Lanthanide Contraction in LnF3 (Ln = Ce-Lu) and Its Chemical and Structural Consequences: Part 1: Location of YF3 in the LnF3 Series According to Its Chemical and Structural Characteristics

A lanthanide contraction (LC) of 14 lanthanides (Ln) from 58Ce to 71Lu consists of the interaction of Ln nucleus with 4f-electrons. Rare earth elements (REEs—R) include Sc, Y, La, and 14 Ln. They are located in 4–6th periods of the subgroup of group III. The electronic structure divides R into short (d- Sc, Y, La) and long (14 f-elements Ce-Lu) homologous series. The most important chemical consequence of LC is the creation of a new conglomerate of 16 RF3 by mixing fluorides of d- (Y, La) and f-elements. This determines the location of YF3 among LnF3. The location of YF3 depends on the structural (formula volumes—Vform) and thermochemical (temperatures and heats of phase transformations, phase diagrams) properties. The location of YF3 between HoF3 and ErF3 was determined by Vform at a standard pressure (Pst) and temperature (Tst). The location of YF3 according to heats of phase transformations ΔHfus and ΔHtrans is in a dimorphic structural subgroup (SSGr) D (Ln = Er-Lu), but without the exact “pseudo ZY”. According to the temperatures of phase transformations (Ttrans) in LnF3 (Ln = Dy-Lu), YF3 is located in the SSGr D between ErF3 and TmF3. The ErF3-YF3 and YF3-TmF3 phase diagrams show it to be between ErF3 and TmF3. The crystals of five β-LnF3 (Ln = Ho-Lu) and β-YF3 were obtained in identical conditions and their crystal structures were studied. Vform (at Pst and Tst) with “pseudo” atomic number ZY = 67.42 was calculated from the unit cell parameters, which were defined with ±5 × 10−4 Å accuracy. It determines the location of YF3 between HoF3 and ErF3.


Introduction
This study opens up a series of investigations on LCs and their chemical and structural consequences in homologous series of LaF 3 and 14 LnF 3 .The (La,Ln)F 3 series differs from the homologous series of Ln compounds by characteristics that make it unique for the precise study of LCs.The formula for the (La,Ln)F 3 series is simple.It determines the qualitative and quantitative chemical compositions that are favorable for the LC study.Fluorine anion has low atomic mass (19).High atomic masses of Ln lead at the beginning of the series in CeF 3 to 71% and at the end of LuF 3 to ~75% of the mass of compressible Ln 3+ .The LC in LnF 3 has an extremely high "sensitivity" to volumetric changes when filling the 4f -orbital.
Despite the difference in the electronic structure, according to IUPAC recommendation, La is classified as Ln.This disadvantage of REE classification was noted by IUPAC as a project to clarify the location of La (2015).In this study, the formula (La,Ln)F 3 is used when discussing issues related to LCs.This formula is not equivalent to a structural formula that isolates chemical elements in equivalent structural positions.The purpose of the (La,Ln) designation is to separate 14 Ln (4f -elements), which are exposed to a LC, from La, which has no f -electrons.When LC is not discussed, the R abbreviations for Y, La, and 14 Ln are used.
Owing to the extreme electronegativity of fluorine 4.0 according to [1] (after helium and neon), RF 3 compounds have a high degree of a chemical bond ionicity; therefore, they are characterized by high melting points (T fus ).They crystallize from the melt in the form of large crystalline blocks, which are suitable for structural studies.All RF 3 are chemically resistant, except SmF 3 , EuF 3, and YbF 3 .They were subjected to partial reduction under the conditions of an experiment on crystal growth and the study of phase diagrams with their participation [2][3][4][5][6][7].
The location of YF 3 in the LnF 3 series is determined not by its Z = 39 but by the structural and chemical characteristics of 39 YF 3 , independent of LC.Therefore, this location is ambiguous.According to the literature, the location of YF 3 depends on its structural (unit cell parameters, formula volumes) or thermochemical (temperature, heat of phase transformation, phase diagrams) properties.In this study, a critical analysis of the structural and thermal characteristics of YF 3 is performed according to the data of various research groups and our own precise structural data.
The term LC was first used in [8], and the name was given to the family of 14 Ln ("similar to lanthanum").The Ln 3+ ionic radius in REE oxides was chosen as a characteristic of LC.According to [8], the radius of R 3+ (r + ) decreases from La 3+ to Lu 3+ by ~15%.These data have been included in the educational literature and are still being cited.The radii were obtained on an incomplete REE series.Owing to the unresolved problem of REE separation in those years, the purity of some oxides by the main component had reached 50% at.Historically, r + in R 2 O 3 has become the first example of a comparative study of LC.
The compression of Ln 3+ ions is expressed as an integral effect, that is, a change in the volume of a crystal.To compare non-cubic crystals, which are all RF 3 , it is convenient to express changes in the unit cell parameters using V form .The ultimate goal of precise LC studies is to obtain the dependence of r + on Z for P st and T st : r Ln = f 0 (Z).
A change in the state parameter T > T st causes structural changes in the RF 3 series: polymorphic (PolTr) and morphotropic transformations.Both transformations proceed with abrupt changes in V form .The RF 3 PolTr exhibit a density anomaly.The high-temperature form is denser (usually opposite).Materials that expand after PolTr at heating are called materials with negative thermal expansion based on a phase transition-type mechanism [9].V form changes with Z according to different dependencies: for the LaF 3 type (hereafter t-) by V t-= f 1 (Z), and for the β-YF 3 type (hereinafter β-) by V β-= f 2 (Z).
The difference in the electronic structure requires dividing the REE into short Sc, Y, La (d-elements), and long (14 f -elements) homologous series.In the short series, 21 Sc→ 39 Y→ 57 La, r + increases in group III in the ∆Z = 18 interval.In the long series, a LC phenomenon, which is unique to the periodic table of elements, is realized.The LC of the elements of period 6 (Ln = 58 Ce-71 Lu) is a result of an interaction in the "Ln nucleus-4f -electrons" atomic subsystem.The minimum "period" of the long series is ∆Z = 1.This corresponds to the transition between neighboring LnF 3 .At the same time, the size of Ln 3+ cation decreases significantly with increasing Z due to LC.
d-REE La occupies a dual position.Having no f -electrons, La heads the Ln family, giving it a name.The IUPAC assignment of La to Ln is caused by the neighborhood of 57 La in the 6th period with 58 Ce at ∆Z = 1.
Yttrium has no f -electrons, and its r + is independent of LC.The indirect effect of LC on the rapprochement of YF 3 structural and chemical properties with LnF 3 properties is due to the influence of LC on Ln 3+ .This is expressed as a decrease in r + with an increase in Z.
The location of LaF 3 at the beginning of the LnF 3 series does not raise any questions.The Periodic Table of elements places it there by Z(La) = 57.This location before 58 CeF 3 is also justified by the structural and chemical proximity of LaF 3 and CeF 3 (∆Z = 1).
A question arises about the location of YF 3 in the LnF 3 series.Unlike the unambiguous location of 57 LaF 3 , the location of 39 YF 3 is determined not by its Z = 39, but by chemical and structural characteristics.The certainty of chemical characteristics is much less than the structural and absolute (Z) ones.In the literature there are several proposed locations of YF 3 .
The structural classification of 16 RF 3 (without ScF 3 ) homologous series and the chemical classification of the phase diagrams of 120 (without ScF 3 ) RF 3 -R'F 3 systems depend on the place of YF 3 in the LnF 3 series.The RF 3 structural classification is the first level of a chemical classification of RF 3 -R'F 3 systems.
To determine the location of YF 3 in the LnF 3 series, only precise information on LC in LnF 3 is suitable.Two conditions ensure its receipt.
The first is the individuality of the homologous series of compounds.In this series of messages, for the first time, LC studies were performed on one (long) homologous series of REE fluorides: LaF 3 and 14 LnF 3 .The high degree of bond ionicity and simple formula of the series give the absence of "blurring" of the boundaries of the change in structural types over the Ln series (for fixed P and T).This "blurring" accompanies all structural classifications of Ln compounds using their large arrays.The choice of compounds for arrays usually does not take into account differences in their chemical bonds.Arrays of compounds are heterogeneous in the chemical bonds.The conclusions of the most fundamental monograph [10] with an overview of 400 homologous series of REE compounds will be discussed in detail in the next message.
The general conclusion in [10] after processing a unique volume of data on LCs in the series of Ln compounds is categorical."It is impossible to obtain an ideal system of REE ionic radii by averaging interatomic distances taken from a large number of structural definitions"."Blurring" the several atomic numbers of the boundaries of "areas of crystal and chemical instability" [10] does not allow us to determine the subtle features of the LC evolution in the Ln series.These data are suitable neither for a precise study of the evolution of LC nor for constructing a specialized (Spec-zd) empirical (Emp) system of ionic radii (SIR) for RF 3 .
The second condition is the completeness of the LnF 3 structural characteristics used to describe the changes in V form during LC.The state of structural knowledge of RF 3 is currently unsatisfactory both in terms of the number of studied compounds (about half) and in terms of the purity of the reagents used, especially in early works.
Structural studies of RF 3 stretched over the years 1929-2023.During this period, significant changes occurred in the composition of RF 3 crystals.It can be said that in the works of 30-70s, the purity of crystals by impurities of neighboring REE was not high.And only in 1971, YF 3 , LaF 3 , PrF 3 , NdF 3 , GdF 3 , HoF 3 , and LuF 3 were published, with total REE content of 35-125 ppmw and with other cations content of 30-55 ppmw [11].Cationic and anionic (oxygen) impurities are difficult to control.The structural data of RF 3 distorted by them are unsuitable for precise studies of LC and the construction of the Spec-zd Emp SIR for (R,Ln)F 3 .
In this series of studies, the crystal structures of all members of the (R,Ln)F 3 series are investigated.The structures of HoF 3 , ErF 3 , TmF 3 , YbF 3 , LuF 3 , and YF 3 are discussed in the present study.The short quasi-system (QS) [12] "from HoF 3 to LuF 3 " is used to obtain "pseudo Z Y ".The location of YF 3 is determined to be between HoF 3 and ErF 3 based on the value of V form .The second message presents the structural data of t-RF 3 with R = La-Nd of the LaF 3 type, "pseudo t-SmF 3 ", and β-LnF 3 (Ln = Sm-Dy) of the β-YF 3 type.The empirical structural data obtained for cations and fluorine anion will become the basis for the Spec-zd Emp SIR for Y 3+ , La 3+ , and 14 Ln 3+ for RF 3 .
The aim of this study is to clarify the most extensive indirect chemical consequence of LC, which is the location of fluoride of the d-element YF 3 in a series of 4f -elements LnF 3 .

2.1.
Obtaining YF 3 and LnF 3 with Ln = Ho-Lu for Structural Studies X-ray diffraction (XRD) analysis of YF 3 and LnF 3 with Ln = Ho-Lu was performed on the samples prepared using modern technology for the synthesis of crystals prone to pyrohydrolysis REE fluorides.
The RF 3 reagents were prepared at the experimental plant (town Pyshma) of the Government Institute of Rare Metals (GIREDMET, Moscow, Russia).RF 3 were melted and fluorinated to purify oxygen impurities.Oxygen content of 0.005-0.08wt.% has been achieved (determination by vacuum melting) [13,14].Differential thermal analysis used for the study of phase diagrams provided control over the oxygen impurity content in RF 3 (in the form of an isomorphic admixture of RF 3−2x O x oxyfluorides) at an acceptable level [15].
The purity of the reagents by the main component was 99.9 wt.%.Each reagent was certified for REE impurities based on X-ray fluorescence analysis.The typical impurity composition of YF 3 produced by Pyshma, according to [16], is listed in Table 1.After fluorination, the samples consisted of large crystalline blocks suitable for structural analysis.To accurately determine the position of YF 3 in the LnF 3 series using structural characteristics the structures of β-YF 3 and five β-LnF 3 (Ln = Ho-Lu) were studied.

X-ray
XRD study were performed using modern equipment for structural analysis under comparable experimental conditions.Only the combination of these factors, which were absent earlier when creating universal (Univ) SIRs, provides high accuracy in describing the evolution of LC in the LnF 3 series and calculating comparable values of r + for the Spec-zd Emp SIR for RF 3 .
Single crystal XRD study of β-YF 3 and β-LnF 3 (Ln = Ho-Lu) was performed at 293 K using an XtaLAB Synergy-DW (Rigaku Oxford Diffraction, Japan-UK-Poland) diffractometer with an Ag-anode X-ray tube.The data were processed using the CrysAlisPro version 171.42.72 (Rigaku Oxford Diffraction, Japan-UK-Poland) software package.
Powder XRD analysis was performed at 293 K with a Rigaku MiniFlex 600 Bragg-Brentano diffractometer using a Cu-anode X-ray tube within the range of 2θ = 10-100 • and with a 2θ step size of 0.02 • .A NIST 640e standard (Si) sample was added to the sample to determine the 2θ correction.The details of the XRD experiments are listed in Table 2.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF 3 and β-LnF 3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.

Determination of "Pseudo ZY" According to Literature Data
The first group of structural properties is the type of structure and unit cell parameters.The most precise (±0.0005Å) measurements of the RF3 unit cell parameters in a The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.

Determination of "Pseudo ZY" According to Literature Data
The first group of structural properties is the type of structure and unit cell parameters.The most precise (±0.0005Å) measurements of the RF3 unit cell parameters in a The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.

Determination of "Pseudo ZY" According to Literature Data
The first group of structural properties is the type of structure and unit cell parameters.The most precise (±0.0005Å) measurements of the RF3 unit cell parameters in a The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.

Determination of "Pseudo ZY" According to Literature Data
The first group of structural properties is the type of structure and unit cell parameters.The most precise (±0.0005Å) measurements of the RF3 unit cell parameters in a The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.The JANA2020 program [17] was used for the structure solution and refinement.The structures were refined within Pnma sp.gr.An isotropic extinction correction was introduced into the fitted models according to the Becker-Coppens formalism [18].The Wickoff positions (W.p.) [19], coordinates, site occupancy factors, and equivalent atomic displacement parameters for β-YF3 and β-LnF3 (Ln = Ho-Lu) at 293 K are listed in Table 3.

Determination of "Pseudo Z Y " According to Literature Data
The first group of structural properties is the type of structure and unit cell parameters.The most precise (±0.0005Å) measurements of the RF 3 unit cell parameters in a Guinier chamber were used [11,20].The YF 3 unit cell parameters [11] differs from that of [20].The reason for this difference is unknown.
The second group includes the thermal properties: the temperatures (T fus ) and enthalpies ∆H fus of melting and T trans and ∆H trans of the PolTrs.These characteristics determine the location of YF 3 in the LnF 3 series for condensed systems with P st and T st .The condensed (at P st ) single-component (Z = const) systems include YF 3 , LaF 3 , and all LnF 3 except volatile (at heating) ScF 3 [21,22].In such systems, PolTr is invariant and proceeds "at a point" T = T trans = const.
The T trans were taken from a review [23] as the average of those published before 2003 for fluorides of f -elements.There is no T trans for YF 3 among them.
∆H fus and ∆H trans for all RF 3 were cited from the fundamental research of one group of authors [11,24].Synthesis and analysis of the basic and impurity RF 3 compositions and purification from oxygen (control by analysis) were performed at Iowa State University, USA.
Phase diagrams of the two-component RF 3 -R'F 3 systems were used for the first time to clarify the location of YF 3 .These systems were studied by one group [25].The phase diagrams of the RF 3 -R'F 3 systems contain data on the T trans of the components.The location of YF 3 in the short QS [12] depends on the thermal properties of the LnF 3 components that form this QS.The generally accepted scheme for the change of T trans and crystal structures of 17 RF 3 was formed by the mid-80s of the last century by three scientific groups: the USA, Russia, and Germany.However, six outdated schemes were also cited.This forces us to repeat up-to-date ideas about RF 3 structures.
The structural classification of RF 3 (without ScF 3 ) based on the type of structure and presence (absence) of polymorphism is presented in Table 4. Four SSGr were allocated.The members of the SSGr A (LaF 3 , CeF 3 , PrF 3 , and NdF  The β-YF 3 unit cell parameters according to [11,20,24,26] together with V form s calculated from them at T st and P st are listed in Table 5.In the right column, the LnF 3 -Ln'F 3 systems are provided, in which V form of YF 3 is located between the V form s of components.The V form s of YF 3 according to [11,26] are close to each other.They locate YF 3 between HoF 3 and ErF 3 .According to [20] YF 3 is located between DyF 3 and HoF 3 .This is contradicted by the only form of β-in both fluorides before T fus .These data were excluded.

Location of YF 3 in the LnF 3 Series in Terms of T fus and ∆H trans
A review of T trans in (La,Ln)F 3 (without ScF 3 andYF 3 ) was done [23].The T trans for each (La,Ln)F 3 was obtained with an accuracy of ±3 • C. The limitation [23] is in the exclusion of YF 3 from the list as a fluoride of d-element.For YF 3 , we adopted T trans from [11].
The blue solid circles in Figure 1 show the T fus (curve 1) and red open rectangles (curve 2) T trans of LnF 3 in the short QS "from DyF 3 to LuF 3 ".The fields of structural modifications are designated as β-and α-.The border between C and D SSGrs is marked with a dash-dotted vertical I.The Vforms of YF3 according to [11,26] are close to each other.They locate YF3 between HoF3 and ErF3.According to [20] YF3 is located between DyF3 and HoF3.This is contradicted by the only form of β-in both fluorides before Tfus.These data were excluded.

Location of YF3 in the LnF3 Series in Terms of Tfus and ΔHtrans
A review of Тtrans in (La,Ln)F3 (without ScF3 andYF3) was done [23].The Тtrans for each (La,Ln)F3 was obtained with an accuracy of ±3 °C.The limitation [23] is in the exclusion of YF3 from the list as a fluoride of d-element.For YF3, we adopted Тtrans from [11].
The blue solid circles in Figure 1 show the Tfus (curve 1) and red open rectangles (curve 2) Ttrans of LnF3 in the short QS "from DyF3 to LuF3".The fields of structural modifications are designated as β-and α-.The border between C and D SSGrs is marked with a dash-dotted vertical I.  [11,24].The ΔHfus and ΔHtrans of dimorphic YF3 are shown in Figure 2 by green icons.The values of the ΔHfus and ΔHtrans of YF3 are projected into the Z region corresponding to ErF3 without intersecting curves 2 and 3, respectively.According to ΔHfus and ΔHtrans, YF3 is located in the SSGr D. However, the location of YF3 cannot be precisely determined because of the proximity of the ΔH values.Despite the high accuracy of thermophysical measurements [11,24], they do not contain strict information regarding the location of YF3.

Location of YF3 Based on the YF3-LnF3 Phase Diagrams at P = Pst, T > Tst
The possible location of YF3 on the basis of phase diagrams was obtained based on the location of YF3 between HoF3 and ErF3 determined from unit cell parameters and Vforms.The composite short "HoF3-YF3-ErF3" QS, including these fluorides (Figure 3), was analyzed.The phase diagrams of the HoF3-YF3 and YF3-ErF3 systems [25] are not included in the full "from LaF3 to LuF3" QS [12].The short "HoF3-YF3-ErF3" QS is called composite to emphasize the violation of the ΔZ = 1 condition for (R,Ln)F3 sequence in the true QS by "inserting" a component-a fluoride of the d-element Y.The "inserted" 39YF3 connects the 67HoF3 and 68ErF3 components of the full QS with continuous lines of liquidus and solidus into the short composite "HoF3-YF3-ErF3" QS.The ∆H fus and ∆H trans of dimorphic YF 3 are shown in Figure 2 by green icons.The values of the ∆H fus and ∆H trans of YF 3 are projected into the Z region corresponding to ErF 3 without intersecting curves 2 and 3, respectively.According to ∆H fus and ∆H trans , YF 3 is located in the SSGr D. However, the location of YF 3 cannot be precisely determined because of the proximity of the ∆H values.Despite the high accuracy of thermophysical measurements [11,24], they do not contain strict information regarding the location of YF 3 .

Location of YF 3
Based on the YF 3 -LnF 3 Phase Diagrams at P = P st , T > T st The possible location of YF 3 on the basis of phase diagrams was obtained based on the location of YF 3 between HoF 3 and ErF 3 determined from unit cell parameters and V form s. The composite short "HoF 3 -YF 3 -ErF 3 " QS, including these fluorides (Figure 3), was analyzed.The ΔHfus and ΔHtrans of dimorphic YF3 are shown in Figure 2 by green icons.The values of the ΔHfus and ΔHtrans of YF3 are projected into the Z region corresponding to ErF3 without intersecting curves 2 and 3, respectively.According to ΔHfus and ΔHtrans, YF3 is located in the SSGr D. However, the location of YF3 cannot be precisely determined because of the proximity of the ΔH values.Despite the high accuracy of thermophysical measurements [11,24], they do not contain strict information regarding the location of YF3.

Location of YF3 Based on the YF3-LnF3 Phase Diagrams at P = Pst, T > Tst
The possible location of YF3 on the basis of phase diagrams was obtained based on the location of YF3 between HoF3 and ErF3 determined from unit cell parameters and Vforms.The composite short "HoF3-YF3-ErF3" QS, including these fluorides (Figure 3), was analyzed.The phase diagrams of the HoF3-YF3 and YF3-ErF3 systems [25] are not included in the full "from LaF3 to LuF3" QS [12].The short "HoF3-YF3-ErF3" QS is called composite to emphasize the violation of the ΔZ = 1 condition for (R,Ln)F3 sequence in the true QS by "inserting" a component-a fluoride of the d-element Y.The "inserted" 39YF3 connects the 67HoF3 and 68ErF3 components of the full QS with continuous lines of liquidus and solidus into the short composite "HoF3-YF3-ErF3" QS.The phase diagrams of the HoF 3 -YF 3 and YF 3 -ErF 3 systems [25] are not included in the full "from LaF 3 to LuF 3 " QS [12].The short "HoF 3 -YF 3 -ErF 3 " QS is called composite to emphasize the violation of the ∆Z = 1 condition for (R,Ln)F 3 sequence in the true QS by "inserting" a component-a fluoride of the d-element Y.The "inserted" 39 YF 3 connects the 67 HoF 3 and 68 ErF 3 components of the full QS with continuous lines of liquidus and solidus into the short composite "HoF 3 -YF 3 -ErF 3 " QS.
If the location of dimorphic YF 3 is in the short composite "HoF 3 -YF 3 -ErF 3 " QS with monomorphic HoF 3 , its T fus = 1155 • C and T trans = 1077 • C [11] should be between that of ErF 3 (T fus = 1146 • C and T trans = 1117 • C [24]).But T fus of YF 3 is higher and T trans is lower than these of ErF 3 (Figure 3).Thus, the location of YF 3 in the phase diagram of the short composite "HoF 3 -YF 3 -ErF 3 " QS cannot be between HoF 3 and ErF 3 .If the location of dimorphic YF3 is in the short composite "HoF3-YF3-ErF3" QS with monomorphic HoF3, its Тfus = 1155 °C and Тtrans = 1077 °C [11] should be between that of ErF3 (Тfus = 1146 °C and Тtrans = 1117 °C [24]).But Тfus of YF3 is higher and Ttrans is lower than these of ErF3 (Figure 3).Thus, the location of YF3 in the phase diagram of the short composite "HoF3-YF3-ErF3" QS cannot be between HoF3 and ErF3.The Ttrans of YF3 (1077 °C) is higher than that of TmF3 (1053 °C).At the same time, the Tfus values of both fluorides are almost identical (1155 and 1158 °C).They have the same types of structures (β-and α-).
The location of YF3 in the phase diagram of the short composite "ErF3-YF3-TmF3" QS is between ErF3 and TmF3.This corresponds to the location of YF3 based on its polymorphism and the structure of modifications.
From the literature data concerning the location of YF3 in the LnF3 series the following statements were obtained: (1) Structural data are not available for the entire (R,Ln)F3 series.These data are not sufficient for precise analysis of LC and determination of "pseudo ZY" of YF3.(2) Structural changes in large arrays of REE compounds of different homologous series with different chemical bonds exhibit uncontrolled shifts in the areas of change in the type of structure along the Z-axis.These data are unsuitable for precise studies of LC. (3) The thermal and thermochemical properties and phase diagrams are related to the common property-Ttrans.This common property determines the location of YF3 between ErF3 and TmF3, which is shifted by Z = 1 compared to the location based on Vform.The reason for this shift remains unknown.(4) The phase diagrams of the short composite "HoF3-YF3-ErF3" QS and the particular HoF3-ErF3 system do not confirm the location of YF3 between HoF3 and ErF3.(5) In the short composite "ErF3-YF3-TmF3" QS, YF3 is located between ErF3 and TmF3.(6) To analyze the subtle features of the LC evolution in the LnF3 series and obtain Speczd Emp SIR for (R,Ln)F3, the structural properties of all REE trifluorides obtained under the same technological conditions are required.

Definition of "Pseudo ZY" Using X-ray Diffraction Data
The integer value Z = 39 does not determine the 39YF3 location ("pseudo ZY") in the LnF3 series.This can be determined by calculating Vform from the 39YF3 unit cell parameters The location of YF 3 in the phase diagram of the short composite "ErF 3 -YF 3 -TmF 3 " QS is between ErF 3 and TmF 3 .This corresponds to the location of YF 3 based on its polymorphism and the structure of modifications.
From the literature data concerning the location of YF 3 in the LnF 3 series the following statements were obtained: (1) Structural data are not available for the entire (R,Ln)F 3 series.These data are not sufficient for precise analysis of LC and determination of "pseudo Z Y " of YF 3 .(2) Structural changes in large arrays of REE compounds of different homologous series with different chemical bonds exhibit uncontrolled shifts in the areas of change in the type of structure along the Z-axis.These data are unsuitable for precise studies of LC. (3) The thermal and thermochemical properties and phase diagrams are related to the common property-T trans .This common property determines the location of YF 3 between ErF 3 and TmF 3 , which is shifted by Z = 1 compared to the location based on V form .The reason for this shift remains unknown.(4) The phase diagrams of the short composite "HoF 3 -YF 3 -ErF 3 " QS and the particular HoF 3 -ErF 3 system do not confirm the location of YF 3 between HoF 3 and ErF 3 .(5) In the short composite "ErF 3 -YF 3 -TmF 3 " QS, YF 3 is located between ErF 3 and TmF 3 .( 6) To analyze the subtle features of the LC evolution in the LnF 3 series and obtain Spec-zd Emp SIR for (R,Ln)F 3 , the structural properties of all REE trifluorides obtained under the same technological conditions are required.

Definition of "Pseudo Z Y " Using X-ray Diffraction Data
The integer value Z = 39 does not determine the 39 YF 3 location ("pseudo Z Y ") in the LnF 3 series.This can be determined by calculating V form from the 39 YF 3 unit cell parameters and obtaining "pseudo Z Y " by the equation V form = f 2 (Z)."Pseudo Z Y " corresponds to the exact place of 39 YF 3 in the LnF 3 series in terms of its structural properties.and obtaining "pseudo ZY" by the equation Vform = f2(Z)."Pseudo ZY" corresponds to the exact place of 39YF3 in the LnF3 series in terms of its structural properties.
The differences in the YF3 location among LnF3 are related to the groups of properties by which this location is determined: structural and thermophysical.It can be assumed that they reflect the contributions of different natures to the total amount of LC.
The separation of the LC contribution (inside the "Ln nucleus-4f electrons" atomic subsystem) from the LnF3 volume changes as a result of polymorphic (morphotropic) changes in the type and density of the structure requires further study and discussion.
The precise determination of the 39YF3 location in the LnF3 series from the structural data (Vform) showed that it is located between HoF3 and ErF3 with "pseudo ZY" = 67.42.
Structural characteristics are used for precise study of LC in the LnF3 series and the volume changes caused by it.Therefore, they were chosen as defining the location of YF3 between HoF3 and ErF3.

Conclusions
LC of 14 Ln 3+ from 58Ce 3+ to 71Lu 3+ consists of the interaction in the internal "Ln nucleus-4f-electrons" atomic subsystem.The REEs include Sc, Y, La and 14 Ln.They are located in 4-6th periods of the subgroup of group III.The electronic structure of R distinguishes the short (d-Sc, Y, La) and long (14 f-elements Ln = Ce-Lu) series.
The first chemical consequence of LC is the generation of the new conglomerate of 16 RF3 by mixing fluorides of 2 d-(Y, La) and 14 f-elements.Its creation is based on the structural and chemical proximity of members of the short and long RF3 series.Thus, LC indirectly determines the location of YF3 in the LnF3 series.The V form = f 2 (Z) curve is well approximated by a second-degree polynomial (red curve in Figure 5): V form = f 2 (Z) = 0.0419•Z 2 − 6.22156•Z + 276.9491. ( V form = 47.948Å 3 of YF 3 determined from this equation corresponds to "pseudo Z Y " = 67.42. In the particular HoF 3 -ErF 3 system this fractional Z value corresponds to the (Ho 0.58 Er 0.42 )F 3 composition.This is close to the composition of the particular HoF 3 -ErF 3 system with the morphotropic β-to α-structural change according to the eutectic phase reaction: Liq ↔ β-(Ho 0.64 Er 0.36 )F 3 + α-(Ho 0.33 Er 0.66 )F 3 (2) The occurrence of "pseudo Z Y " in the region of the equilibrium existence of β-type solid solutions in the HoF 3 -ErF 3 system indicates that YF 3 belongs to the SSGr C.This contradicts the well-studied dimorphism of YF 3 [27] and its affiliation with the SSGr D.
The differences in the YF 3 location among LnF 3 are related to the groups of properties by which this location is determined: structural and thermophysical.It can be assumed that they reflect the contributions of different natures to the total amount of LC.
The separation of the LC contribution (inside the "Ln nucleus-4f electrons" atomic subsystem) from the LnF 3 volume changes as a result of polymorphic (morphotropic) changes in the type and density of the structure requires further study and discussion.
The precise determination of the 39 YF 3 location in the LnF 3 series from the structural data (V form ) showed that it is located between HoF 3 and ErF 3 with "pseudo Z Y " = 67.42.
Structural characteristics are used for precise study of LC in the LnF 3 series and the volume changes caused by it.Therefore, they were chosen as defining the location of YF 3 between HoF 3 and ErF 3 .

Conclusions
LC of 14 Ln 3+ from 58 Ce 3+ to 71 Lu 3+ consists of the interaction in the internal "Ln nucleus-4f -electrons" atomic subsystem.The REEs include Sc, Y, La and 14 Ln.They are located in 4-6th periods of the subgroup of group III.The electronic structure of R distinguishes the short (d-Sc, Y, La) and long (14 f -elements Ln = Ce-Lu) series.
The first chemical consequence of LC is the generation of the new conglomerate of 16 RF 3 by mixing fluorides of 2 d-(Y, La) and 14 f -elements.Its creation is based on the structural and chemical proximity of members of the short and long RF 3 series.Thus, LC indirectly determines the location of YF 3 in the LnF 3 series.

Figure 1 .
Figure 1.The location of YF3 in the LnF3 series based on the average Tfus (1), Ttrans (2) of LnF3 with Ln = Dy-Lu and YF3 (3, 4).Curve 1-Tfus of LnF3 with Ln = Dy-Lu (blue solid circles), curve 2-Ttrans of LnF3 with Ln = Er-Lu (red open rectangles).The Tfus (3) and Ttrans (4) of YF3 are shown by green semiopen icons.Vertical I is the boundary between structural subgroups C (Ln = Tb-Ho) and D (Ln = Er-Lu).Vertical II separates 39Y from the Z-scale for Ln.The Tfus and Тtrans of YF3 are shown by green semi-open icons.These are separated from the data for LnF3 series by vertical II.The arrows to the left of these points intersect curves 1 and 2 near Z = 69, corresponding to 69Tm.The intersections are shown as Y-vertical.According to Тtrans in LnF3 (Ln = Dy-Lu) [23], YF3 is located between ErF3 and TmF3.This is consistent with the location of YF3 in the SSGr D. The ΔHfus for LnF3 with Ln = Tb-Yb are shown in Figure 2 by curves 1 (grey semi-open rectangles) and 2 (blue solid circles).Curve 3 (red semi-open rhombs) corresponds to ΔHtrans for LnF3 of the dimorphic SSGr D (ErF3-YbF3) at Pst[11,24].

Figure 1 .
Figure 1.The location of YF 3 in the LnF 3 series based on the average T fus (1), T trans (2) of LnF 3 with Ln = Dy-Lu and YF 3 (3, 4).Curve 1-T fus of LnF 3 with Ln = Dy-Lu (blue solid circles), curve 2-T trans of LnF 3 with Ln = Er-Lu (red open rectangles).The T fus (3) and T trans (4) of YF 3 are shown by green semi-open icons.Vertical I is the boundary between structural subgroups C (Ln = Tb-Ho) and D (Ln = Er-Lu).Vertical II separates 39 Y from the Z-scale for Ln.The T fus and T trans of YF 3 are shown by green semi-open icons.These are separated from the data for LnF 3 series by vertical II.The arrows to the left of these points intersect curves 1 and 2 near Z = 69, corresponding to 69 Tm.The intersections are shown as Y-vertical.According to T trans in LnF 3 (Ln = Dy-Lu) [23], YF 3 is located between ErF 3 and TmF 3 .This is consistent with the location of YF 3 in the SSGr D. The ∆H fus for LnF 3 with Ln = Tb-Yb are shown in Figure 2 by curves 1 (grey semi-open rectangles) and 2 (blue solid circles).Curve 3 (red semi-open rhombs) corresponds to ∆H trans for LnF 3 of the dimorphic SSGr D (ErF 3 -YbF 3 ) at P st[11,24].

3. 5 .
Location of YF 3 Based on the Phase Diagrams of the YF 3 -LnF 3 Systems in the Short Composite "ErF 3 -YF 3 -TmF 3 " QS at P = P st , T > T st The next possible QS for analyzing the location of YF 3 is the short composite "ErF 3 -YF 3 -TmF 3 " QS, which is shown in Figure 4.It consists of the ErF 3 -YF 3 and YF 3 -TmF 3 systems.Int.J. Mol.Sci.2023, 24, 17013 9 of 12

3. 5 .
Location of YF3 Based on the Phase Diagrams of the YF3-LnF3 Systems in the Short Composite "ErF3-YF3-TmF3" QS at P = Pst, T > TstThe next possible QS for analyzing the location of YF3 is the short composite "ErF3-YF3-TmF3" QS, which is shown in Figure4.It consists of the ErF3-YF3 and YF3-TmF3 systems.

Figure 4 .
Figure 4.The phase diagram of the short composite "ErF 3 -YF 3 -TmF 3 " QS (P = P st , T > T st ).Black solid circles correspond to experimental data.The T trans of YF 3 (1077 • C) is higher than that of TmF 3 (1053 • C).At the same time, the T fus values of both fluorides are almost identical (1155 and 1158 • C).They have the same types of structures (β-and α-).The location of YF 3 in the phase diagram of the short composite "ErF 3 -YF 3 -TmF 3 " QS is between ErF 3 and TmF 3 .This corresponds to the location of YF 3 based on its polymorphism and the structure of modifications.From the literature data concerning the location of YF 3 in the LnF 3 series the following statements were obtained:

Figure 5 .
Figure 5.The location of YF 3 in the LnF 3 (Ln = Ho-Lu) series based on V form . Open blue rectangles-V form s of β-LnF 3 (Ln = Ho-Lu), the solid blue rectangles correspond to V form of β-YF 3 .

Table 3 .
The Wyckoff positions (W.p.), site occupancy factors (s.o.f.), fractional coordinates, and equivalent thermal displacement parameters of atoms in
3. Discussion3.1.Determination of "Pseudo ZY" According to Literature DataThe first group of structural properties is the type of structure and unit cell parameters.The most precise (±0.0005Å) measurements of the RF3 unit cell parameters in a
3. Discussion3.1.Determination of "Pseudo ZY" According to Literature DataThe first group of structural properties is the type of structure and unit cell parame-

Table 5 .
The location of β-YF 3 in the LnF 3 series based on V form (literature data).

Table 5 .
The location of β-YF3 in the LnF3 series based on Vform (literature data).