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

Abstract

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—V_form) and thermochemical (temperatures and heats of phase transformations, phase diagrams) properties. The location of YF₃ between HoF₃ and ErF₃ was determined by V_form at a standard pressure (P_st) and temperature (T_st). The location of YF₃ according to heats of phase transformations ΔH_fus and ΔH_trans is in a dimorphic structural subgroup (SSGr) D (Ln = Er-Lu), but without the exact “pseudo Z_Y”. According to the temperatures of phase transformations (T_trans) 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. V_form (at P_st and T_st) with “pseudo” atomic number Z_Y = 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.

1. Introduction

This study opens up a series of investigations on LCs and their chemical and structural consequences in homologous series of LaF₃ and 14 LnF₃. The (La,Ln)F₃ 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)F₃ 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 CeF₃ to 71% and at the end of LuF₃ to ~75% of the mass of compressible Ln³⁺. The LC in LnF₃ 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)F₃ 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), RF₃ 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 RF₃ are chemically resistant, except SmF₃, EuF_3, and YbF₃. 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 YF₃ in the LnF₃ series is determined not by its Z = 39 but by the structural and chemical characteristics of ₃₉YF₃, independent of LC. Therefore, this location is ambiguous. According to the literature, the location of YF₃ 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 YF₃ 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 Ln³⁺ ionic radius in REE oxides was chosen as a characteristic of LC. According to [8], the radius of R³⁺ (r₊) decreases from La³⁺ to Lu³⁺ 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 R₂O₃ has become the first example of a comparative study of LC.

The compression of Ln³⁺ 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 RF₃, 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 = f₀(Z).

A change in the state parameter T > T_st causes structural changes in the RF₃ series: polymorphic (PolTr) and morphotropic transformations. Both transformations proceed with abrupt changes in V_form. The RF₃ 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 LaF₃ type (hereafter t-) by V_t- = f₁(Z), and for the β-YF₃ type (hereinafter β-) by V_β- = f₂(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, ₂₁Sc→₃₉Y→₅₇La, r₊ increases in group III in the ΔZ = 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 = ₅₈Ce-₇₁Lu) is a result of an interaction in the “Ln nucleus—4f-electrons” atomic subsystem. The minimum “period” of the long series is ΔZ = 1. This corresponds to the transition between neighboring LnF₃. At the same time, the size of Ln³⁺ 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 ₅₇La in the 6th period with ₅₈Ce at ΔZ = 1.

Yttrium has no f-electrons, and its r₊ is independent of LC. The indirect effect of LC on the rapprochement of YF₃ structural and chemical properties with LnF₃ properties is due to the influence of LC on Ln³⁺. This is expressed as a decrease in r₊ with an increase in Z.

The location of LaF₃ at the beginning of the LnF₃ series does not raise any questions. The Periodic Table of elements places it there by Z(La) = 57. This location before ₅₈CeF₃ is also justified by the structural and chemical proximity of LaF₃ and CeF₃ (ΔZ = 1).

A question arises about the location of YF₃ in the LnF₃ series. Unlike the unambiguous location of ₅₇LaF₃, the location of ₃₉YF₃ 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 YF₃.

The structural classification of 16 RF₃ (without ScF₃) homologous series and the chemical classification of the phase diagrams of 120 (without ScF₃) RF₃-R’F₃ systems depend on the place of YF₃ in the LnF₃ series. The RF₃ structural classification is the first level of a chemical classification of RF₃-R’F₃ systems.

To determine the location of YF₃ in the LnF₃ series, only precise information on LC in LnF₃ 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: LaF₃ and 14 LnF₃. 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 RF₃.

The second condition is the completeness of the LnF₃ structural characteristics used to describe the changes in V_form during LC. The state of structural knowledge of RF₃ 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 RF₃ stretched over the years 1929–2023. During this period, significant changes occurred in the composition of RF₃ 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, YF₃, LaF₃, PrF₃, NdF₃, GdF₃, HoF₃, and LuF₃ 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 RF₃ distorted by them are unsuitable for precise studies of LC and the construction of the Spec-zd Emp SIR for (R,Ln)F₃.

In this series of studies, the crystal structures of all members of the (R,Ln)F₃ series are investigated. The structures of HoF₃, ErF₃, TmF₃, YbF₃, LuF₃, and YF₃ are discussed in the present study. The short quasi-system (QS) [12] “from HoF₃ to LuF₃” is used to obtain “pseudo Z_Y”. The location of YF₃ is determined to be between HoF₃ and ErF₃ based on the value of V_form. The second message presents the structural data of t-RF₃ with R = La-Nd of the LaF₃ type, “pseudo t-SmF₃”, and β-LnF₃ (Ln = Sm-Dy) of the β-YF₃ type. The empirical structural data obtained for cations and fluorine anion will become the basis for the Spec-zd Emp SIR for Y³⁺, La³⁺, and 14 Ln³⁺ for RF₃.

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 YF₃ in a series of 4f-elements LnF₃.

2. Results

2.1. Obtaining YF₃ and LnF₃ with Ln = Ho-Lu for Structural Studies

X-ray diffraction (XRD) analysis of YF₃ and LnF₃ with Ln = Ho-Lu was performed on the samples prepared using modern technology for the synthesis of crystals prone to pyrohydrolysis REE fluorides.

The RF₃ reagents were prepared at the experimental plant (town Pyshma) of the Government Institute of Rare Metals (GIREDMET, Moscow, Russia). RF₃ were melted and fluorinated to purify oxygen impurities. Oxygen content of 0.005–0.08 wt. % 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 RF₃ (in the form of an isomorphic admixture of RF_3−2xO_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 YF₃ produced by Pyshma, according to [16], is listed in

Table 1. Impurity composition of the YF₃ samples produced by Pyshma, wt. %.

Nd	<0.0005	Dy	0.0002	Si	<0.001	Tm	0.0005
Sm	0.0002	Ho	<0.001	Mn	<0.00005	Fe	0.0005
Gd	0.0005	Cu	<0.0005	Co	<0.00005	Ti	<0.00005
Tb	0.0001	O	270 ppmw	Ni	0.00005	Cr	0.00005

.

After fluorination, the samples consisted of large crystalline blocks suitable for structural analysis.

2.2. X-ray Diffraction Study of β-YF₃ and Five β-LnF₃ (Ln = Ho-Lu)

To accurately determine the position of YF₃ in the LnF₃ series using structural characteristics the structures of β-YF₃ and five β-LnF₃ (Ln = Ho-Lu) were studied.

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 LnF₃ series and calculating comparable values of r₊ for the Spec-zd Emp SIR for RF₃.

Single crystal XRD study of β-YF₃ and β-LnF₃ (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. Experimental crystallographic characteristics and results of the structure refinement for β-YF₃ and β-LnF₃ (Ln = Ho-Lu) at 293 K (this study).

RF3	β-YF3	β-HoF3	β-ErF3	β-TmF3	β-YbF3	β-LuF3
ICSD ID	2254323	2254302	2254320	2254321	2254415	2254322
Crystal system	Orthorhombic
Sp.gr., Z	Pnma, 6
a (Å)	6.3666 (2)	6.4055 (2)	6.3500 (5)	6.2792 (3)	6.2168 (3)	6.1437 (4)
b (Å)	6.8579 (3)	6.8739 (3)	6.8435 (7)	6.8141 (3)	6.7852 (3)	6.7606 (3)
c (Å)	4.3927 (1)	4.3784 (2)	4.3829 (4)	4.4095 (3)	4.4318 (2)	4.4724 (3)
V (Å 3)	191.79 (1)	192.78 (1)	190.46 (3)	188.67 (2)	186.94 (2)	185.76 (2)
Vform	47.948	48.195	47.615	47.168	46.735	46.440
Dx (g·cm−3)	5.0528	7.6464	7.8205	7.9538	8.1732	8.2942
μ (mm−1)	16.441	21.751	23.486	24.981	26.71	28.387
Tmin, Tmax	0.0891, 0.1878	0.0594, 0.1564	0.0391, 0.1312	0.0628, 0.1605	0.0222, 0.1051	0.0211, 01031
Shape, color	colorless	light yellow	light rose	colorless	colorless	colorless
Diameter (mm)	0.20
Wavelength (Å)	0.56087
Θ range (deg)	4.35–72.65	4.36–72.85	4.36–72.78	4.34–73.03	4.33–72.82	4.31–72.87
Refl. collected	19,376	20,349	20,522	19,403	19,993	19,644
Refl. unique/Rint	3573/4.55	3800/5.14	3342/5.00	3301/5.06	3333/4.65	2895/5.15
Refin. method	Full matrix least squares on F
Param/Restrains	23	38/0	38/0	38/0	38/0	66/0
R/wR, %	2.26/3.70	2.38/3.93	2.05/3.10	2.60/4.01	2.80/4.11	2.51/3.39
Δρmin/Δρmax, Å−3	−2.70/1.48	−4.48/4.39	−4.29/3.64	−4.54/2.84	−4.60/3.64	−4.26/3.87
GOF	1.36	1.47	1.43	1.40	1.62	1.39

.

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 Wyckoff positions (W.p.), site occupancy factors (s.o.f.), fractional coordinates, and equivalent thermal displacement parameters of atoms in β-YF₃ and β-LnF₃ (Ln = Ho-Lu) at 293 K.

RF3	Ion	W.p.	s.o.f.	x/a	y/b	z/c	Ueq
YF3	Y	4c	1	0.367845(12)	¼	0.05981(2)	0.005423(11)
	F(1)	4c	1	0.52302(15)	¼	0.5901(2)	0.00976(12)
	F(2)	8b	1	0.16454(10)	0.06335(8)	0.37686(16)	0.00856(7)
HoF3	Ho	4c	1	0.36809(3)	¼	0.06137(4)	0.00483(5)
	F(1)	4c	1	0.5217(2)	¼	0.5870(3)	0.00925(16)
	F(2)	8b	1	0.16429(16)	0.06318(16)	0.3803(2)	0.00866(10)
ErF3	Er	4c	1	0.36802(3)	¼	0.06027(4)	0.00521(4)
	F(1)	4c	1	0.5231(2)	¼	0.5909(3)	0.00967(14)
	F(2)	8b	1	0.16486(14)	0.06248(12)	0.37654(17)	0.00871(9)
TmF3	Tm	4c	1	0.36725(3)	¼	0.05609(4)	0.00477(4)
	F(1)	4c	1	0.5252(2)	¼	0.5971(5)	0.0103(2)
	F(2)	8b	1	0.16454(16)	0.06304(15)	0.3716(3)	0.00867(12)
YbF3	Yb	4c	1	0.36718(3)	¼	0.05395(5)	0.00577(5)
	F(1)	4c	1	0.5264(3)	¼	0.6017(4)	0.0114(2)
	F(2)	8b	1	0.16510(16)	0.06231(14)	0.3681(2)	0.00897(12)
LuF3	Lu	4c	1	0.36689(7)	¼	0.05044(10)	0.00759(17)
	F(1)	4c	1	0.5278(3)	¼	0.6056(4)	0.0110(2)
	F(2)	8b	1	0.16448(18)	0.06265(13)	0.3634(3)	0.00951(11)

.

3. Discussion

3.1. 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 (±0.0005 Å) measurements of the RF₃ unit cell parameters in a Guinier chamber were used [11,20]. The YF₃ 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 ΔH_fus of melting and T_trans and ΔH_trans of the PolTrs. These characteristics determine the location of YF₃ in the LnF₃ series for condensed systems with P_st and T_st. The condensed (at P_st) single-component (Z = const) systems include YF₃, LaF₃, and all LnF₃ except volatile (at heating) ScF₃ [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 YF₃ among them.

ΔH_fus and ΔH_trans for all RF₃ were cited from the fundamental research of one group of authors [11,24]. Synthesis and analysis of the basic and impurity RF₃ compositions and purification from oxygen (control by analysis) were performed at Iowa State University, USA.

Phase diagrams of the two-component RF₃-R’F₃ systems were used for the first time to clarify the location of YF₃. These systems were studied by one group [25]. The phase diagrams of the RF₃-R’F₃ systems contain data on the T_trans of the components. The location of YF₃ in the short QS [12] depends on the thermal properties of the LnF₃ components that form this QS.

3.2. Location of YF₃ in the LnF₃ Series in Terms of the Structural Types and Unit Cell Parameters of 16 RF₃ (without ScF₃) at P_st and T_st

The generally accepted scheme for the change of T_trans and crystal structures of 17 RF₃ 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 RF₃ structures.

At T < T_fus RF₃ crystallize in four structural types: (1) ScF₃ (ReO₃ type), (2) β-YF₃ (β-), (3) LaF₃ (t-), and (4) α-YF₃ (α-). The α-type is stable close to its melting point and was observed in situ only.

The structural classification of RF₃ (without ScF₃) based on the type of structure and presence (absence) of polymorphism is presented in

Table 4. The SSGrs A–D of RF₃.

SSGrs	RF3	RF3 Structural Types
A	LaF3, CeF3, PrF3, and NdF3 monomorphic	t-
B	PmF3, SmF3, EuF3, and GdF3 dimorphic	(1) t- high-temperature (2) β- low-temperature
C	TbF3, DyF3, and HoF3 monomorphic	β-
D	ErF3, TmF3, YbF3, and LuF3 dimorphic	(1) α- high-temperature (2) β- low-temperature

. Four SSGr were allocated. The members of the SSGr A (LaF₃, CeF₃, PrF₃, and NdF₃) and C (TbF₃, DyF₃, and HoF₃) are monomorphic and have t- and β- structural types up to the melting point, respectively. The members of the dimorphic SSGr B—PmF₃, SmF₃, EuF₃, and GdF₃—have t- (high-temperature) and β- (low-temperature) structural types. The members of the dimorphic SSGr D (ErF₃, TmF₃, YbF₃, and LuF₃) have α- (high temperature) and β- (low temperature) structural types.

The β-YF₃ unit cell parameters according to [11,20,24,26] together with V_forms calculated from them at T_st and P_st are listed in

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

Reference	Unit Cell Parameters, Å			Vform (Tst, Pst)	YF3 Location
	a	b	c
1953 Zalkin [26]	6.353	6.850	4.393	47.79	between HoF3 and ErF3
1971 Spedding [11]	6.367	6.859	4.394	47.97	between HoF3 and ErF3
1974 Greis [20]	6.4027	6.8843	4.3980	48.46	between DyF3 and HoF3

. In the right column, the LnF₃-Ln’F₃ systems are provided, in which V_form of YF₃ is located between the V_forms of components.

The V_forms 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 T_fus. These data were excluded.

3.3. Location of YF₃ in the LnF₃ Series in Terms of T_fus and ΔH_trans

A review of T_trans in (La,Ln)F₃ (without ScF₃ andYF₃) was done [23]. The T_trans 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 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 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.

The T_fus and T_trans 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 T_trans 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 ΔH_fus 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 ΔH_trans for LnF₃ of the dimorphic SSGr D (ErF₃-YbF₃) at P_st [11,24].

The ΔH_fus and ΔH_trans of dimorphic YF₃ are shown in Figure 2 by green icons. The values of the ΔH_fus and ΔH_trans of YF₃ are projected into the Z region corresponding to ErF₃ without intersecting curves 2 and 3, respectively. According to ΔH_fus and ΔH_trans, 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.

3.4. Location of YF₃ Based on the YF₃-LnF₃ Phase Diagrams at P = P_st, T > T_st

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 V_forms. 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.

If the location of dimorphic YF₃ is in the short composite “HoF₃-YF₃-ErF₃” QS with monomorphic HoF₃, its T_fus = 1155 °C and T_trans = 1077 °C [11] should be between that of ErF₃ (T_fus = 1146 °C and T_trans = 1117 °C [24]). But T_fus of YF₃ is higher and T_trans 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.

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 = P_st, T > T_st

The next possible QS for analyzing the location of YF₃ is the short composite “ErF₃-YF₃-TmF₃” QS, which is shown in Figure 4. It consists of the ErF₃-YF₃ and YF₃-TmF₃ systems.

The T_trans of YF₃ (1077 °C) is higher than that of TmF₃ (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 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 Z_Y” 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—T_trans. This common property determines the location of YF₃ between ErF₃ and TmF₃, 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 “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 Spec-zd Emp SIR for (R,Ln)F₃, the structural properties of all REE trifluorides obtained under the same technological conditions are required.

3.6. Definition of “Pseudo Z_Y” Using X-ray Diffraction Data

The integer value Z = 39 does not determine the ₃₉YF₃ location (“pseudo Z_Y”) in the LnF₃ series. This can be determined by calculating V_form from the ₃₉YF₃ unit cell parameters and obtaining “pseudo Z_Y” by the equation V_form = f₂(Z). “Pseudo Z_Y” corresponds to the exact place of ₃₉YF₃ in the LnF₃ series in terms of its structural properties.

The V_forms were calculated from the β-YF₃ and β-LnF₃ (Ln = Ho-Lu) unit cell parameters (Table 2). In Figure 5, the open blue rectangles indicate the change in V_form in the β-LnF₃ (Ln = Ho-Lu) series. The V_form of β-YF₃ is indicated by the solid blue rectangle.

The V_form = f₂(Z) curve is well approximated by a second-degree polynomial (red curve in Figure 5):

V_form = f₂(Z) = 0.0419·Z² − 6.22156·Z + 276.9491.

(1)

V_form = 47.948 ų of YF₃ determined from this equation corresponds to “pseudo Z_Y” = 67.42. In the particular HoF₃-ErF₃ system this fractional Z value corresponds to the (Ho_0.58Er_0.42)F₃ composition. This is close to the composition of the particular HoF₃-ErF₃ system with the morphotropic β- to α- structural change according to the eutectic phase reaction:

Liq ↔ β-(Ho_0.64Er_0.36)F₃ + α-(Ho_0.33Er_0.66)F₃

(2)

The occurrence of “pseudo Z_Y” in the region of the equilibrium existence of β-type solid solutions in the HoF₃-ErF₃ system indicates that YF₃ belongs to the SSGr C. This contradicts the well-studied dimorphism of YF₃ [27] and its affiliation with the SSGr D.

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 (V_form) showed that it is located between HoF₃ and ErF₃ with “pseudo Z_Y” = 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.

4. Conclusions

LC of 14 Ln³⁺ from ₅₈Ce³⁺ to ₇₁Lu³⁺ 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.

In the series of REE compounds with different types of chemical bonds, the shift of the yttrium compounds site is known, explicable, and natural. However, according to studies of different LnF₃ properties, the location of YF₃ may differ. Such differences can be caused by the differences in chemical bonds in different homologous series and by experimental errors that differ in different methods.

The location of YF₃ in the LnF₃ series depends on two groups of properties: structural (unit cell parameters and V_forms) and thermochemical (temperatures and heats of phase transformation, phase diagrams).

For precise structural characterization, crystals of β-YF₃ and five β-LnF₃ (Ln = Ho–Lu) were obtained and studied. V_forms (at P_st and T_st) calculated from the unit cell parameters determine the location of YF₃ between HoF₃ and ErF₃.

According to ΔH_fus and ΔH_trans, YF₃ is located in the LnF₃ dimorphic SSGr D (Ln = Er-Lu). ΔH_fus and ΔH_trans cannot provide a more precise position of YF₃ inside the SSGr D because they are close to each other.

According to T_trans, YF₃ is located between ErF₃ and TmF₃. This differs by +1 from its location which was determined based on V_forms. Simultaneously, this location does not contradict PolTrs and belonging of YF₃ to the SSGr D of LnF₃.

The phase diagrams of the short composite “HoF₃-YF₃-ErF₃” and “ErF₃-YF₃-TmF₃” QS and the particular HoF₃-ErF₃ system were applied for the first time to determine the location of YF₃ in the LnF₃ series. The phase diagrams are included in the group of thermal properties because they contain T_fus and T_trans. The phase diagrams locate YF₃ between ErF₃ and TmF₃.

To determine the location of YF₃, the structures of β-YF₃ and five β-LnF₃ (Ln = Ho-Lu) were studied at 293 K, and their V_forms were calculated. In the short “from HoF₃ to LuF₃” QS using V_form = 47.948 ų the location of YF₃ was determined between HoF₃ and ErF₃ with “pseudo Z_Y” = 67.42.