ni with a wide variety of supplementary elements enables fine-tuning of the properties of the coolant, like the base temperature, cooling capacity, density or others.

The intermetallic compounds according to the invention are mechanically robust, enabling straightforward processing of the coolant, e.g. by drilling, milling, grinding or lathing. Thus, the coolant may be brought into desired shapes easily, providing for simple manufacturing of powerful cooling pills. The compounds according to the present invention are chemically stable and very insensitive to influences of oxygen and humidity making them durable and sustainable. This enables the use without a hermetically sealed protective container which would have to be cooled as well and which would thereby lessen the cooling performance of the coolant. Consequently, the coolant is low-maintenance and suited for long-term use without degradation. The adiabatic coolant according to the present invention has a large volumetric entropy capacity Sv, e.g. of around Sv = 0.15 J/Kcm ³ , which provides an excellent cooling performance per volume and ensures high temperature stability, since temperature fluctuations due to short-term heat inputs are dampened effectively.

At medium temperatures, e.g. below 300 mK, extremely long stability times of several days may be achieved, making the adiabatic coolant reliable while provid ing a user friendly handling. Furthermore, less material is needed of a high Sv compound in order to provide the same cooling capacity as for a lower Sv com pound. This is cost-efficient and economic and also helps in promoting miniaturiza tion of cooling setups. Requiring much smaller magnets and lesser resources for pre-cooling further improves the economic efficiency of ADRs. Overall smaller ADR systems are thus possible, which is particularly beneficial for space-borne cryostats.

With these compounds, cooling below temperatures of 7 K or even 4 K and in par ticular below 2 K and down to approximately 140 mK or even 100 mK is possible completely independent of expensive and scarce ³ He, and without a complex dilu tion refrigerator setup. The invention enables thus a more compact setup design and is user-friendly as no cumbersome gas handling is necessary. Further, the coolant works independently of gravitational force in ADR, thus qualifying for use in zero gravity, e.g., in space-science missions.

The invention includes adiabatic coolants featuring a high thermal conductivity. Thus, no additional thermally conducting components such as metal wires need to be inserted into the coolant, preventing a reduction of the cooling performance due to cooling of the metal wires or heating of the wires due to eddy currents. The high thermal conductivity of the coolant results in a fast absorption of heat, which makes it well-suited for quick and short cooling cycles, e.g. in multi-stage, continu ous cooling systems. At the same time, the absolute electrical metallic conductivity is low, making heating of the coolant due to eddy currents negligible. There are no hints of superconductivity in compounds according to formula (1), which means that no weakening effect on the electronic thermal conductivity is expected, and no signs of a significant Kondo effect.

All these properties make the adiabatic coolant according to the invention straight forwardly applicable in existing (commercial) magnetic cooling systems. Due to its very good temperature stability up to temperatures of approximately 400°C, the adiabatic coolant can without difficulty be used in ultrahigh vacuum applications which require a baking step.

Preferably, the adiabatic coolant comprises a compound according to formula (2):

(Ybi-xAx)a(Nii- _y By)b(Sni-zCz)c (2) wherein z is in the range of 0 to 1. Formula (2) describes a subgroup of the family of intermetallic alloys comprising Yb, Ni and Sn. The subgroup includes YbNhSn consisting of one fraction of amount of substance elemental Yb, two fractions ele mental Ni and one fraction elemental Sn, as well as a variety of sibling com pounds. With compounds of formula (2), an excellent cooling effect can be real ized.

Advantageous embodiments of the invention are given in the dependent claims, the description and the accompanying drawings.

Preferably, in the compound of formula (1 ) or (2), x is in the range of 0 to 0.7, pref erably in the range of 0 to 0.5, more preferably in the range of 0 to 0.3. With de creasing values for x, the Yb density of the alloy increases and thus the Yb-Yb magnetic interaction is less disturbed. Hence, forx = 0, the largest volumetric en tropy capacity Sv and thus the best cooling performance is achieved. However, the cooling performance may remain nearly unchanged forx = 0.1. When substituting Yb by rare earth elements to the degree of x = 0.3, 0.5 or even 0.7, the com- pounds still work as cooling materials and may exhibit the same cooling capacity per Yb ion. Thus, the resulting adiabatic coolants still perform their function, while it is possible to use less expensive material compositions and fine-tune the coolant to the actual requirements. Therefore, further preferred ranges for x are from 0 to 0.1 , from 0.1 to 0.7, from 0.1 to 0.5, from 0.1 to 0.3, but also from 0.3 to 0.7 and from 0.3 to 0.5.

It is further preferred that y is equal to or greater than 0.1. The combination of Ni with a certain amount of one or more members of the group of Al, Ga, Ge, Fe, Mn, V, Co, Cu, Rh, Pd, Ag, Ir, Pt, and Au enables fine-tuning the crystal structure as well as the cooling capacity of the resulting alloy to the required needs.

Preferably, y is equal to or less than 0.9, more preferably equal to or less than 0.7, even more preferably equal to or less than 0.5, even further more preferably equal to or less than 0.3. The phase purity of the compound and/or its crystal structure may be improved by keeping the fraction of dopant small, while the introduction of varying amounts of doping elements enables to adjust, e.g., the density of the compound in order to adapt its overall properties.

Preferably, the ratio of a:b:c is 1:1:1 or 1:17:1 or 1:2:1 or 1:4:1, preferably a is 1, b is 1 or 1.7 or 2 or 4 and c is 1. These ratios ensure a reasonably high Yb density in the adiabatic coolant, helping to achieve a good volumetric entropy capacity Sv. The compound may be polycrystalline and may include several phases with differ ent ratios of a:b:c, which may also make individual contributions to the cooling ca pacity of the material.

Preferably, a compound according to formula (1) has a structure corresponding to a Heusler compound having space group No. 225 or corresponding to a half Heu- sler compound having space group No. 216 or corresponding to a small hexagonal ZrPt2AI structure type having space group No. 194, preferably, the structure is a cubic L2i type structure corresponding to a Heusler compound or a C1 _b structure corresponding to a half Heusler compound having space group No. 216. For Heu sler compounds, the ratio a:b:c is 1 :2:1 , for half Heusler compounds, the ratio a:b:c is 1 :1 :1. The inventors have recognized that the cooling ability may be strongly dependent on the compound's crystal structure, which may influence the presence of weakly coupled Yb moments. For cubic Heusler type structures, a good com pound performance in ADR is observed, but also other crystal structure types, e.g., hexagonal crystal structures may be the main structural phases of a well performing coolant.

Preferably, the compound has a metastable phase. In particular, the metastable phase may include a high temperature phase with a phase transition temperature of, e.g., around 1000°C or 1200°C or 1300°C. The metastable phase may be the phase enabling adiabatic cooling. Sufficient stabilisation of the metastable phase, e.g., stabilisation of a high temperature phase also at low temperatures, may be achieved during synthesis of the compound, e.g., by rapidly cooling down the compound below the phase transition temperature without allowing a phase transi tion. Thus, favourable properties of the metastable phase may be exploited under the conditions prevalent during application of the compound.

The adiabatic coolant is preferably in the form of an ingot, a powdered substance or a sintered powder. An ingot may be obtained as the product of the synthesis of the coolant and used directly even without further processing providing for easy and straightforward handling. The ingot may provide a high material density and thus a good cooling capacity. A powdered substance may either be brought into the shape of a cooling pill or alternatively be used to enclose the sample to be cooled therein. By this approach, the cooling compound may be partially or com pletely brought into form-fitting contact to the sample to be cooled, thereby ena bling a very efficient heat transfer between the coolant and the sample. Sintering of a cooling pill or even of a powder-enclosed sample is also possible, making me- chanically stable cooling pills of any desired shape or size accessible. A powdered and pressed coolant has the advantage of a very large surface area, which may be favourable in absorbing residual gas molecules, e.g., He gas molecules, from a vacuum cooling chamber, thereby improving the quality of the vacuum.

It is also preferred when the adiabatic coolant has at least one flat surface ena bling easy mounting of a sample to be cooled directly to the coolant, e.g. having the form of an ingot or a cooling pill, while offering a well-defined surface for estab lishing proper thermal contact between the coolant and the sample to be cooled. For example, the sample may be pressed onto the flat surface of the coolant. The coolant may also offer several flat surfaces enabling the contacting of several samples to be cooled simultaneously or to easily position the coolant and the sample inside a cooling chamber. For example, the coolant may be of cylindrical shape, offering two flat surfaces, or of conical shape, offering one flat surface. De pending on the sample requirements, also a curved surface of the coolant may be used to provide a high contact area with a sample.

Another aspect of the present invention relates to a method of producing an adia batic coolant as described above and in the claims, comprising the steps of

(1 ) providing each of the elements contained in the final compound of the adia batic coolant in elemental form in an amount depending on the stoichiome try of the adiabatic coolant,

(2) mixing the elements in a crucible,

(3) melting the mixed elements at least once, in particular in an arc melting process to form a melt,

(4) cooling the melt.

This method for producing an adiabatic coolant is quick, easy to perform and cost- efficient. The amount of the elements may be determined by weighing in step (1). The synthesis of the compound may be performed as a one-stage reaction, where all elemental raw materials are mixed together in a crucible in step (2) for perform ing the reaction. The reaction is preferably performed under a protective atmos phere. For melting of the elements in step (3) an oven, e.g., an arc melting fur nace, may be used and the melting may be performed once or more preferably several times in order to improve the homogeneity of the melt and to provide for a chemical reaction which is as complete as possible.

Cooling of the melt in step (4) may either be performed by actively cooling the melt, e.g., by bringing the hot melt in contact with water or water-cooled heat ex changers. Alternatively, sufficient cooling may be achieved by removing the heat source from the melt, e.g. by simply switching off the arc furnace. In particular, a water-cooled Cu crucible used for the synthesis may itself serve as heat exchang er after switching off the furnace. After a successful synthesis, the intermetallic alloys according to the invention may be able to adopt at least two different struc tural modifications. The desired cooling capacity may only be provided by a certain phase, e.g., by a metastable high-temperature phase. The phase transition be tween both modifications occurs at a phase transition temperature which may be, e.g., approximately 950°C, 1000°C, 1200°C or 1300°C. In order to stabilise the high-temperature modification, the temperature of the melt might need to be low ered below the phase transition temperature within a short time, thereby freezing the solidified melt in a high temperature structural phase. In this case, the spatial dimensions of the melt during cooling, e.g. as defined by the crucible, need to be restricted, e.g. to the size of 5x5x5 mm ³ , in order to ensure rapid cooling also at the core of the melt. The resulting material may be polycrystalline as well as brittle.

The crucible used in the method as described above preferably is characterized by the following features: Its material should remain dimensionally stable even at around 120% of the maximum reaction temperature and it should not react chemi cally with the compound of the adiabatic coolant. Also, the crucible should be suf ficiently robust to withstand the possibly strongly exothermic reactions of the ele- ments contained in the alloy, e.g. of Yb and Sn. Examples of ideal crucible shapes include cylindrical or conical shapes. Examples of ideal crucible materials include aluminium oxide (AI2O3), zirconium dioxide (ZrCte), Niobium (Nb), Tantalum (Ta), Tungsten (W) and water-cooled Copper (Cu).

Suitable reaction temperatures may be provided by an oven. Different types of ovens can be used while ideally the following requirements are met: the maximum temperature of the oven should be approximately 50°C higher than the melting point of the highest melting element, i.e. approximately 1500°C if using Ni, 1600°C if using palladium (Pd) and 1820°C if using platinum (Pt). Also, the reaction cham ber should be floodable with a protective gas atmosphere of approximately 700 mbar. Further, like the reaction crucible, the whole oven should be sufficiently ro bust to withstand strong exothermic reactions, e.g. of Yb and Sn. Examples of ide al oven types include arc furnaces, induction furnaces and high-temperature muf fle furnaces.

In step (1) Yb is preferably provided in excess with respect to the stoichiometry of the final compound, in particular in an excess in the range of 8 wt% to 20 wt% based on the total weight of Yb in the final compound. Due to its high vapour pres sure, Yb atoms may evaporate and condense inside the reaction chamber during the synthesis. By adding Yb in excess, enough Yb is provided in order to remain in the melt and thus for the synthesis to result in a defect-free compound with a high Yb density.

The steps (2) and (3) of mixing and melting are preferably performed as a two- stage reaction, wherein preferably in a first stage Yb and optionally further one or more rare earth element(s) other than Yb are mixed in a step (2-1 ) with at least one member selected from the group of members consisting of Sn, In, Tl, Pb, and Bi and are melted in a step (3-1) to obtain an intermediate product, and in a sec ond stage the intermediate product obtained after step (3-1) is mixed in a step (2- 2) with at least one member selected from the group of members consisting of Ni, Al, Ga, Ge, Fe, Mn, V, Co, Cu, Rh, Pd, Ag, Ir, Pt, and Au to obtain a mixture, wherein when Pt or Pd is added in step (2-2), at least a further metal selected from the group of members consisting of Al, Ga, Ge, Fe, Mn, V, Co, Cu, Rh, Ag, Ir, and Au is added to obtain a mixture, and melting the mixture in a step (3-2) to form a melt. By performing the synthesis as two separate partial reactions, well-defined and matched reaction conditions can be applied while performing each partial re action and thus an efficient execution of the partial reactions can be ensured. For example, the reaction temperature may be adjusted separately for each partial reaction. If applicable, also more than two partial reaction steps may be per formed.

Preferably, the method further comprises a step (5) of powdering the product ob tained after step (4), e.g. if the geometric shape of the solidified melt is not suitable for direct use in a cooling application. For this purpose, one or more obtained coolant ingots may be powdered. During powdering, the grain size may be adjust ed to obtain a powder with tailored properties, e.g., with a suited surface area. The obtained powder can be easily molded into a desired shape.

Therefore, the method preferably further comprises a step of forming the pow dered product into a body of required shape and optionally sintering the shaped body. The properties, e.g., the density, of the pressed cooling pill can favourably be adjusted to the requirements by this approach by adjusting the grain size, the pressing force or, if applicable, the sintering conditions such as the sintering tem perature profile. Moreover, a cooling pill formed from pressed powder may also have a required size. In particular, a pressed cooling pill may be larger than the maximum size achievable for an ingot during synthesis. By sintering of the pressed cooling pill, the mechanical stability may be improved and the cooling properties may be adjusted. By pressing a powdered coolant into a container, which may also be sealable, any contact of the coolant with the surroundings may be prevented, enabling use of the coolant also in chemically unfavourable envi ronments.

Preferably, to a further embodiment the method comprises moulding of the adia batic coolant into a shape with at least one flat surface. This can either be achieved for an ingot by performing the synthesis in a crucible generating an ingot with a flat surface or. Alternatively, the ingot may itself be post-processed and re shaped by drilling, milling, grinding, lathing or other mechanical applications. Alter natively, a powdered substance may be pressed to a cooling pill in a mould gener ating at least one flat surface, e.g., in a cylindrical mould. The resulting one or more flat surfaces favourably allow easy mounting of a sample to be cooled on the ingot or cooling pill.

A further aspect of the present invention pertains to the use of an adiabatic coolant as previously described and preferably obtainable by a method as previously de scribed for adiabatic cooling to temperatures below 7 K. In particular, the adiabatic coolant may be used for cooling to minimal temperatures of below 1 K and even below 0.2 K or 0.15 K in an ADR setup. Minimal achievable temperatures may al so be approximately 0.1 K. The cooling process based on the magnetic moments of the adiabatic coolant requires pre-cooling of the adiabatic coolant to tempera tures in the range of several K, e.g. between 1.4 and 5 K, which can be achieved by ⁴ He evaporation cooling, for example. In addition, the adiabatic cooling process requires the generation of high magnetic fields with magnetic flux densities be tween, e.g., 1.8 to 7 T or even more. Because of its flexibility regarding shape and size, the adiabatic coolant as described above may be used in many available ADRs. Due to its favourable properties, e.g., high Sv, high thermal conductivity, weak Yb-Yb coupling, chemical and mechanical stability, as described above in detail, the use of the adiabatic coolant helps to achieve a cost-efficient, simple, user-friendly and reliable cooling to temperatures as low as T _{f «} 100 mK. Another aspect of the present invention pertains to an adiabatic cooling device comprising an adiabatic coolant as described above, preferably obtainable by a method as described above. The cooling process may occur via adiabatic demag netisation using a system that may include pre-cooling stages, magnets, thermal bridges and thermal switches.

Preferably, the adiabatic coolant of the adiabatic cooling device is at least partially arranged around a sample space. This ensures an efficient heat transfer between the coolant and the sample to be cooled. For example, the sample can be partially or even completely embedded in a powdered adiabatic coolant.

Preferably, the device comprises a magnetic field generator and a pre-cooling ap paratus. The magnetic field generator may provide magnetic flux densities up to 8 T, up to 10 T or even up to higher flux densities. The pre-cooling apparatus may be a ⁴ He-based refrigerator and may for example be equipped with a pulse tube cryostat, preferably reaching temperatures down to 1.4 K.

The invention will now be described in further detail and by way of example only with reference to the accompanying drawings as well as by various examples of the adiabatic coolant of the present invention. In the drawings there are shown:

Fig. 1 an SEM analysis of as-cast YbNhSn (Example 1 );

Fig. 2 an X-ray diffraction pattern of YbNhSn recorded at T = 300 K (Exam ple 1);

Fig. 3 crystal structural models which contribute to the structural phases of adiabatic coolants, e.g., YbNhSn (Example 1);

Fig. 4 differential scanning calorimetry results of YbNhSn (Example 1); Fig. 5 the temperature-dependent electrical resistivity of YbNhSn (Example

1 );

Fig. 6 the temperature-dependent magnetic susceptibility of YbNhSn (Ex ample 1);

Fig. 7 the temperature-dependent specific heat capacity of YbNhSn (Ex ample 1);

Fig. 8 the magnetic entropy of YbNhSn (Example 1 );

Fig. 9 calculated estimates of final temperatures T _f for YbNhSn (Example

1 );

Fig. 10 a test setup for determining the cooling performance of adiabatic coolants;

Fig. 11 temperatures reached in ADR experiments with YbNhSn (Example

1 );

Fig. 12 table of properties of known adiabatic coolants and YbNhSn (Exam ple 1);

Fig. 13 an X-ray diffraction pattern of (Ybo _.g Lao _. NhSn (Example 2);

Fig. 14 an X-ray diffraction pattern of (Ybo _. 8Luo _. 2)Ni2Sn (Example 3);

Fig. 15 an X-ray diffraction pattern of (Ybo _. 6Luo _. 4)Ni2Sn (Example 4); Fig. 16 an X-ray diffraction pattern of (Ybo _. 4Luo _. 6)Ni2Sn (Example 5);

Fig. 17 temperature-dependent specific heat capacities of YbNhSn (Example 1), (Ybo _. 8Luo _. 2)Ni2Sn (Example 3) and (Ybo _. 6Luo _. 4)Ni2Sn (Example 4);

Fig. 18 an X-ray diffraction pattern of Yb(Nio _. 8Coo _. 2)2Sn (Example 6);

Fig. 19 an X-ray diffraction pattern of Yb(Nio _. 8Cuo _. 2)2Sn (Example 7);

Fig. 20 an X-ray diffraction pattern of Yb(Nio _. 8Ago _. 2)2Sn (Example 8);

Fig. 21 temperatures reached in ADR experiments with Yb(Nio _. 8Coo _. 2)2Sn (Example 6);

Fig. 22 temperatures reached in ADR experiments with Yb(Nio _. 8Cuo _. 2)2Sn (Example 7);

Fig. 23 temperatures reached in ADR experiments with Yb(Nio _. 8Ago _. 2)2Sn (Example 8);

Fig. 24 an X-ray diffraction pattern of YbNi2(Sno _. 8lno _. 2) (Example 9);

Fig. 25 an X-ray diffraction pattern of YbNi2(Sno _. 8Bio _. 2) (Example 10);

Fig. 26 temperatures reached in ADR experiments with YbNi2(Sno _. 8lno _. 2) (Example 9);

Fig. 27 temperatures reached in ADR experiments with YbNi2(Sno _. 8Bio _. 2) (Example 10). Example 1: YbNhSn

As a first example, intermetallic compound YbNhSn has been synthesised as an adiabatic coolant. Synthesis of the compound has been performed in an arc melt ing process under ultrapure argon atmosphere from elemental Yb, Ni and Sn. These elements have each been weighed and provided in an amount depending on their stoichiometry in the target compound YbNhSn (step (1)) in the molar ratio of a:b:c. , however, Yb was provided in a 10 wt% excess based on the total weight of Yb in the final compound in order to compensate for losses of Yb in the final product due to the low boiling point of Yb of T _b = 1469 K: Because of this, the pro vided amount of Yb may not be available for the chemical reaction completely due to its high vapour pressure, leading to evaporation of unreacted Yb. In particular, at reaction temperatures between 820°C and 1460°C around 10% of the heated Yb vaporize into the gas phase unreacted and condense throughout the reaction chamber upon cooling. Depending on the specific reaction conditions and the spe cific alloy composition, Yb may typically be used in excess of 8 wt% to 20 wt% based on the total weight of Yb in the final compound.

A chemical reaction may consist of a sequence of partial reactions. The synthesis of the adiabatic coolant may thus be performed as a multiple-stage reaction, e.g., a two-stage reaction. For example, the synthesis of YbNhSn alloy was performed by first synthesising YbSn from Yb + Sn and then synthesizing YbNhSn from YbSn + 2Ni because of the hugely different melting points of the elements (T _me it _, Yb ^s 1100 K, Tmeit.Ni ^s 1730 K and T _me it _, sn ^s 500 K). In particular, a two-stage arc-melting process was used. In a first stage, an appropriate amount of Yb and Sn were mixed in a water-cooled Cu crucible (step (2-1)) and melted (step (3-1)) to a small button. The first partial reaction takes place at approximately 820°C, i.e. at the melting point of Yb. Once the elements Yb and Sn are both in the liquid phase, a strong exothermic reaction takes place due to particular features of the binary Yb Sn phase diagram. In a second stage, elemental Ni was mixed with the pre-reacted YbSn intermedi ate product (step (2-2)) and melted (step (3-2)). The second crucial partial reaction takes place at around 1460°C. Above this temperature the activation energy is sufficient for a complete reaction of Yb, Ni and Sn to occur in order to provide YbNhSn. In this step the product was repeatedly melted and turned over to en hance homogeneity and ensure completeness of the chemical reaction.

This is applicable to other compositions of the adiabatic coolant in the following way: In a first partial reaction, the low melting elements may be reacted with one another (e.g., Yb and In, if In is used instead or in addition to Sn). In a second step, the higher melting elements are added and melted with the pre-reacted "low melting mixture". Alternatively, the synthesis may also be performed as a one- stage reaction.

Afterwards, the melt was cooled rapidly in the water-cooled Cu crucible by switch ing off the arc melting furnace. It is possible to obtain the YbNhSn compound in a one-stage reaction as well. For this purpose, Yb, Ni and Sn are all mixed together in the crucible and melted at least once by arc melting at a temperature of, e.g., 3000 to 4000°C. Cooling is performed as described for the two-stage process.

Analysis of the as-cast compound was performed by energy-dispersive X-ray spectroscopy (EDX) analysis with a scanning electron microscope (SEM). The result is shown in Fig.1 and reveals that the resulting compound is not phase-pure, but rather includes a main phase comprising YbNhSn and a minor phase compris ing YbNUSn. The resulting adiabatic coolant is a polycrystalline compound.

Crystal structural analysis of the compound was performed by X-ray powder dif fraction at room temperature (T = 300 K). A corresponding X-ray spectrum is shown in Fig. 2. The Bragg reflections in the X-ray pattern indicate an underlying body-centered cubic structure: Yb, Ni and Sn are mostly arranged in a cubic Heu- sler structure (L2^, Fm-3m, space group No. 225) with a cell parameter of a = 6.364 A and an Yb:Ni:Sn ratio of 1:2:1. The spectrum further reveals minor contri butions of a second phase corresponding to a cubic F-43m (having space group No. 216) structure with an Yb:Ni:Sn ratio of 1:4:1. An overview of the correspond ing crystal structures is shown in Fig. 3

Rietveld refinement of the X-ray spectrum of Fig. 2 revealed approximately 90% of YbNhSn in the cubic Fleusler phase having space group No. 225 and approxi mately 10% of YbNUSn in the cubic 1:4:1 phase having space group No. 216. For the sake of simplicity the compound of Example 1 will simply be referred to as YbNhSn also in the following.

Fig. 4 shows the result of a differential scanning calorimetry experiment performed with YbNhSn. The YbNhSn phase, which is the functional phase for adiabatic cooling of YbNhSn, forms a meta-stable phase at temperatures below 1300 K. Thus, the cooling step (step (4)) of the synthesis is crucial for obtaining a function al and well-performing material for ADR. Nevertheless, the YbNhSn phase is sta ble below 500 K and thus a bake-out of the material in order to remove volatile particles for ultra-high vacuum applications is possible.

Fig. 5 shows the temperature-dependent electrical resistivity of YbNhSn. The posi tive slope proves the metallic character of the compound. As the absolute values of the electrical resistivity are rather low, the compound possesses a high metallic thermal conductivity in accordance with the Wiedemann-Franz law. Further, Fig. 5 also confirms the absence of superconductivity in YbNhSn and thus, no weaken ing of the electronic thermal conductivity is to be expected for this coolant.

Fig. 6 shows the temperature dependence of the inverse susceptibility c ¹ (T) of YbNhSn in an external field of moH = 0.1 T. It displays an almost linear behaviour, which can be fitted with a Curie-Weiss law with an effective magnetic moment Me _ff = 4.77 mb which is indicative of a stable Yb ³⁺ state. The fitted Weiss tempera ture qnn « 0 K is an indicator of a weak Yb-Yb intersite exchange interaction (RKKY interaction).

Fig. 7 shows the temperature dependence of the measured specific heat capacity C/T of YbNhSn in magnetic fields of 0 T to 10 T, which helps to further elucidate the overall strength of the Yb-Yb interaction. In zero field, C/T shows a clear mini mum at around 3.5 K and increases continuously with decreasing T until a broad anomaly appears at To ^s 140 mK. With further decreasing temperature C/T stays approximately constant. The broad anomaly at To is an indicator of magnetic order of local moments dominated by short-range correlations.

At finite magnetic field strengths Schottky anomalies appear in C/T. This confirms the intersite exchange in YbNhSn to be so weak that already magnetic fields be low, e.g., 4 T are sufficient to induce Zeeman splitting of the 4f states. At low tem peratures below approximately 300 mK the specific heat increases strongly show ing a C/T a T ^-3 power law. This increase can be attributed to nuclear Yb contribu tions.

Fig. 8 shows a three-dimensional representation of the 4f-electron magnetic entro py of YbNi ₂ Sn calculated at all measured magnetic fields of Fig. 7. Regions with the same grey shading are isentropic. An isothermal magnetisation wedge con nects all fins up to 8 T at a constant temperature of a surrounding thermal bath T,

= 1 .8 K. Starting at T, and B,, a temperature-versus-field line of an actually meas ured quasi-adiabatic demagnetisation levels to 141 mK at zero field. Projected en tropy values represented by small balls show slight differences from perfectly adi abatic conditions as a result of parasitic heat loads. Fig. 9 shows calculated estimates for the initial temperature Ti-dependence of the final temperature T _f obtained by integrating (dT/dH|e). The calculations suggest that for Ti « 800 mK a base temperature To ^s 100 mK may be possible.

Fig. 10 shows an experimental setup 10 used for testing the cooling performance of YbNhSn or other adiabatic coolants. An ADR setup 10 for testing the practical performance of the adiabatic coolants was built on a Quantum Design Physical Property Measurement System (PPMS). The setup 10 is built on a puck 12 sup porting a thin-wall polyether ether ketone (PEEK) tube 14, which is designed to thermally isolate and mechanically support the compound 16, e.g. YbNhSn from a Fle-bath and a ⁴ Fle blank puck 12. For ventilation, the PEEK tube 14 features a small hole 18. The sample compound 16 is fixed on top of the PEEK tube 14 using fast drying epoxy adhesive 20. A ruthenium oxide (RUO2) thermometer 22, which has been previously calibrated to temperatures below 80 mK in a dilution refrigera tor, was directly glued to the magnetocaloric material using GE varnish and reports the temperature of the sample compound 16. Superconducting wires 24 were used for establishing electrical connections to the thermometer 22 to minimise heat leaks at base temperature.

Results of the cooling performance of YbNhSn are shown in Fig. 11. For testing the performance of a coolant in the ADR setup 10, the setup 10 is cooled down from room temperature under small Fie pressure around 6 mbar to a set bath tem perature Ti using ⁴ Fle-based cooling. As the sample compound 16 reaches the temperature T, set for ⁴ Fle pre-cooling, the initial magnetic field B, is applied to the sample, leading to an alignment of the magnetic moments and thus to heating of the coolant sample 16 due to the resulting decrease of the magnetic entropy due to the MCE. The Fle-bath helps bringing the temperature of the coolant sample 16 down to the bath temperature by absorbing the heat generated due to the magnet isation and to stabilise it there. When the temperature of the adiabatic coolant is at equilibrium with the bath temperature T, again, quasi-adiabatic conditions are es- tablished by evacuating the ⁴ He gas. Only very limited thermal conductivity may then occur through the PEEK tube 14 and the superconducting wires 24 (see Fig. 10). At this point, the magnetic field B, is slowly removed. The thermal energy available in the adiabatic coolant sample 16 causes the magnetic moments to overcome the decreasing magnetic field, leading to rapid cooling of the sample 16 as thermal energy is transferred to magnetic entropy.

For testing the cooling performance of YbNi ₂ Sn, T, was set to 1 .4 K, 1.8 K or 1 .7 K, while B, was set to 2 T, 8 T or 14 T (Fig. 11 , top curve to bottom curve). The base temperatures reached with these parameters were as low as 335 mK, 141 mK or even 116 mK. Several test runs gave highly reproducible results and in general, it was comparably simple to reach and hold a temperature T < 300 mK for at least one hour even with the basic setup design as shown in Fig. 10.

Fig. 12 shows a table summarising the properties of YbNi ₂ Sn in comparison with magnetocaloric materials which are either already popularly used for ADR, e.g., FAA or GGG, or which have been proposed as suitable materials in more recent publications ([1] FeNFI (S0 ₄ ) ₂ 12(H ₂ 0); Vilches et al., Phys. Rev., 148 (1966) 509-516; [2] Gd ₃ Ga ₅ 0i ₂ ; Hornung et al., Chem. Phys., 61 (1974) 282; [3] Ybo _.8i Sco _.i9 Co ₂ Zn ₂ o; Tokiwa et al., Sci. Adv., 2 (2016) e1600835; [4] YbPt ₂ Sn; Gruner et al., J. Phys.: Condens. Matter, 26 (2014) 485002; [5] YbPd ₂ ln; Gastaldo et al., PRB, 100 (2019) 174422).

The magnetic ordering temperature To roughly determines the base temperature which can be reached for a specific compound via adiabatic cooling. Fig. 12 illus trates that YbNi ₂ Sn may allow cooling to lower base temperatures than the recent ly proposed YbPd ₂ ln and YbPt ₂ Sn compounds while being much more cost- efficient due to the low-price raw materials. In comparison to the YbCo ₂ Zn ₂ o com pound, YbNi ₂ Sn features a much higher volumetric entropy capacity Sv. This is also due to the larger density in YbNhSn and positively influences the cooling ca pacity of the compound and improves temperature holding times.

FAA has lower material cost compared to YbNhSn. However, while the cost of YbNhSn is just the cost of the raw material, the cost of (hydrated) paramagnetic salts for practical use in ADR will also include costs for the extra wire harness to assure good thermal contact and for hermetic sealing. In addition, the durability of such compounds is often limited in practical applications due to degradation, lead ing to higher rates of replacing the material.

Further example compounds according to formula (1) have been tested. In a first group of example compounds (Examples 2 to 5), the value of x has been in creased in comparison to YbNhSn from 0 up to 0.6 and thus the content of Yb has been reduced while substituting Yb with either Lanthanum (La) or Lutetium (Lu). Specifically, the tested compounds were

Example 2: (Ybo _.g Lao _. NhSn,

Example 3: (Ybo _. sLuo^NhSn,

Example 4: (Ybo _. 6Luo _. 4)Ni2Sn,

Example 5: (Ybo _. 4Luo _. 6)Ni2Sn.

Compounds of Examples 2 to 5 were synthesised in the same way as Example 1 , except that La or Lu was added in the first melting step.

The crystal structures of these compounds have been analysed by X-ray powder diffraction and the corresponding diffraction patterns are shown in Figs. 13-16. The diffraction patterns were analysed by means of Rietveld refinement using two (Fig. 13) or three (Fig. 14 to 16) structural phases based on the structural models of pure YbNhSn as shown in Fig. 3, namely the cubic Heusler structure having space group 225, the cubic structure having space group 216 and the large hexagonal unit cell structure having space group 194, which were found to be common struc tures of the compounds according to formula (1 ). While some of the compounds might contain additional structural phases, these have not been taken into account in the Rietveld refinement.

Fig. 13 shows the X-ray diffraction pattern of Example 2 ((Ybo _. 9Lao _.i )Ni2Sn). It re veals approximately 54% of a cubic Heusler type structure 225 as the main struc tural phase (peak positions of Heusler 225 are indicated by upper set of marks) and approximately 37% of a large hexagonal phase 194 as a second structural phase (peak positions of large hexagonal phase 194 are indicated by lower set of marks) and a third phase of approximately 9% corresponding to a cubic 1:4:1 structure (peak positions of cubic 1:4:1 phase having space group 216 are indicat ed by middle set of marks). Further peaks in the X-ray pattern reveal the existence of at least one further phase which is unrefined until now.

Fig. 14 shows the X-ray diffraction pattern of Example 3 ((Ybo _. sLuo^NhSn). It re veals approximately 88% of a cubic Heusler type structure having space group 225 (upper set of marks) as the main structural phase and approximately 12% of a cubic 1 :4:1 structure having space group 216 (lower set of marks) as a further structural phase. Thus, the X-ray diffraction pattern is nearly identical to the one observed for Example 1 (YbNhSn).

Fig. 15 shows the X-ray diffraction pattern of Example 4 ((Ybo _. 6Luo _. 4)Ni2Sn). It also reveals approximately 87% of a cubic Heusler type structure having space group 225 (upper set of marks) as the main structural phase and approximately 13% of a cubic 1 :4:1 structure having space group 216 (lower set of marks) as a further structural phase. Thus, the X-ray diffraction pattern is nearly identical to the one observed for Example 1 (YbNhSn) and for Example 3 ((Ybo _. 8Luo _. 2)Ni2Sn). Fig. 16 shows the X-ray diffraction pattern of Example 5 ((Ybo _. 4Luo _. 6)Ni2Sn). It also reveals approximately 85% of a cubic Heusler type structure having space group 225 (upper set of marks) as the main structural phase and approximately 15% of a cubic 1 :4:1 structure having space group 216 (lower set of marks) as a further structural phase. Thus, the X-ray diffraction pattern is nearly identical to the one observed for Example 1 (YbNhSn), just as observed for Example 3 and Example 4.

For Example 3 and Example 4 the temperature-dependent specific heat capacity C/T has been determined as shown in comparison to the specific heat capacity of Example 1 in Fig. 17. The specific heat capacity of the Lu-substituted compounds of Example 3 and Example 4 is nearly identical to the heat capacity observed for Example 1 and thus suggests the same weak magnetic exchange and a similar cooling capacity per Yb-ion as in YbNhSn (Example 1). Basically, the Lu- and La- substituted compounds of the first group of examples may be interpreted as "dilut ed YbNhSn", showing the same properties as YbNhSn of Example 1 while having a reduced concentration of magnetic moments.

In a second group of example compounds (Examples 6 to 8), the value of y has been increased in comparison to YbNhSn from 0 to 0.2 and thus the content of Ni has been reduced while substituting Ni with either Cobalt (Co), Copper (Cu) or Silver (Ag). Specifically, the tested compounds were

Example 6: Yb(Nio _. 8Coo _. 2)2Sn Example 7: Yb(Nio _. 8Cuo _. 2)2Sn,

Example 8: Yb(Nio _. 8Ago _. 2)2Sn.

Compounds of Examples 6 to 8 were synthesised in the same way as Example 1 , except that Co, Cu or Ag was added in the second melting step. The X-ray powder diffraction spectra of these compounds as well as correspond ing Rietveld refinements are shown in Figs. 18-20.

Fig. 18 shows the X-ray diffraction pattern of Example 6 (Yb(Nio _. 8Coo _. 2)2Sn). It re veals approximately 97% of a large hexagonal structure having space group 194 (lower set of marks) as the main structural phase. Further peaks in the X-ray pat tern reveal approximately 2% of a cubic 1 :4:1 structural phase having space group 216 (middle set of marks) and approximately 1 % of a cubic Fleusler type structure having space group 225 (upper set of marks) as further structural phases. Further faint peaks indicate the existence of traces of at least one additional phase which is unrefined until now.

Fig. 19 shows the X-ray diffraction pattern of Example 7 (Yb(Nio _. 8Cuo _. 2)2Sn). It re veals approximately 72% of a large hexagonal structure having space group 194 (lower set of marks) as the main structural phase and approximately 23% of a cu bic 1 :4:1 structure having space group 216 (middle set of marks) and approximate ly 5% of a cubic Fleusler type structure having space group 225 (upper set of marks) as further structural phases. Further, faint peaks indicate the presence of traces of at least one additional structural phase.

Fig. 20 shows the X-ray diffraction pattern of Example 8 (Yb(Nio _. 8Ago _. 2)2Sn). It re veals approximately 84% of a large hexagonal structure having space group 194 (lower set of marks) as the main structural phase and approximately 8% of a cubic Fleusler type structure having space group 225 (upper set of marks) and approxi mately 8% of a cubic 1 :4:1 structure having space group 216 (middle set of marks) as further structural phases. The presence of traces of at least one additional phase is revealed by further faint peaks.

All of Examples 6 to 8 show a large hexagonal structure having space group 194 as the main structural phase. The cubic Fleusler type structure with space group 225, which is typical for YbNhSn of Example 1 , plays only a minor role in Exam ples 6 to 8, nevertheless a cooling effect was observed.

For Examples 6 to 8 the cooling performance was determined using an experi mental setup 10 as shown in Fig. 10 and as described above with an initial tem perature Ti = 1.8 K and an initial magnetic field B, = 9 T. The results are shown in Figs. 21-23.

Fig. 21 shows the cooling performance of Example 6 (Yb(Nio _. 8Coo _. 2)2Sn). A final temperature T _{f «} 450 mK can be reached.

Fig. 22 shows the cooling performance of Example 7 (Yb(Nio _. 8Cuo _. 2)2Sn). A final temperature T _{f «} 270 mK can also be reached.

Fig. 23 shows the cooling performance of Example 8 (Yb(Nio _. 8Ago _. 2)2Sn). A final temperature T _{f «} 270 mK can be reached similar to Example 7 (Fig. 22).

In a third group of example compounds (Examples 9 and 10) according to formula (2), the value of z has been increased in comparison to Example 1 from 0 to 0.2 and thus the content of Sn has been reduced while substituting Sn with either In dium (In) or Bismuth (Bi). Specifically, the tested compounds were

Example 9: YbNi2(Sno.8lno.2),

Example 10: YbNi2(Sno.8Bio.2).

Compounds of Examples 9 and 10 were synthesised in the same way as Example 1 , except that In or Bi were added in the first melting step.

The X-ray powder diffraction spectra of these compounds and corresponding Rietveld refinements are shown in Figs. 24-25. Fig. 24 shows the X-ray diffraction pattern of Example 9 (YbNi2(Sno _. 8lno _. 2)). It re veals approximately 66% of a large hexagonal structure having space group 194 (lower set of marks) as the main structural phase and approximately 18% of a cu bic Heusler type structure with space group 225 (upper set of marks) and approx imately 15% of a cubic 1 :4:1 structure having space group 216 (middle set of marks) as additional structural phases. The presence of traces of at least one fur ther phase is indicated by further faint peaks.

Fig. 25 shows the X-ray diffraction pattern of Example 10 (YbNi2(Sno _. 8Bio _. 2)). It re veals approximately 50% of a large hexagonal structure having space group 194 (lower set of marks) as the main structural phase and approximately 40% of a cu bic Fleusler type structure having space group 225 (upper set of marks) and ap proximately 10% of a cubic 1 :4:1 structure having space group 216 (middle set of marks) as further structural phases. Further faint peaks indicate the presence of traces of at least one additional phase.

Also for the third group of example compounds (Examples 9 and 10) the cooling performance was determined using an experimental setup 10 as shown in Fig. 10 and as described above with an initial temperature T, = 1.8 K and an initial mag netic field Bi = 9 T. The results are shown in Figs. 26-27.

Fig. 26 shows the cooling performance of Example 9. A final temperature T _{f «} 220 mK can be reached.

Fig. 27 shows the cooling performance of Example 10. A final temperature T _{f «} 210 mK can be reached and stably held for an extended period of time. Thus, the compounds of Examples 1 to 10 are all suitable adiabatic coolants. The best cooling performance in the group of tested compounds is reached by Exam ple 1.

List of reference signs

10 experimental ADR setup 12 puck 14 polyether ether ketone (PEEK) tube

16 sample compound

18 ventilation hole

20 epoxy adhesive

22 ruthenium oxide (RuCte) thermometer 24 superconducting wires