Since Kroll published his own biographical note in 1955 , quotes from this publication will be used hereafter in the context of his patent portfolio.
“The laboratories of the Technische Hochschule in Charlottenburg, Germany, where I studied iron metallurgy from 1910 to 1917, were well equipped with all sorts of furnaces. I spent the years of the First World War there as an assistant to the professor of iron metallurgy, W. Mathesius, and worked on my doctoral thesis under K. A. Hofman on the production of pure boron.”
Kroll, still doctoral student at the Technische Hochschule in Berlin-Charlottenburg, was in the process of finishing his thesis on the production of pure boron, a study he had started in 1910 under Professor K. A. Hofman. At the same time, he started investigating lead alloys under Professor W. Mathesius.
Kroll’s interest was directed towards developing, in general, a process for making alloys of the alkaline-earth metals. 
Kroll’s first patent related to lead-calcium alloys followed by a second patent relating to lead-barium and lead-strontium alloys.
The lead-barium alloys, in particular, became of great importance to the German railway industry during World War I, when they were used for making bearings.
The German company Metallbank & Metallurgische Gesellschaft A.G. (M&M), later called Metallgesellschaft , was engaged in 1916 in developing these bearings, which later received the name of “Lurgimetall”.
“Lurgimetall” is a lead-based alloy, nominally containing 96.3-97.3% lead, 2-3% barium, 0.4% calcium, and 0.3% sodium.
The following table lists the main patents relating to the “Lurgimetall” technology owned by M&M, including the two patents specifically designating Kroll as inventor. The patents are arranged in chronological order according to their filing dates.
The 2 patents filed in December 1916, and naming Kroll as inventor, relate to a process for preparing lead-based alloys while the other 4 patents, which do not designate an inventor, cover various embodiments of the alloy itself.
The table shows that M&M had developed a lead-calcium alloy in 1916 (German patent 363,125, filed on 13/09/1916 and granted on 04/11/1922).
The two “process” patents of 1916 were probably filed initially by Kroll in his own name and subsequently assigned to M&M when he took up employment with them.
Kroll stated in 1956 that he left the Technische Hochschule Charlottenburg in 1918 (towards the end of World War I), to take on a job with a “deutsches Metallunternehmen”, i.e. M&M. 
The three later “product” patents do not mention an inventor. Kroll was probably not directly involved in these inventions as he took up employment with M&M in late 1918 only. There is no good reason to doubt that Kroll was involved in determining the formulation of the final composition, commercialised as “Lurgimetall”. Kroll’s exact involvement and the timing thereof is not known, but it must be kept in mind that he had invented a process for making the alloy and that he had applied for more patents in his own name in the field in 1917.
Katrin Steffen, in an article on Kroll’s supervisor in M&M, Polish engineer Czochralski, wrote: 
Im Frankfurter Labor der Metallgesellschaft, dem “industriellen Zwilling des KWI für Metallforschung”, in dem es Czochralskis Aufgabe war, nach neuen Materialien für die Industrie, den Transport und das Militär zu suchen, erzielte er auf dem Gebiet der Materialforschung Fortschritte, die bedeutsam wurden, weil Deutschland noch vom Embargo für strategische Materialien betroffen war. Dazu gehörte vor allem das 1924 erlangte Patent auf eine Metalllegierung für das Eisenbahnwesen, die nicht mehr das teure und importabhängige Zinn enthielt. Dieses Patent wurde von der Reichsbahn gekauft, daher erhielt es den Namen «Bahnmetall». Auch diese «Erfindung» aber war der Vorarbeit und der Zusammenarbeit mehrerer Ingenieure in dem Frankfurter Labor zu verdanken. Die Lagermetall-Patente aus den Anfängen von Czochralskis Tätigkeit in Frankfurt beruhten auf den grundlegenden Vorarbeiten des Ingenieurs Wilhelm Kroll, einem Assistenten von Walther Mathesius aus Berlin, und dessen «Lurgimetall» genannter Legierung. Czochralski hatte das von Kroll als «halbe Improvisation» vorgeschlagene Lurgimetall, das von der Deutschen Eisenbahn im Ersten Weltkrieg erfolgreich verwendet wurde, durch genauere Eingrenzung des Verhältnisses zwischen Blei, härtenden Erdalkalien und kornverfeinerndem Alkali für Jahrzehnte standardisiert. Später wurde es durch die Hinzufügung von Lithium modifiziert und mit Rücksicht auf den Hauptabnehmer «Bahnmetall» genannt. Es wurde ein durchschlagender Erfolg.
Das Bahnmetall-Patent wurde von den USA, Großbritannien, Frankreich und auch Polen abgenommen. Es brachte Czochralski beträchtliche finanzielle Mittel ein, denn er – sowie anteilig zwei seiner Mitarbeiter – erhielten zehn Prozent des Reingewinns aus dem Verkauf des nach dem Patent hergestellten Metalls.
It is very likely that Kroll was one of the beneficiaries of these royalties mentioned by Steffen.
The brochure entitled W.J. Kroll, A Luxembourg scientist  states that:
Kroll scored a first important professional success in the year 1918, when he invented a new, very efficient bearing alloy on the basis of lead, which was sold in large quantities under the name “Lurgimetall”. This invention by itself laid already the foundation of his financial independence. Kroll developed this alloy while he was working at the lead refinery of Kall/Schleiden, Germany, then belonging to the Metallgesellschaft in Frankfurt/Main (MG-Lurgi)  .
This last statement needs to be clarified: Kroll had invented his process before he joined M&M and, indeed, developed it further while working for M&M. His basic inventions are shown to predate the employment with M&M for the following reasons:
the 2 above-mentioned patents were filed in 1916, more than a year before Kroll went to work for M&M.
in these two patents he is reported as living in Luxembourg.
Katrin Steffen’s statement reported above:
Die Lagermetall-Patente aus den Anfängen von Czochralskis Tätigkeit in Frankfurt beruhten auf den grundlegenden Vorarbeiten des Ingenieurs Wilhelm Kroll, einem Assistenten von Walther Mathesius aus Berlin, und dessen “ Lurgimetall “ genannter Legierung
supports the point of view that Kroll had made his first two inventions on the Lurgimetall before he joined M&M.
From French patent No 514,099, it can be seen that Kroll had filed on 3 February1917, 11 June 1917, 3 September 1917 and on 5 September 1917 patent applications in Germany on making alloys of the alkaline-earth metals. These patent applications did not proceed to grant in Germany but formed the basis for a second family of patents which he filed in 1920 in his own name, after he had left M&M. Kroll licensed this technology to M&M.
German patent No 410,533 filed on 23 November 1917, is Kroll’s basic patent leading to the process of debismuthising lead, which he further developed after having left M&M. Kroll sold this technology later to the German companies Th. Goldschmidt A.G. and M. Lissauer & Cie.
“I was hired at the end of the war by the Metallgesellschaft in Frankfurt/Main, and sent to their lead refinery at Call/Eifel, in the mountains. There I put to practice an idea of mine, to produce calcium lead to be used as bearing alloy and as a substitute for scarce tin Babbitt metal. I tried first to react calcium carbide with lead,which worked fine in the laboratory, but I did not succeed on an industrial scale because of the high temperature involved when working in the absence of fluxes.
Then I decided to react fused sodium lead with calcium chloride but, to lower the melting point of the salts, I used a mixture of calcium/barium chloride and obtained a calcium/barium lead alloy, which was later sold in large quantities for bearings under the name “Lurgimetall”.
The statement: … “There I put to practice an idea of mine”…seems to refer to the “idea“ which had already found its expression in the patent applications filed in 1916.
It is interesting to note that Kroll received royalty payments from Metallgesellschaft (former M&M) until at least 1941. On 18 July 1941 the Continental Illinois National Bank and Trust Company of Chicago sent the following enquiry to the Luxembourg ambassador in Washington :
“We have received a cable request from the Reichsbank, Berlin, Germany dated June 21 1941 to charge their dollar account with us $373.36 and pay a like amount to Mr. W. Kroll, Red Coach Inn, Niagara Falls, New York by order of the Metallgesellschaft, Frankfurt A.M., representing license fees.
Mr. Kroll, he advised us that the amount represents license fees which are due to him for patent rights by Metallgesellschaft, Frankfurt a. M., Germany, for many years.
The patent concerns a process for making hard lead, which is used for bearing metal, and partly as a substitute for antimonial lead.
In view of Mr. Kroll's statements in connection with his interest in Luxembourg, we deemed it advisable to bring the circumstances to your attention and would appreciate your acknowledgment of the transaction for the completion of our files.”
Thus the bank asked for clearance to transfer the relatively modest amount of $373.36  to be paid to Kroll. The basic Lurgimetall patents having already expired in 1937, the 1941 royalty payments were probably related to other patents in Kroll’s name that he had licensed to Metallgesellschaft (M&M).
Kroll expressed his surprise at this query as he had received payments previously in the US without requests for clarification.
 Journal of the Franklin Institute, Vol. 260, September 1955, pages 169-192
 beryllium, magnesium, calcium, strontium, barium, and radium
“Metallbank A.G.” and “Metallurgische Gesellschaft” merged in 1910 and became ”Metallgesellschaft” in 1928
 d’Lëtzeburger Land, 9 March 1956, page 3
 Katrin Steffen, Wissenschaftler in Bewegung: Der Materialforscher Jan Czochralski zwischen den Weltkriegen, Zeitschrift für moderne europäische Geschichte (2008), pp. 237-261
 W. J. Kroll, A Luxembourg Scientist, Fondation Nicolas Lanners 1998, page 11
 In the “Journal of the Franklin Institute, 1955, page 17” Kroll erroneously used the name Metallgesellschaft for his former employers and so does the brochure W.J. Kroll, A Luxembourg scientist of 1998.